Copyright: StatSoft, Inc. 1984-1996


STATISTICA Help Index
STATISTICA Electronic Manual Index

The Electronic Manual provides comprehensive reference information on all procedures, facilities, and options of the STATISTICA system.  To choose a topic, point to it and click the left-mouse-button, or press TAB to highlight the underlined topic and press ENTER.

Toolbars	Graphics	General Conventions	Spreadsheet Window

Menus	Data Management	Keyboard Commands	Scrollsheet Window

Statistics (Index)	Mouse Conventions	Text/output Window

Statistical Advisor	Customizing STATISTICA	Graph Window

Exchanging Information (Data, Graphs) with Other Applications

STATISTICA Command Language (SCL)

STATISTICA BASIC (Programming Language)

Glossary

References

Guided Tour

WEB Page


Customizing STATISTICA

STATISTICA Defaults: General

STATISTICA Defaults: Display

Print

Stats Graphs

User Graphs

Global Defaults (Graphics)

General Layout Dialog


STATISTICA Toolbars

Spreadsheet Window Toolbar

View (All) Variable Specs Toolbar

Scrollsheet Window Toolbar

Graph Window Toolbar

Text/output Window Toolbar

Graph Data Editor Toolbar

Megafile Manager Toolbar

Auto Task Buttons Toolbar


STATISTICA Pull-down Menus

Spreadsheet Window

Scrollsheet Window

Graph Window

Megafile Manager Window

Text/output Window


STATISTICA Graphics

Graphics (Overview)

Stats Graphs

Quick Stats Graphs

Custom Graphs

Blank Graphs

User-defined Graphs

Block Stats Graphs


STATISTICA General Conventions

Selecting Variables

Printing

Exchanging Information (Data, Graphs) with other Applications

General Options (weight, selection conditions)

Queues of Windows dialog

Macros

STATISTICA BASIC (Programming Language)

STATISTICA Command Language (SCL)

STATISTICA File Server


  STATISTICA Data Management

Data Spreadsheet - Overview

Drag-and-Drop Facility

Data Management Module

STATISTICA BASIC (Programming Language)

DDE (Creating Dynamic Data Links)

Exchanging Information (Data, Graphs) with other Applications

Dates

Megafile Manager


STATISTICA Statistics

Elementary Concepts	  Log-Linear Analysis

  ANOVA/MANOVA	  Multidimensional Scaling

  Basic Statistics	  Nonlinear Estimation

  Canonical Analysis	  Nonparametrics

  Cluster Analysis	  Process Analysis

  Correspondence Analysis	  Quality Control

  Data Management	  Reliability & Item Analysis

  Discriminant Function Analysis	  SEPATH (Structural Equation Modeling)

  Experimental Design	  Survival Analysis

  Factor Analysis	  Time Series and Forecasting

  Linear Regression

See also,	  STATISTICA File Server

  Megafile Manager


Exchanging Information (Data, Graphs) with other Applications

In addition to file import/export facilities, STATISTICA supports multiple Clipboard formats, OLE client and server functions, and DDE/API capabilities in order to exchange data and/or graphs with other applications.  For more information on these capabilities, see below.

Using Clipboard	Describes the Clipboard operations.

Using OLE	Describes OLE (Object Linking and Embedding) operations.

Using DDE	Describes DDE (Dynamic Data Exchange) operations.

Using Import/Export Options	Describes importing and exporting operations.


Using Clipboard

Copy

Paste

Paste Special

Metafile Mode Screen/Printer Resolution


Using OLE

Overview of Object Linking and Embedding (OLE)

Metafile Mode Screen/Printer Resolution


Using DDE

DDE (Creating Dynamic Data Links)

Paste Link

Spreadsheet Links


Using Import/Export Options

Import from:

Quick Import Options

ODBC

Extended Import Options

Export to:

Quick Export Options

Extended Export Options


Extended Import Options

Unlike the Quick Import and ODBC options accessible in every module, these data import facilities are accessible only in the Data Management module and they offer some additional options for specialized data transfers.  For example, they offer options to exchange STATISTICA's double-notation and labeled data with applications which do not support labeled values; also, they support fixed format (e.g., undelimited) ASCII import, as well as some less often used file formats (e.g., STG or SPSS).

STG File	dBASE File

Megafile Manager File	Paradox File

Excel File	SPSS File

Lotus File	ASCII Free

Quattro File	ASCII Fix


Extended Export Options

Unlike the QuickExport  options accessible in every module, these data export facilities are accessible only in the Data Management module and they offer some additional options for specialized data transfers.  For example, they offer options to exchange STATISTICA's double-notation and labeled data with applications which do not support labeled values; also, they support fixed format (e.g., undelimited) ASCII import, as well as some less often used file formats (e.g., SPSS).

MFM (Megafile Manager)

Excel

Lotus, Symphony, and 3D Lotus files

Quattro

dBASE III and IV

Paradox

SPSS Portable File format

ASCII (free and fixed format)

CSS/3 (STATISTICA's DOS version)


Importing Data via the Quick Import Facility

To import a foreign data file using the Quick Import facility, select the Quick Import option from the File pull-down menu in any module, then follow the steps outlined below.  For example, consider the file My_file.txt which contains the following rows and columns:

A,B,C,D

1,2,

10,50,100,2000

Step 1:	From the File pull-down menu, select the Quick Import option to open the Select File to Import dialog.

Step 2:	Specify My_file.txt in the Select File to Import dialog.

Step 3:	In the resulting Quick Import from ... dialog, select Comma as the Field Separator and the option Get variable names from first row.  Click OK to bring up the Save Imported File As dialog.

Step 4:	After the Save Imported File As dialog appears on your screen, enter a name under which the file will be saved in STATISTICA.  Click OK to complete the importing process.

As STATISTICA imports the file via the Quick Import facility, it will create as many rows as there are lines in the ASCII file.  STATISTICA will also search for the longest record in the ASCII file.  The length of this record will determine the number of variables in the STATISTICA data file.  For any record in the ASCII file that is smaller than this record, STATISTICA will fill the values with missing data (up to the length of the longest record).

For example, in the above text file, the longest record is either line 1 or line 3 with four values each.  Therefore, when importing the data, two missing data values will be added to the end of record 2.  The resulting imported values will appear as follows in the spreadsheet (with the first row becoming the spreadsheet variable names):

 A    B    C    D

-------------------

 1    2

10   50   100  2000


Quick Import

Importing data to STATISTICA by converting foreign data files (e.g., worksheets or data bases) is one of several ways (offered in STATISTICA) of accessing data from other applications.  Other methods include establishing dynamic links (DDE, see Current Specs) between data files and using the Clipboard (which in STATISTICA recognizes special Clipboard formatting conventions used by other Windows applications such as Excel or Lotus).

This option will allow you to quickly import files from spreadsheet and data base programs, and from ASCII (text) files.  STATISTICA also features an interface to a wide variety of data base formats via the ODBC option, and an additional comprehensive set of data import facilities (see Import Files) in the Data Management module, which support a large selection of data file formats and offer some additional options for specialized data transfers (e.g., options to split/merge data values and their labels while transferring data to/from file formats which do not support labeled values).  The Quick Import and ODBC options are available from the File pull-down menu of every STATISTICA module.

When you click on the Quick Import option in the File pull-down menu and select the desired file to import, the Quick Import from ... dialog will open.

Quick Import from ... dialog:

Import Data Base Files

Import Spreadsheet Files

Import Text Files

Example:  Importing Data via the Quick Import Facility

Importing Text Values Longer than 8 Characters.  If the text values imported using the Quick Import options are longer than 8 characters, then value labels will be created to store the long text values in their entirety; the first 8 characters of each value will be used to create the respective STATISTICA text values.  Note that if this would produce text values which are not uniquely related to the long labels (i.e., create a situation when the same text value would be accompanied by different value labels in different cases), then the last character(s) of the text values will be replaced by digits to create unique text values for the respective value labels.

For example, if the values in the source data set (to be imported) are:

Arizona, the south region

Arizona, the north region

Arizona, the central part

then those values will be stored as value labels, and the corresponding (unique) 8-character text values will be created as:

Arizona1

Arizona2

Arizona3

The same conventions apply when you import data to the STATISTICA spreadsheet via the Clipboard [e.g., by copying a block of values in a foreign spreadsheet (highlight a block in the spreadsheet and press CTRL+C) and pasting them to the STATISTICA spreadsheet (place the cursor in the desired position and press CTRL+V)].  If the text values are longer than 8 characters, then they will be interpreted as STATISTICA value labels and the respective (short) text values will be created from the first 8 characters of each long text (as illustrated above).

See also, ODBC.


Quick Import - Spreadsheet Files

The following options are available in this dialog if you are importing a Lotus, Excel, or Quattro file.  Note that if the selected spreadsheet file includes multiple worksheets, then STATISTICA will display a list in which you can select the desired worksheet to import.

Imported file:  The name of the selected file to import will be displayed here.

Select sheet.  Specify the desired sheet to be imported here.  This option is only available if a Lotus 1-2-3 (Release 3 or later) file or a Quattro file is being imported.

Range:  This option permits selection of a specific range of cases and/or variables to be imported.

Variables:  Specify the range of variables (columns) to be imported (From which variable, To which variable, inclusive).

Cases:  Specify the range of cases (rows) to be imported (From which case, To which case, inclusive).

Get case names from 1st column of specified range:  Select this option in order to import case names from the first column of the specified range (see above).  If this field contains more than 20 characters, then only the first 20 will be used as the case name.  If this column contains numeric values instead of text, the case names will be created as "text images" of these values.

Get variable names from 1st row of specified range:  Select this option to use the labels from the first row of the specified import range (see above).  If any label is longer than eight characters, it will be truncated and only the first eight characters will be used as the variable name.


Quick Import - Data Base Files

The following options are available in this dialog if you are importing a dBase or Paradox file.

Imported file:  The name of the selected file to import will be displayed here.

Range:  This option permits selection of a specific range of cases and/or variables to be imported.

Variables:  Specify the range of variables (columns) to be imported (From which variable, To which variable, inclusive).

Cases:  Specify the range of cases (rows) to be imported (From which case, To which case, inclusive).

Get case names from 1st column of specified range:  Select this option in order to import case names from the first column of the specified range (see above).  If this field contains more than 20 characters, then only the first 20 will be used as the case name.  If this column contains numeric values instead of text, the case names will be created as "text images" of these values.

Importing Text Values Longer than 8 Characters.  If the text values imported using the Quick Import options are longer than 8 characters, then value labels will be created to store the long text values in their entirety; the first 8 characters of each value will be used to create the respective STATISTICA text values.  Note that if this would produce text values which are not uniquely related to the long labels (i.e., create a situation when the same text value would be accompanied by different value labels in different cases), then the last character(s) of the text values will be replaced by digits to create unique text values for the respective value labels.  For example, if the values in the source data set (to be imported) are:

Arizona, the south region

Arizona, the north region

Arizona, the central part

then those values will be stored as value labels, and the corresponding (unique) 8-character text values will be created as:

Arizona1

Arizona2

Arizona3

The same conventions apply when you import data to the STATISTICA spreadsheet via the Clipboard [e.g., by copying a block of values in a foreign spreadsheet (highlight a block in the spreadsheet and press ctrl+c) and pasting them to the STATISTICA spreadsheet (place the cursor in the desired position and press ctrl+v)].  If the text values are longer than 8 characters, then they will be interpreted as STATISTICA value labels and the respective (short) text values will be created from the first 8 characters of each long text (as illustrated above).


Quick Import - Text Files

The following options are available in this dialog if you are importing a text file.

As STATISTICA imports the file via the Quick Import facility, it will create as many rows as there are lines in the ASCII file.  STATISTICA will also search for the longest record in the ASCII file.  The length of this record will determine the number of variables in the STATISTICA data file.  For any record in the ASCII file that is smaller than this record, STATISTICA will fill the values with missing data (up to the length of the longest record).

Imported file:  The name of the selected file to import will be displayed here.

Field Separator:  Specify the character which is used in the input file as the delimiter.  You can select the type of delimiter used from four predefined separators (Tab, Space, Comma, or Semicolon), or specify the separator via the User-defined edit field.  For more extensive field separator options, see Import ASCII Free File in the Data Management module.

Get case names from first column:  Select this option in order to create case names from the first field of each record in the ASCII file.  If this field contains more than 20 characters, then only the first 20 will be used as the case name.  If this field contains numeric values instead of text, then the case names will be created as "text images" of these values.

Get variable names from first row:  Select this option in order to create variable names from the first record in the ASCII file.  If any field in the first record is longer than eight characters, it will be truncated and only the first eight characters will be used as the variable name.


Importing SAS Data Files into STATISTICA

It is possible to import SAS data files into STATISTICA via ODBC. First, make sure that the SAS libraries you wish to access are specified in the Libraries section of the SAS ODBC Driver Configuration dialog.  To specify these libraries go to the Control Panel in the Windows Program Manager (or press the start button and select Settings..Control Panel in Windows 95) and double-click on the 32-bit ODBC icon.  Select the SAS 32-bit ODBC driver in the Data Sources dialog and press the Setup button.  Go to Libraries and specify the Library Name and Host File Name and then press the <<Add<< button.  Click OK to accept the SAS ODBC driver configuration.

From the STATISTICA File pull-down menu, select the Import Data option.  Make sure the 32-bit ODBC option is checked, then select ODBC from the menu.  Select the SAS 32-bit ODBC driver in the SQL Data Sources dialog.  Click OK to accept the data source and click OK again to accept the SAS ODBC driver configuration.  Select the desired tables, add the desired fields to the Fields to Retrieve section, and (optionally) specify conditions for row selection in the ODBC Import dialog.  Make sure the Edit SQL Query box is checked and click OK.  In the Edit SQL Query dialog, add libref. in front of the name of the data file and remove any quotation marks.

Example:  Assume the SAS data file DATA1 contains the variables _NAME_,X1, X2, and X3 and is located in the SAS data library STUDY.  The following query statement is generated if you select all three variables in the Fields to Retrieve dialog:

SELECT DATA1.'_NAME_',DATA1.X1, DATA1.X2, DATA1.X3 FROM DATA1

After the FROM command, DATA1 must be changed to STUDY.DATA1 and the quotation marks on _NAME_ must be removed so that the resulting query will be displayed in the Edit SQL Query dialog:

SELECT DATA1._NAME_, DATA1.X1, DATA1.X2, DATA1.X3 FROM STUDY.DATA1

Click OK to accept the query.


Import - ODBC

This option will allow you to easily import data from a wide variety of data bases (including many large system data bases (Oracle, Sybase, etc.) using Microsoft Open Data Base Connectivity (ODBC ) conventions.  The ODBC import facilities in STATISTICA support multiple data base tables; specific records (rows of tables) can be selected by entering SQL query statements.  The steps necessary to import data via ODBC are outlined below:

•	When you select the Import Data - ODBC option from the File pull-down menu of any module, you will first be prompted to select the data source (name of the server or directory on which the data resides, e.g., dBASE) in the resulting Windows SQL Data Sources dialog.

•	Next, specify the name and location of the file containing the data in the standard Windows Select Directory dialog.

•	Now, the ODBC Import - Select Fields and Specify Conditions for Row Selection dialog will open in which you can specify the desired tables, fields, rows, etc. to be imported.

Note that in order to use this option, the ODBC drivers (appropriate for the data format to be accessed) needs to be installed on your system.  The list of currently installed drivers (including those installed by STATISTICA) is displayed in the SQL Data Sources dialog.  If a driver for the data base you intend to access is not included in the list, please contact the respective data base manufacturer.  If you wish to import using a 16-bit ODBC driver, then deselect the 32-bit ODBC option (available by selecting File..Import Data from the File pull down menu).

For more information on importing data from SAS via ODBC, see Importing SAS Data Files.


ODBC Import - Select Fields and Specify Conditions for Row Selection

When you select the Import - ODBC option from the File pull-down menu and select the data source, this dialog will open.  Here, you can specify the desired tables, fields, rows, etc. to be imported.

ODBC Import - Select Fields and Specify Conditions for Row Selection dialog:

Tables

Fields

Fields to Retrieve

Row Selection

Edit SQL Query


ODBC Import - Select Fields and Specify Conditions for Row Selection - Tables

This area of the ODBC Import - Select Fields and Specify Conditions for Row Selection dialog displays all of the tables in the previously selected data base directory.  Click on the {uncheck.bmp} next to the desired table in order to open (activate) the table and display the names of Fields (columns) in that table.  Alternatively, you can double-click on the Table name or press the space bar to cycle through the available tables.

If only one Table is available in the directory, then when you open this dialog, the table will automatically be activated and its Fields will be displayed.


ODBC Import - Select Fields and Specify Conditions for Row Selection - Fields

Once you select the desired Table in the ODBC Import - Select Fields and Specify Conditions for Row Selection dialog, the names of Fields (columns) associated with that table will be displayed in this area of the dialog.  Select the desired fields by highlighting them [continuously or dis-continuously (by holding down the CTRL key while clicking on the names)] in this box and then clicking on the Add>> button to transfer the selected field names to the Fields to Retrieve box (where they can be managed).


ODBC Import - Select Fields and Specify Conditions for Row Selection - Fields to Retrieve

This area of the dialog represents the fields to be imported from the selected Tables.  Here, you can manage previously selected Fields (columns):  you can delete, cut, copy, and/or paste the field names in order to rearrange the list of fields.  Note that the order in which the fields are displayed here will be the order in which they will appear in the resulting STATISTICA data file.


ODBC Import - Select Fields and Specify Conditions for Row Selection - Row Selection

Specify here, either all rows (Select all Rows) or a subset of rows (WHERE...) to be imported.  If you specify the option Select all Rows, then when importing data via ODBC, STATISTICA will create a SELECT statement in order to retrieve all user-specified fields from the respective tables.  If you want to import only a subset of rows, select the WHERE... option and write a correct SQL WHERE statement.  For SQL syntax, please consult an SQL manual.


ODBC Import - Edit SQL Query

When you check the Edit SQL Query option in the ODBC Import - Select Fields and Specify Conditions for Row Selection dialog and click the OK button, this dialog will open.

This dialog, intended for advanced ODBC/SQL users, allows for custom-editing of the complete SQL statement that will be submitted to the ODBC driver in order to import the specified data.  Initially, the edit box contains the query generated by STATISTICA, based on the specifications and selections made by the user in the ODBC Import - Select Fields and Specify Conditions for Row Selection dialog.

By clicking on the Cut, Copy, and Paste buttons, you can use these standard Windows features to edit the text in the edit box.


ODBC Import - SQL Error

This dialog is displayed if the interaction with ODBC fails.  The dialog displays the name of the function which could not be successfully executed, the error code (SQL State), and a brief description of the error (if one is available).

There are a wide range of problems that may occur when interacting with the ODBC facility.  These errors may be the result of particular features in the user's system (e.g., obsolete ODBC drivers, special character sets used by the database, mirrored tables, etc.).  Sometimes these problems can be eliminated by custom-editing the SQL statement that is generated by STATISTICA and later submitted to the ODBC driver manager for execution.  Users who are familiar with SQL syntax can edit that statement by checking the Edit SQL Query checkbox in the main ODBC Import - Select Fields and Specify Conditions for Row Selection dialog before clicking the OK button.  When this option is checked, the Edit SQL Query dialog will be displayed, and will enable verification and modification of the SQL statement.


ODBC Import - Templates

This dialog is displayed when you select the Import - ODBC/Templates from the File pull-down menu.  This option allows you to create templates to automate the import of databases via ODBC (e.g., predefined templates can be used in interactive mode, via macros, or as SCL scripts of commands).

ODBC Import - Template dialog:

Data Source:  Enter the name of the data source as it appears in the ODBC.INI file, e.g., as "MS Access Data" or "dBase Data."  This field is required, and cannot be left blank.

Login:  Enter the user name or identifier (this field can be left blank if the data source does not require a login for access).

Password:  Enter the password for access to the database (this field can be left blank if the database is not password-protected).

Other Attributes:  Enter any additional information required by ODBC to connect to the data source (e.g., the database name or location).  This information is usually used to identify and locate the exact database that will be used for import.  For example:

DBQ=c:\data\access.dta\mydata.mdb

or

DBQ=c:\data\dbase.dta

In most cases, some information must be provided in this field in order for ODBC to successfully connect to the data source.

Enter SQL Query:  Enter a SELECT statement (following SQL syntax conventions) that will specify which fields and records are to be imported from the data source.  (For SQL syntax, please consult an SQL manual.)

Open/Save:  These buttons allow the user to load and save the specifications for the ODBC/Templates dialog.

By clicking on the Cut, Copy, and Paste buttons, you can use these standard Windows conventions to edit the text in the SQL Query edit box.

Note:  If you wish to import using a 16-bit ODBC driver, then deselect the 32-bit ODBC option (available by selecting File..Import Data from the File pull down menu).

For information on using ODBC to interactively import databases into STATISTICA, see Import - ODBC.


ODBC Import - 32-bit ODBC

By default this option is checked allowing you to import data into STATISTICA using a 32-bit ODBC driver.  Deselect this option to import data using a 16-bit ODBC driver.

For information on using ODBC to interactively import databases into STATISTICA, see Import - ODBC.

For information on creating templates to automate the import of databases via ODBC (e.g., predefined templates can be used in interactive mode, via macros, or as SCL scripts of commands), see Import ODBC-Templates.


Quick Export

This option will allow you to export files to Excel, Quattro, Lotus 1-2-3, ASCII (text) files, and STATISTICA 4.5..  STATISTICA features a selection of comprehensive data export facilities (see Export Files) in the Data Management module, which support a large selection of data file formats and offer some additional options for specialized data transfers (e.g., options to split/merge data values and their labels while transferring data to/from file formats which do not support labeled values).  However, the Quick Export option is available from the File pull-down menu of all STATISTICA modules.

When you click on the Quick Export option in the File pull-down menu, the Quick Export dialog will open.

Quick Export ... dialog:

To:  The STATISTICA file will be exported in the file format that you select here.  The formats available in this dialog are:

dBASE

Excel 3

Excel 4-7

Lotus 1-2-3

Lotus for Windows (1, 4)

Quattro

ASCII (text) files

STATISTICA 4.5

For other format options, see Data Management.

Options button:  Click on this button to bring up a dialog of export options specific to the file format selected above.  Please note that there are no options available when exporting to STATISTICA 4.5.  For more information on the specific options available for the Quick Export facility, see:

Excel/Lotus/Quattro Quick Export Options

Text (ASCII) File Quick Export Options

If STATISTICA 4.5 has been selected, the options button will be deselected.  Selecting STATISTICA 4.5 will save the current data file in a STATISTICA 4.5 format.  Because certain variable specification categories (time, scientific, currency, percentage) are not available in STATISTICA 4.5, variables using these specification categories will be saved as numeric values.  Additionally, the STATISTICA 4.5 format only supports data sets with up to 300 variables.  You will not be able to export a data set (to STATISTICA 4.5 format) with more than 300 variables.

Example:  Exporting Data via the Quick Export Facility


Excel/Lotus/Quattro Quick Export Options

Range:  This option permits selection of a specific range of cases and/or variables to be exported.

Variables:  Specify the range of variables to be exported (From which variable, To which variable, inclusive).

Cases:  Specify the range of cases to be exported (From which case, To which case, inclusive).

Put case names in the first column:  Select this option in order to put the case names into the first column of the exported file.

Put variable names in the first row:  Select this option in order to put the variable names in the first row of the exported file.

Variables w/Text Values:  These options allow you to export either text or numeric values.

Use text values:  Select this option if you want to export the text values of variables

Use numbers:  Select this option if you want to export the numeric equivalents of text values of variables.

In order to export both text values and their numeric equivalents and/or export their labels, use the comprehensive export facility available in Data Management which also offers options to store value labels and/or double-notation pairs as values in file formats which do not support labels as double-notation.

Value labels can also be transferred to the applications via the Clipboard (see Spreadsheet View Text Values).


Text (ASCII) File Quick Export Options

Field Separator:  Select the type of delimiter that will be used in the output file.  You can specify one of four predefined separators (TAB, SPACE, COMMA, or SEMICOLON), or a User-defined separator.  For more extensive field separator options, use the Data Management Export facility.

Range:  This option permits selection of a specific range of cases and/or variables to be exported.

Variables:  Specify the range of variables to be exported (From which variable, To which variable, inclusive).

Cases:  Specify the range of cases to be exported (From which case, To which case, inclusive).

Put case names in the first column:  Select this option in order to put the case names into the first field of each record of the exported file.

Put variable names in the first row:  Select this option in order to put the variable names in the first record of the exported file.

Variables w/Text Values:  These options allow you to export either text or numeric values.

Use text values:  Select this option if you want to export the text values of variables

Use numbers:  Select this option if you want to export the numeric equivalents of text values of variables.

In order to export both text values and their numeric equivalents and/or export their labels, use the comprehensive export facility available in Data Management which also offers options to store value labels and/or double-notation pairs as values in file formats which do not support labels as double-notation.

Value labels can also be transferred to the applications via the Clipboard (see Spreadsheet View Text Values).


Exporting Data via the Quick Export Facility

To export a STATISTICA file using the Quick Export facility, consider the STATISTICA example data file Adstudy.sta (25v x 50c) and follow the steps outlined below.

Step 1:	Select the Quick Export option from the File pull-down menu to open the Quick Export dialog.

Step 2:	Select the desired file type into which the data will be exported.  For this example, select Excel 3.

Step 3:	Click on the Options button to open the Quick Export to Excel 3 - Options dialog.  For this example, select the Put case names in the first column and Put variable names in the first row options and choose to export text values for Variables with text values.  Click OK in this dialog.

Step 4:	The Save Exported File As ... dialog will now appear on your screen.  Enter here, a name under which the file will be saved.  Click OK to complete the exporting process.

The resulting Excel 3 file will contain 26 columns (an additional column was added for the case names) and 51 rows (an additional row was added for the variable names).


Overview of Object Linking and Embedding (OLE)

STATISTICA offers comprehensive support for Object Linking and Embedding (OLE) in both server mode and client mode.  These facilities allow the user to create and maintain dynamic links between STATISTICA graphics objects and documents in other OLE-compatible applications (e.g., word processors, spreadsheets, drawing programs, or STATISTICA itself).  STATISTICA objects can be linked or embedded in other application documents; also any foreign, OLE compatible objects can be linked or embedded to STATISTICA graphic documents.  STATISTICA supports complex (e.g., nested) compound documents.  Also, foreign document files can be linked or embedded to STATISTICA documents by dragging them by mouse directly from File Manager (across application windows) and dropping them onto STATISTICA graphs.

For more information, see the following topics:

Pasting STATISTICA Graphs to Other Applications

Creating Links to STATISTICA Graph Files

Creating New STATISTICA Objects in Client Applications

Linking and Embedding Foreign (or STATISTICA) Objects in STATISTICA Graphs


Overview of Object Linking and Embedding (OLE) - Pasting STATISTICA Graphs to Other Applications

An OLE link is automatically created when a STATISTICA graph is pasted into a document in another application.  If that application supports OLE, then the graph is pasted in STATISTICA Graph (OLE object) format and later can be edited using all STATISTICA graph customization facilities by double-clicking on the graph in the client application to call STATISTICA in the server mode.  If a STATISTICA module is open (i.e., running in the background), that module will be activated to edit the graph; otherwise the Basic Statistics module will open.  When the editing is completed, you can use any of the standard OLE conventions to exit the STATISTICA server mode and update the graph in the client application (use the options Update, Update and Return to..., etc. in STATISTICA pull-down menu File; those options are available only if STATISTICA is running in the server mode).  Please refer to Volume II of the manual (Chapter 2, Example 6) for a step-by-step example.


Overview of Object Linking and Embedding (OLE) - Creating Links to STATISTICA Graph Files

If a STATISTICA graph is saved (in an *.stg file), it can be linked to a client document (e.g., a word processor file) using the Paste Link or Insert (or Insert Object, depending on the application) option in the client application.  If an Insert option is used, a dialog will open, allowing the user to select a Link from the list of available OLE-compatible file formats.  Select the desired file to be inserted (in most word processors, the object will be inserted at the current cursor position; some programs allow the user to select the desired location with the mouse).  If the client application is STATISTICA, then you can either paste the graph in the default location (upper-left corner or select the location and size with the mouse, see Paste Link).  Once inserted, the graph can be edited by double-clicking (to call the STATISTICA server) as described in the previous paragraph.  Most OLE-compatible applications support options to update (manually or automatically) the linked objects.

Also, most OLE-compatible applications will allow you to create a link to file when you paste STATISTICA graphs (via Clipboard); use the Paste Link option from the Edit pull-down menu in the client application.  You can also use the Paste Special option in the client application; if the STATISTICA graph is saved to a file, then the Paste Link radio button in the Paste Special dialog will be available.


Overview of Object Linking and Embedding (OLE) - Creating New STATISTICA Objects in Client Applications

Using OLE conventions, STATISTICA can also be called from client applications to create new objects (e.g., statistical graphs, diagrams, etc.).  Use the Insert (or Insert Object, depending on the application) option in the client application; in the resulting dialog, select New, and then select STATISTICA from the list of available OLE-compatible applications.  STATISTICA will open in the server mode and will automatically create a Blank Graph window; this window can be used to create a new graph, combination of graphs, or other artwork to be inserted as an OLE object to the client application (exit STATISTICA to the client application as described in Pasting STATISTICA Graphs to Other Applications).  Please refer to Volume II of the manual (Chapter 11, Example 2) for a step-by-step example.

Note that instead of creating a new graph from scratch (as illustrated in the example mentioned above, Volume II, Chapter 11, Example 2), you can use the Paste Resplace All option in the STATISTICA pull-down menu Edit to replace the contents of the blank graph with the contents of any other STATISTICA graph.


Overview of Object Linking and Embedding (OLE) - Linking and Embedding Foreign (or STATISTICA) Objects in STATISTICA Graphs

As mentioned before you can paste STATISTICA graphs to other applications (see Pasting STATISTICA Graphs to Other Applications), create links in other applications to STATISTICA graph files (see Creating Links to STATISTICA Graph Files), and create new STATISTICA objects in client applications (see Creating New STATISTICA Objects in Client Applications).  You can also perform these same operations within STATISTICA, thus using STATISTICA as an OLE client (and not server).  STATISTICA can act simultaneously as a server and client and compound graphs can be created consisting of STATISTICA graphic objects which can be edited or updated using the standard OLE conventions (see, Paste Special, Paste Link, Insert Object).  In addition, several procedures in STATISTICA [e.g., Quality Control, and some Stats Graphs (such as scatterplots with box plots)] will automatically generate compound graphs.  Multiple graph displays can also be created in STATISTICA via the Multiple-Graph AutoLayout Wizard (see also Blank Graphs).

You can also drag files from the Windows File Manager across applications and drop them into a STATISTICA graph.  These files will be treated in one of three ways when they are dropped in STATISTICA:

(1)	If the file originated from an OLE-compatible document, then it will be displayed in the STATISTICA graph as a pasted OLE object.  You can use the Edit - Object option or double-click on the pasted object in order to edit it.

(2)	If the file did not originate from an OLE-compatible document, but it is registered as being produced by a specific application, then this application's icon will be displayed.  You can double-click on this icon in order to edit the contents of the file.

(3)	If neither of the above conditions applies, then the Windows Packager icon will represent the file.  You can double-click on this icon in order to call the Packager.


STATISTICA Initialization File

Whenever you change STATISTICA's system defaults via a dialog option (e.g., you change the default number of Scrollsheets or Graphs displayed on screen), those changes will automatically be written to the STATISTICA initialization file (statist.ini).  You can also change the system defaults by editing the statist.ini file directly.  In most cases, it will be easier to change the defaults via STATISTICA's comprehensive and interactive dialogs, however, in some cases it may be necessary to enter the appropriate command in the statist.ini file (e.g., changing the Text/output Window font).  The following list summarizes the most useful commands for the initialization file and provides "jumps" to the appropriate dialog topic.

Note that the statist.ini file is divided into sections (each section is defined by its name in brackets, e.g., [STATISTICA]) with the appropriate commands after the section title.  Each command in this file is made up of two parts; the specific option that will be changed (on the left of the equal sign) and the entry that defines the change (on the right of the equal sign).  If you want to use a system default, then do not enter that command in this file (i.e., if a command is missing, then STATISTICA interprets that as meaning "use system default").

Section	Statement	Explanation

[STATISTICA]

StaFile=filename.sta	Open this data file when module opens.

SelectFile=filename.sel	Specifies the selection condition file.

Select=number	Enter 1 for off, 2 for text, or 3 for file;

see also Case Selection Conditions.

SelectInclude=0 or 1	Applicable only when you select 2 above;

enter 0 to include or 1 to exclude cases;

see also selection condition.

Weight=Variable	Specifies the weight variable number.

PrintHeader=text	Uses this text for the page header.

PrintFlag=number	Choose 1 for off, 2 for disk file, or 3 for printer;

see also Page/Output Setup.

PrintLevel=number	Choose 1 (brief), 2 (short), 3 (medium), or 4 (long);

see also Page/Output Setup.

PrintFile=filename.txt	Applicable only when you select disk file above;

enter the output file name.

PrintEjectPage=1	Ejects each page before page is filled;

see also Print/Eject Current Page.

PrintPage=1	Prints the page number in the output.

PrintDateTime=1	Prints the current date and time in the output;

see also Page/Output Setup.

PrintCenterTitles=1	Centers the titles in the output.

PrintFont=numbers	Enter font specifications for printed output.

PrintBorder=number	Specifies desired border thickness;

from 0 (no border) to 7 (thickest border);

MaxScrollsheet=no.	Specifies the Scrollsheet queue;

min = 1, max = 20;

MaxGraph=number	Specifies the graph queue;

min = 1, max = 20;

StartAnalyze=0	Does not display Startup Panel upon entry.

FrameMaximized=0	Does not display window frame upon entry.

StatusBar=0	Does not display Status Bar upon entry.

FullMenus=0	Does not display Full Menus upon entry.

StartOutput=1	Opens Text/output Window upon entry.

ProgressBar=0	Does not yield to Windows (multitasking).

ViewerAutoMove=no.	Use 0 for none, 1 for down, or 2 for right;

see also STATISTICA Defaults: General.

MenuIcons=0	Does not display Menu Icons upon entry.

DilalogIcons=0	Does not display Dialog Icons upon entry.

ProgressBar=0	Does not display Progress Bar upon entry.

AskSaveScrollsheet=0	No prompt to save modified Scrollsheet;

see also STATISTICA Defaults: General.

PrintScrollsheets=1	Prints all active Scrollsheets;

see also STATISTICA Defaults: General.

ScrCol=numbers	colors for Normal text, Active text, and Highlighted text;

see also Results Text - Colors.

EditorResultsFont=1	Text/output Window font = Results text font.

[Task Switcher]

Modules=0 1 2 ...	Specifies the modules listed in the Task Switcher.

SwitchAndClose=0	Designates the module switching mode;

(1=single application mode).

[SS_Colors, V_Colors, G_Colors, MM_Colors]

Note that this section applies to the color of Scrollsheet, spreadsheet, Megafile Manager, and the Graph Data Editor components (e.g., titles, info box, data, toolbar, etc.).  These options can also be set in the appropriate Customize Colors dialog.

InfoText=number	Controls the color for Info Text.

InfoBackgr=number	Designates the color for Info area background.

HeaderText=number	Specifies the color number for Title Text.

HeaderBackgr=number	Specifies the color number for Title area background.

ShowText=number  	Designates the color for Toolbar Text.

ShowBackgr=number	Specifies the color number for Toolbar background.

ColNamText=number	Designates the Column Names color.

ColNamBackgr=no.	Designates the Column Names background color.

RowNamText=number	Specifies the color number for Row Names.

RowNamBackgr=no.	Specifies the color for Row Names background.

DataText=number	Designates the color for Data Text.

DataBackgr=number	Enter the color choice for Data area background.

HiliteText=number	Enter the color choice for the Highlighted Text.

HiliteBackgr=number	Specifies the color for Highlighted Text background.

MainLine=number	Enter color for lines between col. & row names.

GridVLine=number	Designates the color for Vertical Grid Lines.

GridHLine=number	Enter the color for Horizontal Grid Lines.

[Fonts]

Note that this section applies to the font style, size, etc., of text.  These options can also be set in the appropriate Define Font dialog.

Scrollsheet=numbers	Designates font style, size, etc., for Scrollsheet text.

Viewer=numbers	Specifies font style, size, etc., for spreadsheet text.

DataLayout=numbers	Select the font style, size, etc., for Graph Data Editor text.

Megafile=numbers	Enter font style, size, etc., for Megafile Manager text.

ResultsFont=numbers	Enter font style, size, etc., for the Results text.

[UserGraphs]

This section applies to user-defined graphs.  Each user-defined graph which is saved via the Add as User-defined Graph to Menu button will be listed in this section.

User1=path	where path is the location and name of this user-defined graph.

(e.g., C:\Stat\Examples\user1.sug)

User2=path

.

.

.

User16=path


Matrix File Format

STATISTICA's statistical matrix files (e.g., Correlation, Covariances, Similarities, and Dissimilarities) can be used in the modules which support the matrix input file format (e.g., Multiple Regression, Canonical Correlation, Reliability and Item Analysis, Cluster Analysis, Multidimensional Scaling, Factor Analysis, etc.).  Most STATISTICA modules will read both full and lower triangular matrices.  However, in order for STATISTICA to recognize the file as a matrix file, the file must meet the following conditions:

•	The number of cases (rows) = the number of variables (columns) + 4.

•	The matrix must be a square matrix and the case names should be the same as the variable names.

•	The last four cases contain the following case names and information:

Means:  The mean of each variable is given in this row; this case can be left empty (i.e., do not enter anything in this row) for Similarities and Dissimilarities matrices.

Std.Dev.:  The standard deviation of each variable is given in this row; this case can be left empty (i.e., do not enter anything in this row) for Similarities and Dissimilarities matrices.

No.Cases:  This required number is the number of cases from which the matrix was produced, not the number of cases (rows of data) in this matrix file.

Matrix:  This required number represents the type of matrix file; 1 = Correlation, 2 = Similarities, 3 = Dissimilarities, and 4 = Covariance.

NOTE:  When entering these last four cases into the matrix file manually, be sure to spell the case names exactly as they appear above (i.e., Means, Std.Dev., No.Cases, and Matrix).

Examples of Correlation Matrix Files:

The following matrix is a lower triangular correlation matrix:

Types of Matrices

Multiple Correlation Matrices


Matrix File Format - Types of Matrices

Correlation (value of the last case [Matrix]:  1):  Square correlation matrices are symmetrical and contain the correlation coefficients for all pairs of specified variables.  You can create correlation matrices by saving correlations in the appropriate dialogs (for example, see the option Save Correlation Matrix in the Multiple Regression - Reviewing Descriptive Statistics dialog).  You can also manually create a correlation matrix by entering the correlations into a regular spreadsheet (see Creating a Correlation Matrix) and including in the file, the last four cases which describe the matrix (see Matrix File Format).

Similarities (value of the last case [Matrix]:  2):  The similarities between objects (e.g., variables) are expressed in this matrix.  You can import or manually create this type of matrix file by entering the correlations into a regular spreadsheet (see, see Creating a Correlation Matrix) and including in the file, the last four cases which describe the matrix (see Matrix File Format).  Similarities matrices can be used in Multidimensional Scaling analyses.

Dissimilarities (value of the last case [Matrix]:  3):  The dissimilarities (distances) between objects (e.g., variables) are expressed in this matrix.  You can create this matrix manually (see Creating a Correlation Matrix) or it can be created for you by using the Save Distance Matrix option in the Cluster Analysis - Joining Results dialog.  Dissimilarities matrices can be used in Multidimensional Scaling analyses.

Covariance (value of the last case [Matrix]:  4):  Square covariance matrices contain the covariances for all pairs of specified variables on the off-diagonal and the variances for each variable on the diagonal of the matrix.  Covariance matrices can be saved in the Structural Equation Modeling module, or you can manually create a covariance matrix by entering the covariances into a regular spreadsheet (see Creating a Correlation Matrix) and including in the file, the last four cases which describe the matrix (see Matrix File Format).


Matrix File Format - Multiple Correlation Matrices

Multiple correlation matrices are an extension of the standard square matrix format (see Types of Matrices).  The matrices are formatted in a sequence.  Each matrix represents some measures of relations (e.g., correlation coefficients) for all pairs of specified variables for a specific group.  For example, two matrices are shown in the multiple correlation matrix below (one for each group).

Example of a Multiple Correlation Matrix File:

Multiple correlation matrices can be used as input for analyses such as those in the Structural Equation Modeling module.  Multiple correlation matrices can be created via the Correlation - Save option in the Quick Basic Stats - Extended Options dialog when a grouping variable is specified.  Note that the order in which the matrices are displayed in the spreadsheet depend on the order in which the codes are specified in the Select codes for grouping variable dialog.

You can also manually create a multiple correlation matrix by entering the correlations into a regular spreadsheet (see Creating a Correlation Matrix) and including after each matrix, the last four cases which describe the matrix (see Matrix File Format).


Spreadsheet Window Toolbar Buttons

The following is a list of toolbar buttons for the spreadsheet window.  For quick access to information about the spreadsheet window, see Spreadsheet Window Overview.

For more information on specific dialogs or options, click on the [image] button in the upper-right corner of the dialog.

For more general information, see STATISTICA Index.

  Change Show Window

  STATISTICA Module Switcher

  Workbook Management

  All Specs

  Modify Variables Menu

  Modify Cases Menu

  Spreadsheet View Text Values

  View Case Names

  Zoom In Tool

  Zoom Out Tool

  Increase Column Width (also available by dragging)

  Decrease Column Width (also available by dragging)

  Spreadsheet Global Width (also available by dragging)

  Increase Decimal Tool

  Decrease Decimal Tool

  Recalculate Variable(s)

  Text Values Manager

  Quick Basic Stats

  Custom 2D Graphs

  Custom 3D Sequential Graphs

  Custom 3D Scatterplots and Surfaces

  Custom Matrix Plots

  Custom Icons Plots

  Quick Stats Graphs

  Graphs Gallery

  Open Data File

  Save File As

  Print Data

  Cut

  Copy

  Paste

  Undo

  Electronic Manual


Scrollsheet Window Toolbar Buttons

The following is a list of toolbar buttons for the Scrollsheet window.  For quick access to information about the Scrollsheet window, see Scrollsheet Window Overview.

For more information on specific dialogs or options, click on the [image] button in the upper-right corner of the dialog.

For more general information, see STATISTICA Index.

  Change Show Window

  STATISTICA Module Switcher

  Workbook Management

  Options

  Columns

  Rows

  Zoom In Tool

  Zoom Out Tool

  Increase Column Width (also available by dragging)

  Decrease Column Width (also available by dragging)

  Scrollsheet Global Width (also available by dragging)

  Increase Decimal Tool

  Decrease Decimal Tool

  Mark Selection

  Quick Basic Stats

  Custom 2D Graphs

  Custom 3D Sequential Graphs

  Custom 3D Scatterplots and Surfaces

  Custom Matrix Plots

  Custom Icons Plots

  Quick Stats Graphs

  Graphs Gallery

  Open Scrollsheet File

  Save Scrollsheet As

  Print Scrollsheet

  Cut

  Copy

  Paste

  Electronic Manual


Zoom Options Dialog

When you first click on either the Zoom In or Zoom Out Toolbar buttons (or select either the Scrollsheet Zoom In or Scrollsheet Zoom Out option), the Zoom Options dialog will open if the current font will not zoom (scale) continuously.  (Some fonts do not scale continuously, but only in relatively large increments.)

Zoom Options dialog:

OK (Default Font) button:  Click this button to accept the default font and exit this dialog in order to increase the font.

Select Font button:  Click on this button to open the Font dialog in order to select a different font for the Scrollsheet or spreadsheet.


  Zoom In Tool

Change the scale of the window to the next higher magnification by clicking on this button (the scale of the entire window will increase proportionally).  When you first click on this button, the Zoom Options dialog may open (depending on the current type of font in the Scrollsheet), offering you a change of font if the current font will not zoom (scale) continuously.

You can also decrease the scale (see Zoom Out Tool) in the same increments that you increased it.


  Zoom Out Tool

Change the scale of the window to the next smaller magnification by clicking on this button (the scale of the entire window will decrease proportionally).  When you first click on this button, the Zoom Options dialog may open (depending on the current type of font in the Scrollsheet), offering you a change of font if the current font will not zoom (scale) continuously.

You can also increase the scale (see Zoom In Tool) in the same increments that you decreased it.


  Increase Decimal Tool

You can add one decimal place to the formatted length of values in spreadsheets (see Spreadsheet Edit Specs) or Scrollsheets (see Scrollsheet Edit Column Specs) each time you click on this button.  This option will only affect the display of the Scrollsheet or spreadsheet values and not the precision of the stored values.  (To decrease the number of decimal places, see Decrease Decimal Tool button.)


  Decrease Decimal Tool

You can remove one decimal place from the formatted length of values in spreadsheets (see Spreadsheet Edit Specs) or Scrollsheets (see Scrollsheet Edit Column Specs) each time you click on this button.  This option will only affect the display of the Scrollsheet or spreadsheet values and not the precision of the stored values.  (To increase the number of decimal places, see Increase Decimal Tool button.)


  Increase Column Width

Gradually increase the width the currently highlighted column in the Scrollsheet or spreadsheet by clicking on this button.  This option will only affect the display of the Scrollsheet or spreadsheet and not the precision of the stored values.  (To decrease the column width, see Decrease Column Width.)


  Decrease Column Width

Gradually reduce the width the currently highlighted column in the Scrollsheet or spreadsheet by clicking on this button.  This option will only affect the display of the Scrollsheet or spreadsheet and not the precision of the stored values.  (To increase the column width, see Increase Column Width.)


  Spreadsheet Edit Variables Menu

Add Variables	Edit Text Values

Move Variables	Date Values

Copy Variables	Recalculate Variables

Delete Variables	Shift (Lag) Variables

Current Specs	Rank Variables

All Specs	Recode Variables


  Spreadsheet Edit Cases Menu

Add Cases

Move Cases

Copy Cases

Delete Cases

Edit Case Names


About STATISTICA

Select this command to display the STATISTICA version, copyright notice, and license information.


Scrollsheet Window - Overview

A Scrollsheet is a spreadsheet-like, scrollable table used in STATISTICA for editing data and displaying the results of analyses.  Scrollsheets offer a variety of options to facilitate reviewing results (e.g., user-controlled display format, split-screen scrolling) and visualizing them in predefined and custom-defined graphs (see Quick Stats Graphs and Custom graphs).  Also, values in Scrollsheets can be edited, including Excel-style moving block via Drag-and-Drop techniques, and examined via the Block Statistics facilities.

For more information, see:

What is the difference between Scrollsheets and spreadsheets?

Split-Scrolling

Drag-and-Drop facilities

Toolbars, flying menus

Converting data spreadsheets into Scrollsheets

Converting Scrollsheets into standard data files (spreadsheets)

Queues of Scrollsheets

Auto-report (Automatically Print All Scrollsheets)

Saving Scrollsheets in a Scrollsheet format

Saving Scrollsheets as data files

Adding rows or columns to the current Scrollsheet

Selecting (highlighting) the entire Scrollsheet

Editing the contents of a Scrollsheet cell (and not overwriting it)

STATISTICA File Server

Toolbar and pull-down menu Scrollsheet options:

Scrollsheet Window Toolbar

File Menu	Options Menu

Edit Menu	Window Menu

View Menu	Help Menu

Analysis Menu	Continue Button

Graphs Menu


Scrollsheet Window Overview - What is the difference between Scrollsheets and spreadsheets?

All differences between these two--on the surface very similar--main types of "documents" in STATISTICA are related to the difference in their contents:  Scrollsheets are used to display results from analyses, whereas spreadsheets hold input data files.  Both types of tables look similar and they offer very similar facilities, including the graphics options (both Custom and Stats graphs are available from Scrollsheets and from spreadsheets).  Also, both offer easy access to Quick Basic Stats and Block Stats facilities.  However, each of them offers specialized facilities which are applicable to their respective contents.  For example, data spreadsheets feature integrated data management, restructuring, transformation and recoding facilities (see Spreadsheet Window Overview), whereas Scrollsheets offer specialized graphs related to the types of statistical output they contain or integrated facilities to identify cells or rows containing results which meet particular statistical criteria (e.g., significance level).


Scrollsheet Window Overview - Split Scrolling

Scrollsheet Window Overview - Split-Scrolling

Scrollsheets can be split into up to four sections (panes) by dragging the split box (the black rectangle at the top of the vertical scrollbar or to the left of the horizontal scrollbar).  This is useful if you have a large Scrollsheet and you want to review results from different parts of the Scrollsheet.  When you point with the mouse at the split box, the cursor changes to [image] (or [image]).  Now, to position the split, hold down the left-mouse-button and drag to the desired position.  You can change the position of the split by dragging the split box (now located between panes) to a new position.  Note that vertically split panes scroll together when you scroll vertically while horizontally split panes scroll together when you scroll horizontally.


Scrollsheet Window Overview - Drag-and-Drop

The standard (MS Excel-style) Drag-and-Drop facilities [moving, copying, clearing, inserting, duplicating, and extrapolating series (AutoFill)] are supported in spreadsheets.


Scrollsheet Window Overview - Toolbars, Flying Menus

The differences and similarities between spreadsheets and Scrollsheets are reflected in the appearance of the toolbars which accompany each of the two types of document-windows as well as in the contents of the flying menus which can be brought up by clicking the right-mouse-button on individual cells.  Note that these two types of documents can easily be converted into one another (see Converting Spreadsheets into Scrollsheets).


Scrollsheet Window Overview - Converting Data Spreadsheets into Scrollsheets

The Convert to Scrollsheet... option can be used to convert the data file or the currently highlighted block of data into a Scrollsheet; an intermediate dialog will allow you to select options.  A data file saved this way into a Scrollsheet can later be opened (e.g., for reference) at any point of the data analysis without affecting the main data file residing in the data spreadsheet and used as input data (the default file name extension for Scrollsheet files is *.scr).


Scrollsheet Window Overview - Converting Scrollsheets into Standard Data Files (Speadsheets)

Scrollsheet Window Overview - Converting Scrollsheets into Standard Data Files (Spreadsheets)

The Save as Data... option can be used to convert the contents of the current Scrollsheet or the currently highlighted block into a standard STATISTICA data file.  A data file created this way can later be opened for input as a regular data file, thus allowing you to submit output from one analysis as input for another.


Scrollsheet Window Overview - Queues of Scrollsheets

Statistical analyses may produce large amounts of output.  Scrollsheets offer flexible ways to organize the output regardless of its size.  New Scrollsheets are generated by subsequent analyses in a "queue," where older Scrollsheets are closed automatically as new ones are created (to avoid having too many open windows at once).  The Scrollsheets are closed on a first-in-first-out basis, and the default length of the queue is 3.  In other words, when the fourth Scrollsheet is created, then the first one is closed (with no warning unless you have edited or customized it).

The length of the queues.  In some instances, you may want to increase the length of this queue.  Use the Scrollsheet Manager in the pull-down menu Window to temporarily change the length of the queue for the current session [the setting will return to the default length of 3 when you close the current module of STATISTICA, the STATISTICA Defaults: General option (accessible from the pull-down menu Options) can be used to adjust the queue length permanently].  In addition, the Scrollsheet Manager dialog can be used to "lock" specific Scrollsheets (see Window Manager Dialog for more details).

Note that an option is provided to automatically print (or send to the output file and/or the on-screen Text/output Window) each Scrollsheet which is generated on the screen.


Scrollsheet Window Overview - Auto-report (Automatically Print All Scrollsheets)

In order to create a log of all Scrollsheets, select the Automatically Print All Scrollsheets (and optionally graphs) option(s) in the Page/Output Setup dialog (accessible in the pull-down menu File or by double-clicking on the Output field on the status bar at the bottom of the STATISTICA window).


Scrollsheet Window Overview - Saving Scrollsheets in a Scrollsheet Format

Use options Save (CTRL+S) or Save As... (F12) in the File menu.  By default, Scrollsheets are saved in the Scrollsheet file format (file name extension *.scr); saved Scrollsheets can be opened again at any point of the analysis in any STATISTICA module.  Such Scrollsheet files also can be printed in batch using the Print Files facility (in the pull-down menu File), and are automatically added to the Workbook list where you can set some of them to Auto-open (then the selected Scrollsheet files will be opened automatically whenever the data file from which the Scrollsheets were made is opened).


Scrollsheet Window Overview - Saving Scrollsheets as Data Files

Use the option Save as Data in the File menu to save a Scrollsheet as a standard STATISTICA data file which can then be used for input in subsequent analyses (file name extension *.sta).


Scrollsheet Window Overview - Adding Rows or Columns to the Current Scrollsheet

Use the options Append Columns and Append Rows in the Scrollsheet pull-down menu Edit.  The extra space can be used for notes or input pasted from the Clipboard.


Scrollsheet Window Overview - Selecting (Highlighting) the Entire Scrollsheet

Following the standard spreadsheet convention, click in the upper left corner of the Scrollsheet.  This shortcut is useful, for example, when you intend to copy the entire file to the Clipboard.  Note that by clicking twice in the upper-left corner area, you will de-select (i.e., select and then de-select) the entire Scrollsheet.


Scrollsheet Window Overview - Editing the Contents of a Scrollsheet Cell

To avoid clearing the contents of the cell (at the point when you start entering a correction), first double-click on the cell before you start typing.  This will enter the editing mode and will position the cursor within the cell.  Alternatively, you can follow the "old" spreadsheet convention and press F2, which will also enter the edit mode for the currently highlighted cell.  (See also Scrollsheet Edit Cell.)  You can also edit the Scrollsheet header, column names, and row names.


Spreadsheet Window - Overview

STATISTICA stores its data in disk files optimized for quick access and storage efficiency.  The general organization of these files is similar to that of database management programs; it may be helpful to think of each file as a "table," where rows represent records (e.g., patients, subjects, samples) and each record consists of the same number of fields (for example, five types of data [measurements] available about each patient).  Values in spreadsheets can be edited, including Excel-style moving block via Drag-and-Drop techniques.

For more information, see:

Cases and variables

Case names

Text values

Data Values (Numeric, Text) and Labels

Other information about variables stored in STATISTICA data file

Headers, comments, Workbook

Colors, fonts, sizes

STATISTICA Workbooks

Split-Scrolling

Drag-and-Drop facilities

STATISTICA File Server

Block Stats/Columns

Block Stats/Rows

Fill/Standardize Blocks

Toolbar and pull-down menu spreadsheet options:

Spreadsheet Window Toolbar

File Menu	Graphs Menu

Edit Menu	Options Menu

View Menu	Window Menu

Analysis Menu	Help Menu


STATISTICA File Server

The STATISTICA File Server application is a small, rapidly loading module of STATISTICA which provides all standard STATISTICA on-line facilities (e.g., Quick Basic Stats, all Graphs) and tools for accessing and modifying all STATISTICA files, including data files (file name extension *.sta), Scrollsheet files (file name extension *.scr), and graphics files (file name extension *.stg).  STATISTICA files may be opened directly into the STATISTICA File Server by simply double-clicking on the file name in the Windows File Manager.

One of the advantages of using the STATISTICA File Server application is that you may have as many instances of the File Server open at one time as your operating system will allow, permitting you to edit and review many data files at once.  In addition, the STATISTICA File Server application provides OLE support for STATISTICA files in other applications (if there is not any other module of STATISTICA currently running).

Custom-designing new modules of STATISTICA.  You can use the File Server application as a foundation to develop your own "specialized STATISTICA modules" or "STATISTICA applications written in STATISTICA BASIC or a combination of SCL (STATISTICA Command Language) and BASIC."  The Auto Task Buttons toolbar can be used as a convenient startup panel for the new module.  Each button on the toolbar can be set up to execute a different, custom-designed computational, graphics, or data management procedure.

See also, File Open/Save As.


Spreadsheet Window Overview - Cases and Variables

STATISTICA data are organized into cases and variables.  If you are unfamiliar with this notation, you can think of cases as the equivalent of records in a data base management program (or rows of a spreadsheet), and variables as the equivalent of fields (columns of a spreadsheet).  Each case consists of a set of values of variables.


Spreadsheet Window Overview - Case Names

The first column in the file may contain names of cases (optional, see Edit Case Names).


Spreadsheet Window Overview - Text Values

Variables may contain text values.  Internally, STATISTICA will reference text values in "double-notation," that is, STATISTICA will assign numeric equivalents to those values; therefore, where applicable, you can perform all statistical analyses on those variables, as if they were numeric values.  For example, suppose the program (or you) made the following assignments:

1 - Male, 2 - Female (for variable Gender),

and

1 - C, 2 - H (for variable Educat)

You can switch between viewing text values:

Gender	Educat

-------------------

Male	C

Male	H

Female	C

Female	H

.	.

.	.

.	.

or their numeric equivalents:

Gender	Educat

-------------------

1	1

1	2

2	1

2	2

.	.

.	.

.	.

in the Spreadsheet by pressing the [image] button on the spreadsheet toolbar (see also, Text Values Manager and Data Values (Numeric, Text) and Labels).


Spreadsheet Window Overview - Other Information about Variables Stored in STATISTICA Data Files

In addition to the raw data, STATISTICA system data files can also store other (optional) information related to individual variables, such as:

Display formats (e.g., the number of decimals or date-value formats),

Missing Data codes (i.e., specific values which you intend to ignore in calculations),

Long variable names and comments (see Current Specs),

Long labels and comments attached to individual values (see Data Values (Numeric, Text) and Labels).,

Formulas which can be used to define, recode, or transform each variable (see Current Specs),

Dynamically-updated links between the data file and other Windows-compatable data files, that is, Windows Dynamic Data Exchange (DDE) links.

Most of those specifications of a variable can be accessed by double-clicking on the variable's name in the data spreadsheet.

In addition, links to Graphs created from the respective portions of the spreadsheet data can be maintained (applies to Stats Graphs, Quick Stats Graphs, Custom Graphs, and Block Stats Graphs).


Spreadsheet Window Overview - Headers, Comments, Workbook

Each STATISTICA data file may also contain the following text identification (see also, Header):

a one-line header information (displayed in the title area of the spreadsheet) which can be used to label reports,

multi-line comments or notes about the file (in the form of a paragraph of text), and

a list of names of supplementary files (e.g., graphs, Scrollsheets, text/graphics reports, batch or data transformation programs) associated with the current data set (see information on Workbooks).

They are accessible by double-clicking on the title area of the spreadsheet (or by pressing the Workbook [image] toolbar button or by selecting the Header... option in the pull-down menu Edit).


Spreadsheet Window Overview - Colors, Fonts, Sizes

Also, all customizations of the appearance of the data file (such as column width and height, colors, or font) are stored along with the data and can be used, for example to facilitate identifying specific files or data sets from specific projects.


Spreadsheet Window Overview - STATISTICA Workbooks

STATISTICA data files (file name extension *.sta) can be considered to be "Workbooks" of files because they contain (automatically store) information about all supplementary files (e.g., graphs, reports, programs) used with the current data set.  A log of these files can be reviewed by pressing the Workbook [image] toolbar button or by double-clicking on the title area (header) of the data spreadsheet.

Specific files (from the list of Workbook files) can be opened from the Data File Header, Notes, and Workbook Info dialog or check-marked to open automatically (Auto [image]) when you open the data file, so that all supplementary information (e.g., graphs or reports from a previous stage of the analysis) is available whenever you open the data set.  For more specific information on Workbooks, see Header....


Spreadsheet Window Overview - Split-Scrolling

Spreadsheets can be split into up to four sections (panes) by dragging the split box (the black rectangle at the top of the vertical scrollbar or to the left of the horizontal scrollbar).  This is useful if you have a large spreadsheet and you want to compare values or copy and paste from different parts of the spreadsheet.  When you point with the mouse at the split box, the cursor changes to [image] (or [image]).  Now, to position the split, hold down the left-mouse-button and drag to the desired position.  You can change the position of the split by dragging the split box (now located between panes) to a new position.  Note that vertically split panes scroll together when you scroll vertically while horizontally split panes scroll together when you scroll horizontally.


Spreadsheet Window Overview - Drag-and-Drop

The standard (MS Excel-style) Drag-and-Drop facilities [moving, copying, clearing, inserting, duplicating, and extrapolating series (AutoFill)] are supported in spreadsheets.


Window Menu

The following options are available from the Window pull-down menu.

Scrollsheet Manager

Graph Manager

Cascade

Tile Horizontally

Tile Vertically

Arrange Icons

Close All but Data File


Cascade

Select this option to arrange the open STATISTICA windows in an overlapping pattern so that the title bar of each window is visible.


Tile Horizontally

This option will arrange the open STATISTICA windows in a horizontal (side by side) pattern.  When you select this option, STATISTICA will automatically optimize the display of the open windows (with the preference given to tiling horizontally).  Graphics windows will maintain their original proportions unless you have de-selected the Fixed Proportions option from the Graphics View pull-down menu.


Tile Vertically

This option will arrange the open STATISTICA windows in a vertical pattern.  When you select this option, STATISTICA will automatically optimize the display of the open windows (with the preference given to tiling vertically).  Graphics windows will maintain their original proportions unless you have de-selected the Fixed Proportions option from the Graphics View pull-down menu.

Keyboard Shortcut:  ALT+SHIFT+F6


Arrange Icons

Select this option to arrange all iconized windows into rows.


Close All but Data File

This option will close all open (and unlocked) Scrollsheets, graphs, and related windows (e.g., graph data) in STATISTICA; the data spreadsheet will remain open.  This option is useful when you need to "clear" the screen to start a new analysis.  Note that windows opened from files are automatically locked, and will be unaffected by this option.

Keyboard Shortcut:  CTRL+L


Help Menu

These options are available from the Help pull-down menu, and they allow you to access various parts of the STATISTICA Electronic Manual.

Index	Spreadsheet	Advisor	WEB Page

Search Help On	Scrollsheet	Guided Tour	About

Glossary	Graph

Text/Output

Keyboard


Help Menu - Search Help On ...

Select this option from the Help pull-down menu in order to search for specific topics in the STATISTICA Help files (this option is equivalent to clicking on the Search button in the Help dialog).  When you select this option, the standard Windows Search dialog will open in which you can specify a topic or keyword that you want to search for.  Once you have typed in the keyword, a list of topics associated with that keyword will be displayed.  Highlight one of the general topics and click on the Show Topics button in order to display more specific topics that you can choose from.  When you have selected the specific help topic that you want, click on the Go To button in order to view that help topic.


Help Menu - Guided Tour

Select this option from the Help pull-down menu in order to launch a "Guided Tour" (overview) of STATISTICA.  The "Guided Tour" program (overview.exe) is distributed only with our CD ROM version; however, it can be downloaded from the StatSoft WEB page (http://www.statsoft.com).

If you select this option and you have not installed the "Guided Tour," a STATISTICA Message dialog will prompt you to install the Tour from the STATISTICA CD or to download the Tour from the StatSoft WEB page (http://www.statsoft.com).  You can copy the StatSoft WEB address to the Clipboard by pressing the Copy WEB Address button in this message dialog.

Note that if you have the STATISTICA CD, you can run the Tour directly from the CD without copying or downloading it to your hard drive.


Help Menu - WEB Page

Select this option from the Help pull-down menu to bring up a dialog box with information about the StatSoft WEB page.  You can copy the StatSoft WEB address to the Clipboard by pressing the Copy WEB Address button.

We invite you to visit the StatSoft WEB page often:

•	For the most recent information about STATISTICA, downloadable upgrades, new releases, new products, news about StatSoft, etc., access the "What's New..." section of the WEB site.

•	For a comprehensive list of "Frequently Asked Questions" (including useful tips, solutions to hardware/software compatibility problems, etc.), access the "Technical Support" section of the WEB site.

•	For a library of STATISTICA BASIC programs (written by users), access the "Technical Support" section of the WEB site (to submit your own programs to this "user-exchange forum," send us e-mail to info@statsoft.com).


  Cut

Cut removes the contents of the currently highlighted cells, text, or graph object and puts it on the Clipboard.  This action deletes the data in the Scrollsheet or spreadsheet (see also Clipboard Operations in the Spreadsheet) and replaces it with missing data until new values are entered or pasted in.  Highlighted text is simply deleted from the Text/output Window.  Cut replaces the previous contents of the Clipboard with the deleted values or text.

Keyboard Shortcut:  CTRL+X (or SHIFT+DEL)


  Copy

This option copies the contents of the currently highlighted cells or text in the Scrollsheet, spreadsheet, or Text/output Window or of the currently highlighted graph object to the Clipboard.

For Scrollsheets or spreadsheets (see also Clipboard Operations in the Spreadsheet), selecting this option will copy not only the contents in the highlighted block of cells in a Scrollsheet or spreadsheet, but also the row names and column names associated with the highlighted cells (use Copy Raw to copy only the highlighted Scrollsheet or spreadsheet block without the Row and Column Names).

This STATISTICA format (i.e., including row and column names) is maintained in the Clipboard only as long as you do not close the module in which the Copy operation was performed.  After closing that module the STATISTICA format is no longer available, thus, other modules will not be able to perform "smart" Paste operations (i.e., recognize column and row names).

For graphs and graph objects, selecting this option will copy the graph or object to the Clipboard in the following Clipboard formats:

STATISTICA Graph (OLE object), see STATISTICA Graph

Picture (Windows Metafile), see Metafile

Bitmap, see Bitmap

The Paste Special option will allow you to paste the graph or object in the desired format.  You can control the resolution (screen or printer resolution) of the copied metafile representation of the graph object via the Metafile Mode Screen/Printer Resolution options from the Page/Output Setup - Graphs dialog.

Copy replaces the previous contents of the Clipboard with the contents of the highlighted cells, text, or graph object.

Keyboard Shortcut:  CTRL+C or CTRL+INS


Clipboard Operations in the Spreadsheet

When you copy or move a block in the spreadsheet (e.g., via Drag-and-Drop), the values which are copied will depend on the display mode of the spreadsheet.

Numeric values or value labels:  If the spreadsheet is displaying numeric values (or value labels) when the block is copied to the Clipboard, then only those numeric values (or value labels) will be copied.

Text values:  If the spreadsheet is displaying text values when the block is copied to the Clipboard, then not only are the text values copied to the Clipboard, but also the corresponding numeric values and value labels (if any).  This may result in the assignment of text values to numeric values that did not previously have text value equivalents (see below).


Copy Raw

Copy only the data highlighted in the spreadsheet or Scrollsheet to the Clipboard.  Unlike the Copy option, this option does not copy the row names or column names associated with the highlighted data.  Copy Raw replaces the previous contents of the Clipboard with the highlighted contents of the spreadsheet or Scrollsheet.


  Paste

This option pastes (inserts) the current contents of the Clipboard to the STATISTICA Spreadsheet, Scrollsheet, graph, or Text/output Window.

When you use this operation in STATISTICA spreadsheet (see also Clipboard Operations in the Spreadsheet), Scrollsheets, or Text/output Windows, the current position of the cursor designates the starting place (the upper left-hand corner) for the pasting to begin.  Paste will then fill the area until everything in the Clipboard is pasted.  This option is not available (dimmed) if the Clipboard is empty (or contains an incompatible format, e.g., a picture when you are pasting into a Scrollsheet).

Keyboard Shortcut:  CTRL+V or SHIFT+INS

Pasting in Graphs

When you paste a graphic object in a STATISTICA graph using the Paste option, the object will be pasted in the upper-left corner of the graph.  You can then reposition or resize the object accordingly (see Resizing an Object); other options are available when you use the Paste Special facility.

Technical Note:  When an object is copied to the Clipboard from STATISTICA, these graphic representations (formats) of the object will be created in the Clipboard, in the following order of priority (hierarchy):  STATISTICA Graph, Metafile (i.e., picture), and then Bitmap.  For text objects, the order is STATISTICA Graph, raw text, and then Bitmap.  When an object (or text) is copied from another application (e.g., Excel), the order may not be the same as that listed above because both the selection of Clipboard formats produced by an application and the order of these formats is determined by the source application.  Therefore, when you use the Paste option, the format that is used may not be the best or desired format for the object.  In this situation, it is best to use the Paste Special option which will allow you to select the most applicable graphic format for the Clipboard object.  For example, if you want to paste a large piece of artwork (e.g., a 256 color bitmap) from another application, you would first copy that artwork (from within that application) to the Clipboard (the resulting hierarchy of formats available in the Clipboard would be determined by the source application; in this example, let's assume that the hierarchy is Bitmap and then Metafile).  Now, when you click on the Paste option in STATISTICA, the artwork would be pasted in as a bitmap (since this is the highest priority format in the Clipboard); however, the Metafile format may be more suitable for customizations which you are planning and more efficient (in terms of required storage space).  If the Paste Special option is used, then you could elect to paste the artwork in the STATISTICA graph as a Metafile.

OLE pasting.  See the Object Linking and Embedding Overview for information on the OLE facilities supported when pasting STATISTICA graphs into other applications.


Metafile Mode Screen/Printer Resolution

This option (available from the Page/Output Setup - Graphs dialog) controls the resolution and representation (colors) of graphics metafiles (Picture) created by STATISTICA when graphs (or graphic objects) are copied to the Clipboard or saved in metafile (Picture) format.

In order to produce the highest resolution Windows graphics metafile representation in the Clipboard (or metafiles), use the default Printer Resolution option.  When this option is selected and a graph or graph object is copied to the Clipboard, the metafile (picture) representation created in the Clipboard will depend on the current printer driver; typically the metafile representation created in Printer Resolution will be larger (in terms of the number of bytes) than a representation of the same graph created at Screen Resolution.

When Screen Resolution is selected and a graph or graph object is copied to the Clipboard, the metafile (picture) representation created in the Clipboard will depend on the current screen driver; the metafile representation will be smaller.

Note that graphs which have been copied to the Clipboard using the Printer Resolution option and then pasted into a word processing document (e.g., MS Word for Windows) will appear in color only if the current printer driver supports color (solid fill color patterns will appear in their original colors regardless of the printer driver).

Note also that graphs which have been copied to the Clipboard using the Screen Resolution option and then pasted into a word processing document (e.g., MS Word for Windows), will appear in color in that application.  If you double-click on the graph representation in the word processing document and edit the graph in STATISTICA, then the word processing application may override the original choice of screen resolution and instead update the graph representation using the higher printer resolution, resulting in a black-and-white representation in the word processing document.

Applications (limitations of the graphics metafile representations).  The main application of this option is to reduce the size (in bytes) of metafiles created from STATISTICA graphs (either in the Clipboard or when saving graphs as metafiles).  Note that the metafile graphics format, which is the default format for representing graphs in many procedures of the Windows system, is not well suited for handling very large or complex graphic objects (e.g., 2 megabytes or larger, such as complex graphs produced from large data sets in STATISTICA).  Also, some popular Windows applications cannot handle large graphics metafiles (e.g., MS Word 6.0).  Changing to the Screen Resolution may (in borderline cases) allow you to use the metafile in other applications.  Note that when the metafile is still too large (after switching to the Screen Resolution) to be used in another application, you can always use the bitmap representation (via Paste Special or disk files) which does not impose similar limitations (however, the quality of bitmap representations are often lower).


Clear

This option deletes text or the contents of the currently highlighted cells.  In the Scrollsheet or spreadsheet, the deleted values are replaced with missing data until new values are entered or pasted in.  Unlike the Cut option, Clear does not copy the text or contents of the cells to the Clipboard, therefore, it will not affect the contents of the Clipboard.

Keyboard Shortcut:  DEL


Paste Link

In the data spreadsheet:  Use this option to establish a DDE (Dynamic Data Exchange) link between another application (the source or server) and STATISTICA (the client) using the standard Windows Paste Link option (the current contents of the Clipboard must contain a linkable object).  With this option, you can paste cells copied from a Windows application to a block of cells in a STATISTICA Spreadsheet (from the highlighted cell down and to the right), permanently linking the data in the spreadsheet with the source of the data (server).  When you use this option, the DDE link is created and stored in the Long Name of the current variable (see Current Specs).  You can also edit a DDE link in the Links Manager dialog.  For more information on DDE links, see Creating Links (Dynamic Data Exchange).

See also, How to Establish a DDE Link and DDE with Excel 7.0:  Troubleshooting.

In Graphs:  Use this option in order to paste the Clipboard object into the current graph while maintaining a link to the source document (the current contents of the Clipboard must contain a linkable object).  When you use this option, STATISTICA will choose for you the best format [e.g., STATISTICA Graph object, Picture (i.e., Windows metafile), or Bitmap, depending upon the current Clipboard contents] in which to paste the object into the graph.  In order to select the type of format as well as other options, use the Paste Special option from the Edit pull-down menu.


How to Establish a DDE Link

Follow the steps outlined below to establish a DDE link using the Paste Link option.

Step 1.	Open the source file and copy to the Clipboard the block of data (or text) that you want to link with the client (STATISTICA) file.  Now, leaving this server file open, switch to the desired STATISTICA module.

Step 2.	In the STATISTICA spreadsheet, designate (highlight) the cell that will "anchor" the  data to be pasted into the spreadsheet (the data will be pasted down and to the right of this "anchor" cell).

Step 3.	Click on the Paste Link option to establish the link.  STATISTICA will automatically write the DDE path (see Creating Links (Dynamic Data Exchange)) and store it in the variable long name and in the Links Manager.

See also, DDE with Excel 7.0:  Troubleshooting.


DDE with Excel 7.0: Troubleshooting

The statement defining the link for Excel 5.0 is specified as application, file, and range, and as part of the range you can specify in which sheet the data are located.  However, the Excel 7.0, DDE server may produce a nonstandard statement (it includes a different specification of the sheet, and the link cannot be established; i.e., the Paste Link option in the Edit menu does not produce a working DDE link).

The first fix is to edit the statement (generated by Excel 7.0) that defines the link (in STATISTICA) by deleting out the nonstandard specification of the sheet.  For example, if the DDE server creates the following link,

@Excel|C:\EXCEL\[DATA.XLS]Sheet1!R1C1:R11C1

you will need to delete the reference to Sheet1 in order for the link to be established.  The link would then be

@Excel|C:\EXCEL\DATA.XLS!R1C1:R11C1

You can edit links in the Current Specs dialog (accessible by double-clicking on the name of the variable, to which the link is to be established), the All Specs dialog (accessible via the All Specs [image] spreadsheet toolbar button) or the Link Manager dialog (available by selecting Edit..Links from the Edit pull down menu.

The limitation here is that you can only create a link with the first sheet in any Excel 7.0 file.  If your data are in sheet one, this is not a problem.  If the data are not in sheet one, you would need to link the data to a new Excel 7.0 file and place them in sheet number one.


Creating Links (Dynamic Data Exchange)

You can establish a DDE (Dynamic Data Exchange) link between a "source" (or server) file (e.g., an Excel spreadsheet) and a STATISTICA data file (the "client" file), so that when changes are made to the data in the source file, the data will be automatically updated in the STATISTICA spreadsheet (client file).  A common application for dynamically linking two files would be in industrial settings, where the STATISTICA data file would be dynamically linked with a measurement device (e.g., in order to automatically update specific measurements hourly).  DDE links can be established using the Paste Link or Current Specs options (see below) and they can be managed in the Link Manager.  The DDE facility can also be used to run STATISTICA from macros created in other applications (see Creating Links using STATISTICA Command Language and the Run Module).

You can dynamically link a source file with a STATISTICA data file in three ways:

Paste Link

Variable Long Name

STATISTICA Command Language and Run Module

Note:  You can temporarily disable a link in the Link Manager in order to run an analysis using the linked data file.  If you do not disable the link and the data are updated while it is being analyzed in STATISTICA, then the resulting analysis may not be meaningful.

See also, DDE with Excel 7.0:  Troubleshooting.


Creating Links (Dynamic Data Exchange) - Paste LInk

This option (available from the Edit pull-down menu, see Paste Link) is the fastest and easiest way to establish a DDE link.

For step by step instructions, see How to Establish a DDE Link.

See also, DDE with Excel 7.0:  Troubleshooting.


Creating Links (Dynamic Data Exchange) - Variable Long Name

DDE links are stored and can be established (and edited) in the Long Name option of the Current Specs dialog.  To establish a DDE link here, type in the link statement (DDE path).  The four parts of the link statement (e.g., @Excel|c:\Excel\file.xls!r2c2:r4c4;c1;r1) are described below.

(1).	@Source Application| :  Specify first the source (or server) application (in the above example, the source application is Excel).  The Source Application must be separated from the rest of the link statement by a "|".  You also need to designate whether the DDE link is "hot" (place an "@" in front of the Source Application to indicate that the client file will be updated whenever the server file is changed) or "cold" (place a "^" in front of the Source Application to indicate that the client file will be updated only when the user requests it or changes it back to "hot").

(2).	Topic! :  The Topic designates the name (and path) of the file in the source application and must be separated from the rest of the link statement by a "!" (be sure to establish the full path name for the file).  In the above example, the Topic (c:\Excel\file.xls!) designates not only the name of the Excel file (file.xls) but also the drive and directory that the file is in (e.g., c:\Excel).  How you identify the source file depends on the source application that you are using (refer to your source application for information on how to designate the Topic; when you use the Paste Link option, this will automatically be designated for your specific application).

(3).	Item; :  Specify here the cell, range, named range, or some other name specific to your source application followed by a ";" (to separate it from the rest of the DDE path).  What you specify here is dependent upon the source application (refer to your source application for information on how to designate the Item; when you use the Paste Link option, this will automatically be designated for your specific application).  In the above example, a range in the Excel spreadsheet is defined (e.g., r2c2:r4c4; specifies the block "from row number 2, column number 2 to row number 4, column number 4").

(4).	Column;row :  This part of the DDE path is optional; by default (when no starting row or column is specified), STATISTICA places the first value in the range of linked data into the first cell (row) of the highlighted variable in the spreadsheet and continues placing values down and to the right of this "anchor" cell.  If you wish to "anchor" the linked data in a different cell (area) of the spreadsheet, you can designate the column number and row number (separated by a ";") to identify the position of that cell.  Alternatively, you can designate only the column (variable) number and STATISTICA will use the first cell (row) in that column as the "anchor."  Because this portion of the DDE path is optional, it is not automatically designated when you use the Paste Link option.

See also, DDE with Excel 7.0:  Troubleshooting.


Creating Links (Dynamic Data Exchange) - STATISTICA Command Language and Run Module

You can build STATISTICA Command Language (SCL) commands or entire SCL programs into macros created within and run from other Windows applications (e.g., Excel, MS Word, Ami Pro, Quattro Pro).

See Creating Links using STATISTICA Command Language and the Run Module for an example of an Excel macro that uses SCL commands and the STATISTICA Run Module in order to compute some descriptive statistics (a comment explaining each line is given after the example).


Creating Links using STATISTICA Command Language and the Run Module

This simple example illustrates how you can open a STATISTICA module, run a program and then return to the Windows application.  You can also include in the macro, commands to copy the STATISTICA text output and/or graphs to the Clipboard and then paste it back to the Windows application so that the output can be used in that application (e.g., as part of a report in MS Word).  A comment explaining each line is given after the example.

Excel macro DDE_EX.XLM:

channel=INITIATE("STA_RUN","SYSTEM")

=EXECUTE(channel, "DESC VARS=ALL")

=TERMINATE(channel)

=RETURN()

Line 1:	Opens a DDE channel to STATISTICA (specifically the Run Module).  Note, STATISTICA needs to be on the path, or STA_RUN needs to be running in order to open a DDE channel.

Line 2:	Tells STATISTICA to execute the SCL command "DESC VARS=ALL" (i.e., compute descriptive statistics on all variables).

Line 3:	Tells Excel to close the DDE conversation.

Line 4:	Returns to the source application.


Define Colors for Scrollsheet/Spreadsheet

Customizes the colors of the current Scrollsheets and spreadsheets in the Customize Colors dialog.  You can view the color changes in the sample Scrollsheet/spreadsheet below the selections in this dialog before finalizing your choices.  Each of the options available in this dialog will open the standard Color dialog, where you can select colors from a standard color palette or customize a color (via the Define Custom Colors button).

Spreadsheets and Scrollsheets are saved along with their ( custom-defined, if any) colors.

Keyboard Shortcut:  SHIFT+F9

Customize Colors dialog:

Screen Element

Lines

Defaults

Color dialog

Example


Define Colors for Scrollsheet/Spreadsheet - Screen Element

Select the Scrollsheet/spreadsheet element that you would like to customize (see below for a list of these elements).  Each Scrollsheet/spreadsheet element is customized separately, and for each element you can customize only the text foreground (Text button), only the background (Backgr. button), or both.  Only solid colors are available for Text; if a patterned color is selected, then STATISTICA will use the solid color closest to the selected patterned color.

•	Info Box (i.e., the upper left corner of the sheet)

•	Titles

•	Toolbar

•	Column Names

•	Row Names

•	Data Area

•	Highlight


Define Colors for Scrollsheet/Spreadsheet - Lines

This option customizes the colors of the lines in the Scrollsheet/spreadsheet.

Main button:  Changes the color of the lines separating the Row Names and Column Names in the Scrollsheet/spreadsheet.

Grid Vert button:  Changes the color of the vertical lines separating the data values in the Scrollsheet/spreadsheet.

Grid Horz button:  Changes the color of the horizontal lines separating the data values in the Scrollsheet/spreadsheet.


Define Colors for Scrollsheet/Spreadsheet - Defaults

You can choose to make your customized colors the default colors if you click on the Save as Default option.  To restore STATISTICA's default color selections, click on the Use System Defaults button.


Define Colors for Scrollsheet/Spreadsheet - Color Dialog

Accessed within the Customize Colors dialog whenever you select an element of the spreadsheet/Scrollsheet to customize.

Basic Color Palette:  Click on a color to select it for the Scrollsheet/spreadsheet element in this color palette.

Custom Colors:  Click the Define Custom Colors button to bring up the Color Refiner Box from which you can create a customized color and add it to the Custom Colors Palette.  You can create a color by adjusting its Hue, saturation (Sat) and luminosity (Lum) manually, by specifying its Red, Green and Blue values manually, or by dragging the cursor to the desired color in the Color Refiner Box and adjusting the Luminosity Bar.  Click on the Add to Custom Colors button to add the new color to the selected square in the Custom Colors Palette.


Customizing Color

In this example, we will customize the color of the Scrollsheet titles.

Step 1:	Select the Colors option from the View pull-down menu.

Step 2:	Let's change the color of the Scrollsheet titles by selecting the screen element Titles.  Click on the Text button and select the color that you want the text in the titles to be (say, blue).  Now let's choose a contrasting color for the title background by clicking on the Backgr. button selecting a color in the Color dialog.  You can repeat Step 2 for every screen element that you want to change the color for.

Step 3:	Click on the OK button to close the Customize Colors dialog and change the colors in the current Scrollsheet.


Define Font Dialog Box

Selecting the Font option from the View pull-down menu will bring up the Font dialog.  You can edit the type of font, the font style, and the font size in the current spreadsheet, Scrollsheet, or other STATISTICA facilities.  As you make your selections, you can view a sample text in the Sample window of this dialog.

Spreadsheets and Scrollsheets are saved along with their specific font and color settings.

Keyboard Shortcut:  CTRL+F9

Font dialog:

Font:  Specify the name of the font that you want to use here.  Click on the font type to select it.

Font Style:  The available font styles depend on the type of font that you select.  First select the font type, then click on the font style that you want to select.

Font Size:  The available font sizes depend on the type of font that you select.  First select the font type, then click on the font size that you want to select.

Save as Default:  Click on this option to save the font settings as the default settings for the spreadsheet/Scrollsheet (different defaults can be selected for spreadsheets and Scrollsheets).

Apply:  Use this option when you are entering a font size that may not be supported by the font type.  You can view the results of the font size in the view box before using it in STATISTICA.


File Open/Save As Dialog

This general dialog will allow you to open or save many types of files available in STATISTICA (e.g., spreadsheet, Scrollsheet, graph, STATISTICA BASIC, Megafile Manager, or text/output files).  No matter which type of file you are opening or saving, the following options are available in this dialog.

File Name

Files of Type

Directories

Drives

Workbook Files

The following option is available only for the Text/output files.

Save as Text

Opening Files:  STATISTICA Files can be opened in one of several ways:

1.	Select the appropriate Open option from the File pull-down menu or click on the [image] toolbar button to bring up the File Open/Save As dialog (described below).

2.	Double-click on the file name in the Windows File Manager in order to open the file in the STATISTICA File Server application.

3.	Drag a file from the Windows File Manager and drop it on a STATISTICA module icon in order to open that module with the desired file.

4.	Set the desired files to Auto Open in the Data File Header, Notes, and Workbook Info dialog.  When the associated data file is opened, these files will then open automatically.


File Open/Save As Dialog - File Name

Select from the list of files or enter the file name here.  The main types of files used by STATISTICA have the following extensions (see STATISTICA File Name Extensions for a complete list of file name extensions used by STATISTICA):

•	Spreadsheet--STATISTICA system data files (includes data, variable names, long labels, formulas, and links, case names, text values variable specifications, file notes, and other information) file name extension:  *.sta.

•	Scrollsheet--STATISTICA output windows (includes the formatted output table) file name extension:  *.scr.

•	Graph (includes graphs, graph customizations, embedded graphic objects, links, and graph data) file name extension:  *.stg.

•	Text (such as text files created or used in the Text/output Window and saving Graphic Text Editor data as text files) file name extension:  *.txt.

•	Rich Text Format (such as RTF files created or used in the Text/output Window) file name extension:  *.rtf.

•	STATISTICA BASIC file name extension:  *.stb.

•	Megafile Manager file name extension:  *.mfm.


File Open/Save As Dialog - List Files of Type

File Open/Save As Dialog - Files of Type

Choose to list in the File Name section all the files of a specific type (i.e., spreadsheet/Scrollsheet/Graph files, backup files, Megafile Manager files, or all files).  In order to open a non-STATISTICA format data file (e.g., Excel, Lotus, Quattro, dBASE, Paradox, ASCII, and others) use the Quick Import option (or the Import Data option in the Data Management module).


File Open/Save As Dialog - Directories

Specify the Directory in which the file is located.


File Open/Save As Dialog - Drives

Specify the Drive in which the file is located.


File Open/Save As Dialog - Workbook Files

Click on this combo box in order to select a file from a list of supplementary files (e.g., graph files, *.ini files, import/export files, Scrollsheet files, etc.) associated with the current data file (a log of all supplementary files associated with the current data file is maintained in the STATISTICA Workbook).  For easy access to a desired file, this list is sorted by file type (e.g., *.scr file) that you would like to open/save.  Files which are not relevant for the current open/save operation are dimmed (they are included for reference only).


File Open/Save As Dialog - Save as Text

This option is only applicable to the Text/output Window (including STATISTICA BASIC program files, Command Language (SCL) program files, SEPATH command files, and all other applications of the Text/Output Window).  Select this option in order to save the contents of the Text/output Window in the standard ASCII text format (file name extension *.txt).  If this option is not selected, STATISTICA will save the file in the RTF format to preserve all special formatting (font, spacing, graphs, etc.).  The default (RTF) format is normally preferable, but the resulting file cannot be edited with programs which do not support the RTF format.  If you save it as text, the file can be processed by virtually any program, however, all formatting information and graphs will not be preserved.


STATISTICA File Name Extensions

File name extensions are used in STATISTICA to designate the type of information that is stored in the file.  Whenever you open or save a file in STATISTICA (see File Open/Save As dialog), you can either accept the default file name extension or use a different one.  STATISTICA file name extensions and a brief description of the type of file are given below.

STATISTICA Files:

•  .STA 	Spreadsheets (Workbook system data files including lists of related supplementary files)

•  .SCR 	Scrollsheets (scrollable tables with results)

•  .RTF 	STATISTICA report (output) files containing formatted (Rich Text Format) text and graphs

•  .TXT 	All other non-RTF text supplementary files saved in ASCII format (e.g., multiple case selection conditions, data recoding specifications, data verification conditions, etc.).

•  .STG 	Graphics files (including all data presented in the graphs)

•  .SUG	User-defined graph specification files (added to the menu Graphs)

•  .ATB	Auto Task Buttons configuration files

•  .AXD 	Graph axis (single or multiple) definition files

•  .SEL 	Case selection conditions files

•  .STM 	Macro files (see Auto Task Buttons)

•  .MFM 	Megafile Manager files

•  .STB 	STATISTICA BASIC program files

•  .MML 	MML program files

•  .SCL 	STATISTICA Command Language (SCL) files

•  .CMD 	SEPATH program files

•  .HLP 	STATISTICA Electronic Manual files

•  .INI 	STATISTICA configuration files (including the global configuration file and specific files such as for quality control charts, contour/surface definitions, etc.)

•  .PAL 	Color palette selection files

Files from Other Applications:

•  .CSS 	CSS (and STATISTICA/DOS) data files

•  .CSG 	CSS (and STATISTICA/DOS) graph files

•  .WMF 	Windows graphic metafile files

•  .BMP 	Windows device-independent bitmap graphics files

•  .XLS 	Excel worksheet files

•  .W* 	Lotus, Symphony, and QuattroPro worksheet files

•  .DBF 	dBASE files

•  .DB 	Paradox files

•  .POR 	SPSS portable files

•  .TXT or .FRE  ASCII (free format text) files

•  .FIX 	ASCII (fixed format text) files


Window Manager Dialog

Selecting this option will allow you to manage the number of (unlocked, see below) Scrollsheets or graphs that can be displayed on the screen at one time.  In STATISTICA, Scrollsheets and graphs are automatically managed in separate "queues" on a "first in-first out" basis.  For example, if the Scrollsheet queue depth is set to 3, then when the fourth Scrollsheet is created, the first one will close automatically.  There is no one recommended depth of the queue; the number of entries should be adjusted according to the type of analysis, size of the screen and individual preferences.  You can change the depth of the queue in the Window Manager dialog; you can also control the number of windows (Scrollsheets or graphs) in the screen either by locking them or closing them manually.

Window Manager dialog:

Queue:  Specify here the maximum number of unlocked windows to keep on screen.  You can specify a number between 0 and 20; however if you specify 0, the size of the queue will be unlimited (then you will need to close windows manually to avoid cluttering the screen and exhausting the memory resources of the computer).

Discardable windows:  This is a list of all the unlocked (discardable) windows on screen.  When you highlight a window in this list and click on the Lock button (see below), you will lock the window, removing it from the queue.

Locked windows:  This is a list of all the locked windows on screen.  You can add a window to this list by highlighting its name in the Discardable Window list (see above) and then click on the Lock button (see below); in order to remove a locked window, close it manually.

Lock button:  Individual windows may be removed from the queue by locking them via the Lock button in this dialog.  To lock a window, first highlight its name in the Discardable Window list (see above) and then click on the Lock button.  Locked windows will remain on screen as long as you do not close them manually or exit the module or STATISTICA.


  Printing

Output from Analyses

Printing Graphs

Printing Data

Printing from the Text/output Window


  Printing Scrollsheet Output from Analyses

In STATISTICA, you can print (or save to a file) the Scrollsheet output from analyses either automatically (i.e., the contents of each displayed Scrollsheet will be directed to the printer and/or the Text/output Window) or manually (i.e., the user selects which individual Scrollsheets or parts of Scrollsheets will be printed and/or sent to the Text/output Window).

Before you can print the results of analyses, you will first need to specify the output destination (i.e., File, Printer, and/or Window) in the Page/Output Setup dialog (select the Page/Output Setup option from the File pull-down menu, the Print option from the Options pull-down menu or double-click on the Output field on the Status Bar).  While you are in this dialog, select the amount of supplementary information to be printed along with the Scrollsheets (i.e., the report format:  Brief, Short, Medium, or Long).  Each of these four report formats are described in Page/Output Setup.

Automatic Printing:  If this mode is selected (select Automatically Print All Scrollsheets option in the Page/Output Setup dialog), then in addition to the supplementary information (the amount depends on the current report format setting in the Page/Output Setup dialog), all output from analyses will automatically be printed either to the printer or to the output file (as well as to the Text/output Window if it is selected in the Page/Output Setup dialog).  This mode of printing is useful when you want to maintain a complete log of all output displayed during the course of the analysis.

Manual Printing:  The only difference between manual (de-select the Automatically Print All Scrollsheets option in Page/Output Setup dialog) and automatic printing is that when you are printing manually, only the supplemental information is printed automatically (and sent automatically to the Text/output Window if it is selected in the Page/Output Setup dialog), whereas the Scrollsheets (or their parts) are printed only if you request it by selecting the Print option from the File pull-down menu (or click the Print Scrollsheet Toolbar button).

Printing Mode:  In order to speed up processing, STATISTICA internally stores the output from an analysis in a buffer.  You can control how this stored output will be printed when you select the printing mode in the Page/Output Setup dialog.

  Automatically Eject Each Filled Page:  When this option is selected, STATISTICA will store the results of an analysis only until there is enough to fill one page.  When the page is full, it will be sent to the printer or output file (whichever destination you selected in the Page/Output Setup dialog).  STATISTICA will continue storing the results and sending the output to the printer or output file one page at a time.  You can use the Print/Eject Current Pages option from the File pull-down menu at any point in the analysis to immediately send whatever output has accumulated to the pre-selected destination.

  Automatically Eject Each Filled Page:  When the Automatically Eject Each Filled Page option is de-selected, STATISTICA will store all of the results of an analysis and will not print or send it to an output file until you either close the active module or select the Print/Eject Current Pages option from the File pull-down menu.  (The Print/Eject Current Pages option can be used at any point in the analysis to immediately send whatever output has accumulated to the printer or output file.)


Spreadsheet File Menu

These options are available from the File pull-down menu.

New Data

Import Data

Quick

ODBC

Open Data

Open Other

New Data

Data File

Graph File

Scrollsheet

Text/Output

STATISTICA BASIC

Command Language (SCL)

Save

Save As

Quick Export

Convert to Scrollsheet

Print/Eject Current Pages

Print

Print Files

Page/Output Setup

Printer Setup

Exit


Open STATISTICA BASIC File

Selecting this option will bring up the Open STATISTICA BASIC File dialog from which you can select a previously-saved STATISTICA BASIC program file (a file with the extension *.stb) to open.


Open Command Language (SCL) File

Selecting this option will bring up the Open SCL File dialog from which you can select a previously-saved Command Language (SCL) program file (a file with the extension *.scl) to open.


New Data

This option (from the File pull-down menu) will enable you to open a new file in which you can enter data.  When you select this option, the New Data:  Specify File Name dialog will open allowing you to select a file name under which to save the new Spreadsheet.  After selecting the file name, a 10 variables by 10 cases spreadsheet will be created.  You can now enter data into the spreadsheet, add/delete cases and variables, edit the variable names and specifications (see Spreadsheet Edit Specs) or case names (see Spreadsheet Edit Case Names), as well as perform other spreadsheet operations (see Spreadsheet Edit Menu).

You can also Create a New Data File in the Data Management module according to your detailed file specifications [specify the number of variables and cases, automatically create specific sequential variable numbers, define the defaults (e.g., formats), etc.], or create a new file using all specifications of an existing file (including the numeric-text value assignments and value labels).


  Open Data

Selecting this option will bring up the Open Data File dialog from which you can select a STATISTICA data file (file with the extension *.sta) to open.  STATISTICA data files contain data values and also labels and formats (see:  Current Specs), headers and notes (see:  File Header) and other information.  In order to open a non-STATISTICA format data file (e.g., Excel, Lotus, Quattro, dBASE, Paradox, ASCII, and others) use the Import Data option.

Opening multiple data files.  Only one data file can be open in a module at one time; however, you can open multiple files (e.g., and copy and paste between them) in different modules or using the STATISTICA File Server application.  Multiple File Server applications can run simultaneously, each with a different data file open.

Keyboard Shortcut:  CTRL+O


  Open Graph

Selecting this option will bring up the Open Graph File dialog from which you can select a STATISTICA graph file (file with the extension *.stg) to open.  The STATISTICA graph file contains not only the graph (in the STATISTICA Graph format) but also all customizations (e.g., drawings, embedded objects, etc.) and the data values represented in the graph.  The data can be edited or manipulated after the graph file is opened.

STATISTICA graphs are OLE objects and therefore you cannot simultaneously open more than one instance of the same object by the system (either in the same or different modules).  For that reason, if you attempt to open a graph file that is currently open in any module, then you will be asked whether or not you want to revert to the saved graph.  If you revert to the saved graph, the graph which is already opened will be closed and any changes made to that graph will be lost.  If you choose not to revert to the saved graph, STATISTICA will automatically switch to the module in which the graph was originally opened.

Keyboard Shortcut:  SHIFT+F3


  Open Other

This sub-menu is common to all menus (spreadsheet, Scrollsheet, graph, Text/output Window), allowing access to all types of STATISTICA files.  These options allow you to open a New Data file, Data File, Graph File, Scrollsheet File, Text/output File, STATISTICA BASIC Program or Command Language (SCL) program file.  When you select the New Data option, the New Data:  Specify File Name dialog will open from which you can select a file name under which the new spreadsheet will be saved.  After selecting the file name, a 10 variables by 10 cases spreadsheet will be created.

Selecting any of the other options listed above will open the respective File Open/Save As dialog in which you can select the file name to open.

Note that the hot keys are consistent across all menus which allows you to use them in creating macros, etc.

For more information on the options available in the Open Other sub-menu, see:

New Data

Data File

Graph File

Scrollsheet

Text/Output

STATISTICA BASIC

Command Language (SCL)

Keyboard Shortcut.  ctrl+o


  Open Scrollsheet

Selecting this option will bring up the Open Scrollsheet dialog from which you can select a Scrollsheet file (file with the extension *.scr) to open.  Scrollsheet files contain the output data and all formatting and customization information (e.g., highlights, custom colors, etc.).

Keyboard Shortcut:  CTRL+F11


  Spreadsheet Save

Save a spreadsheet data file with this option.  If the file has not been saved before, then the Save File As dialog will open in which you can specify the file name, and disk location for it to be saved.  Once the file name and location have been specified, whenever you select Save, the spreadsheet will automatically be saved, overwriting the previous copy of the file.  If you want to change the name or location of the file, select the Save As option.

Keyboard Shortcut:  CTRL+S


Save As

This option will open the Save File As dialog.  By default, the current file name and disk location will be displayed in this dialog.

Spreadsheet window:  When you select this option, you can save the data file under a new file name or the default name, or specify a different disk location for the spreadsheet data file.

Graph Data Editor window:  When you select this option, you will be able to save the numeric data from the graph into a tab-delimited text (ASCII) file.

Workbook files:  Click on this combo box in order to select a file name from a list of supplementary files (e.g., graph files, *.ini files, import/export files, Scrollsheet files, etc.) associated with the current data file (a log of all supplementary files associated with the current data file is maintained in the STATISTICA Workbook).  For easy access to a desired file name, this list is sorted by the type of file (e.g., *.scr file) that you would like to save.  Files which are not relevant for the current save operation are dimmed (they are included for reference only).

Keyboard Shortcut:  F12


  Convert to Scrollsheet

Create a Scrollsheet from the current spreadsheet (data file) with this option.  When you choose this option, the Select Subset for Scrollsheet dialog will open in which you can specify the range of the data file (by default, either all of the data or the currently highlighted block of data) to include in the Scrollsheet.  Variable names and case names will become the Scrollsheet Column and Row Names (respectively), the file name, File Header and the range (subset) of data selected will become the Scrollsheet titles.

Keyboard Shortcut:  F11

Select Subset for Scrollsheet dialog:

First Case:  Specify the first case number (inclusive) in the range of cases to be included in the Scrollsheet.

Last Case:  Specify the last case number (inclusive) in the range of cases to be included in the Scrollsheet.

First Variable:  Specify the first variable name or number (inclusive) in the range of variables to be included in the Scrollsheet.  Double-click on the variable edit field to select a variable from a list of current variables in the spreadsheet.

Last Variable:  Specify the last variable name or number (inclusive) in the range of variables to be included in the Scrollsheet.  Double-click on the variable edit field to select a variable from a list of current variables in the spreadsheet.


Print/eject Current Page

Print/Eject Current Pages

The option does not apply to the Text/output Window, but only to output from an analysis that is stored in STATISTICA's internal buffer.  When you run an analysis and the Output is set to Printer or File, STATISTICA will internally store the output either until the output fills a page (if the Automatically Eject Each Filled Page option is selected) or until the analysis is complete (if the Automatically Eject Each Filled Page option is de-selected) before sending it to the printer or output file.  The Print/Eject Current Pages option will override this internal storage and immediately print (or send to an output file) whatever output has accumulated (technically, a "form feed" will be issued).


  Print Data

Prints the active spreadsheet either to an output file (for later printing), to the printer (for immediate printing), or to the Text/output Window as designated in the Page/Output Setup dialog.  When you select the Print option, the Print Data Dialog will open.

Shortcut:  Click on the Print  [image]  Toolbar button, to bypass the Print Data dialog (i.e., the previously selected settings or the default settings will be used) and print the spreadsheet.  Note that if a block is selected in the spreadsheet, then that block will be printed, otherwise, the entire spreadsheet is printed.

Keyboard Shortcut:  CTRL+P

Print Data dialog:

Print

Variables

All Data

Print Data Value Options

Print/Eject Pages after this Printout

Setup


  Print Data - Print

You can choose the parts of the spreadsheet to print by clicking on each option to select or de-select it.  (Note that whatever parts of the spreadsheet that you manually choose to print here will override your selection of output style in the Page/Output Setup dialog if the two choices conflict.  For example, if you choose the Brief output style in the Page/Output Setup dialog and then select all of the printing options described below, then the selections in the Print Data dialog will be used when printing the spreadsheet.)

Data Values:  Click this option to include the spreadsheet contents (data values) in the output.

Variable Specs:  Clicking this option will include a table of all of the variable specifications (name, missing data code, format and variable long name as designated in the Current Specs dialog) in the output.

Text Value Assignment:  Clicking this option will include a separate table of text value assignments (text values, numeric equivalents, and value labels as designated in the Text Values Manager dialog) in the output.

File Info/Notes:  Click on this option to include the file header and file info/notes (see:  File Header) in the output.


  Print Data - Variables

Select the spreadsheet variables to be included in the output (by default:  All, or the variables in the current block if one is selected in the spreadsheet).  Clicking this button will open the Select Vars for Printing dialog from which you can make the variable selection.


  Print Data - All Data

Click on this button to automatically select all variables and cases in the data file.  This button provides a shortcut to quickly change the selection of block data in this dialog (in effect when a block is highlighted in the spreadsheet) to all variables and cases.


  Print Data - Print Data Value Options

Cases:  You can define a subset of cases to be included in the output by specifying the range of cases that you want printed (From what case, To what case, inclusive).

Case Names:  Click on this option to include the case names in the output.

Text Values:  Click on this option to print the text values instead of numeric values of variables in the spreadsheet.

Column Width:  Choose the spreadsheet column width to be either the formatted width (By Format) or the minimum 8 character width (Min 8 Char), the latter will allow you to print full variable names (regardless of the current value formats).


  Print Data - Print/Eject Pages after this Printout

When selected, this option will cause the requested printout to automatically be sent to the printer or output file when you click OK in this dialog or when you press the Print button on the toolbar (any other text previously left in the internal buffer will also be printed).  Thus, each requested printout (table) will start on a new page.  If this option is de-selected, then output will be stored in the internal buffer, and sent to the printer depending on the current setting of the check box Automatically Eject Each Filled Page (either whenever there is enough to fill one page or all at once later, e.g., when you exit the module or when you empty the buffer by using the option Print/Eject Current Pages).  Note that this option will only apply locally (temporarily) to the current STATISTICA module and the current session, whereas selecting the Print/Eject Pages after Each Printout option in the Page/Output Setup dialog will apply globally (permanently).


  Print Data - Setup

Click on this button to open the Text Output Printer Setup dialog in which you can select the quality (i.e., resolution) of the printout and the number of copies.  The selected printer is also displayed in this dialog and can be changed by clicking on the Setup button to open the Print Setup dialog in which you can make the printer selection, change the page orientation or paper size and source.


Text Output Printer Setup

This dialog allows you to select the print quality (i.e., resolution) and number of copies for the text output.  The selected printer is also displayed in this dialog and can be changed by clicking on the Setup button to open the Print Setup dialog in which you can make the printer selection, change the page orientation or paper size and source.


Page/Output Setup

Page/Output Setup - Text/Scrollsheets/Spreadsheets

Before printing the text, spreadsheet, or Scrollsheet, select the destination (printer, output file, and/or Text/output Window) for the output as well as other options from the Page/Output Setup dialog.  This dialog can be accessed either by double-clicking the Output field of the window Status Bar, from the Page/Output Setup option of the File pull-down menu, or from the Print option of the Options pull-down menu.  All of the selections that you make here will become default selections and will be applied globally whenever you open a STATISTICA module.

The following options are available if you select Text/Scrollsheets/Spreadsheets as the source of output (see also, Graphs).

Keyboard Shortcut:  SHIFT+F4

Page/Output Setup dialog:

Output

Supplementary Info.

Output File(Text)

Page #

Lines

Font

Margins/Setup

Output Header

Date and Time

Center Titles

Auto-report

Automatically Print/Eject Pages after Each Printout

Automatically Eject Each Filled Page

Print Tabs in Text Output Tables


Page/Output Setup - Graphs

Before printing the graph, select the destination (printer and/or Text/output Window) for the output as well as other options from the Page/Output Setup dialog.  This dialog can be accessed either by double-clicking the Output field of the window Status Bar, from the Page/Output Setup option of the File pull-down menu, or from the Print option of the Options pull-down menu.  All of the selections that you make here will become default selections and will be applied globally whenever you open a STATISTICA module.

The following options are available if you select Graphs as the source of output (see also, Text/Scrollsheets/Spreadsheets).

Keyboard Shortcut:  SHIFT+F4

Page/Output Setup dialog:

Output

Metafile Mode

Use Dithered Color

Minimum Line Thickness (Printer Pixel)

Graph Size in the Text/output Window

Advanced

Margins/Setup

Auto-report


Page/Output Setup - Metafile Mode

These options control the resolution and representation (colors) of all graphics metafiles (Picture) created by STATISTICA (e.g., metafiles in the Clipboard, graphs saved as metafiles, or graphs are sent to the Text/output Window in metafile format.

Default Printer Resolution.  In order to produce the highest resolution Windows graphics metafile representation in the Text/output Window, use the Printer Resolution option.  When this option is selected and a graph printed to the Text/output Window, the metafile (picture) representation created in the Text/output Window will depend on the current printer driver.

Screen Resolution.  When the Screen Resolution option is selected and a graph is sent to the Text/output Window, the metafile (picture) representation created in the Text/output Window will depend on the current screen driver.

See also Metafile Mode Screen/Printer Resolution.


Page/Output Setup - Use Dithered Color

Use Dithered Color to Fill Background:  When you select this option, STATISTICA will use a dithered color to fill the graph background and the background of custom text, legend, embedded objects, etc. (see Background).  If de-selected, then the graph will be printed without the specified colored background (i.e., the color of the paper will be the background color).  By default, this option is de-selected (i.e., the background color is not printed) to allow for the optimal appearance of the graph when printed (a dithered background improves readibility of graphs on-screen but it often reduces readability of hard copies unless a very high resolution or a color printer is used).

Use Dithered Color for Solid Lines:  Select this option if you want the colors of solid lines in the graph to appear dithered when printed, otherwise, the lines will appear solid in the printout (this option may be useful when the lines are thick, otherwise, the lines may appear "broken").

See also Print Options


Page/Output Setup - Minimum Line Thickness (Printouts and Metafiles)

Specify here the minimum line thickness for printouts and metafiles (in printer or other device pixels).  This option is particularily relevant when using a high resolution output device (e.g., 1200 DPI where single-pixel lines are too thin) and also when you set the default size of a graph in the Text/output Window to a small size (e.g., 2x3, see the option Graph Size in Text/output Window).

Unless you increase the default setting of this option (2 printer pixels), the width of all lines printed by STATISTICA is determined either by the individual settings of the line width for specific graph components (by default .5 point, see Points, Lines, Area Patterns Dialog) or by 2 (device) pixels, whichever is greater.  This option allows you to determine the minimum printed line thickness; e.g., if you set it to 3, then all printed lines will be at least 3 printer pixels wide even if they are set to a smaller setting in some Points, Lines, Area Patterns dialogs.

If the setting of the Graph Size in Text/output Window option is set to a size smaller than Full, then the line thickness will be proportionally thinner.  You may need to adjust the minimum line thickness in order to compensate.

See also Print Options.


Page/Output Setup - Graph Size in Text/Output Window

You can select from several pre-defined graph sizes (in inches or centimeters) or specify a custom graph size which will determine the size of the graph printed to the Text/output Window.

Graphic object size and the minimum line setting.  Note that when you reduce the STATISTICA graph in the Text/output Window (for example to 2x3), then very thin lines may become unreadable.  Therefore, you may want to adjust the minimum line thickness setting in the Page/Output Setup dialog to a respectively larger setting.


Page/Output Setup - Advanced Options

Selecting this option will open the Advanced Options dialog with additional, less often used options controlling creation of graphic output including graphic OLE objects.


Page/Output Setup - Margins/Setup

Click on this button to open the Graph Margins dialog in which you can position the graph on the printed page by adjusting the margins (specify the Left, Top, Right, and Bottom margin widths) according to a specific measure (Percent, Centimeter, or Inch).


Page/Output Setup - Output (Text/Scrollsheets/Spreadsheets)

Select the output destination here.

Off:  If this option is selected, then no text output will be printed or sent to an output file.

File (text):  Choose to send the contents of a Scrollsheet or spreadsheet to a user selected output (text) file.  When you select this option and then click OK, the Specify Output File dialog will open, allowing you to name the output file.  Alternatively, after selecting this option, you can click on the Output File (Text) button to specify a file under which the output will be saved.

Printer:  When selected, this option sends the contents of the spreadsheet or Scrollsheet to the printer.

Window:  When you select this option, then independent of the output destination selected above (i.e., File or Printer), the output requested from Scrollsheets or spreadsheets will be sent to the Text/output Window.  Note:  The most recently saved Text/output Window will be opened when you select this option.  To save the output in this window, use the Save option from the File pull-down menu or click CTRL+S.


Page/Output Setup - Output (Graphs)

Select the output destination here.

Off:  If this option is selected, then no graph will be printed or sent to an output file.

Printer:  When selected, this option sends the contents of the graph to the printer.

Window:  When you select this option, then independent of the output destination selected above (i.e., Printer), the output requested from graphs will be sent to the Text/output Window.

NOTE:  In order to save a graph to a file, use the Save option or the Print to File option in the Print Options dialog (accessible by clicking on the Print Graph option) from the graphics window File pull-down menu.


Page/Output Setup - Supplementary Information

Select the amount of supplementary information to be printed here.

Brief:  Select this most "economical" output style if you want to print only the contents of the selected spreadsheets or Scrollsheets (i.e., no page headers, job headers, or any information about the variables or conditions specified for the analyses will be output).

Short:  This output style will include the page header (name of the module, date/time, page number), current data file name, information on Case Selection Conditions and Case Weights (if any were specified), the Output Header (see below), the spreadsheet or Scrollsheet contents, a list of (short) names of all variables selected for each analysis, and missing data values.

Medium:  This report format is more space-consuming, including (in addition to the Scrollsheet or spreadsheet) all information from the Short format and, additionally, the long variable labels (e.g., formulas), reserving one line of output for each variable.

Long:  The Long report style provides the most comprehensive information on each variable selected for analysis.  In addition to all information included in the Medium report format, it also includes a complete list for each selected variable of all its "double" values, that is, values that have both numeric and text components, and/or values that have value labels.

(Note that while printing spreadsheets, whatever parts of the spreadsheet data file that you manually choose to print in the Print Data dialog will override your selection of output style here if the two choices conflict.  For example, if you choose the Brief output style here and then select all of the printing options in the Print Data dialog, the selections in the Print Data dialog will be used when printing the spreadsheet.)


Page/Output Setup - Output File (Text)

This button is available when you select File as the output destination and dimmed otherwise.  When you click on this button, the Specify Output File dialog will open.  Here, you will be able to specify the filename (file name extension *.txt) under which the text (ASCII) output from Scrollsheets or spreadsheets will be saved.  These output files can later be opened in the Text/output Window in order to review, print, or edit the output.  Note, however, that unlike the report files generated by directing output to the Text/output Window, these disk ASCII text files contain no graphs and no formatting information (font, margins, page layout, etc.).


Page/Output Setup - Page #

Specify the page number of the first page of text output here.  The following pages will be numbered sequentially, based on the page number here (useful when you continue an existing report).  Note that pages cannot be numbered sequentially if you run more than one module of STATISTICA simultaneoulsy (i.e., not in the single application mode, see STATISTICA Module Switcher) and those modules interchangeably produce output.


Page/Output Setup - Lines

Choose one of several line thicknesses (or no lines) for the lines in the output tables.  If you do not want any borders around or lines in the output tables, select the blank box in this option.  Now, whenever you print a Scrollsheet or spreadsheet, the border lines will be suppressed and the printing will go much faster.


Page/Output Setup - Output Header

Specify the output header here.  This header will be included as the title on every printed page.


Page/Output Setup - Date and Time

Click this option if you want to include the date and time as part of the page header (see the Short output setting).


Page/Output Setup - Center Titles

Click this option if you want to center (instead of left-justify) the Output Header.


Page/Output Setup - Font

Clicking this button will open the Font dialog from which you can select the font and font size of the printed output.


Page/Output Setup - Margins

Click on this button in order to open the Text Output Margins dialog in which you can specify the page margins for the printed text from Scrollsheets, Spreadsheets, or the Text/output Window.  You can specify the margins for printed graphs in either the Print Preview or Page Setup dialogs.


Page/Output Setup - Automatically Print/Eject Pages after Each Printout

When selected, this option will cause the requested printout to automatically be sent to the printer or output file when you click OK in the Print Data or Print Scrollsheet dialogs or when you press the Print button on the toolbar (any other text previously left in the internal buffer will also be printed).  Thus, each requested printout (table) will start on a new page.  If this option is de-selected, then output will be stored in the internal buffer, and sent to the printer depending on the current setting of the check box Automatically Eject Each Filled Page (either whenever there is enough to fill one page or all at once later, e.g., when you exit the module or when you empty the buffer by using the option Print/Eject Current Pages).


Page/Output Setup - Automatically Eject Each Filled Page

When this option is selected, STATISTICA will store the results of an analysis in its internal buffer only until there is enough to fill one page.  When the page is full, it will be sent to the printer or output file (whichever destination you selected in the Output option above).  STATISTICA will continue storing the results and sending the output to the printer or output file one page at a time.  You can use the Print/Eject Current Pages option from the File pull-down menu at any point in the analysis to immediately send whatever output has accumulated to the printer or output file.

When this option is de-selected, printing will take less time overall:  STATISTICA will store all of the results of an analysis and will not print or send it to an output file until you either close the active module or select the Print/Eject Current Pages option from the File pull-down menu.  Use the Print/Eject Current Pages option at any point in the analysis to immediately send whatever output has accumulated to the printer or output file.


Page/Output Setup - Auto-Report (Text/Scrollsheets/Spreadsheets)

Auto-Retrieve the Text/Output Window Contents:  Check this option in order to automatically open the most recently saved text (file name extension *.txt) or Rich Text Format (file name extension *.rtf) file in the new Text/output Window (e.g., in order to append the current output to the results of a previous analysis).  When this option is un-checked, then a blank Text/output Window will be opened from the Page/Output Setup dialog.

Auto-Exit from Scrollsheets and Graphs:  When Scrollsheets or graphs are created in batch as the result of an analysis (e.g., Categorized Scatterplots option in the Descriptive Statistics dialog), you can select this option to suppress the display of the Continue button when the queue is full.  Now when you select the Automatically Print All Scrollsheets and/or Automatically Print All Graphs options, the graphs or Scrollsheets will be printed in batch, without interruption.

Automatically Print All Scrollsheets (Auto-Report):  If this mode of printing is selected, then in addition to the supplementary information (the amount depends on the current report format setting selected in the Supplementary Information option), all output from analyses will automatically be printed either to the printer or to the output file (and/or Text/output Window).  This mode of printing is useful when you want to maintain a complete log of all output displayed during the course of the analysis.

If you choose to de-select the Auto-report (Automatically Print All Scrollsheets) option, then Scrollsheets (or their parts) are printed only upon request by selecting the Print option from the File pull-down menu (or click the Print Scrollsheet Toolbar button).


Page/Output Setup - Auto-Report (Graphs)

Auto-Retrieve the Text/Output Window Contents:  Check this option in order to automatically open the most recently saved text (file name extension *.txt) or Rich Text Format (file name extension *.rtf) file in the new Text/output Window (e.g., in order to append the current output to the results of a previous analysis).  When this option is un-checked, then a blank Text/output Window will be opened from the Page/Output Setup dialog.

Auto-Exit from Scrollsheets and Graphs: When Scrollsheets or graphs are created in batch as the result of an analysis (e.g., Categorized Scatterplots option in the Descriptive Statistics dialog), you can select this option to suppress the display of the Continue button when the queue is full.  Now when you select the Automatically Print All Scrollsheets and/or Automatically Print All Graphs options, the graphs or Scrollsheets will be printed in batch, without interruption.

Automatically Print All Graphs:  When you select this option, STATISTICA will automatically send to the printer and/or Text/output Window (if Window was previously selected), or save to an output file (see NOTE, below), graphs as they are created.  If this option is de-selected, then you will need to use the Print Graph option or the graphics window Print Graph Toolbar button to print only selected graphs.  See also the option Auto-Exit from Scrollsheets and Graphs.

Note.  Graphic printer output is always directed to the printer unless you select the Print to File option in the Print Options dialog (accessible by clicking on the Print Graph option from the graphics window File pull-down menu).


Page/Output Setup - Print Tabs in Text Output Tables

When this option is selected, STATISTICA will print tab-delimited text in the output tables of the Text/output Window.

When this option is de-selected, STATISTICA will do one of two things depending on the setting of the Lines option in this dialog:

(1)	If the Lines combo box is set to Off (i.e., line width = 0), then STATISTICA will print space-delimited text in the output tables of the Text/output Window.

(2)	If the Lines combo box is set to any line width other than 0 (i.e., any setting other than Off), then STATISTICA will use "+" and "-" characters to create the table in the Text/output Window.

Note that when tabs are used in text output tables, it allows you to use non-proportional fonts (e.g., Times Roman) when pasting the table into a word processor program (e.g., MS Word).  Also you can paste the table into a spreadsheet such that each value will be placed in a different cell.

If spaces or "+" and "-" characters are used to separate the entries in the table, then when you paste the table into a word processor, you will need to use a proportional font (e.g., Courier) in order for the entries in the table to line up.


Advanced Options

This dialog will open whenever you click on the Advanced button in the Page/Output Setup - Graphs dialog.

Advanced Options dialog:

Metafiles in the Text/output Window:  These options control the resolution and representation (colors) of all graphics metafiles (Picture) created by STATISTICA which are sent to the Text/output Window.

STATISTICA Printer Resolution.  When this option is selected and a graph is sent to the Text/output Window, the metafile (Picture) representation created in the Text/output Window will depend on the print options in effect for the current STATISTICA session.

Default Printer Resolution.  When this option is selected and a graph printed to the Text/output Window, the metafile (Picture) representation created in the Text/output Window will depend on the current (default) settings of the printer driver. (It will not be affected by the driver options changed in the current STATISTICA session).

Screen Resolution.  When the Screen Resolution option is selected and a graph is sent to the Text/output Window, the metafile (Picture) representation created in the Text/output Window will depend on the current screen driver.

See also Metafile Mode Screen/Printer Resolution.

Bitmap Mode (Clipboard, Save):  These options control the resolution and representation (colors) of all graphics bitmaps (Bitmap) created by STATISTICA by either copying to the Clipboard or saving as a bitmap.

Default Printer Resolution.  When this option is selected, the bitmap representation will depend on the current printer driver.

Screen Resolution.  When the Screen Resolution option is selected, the bitmap representation will depend on the current screen driver.

OLE Server Mode:  These options control the resolution and representations (colors) of all graphics created by STATISTICA which are then embedded in another application using OLE.

Metafiles/bitmaps:  The same three options are available in each combo box: default, printer resolution, and screen resolution.  The default mode uses the resolution requested by the client.  When printer resolution is selected, the representation will depend on the current printer driver.  When screen resolution is selected, the representation will depend on the current screen driver.

Enable Error Checking in Metafiles:  Checking this box will enable the Metafile Error Checking option.  This option ensures that metafiles will not exceed the Windows Metafile Format capacity; however, it is slower than the default mode.


Text Output Margins

In this dialog, you can position the desired text (e.g., from spreadsheets, Scrollsheets, or the Text/output Window) on the printed page by adjusting the margins (specify the Left, Top, Right, and Bottom margin widths) according to a specific measure (Percent, Centimeter, or Inch).  Note that these margin settings are independent of the margin settings for the graphics output (which can be adjusted in the Print Preview or Graph Margins dialogs).

To adjust the paper size and orientation (portrait or landscape) use the Printer Setup option in the pull-down menu File.


Printer Setup

Selecting this option from the File pull-down menu, will open the Print Setup dialog in which you can choose a printer, the print orientation, and paper size and source for printing graphs and text output.

Note that you can maintain separate print selections for graphs and text output (i.e., output from Scrollsheets or spreadsheets).  For example, you can select a Landscape page orientation for printing text output in the Print Setup dialog accessible from the spreadsheet or Scrollsheet window File pull-down menu, and a Portrait page orientation for printing graphs in the Print Setup dialog accessible from the graph window File pull-down menu.

Print Setup dialog:

Printer:  Select either the default printer or a specific printer from a list of printers installed in your system.

Orientation:  Select either Landscape or Portrait page orientation for printing the graph or text output.

Paper:  You can select the paper size and source in these combo boxes.


Exit

Select this option to end your STATISTICA session.  If you have made any changes to spreadsheets, Scrollsheets, text, or graphs and Exit before saving them, STATISTICA will prompt you to save the modified objects.

Keyboard Shortcut:  ALT+F4


Spreadsheet Edit Menu

Edit Cell	Paste Link

Variables	Find

Cases	Replace

Workbook	Clear

Undo	Transpose

Cut	Fill Block

Copy	Block Stats/Columns

Copy Raw	Block Stats/Rows

Paste	Screen Catcher

Links


 Undo

Select this option in order to reverse (undo) the last specific command or action in the spreadsheet (such as editing, moving or copying blocks, random fill, recoding or ranking variables, etc).  The STATISTICA spreadsheet supports multi-level undo (with 16 buffers); therefore, you can undo multiple actions by selecting this option consecutively (up to 16 times).

Keyboard Shortcut:  CTRL+Z (or ALT+Bksp)


Block Stats/Columns

Click on this option from the spreadsheet or Scrollsheet Edit pull-down menu (or flying menu) in order to calculate either the means, medians, standard deviations, valid n's, sums, the minimum value, the maximum value, the 25'th percentile, or the 75th percentile of the values of the variables (columns) in the highlighted block, or choose to calculate All of the above statistics.  The calculated values will be added after the last row of the spreadsheet or Scrollsheet in new rows (STATISTICA will create case names with the names of the the statistics and case numbers in the selected block).

You can also create several types of statistical graphs for the data in the highlighted block (see Block Stats Graphs); raw data from the block can be plotted using the Custom Graphs facilities.

Note:  If your data file is very large (e.g., over 10 megabytes), you may want to set the Ask before inserting rows and columns option in the STATISTICA Defaults:  General dialog so that STATISTICA will ask for confirmation before expanding the data file.


Block Stats/Rows

Click on this option from the spreadsheet or Scrollsheet Edit pull-down menu (or flying menu) in order to calculate either the means, medians, standard deviations, valid n's, sums, the minimum value, the maximum value, the 25'th percentile, or the 75th percentile of the values of the cases (rows) in the highlighted block, or choose to calculate All of the above statistics.  The calculated values will be added after the last column of the spreadsheet or Scrollsheet in new columns (labeled with the selected statistics).

You can also create several types of statistical graphs for the data in the highlighted block (see Block Stats Graphs); raw data from the block can be plotted using the Custom Graphs facilities.

Note:  If your data file is very large (e.g., over 10 megabytes), you may want to set the Ask before inserting rows and columns option in the STATISTICA Defaults:  General dialog so that STATISTICA will ask for confirmation before expanding the data file.


  Block Stats Graphs

Block Stats Graphs are similar to Custom Graphs in that they convert values from a selected part (block) of the Scrollsheet or spreadsheet into graphs.  However, unlike Custom Graphs which allow you to visualize any combination of raw values from a Scrollsheet or spreadsheet, Block Stats Graphs produce statistical summary graphs; these graphs allow you to compare distributions of values in columns (or rows) of the selected block by plotting representations of all columns (or rows) in a single graph.  Also, these graphs offer an effective means of exploring (and efficiently summarizing) numeric output from analyses displayed in Scrollsheets (e.g., histograms of Monte Carlo output scores in the SEPATH module, or a box plot of aggregated means from a multivariate multiple classification table in the ANOVA/MANOVA module.

The following statistical graphs are available from the spreadsheet and Scrollsheet Block Stats/Columns and Block Stats/Rows flying menu options.

  Histograms

  Box Plot/Means

  Box Plot/Medians

  Normal Prob. Plots

Block Stats Graphs can be called from the flying menu, Graphs pull-down menu, or the Graphs Gallery dialog.  If the Block Stats Graphs are called from the Graphs Gallery, and a Scrollsheet is currently selected, then the highlighted block from the Scrollsheet will be processed.  For all other cases (e.g., when a graph or Text/output Window is current), then the spreadsheet will be brought to the front of the window and the highlighted block will be processed.

When a Block Stats Graph is created from the spreadsheet, then whenever the spreadsheet data are updated, the Block Stats Graph will automatically be updated (see STATISTICA Defaults: General).


  Block Stats Graphs - Histograms

When you select the Block Stats/Columns option, a 2D histogram with a fitted normal curve will be created for each column of the block, and plotted in one graph (a multiple histogram) to allow for comparisons between the frequency distributions of values in block columns.  In order to create a univariate histogram, select a block containing only one column.

Similarly, if you select the Block Stats/Rows option, then a 2D histogram will be created for each row of the block, and plotted in one graph (a multiple histogram) to allow for comparisons between the frequency distributions of values in block rows.  In order to create a univariate histogram, select a block containing only one row.

Notes:  If the Block Stats Graphs are called from the Graphs Gallery, and a Scrollsheet is current, then the highlighted block from the Scrollsheet will be processed.  For all other cases (e.g., when a graph or Text/output Window is current), then the spreadsheet will be brought to the front of the window and the highlighted block will be processed.

When a Block Stats Graph is created from the spreadsheet, then whenever the spreadsheet data are updated, the Block Stats Graph will automatically be updated (see STATISTICA Defaults: General).

For more information on 2D histograms, see Quick Stats Graphs - Histogram of ... or Stats Graphs - 2D Histograms.


Block Stats Graphs - Box Plots/Means

  Block Stats Graphs - Box Plot/Means

When you select the Block Stats/Columns option, a box plot of means (and standard errors and standard deviations) will be created for the columns of the block.  Each box will represent data from one column.

Similarly, if you select the Block Stats/Rows option, then a box plot of means (and standard errors and standard deviations) will be created for the rows of the block.  Each box will represent data from one row.

Notes:  If the Block Stats Graphs are called from the Graphs Gallery, and a Scrollsheet is current, then the highlighted block from the Scrollsheet will be processed.  For all other cases (e.g., when a graph or Text/output Window is current), then the spreadsheet will be brought to the front of the window and the highlighted block will be processed.

When a Block Stats Graph is created from the spreadsheet, then whenever the spreadsheet data are updated, the Block Stats Graph will automatically be updated (see STATISTICA Defaults: General).

For more information on box plots, see Quick Stats Graphs - Box-Whisker of ... or Stats Graphs -2D Box Plots.


Block Stats Graphs - Box Plots/Medians

  Block Stats Graphs - Box Plot/Medians

When you select the Block Stats/Columns option, a box plot of medians (and min/max values and 25th and 75th percentiles) will be created for the columns of the block.  Each box will represent data from one column.

Similarly, if you select the Block Stats/Rows option, then a box plot of medians (and min/max values and 25th and 75th percentiles) will be created for the rows of the block.  Each box will represent data from one row.

Notes:  If the Block Stats Graphs are called from the Graphs Gallery, and a Scrollsheet is current, then the highlighted block from the Scrollsheet will be processed.  For all other cases (e.g., when a graph or Text/output Window is current), then the spreadsheet will be brought to the front of the window and the highlighted block will be processed.

When a Block Stats Graph is created from the spreadsheet, then whenever the spreadsheet data are updated, the Block Stats Graph will automatically be updated (see STATISTICA Defaults: General).

For more information on box plots, see Quick Stats Graphs - Box-Whisker of ... or Stats Graphs -2D Box Plots.


  Block Stats Graphs - Normal Prob. Plots

When you select the Block Stats/Columns option, a normal probability plot will be created for the values in each column of the block, and plotted in one graph (a multiple normal probability plot) to allow for comparisons between the normality of the distribution of values in the block columns.  In order to create a univariate normal probability plot, select a block containing only one column.

Similarly, if you select the Block Stats/Rows option, then a normal probability plot will be created for the values in each row of the block, and plotted in one graph (a multiple normal probability plot) to allow for comparisons between the normality of the distribution of values in the block rows.  In order to create a univariate normal probability plot, select a block containing only one row.

Note that if the data in columns (or rows) that are compared in the graph have different ranges, then the comparison will be biased as the range will affect the slope of the fit.  To avoid this bias, bring the data to a common range (e.g., via standardization or other transformations) before creating this graph.

Notes:  If the Block Stats Graphs are called from the Graphs Gallery, and a Scrollsheet is current, then the highlighted block from the Scrollsheet will be processed.  For all other cases (e.g., when a graph or Text/output Window is current), then the spreadsheet will be brought to the front of the window and the highlighted block will be processed.

When a Block Stats Graph is created from the spreadsheet, then whenever the spreadsheet data are updated, the Block Stats Graph will automatically be updated (see STATISTICA Defaults: General).

For more information on normal probability plots, see Quick Stats Graphs - Probability Plot of ... or Stats Graphs - Probability Plots.


Spreadsheet Edit Menu - Variables

Add	Text Values

Move	Date Values

Copy	Recalculate

Delete	Shift (Lag)

Current Specs	Rank

All Specs	Recode


Spreadsheet Edit Menu - Cases

Add

Move

Copy

Delete

Names


Spreadsheet Edit Menu - Transpose

Block

Data File


Spreadsheet Edit Menu - Fill Block

Fill Block Down

Fill Block Right


Spreadsheet Edit Cell

Edit Cell allows you to edit the currently highlighted cell in the spreadsheet (or Graph Data Editor).  You can start editing either by selecting this option, pressing F2, typing over the highlighted cell, or by typing over the entry.  While editing, this option is dimmed.

Keyboard Shortcut:  F2


Spreadsheet Edit (Current) Specs

Specifications of the currently highlighted variable (i.e., variable name and format, missing data value, and label, formula or link) can be edited in the Current Specs dialog.  This dialog is accessible from the spreadsheet  Edit - Variables pull-down menu or the Vars toolbar button option Current Specs; it can also be accessed by double-clicking on the variable name in the spreadsheet.

Current Specs dialog:

Name

MD Code

Display Format

Long Name-Label

Long Name-Formula with

Long Name-Link

  Buttons

All Specs

Text Values

Values/Stats

Graphs


Spreadsheet Edit (Current) Specs - Name

Edit the variable name here.  Variable names can be up to 8 characters long, cannot start with the characters: period (.), minus (-), plus (+), or a digit (i.e., 0-9) and cannot contain spaces, unprintable characters, or the keyboard characters used in data transformations and STATISTICA programming languages (" # & ' ( ) + * , - . / ; : < = > [ ] ^ \ { } ~).  If any of these characters appear in a variable name, then STATISTICA will replace them with an underscore (except in the case when a period [.], minus [-], or plus [+] character is used as the first character, then this name will be considered invalid).  The program does not differentiate between upper and lowercase letters entered in variable names (all letters are converted to uppercase).


Spreadsheet Edit (Current) Specs - MD Code

Enter a value for the missing data code (value of the variable that indicates data points for which no data are available) or accept the default code of -9999.  Missing data values are displayed as blanks in the cells of the spreadsheet (the value can be viewed in the spreadsheet toolbar Show Field when a blank cell is highlighted) and are ignored in all data analyses.

See also:

Pairwise MD Deletion

Casewise MD Deletion


Spreadsheet Edit (Current) Specs - Format

Column Width:  Edit the width (from 1 to 30) of the column here.  The default format width is 8 characters.  The display format affects only the way in which values are displayed in the spreadsheet and other data listings, and not the internal storage precision of the number.

Decimals:  Specify the number of decimal places (less than the column width) to be displayed in the spreadsheet and other data listings (applicable to Number, Scientific, Currency, and Percentage categories, see below).  The default format is 3 decimal places.  The display format affects only the way in which values are displayed in the spreadsheet and other data listings, and not the internal storage precision of the number.  For variables containing single Date values (see Date Operations and Dates), specifying a Number format will display the dates as Julian values (e.g., as 24858 instead of 1/21/1968).  For variables containing Time values, specifying a Number format will display the time as a decimal value (e.g., as 24858.9375 instead of 1/21/1968 10:30 PM, or as .78125 instead of 18:45)

Category/Representation:  For each Category that you choose, you can also choose a Representation by which to display the values of the current variable.

Number:  Select this format if the values of the variable are numeric or numeric with text equivalents.  When you select this category, you can specify the number of decimal places to be displayed in the spreadsheet via the Decimals option (see above).

Representation:  These values are represented in decimal format with or without commas (e.g., 1000 or 1,000).  Negative values of the variable can be represented either with a negative sign (e.g., -1000) or with parentheses enclosing the number (e.g., (1000)).  There are four representations available under this category:

1000.00	-1000.00

1,000.00	-1,000.00

1000.00	(1000.00)

1,000.00	(1,000.00)

Note that a European representation (e.g., 1,20) is supported by STATISTICA if you select this style in the Windows Control Panel.  If this style is not selected in the Control Panel and you enter a comma in the decimal place, STATISTICA will treat the value as a text value.

Date:  Select this variable format in order for variables to be interpreted as dates (e.g., variables containing Julian date values imported or pasted from Excel).  Note that in order to be displayed as a valid date, all values in the variable must be correct dates or explicitly defined text values (see also, Date Operations and Dates).

Representation:  Select the desired date representation from the list of date formats (for more information, see Dates).  In the View Variable Specs window, the various Date representations are represented by the following keywords (which can also be entered directly in the Format column of this window):

3/6/87	DATE1

03/06/1987	DATE2

6-Mar-87	DATE3

6-Mar	DATE4

Mar-1987	DATE5

06/03/87	DATE6

Windows Format	DATE7

Note that if the Windows Format is selected, STATISTICA will format the date display using the specifications given in the International dialog (Windows 3.1) or the Regional Settings dialog (Windows 95) of the Control Panel.

Time:  This category will display the values of the variables in one of several time formats. Time values of variables are stored in the data as (optional) decimal values representing the fraction of the day since midnight; for example, 6:00AM is stored as 0.25.  Time values stored in this manner can be used in subsequent analyses and transformed using arithmetic operations; at the same time, they can be displayed as times in reports or graphs (e.g., used to label scale values).  STATISTICA will format the display of time values according to the current settings in the International Time Format option of the Windows Control Panel.

Representation:  Time can be represented in one of several formats.  You can choose from a date-time combination [with either 24-hour time or 12-hour (AM/PM) time format], or just time [either a 24-hour time or 12-hour (AM/PM) time format] in hours and minutes or hours, minutes, and seconds.  You could also select the Windows Format which will use the current settings in the International dialog (Windows 3.1) or the Regional Settings dialog (Windows 95) of the Windows Control Panel.  In the View Variable Specs window, the various Time representations are represented by the following keywords (which can also be entered directly in the Format column of this window):

3/6/87 10:30 PM	TIME1

87/3/6 22:30	TIME2

10:30 PM	TIME3

22:30	TIME4

10:30:25 PM	TIME5

22:30:25	TIME6

Windows Format	TIME7

Scientific:  This category allows you to display the values of the variable in scientific notation.  When you select this category, you can specify the number of decimal places to be displayed in the spreadsheet via the Decimals option (see above).

Representation:  The first representation (standard scientific notation) will display all numbers in the column in scientific notation according to the following rules:

For example, 1.2345E-02 or -3.2100E+08.

The second representation will apply the scientific format only to those (small) values of the variable which would be displayed as 0 (zero) in Number format [i.e., they are from the interval (-1,1) and the significant digits start after the position specified by the Decimals edit field].  For example, if Decimals = 4, and the value is 0.0000123, then in Number format, the value would be displayed as 0.0000, whereas, in the second Scientific representation, the number would be displayed as 1.230E-5 (displaying 4 digits before E).

Currency:  Select this category in order to display the values of the variable in a currency format.  When you select this category, you can specify the number of decimal places to be displayed in the spreadsheet via the Decimals option (see above).

Representation:  Currency values are displayed with a currency symbol before or after the number (depending on the configuration specified on the user's computer; e.g., $, DM, etc., see the Windows Control Panel).  You can choose to represent negative values of the variable either with a negative sign (e.g., $-1,000) or with parentheses enclosing the number (e.g., ($1,000)).

Percentage:  Selecting this format will display the values of the variable as percentages.  When you select this category, you can specify the number of decimal places to be displayed in the spreadsheet via the Decimals option (see above).  The percentage is based on what fraction of 1 the value of the variable represents.  For example, the value 0.23 will be translated to 23% while 23.4 will be translated to 2340%.

Representation:  Percentages are represented with a % character at the end of the number.


Spreadsheet Edit (Current) Specs - Long Name Label

For each variable, you can assign a long variable name up to 128 characters long.  The label can contain notes, including any printable characters.

The long names can also contain Formulas or Link specifications.


Spreadsheet Edit (Current) Specs - Long Name Formula

Spreadsheet Edit (Current) Specs - Long Name Formula with

When you enter a long variable name that starts with an equal sign, STATISTICA will assume that it is a formula and will verify it for formal correctness.  If the formula is formally correct, you will then be given the choice to recalculate the variable now or later (via the Recalculate dialog).  You can use variable formulas to verify data, transform a variable, recode a variable or create values of the variable based on logical conditions (e.g., =(v0<=100)*1 + (v0>100)*2 will assign a value of 1 to cases number 1 through 100 and 2 to cases above 100).  Refer to variables by their names (e.g., Test1, Income) or numbers (e.g., v1, v2, v3, ...); v0 is the case number.  A comment may be added to a formula following a semicolon.  For a detailed formula syntax summary see Summary of STATISTICA Formula Syntax.

Examples:

=(v1+v2+v3)/3 ; Computes the average of the first 3 variables

=(v0<=10)*1+(v0>10)*2 ; Recodes cases 1-10 as 1, rest as 2

=vnormal(rnd(1),50,3) ; Generates random numbers from a Normal distribution (μ=50,σ=3)

Note that you can click on the [image] button in this dialog in order to open the Function Wizard dialog.  From this dialog, you can choose the desired part of the formula (e.g., an operator, distribution, math function).  When you click OK in this dialog, the selection will be pasted in the current cursor position in the edit field.


Spreadsheet Edit (Current) Specs - Long Name Link

In addition to notes and formulas, the long variable names can also contain DDE link specifications.  Following the MS Windows DDE (Dynamic Data Exchange) conventions, you can link a variable (or block of data) in STATISTICA to a variable (or block) in a spreadsheet in another program, allowing you to automatically update the spreadsheet whenever the "source" (server) file changes.  The most common way to establish a DDE link between another application and STATISTICA is the standard Windows Paste Link and Links options in the Edit pull-down menu.  However, a link statement can also be entered directly into the Long Name option of this dialog (see Creating Links (Dynamic Data Exchange) for detailed steps on establishing a DDE link using this option, syntax conventions, and Links Manager for information on managing DDE links).  An example of a link statement (to link a block of data in STATISTICA with a block of data in Excel) is:  @Excel|c:\file.xls!r2c2:r4c4.  This example statement establishes a dynamic link with the block "from row number 2, column number 2 to row number 4, column number 4" in the Microsoft Excel Spreadsheet file file.xls (be sure to establish the full path for the file when specifying the file name in the link statement, i.e., c:\Excel\file.xls).


Spreadsheet Edit (Current) Specs - All Specs

Clicking on this button will close this dialog (saving any changes) and bring up the View Variable Specs window in which you can view the specifications for each of the variables in the data file.


Spreadsheet Edit (Current) Specs - Text Values

Pressing this button will close this dialog (saving any changes) and bring up the Text Values Manager dialog.


Spreadsheet Edit (Current) Specs - Values/Stats

Click on this button to open the Variable Values Window in which you can view the values of the variable as well as descriptive statistics (n, mean, and standard deviation) for that variable.


Spreadsheet Edit (Current) Specs - Graphs

Pressing this button will close this dialog (saving any changes) and bring up a menu of Quick Stats Graphs Options.


Spreadsheet Edit (Current) Specs - <<, >> Buttons

Spreadsheet Edit (Current) Specs - [image], [image] Buttons

Click on these buttons in order to bring up the Current Specs dialog for the previous ( [image]) variable or for the next ( [image]) variable.  Note that when you click on either of these buttons, STATISTICA will first implement the changes made for the current variable before going to the dialog for the next or previous variable.  If you do not want to implement any changes before going to the next or previous dialog, you will need to Cancel the current dialog and then bring up the Current Specs dialog for the desired variable.


Summary of STATISTICA Spreadsheet Formula Syntax

Specified formulas must start with an equal sign.  When you enter a label that starts with an equal sign, STATISTICA will assume that it is a formula and will verify it for formal correctness, see Examples.

Syntax Summary:

•	Refer to variables either by their numbers (e.g., = v1 - v2) or name (e.g., = Retail - Cost)

•	v0 is the case number (e.g., the formula = v0 + 1 will assign to the current variable the value of the case number plus 1).

•	Semicolon starts a comment:  e.g., = v1 + v2 ; this is a comment

•	Operators:

Arithmetic:  +, -, *, /, ** or ^ (exponentiation), ( )

Relational:  <, >, >=, <=, <>

Logical:  (see Examples)

AND (equivalent to &)

OR (equivalent to |)

NOT (equivalent to ~)

Note: A common error is caused by omitting parenthesis needed to adjust for the precedence of operators; for example, the expression x > 0 and x < 1 is incorrect and needs parentheses: (x > 0) and (x < 1) because relational operators (here, > and <) have a lower precedence than the conjuction (and).

•	Constants:  Pi = 3.14..., Euler (e) = 2.71...

•	abs(x) - absolute value of x

•	arcsin(x) - arc sine of x

•	cos(x) - cosine of x

•	exp(x) - e to the power of x

•	log(x) - natural logarithm of x

•	log2(x) - binary logarithm of x

•	log10(x) - common logarithm of x

•	max(x,y) - returns the greater of x and y

•	min(x,y) - returns the lesser of x and y

•	rnd(x) - random number in the range of 0 to x

•	sign(x) - sign of x:  if x>0 then +1, if x<0 then -1, if x=0 remains 0

•	sin(x) - sine of x

•	sinh(x) - hyperbolic sine of x

•	sqrt(x) - square root of x

•	tan(x) - tangent of x

•	trunc(x) - truncate x to an integer "towards zero"

•	Distribution functions and their integrals

If the value of any variable used in the formula is missing (in the current case), then the expression evaluates to missing data (for the current case).

Logical operators can be used to define conditional transformation expressions (see Examples).

For more extensive data recoding, use the Recode Values of Variable dialog accessible from the spreadsheet.

For more extensive data transformations, use STATISTICA BASIC (a programming language available from the Analysis pull-down menu of every module which supports a variety of special facilities for statistical data management and transformations).

Examples


Examples of STATISTICA Spreadsheet Formulas

The following are examples of STATISTICA spreadsheet formulas.

1.	This formula will compute the average of three variables.

=(Measur1+Measur2+Measur3)/3

2.	This formula will recode cases 1-10 as 1, and the rest as 2.  Note that a logical expression evaluates to 1 if it is true and to 0 if it is false.

=(v0<=10)*1+(v0>10)*2

3.	This formula returns the value of 5 if v1=1 and v2=5, and 0 otherwise.  Note that a logical expression evaluates to 1 if it is true and to 0 if it is false.

=((v1=1) AND (v2=5))*5

4.	This formula returns the value of 5 if either or both conditions hold, and 0 otherwise.  Note that a logical expression evaluates to 1 if it is true and to 0 if it is false.

=(((v1=1)OR(v2=5))<>0)*5

5.	This formula returns probability density values of the Student's t distribution based on the values of v4 and 15 degrees of freedom.

=student(v4,15)

6.	This formula assigns consecutive integers to the consecutive sets of 10 cases (i.e., cases number 1 through 10 will be assigned 0, cases number 11-20 will be assigned 1, and so on.

=trunc((v0-1)/10)


Spreadsheet Formulas - Distribution Functions, their Integrals and Inverse Distribution Functions

STATISTICA provides a predefined broad selection of distribution functions, their integrals and inverse distribution functions that can be used in spreadsheet formulas like all other functions.

Below is a listing of all available distributions (parameters are given in parenthesis).

Density or	Inverse

Probability	Distribution	Distribution

Distribution	Function	Function	Function

Beta Distribution	beta(x,ν,ω)	ibeta(x,ν,ω)	vbeta(x,ν,ω)

Binomial Distribution	binom(x,p,n)	ibinom(x,p,n)

Cauchy Distribution	cauchy(x,η,θ)	icauchy(x,η,θ)	vcauchy(x,η,θ)

Chi-square Distribution	chi2(x,ν)	ichi2(x,ν)	vchi2(x,ν)

Exponential Distribution	expon(x,λ)	iexpon(x,λ)	vexpon(x,λ)

Extreme Distribution	extreme(x,a,b)	iextreme(x,a,b)	vextreme(x,a,b)

F Distribution	F(x,ν,ω)	iF(x,ν,ω)	vF(x,ν,ω)

Gamma Distribution	gamma(x,c)	igamma(x,c)	vgamma(x,c)

Geometric Distribution	geom(x,p)	igeom(x,p)

Laplace Distribution	laplace(x,a,b)	ilaplace(x,a,b)	vlaplace(x,a,b)

Logistic Distribution	logis(x,a,b)	ilogis(x,a,b)	vlogis(x,a,b)

Lognormal Distribution	lognorm(x,μ,σ)	ilognorm(x,μ,σ)	vlognorm(x,μ,σ)

Normal Distribution	normal(x,μ,σ)	inormal(x,μ,σ)	vnormal(x,μ,σ)

Pareto Distribution	pareto(x,c)	ipareto(x,c)	vpareto(x,c)

Poisson Distribution	poisson(x,λ)	ipoisson(x,λ)

Rayleigh Distribution	rayleigh(x,b)	irayleigh(x,b)	vrayleigh(x,b)

Student's t Distribution 	student(x,df)	istudent(x,df)	vstudent(x,df)

Weibull Distribution	weibull(x,b,c,θ)	iweibull(x,b,c,θ)	vweibull(x,b,c,θ)


  Spreadsheet Edit Text Values

The Text Values Manager is used to edit text values (and their equivalent numeric representations) of the variable that is currently highlighted in the spreadsheet.  In this dialog, the correspondence between the numeric data, text data, and value labels can be managed.  Values can be entered, sorted, modified, copied from variable to variable, and more.  (See also Data Values (Numeric, Text) and Labels.)

Shortcuts:  Double-click on a variable (column) name, then click on the Text Values button in the resulting dialog; Click on the right-mouse-button and select the Text Values option from the "flying menu."

Example

Text Values Manager dialog:

Creating a "Text-Numeric" Assignment

Editing a "Text-Numeric" Assignment

Text Value

Numeric Value

Value Label

Fill Down

Clear All

Sort by ...

Get From Case Names

Get From Variable


  Spreadsheet Edit Text Values - Creating a "Text-Numeric" Assignment

Enter the respective two values (text, numeric) into the first two fields of a row, e.g., MALE and 1 (the Value Label is optional).  See also Data Values (Numeric, Text) and Labels.


  Spreadsheet Edit Text Values - Editing a "Text-Numeric" Assignment

Press TAB to move to the next field (or row); the contents of the last row are automatically copied (they can be edited or typed over).  To change a field, type over it; to edit a field, press F2 or double-click on it.  Use the Insert key to insert a new line after the current line and the Delete key to delete the current line.  See also Data Values (Numeric, Text) and Labels.


Spreadsheet Edit Text Values - Text Value

  Spreadsheet Edit Text Values - Text Values

You can manage text values here.  Text values can be up to 8 characters long and may contain any keyboard character.  The program does differentiate between upper and lowercase letters entered in text values (e.g., "Smith" is not equivalent to "SMITH").

You can switch between viewing text values or their numeric equivalents in the Spreadsheet by pressing the [image] button on the spreadsheet toolbar (see also, Text Values Manager and Data Values (Numeric, Text) and Labels).


  Spreadsheet Edit Text Values - Numeric Value

You can manage numeric values that are assigned to text values here.  With this unique double-notation of variables (where each value can have simultaneously both numeric and text representations), if a variable containing text values is selected for an analysis that requires numeric data, then its numeric values are automatically used.

You can switch between viewing text values or their numeric equivalents in the Spreadsheet by pressing the [image] button on the spreadsheet toolbar (see also, Text Values Manager and Data Values (Numeric, Text) and Labels).


  Spreadsheet Edit Text Values - Value Label

Each value of a variable can have a label assigned to it.  You can enter and manage that label here. Value labels can also be displayed and edited directly in the spreadsheet (see below).  Value labels can be up to 40 characters long and contain notes including any printable characters.  Value labels are automatically used in the output of all analyses which involve individual values (e.g., frequencies, crosstabulations, breakdowns, etc.).

To display value labels in the spreadsheet, press the [image] button while holding down the CTRL key or select the Text Values - Value Labels option in the spreadsheet View pull-down menu.  For more information, see Text Values Manager and Data Values (Numeric, Text) and Labels).


  Spreadsheet Edit Text Values - Fill Down

This button automatically assigns consecutive integers (based on the numeric value associated with the first text value in the table) to text values.  For example, if you wanted numeric equivalents from 5 to 7 to be associated with three text values, first assign a value of 5 in the number field associated with the first text value, then press <Fill Down> to automatically assign the next two text entries numeric values of 6 and 7, respectively.


  Spreadsheet Edit Text Values - Clear All

This button will clear all the entries in all fields in the Text Value Manager dialog.


  Spreadsheet Edit Text Values - Sort by ...

Sort by Text-incr:  Sorts the Text, Numeric, and Value Labels in the Text Value Manager dialog in increasing order alphabetically using the Text Values as a sorting key.

Sort by Text-decr:  Sorts the Text, Numeric, and Value Labels in the Text Value Manager dialog in decreasing order alphabetically using the Text Values as a sorting key.

Sort by Num-incr:  Sorts the Text, Numeric, and Value Labels in the Text Value Manager dialog in increasing order numerically using the Numeric Values as a sorting key.

Sort by Num-decr:  Sorts the Text, Numeric, and Value Labels in the Text Value Manager dialog in decreasing order numerically using the Numeric Values as a sorting key.


  Spreadsheet Edit Text Values - Get from Case Names

Select this option to copy the case names into the Text Values Manager


  Spreadsheet Edit Text Values - Get from Variable

Select this option to copy the text values from a specified variable into the Text Value Manager.


  Editing Text Values in the Spreadsheet

For this example, let's edit the text values (Male and Female) in a variable called Gender.

Step 1:	Click on the right-mouse-button on any value of the variable Gender in the spreadsheet and then select the Text Values option from the "flying menu" to open the Text Values Manager dialog.

Step 2:	To change the text value "Male" to "Boys", click on "Male" in the Text Values Manager dialog and type in the value "Boys".

Step 3:	Press TAB to move to the next field (the numeric value associated with "Boys") and again to move to the Value Label Field.  Now you can type in a short label describing the value "Boys" (e.g., type in the text string "Boys in single parent homes").

Step 4:	Now that we have edited a text value and entered a value label, click on the OK button to exit this dialog and implement the changes to the variable.


  Spreadsheet Global Width

The value entered in this dialog (minimum = 1, maximum = 30) determines the width of every column in the spreadsheet.  (This is a global operation, in that the value which you specify here will be applied to every column in the spreadsheet.)


  Scrollsheet Global Width

Specify the width of Scrollsheet columns (the total column width consists of the width of the active field and the margins) and row names in the Customize Width dialog.  (This is a global operation, in that the value which you specify here will be applied to every column and row in the Scrollsheet).

Customize Width dialog:

Column Width:  Specify the global width (minimum = 1, maximum = 80) of the active field of the columns here.

Margin Width:  The number that you specify here (minimum = 1, maximum = 10) will determine how many blank spaces to leave on either side of the active field.

Row Name Width:  Specify the row names (i.e., first column) width (minimum = 1, maximum = 40).


  Spreadsheet Recalculate

You can recalculate a variable (or group of variables) based on the formulas entered in the Current Specs dialog of each variable.

Recalculate Dialog:

All Variables:  Use this option to simultaneously recalculate all variables containing formulas.

Variable:  You can recalculate a single variable by specifying its name here.  Double-click on the variable edit field to select a variable from a list of current variables in the spreadsheet.

Subset:  By default, all cases will be recalculated (the first and last case numbers in the data set will be automatically entered below), or if a block is highlighted in the spreadsheet, only the cases included in the block will be recalculated (the first and last case numbers in the block will automatically be entered below).  However, should you want to recalculate a block of cases that is different from the default entries, enter the case numbers in the From Case and To Case windows.

From Case:  Specify the first case (inclusive) in the block of cases to be recalculated.

To Case:  Specify the last case (inclusive) in the block of cases to be recalculated.

Auto-recalculate when the data change:  Select this option in order to automatically recalcuate all of the spreadsheet formulas when the data are changed in the spreadsheet.

Shortcut:   Press F9 in the spreadsheet in order to bypass this dialog and recalculate all valid formulas in the current data set.


Spreadsheet Shift (Lag) Variables

Use this option to shift a selected variable backward ("up") or forward ("down"), relative to the other variables in the file, by a specified number of cases (lag).  STATISTICA will add blank cases to the remaining variables in the file either before the first case (if the selected variable is shifted backward) or after the last case of the data file (if the selected variable is shifted forward).

Shift Variable dialog:

Variable:  Select the variable to be shifted here.  Double-click on the variable edit field to select a variable from a list of current variables in the spreadsheet.

Lag:  Specify the magnitude of the shift (i.e., the number of cases by which to move the variable).

Direction:  Choose to either move the variable forward ("down") or backward ("up") by clicking on the appropriate option button.


Spreadsheet Add Variables

This option will add empty (blank) column(s) in the designated postion, thus the size of the file will increase.  You can add variables to the spreadsheet by designating the number of new variables to add, as well as where to add them (after which variable) in the Add Variables dialog (accessible from the spreadsheet Edit - Variables pull-down menu).

Add Variables dialog:

Number of Variables to Add:  Choose the desired number of variables to add to the current spreadsheet.  You may include up to 4092 variables in the STATISTICA data spreadsheet or up to 32,000 variables (with up to 255 characters per variable) in Megafile Manager.

Insert After Variable:  Designate the location (variable) in the spreadsheet that the new variable(s) will be added after.  The new variables will be added to the right of the variable specified here.  You can click on the variable edit field in the Add Variables dialog to bring up the list of variables in the current spreadsheet in order to select a variable that the new variable(s) will be placed after.

How to insert (move) before variable 1


Spreadsheet Move Variables

Unlike the Clipboard operations of cutting and pasting the contents of a highlighted range or block of values in the spreadsheet, this option will remove both the contents of the column(s) and the column(s) itself (regardless of whether or not all cases or only a subset of cases are currently highlighted for the respective variables) and insert the columns in the designated position in the spreadsheet, thus the size of the file will remain the same.  You can move one or more variables in the spreadsheet by designating the range (inclusive) of variables to be moved and the location (variable to insert after) in the Move Variables dialog (accessible from the spreadsheet Edit - Variables pull-down menu).

You can easily replace the selection of one variable name with another by clicking on the variable edit field in the Move Variables dialog to bring up the list of variables in the current spreadsheet from which you can select the desired variable.

Move Variables dialog:

From Variable:  Designate the first variable (inclusive) in the range of variables to be moved.  (Note that if you are moving only one variable, then designate the same variable in both the From Variable and To Variable lists.)

To Variable:  Designate the last variable (inclusive) in the range of variables to be moved.

Insert After:  Designate the location (variable) in the spreadsheet that the variable(s) will be moved after (you cannot insert a range of variables after a variable that is included in the range of variables to be moved).  The range of variables will be "cut" from their current spreadsheet location and moved to the right of the variable specified here.

How to insert before variable 1


How to Insert (Move) Before Variable 1;

How to Insert (Move) Before Variable 1

One way to move and insert the values of a variable or block of variables before variable 1 is to use the Drag-and-Drop facilities in STATISTICA.  To do this, first hightlight the desired block.  Then, move the cursor to one of the borders of the block where it will change into an arrow.  Now, to move and insert the block, press SHIFT while dragging the block (see Move/Copy Block).  Next, position the insertion bar between the case name column and the first variable column and release the mouse-button to complete the insert.  Note that this method does not move the selected variable(s) (i.e., their long value labels, formats, assignments of text/numerical values, etc.) but only the values of the selected block.

An alternative way to move and insert an entire variable or block of variables before variable 1, is to first move the variable(s) after variable number 1 and then move variable number 1 to the right of the moved variable(s) (you can also use the Spreadsheet Copy Variables option to first copy the variables and then move them).


Spreadsheet Copy Variables

Unlike the Clipboard operations of copying and pasting the contents of a highlighted range or block of values in the spreadsheet, this option will copy both the contents of the columns and the columns themselves (regardless of whether or not all cases or only a subset of cases are currently highlighted for the respective variables) in the designated postion, thus the size of the file will increase.  You can place a copy of the specified variable(s) at a designated location by specifying the range (inclusive) of variables to be copied and the spreadsheet location (insert after which variable) in the Copy Variables dialog (accessible from the spreadsheet Edit - Variables pull-down menu).

The copy will include not only the data but also the format, long name, formulas, the numeric-text value assignment, etc.  You can easily replace the selection of one variable name with another by clicking on the variable edit field in the Copy Variables dialog to bring up the list of variables in the current spreadsheet from which you can select the desired variable.

Copy Variables dialog:

From Variable:  Designate the first variable (inclusive) in the range of variables to be copied.  (Note that if you are copying only one variable, then designate the same variable in both the From Variable and To Variable lists.)

To Variable:  Designate the last variable (inclusive) in the range of variables to be copied.

Insert After:  Designate the location (variable) in the spreadsheet that the variable(s) will be placed after copying (you cannot insert a block of variables after a variable that is included in the range of variables to be copied).  The copied variables will be located to the right of the variable specified here.

How to insert before variable 1


How to Insert (Copy) Before Variable 1;

How to Insert (Copy) Before Variable 1

One way to copy and insert the values of a variable or block of variables before variable 1 is to use the Drag-and-Drop facilities in STATISTICA.  To do this, first hightlight the desired block.  Then, move the cursor to one of the borders of the block where it will change into an arrow.  Now, to copy and insert the block, press SHIFT while dragging the block (see Move/Copy Block).  Next, position the insertion bar between the case name column and the first variable column and release the mouse-button to complete the insert.  Note that this method does not copy the selected variable(s) (i.e., their long value labels, formats, assignments of text/numerical values, etc.) but only the values of the selected block.

An alternative way to copy and insert an entire variable or block of variables before variable 1, first copy the variable(s) after variable number 1 and then move variable number 1 to the right of the copied variable(s) using the Spreadsheet Move Variables option.


Spreadsheet Delete Variables

Unlike deleting (clearing) the contents of a highlighted range or block of values in the spreadsheet, this option will remove both the contents of the column(s) and the column(s) itself (regardless of whether or not all cases or only a subset of cases are currently highlighted for the respective variables), thus the subsequent variables will be moved to the left and the size of the file will decrease.  One or more variables can be deleted from the current spreadsheet when you designate the range (inclusive) of variables to be deleted in the Delete Variables dialog (accessible from the spreadsheet Edit - Variables pull-down menu).

You can easily replace the selection of one variable name with another by clicking on the variable edit field in the Delete Variables dialog to bring up the list of variables in the current spreadsheet from which you can select the desired variable.

Delete Variables dialog:

From Variable:  Designate the first variable (inclusive) in the block of variables to be deleted.  (Note that if you are deleting only one variable, then designate the same variable in both the From Variable and To Variable lists.)

To Variable:  Designate the last variable (inclusive) in the block of variables to be deleted.


Spreadsheet Rank Variables

Rank the values of one or more variables in this dialog.  You are given several different options by which to perform the ranking.  The values of the variable in the spreadsheet will be replaced with the rankings of those values.  If you want to preserve the original values of the variable, make a copy of this variable (using the Copy Variables option) and perform the ranking on the duplicated variable.

Rank Variables dialog:

Variables button:  Clicking on this button will bring up the Select Variables dialog from which you can select one or more variables to rank.

Cases button:  Click on this button to open the Case Selection Conditions dialog.  Here you can specify a subset of cases to be ranked.  The condition specified here will apply to every variable selected above.

Weight button:  Before ranking, you can weight the variables selected above by another variable in the spreadsheet.  When you click on this button, the Weight Window dialog will open from which you can select the weighting variable.

Assign Rank 1 to:  You can choose to rank the values in ascending (smallest value of variable starts with 1) or descending (largest value of variable starts with 1) order.

Ranks for Ties:  There are four options available to assign ranks to tied values.

•	Mean:  Assign the ranks of tied values the mean of those ranks.

•	Sequential:  Rank each tied value sequentially (ignore ties).

•	Low:  Assign the lowest rank of the values in the tie as the rank for each value in the tie.

•	High:  Assign the highest rank of the values in the tie as the rank for each value in the tie.

Type of Ranks:  Choose the type of rank that you want to perform by clicking on the appropriate option button.

•	Regular:  Rank range is from 1 to n.

•	Fractional:  Rank range is from 0 to 1.

•	Fractional %:  Ranks are percentages based on the fractional ranking of the values of variables.


Spreadsheet Recode Values

You can recode or "translate" the original values of the currently highlighted variable into some new values (dependent upon the values of any variables in the current data set) in the Recode Values of Variable dialog.  Using this facility, you can recode values of the variable into up to 17 "category" values (16 defined categories and "undefined" values).

This "quick Recode" facility (available from the spreadsheet at any point of an analysis) can be used to assign codes (or "category values", typically small integers) to a variable.  A typical application of this tool is to create values of a new "grouping" variable in order to identify subsets of data as groups to be compared in subsequent analyses.  For example, "assign the value of 1 to subjects older than 17, and 2 to subjects younger than 18" or "assign the value of 1 to male subjects, 18 to 25 years old with cholesterol levels below 200; 2 to male subjects 18 to 25 years old with cholesterol levels above 200; and assign the missing data value to all other subjects."

In order to recode data in a way that requires that the values of the target variable are not fixed but calculated following some specific formulas (e.g., as an average of values of some other variables), use the spreadsheet formulas or the user-defined recoding functions in the STATISTICA BASIC programming language.

Example

Recode Values of Variable dialog:

Category

Variables

Open All

Save All

Print

Other


Spreadsheet Recode Values - Categories

Use up to 16 categories to recode a variable.

Include/Exclude if:  When you choose Include if and the recode condition evaluates to true, the original values of the recoded variable for cases (observations) that meet the condition will be replaced with the New Value (see below) that you have specified.  Exclude if will assign the New Value to the original values for cases (observations) that do not meet the specified recode condition.

Recode condition:  Specify the recode condition in the blank Category line following the standard STATISTICA Case Selection Conditions.

•	Operators:  =, <>, <, >, <=, >=, NOT, AND, OR

•	Variable Names:  Specify either variable numbers (e.g., v1, v2, v3, . . . ) or variable names (e.g., GENDER, Date, time, . . .).

•	Case Number:  v0

•	Examples:  v1=0 OR v2>=0;

(v1<1 OR v9='YES' ) AND v4<>0

•	Note:  Be sure to use single quotation marks to reference the text values of variables, e.g., 'Yes'.

Open/Save button:  Use this option to open (and use for recoding) an existing standard STATISTICA Case Selection Condition file (those which can be used to select/filter cases for all analyses in the program) as well as save the current condition in each Category.  Clicking on the Open/Save button will open the Case Selection Condition dialog where you can edit, save or open case selection conditions (these are the same conditions which are used for processing subsets of cases throughout the program).  Case selection conditions saved in this dialog are saved under the file name extension *.sel.  These case selection conditions are then used as recoding conditions when you click <OK> in the Case Selection Condition dialog.

New Value:  Specify the new value to replace the original values here.  You can choose either a specific value (Value option button) or the missing data value (MD code option button) as the new value.


Spreadsheet Recode Values - Variables

Clicking this button will open the Variables dialog from which you can view the variables in the spreadsheet.


Spreadsheet Recode Values - Open All

This button opens the Open Recode Conditions File dialog from which you can select a file (containing all of the recode categories) to open into the Recode Values of Variables dialog.  Files opened from this dialog are text files with the file name extension *.txt.


Spreadsheet Recode Values - Save All

This button opens the Save Recode Conditions File dialog from which you can designate a file into which all of the recode conditions will be saved.  This file will be saved in text file format (*.txt extension).


Spreadsheet Recode Values - Print

Clicking this button will print the contents of all currently defined recode conditions.  You can send the contents of this dialog either to a printer file, the printer, and/or Text/output Window depending on your selection in the Page/Output Setup dialog.


Spreadsheet Recode Values - Other

If no conditions are met by a case (observation) when the variable is recoded, you can choose to either set the original values of the recoded variable to missing (click on the MD code option button), designate an alternative value (click on the Value option button then enter a value), or leave the original values as they are (click on the Unchanged option button).


Recoding Values

The following set of (two) recoding conditions will convert ("translate") all cases (observations) in the currently highlighted variable into 1 (if the value of variable number 1 for those cases is positive or zero) or into -1 (if the value of variable number 1 for those cases is negative).

Category 1:	Include if:  v1>=0	New value:  1

Category 2:	Include if:  v1<0	New value:  -1

Note that recoding conditions may be defined such that the new values of the current variable do not depend on the old values of that variable, but only on values of some other variables in the data set.  In other words, the currently highlighted variable does not have to be included in the text of the recoding conditions; for instance in this example, the currently highlighted variable could be variable number 3, and its new ("recoded") values will depend only on values of variable number 1.  If the currently highlighted variable was variable number 1, then its values would be "translated" into new ones (positive values would "become" 1 and negative values would "become" -1).


Spreadsheet Edit Case Names

This dialog lists the case names in a table where you can review or edit them.  Case names are used as labels only (and not Text Values), thus they can contain all printable characters (the same as Value Labels).  You can access this dialog either by selecting the Case Names options from the Edit pull-down menu or by double-clicking on the case name that you want to edit.

Case Name Manager dialog

Case Names:  Edit case names in the table in the Case Name Manager dialog.  The middle field of three fields in the table is editable.  When you first open this dialog, the case name currently highlighted in the spreadsheet will appear in the editing (middle) field with the equivalent case number along side of it.  After you edit this name, you can scroll up or down (using the scrollbar or arrow keys) to place a different name in the editing field and the case numbers will scroll with the names.

Options button:  Clicking this button will open the Case Names Options dialog where you can adjust the case name width, get the case names from the entries in another variable or perform Clipboard operations on case names.


Spreadsheet Create Case Names

This dialog appears if there are no case names in the current data file, and you have selected the Case Names options from the Edit pull-down menu or double-clicked on the case name.

Case names are used as labels only (and not Text Values), thus they can contain all printable characters (the same as Value Labels).

Width:  Specify the case name width here (maximum width is 20 characters).

For more information, see Edit Case Names).


Spreadsheet Case Name Options

When you are editing case names in the Case Name Manager dialog, you can open the Case Names Options dialog for more editing options.

Case Names Options dialog:

Width:  Adjust the case name width here (maximum width is 20 characters).  Note that unlike the Variable Width (a "display format"), which affects only the display of data and not data themselves, the current setting of the case name width will affect the amount of space reserved in the data file for case names.  Thus, decreasing the width will "cut" (delete) parts of the case names which do not fit the new width setting.  If you set the width to 0, then the case names will be deleted note that the display of the names can also be turned off without deleting the case names, see below).

Get From:  If you want, you can get the case names from a variable in the current data set.  Click on the option Variable and then specify the variable number that you want the case names taken from.

Clipboard:  You can select the following Clipboard operations to manage Case Names.

Paste:  Clicking this option will paste the contents of the Clipboard into the case names column (from the currently highlighted case on down).

Copy:  Clicking this option will copy case names (from the currently highlighted case on down) from the spreadsheet to the Clipboard.

Note:  To control the display of case names in the spreadsheet, use the [image] toolbar button.


Spreadsheet Add Cases

This option will add empty (blank) row(s) in the designated postion, thus the size of the file will increase.  You can designate the number of new cases to add, as well as where to add them (after which case) in the Add Cases dialog.

Add Cases dialog:

Number of Cases to Add:  Choose the desired number of cases to add to the current spreadsheet.  The number of cases that you can add to a spreadsheet is unlimited.

Insert After Case:  Designate the case number after which the new case(s) will be added.  The added cases will be located after the case specified here.

How to Insert (Move) Before Case 1


Spreadsheet Move Cases

Unlike the Clipboard operations of cutting and pasting the contents of a highlighted range or block of values in the spreadsheet, this option will remove both the contents of the row(s) and the row(s) itself (regardless of whether or not all variables or only a subset of variables are currently highlighted for the respective cases) and insert the cases in the designated position in the spreadsheet, thus the size of the file will remain the same.  You can move one or more cases (rows) in the spreadsheet by designating the range (inclusive) of cases to be moved and the location (case to insert after) in the Move Cases dialog.

Move Cases dialog:

From Case:  Designate the first case (inclusive) in the range of cases to be moved.  (Note that if you are moving only one case, then designate the same case in both the From Case and To Case lists.)

To Case:  Designate the last case (inclusive) in the range of cases to be moved.

Insert After:  Designate the location (case) in the spreadsheet that the case(s) will be moved after.  The moved cases will be located after the case specified here.

How to move before case 1


How to Move Before Case 1

One way to move and insert the values of a case or block of cases before case 1 is to use the Drag-and-Drop facilities in STATISTICA.  To do this, first highlight the desired block.  Then, move the cursor to one of the borders of the block where it will change into an arrow.  Now, to move and insert the block, press SHIFT while dragging the block (see Move/Copy Block).  Next, position the insertion bar between the variable names and the first row of the spreadsheet and release the mouse-button.  Note that this method does not move the selected case(s) (i.e., the case names will not be moved) but only the values of the selected block.

In order to move the entire case or block of cases before case 1, use the move option (accessible via the [image] toolbar button) and enter case 0 in the Insert After edit field.  Not only will the values of the selected block be moved, but also the case names.


Spreadsheet Copy Cases

Unlike the Clipboard operation of copying the contents of a highlighted range or block of values in the spreadsheet, this option will copy both the contents of the row(s) and the row(s) itself (regardless of whether or not all variables or only a subset of variables are currently highlighted for the respective cases).  The subsequent cases will be inserted (see Insert After, below) into the spreadsheet resulting in an increase in the size of the file.  You can place a copy of the specified case(s) at a designated location by specifying the range (inclusive) of cases to be copied and the spreadsheet location (insert after which case) in the Copy Cases dialog.

Copy Cases dialog:

From Case:  Designate the first case (inclusive) in the block of cases to be copied.  (Note that if you are copying only one case, then designate the same case in both the From Case and To Case lists.)

To Case:  Designate the last case (inclusive) in the block of cases to be copied.

Insert After:  Designate the location (case) in the spreadsheet that the case(s) will be placed after copying.  The copied cases will be located after the case specified here.

How to copy before case 1


How to Copy Before Case 1

One way to copy and insert the values of a case or block of cases before case 1 is to use the Drag-and-Drop facilities in STATISTICA.  To do this, first highlight the desired block.  Then, move the cursor to one of the borders of the block where it will change into an arrow.  Now, to copy and insert the block, press SHIFT while dragging the block (see Move/Copy Block).  Next, position the insertion bar between the variable names and the first row of the spreadsheet and release the mouse-button.  Note that this method does not copy the selected case(s) (i.e., the case name will not be copied) but only the values of the selected block.

In order to copy a case or block of cases before case 1, use the copy option (accessible via the [image] toolbar button) and enter case 0 in the Insert After edit field.  Not only will the values of the selected block be copied and inserted before case 1, but also the case names.


Spreadsheet Delete Cases

Unlike deleting (clearing) the contents of a highlighted range or block of values in the spreadsheet, this option will remove both the contents of the row(s) and the row(s) itself (regardless of whether or not all variables or only a subset of variables are currently highlighted for the respective cases), thus the subsequent cases will be moved up and the size of the file will decrease.  You can delete one or more cases (rows) from the current spreadsheet when you designate the range (inclusive) of cases to be deleted in the Delete Cases dialog.

Delete Cases dialog:

From Case:  Designate the first case (inclusive) in the block of cases to be deleted.  (Note that if you are deleting only one case, then designate the same case in both the From Case and To Case lists.)

To Case:  Designate the last case (inclusive) in the block of cases to be deleted.


Find Value

The Find dialog will enable you to search for a specific data value (in the currently highlighted variable) or case name in the spreadsheet.

Shortcut:  CTRL+F

Find dialog:

Find What:  Specify the variable value (text or numeric) or the case name that you want to search for in the spreadsheet.

Direction:  Find will search either above (select the Up option button) or below (select the Down option button) the cursor position, but will stop the search when it reaches the top or bottom of the file.

Search:  Choose to search for Values in the current variable or for Case Names (this option is only applicable to spreadsheets).

Find Next button:  After you have specified the above options, click on this button to begin the search.  When there is more than one match, Find will pause so that you can either exit (via the Cancel button) the dialog, or click Find Next to search for the next match.

Hint:  You can repeat the search by pressing CTRL+F.


Replace Value

The Replace dialog will enable you to search for a specific data value in the currently highlighted variable (or for a specific case name) and replace it with a different value.

Shortcut:  CTRL+H

Replace dialog:

Find What:  Specify the variable value (text or numeric) or the case name that you want to search for and replace.

Replace With:  Specify the value (text or numeric) here that will be used to replace the value, text, or case name that you are searching for.

Direction:  Replace will search either above (select the Up option button) or below (select the Down option button) the currently highlighted cell or text, but will stop the search when it reaches the top or bottom of the file.

Search:  Choose to search for Values in the current variable or for Case Names (this option is only applicable to spreadsheets).

Find Next button:  After you have specified the above options, click on this button to begin the search.  When STATISTICA has found the specified text, value, or case name, you will be given the following choices to replace it:

Yes:  Click this button to replace the text or value with your specified replacement.

No:  Click this button to skip over this value (it will not be replaced).

Yes to All:  Click this button to replace all of the text or values that match without asking for confirmation.

Cancel:  Click this button to quit the search and leave the dialog.

Replace All button:  Click this button instead of the Find Next button to replace all values or text that match.  You will not be prompted to accept or reject each replacement.


Spreadsheet Transpose Block

Transpose a square block of data in the spreadsheet.  This option will only transpose the data values defined by the highlight and not the data file (see Transpose Data File).


Spreadsheet Transpose Data File

This option will allow you to turn cases into variables and variables into cases by transposing the spreadsheet data file.  (You can transpose a square block of data when you select the Transpose Block option.)  Text value equivalents in the data file will be lost when the file is transposed, because the text/numeric assignments are specifications of variables (i.e., columns) and not cases (i.e., rows) in STATISTICA data files.  Case names (if any) from the original file will become Long Variable Names.  Case names of the transposed file will be created from the former (8 character) variable names and up to 12 characters of the former Long Variable Names (for a total of 20 characters).  You can transpose a square block of data when you select the Transpose Block option.


Spreadsheet/Scrollsheet Fill/Copy Down

This option will copy the entries in the first row of a highlighted block of cells in the spreadsheet/Scrollsheet down the entire block (i.e., into the remaining cells in the block).  If you need to copy a value to consecutive cases of one variable only, highlight a one-column block; its first ("top") value will be copied down to the end of the highlight.

To copy across variables, see the Fill Right option.  You can also use the Drag-and-Drop facility to copy a block of values or to extrapolate values from a block.  Use Fill Random Values in order to fill the cells in the block with random values (following the Uniform distribution).


Spreadsheet/Scrollsheet Fill/Copy Right

This option will copy the entries in the first column of a highlighted block of cells in the spreadsheet/Scrollsheet, across the entire block (to the right of the first column), into the remaining cells in the block.  If you need to copy a value to consecutive cells (variables) of one case only, highlight a one-row block; its first (leftmost) case will be copied to all consecutive cells of the case.

To copy down rows, see the Fill Down option.  You can also use the Drag-and-Drop facility to copy a block of values or to extrapolate values across a block.  Use Fill Random Values in order to fill the cells in the block with random values (following the Uniform distribution).


Spreadsheet/Scrollsheet Fill Random Values

This option will fill the highlighted block with random values (in the range of 0 to 1) following the Uniform distribution.

To copy down rows, see Fill Down; to copy across columns, see Fill Right.  Note that you can also use the Drag-and-Drop facility to copy a block of values or to extrapolate values across a block.


Spreadsheet/Scrollsheet Standardize Columns

When you select this option, the values in each column of the highlighted block will be standardized.  The standardized values are computed as follows:

Std. Value = (raw value - mean of highlighted column) / std. deviation

You can standardize the values in highlighted rows via the option Standardize Rows.  You can also standardize selected variables via the Data Management option Standardize Variables (that procedure works independent of the currently selected block but takes into account the current case selection conditions and weights).


Spreadsheet/Scrollsheet Standardize Rows

When you select this option, the values in each row of the highlighted block will be standardized.  The standardized values are computed as follows:

Std. Value = (raw value - mean of highlighted row) / std. deviation

You can standardize the values in highlighted columns via the option Standardize Columns.  You can also standardize selected variables via the Data Management option Standardize Variables (that procedure works independent of the currently selected block but takes into account the current case selection conditions and weights).


Screen Catcher

This option (accessible also at any point in the program by pressing ALT+F3) invokes the "Screen Catcher", a utility which allows you to select any rectangular area of the screen (or the entire screen) and copy it as bitmap to the Clipboard.  The copied area may contain graphs, Scrollsheets, spreadsheets, or even screens from other applications (if they are currently displayed on the screen).  The copied bitmap may then be pasted into STATISTICA graphs, or any other application which supports bitmaps.

After selecting this option, position the cursor in one corner of the area that you want to copy.  Now, while holding down the left-mouse-button, drag the cursor over the area that you want to copy (you can drag across windows).  When you release the mouse button, the selected area will be copied to the Clipboard.  Note that when selecting the area to be captured, you can rotate by 180°, and/or reverse (produce a mirror image of) the area captured to the Clipboard by choosing one of four directions of dragging the mouse.  The following four examples illustrate the rotation effects which can be achieved by dragging the mouse in different directions over the area to be captured:

Keyboard Shortcut:  ALT+F3


Spreadsheet Links

This option opens the Links Manager dialog from which you can edit the DDE (Dynamic Data Exchange) link(s) between a source (or server) application and STATISTICA (the client application).  These links are stored (and can also be edited) in the Long Name option of the Current Specs dialog.  You can also establish a link using the Paste Link option.  For more information on establishing DDE links, see Creating Links (Dynamic Data Exchange).

Links Manager dialog:

Links:  This window displays all the DDE links in STATISTICA.  You can edit a link by highlighting it in this window and then clicking on the Change Link button (see below).

Update:  Displays the status of the DDE link that is currently highlighted in the Links window.  DDE links can be either "hot" (automatic status, the "@" symbol precedes the link statement) or "cold" (manual status, the "^" symbol precedes the link statement).  Automatic status means that the linked data in the STATISTICA spreadsheet (client file) will automatically be updated whenever any changes are made to the data in the server application.  Manual status means that the DDE link is temporarily disabled and that you will have to manually update the client file using the Update Now button or by changing the status back to "hot" (using the Change Link button).

Update Now button:  Click on this button to manually update the DDE link (that is currently highlighted in the Links window) in the client file (STATISTICA spreadsheet data file).

Cancel Link button:  Click on this button to temporarily disable the currently highlighted DDE link.  NOTE:  When you are about to run an analysis on the linked data file, be sure to use this option to temporarily disable the link so that the data are not changing as the analysis is running.  You can resume the link by clicking on the Update Now button.

Change Link button:  Click on this button to open the Current Specs dialog in which you can edit the DDE link in the Long Name-Link option (see Creating Links (Dynamic Data Exchange) for detailed information concerning the parts of the DDE path).


DDE Error

This dialog will open whenever STATISTICA needs to re-establish a remote (Dynamic Data Exchange) link (i.e., whenever the server is closed and inactive, or the DDE topic is not opened).

DDE Error dialog:

Automatic Load button:  Click on this button when you want to re-establish the remote link and automatically load the source application file/topic (listed at the top of this dialog; see Creating Links (Dynamic Data Exchange) for more information on the DDE).  In order for STATISTICA to re-establish the remote link, the application needs to either be registered in the Windows registration database (a systemwide source of information about applications) or the application must be on the DOS path and the file/topic must be loadable by command line.

Manual Load button:  Use this option to manually load the specified file/topic.  In order to use this option, follow the steps outlined below.

Step 1:  Once you have decided to manually load the specified file/topic (but before you click on the Manual Load button), switch to the Windows Program Manager (or equivalent) and open the source application (e.g., Excel).

Step 2:  Load the appropriate file in the source application.

Step 3:  Switch back to the STATISTICA module and click on the Manual Load button to manually load the file/topic.

Cancel button:  Click on this button to temporarily disable the link.


Spreadsheet View Menu

Text Values	Numeric Values

Text Values

Value Labels

Case Names	Titles

Full Var Names	Toolbar

Font	Change Show

Colors	Status Bar

Text/output Window	Auto Task Buttons


View Auto Task Buttons Toolbar

This option allows you to toggle on and off the display of the Auto Task Buttons toolbar.  Note that any Hot Keys assigned to Auto Task Buttons can be used regardless of the display setting of the toolbar.

Keyboard Shortcut:  CTRL+M.


Data Values (Numeric, Text) and Labels

Spreadsheet View Text and Numeric Values and Value Labels - Data Values (Numeric, Text) and Labels

What is the "double-notation" (text/numeric) of values?  In STATISTICA, each value may have two identities:  numeric (e.g., 1) and text (e.g., Male).  This double-notation simplifies the use of text values.  For example, when entering data, you could enter the values 1 and 2 in variable Gender to refer to males and females, respectively.  Later, you can type Male into any cell containing a 1, and at the point when you complete the entry, all 1's in this column will automatically change to Male.  In other words, because 1 did not have a text equivalent, the program will understand that you intended to assign the text value Male to 1 in this variable.  You can repeat the same steps for 2 and Female.  This feature simplifies entering text values; at the same time you do not lose any advantages of using the numeric data (they can still be used in subsequent numeric analyses).  Additionally, each unique text value may have a long value label assigned to it (see Spreadsheet View Text and Numeric Values and Value Labels).

How to switch between displaying text and numeric values and value labels in the data spreadsheet:  As explained above, STATISTICA supports a double-notation of values, where each value of a particular variable can simultaneously have a numeric and text identity.  You can switch between displaying text or numeric values or value labels (if any) using the spreadsheet toolbar button [image] (hold down the CTRL key while clicking on the [image] button to display value labels).

How to enter/edit the assignments between numeric and text values:  You can enter/edit text and numeric values in any of the following ways:

•	Click on the [image] toolbar button to open the Text Values Manager dialog (where the text/numeric assignments can be made, as well as managed, i.e., sorted, selectively transferred from other variables, etc.).  An option available in the Text Values Manager allows you to copy to the current variable the text values from other variables or from case names (see the Copy from box in the Text Values Manager dialog).  When you need to copy the numeric/text value assignments and long value labels from one file to another, use the Merge files facility (in the Data Management module).  One of the merge options available from the merge type selection dialog allows you to concatenate or replace text values with values from another file.

•	Click on the [image] button to switch the spreadsheet display to numeric or text values and enter/edit the respective values (hold down the CTRL key while clicking on the [image] button to display value labels).

•	You can paste text or numeric values from another variable or another application into the spreadsheet (be sure the spreadsheet display mode matches the values that you are pasting into the spreadsheet; e.g., display text values in the spreadsheet before pasting text values into the spreadsheet).  Note that if you copy to the Clipboard a block of spreadsheet data, then the contents of the copied block depends on the current display mode (e.g., to copy text values, be sure to set the display mode to Text Values).  The only exception are Clipboard operations within the STATISTICA spreadsheet (when text values or value labels are displayed), where the copied (or cut) block that is to be pasted to another location of the STATISTICA spreadsheet will always contain the full representation of the selected data (i.e., numeric values, text values, and their value labels, if any).

•	You can create text values in the spreadsheet by importing them (see the Quick Import options).

Importing Text Values Longer than 8 Characters.  If the text values imported using the Quick Import options are longer than 8 characters, then value labels will be created to store the long text values in their entirety; the first 8 characters of each value will be used to create the respective STATISTICA text values.  Note that if this would produce text values which are not uniquely related to the long labels (i.e., create a situation when the same text value would be accompanied by different value labels in different cases), then the last character(s) of the text values will be replaced by digits to create unique text values for the respective value labels.  For example, if the values in the source data set (to be imported) are:

Arizona, the south region

Arizona, the north region

Arizona, the central part

then those values will be stored as value labels, and the corresponding (unique) 8-character text values will be created as:

Arizona1

Arizona2

Arizona3

The same conventions apply when you import data to the STATISTICA spreadsheet via the Clipboard [e.g., by copying a block of values in a foreign spreadsheet (highlight a block in the spreadsheet and press ctrl+c) and pasting them to the STATISTICA spreadsheet (place the cursor in the desired position and press ctrl+v)].  If the text values are longer than 8 characters, then they will be interpreted as STATISTICA value labels and the respective (short) text values will be created from the first 8 characters of each long text (as illustrated above).


View Text and Numeric Values and Value Labels

  Spreadsheet View Text and Numeric Values and Value Labels

This option will switch between displaying text, numeric equivalent values and value labels (if any) of all variables with text values in the spreadsheet data file.  You can switch between the different displays by clicking on the [image] toolbar button (hold down the CTRL key while clicking on the [image] button to display value labels).

Numeric and Text Values

Value Labels

See also, STATISTICA Defaults: General


View Text and Numeric Values and Value Labels - Value Labels

  Spreadsheet View Text and Numeric Values and Value Labels - Value Labels

Displaying and Editing Value Labels.  Value labels are comments or descriptions (up to 40 characters long) that can be assigned to specific text/numeric values in STATISTICA data sets, for example:

Numeric  Text        Value

Value:   Value:      Label:

-------  --------    --------------------------------------

  1      Arizona1    Arizona, the south region of the state

  2      Arizona2    Arizona, the north region of the state

  3      Arizona3    Arizona, the central part of the state

Value labels can be displayed and edited directly in the spreadsheet (as well as in the Text Values Manager dialog).  If any values in the current data set have value labels, then the Text/Numeric Value display toolbar button ( [image]), allows you to toggle over three display settings: Numeric Values, Text Values, and Value Labels (hold down the CTRL key while clicking on the [image] button to display value labels).  Additionally, you can select the display mode from the spreadsheet View pull-down menu.  The current display mode is indicated by the text in the upper-left corner of the spreadsheet.  Note that text values and value labels will be displayed only for those variables with text values.  If no text values exist for the data file, then clicking on the [image] toolbar button (or optionally, selecting the View - Text Values pull-down menu option) will bring up the message "No text values in this data file."

How to Enter Value Labels.  If the values in the current data set do not have any value labels but do have text values, then you can enter value labels in any of the following ways:

•	Click on the [image] toolbar button to open the Text Values Manager dialog (where they can be assigned to specific text/numeric values, as well as managed, i.e., sorted, selectively transferred from other variables, etc.).

•	When the spreadsheet is in Text Values display (toggle the [image] toolbar button until the text values are displayed), hold down the CTRL key while clicking on the [image] toolbar button in order to go to Value Labels display.  Note that the numeric values will be displayed and now you can enter the value labels directly in the spreadsheet.

•	You can paste value labels from another variable or another application into the spreadsheet.  Note that if you copy to the Clipboard a block of spreadsheet data, then the contents of the copied block depends on the current display mode (e.g., to copy value labels, be sure to set the display mode to Value Labels).  The only exception are Clipboard operations within the STATISTICA spreadsheet (when text values or value labels are displayed), where the copied (or cut) block that is to be pasted to another location of the STATISTICA spreadsheet will always contain the full representation of the selected data (i.e., numeric values, text values, and their value labels, if there are any).

Importing Text Values Longer than 8 Characters.  If the text values imported using the Quick Import options are longer than 8 characters, then value labels will be created to store the long text values in their entirety; the first 8 characters of each value will be used to create the respective STATISTICA text values.  Note that if this would produce text values which are not uniquely related to the long labels (i.e., create a situation when the same text value would be accompanied by different value labels in different cases), then the last character(s) of the text values will be replaced by digits to create unique text values for the respective value labels.  For example, if the values in the source data set (to be imported) are:

Arizona, the south region

Arizona, the north region

Arizona, the central part

then those values will be stored as value labels, and the corresponding (unique) 8-character text values will be created as:

Arizona1

Arizona2

Arizona3

The same conventions apply when you import data to the STATISTICA spreadsheet via the Clipboard [e.g., by copying a block of values in a foreign spreadsheet (highlight a block in the spreadsheet and press ctrl+c) and pasting them to the STATISTICA spreadsheet (place the cursor in the desired position and press ctrl+v)].  If the text values are longer than 8 characters, then they will be interpreted as STATISTICA value labels and the respective (short) text values will be created from the first 8 characters of each long text (as illustrated above).


View Case Names

    Spreadsheet View Case Names

This option will toggle between displaying case names (see button on right) or case numbers (see button on left) in the spreadsheet data file.  When checked, the default setting for the spreadsheet will be to display case names, otherwise (when unchecked), only the case numbers will be displayed.


Spreadsheet View Variable Specs

  Spreadsheet View (All) Variable Specs

View the variable specifications for all variables when you select this option.  Included in this window are each variable's Number and Name, its missing data code (MD Code), the value Format, and Long Variable Name or formula.  You can edit the variable specifications either here (individually or for all variables) or in the Current Specs dialog (for the current variable only).

The Format column displays the current representation by which the values of the variable are displayed in the spreadsheet.  The different representations of the variable formats Number, Scientific, Currency, and Percentage are displayed here simply as the width of the column and the number of decimals (e.g., 14.5).  The different representations of the variable formats Time and Date are displayed here using specific keywords (e.g., DATE2, TIME6).  Those keywords are described in the Current Specs dialog.  You can use the Fill Block Down option in order to copy a variable format to several variables.  To do this, highlight a block in the Format column with the desired format being the first cell in that block.  Next, click with the right-mouse-button on that block and select the option Fill Block Down.  STATISTICA will copy the desired format to each variable in the block.  This capability is useful when you need to reformat many variables at once.

When the View (All) Variable Specs window is open, the following toolbar buttons and menu options will be available.

View (All) Variable Specs Toolbar Buttons

Pull-down Menu Options

File

Edit

View

Analysis

Options

Window

Help

For quick access to information about the spreadsheet or Scrollsheet windows, see Spreadsheet Window Overview and Scrollsheet Window Overview.  For more information on specific dialogs or options, click on the [image] button in the upper-right corner of the dialog.  For more general information, see STATISTICA Index.


Spreadsheet View Variable Specs - Toolbar buttons

  Spreadsheet View (All) Variable Specs - Toolbar Buttons

The following toolbar buttons are available when you open the View (All) Variable Specs window in order to view the variable specifications for all variables in the spreadsheet.

For more information on specific dialogs or options, click on the [image] button in the upper-right corner of the dialog.

  STATISTICA Module Switcher

  Workbook Management

  View spreadsheet (brings the current spreadsheet to the top of the Window)

  Print Variable Specs

  Open Data File (opens a different data file)

  Save Data As (saves the current data file)

  Copy

  Paste

  Electronic Manual


Spreadsheet View Variable Specs - File Pull-down Menu

  Spreadsheet View (All) Variable Specs - File Pull-down Menu

New Data	Save

Open Data	Save As

Open Other	Print/Eject Current Page

New Data	Print

Data File	Print Files

Graph File	Page/Output Setup

Scrollsheet	Printer Setup

Text/Output	Exit

STATISTICA BASIC

Command Language (SCL)


Spreadsheet View Variable Specs - Edit Pull-down Menu

  Spreadsheet View (All) Variable Specs - Edit Pull-down Menu

Cell	Cut

Add Vars	Copy

Move Vars	Paste

Copy Vars	Clear

Delete Vars	Fill Block Down

Text Values	Screen Catcher


Spreadsheet View Variable Specs - View Pull-down Menu

  Spreadsheet View (All) Variable Specs - View Pull-down Menu

Data

Font

Colors

Text/output Window

Toolbar

Change Show

Status Bar


Spreadsheet View Variable Specs - Analysis Pull-down Menu

  Spreadsheet View (All) Variable Specs - Analysis Pull-down Menu

Startup Panel

Resume Analysis

STATISTICA BASIC

Command Language (SCL)

Quick Basic Stats

  Descriptive Statistics

  Correlation Matrices

  Frequency Tables

  Probability Calculator

  More....

Other Statistics


Spreadsheet View Variable Specs - Options Pull-down Menu

  Spreadsheet View (All) Variable Specs - Options Pull-down Menu

Selection Conditions	Display

Weight	Print

General

Macro

Command Langage (SCL)	Keyboard Macro

STATISTICA BASIC	Recorded Show Macro

Quick Open File	Customize Auto Task Buttons


Spreadsheet View Variable Specs - Window Pull-down Menu

  Spreadsheet View (All) Variable Specs - Window Pull-down Menu

Scrollsheet Manager

Graph Manager

Cascade

Tile Horizontally

Tile Vertically

Arrange Icons

Close All


Spreadsheet View Variable Specs - Help Pull-down Menu

  Spreadsheet View (All) Variable Specs - Help Pull-down Menu

Index	Search Help On

Spreadsheet	Glossary

Scrollsheet	Keyboard

Graph	Advisor

Text/Output	About


View Data

This option allows you to rearrange the order of overlapping windows (e.g., Scrollsheets, graphs, Text/output Window) on the screen in order to bring the spreadsheet data file to the top and make it the active window so that you can view the data.


Spreadsheet View Full Variable Names

When the format width of the values of a variable (as specified in the Current Specs dialog) is less than 8 characters (the maximum width of a variable name), then the displayed variable name is "cut" to the formatted width of its values.  In order to view (display) the entire variable name, select the Full Var Names option from the spreadsheet View pull-down menu.  When this option is checked, if any columns are set (formatted) to less than the length of their respective variable name, then the width of this column will be automatically increased to allow the display of the full variable name.


Spreadsheet View Titles

With this option, you can choose to display the spreadsheet with a title (when checked, a one-line title will be included in the spreadsheet display) or without a title (Title will appear unchecked in the View pull-down menu).  The data file header (managed in the Data File Header, Notes, and Workbook Info dialog) is used as the spreadsheet title.  De-selecting the titles will only suppress the display (i.e., it will not delete the File Header).  You can edit the title by double-clicking on the title area of the spreadsheet (or select the Header option from the Edit pull-down menu) to open the Data File Header, Notes, and Workbook Info dialog.


Spreadsheet View Toolbar

View Toolbar

When you click on this option from the View pull-down menu, you will be able to select from several ways to display the toolbar (described below) in the window or you can toggle between displaying the toolbar and hiding it.

Off:  Select this option to temporarily remove the toolbar from the window.  (In order to once again display the toolbar, select one of the options described below.)

1 line:  When you select this option, the toolbar will be displayed in one line in the spreadsheet window.

2 lines:  Select this option to display the toolbar buttons in two lines.

Right & Top:  This option will display half of the toolbar at the top of the window and the other half along the right side of the window.

Left & Top:  This option will display half of the toolbar at the top of the window and the other half along the left side of the window.

Large Buttons:  Select this option to toggle between displaying normal and large buttons in the toolbar (when checked, large toolbar buttons will be displayed, which may be desirable when using higher resolutions, e.g., 1024x768).

Shortcut:  Double-click on the toolbar to rotate through the different configurations.


  Change Show

Change Show displays the contents of the currently highlighted cell (or cursor position or text rotation angle in graphs or line and column number in the Text/output Window) in the Show toolbar window.  Click on this option to toggle between the different sizes (lengths) of the Show toolbar window.

  Spreadsheet Window

  Scrollsheet Window

  Graph Window

  Text/output Window


  Change Show - Spreadsheet Window

When the spreadsheet display width of the values of a variable (as specified in the Current Specs dialog) is less than necessary to see all significant digits, use this option to adjust the Show window length and view the full length of a value of a variable.  Alternatively, click on the Show window with the mouse.


  Change Show - Scrollsheet Window

When the display width of the columns (as specified in the Scrollsheet Column Specs dialog) is less than necessary to see all significant digits, use this option to adjust the Show window length and view the full length of the value.    Alternatively, click on the Show window with the mouse.


  Change Show - Graph Window

Use this option to adjust the Show window length and view the full length of the cursor coordinates or text rotation angle in the graph (alternatively, click on the Show window with the mouse).

Depending on the current Graphics mode (Dynamic or Fixed), the cursor coordinates displayed in the Toolbar Show window represent either the X- and Y-axis scale coordinates (respectively) or window coordinates as percentages of the total window width and height (the lower left corner is [0%, 0%] the upper right corner is [100%, 100%]).

Graphics Toolbar window:	Fixed Mode

Dynamic Mode

Text rotation angle


  Change Show - Text/output Window

This window displays the current cursor position (row number and column number) in the Text/output Window.


View Status Bar

Toggle between displaying the window Status Bar (the bar at the bottom of the screen) and hiding it with this option.  When checked, the Status Bar will be displayed.  While executing a task, STATISTICA will use the Status Bar to display the progress of the task (see Progress Bar, below).

Status Bar

Progress Bar


Status Bar

Comment:  This area of the Status Bar is reserved for a brief (one line) description of the highlighted pull-down or cell-related menu or option.  When nothing is highlighted (data are not being processed and STATISTICA is waiting for the next command), the word Ready is displayed.  Double-click on the comment area in the Status Bar to open the main Help menu.

Output:  Displays the current destination (as specified in the Page/Output Setup dialog) for the output of an analyses.  Double-click on Output in the Status Bar to open the Page/Output Setup dialog from which you can select the output destination (Off, File, Printer and/or Window) and other output options.

Sel:  Displays the current status (On or Off) of the case selection conditions.  Double-click on Sel in the Status Bar to open the Case Selection Conditions dialog from which you can specify the case selection conditions.

Weight:  Displays the current status (On or Off) of the variable weighting conditions.  Double-click on Weight in the Status Bar to open the Define Weight dialog from which you can specify the variable weighting conditions.

REC:  This message will flash in the right-hand side of the status bar when you are recording a macro (either a sequence of keystrokes or mouse movements).  For more information on recording macros, see Customize Auto Task Buttons.


Progress Bar

Progress:  This area of the Progress Bar is reserved for displaying the amount of task completed.

Elapsed Time:  STATISTICA displays the elapsed time in seconds since the beginning of the task.

CANCEL button:  Click on this button to interrupt the task in progress; graph redraw may be interrupted by a click of the mouse (anywhere on the screen).

You can control the display of the Progress Bar  for Stats Graph and Quick Stats Graph procedures via the STATISTICA Defaults:  Stats Graphs dialog.


Graphs Menu

  Quick Stats Graphs	  Stats Categorized Graphs

  Stats 2D Graphs	  Multiple Graph Layouts

  Stats 3D Sequential Graphs	  Blank Graphs

  Stats 3D XYZ Graphs	  Custom Graphs

  Stats Matrix Plots	  Block Stats Graphs

  Stats Icon Plots	  Stats User-defined Graphs

  Graph Data Links


Graphs Menu - 2D Graphs

Graphs Menu - Stats 2D Graphs

The following 2D graphs are available from the Graphs pull-down menu.

  2D Histograms	  2D Range Plots

  2D Scatterplots	  2D Box Plots

  Scatterplots w/Histograms	  2D Line Plots

  Scatterplots w/Box Plots	  Sequential/Stacked Plots

  Probability Plots	  Pie Charts

  Quantile-Quantile Plots	  Missing/Range Data Points

  Probability-Probability Plots	  2D Custom Function Plots


Graphs Menu - 3D Sequential Graphs

Graphs Menu - Stats 3D Sequential Graphs

The following 3D sequential graphs are available from the Graphs pull-down menu.

  Raw Data Plots

  Bivariate Histograms

  Range Plots

  Box Plots


Graphs Menu - 3D XYZ Graphs

Graphs Menu - Stats 3D XYZ Graphs

The following 3D XYZ graphs are available from the Graphs pull-down menu.

  Scatterplots	  Ternary Plots

  Surface Plots	  Categorized Plots

  Contour Plots	  Categorized Ternary Plots

  Trace Plots	  Custom Function Plots


Graphs Menu - Categorized Graphs

Graphs Menu - Stats Categorized Graphs

The following categorized graphs are available from the Graphs pull-down menu.

  Histograms	  Box Plots

  Scatterplots	  Pie Charts

  Probability Plots	  Missing/Range Data Plots

  Quantile-Quantile Plots	  3D XYZ Plots

  Probability-Probability Plots	  3D Ternary Plots

  Line Plots


Graphs Menu - Blank Graphs

The following blank graphs are available from the Graphs pull-down menu.

  Default Proportion

  Printer/Page Proportions


Multiple-Graph Layouts

The following multiple-graph layouts and templates are available from the Graphs pull-down menu.

  Multiple-Graph AutoLayout Wizard

  Templates


  Multiple-Graph AutoLayout Wizard

Compound graphs are those that contain linked or embedded OLE objects.  STATISTICA can automatically create compound graphs (e.g., in the Quality Control module where one display contains 4 different types of graphs) or you can use the Multiple-Graph AutoLayout Wizard to create them yourself (see below).  STATISTICA supports a comprehensive selection of facilities to insert OLE-compliant objects in STATISTICA graphics documents (see Exchanging Information (Data, Graphs) with other Applications).

In order to create a multiple graph template into which Clipboard objects may be pasted (using Paste Replace), use the Graph AutoLayout - Template option.

In order to create a multiple graph layout in which pre-selected graphs will be placed on the same page, use the Graph AutoLayout - Wizard option.  The AutoLayout Wizard assists you (in two steps) in selecting graphs to be placed on the same page (graphs may be selected from currently open windows or from graph files previously saved to disk; see below).

Step 1.  In the first step of the AutoLayout Wizard, you can select the graphs (files or windows) for the multiple graph layout (note that the order of the selected graphs can be changed in the AutoLayout Wizard - Step 2 dialog).

AutoLayout Wizard - Step 1 dialog:

Add Graphs

Remove

Link/Embed

Graphs Gallery

Step 2.  Click OK in this dialog to go to the next step in creating a multiple graph layout - AutoLayout Wizard - Step 2.

See also, Graphs Gallery.


  Multiple-Graph AutoLayout Wizard Step 1 - Graphs Gallery

Click on the [image] button in order to open the Graphs Gallery dialog.  This dialog allows you to quickly and easily "switch" between different types of graphs (e.g., Stats Graphs, Custom GraphsBlock Stats Graphs, etc.).


  Multiple-Graph AutoLayout Wizard Step 1 - Add Graphs

Graphs can be added to the multiple layout either from disk (i.e., previously saved graphs) or from current graphs in the program (from all modules of STATISTICA running, see below).  The following options are available:

Embed Files:  When you click on this button, the File Open dialog will open in which you can select one or more previously saved graph files to be embedded in the multiple graph layout.  Press on the CTRL button in order to select multiple files (continuously or discontinuously) from the list of files.  Once selected, the status (i.e., link/embed) of the file can be changed via the Link/Embed radio buttons.

Link Files:  When you click on this button, the File Open dialog will open in which you can select one or more previously saved graph files to be linked in the multiple graph layout.  Press on the CTRL button in order to select multiple files (continuously or discontinuously) from the list of files.

All Windows:  Click on this button in order to add the names of all current graphs in all open STATISTICA application windows.  The graphs will be added in the order in which they were created.  These current graphs from the STATISTICA application windows will be embedded by default.  However, if a current graph was previously saved, then the status of that graph can later be changed to linked via the Link/Embed radio buttons.

Blank:  Click on this button in order to insert "blanks" into the multiple graph layout.  These "blanks" can be used to maintain space between graphs in the multiple layout, you can use the Paste Replace option to replace them with OLE objects, or you can add extra text in place of the "blanks."


  Multiple-Graph AutoLayout Wizard Step 1 - Remove

Click on this button to remove the highlighted graph from the list of graphs.  Note that the list of graphs can be reordered in the next dialog AutoLayout Wizard - Step 2.


  Multiple-Graph AutoLayout Wizard Step 1 - Link/Embed

These radio buttons display the status of the highlighted graph in the list of graphs.  You can also change the status of the graphs (e.g., from linked to embedded) by clicking on the desired radio button.


 AutoLayout Wizard - Step 2

In this step, you can choose from several pre-selected layouts for either the Template or AutoLayout Wizard.  The following options are available in this dialog.  After selecting the desired layout and other options, click OK to create the Multiple AutoLayout Graph.  Each compound graph can be edited by double-clicking on it.

AutoLayout Wizard - Step 2 dialog:

AutoLayout

Graphs

Page Layout

Create

Margins

Change Graph List

Link/Embed

Mapping Mode

The component graphs arranged by the Wizard (see above) can later be replaced with new objects (e.g., different STATISTICA graphs or other artwork) using the Paste Replace Object option (see the Paste Special dialog).

See also Graphs Gallery.


 AutoLayout Wizard Step 2 - AutoLayout

Depending on how many graphs are in the Graphs list, this area of the dialog will display all possible layouts for those graphs.  Click on the desired layout in order to select it.


 AutoLayout Wizard Step 2 - Graphs

This area of the dialog lists the previously selected graphs from the AutoLayout Wizard - Step 1 dialog or the specified number of blank graphs from the Template.  You can rearrange the graphs in this list by highlighting one or more (in a continuous or dis-continuous list) graphs and then moving the mouse cursor either before the first graph, between two graphs, or after the last graph.  When you move the cursor to one of these positions in the list, it will change to a "broken, double-headed arrow."  When it appears like this, click on the left-mouse-button in order to move the highlighted graph(s) to this insertion point.


 AutoLayout Wizard Step 2 - Page Layout

Choose one of the three graph proportions with these options.

Screen:  When you select this option, the proportions of the Multiple AutoLayout Graph window will follow the default graph window proportions (i.e., they will not necessarily be the same as the current printer/page proportions, e.g., portrait/landscape, margins, etc., see Print Preview).  The default graph window porportion depends on the settings in the Graph Mapping Defaults dialog.  The graph proportion can later be adjusted via the Use Print Proportion option from the View pull-down menu (so that the graph will fill the physical size of the printed page) or the Change Proportions option in the View pull-down menu.

Printer:  When you select this option, the proportions of the Multiple AutoLayout Graph window will be proportional to the current printer page proportions, as specified in the Print Preview, Margins, and Printer Setup dialogs (e.g., portrait or landscape).  The Multiple AutoLayout Graph proportion will automatically be adjusted so that the graph will fill the physical size of the printed page.  The graph proportions can later be adjusted to the default proportions via the Restore Original Settings option in the View pull-down menu.

Slide (3x4):  When you select this option, the proportions of the Multiple AutoLayout Graph window will be 3x4 (for creating slides).


 AutoLayout Wizard Step 2 - Create

With these options, you can add a Title, Subtitle (immediately below the title), and/or a Footnote (at the bottom of the graph) to the Multiple AutoLayout Graph.  When you click OK in this dialog, STATISTICA will display the text "Double-click Here to Edit Graph ...".  Simply double-click on the desired title or footnote in order to bring up the Graphic Text Editor in which you can edit it.


 AutoLayout Wizard Step 2 - Margins

Specify here the outside and between-graphs margin (up to 25% of the total graph) in the Multiple AutoLayout Graph.


 AutoLayout Wizard Step 2 - Change Graph List

Click on this button in order to remove or add graphs to the Graphs list. When you click on this button, the AutoLayout Wizard - Step 1 dialog will open in which you can make your changes to the list.  Click OK in this dialog in order to return to the AutoLayout Wizard - Step 2 dialog.


 AutoLayout Wizard Step 2 - Link/Embed

These radio buttons display the status of the highlighted graph in the Graphs list.  You can also change the status of the graphs (e.g., from linked to embedded) by clicking on the desired radio button.


Multiple-Graph Layout - Template

  Multiple-Graph Layout - Templates

Select the Multiple-Graph Layout - Templates option in order to create a Multiple AutoLayout Graph containing the specified number of blank graphs ("place holders").  This graph is useful when you want to use the Paste Replace Object option to replace each blank graph with OLE objects.  When you select this option, the Graph Template dialog will open.  Here, you can specify the number (2 to 25) of blank graphs to be included in the Multiple AutoLayout Graph.

Clicking OK in this dialog will bring up the AutoLayout Wizard - Step 2 dialog in which you can select the desired layout and other options.  Note that you can click on the Change Graph List in this dialog in order to bring up to AutoLayout Wizard - Step 1 dialog.  Here, you can add current graphs or graphs from file to the list of blank graphs, then proceed as described in the AutoLayout Wizard - Step 1 dialog.  Alternatively, you can create a Multiple AutoLayout Graph with current graphs or graphs from file and blank graphs using the Graph AutoLayout - Wizard option.

The blank component graphs in the template (see above) can later be replaced with objects (e.g., STATISTICA graphs or other artwork) using the Replace Object option (see the Paste Special dialog).

Graphs Gallery:  Click on the [image] button in order to open the Graphs Gallery dialog.  This dialog allows you to quickly and easily "switch" between different types of graphs (e.g., Stats Graphs, Custom Graphs Block Stats Graphs, etc.).


Graphs Menu - Custom Graphs

The following custom graphs are available from the Graphs pull-down menu.

  2D Graphs

  3D Sequential Graphs

  3D XYZ

  Matrix Plots

  Icons Plots

  Ternary Plots


  Swap Variables

You can swap variables ("primary"-Y and "secondary"-X) in Quick Stats Graphs by selecting the Swap Variables option in the Quick Stats Graphs right-mouse button menu.  By default, the graphs in this menu will display the column variable name associated with the highlighted cell in the Scrollsheet or spreadsheet in the first section of graphs in the menu and the row variable name (the grouping variable) in the second section of the graphs in the menu.  You can switch the variables, making the column variable the "secondary" (X or categorical) variable and the row variable the "primary" (or "plotted values") variable when you select this option.


Specific Quick Stats Graphs

When you click on the right-mouse button in the Scrollsheet, a menu of graphs and other options associated with the cell will appear.  When you select the Quick Stats Graphs option, a sub-menu will appear offering specific statistical graphs.  In most cases, a graph specific to the type of analysis that was run will be the first graph offered.  For example, for a Scrollsheet resulting from Descriptive Statistics, the specific graph offered is a histogram with an overlaid normal curve; while a scatterplot with a 95% confidence interval is offered after a correlation analysis is run.  Each of these specific graphs can be created from the other Quick Stats Graphs options; however, STATISTICA provides them at the appropriate time in order to make it easier for you to create the graphs.


  Spreadsheet and Scrollsheet Quick Stats Graphs

"Quick Stats Graphs" are one of two general categories of graphs accessible from all Scrollsheets and spreadsheets in STATISTICA; see the Graphics Overview.  Unlike "Custom Graphs" (which provide a general tool to visualize numerical output and allow you to custom-define graphs by specifying any subsets or combinations of rows, columns, or both to be represented in a graph), "Quick Stats Graphs" are predefined statistical graphs.  They represent either standard methods to graphically summarize raw data (e.g., various scatterplots, histograms, or plots of central tendencies such as medians) or standard graphical analytic techniques (e.g., categorized normal probability plots, detrended probability plots, or plots of confidence intervals of regression lines).

Selecting this option will open a menu from which you may choose one of the following graphs.  As these graphs are generated, STATISTICA will take into account the current case selection and weighting conditions of the variables that are being plotted.

For a general overview of the graphics facilities in STATISTICA, see Graphics (Overview).

Note:  You can also use the right-mouse-button to access these options.

Specific Graphs

  Values/Stats of...	  2D Histogram by...

  Histogram of ...	  3D Histogram by...

  Box-Whisker of ...	  Box-Whisker by...

  Probability Plot of ...	  Probability Plot by...

  Scatterplot by...	  Matrix Scatterplot

  Swap Variables (available from the right-mouse button Quick Stats Graphs menu)


Spreadsheet and Scrollsheet Quick Stats Graphs - Values/Stats of Vx

  Spreadsheet and Scrollsheet Quick Stats Graphs - Values/Stats of . . .

This Quick Stats Graphs option allows you to view the values of the currently selected variable and its specifications as well as the descriptive statistics for that variable.  When you highlight a variable and select this option, the Variable Values Window will open in which the variable name, missing data value, format and long variable name (if any) are displayed (these can be edited in the Current Specs dialog).  The Variable Values Window also contains a sorted list of all data values (for that variable) that you can browse through and some descriptive statistics (n, mean, and standard deviation) for that variable.

  The descriptive statistics can be copied to the Clipboard by pressing the Copy button.

For a general overview of the graphics facilities in STATISTICA, see Graphics (Overview).


Spreadsheet and Scrollsheet Quick Stats Graphs - Histogram of Vx

  Spreadsheet and Scrollsheet Quick Stats Graphs - Histogram of . . .

Selecting this Quick Stats Graphs option will display a histogram (a graphical representation of a frequency table) of the values of the currently highlighted variable either with (select Normal Fit) or without (select Regular) a normal fit to the data.

If the selected variable is categorical (usually 10 or less categories), then STATISTICA will use those categories as the histogram intervals.  If the variable has either more than 10 categories or the values are non-integers (continuous), then STATISTICA will divide the values into about 10 to 12 intervals based on the range of the values.  These intervals are then used in the histogram.

You can also create a categorized histogram with the Histogram By... option.  Many other types of histograms are available in STATISTICA's Stats Graphs accessible from the pull-down menu Graphs.  For a general overview of the graphics facilities in STATISTICA, see Graphics (Overview).

Note:  In order to visualize frequency distributions of values in cases (and not variables), use the Block Stats Graphs - Histograms of Rows option from the Graphs pull-down menu (instead of transposing your data file).


Spreadsheet and Scrollsheet Quick Stats Graphs -Box-Whisker of Vx

  Spreadsheet and Scrollsheet Quick Stats Graphs - Box-Whisker of . . .

The box plots resulting from this Quick Stats Graphs option represent the central tendency and variability of the currently highlighted variable.  As measures of central tendency, you can choose between plotting the means and medians and their respective measures of variability; standard deviations or standard errors (associated with the means), and ranges (associated with the medians).  Choose one of four types of box plots to represent the distribution of the values of the currently highlighted variable.

  Median/Quart./Range:  This box plot describes the central tendency of the variable in terms of the median of the values (represented by the smallest box in the plot).  The spread (variability) in the variable values are represented in this plot by the quartiles (the 25th and 75th percentiles, larger box in the plot) and the minimum and maximum values of the variable (the "whiskers" in the plot).

  Mean/SE/SD:  Here, the smallest box in the plot represents the mean (central tendency) of the variable, while the dispersion (variability) is represented by ± 1 times the standard error (large box) and ± 1 times the standard deviation about the mean ("whiskers").

  Mean/SD/1.96*SD:  This plot will show the mean (small box in the plot) of the variable surrounded by a larger box (± 1 times the standard deviation).  If the distribution is normal, then the "whiskers" in this plot represent a "95% confidence interval" defined as the variable mean ± 1.96 times the variable standard deviation.

  Mean/SE/1.96*SE:  Once again, this plot will show the mean (small box in the plot) of the variable surrounded by a larger box.  However, in this plot, the larger box represents ± 1 times the standard error.  If the distribution is normal, then the "whiskers" in this plot represent a "95% confidence interval" defined as the variable mean ± 1.96 times the variable standard error.

Many other types of box and whisker graphs are available via STATISTICA's Stats Graphs.  For a general overview of the graphics facilities in STATISTICA, see Graphics (Overview).  In order to produce box plots representing the distribution of the values in cases (and not variables), use either the Block Stats Graphs - Box Plot/Means of Rows or Block Stats Graphs - Box Plot/Medians of Rows option from the Graphs pull-down menu (instead of transposing your data file).

Hint:  In box and whisker graphs, you can change the small box used to represent the central tendency (mean or median) to a horizontal line by changing this plot type to Min-Max X in the appropriate Plot Layout dialog.  To call up the appropriate Plot Layout dialog, double-click on the plot legend symbol for the mean (or median).


Spreadsheet and Scrollsheet Quick Stats Graphs -Probability Plot of

  Spreadsheet and Scrollsheet Quick Stats Graphs - Probability Plot of ...

These Quick Stats Graphs plots visualize normality of the distribution of the currently highlighted variable.  The assumption of normality (that the data follow a normal distribution) often needs to be tested, since many statistical procedures assume that the distribution of an analyzed variable is normal.  You can choose from three different types of normal probability plots to visually verify the normality of a variable when you select this option.

  Normal Probability plot

  Half-Normal Probability plot

  Detrended normal probability plot

Note that you can visually compare the normality of the values of a variable in graphs identified by a grouping variable by selecting the Probability Plot By ... option.

Many other types of probability plots are available in STATISTICA's Stats Graphs accessible from the pull-down menu Graphs.  In order to produce normal probability plots of the values in cases (and not variables), use the Block Stats Graphs - Normal Prob. Plots of Rows option from the flying menu, Graphs pull-down menu, or the Graphs Gallery (instead of transposing your data file).  Note that if more than one row (or column) is highlighted, then a multiple normal probability plot will be produced.  For a general overview of the graphics facilities in STATISTICA, see Graphics (Overview).


Categorized Histograms

This option offers an extension of the regular Histogram option, allowing you to examine the distribution of values of the selected variable(s) broken down (categorized) by some other grouping or independent variable(s).  One or two grouping variables can be represented on one graph (i.e., a graph may represent a one-way or two-way categorization of cases).  If two grouping variables are selected, a "crosstabulation of graphs" is produced.

In the categorized histograms called from the Results dialogs, the categorization (i.e., the breakdown into subsets of cases) based on the grouping variables uses the grouping codes (e.g., MALE, FEMALE) used in the current analysis (e.g., ANOVA or Breakdowns).  If no grouping codes are used in the analysis, the program will ask for the codes before the graph is produced.

One-way categorized histograms are available directly from all Scrollsheet and spreadsheets by using the Quick Stats Graphs option (see Spreadsheet and Scrollsheet Quick Stats Graphs - Histograms by...).  Your can also visualize frequency distributions of values in cases (and not variables), use the Block Stats Graphs - Histograms option from the flying menu, Graphs pull-down menu, or the Graphs Gallery (instead of transposing the data file).

A wide variety of categorized histograms are also available from the Stats Categorized Graphs options (in the pull-down menu Graphs, see Stats Graphs).  These graphs offer a selection of categorization methods (including user-defined intervals, multiple subsets defined by logical expressions, and others).  For a general overview of the graphics facilities in STATISTICA, see Graphics (Overview).


Categorized Scatterplots

This option allows you to plot the values of a selected variable against the values of another selected variable broken down (categorized) by some other grouping or independent variable(s).  One or two grouping variables can be represented on one graph (i.e., a graph may represent a one-way or two-way categorization of cases).  If two grouping variables are selected, a "crosstabulation of graphs" is produced.  In some cases, each categorized scatterplot is plotted with a linear regression line fitted to the data and a 95% confidence interval for that line (the probability value for the confidence interval as well as the fitted function can be adjusted in the Plot Layout dialog accessible from within the graph).

In the categorized scatterplots called from the Results dialogs, the categorization (i.e., the breakdown into subsets of cases) based on the grouping variables uses the grouping codes (e.g., MALE, FEMALE) used in the current analysis (e.g., ANOVA or Breakdowns).  If no grouping codes are used in the analysis, the program will ask for the codes before the graph is produced.

One-way categorized histograms are available directly from all Scrollsheet and spreadsheets by using the Quick Stats Graphs option (see Spreadsheet and Scrollsheet Quick Stats Graphs - Scatterplot by...).

A wide variety of categorized scatterplots are also available from the Stats Categorized Graphs options (in the pull-down menu Graphs, see Stats Graphs).  These graphs offer a selection of categorization methods (including user-defined intervals, multiple subsets defined by logical expressions, and others).  For a general overview of the graphics facilities in STATISTICA, see Graphics (Overview).

In order to produce a scatterplot matrix for each of the selected groups in the grouping variable, see Categorized Scatterplot Matrix.


Categorized Normal Probability Plots

Categorized Probability Plots

This option produces probability plots (see below for a description of each type of probability plot) for each category of the grouping variable(s).  One or two grouping variables can be represented on one graph (i.e., a graph may represent a one-way or two-way categorization of cases).  If two grouping variables are selected, a "crosstabulation of graphs" is produced.

In the categorized probability plots called from the Results dialogs, the categorization (i.e., the breakdown into subsets of cases) based on the grouping variables uses the grouping codes (e.g., MALE, FEMALE) used in the current analysis (e.g., ANOVA or Breakdowns).  If no grouping codes are used in the analysis, the program will ask for the codes before the graph is produced.

•	Categorized Normal Probability plot

•	Categorized Half-Normal Probability plot

•	Categorized Detrended Normal Probability plot

One-way categorized normal probability plots are available directly from all Scrollsheets and spreadsheets by using the Quick Stats Graphs option (see Spreadsheet and Scrollsheet Quick Stats Graphs - Probability Plot by...).  In order to produce normal probability plots of the values in cases (and not variables), use the Block Stats Graphs - Normal Prob. Plots of Rows option from the flying menu, Graphs pull-down menu, or the Graphs Gallery (instead of transposing your data file).  Note that if more than one row is highlighted, then a multiple normal probability plot will be produced.

A wide variety of categorized normal probability plots are also available from the Stats Categorized Graphs options (in the pull-down menu Graphs, see Stats Graphs).  These graphs offer a selection of categorization methods (including user-defined intervals, multiple subsets defined by logical expressions, and others).  For a general overview of the graphics facilities in STATISTICA, see Graphics (Overview).


Categorized Box and Whisker Plots

The categorized box and whisker plot typically will summarize the distribution of a variable broken down (categorized) by some other grouping or independent variable(s), by three components:

(1)	A central line to indicate central tendency or location;

(2)	A box to indicate variability around this central tendency;

(3)	Whiskers around the box to indicate the range of the variable (or another measure of variability).

One, two, or three grouping variables can be represented on one graph (i.e., a graph may represent a one-way, two-way, or three-way categorization of cases).  If two or three grouping variables are selected, a "crosstabulation of graphs" is produced.

In the categorized box and whisker plots called from the Results dialogs, the categorization (i.e., the breakdown into subsets of cases) based on the grouping variables uses the grouping codes (e.g., MALE, FEMALE) used in the current analysis (e.g., ANOVA or Breakdowns).  If no grouping codes are used in the analysis, the program will ask for the codes before the graph is produced.

Usually, you can choose to plot for each categorized variable:

(1)	Medians (central line), quartiles (box), and ranges (whiskers);

(2)	Means, standard errors of the means, and standard deviations;

(3)	Means, standard deviations, and 1.96 times the standard deviations (95% normal confidence interval for individual observations around the mean);

(4)	Means, standard errors of the means, and 1.96 times the standard errors of the means (95% normal confidence interval for means).

One-way categorized box and whisker plots are available directly from all Scrollsheet and spreadsheets by using the Quick Stats Graphs option (see Spreadsheet and Scrollsheet Quick Stats Graphs - Box-Whisker by...).  In order to produce box plots representing the distribution of the values in cases (and not variables), use either the Block Stats Graphs - Box Plot/Means of Rows or Block Stats Graphs - Box Plot/Medians of Rows option from the flying menu, Graphs pull-down menu, or the Graphs Gallery (instead of transposing your data file).

A wide variety of categorized box and whisker plots are also available from the Stats Categorized Graphs options (in the pull-down menu Graphs, see Stats Graphs).  These graphs allow the user to plot multiple dependent variables in one graph, support different graph layout formats, and offer a selection of categorization methods (including user-defined intervals, multiple subsets defined by logical expressions, and others).  For a general overview of the graphics facilities in STATISTICA, see Graphics (Overview).


  Spreadsheet and Scrollsheet Quick Stats Graphs - Scatterplot by...

The Quick Stats Graphs - Scatterplot by option will allow you to plot the values of the currently highlighted variable against the values of another variable.  The scatterplot visualizes a relation between two variables X and Y (e.g., weight and height).  Individual data points are represented in two-dimensional space, where axes represent the variables.  The two coordinates (X and Y) that determine the location of each point correspond to its specific values on the two variables.  (See also, Categorized Scatterplots.)

When you select this option, you will be able to choose between a standard scatterplot (Regular) or a scatterplot with a linear or polynomial regression line fitted to the data (by default with a 95% confidence interval).  Once you have made your selection, the Select Variable dialog will open from which you may select the variable to be plotted against the highlighted variable.

The three types of plots are listed below.

  Regression, 95% Confidence Interval

  Polynomial, 95% Confidence Interval

  Regular

  with Histograms

  with Box Plots

Note that you can produce a matrix of scatterplots (representing the correlations between the variables that you select) when you choose the Matrix Scatterplot option.  Many other types of Scatterplots are available via STATISTICA's Stats Graphs (see the Graphs pull-down menu or Graphs Gallery).  For a general overview of the graphics facilities in STATISTICA, see Graphics (Overview).

In order to produce a scatterplot matrix for each of the selected groups in the grouping variable, see Categorized Scatterplot Matrix.


  Spreadsheet and Scrollsheet Quick Stats Graphs Scatterplot by... - with Histograms

Choose this option in order to create a compound graph containing a regular scatterplot of the variables with frequency distribution histograms for each variable displayed along the X- and Y-axis of the scatterplot, respectively.  Each component graph in this compound graph can be edited by double-clicking it.

Note that the categorization methods used in the histograms, the layout of the display and other features of the graph can be customized if this graph is selected from the Stats Graphs menu (see the Graphs pull-down menu or Graphs Gallery).


  Spreadsheet and Scrollsheet Quick Stats Graphs Scatterplot by... - with Box Plots

Choose this option in order to create a compound graph containing a regular scatterplot of the variables with box plots for each variable displayed along the X- and Y-axis of the scatterplot, respectively.  Each component graph in this compound graph can be edited by double-clicking it.  This graph is particularly useful as an aid in deciding if particular data points in a scatterplot meet a user-specified criterion of being an extreme value or outlier (see Outliers and Extremes).

Note that the measures of central tendency and variability used in the box plots, the layout of the display and other features of the graph can be customized if this graph is selected from the Stats Graphs menu (see the Graphs pull-down menu or Graphs Gallery).


  Spreadsheet and Scrollsheet Quick Stats Graphs Scatterplot by... - Regression, 95% CI

Choose this option when you want a scatterplot with a linear regression line fitted to the data and a 95% confidence interval for that line (the probability value for the confidence interval can be adjusted in the Plot Layout dialog accessible from within the graph).


  Spreadsheet and Scrollsheet Quick Stats Graphs Scatterplot by... - Polynomial, 95% CI

This option will produce a scatterplot with a polynomial fit (by default, of the 5th degree) to the data and a 95% confidence interval for that line (the probability value for the confidence interval and other functions to be fitted can be requested in the Plot Layout dialog accessible from within the graph).  The order of the fitted polynomial function can be changed in the Fitting Options dialog (accessible by clicking on the Fit Options button in the Plot Layout dialog).


  Spreadsheet and Scrollsheet Quick Stats Graphs Scatterplot by... - Regular

When you select this option, a regular scatterplot of the two variables will be produced, without a regression line.


  Spreadsheet and Scrollsheet Quick Stats Graphs - 2D Histogram by...

This Quick Stats Graphs option offers an extension of the regular Histogram option, allowing you to examine the distribution of values of the currently highlighted variable broken down (categorized) by some other grouping or independent variable (see also, Categorized Histograms).  For example, you may want to break down the distribution of test scores by the sex of the students.

In some Scrollsheets, the selection of the grouping variable is pre-determined by some global grouping variable (i.e., the grouping variable designated in an analysis dialog).  When this is the case, STATISTICA will incorporate the (pre-determined) grouping variable name in the appropriate Scrollsheet Quick Stats Graphs option (e.g., 2D Histogram by Gender).  In most other cases, STATISTICA will prompt you to select the grouping variable via the Select Variable dialog.

When you are prompted to select a grouping variable that will be used to categorize the values of the currently highlighted variable, the Select Variable dialog will open.  Once you have selected the grouping variable from this dialog, another dialog will open (Codes dialog) prompting you to enter the values (codes) for the previously specified grouping variable (if you leave the list of codes empty, all distinctive values of the grouping variable will automatically be used).  After the codes have been entered, a plot displaying separate histograms for each category of the grouping variable will be produced.

Many other types of histograms are available in STATISTICA's Stats Graphs accessible from the pull-down menu Graphs.  For a general overview of the graphics facilities in STATISTICA, see Graphics (Overview).

Note:  In order to visualize frequency distributions of values in cases (and not variables), use the Block Stats Graphs - Histograms of Rows option from the flying menu, Graphs pull-down menu, or the Graphs Gallery (instead of transposing your data file).


Spreadsheet and Scrollsheet Quick Stats Graphs-3D Histogram by

  Spreadsheet and Scrollsheet Quick Stats Graphs - 3D Histogram by...

Plot one of four bivariate (3-dimensional) histograms when you select this Quick Stats Graphs option.  In many Scrollsheets, (e.g., correlation matrices and other "matrix" tables) the selection of the second variable is determined by the currently highlighted position on the Scrollsheet.  In other cases however, as in the 2D Histograms, when you choose one of these plots (described below), the Select Single Variable will open in which you will need to select a variable to be plotted with the currently highlighted variable.  The types of 3D histograms available from this option are based on the types of data that you could have (continuous or discrete) in your data file.  Both variables will be divided into categories for this plot.  When a selected variable is categorical (usually 10 or less categories), STATISTICA will use those categories as the histogram intervals for that variable.  If a variable has either more than 10 categories or its values are non-integers (continuous), then STATISTICA will divide the values into about 10 to 12 intervals based on the range of the values.  A brief description of each histogram is as follows.

  Continuous by Continuous

  Discrete by Discrete

  Continuous by Discrete

  Discrete by Continuous

Many other types of 3D histograms are available in STATISTICA's Stats Graphs accessible from the pull-down menu Graphs.  For a general overview of the graphics facilities in STATISTICA, see Graphics (Overview).


Spreadsheet and Scrollsheet Quick Stats Graphs 3D Histogram by - Continuous by Continuous

  Spreadsheet and Scrollsheet Quick Stats Graphs 3D Histogram by... - Continuous by Continuous

Choose this option if both currently highlighted variables are continuous and/or you want STATISTICA to perform an automatic categorization.  Each variable's values will be categorized according to the automatic categorization conventions.


Spreadsheet and Scrollsheet Quick Stats Graphs 3D Histogram by - Discrete by Discrete

  Spreadsheet and Scrollsheet Quick Stats Graphs 3D Histogram by... - Discrete by Discrete

When you have highlighted a discrete variable in the spreadsheet or Scrollsheet and you want to plot another discrete variable on the second axis of the bivariate histogram, choose this option.  After you have selected the second variable, the Select Codes dialog will open in which you will designate the codes for each variable.  (Click on the OK button to accept all of the codes for both variables.)


Spreadsheet and Scrollsheet Quick Stats Graphs 3D Histogram by - Continuous by Discrete

  Spreadsheet and Scrollsheet Quick Stats Graphs 3D Histogram by... - Continuous by Discrete

This option will allow you to plot a continuous (or to be categorized automatically) variable (the currently highlighted variable) against a discrete variable.  The values of the first variable will be categorized according to the STATISTICA conventions, however, you will be given the option to specify the codes for the discrete variable in the Select Codes dialog.


Spreadsheet and Scrollsheet Quick Stats Graphs 3D Histogram by - Discrete by Continuous

  Spreadsheet and Scrollsheet Quick Stats Graphs 3D Histogram by... - Discrete by Continuous

This option is similar to the Continuous by Discrete option, except that the first (highlighted) variable in the spreadsheet or Scrollsheet is the discrete (or to be manually categorized) variable.  Once again, STATISTICA will categorize the values of the continuous variable that you have selected in the Select Single Variable dialog, and the Select Codes dialog will allow you to specify the codes for the discrete variable.


  Spreadsheet and Scrollsheet Quick Stats Graphs - Box-Whisker by...

Choose one of four types of Quick Stats Graphs box plots to represent the distribution of categorized values of the currently highlighted variable.  The box plots resulting from this option represent the currently highlighted variable's central tendency and variability for each category of the grouping variable.  As measures of central tendency, you can choose between plotting the means and medians of the values in each category and for each, their respective measures of variability; standard deviations or standard errors, and ranges (other options are available via STATISTICA's Stats Graphs; see also, Categorized Box and Whisker Plots).

In some Scrollsheets, the selection of the grouping variable is pre-determined by some global grouping variable (i.e., the grouping variable designated in an analysis dialog).  When this is the case, STATISTICA will incorporate the (pre-determined) grouping variable name in the appropriate Scrollsheet Quick Stats Graphs option (e.g., Box-Whisker by Gender).  In most other cases, STATISTICA will prompt you to select the grouping variable via the Select Variable dialog.

When you are prompted to select a grouping variable that will be used to categorize the values of the currently highlighted variable, the Select Variable dialog will open.  Once you have selected the grouping variable from this dialog, another dialog will open (Codes dialog) prompting you to enter the values (codes) for the previously-specified grouping variable (if you leave the list of codes empty, all distinctive values of the grouping variable will automatically be used).  After the codes have been entered, a plot displaying separate box and whisker plots for each category of the grouping variable will be produced.

  Median/Quart./Range

  Mean/SE/SD

  Mean/SD/1.96*SD

  Mean/SE/1.96*SE

Many other types of box and whisker plots and other range and variability graphs are available via STATISTICA's Stats Graphs.  In order to produce box plots representing the distribution of the values in cases (and not variables), use either the Block Stats Graphs - Box Plot/Means of Rows or Block Stats Graphs - Box Plot/Medians of Rows option from the flying menu, Graphs pull-down menu, or the Graphs Gallery (instead of transposing your data file).  For a general overview of the graphics facilities in STATISTICA, see Graphics (Overview).

Hint:  In box and whisker graphs, you can change the small box used to represent the central tendency (mean or median) to a horizontal line by changing this plot type to Min-Max X and adjusting the Bar Type line width (by default 0, for box and whisker graphs) in the appropriate Plot Layout dialog.  To call up the appropriate Plot Layout dialog, double-click on the plot legend symbol for the mean (or median).


Spreadsheet and Scrollsheet Quick Stats Graphs Box-Whisker by... - Mean/Quart./Range

  Spreadsheet and Scrollsheet Quick Stats Graphs Box-Whisker by... - Median/Quart./Range

This box plot describes the central tendency of each category of the variable in terms of the median of the values in the category (represented by the smallest box in the plot).  The spread (variability) in each category's values are represented in this plot by the quartiles (the 25th and 75th percentiles, larger box in the plot) and the minimum and maximum values of the variable (the "whiskers" in the plot).


  Spreadsheet and Scrollsheet Quick Stats Graphs Box-Whisker by... - Mean/SD/SE

Here, the smallest box in the plot represents the mean (central tendency) of the category values, while the dispersion (variability) is represented by ± 1 times the standard error (large box) and ± 1 times the standard deviation about the mean ("whiskers").


  Spreadsheet and Scrollsheet Quick Stats Graphs Box-Whisker by... - Mean/SD/1.96*SD

This plot will show the mean (small box in the plot) of a category surrounded by a larger box (± 1 times the standard deviation).  If the distribution is normal, then the "whiskers" in this plot represent a "95% confidence interval" defined as the category mean ± 1.96 times the category standard deviation.


  Spreadsheet and Scrollsheet Quick Stats Graphs Box-Whisker by... - Mean/SE/1.96*SE

Once again, this plot will show the mean (small box in the plot) of the category surrounded by a larger box.  However, in this plot, the larger box represents ± 1 times the standard error.  If the distribution is normal, then the "whiskers" in this plot represent a "95% confidence interval" defined as the category mean ± 1.96 times the category standard error.


  Spreadsheet and Scrollsheet Quick Stats Graphs - Probability Plot by...

These Quick Stats Graphs plots visualize the normality of the distribution of the currently highlighted variable.  The assumption of normality (the data follow a normal distribution) is a very important assumption in statistics (see Elementary Concepts), and normal probability plots are often used to visually verify this assumption.  When you select this option, you can choose from three different types of normal probability plots to examine the normality of values of a variable as categorized by a grouping variable (see also, Categorized Normal Probability Plots).

In some Scrollsheets the selection of the grouping variable is pre-determined by some global grouping variable (i.e., the grouping variable designated in an analysis dialog).  When this is the case, STATISTICA will incorporate the (pre-determined) grouping variable name in the appropriate Scrollsheet Quick Stats Graphs option (e.g., Probability Plot by Gender).  In most other cases, STATISTICA will prompt you to select the grouping variable via the Select Variable dialog.

When you are prompted to select a grouping variable that will be used to categorize the values of the currently highlighted variable, the Select Variable dialog will open.  Once you have selected the grouping variable from this dialog, another dialog will open (Codes dialog) prompting you to enter the values (codes) for the previously-specified grouping variable (if you leave the list of codes empty, all distinctive values of the grouping variable will automatically be used).  After the codes have been entered, a plot displaying separate probability plots for each category of the grouping variable will be produced.

  Normal Probability plot:  This option produces standard normal probability plots for each category of the currently highlighted variable.  For more information on how the standard normal probability plot is constructed, see Normal Probability Plots.

  Half-Normal Probability plot:  For more information on how the half-normal probability plot is constructed, see Half-Normal Probability Plots.

  Detrended Normal Probability plot:  For more information on how the detrended normal probability plot is constructed, see Detrended Normal Probability Plots.

Many other types of probability plots are available in STATISTICA's Stats Graphs accessible from the pull-down menu Graphs.  In order to produce normal probability plots of the values in cases (and not variables), use the Block Stats Graphs - Normal Prob. Plots of Rows option from the flying menu, Graphs pull-down menu, or the Graphs Gallery (instead of transposing your data file).  Note that if more than one row is highlighted, then a multiple normal probability plot will be produced.  For a general overview of the graphics facilities in STATISTICA, see Graphics (Overview).


  Spreadsheet and Scrollsheet Quick Stats Graphs - Matrix Scatterplot...

Select this Quick Stats Graphs option to produce a visual (scatterplot) representation of the correlations between several variables in a matrix format.  In Matrix Scatterplot, one or two lists of variables can be selected in the Select Variables for Matrix dialog, and one scatterplot is generated for each pair of variables.  If you select all of the variables in only the first list, then a square matrix of scatterplots is produced.  You can generate a rectangular matrix of scatterplots by selecting only specific variables in the first list and then a different set of variables in the second list.

When you select the Matrix Scatterplot option, you can choose between two methods of missing data (MD) deletion.  If you select Casewise MD Deletion, then when the scatterplots are generated, the cases that have missing data in at least one of the selected variables, will be excluded from each scatterplot.  With this type of missing data deletion, all scatterplots will be based on the same set of observations.  However, you could easily end up with no "valid" cases if the missing data are randomly distributed across cases, because each of them might have at least one missing data value for one of the selected variables.  If you select Pairwise MD Deletion, then each individual scatterplot in the matrix will be based on cases that have valid data for that pair of variables.

Many other types of matrix plots are available in STATISTICA's Stats Graphs accessible from the pull-down menu Graphs.  For a general overview of the graphics facilities in STATISTICA, see Graphics (Overview).

In order to produce a scatterplot matrix for each of the selected groups in the grouping variable, see Categorized Scatterplot Matrix.


Spreadsheet Options Menu

Selection Conditions	Macro

Weight	Command Langage (SCL)

General	STATISTICA BASIC

Display	Quick Open File

Print	Keyboard Macro

Stats Graphs	Recorded Show Macro

User Graphs	Customize Auto Task Buttons


Scrollsheet Options Menu

General	Stats Graphs

Display	User Graphs

Print

Macro

Command Langage (SCL)	Keyboard Macro

STATISTICA BASIC	Recorded Show Macro

Quick Open File	Customize Auto Task Buttons


STATISTICA Defaults:  General

You can customize the general display and operation of STATISTICA by selecting (or de-selecting) several options offered in the General Options dialog.  The selections that you make here will then be used as the default operating conditions whenever you open STATISTICA.

General Options dialog:

STATISTICA Startup Options

Queues of Windows

Graph Data Links (Auto-Update)

Workbook

Recently Used File List

Auto-move in Spreadsheet after Enter

Editing Text Values

Drag-and-Drop

Multitasking Mode (yield to windows while processing)

Ask Before Closing a Modified Scrollsheet

Module Switching:  Single Application Mode

Percentiles


STATISTICA Defaults:  General - Editing Text Values

Overwrite text values:  When this option is de-selected, then when you enter a new text value over an existing one, a new numeric equivalent will be assigned to the new text value; that is, the entry of a new text value will not affect other text values for this variable (the associations between text and numeric values will not change for the current variable).  This is the default data entry mode.

When this option is selected, then when a new text value is entered over an existing one, the newly entered text value will replace the existing text value in the table of relations (assignments) between text and numeric values, and the existing numeric equivalent (i.e., numeric value in the current cell) will be reassigned to the new text value.  This will cause all cells of the current variable which contain the original text value to be overwritten by the new text value.

Note that this "double-notation" of values can be managed in the Text Values Manager dialog.  See also Spreadsheet View Text and Numeric Values and Value Labels.

Overwrite value labels:  When this option is selected, then when a new value label is entered over an existing value lable (when the spreadsheet is in Value Label display, see Spreadsheet View Text and Numeric Values and Value Labels), the new label will replace the existing one and the text value and numeric equivalent will remain the same as before.  This is the default mode, where value labels are treated as "comments" assigned to values (see also the next paragraph).

When this option is de-selected, then when a new value label is entered over an existing one, STATISTICA will first try to match it with an existing value label (for the current variable).  If there is a match, then that text value and numeric equivalent will be used.  If there is no match, then a new text value will be generated from the first 8 characters and a new numeric value will be assigned to this text value (in either case, the numeric value for the cell, and the text value associated with it will change).  Note that if the resulting text value is not unique, then a number will be placed at the end to make it unique (e.g., state2).  This is a non-default mode, where value labels are treated as "extensions of values" and not merely as "comments" assigned to values.


STATISTICA Defaults:  General - Percentiles

This option allows you to select from among six methods for computing percentile values, including medians (50th percentile) and quartiles (25th and 75th percentiles).  The method that you select here will apply to every place in the STATISTICA program where medians, quartiles, or percentiles are computed, for example, to the computation of:

•	percentiles in the Nonparametrics & Distributions module;

•	medians and quartiles in the Basic Statistics module;

•	medians and quartiles in 2D Box Plots;

•	medians and quartiles in box-whisker plots in Reproducibility and Repeatability studies;

•	medians and quartiles in box-whisker plots in Discriminant Analysis, Reliability and Item Analysis, Basic Statistics, Multiple Regression, and all other modules of STATISTICA that offer box-whisker plots as an option from the dialog.

For the following methods, let n be the number of cases, and p be the percentile value divided by 100 (e.g., 50/100 = .5 for the median).  Then, the available choices for computing percentiles are:

Weighted average at Xnp method.  (Weighted average centered at Xnp).  Express np (n times p) as np=j+g where j is the integer part of np, and g is the fractional part of np; then compute:

PercentileValue = (1-g)x + gx

                        j    j+1

Note that X0 in the above computation is replaced by X1 (e.g., if j = 0, then the above formula would be (1-g)x1 + gx(0+1) ).

Example

Weighted average at X(n+1)p method.  (Weighted average centered at X(n+1)p).  Express (n+1)p as (n+1)p=j+g where j is the integer part of (n+1)p, and g is the fractional part of (n+1)p; then compute:

PercentileValue = (1-g)x + gx

                        j    j+1

Note that Xn+1 in the above computation is replaced by Xn (e.g., if j = n, then the above formula would be (1-g)xn + gxn ).

Example

Empirical distribution function method.  Express np (n times p) as np=j+g where j is the integer part of np, and g is the fractional part of np; then choose the percentile value as:

PercentileValue = x                if g=0

                   j

PercentileValue = x                if g>0

                   j+1

Example

Empirical distribution function with averaging method.  Express np (n times p) as np=j+g where j is the integer part of np, and g is the fractional part of np; then compute the percentile value as:

PercentileValue = (x  + x   )/2    if g=0

                    j    j+1

PercentileValue = x                if g>0

                   j+1

Example

Empirical distribution function with interpolation (MS Excel) method.  Express (n-1)p ((n-1) times p) as (n-1)p=j+g where j is the integer part of (n-1)p, and g is the fractional part of (n-1)p; then compute the percentile value as:

PercentileValue = x                       if g=0

                   j+1

PercentileValue = x    + g(x   - x   )    if g>0

                   j+1      j+2   j+1

Example

Closest observation method.  (Observation closest to np) Compute j as the integer part of np+1/2, then compute:

PercentileValue = x

                   j

Example


Example of Weighted Average at Xnp Percentile Method

To illustrate this method of computing percentiles, consider the following sorted data:

1, 2, 4, 7, 8, 9, 10, 12, 13

Here, n = 9 and let p = .25 (the 25th percentile).  Express np (n times p) as:

np = 9*.25 = 2.25 = j + g

therefore, j = 2 and g = .25.  Now compute the 25th percentile as:

25th Percentile = (1-.25)x + .25x

                          2      3

                = (.75)2 + (.25)4

                = 2.5


Example of Weighted average at X(n+1)p Percentile Method

To illustrate this method of computing percentiles, consider the following sorted data:

1, 2, 4, 7, 8, 9, 10, 12, 13

Here, n = 9 and let p = .25 (the 25th percentile).  Express (n+1)p as:

(n+1)p = 10*.25 = 2.5 = j + g

therefore, j = 2 and g = .5.  Now compute the 25th percentile as:

25th Percentile = (1-.5)x + .5x

                         2     3

                = (.5)2 + (.5)4

                = 3.0


Example of Empirical Distribution Function Percentile Method

To illustrate this method of computing percentiles, consider the following sorted data:

1, 2, 4, 7, 8, 9, 10, 12, 13

Here, n = 9 and let p = .25 (the 25th percentile).  Express np (n times p) as:

np = 9*.25 = 2.25 = j + g

therefore, j = 2 and g = .25.  Now, since g>0, compute the 25th percentile as:

25th Percentile = x

                   3

                = 4.0


Example of Empirical Distribution Function with Averaging Percentile Method

To illustrate this method of computing percentiles, consider the following sorted data:

1, 2, 4, 7, 8, 9, 10, 12, 13

Here, n = 9 and let p = .25 (the 25th percentile).  Express np (n times p) as:

np = 9*.25 = 2.25 = j + g

therefore, j = 2 and g = .25.  Now, since g>0, compute the 25th percentile as:

25th Percentile = x

                   3

                = 4.0


Example of Empirical Distribution Function with Interpolation (Excel) Percentile Method
Example of Empirical Distribution Function with Interpolation (MS Excel) Percentile Method

To illustrate this method of computing percentiles, consider the following sorted data:

1, 2, 4, 7, 8, 9, 10, 12, 13

Here, n = 9 and let p = .25 (the 25th percentile).  Express (n-1)p as:

(n-1)p = 8*.25 = 2.0 = j + g

therefore, j = 2 and g = 0.  Now, since g=0, compute the 25th percentile as:

25th Percentile = x

                   3

                = 4.0


Example of Closest Observation Percentile Method

To illustrate this method of computing percentiles, consider the following sorted data:

1, 2, 4, 7, 8, 9, 10, 12, 13

Here, n = 9 and let p = .25 (the 25th percentile).  Express np as:

np + 1/2 = (9*.25) + .5 = 2.75 = j + g

therefore, j = 2.  Now, compute the 25th percentile as:

25th Percentile = x

                   2

                = 2.0


STATISTICA Defaults:  General - Startup Options

The following options will be implemented at startup of a STATISTICA module.

Maximize STATISTICA Window:  Select this option if you want the STATISTICA window to be maximized at startup.  When this option is de-selected, STATISTICA will be run in windowed mode.

Display Startup Panel:  Select this option if you want the STATISTICA module Startup Panel to be displayed whenever the module is opened.  If this option is de-selected, then the Startup Panel will not be displayed upon entry into a module (but will be accessible, as usual, via the Startup Panel option of the Analysis pull-down menu or via the keyboard shortcut CTRL+T).  Note that suppressing the Startup Panel will have only visual and not functional consequences, as it is a modeless dialog box and clicking anywhere outside the panel will automatically iconize it.

Open Text/output Window:  Select this option if you want the Text/output Window to automatically come up whenever a STATISTICA module opens.


STATISTICA Defaults:  General - Queues of Windows

In STATISTICA, Scrollsheets and graphs are automatically managed in separate "queues" on a "first in-first out" basis.  You can change the depth of each queue here, or in the Window Manager dialog.  Specify a number between 0 and 20; however if you specify 0, you will "turn off" the queue mechanism and the size of the queue will be unlimited (then you will need to close windows manually to avoid cluttering the screen and exhausting the memory resources of the computer).

Number of Scrollsheets:  Specify here the maximum number of unlocked Scrollsheets to keep on screen.  (See the Window Manager dialog for more information on locking and unlocking Scrollsheets.)

Number of Graphs:  Specify here the maximum number of unlocked graphs to keep on screen.  (See the Window Manager dialog for more information on locking and unlocking graphs.)


STATISTICA Defaults:  General - Auto-Move in Spreadsheet after Enter

When you enter or edit data in the spreadsheet, this option will allow you to control the movement of the cursor after you press on the ENTER key.  You can choose to have the cursor move down to the next cell in the column (or to the top of the next column if you are in the last cell in the column), move right to the next cell in the row (or to the beginning of the next row if you are in the last cell of the row), or off (the cursor does not move after you hit ENTER).


STATISTICA Defaults:  General - Multitasking Mode

Selecting this option will allow you to switch between Windows applications or different STATISTICA modules (use the CTRL+ESC keys to bring up the Task List dialog, or ALT+TAB to toggle between applications) whenever STATISTICA is processing data.  If you are processing a large data file that may require some time, then this option will free you to use another program while you are waiting.  However, if this option is de-selected, then the data may be processed somewhat faster.  Note that when STATISTICA is not processing data, you will always be able to switch between Windows applications or different STATISTICA modules.  Note also that when this option is disabled, you will not be able to interrupt redrawing of graphs by clicking the mouse or pressing a key.


STATISTICA Defaults:  General - Ask Before Closing a Modified Scrollsheet

Select this option if you want a warning message to appear each time you close a modified Scrollsheet.  This message will also give you an opportunity to save the modified Scrollsheet (under the filename extension *.scr) before closing it.  If this option is de-selected, then the warning will not appear whenever you close a modified Scrollsheet.


STATISTICA Defaults:  General - Module Switching

When you select this option (choose Single Application mode), then switching between modules (by double-clicking on a new module name in the Module Switcher) during a STATISTICA session will not open new application windows.  Each new module will be opened into the same window, replacing the module used before.  If this option is de-selected (Multiple Module Application Windows mode), then you will be able to switch between STATISTICA modules (using the Module Switcher) without closing the previous ones.  Note that in the Multiple Module mode, you can also switch in the Single Application manner if you press the End & Switch To button on the Module Switcher (instead of double-clicking on the module name).


STATISTICA Defaults:  General - Graph Data Links (Auto Update)

When you create either a Stats Graph, Quick Stats Graph, Block Stats Graph, or Custom Graph from a spreadsheet, the spreadsheet data may remain linked with the graph data in the Graph Data Editor.  When the data are linked, you can make changes to the spreadsheet data and the respective graph(s) will automatically be updated to reflect those changes.

These options control the default settings for links between graphs of respective categories and their data sets.  The four settings: Auto, Manual, Locked, and No link correspond to the options controlled (for individual graphs) in the Graph Data Links - Update dialog.

Stats/Quick Stats Graphs:  Select this option to set the default data link status for Stats Graphs and Quick Stats Graphs.

Custom/Block Stats Graphs:  Select this option to set the default data link status for Custom Graphs and Block Stats Graphs.

QC Graphs:  Select this option to set the default data link status for Quality Control charts.

Note that embedded graphs (e.g., Scatterplots w/Histograms, Scatterplots w/Box Plots, embedded graphs created with the Multiple-Graph AutoLayout Wizard, or compound graphs created in the Quality Control module) can also be updated automatically.

You can manage links between the spreadsheet and current Stats, Quick Stats, Block Stats, Custom, or Quality Control graphs or embedded graphs, in the Graph Data Links dialog (accessible from the graph window Graphs pull-down menu); for example, links can be temporarily disabled to allow for extensive data editing without interuption by updating all graphs after every edit action.

See also Dynamic Graph Data Links - Overview.


STATISTICA Defaults:  General - Workbook

The following options allow you to control STATISTICA's Workbook facility.  For more information on the Workbook facility and its options, see Data File Header, Notes, and Workbook Info.

Disable Workbook Facility:  The Workbook facility maintains a log of supplementary files for the current data file and offers several options for managing those files.  When this option is selected, the Workbook facility will be disabled.  See When the Workbook Facility should be Disabled.

Inhibit Auto-Open of Workbook Files:  The Workbook facility allows you to select up to 9 supplementary files to open automatically whenever the associated data file is opened (see Data File Header, Notes, and Workbook Info).  When you select this option, the Auto [image] option will be inhibited and no supplementary files will open when the data file is opened.

Save Workbook Changes without Asking:  When the current data file is saved, all Workbook changes are automatically saved along with it.  However, if you close a data file without saving it, the program will either prompt you to save the Workbook changes (deselect this option) or it will automatically save the Workbook changes without prompting you (select this option), depending on the current setting of this option.  The manual confirmation of saving Workbook changes can be useful when the data set is extremely large (and thus saving it is time consuming); see also When the Workbook Facility should be Disabled.


STATISTICA Defaults:  General - Recently Used File List

Specify here the number (up to 16) of recently used files that will be displayed in the File pull-down menu.


STATISTICA Defaults:  General - Drag-and-Drop

The following options allow you to control STATISTICA's Drag-and-Drop facility.

Disable All Drag-and-Drop Functions:  When selected, this option will disable all Drag-and-Drop functions in the spreadsheet and Scrollsheet.  You will still be able to edit spreadsheets and Scrollsheets using the standard editing features for cases and variables from the Edit pull-down menu, however, you will not be able to use any of the block operations specific to the Drag-and-Drop facility.

Default Action (without Control Key):  The mode that you select here determines the default function of the Drag-and Drop facility.

Move (Delete Original):  If you select this mode, then when the block is selected and you drag it to a different location in the spreadsheet or Scrollsheet, it will be moved to the new location (i.e., the block will be cut from the original position and pasted into the new position).  In this mode, if you hold down on the CTRL key while dragging the block, the block will be copied to the new location.  (This is the standard Excel-style of the Drag-and-Drop facility.)

Copy (Keep Original):  If you select this mode, then when the block is selected and you drag it to a different location in the spreadsheet or Scrollsheet, it will be copied to the new location (i.e., the original block will remain and only a copy will be pasted into the new position).  In this mode, if you hold down on the CTRL key while dragging the block, the block will be moved to the new location.  (This is a non-standard style, however, it often proves to be useful in the management of data-base-format data sets when copying blocks is often a more common operation than moving blocks.)

Ask before inserting rows and columns:  Select this option in order to have STATISTICA prompt you before inserting any rows or columns during a Drag-and-Drop or Block Statistics operation.  The prompt will ask you if you want to insert a specified number of rows/columns and you can click Yes to complete the action or No to cancel it.  When this option is de-selected, the insert action will be completed without any prompt from STATISTICA.


Save Workbook Information

When you save a STATISTICA data file, the Workbook information is automatically saved along with it.  If you open another or close the data file without first saving it, then the Save Workbook Information dialog will open.  The following options are available in this dialog:

Save and don't ask anymore:  This option is analogous to the Save Workbook Changes without Asking option in the STATISTICA Defaults:  General dialog.  When you click on this button, the Workbook changes will be saved for the current file and automatically saved for subsequent files without prompting.  Note that you can change the automatic save status in the STATISTICA Defaults:  General dialog.

Save:  Click on this button to save the Workbook changes for the current STATISTICA data file; the current dialog will reappear the next time you open a data file, access or save any supplementary files, and then attempt to close or exit the data file.

Don't Save:  Click on this button if you do not want to save any of the Workbook changes for the current data file.

Disable Workbook:  Analogous to the Disable Workbook Facility option in the STATISTICA Defaults:  General dialog, this option will disable the Workbook facility without saving the Workbook changes.  Note that you can enable/disable the Workbook facility in the STATISTICA Defaults:  General dialog.  See also When the Workbook Facility should be Disabled.

Cancel:  Click on this button to close the dialog and return to the STATISTICA data file.


Drag-and-Drop Overview

STATISTICA spreadsheets support all standard spreadsheet (Excel-style) block Drag-and-Drop operations (copy, move, insert, etc.) and block extension operations, as well as mouse-controlled column width, variable-speed scrolling, split scrolling, etc.  The Drag-and-Drop operations can be disabled by selecting the Disable All Drag-and-Drop Functions option in the STATISTICA Defaults: General dialog.  Scrollsheets support the same Drag-and-Drop facilities except for inserting.

Variable-speed Scrolling

Move/Copy Block

Insert Block

Expanding the data file

Clear Block

Extrapolate (AutoFill)


Drag-and-Drop Overview - Variable-speed Scrolling

You can control the speed at which you scroll when you extend a block outside the current display window.  You can scroll one line at a time by moving the cursor a short distance away from the spreadsheet (or Scrollsheet) when a block is selected or you can scroll one page at a time by moving the cursor further away from the spreadsheet (or Scrollsheet).


Drag-and-Drop Overview - Move/Copy Block

Moving a Block:  You can move a block by pointing to the border of the selection (the cross-cursor will change to an arrow) and dragging it to a new location.

If you hold down the CTRL key while dragging (a "plus" character will appear next to the cursor), then STATISTICA will copy the selected block to the new location.

Copying a Block:  You can copy a block by pointing to the border of the selection (the cross-cursor will change to an arrow) and while holding down the CTRL key, drag it to a new location.

NOTE:  If you perform more copying operations than moving, you can change the default (i.e., without holding down the CTRL key) result of this operation from Move to Copy, by setting the Default Action (without Control Key) option to Copy in the STATISTICA Defaults:  General dialog.


Drag-and-Drop Overview - Insert Block

To insert a block between columns or rows, press SHIFT while dragging the block.

If you point the cursor between rows, an insertion bar will appear between the rows and when you release the mouse button, the block will be inserted between those two rows (creating new case(s)).

If you point the cursor between columns, an insertion bar will appear between the columns and when you release the mouse button, the block will be inserted between those two columns (creating new variable(s)).

The SHIFT key can be used in combination with the CTRL key in order to copy and insert or move and insert (depending on the setting of the Default Action (without Control Key) option in the STATISTICA Defaults:  General dialog.

Note that all Drag-and-Drop with Insert (press the SHIFT key) operations will change the size of the data file (the Insert operation is not available in Scrollsheets); the same is true of simple dragging blocks outside the boundaries of the current data file.  However, dragging (without Insert) within the current data file boundaries produces results identical to using the Clipboard (except that the Clipboard is not used).


Drag-and-Drop Overview - Expanding the Data File

You can use the Drag-and-Drop operations to increase the size of the spreadsheet by moving or copying a block [either all or some of the variable(s) or case(s)] beyond the spreadsheet boundaries.

You can also expand the spreadsheet using the Insert operation.  This operation will insert the block between cases or variables, thereby increasing the size of the spreadsheet.  Note that whether you move, copy, or insert new cases or variables, when the block contains only part of a variable or case, then STATISTICA will fill the remaining values in the variable/case with missing data.

Note:  If your data file is very large (e.g., over 10 megabytes), you may want to set the Ask before inserting rows and columns option in the STATISTICA Defaults:  General dialog so that STATISTICA will ask for confirmation before expanding the data file.


Drag-and-Drop Overview - Clear Block

To clear a block, drag the block Fill Handle (a small solid square located on the lower-right corner of the block) within the selected block.  After highlighting the block, move the cursor to the lower-right corner of the block displaying the Fill Handle.  When it changes to a "plus sign," hold down on the left-mouse-button and drag within the selected block.  As you are dragging, the values within the block will become dimmed.  When you release the left-mouse-button, the dimmed values will be deleted.


Drag-and-Drop Overview - Extrapolate (AutoFill)

A horizontal or vertical series in a block can be extrapolated by dragging the block Fill Handle (a small solid square located on the lower-right corner of the block).  STATISTICA can create series of values such as sequential numbers, linear extrapolations, and dates (e.g., you can extend a series such as 1, 2, 3 to include 4, 5, 6, ...).

You can extrapolate (AutoFill) a block in the following manners:

•	If the initial selection contains repeated values, these values will be duplicated in the extended block.

•	Non-identical values are extended by linear regression to compute extrapolated values for the series.

•	If the block contains the same text values (i.e., all the cells have the text value 'GENDER'), then this text value will be copied into the extended block.  If the block contains several different text values, then the values (beginning with the numeric value of the last text value in the block) will be extended by linear regression to compute extrapolated values for the series.

•	If a variable in the block contains dates (i.e., the variable format is set to Dates in the Current Specs dialog), then based on the pattern of dates, STATISTICA will extrapolate the dates appropriately.

•	If a variable in the block contains text names (i.e., not dates) of months (e.g., JAN, FEB, MAR, ...), days (e.g., MON, TUE, WED, ...), or quarters (e.g., Q1, Q2, ...), then STATISTICA will extrapolate either up, down, or to the left or right of the block, the rest of the names in the series (e.g., APR, MAY, ..., DEC; THR, FRI, SAT, SUN; Q3, Q4, respectively).  The syntax for specifying these names is given below (note that it does not matter whether you use upper case or lower case letters, however you need to be consistent throughout the series; e.g., use Jan, Feb, Mar, ..., not Jan, feb, Mar, ...):

Months:	The names of months can be spelled out, or abbreviated in the following manner (note that the names are limited to 8 characters, therefore, "September" is shortened to "Septembe"):

•	January, February, March, April, May, June, July, August, Septembe, October, November, December

•	Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec

Days:	The names of the days can be spelled out, or abbreviated in the following manner (note that the names are limited to 8 characters, therefore, "Wednesday" is shortened to "Wednesda"):

•	Monday, Tuesday, Wednesda, Thursday, Friday, Saturday, Sunday

•	Mon, Tue, Wed, Thu, Fri, Sat, Sun

•	M, Tu, W, Th, F, Sa, Su

Quarters:	The names of quarters of the year can be specified as follows in the variable:

•	Q1, Q2, Q3, Q4

Extrapolating (AutoFilling) a block upwards or to the left:  In the same manner as extrapolating a block down or right, a block may be extrapolated by dragging the Fill Handle up or to the left past the original start of the block.  NOTE:  If you drag the Fill Handle up or to the left and stop within the original selection without going past the top or left side of the selection, you will delete data within the selection (data to be deleted are indicated in gray as you drag within the selection).

Note that you can use the Fill Block commands on the pop-up menu or Edit pull-down menu to copy to adjacent cells within the currently selected block.


STATISTICA Defaults:  Display

You can customize STATISTICA's window display by selecting (or de-selecting) several options offered in the STATISTICA Defaults:  Display dialog.  The selections that you make here will then be used as the default window display whenever you open STATISTICA.  Note that the color and font settings that you select here will not affect the current spreadsheet or Scrollsheets (use the respective View options instead) but will only affect the configuration used by STATISTICA when creating new spreadsheets (via New Data) or Scrollsheets.

Display Options dialog:

Status Bar

Full Menus

Icons in Menus

Icons in Dialog Boxes

Toolbar Button ToolTips

Auto Task Buttons

3D Dialog Boxes

Toolbars

Fonts

Colors


STATISTICA Defaults:  Display - Toolbar Button ToolTips

When you select this option, the ToolTips (a balloon-style Help for toolbar buttons in STATISTICA) will be displayed when you point to a toolbar button.  If this option is de-selected, then the ToolTips will not be displayed when you point to a toolbar button.


STATISTICA Defaults:  Display - Auto Task Buttons

When you select the Auto Task Buttons option in this dialog (or from the pull-down menu View), the Auto Task Buttons toolbar will (by default) be displayed in the STATISTICA window.  If this option is de-selected, then the Auto Task Buttons toolbar will be hidden.  Note that any Hot Keys assigned to Auto Task Buttons can be used regardless of the display setting of the toolbar.

Keyboard Shortcut:  Press CTRL+M to toggle on/off the Auto Task Buttons toolbar.


STATISTICA Defaults:  Display - Toolbars

This option allows you to select the default way in which to display (or hide) the toolbar in the window.

Large Buttons.  Set this check box in order to display large toolbar buttons; this option is useful when a high-resolution (e.g., 800x600 or 1024x768) is used on a small size monitor.  If this check box is not set, then standard size toolbar buttons will be displayed.

Toolbar display:  Select the desired display style for the toolbar.

Off:  Select this option to temporarily remove the toolbar from the window.  (In order to once again display the toolbar, select one of the options described below.)

1 line:  When you select this option, the toolbar will be displayed in one line in the spreadsheet window.

2 lines:  Select this option to display the toolbar buttons in two lines.

Right & Top:  This option will display half of the toolbar at the top of the window and the other half along the right side of the window.

Left & Top:  This option will display half of the toolbar at the top of the window and the other half along the left side of the window.


STATISTICA Defaults:  Display - Show Status Bar

When you select this option, the window Status Bar (the bar at the bottom of the screen) will be displayed.  If this option is de-selected, then the status bar will be hidden.


STATISTICA Defaults:  Display - Use Full Menus

With this option, you can choose between viewing full menus (when selected, names of options and their respective keyboard shortcuts, if any, will be displayed) or short menus (when de-selected, only the names of options will be displayed) in all pull-down menus.


STATISTICA Defaults:  Display - Display Menus with Icons

Choose to display icons with STATISTICA menu items when you select this option.  If de-selected, then the icons on menus resulting from the right-mouse button option, Toolbar buttons, and pull-down menus will not be displayed (after de-selecting this option, you may need to close the module and reopen it before the pull-down menu icons are removed).


STATISTICA Defaults:  Display - Display Dialog Boxes with Icons

Icons are also used in dialog boxes to help identify what options are available (select this option).  If you prefer, you can remove these icons from the display by de-selecting this option.


STATISTICA Defaults:  Display - 3D Dialog Boxes

By default, dialog boxes in STATISTICA feature 3D effects to improve readability of dialog options.  If you prefer, you can remove the 3D effects by de-selecting this option.


STATISTICA Defaults:  Display - Fonts

You can change the default font of entries in the Scrollsheet, Spreadsheet, Graph Data Editor, or Dialog/Results (the summary section of results dialogs) by clicking on the appropriate button.


STATISTICA Defaults:  Display - Colors

Change the color of spreadsheets, Scrollsheets, and the Graph Data Editor by clicking on the appropriate button to bring up the Customize Color dialog.  You can click on the Dialog/Results button to open the Results Text - Colors dialog in which you can select the colors for the specific results components.


Results Text - Colors

This dialog will allow you to change the colors of specific components of the summary section of results dialogs.  When you click on the appropriate button, a Colors dialog will open in which you can select a color for the Normal text (the text that describes the names of individual fields), the Active text (the text that describes the values of fields), or the Highlighted text (the text color in specialized dialogs such as in Multiple Regression - Results, which is used to indicate significance).  You can view the changes in the dialog Sample box after they are made, but before you exit the dialog.


  Selecting a Weighting Variable

This option will allow you to "adjust" the contribution of individual cases to the outcome of an analysis by "weighting" those cases in proportion to the values of a selected variable.  Selecting this option (either by clicking on the Weight option on the spreadsheet Status Bar, the Weight button on the Startup Panel or an analysis definition menu, or by selecting this option from the Options pull-down dialog) will open the Define Weight dialog in which you can specify the weighting variable.

Some statistical procedures can use fractional weights, and in those cases, specific weighting information will be described in the help windows of those STATISTICA modules.  Unless specified otherwise, the values of the weights are rounded to the nearest integer and used as "multipliers of cases" when the file is processed.

Keyboard Shortcut:  F7

Define Weight dialog:

Weight Variable:  Type in the variable name that you want to be used as the weighting variable or double-click on this variable edit field to open the Select Variable dialog.  The Select Variable dialog will display a list of spreadsheet variables from which you can select the weighting variable.

Status:  The status of this dialog is displayed in the window Status Bar and identifies whether the weighting variable is in use (On) or not (Off).


  Case Selection Conditions

Select this option when you want to include only a subset of cases in an analysis (i.e., use "case filters").  You can access the Case Selection Conditions dialog either by clicking on the Sel option from the Status Bar, clicking on the Select Cases button on the Startup Panel or an analysis definition dialog, or by selecting the Select option from the Options pull-down menu.

Keyboard Shortcut:  F8

Case Selection Conditions dialog:

Edit/Enter Selection Conditions

Examples

Syntax Summary

Header

Status

Variables

Open

Save As

The case selection conditions entered here are used to select cases for analysis, and if saved to a file, they are stored along with their header in a compressed file format.  However, the saved conditions can also be used in (i.e., opened into) all those dialogs where multiple sets of case selection conditions are entered to identify multiple subsets of data (e.g., Recode, Verify Data, and Multiple Subset Graphs).

Note that the case selection conditions are ignored by the spreadsheet formulas; they are also ignored by STATISTICA BASIC unless the SelectionConditions function is used.


  Case Selection Conditions - Enter/Edit Selection Conditions

You can enter new or edit existing logical conditions in the edit window.  The selection conditions that you specify here will determine whether or not a particular case will be included in the analysis (i.e., cases satisfying the logical conditions will be analyzed if the default Include If option is used) or excluded from the analysis (i.e., cases satisfying the logical conditions will be excluded from the analysis when you choose the Exclude If option).


  Case Selection Conditions - Syntax Summary

•	Refer to variables either by their numbers (e.g., v1 = 1) or their names (e.g., Gender = 1); note that you can type variable names in either upper or lower case letters (i.e., 'GENDER' is equivalent to 'gender').

•	Enclose text values of a variable in single quotation marks (e.g., v1 = 'MALE'); note that for selection conditions, you can type text values in either upper or lower case letters (i.e., 'Yes' is equivalent to 'YES').

•	Use parentheses to specify complex logical conditions (see the example above) or change the default precedence of operators.

•	Logical Operators:

 =	(equal)

# , <>, ><	(not equal)

<	(less than)

>	(greater than)

<=	(less than or equal to)

>=	(greater than or equal to)

NOT, ~	(logical NOT)

AND, &	(logical AND)

OR, !	(logical OR)


  Case Selection Conditions - Header

Enter one line (up to 77 characters) of comment about the case selection conditions file here (to be saved along with the conditions).


  Case Selection Conditions - Status

The status of this dialog is displayed in the window Status Bar and identifies whether the case selection condition will affect the processing of data (On) or not (Off).


  Case Selection Conditions - Variables

Click on this button to open the Review Variable dialog from which you can review the variable names.


  Case Selection Conditions - Open

When you click on this button, the Open Selection Conditions Files dialog will open allowing you to open a previously-saved case selection condition file.


  Case Selection Conditions - Save As

Save case selection conditions in a file when you click on this button to bring up the Save Selection Conditions dialog.  Case selection conditions can later be reopened using the Open button.


Case Selection Condition Examples

•	Include if:	v0 <= 50;	this selection condition will include only cases 1 through 50 in the analysis.

•	Include if:	v1 = 1;	this selection condition will include in the analysis only the cases where the value of variable 1 is equal to 1.

•	Include if:	v1 = 'MALE';	you can also use the text values of a variable in case selection conditions.  Note that whenever you use text values, be sure to include them in single quotation marks.

•	Exclude if:	(v1 <= 10) OR (v2 = v3); this condition would exclude from an analysis those cases where the value of v1 was less than or equal to 10 or those cases where the values of v2 equaled v3.


  Data File Header, Notes, and Workbook Info

This dialog allows you to enter a one-line File Header which appears at the top of the spreadsheet, detailed file information or notes about the data set's contents, source, etc., and to manage the Workbook file list, that is, the list of all supplementary files (e.g., graphs, reports, programs) used with the current data set.

Data File Header, Notes, and Workbook Info dialog:

One-line Data File Header

File Information/Notes

Workbook


  Data File Header, Notes, and Workbook Info - One-line Data File Header

Enter one line (up to 77 characters) of comment about the file here.  The One-Line Header is saved as part of the file, displayed in the header section of the data spreadsheet and is printed along with the spreadsheet data file when the File Info/Notes option is selected in the Print Data dialog or along with the output of analyses when either a Short, Medium or Long report style is selected in the Page/Output Setup dialog.  The header is also included in the title area of all Custom Graphs produced from the current data set.


  Data File Header, Notes, and Workbook Info - File Information/Notes

Enter or edit notes about the spreadsheet data file here.  These notes can be up to 512 characters in length and can include any printable characters.  To start a new line in this edit box, press CTRL+ENTER; to enter a tab stop, press CTRL+TAB.

The File Information/Notes are printed along with the spreadsheet data file when the File Info/Notes option is selected in the Print Data dialog.


  Data File Header, Notes, and Workbook Info - Workbook

STATISTICA data set files can be considered to be "Workbooks" of files because they contain lists of all supplementary files related to the data sets.

This area of the Data File Header, Notes, and Workbook Info dialog contains the Workbook management options.  Workbooks help to organize sets of supplementary files (e.g., Scrollsheets, graphs, text/graphics reports, user programs, recodes, etc.) which have been created or used (e.g., reviewed) during the analysis of a data set.  Whenever you open or save a file (e.g., a graph), its name is automatically added to the queue of files in the Workbook file list box.  The length of this queue (by default 32) can be changed; when the queue is full, the oldest files are dropped from the list (unless they are locked, see below) as new files are added.  An updated list of these files is automatically saved with the data file (this option can be changed in the STATISTICA Defaults: General dialog; see also When the Workbook Facility should be Disabled).

The Workbook list of files is also accessible in every Open/Save dialog in STATISTICA, so that you can easily select them (when you are opening a file) or overwrite them (when you are saving a file).

Supplementary files (from the list of Workbook files) can be opened in the following ways:

(1)	Double-click on the desired file name in the list of supplementary files.  The selected file will open behind the Data File Header, Notes, and Workbook Info dialog.

(2)	Select (highlight) one or more files to open in the list box and then click on the Open Files button (in the Data File Header, Notes, and Workbook Info dialog).  The Data File Header, Notes, and Workbook Info dialog will close and the selected file(s) will open in sequence.

(3)	Use the Auto [image] option to select files that will automatically open whenever the current data file is opened (see below).

The Workbook is accessible by double-clicking on the title area of the spreadsheet, by pressing the Workbook [image] toolbar button, or by selecting the Header... option in the pull-down menu Edit.

The Workbook options are described below:

 Lock:  Supplementary files can be locked [image] so that they will not be removed from the Workbook list as the queue is updated or changed.

Auto [image]:  Select [image] up to 9 supplementary files in order to automatically open them when you open the data file (so that all supplementary information, e.g., graphs or reports from a previous stage of the analysis, is available whenever you open the data file).  When this check-box is dimmed, then these files cannot be automatically opened or opened by double-clicking on them in this list (e.g., this applies to foreign data files as well as all non-document files such as axis definition, surface/contour specifications, etc.).

Note that you can cycle through the checkboxes in the Workbook list using the space bar to select (or deselect) files to be locked and/or automatically opened.

Files in the Current Workbook:  A log of all of the supplementary files used with or created from the current data file is given in this area of the dialog.  The queue is managed on a first-in-first-out basis, that is, when the queue is full, the oldest file will be removed from the list as a new file is added (unless the file is locked, see above).  The types of supplementary files listed here include previously saved graphs, Scrollsheets, reports, programs (e.g., STATISTICA BASIC or SCL programs), import/export files, case selection conditions, etc.

Queue Size:  Specify here, the number of files to be maintained in the supplementary files list.  The maximum number of files that can be maintained in this list is 32.  The queue is managed on a first-in-first-out basis, that is, when the queue is full, the oldest file will be removed from the list as a new file is added (unless the file is locked, see above).

Add Files:  Click on this button in order to open a multiple file selection dialog in which you can select one or more previously saved files to add to the supplementary list of files.  You can select the multiple files in this dialog in either a continuous (drag) or discontinuous (press the CTRL key) list.

Remove Files:  Click on this button in order to remove (i.e., delete) highlighted files from the Files in Current Workbook list.

Open Files:  When you click on this button, the files highlighted in the Files in Current Workbook list will be opened sequentially after the Data File Header, Notes, and Workbook Info dialog closes.  To open a file while leaving this dialog open, double-click on the file name in the list.


When the Workbook should be Disabled

  When the Workbook Facility should be Disabled

Normally, the Workbook facility works in an automatic manner which is transparent for the user.  Data files are sometimes saved upon exiting the program (or changing the data file) even if you did not change (edit) the data set so that the Workbook information in the data file can be updated.  However, unless the data set is extremely large, it does not cause any noticeable delay.  The only circumstances when it is recommended to disable the Workbook facility (use the STATISTICA Defaults:  General dialog), is when the data set is extremely large and saving it causes a noticeable delay; then, disabling the Workbook facility will suppress the automatic saving of the data file to update the Workbook list.

See also, STATISTICA Defaults:  General - Workbook.


  Open Text File

Selecting this option will bring up the Open Text File dialog from which you can select a text (file name extension *.txt) or RTF file (file name extension *.rtf) to open in the Text/output Window.


  Save As

Selecting this option will bring up the Save As dialog in which you can save the contents of the Text/output Window as a text file (file name extension *.txt) or in RTF format (file name extension *.rtf).

Shortcut:  F12


  Scrollsheet Columns Toolbar Button

The following options are available from the Columns [image] toolbar button:

Edit Column Specs

Append Columns


  Scrollsheet Rows Toolbar Button

The following options are available from the Rows [image] toolbar button:

Edit Row Name

Append Rows


Scrollsheet File Menu

These options are available from the Scrollsheet File pull-down menu.

Open Scrollsheet

Open Other

New Data

Data File

Graph File

Scrollsheet

Text/Output

STATISTICA BASIC

Command Language (SCL)

Save

Save As

Save As Data

Print/Eject Current Pages

Print

Print Files

Page/Output Setup

Printer Setup

Exit


  Scrollsheet Save

Save a Scrollsheet with this option (file name extension *.scr).  If the current Scrollsheet has not been saved before (i.e., it has no file name yet), then the Save File As dialog will open in which you can specify the file name and disk location in which to save it.  Once the file name and location have been specified, whenever you select Save the Scrollsheet will be automatically saved, overwriting the previous copy of the file.  If you want to change the name or location of the file, select the Save As option.

Keyboard Shortcut:  CTRL+S


Scrollsheet Save As

Save a Scrollsheet with this option.  Every time you select this option, the Save File As dialog will open in which you can specify the file name and disk location for the Scrollsheet.

Keyboard Shortcut:  F12


Scrollsheet Save As Data

Selecting this option will bring up the Save Scrollsheet As dialog, where you can save the contents of the Scrollsheet in spreadsheet (data file) format (files with the file name extension *.sta), thus allowing you to use the contents of the output Scrollsheet as input for an analysis, or to export it to another file format.  When STATISTICA makes a spreadsheet out of a Scrollsheet, it uses the Scrollsheet Row Names column as the spreadsheet Case Names and assigns the Scrollsheet Column Headings as the spreadsheet Variable Names and Long Variable Labels (corresponding to the first and the second line of Scrollsheet column names, respectively).  STATISTICA also uses the Scrollsheet Title as the spreadsheet File Header.


  Scrollsheet Print

Print the active Scrollsheet either to an output file (for later printing, revising, or incorporating into other documents), to the printer (for immediate printing) and/or to the Text/output Window as designated in the Page/Output Setup dialog.  When you select the Print option, the Print Scrollsheet dialog will open.

Keyboard Shortcut:  CTRL+P

Shortcut:  Click on the Print [image] Toolbar button, to bypass the Print Data dialog (i.e., the previously selected settings or the default settings will be used) and print the Scrollsheet.  Note that if a block is selected in the Scrollsheet, then that block will be printed, otherwise, the entire Scrollsheet is printed.

Print Scrollsheet dialog:

Range

Marked Cells

Print/Eject Pages after this Printout

Setup


  Scrollsheet Print - Range

Choose the range of the Scrollsheet to be printed.

All:  Print all of the active Scrollsheet.

Selection:  Print only the highlighted block of cells in the active Scrollsheet.

Column:  Print only the column in which the cursor is located.

Row:  Print only the row in which the cursor is located.

Cell:  Print only the cell in which the cursor is located.


  Scrollsheet Print - Marked Cells

The following options are printing options for marked cells in the Scrollsheet.  Marked cells are cell entries that are manually marked using the Mark Selection option or cell entries that are marked by a STATISTICA analysis (i.e., in the case of a Correlation analysis, significant correlations are marked).

Print All, Identify Marked Cells:  This option will print all of the selected Scrollsheet range (see above) and place an asterisk ( * ) to the right of each marked cell in the printout.

Print All, Ignore Marks:  Print all of the selected Scrollsheet range, but do not identify any of the marked cells.

Print Only Marked Cells:  Prints only the marked cells in the Scrollsheet.  All of the column and row headings will be printed, but the unmarked cells will be empty (i.e., no entries in these cells).

Print All, Identify Marked Column Names:  When there are marked cells in the selected Scrollsheet range, choose this option to mark in the output only the Column Name associated with a marked cell instead of marking each individual cell.

Print All, Identify Marked Row Names:  When there are marked cells in the selected Scrollsheet range, choose this option to mark in the output only the Row Name associated with a marked cell instead of marking each individual cell.


  Scrollsheet Print - Print/Eject Pages after this Printout

When selected, this option will cause the requested printout to automatically be sent to the printer or output file when you click OK in this dialog or when you press the Print button on the toolbar (any other text previously left in the internal buffer will also be printed).  Thus, each requested printout (table) will start on a new page.  If this option is de-selected, then output will be stored in the internal buffer, and sent to the printer depending on the current setting of the check box Automatically Eject Each Filled Page (either whenever there is enough to fill one page or all at once later, e.g., when you exit the module or when you empty the buffer by using the option Print/Eject Current Pages).  Note that this option will only apply locally (temporarily) to the current STATISTICA module and the current session whereas, selecting the Print/Eject Pages after Each Printout option in the Page/Output Setup dialog, will apply globally (permanently).


  Scrollsheet Print - Setup

Click on this button to open the Text Output Printer Setup dialog in which you can select the quality (i.e., resolution) of the printout and the number of copies.


Scrollsheet Edit Menu

These options are available from the Scrollsheet Edit pull-down menu.

Edit Cell	Cut

Column Specs	Copy

Row Name	Copy Raw

Titles	Paste

Info Box	Clear

Append Columns	Screen Catcher

Append Rows


Scrollsheet Append Columns/Rows

The Append Columns and Append Rows options will allow you to add blank columns or rows after the last column or row in the current Scrollsheet.  When you click on the appropriate option from the Scrollsheet Edit pull-down menu, the resulting dialog will ask you to specify the number of columns or rows that you want to add.  Click OK in the dialog to add the specified number of rows or columns to the Scrollsheet.  The new space can be used for notes or information copied from Scrollsheets or other screens.


Scrollsheet Edit Cell

Edit Cell allows you to edit the currently highlighted cell in the Scrollsheet.  After selecting it, this option is dimmed until you have completed editing the cell.

Keyboard Shortcut:  F2, or double-click on the cell.


Scrollsheet Edit Column Specs

Edit the column specifications of the currently highlighted column by selecting the Column Specs option from the Edit pull-down menu (or, alternatively, double-click on the Column Name) to bring up the Scrollsheet Column Specs Dialog.  Each column's specifications are edited separately from the others (with the exception of the Global Width and Margin Width options (see below) which apply to all of the columns in the Scrollsheet).

Keyboard Shortcut:  CTRL+F2

Scrollsheet Column Specs dialog:

First Line

Second Line

Format

Global Width

Margin Width


Scrollsheet Edit Column Specs - First Line

Enter the first line of the column heading here.  The length of each line of the column heading is limited to the current column width (see Global Width below) and can contain any printable characters.  If the second line is empty and the text of the first line is larger than the current column width, then the text will continue to the second line (when displayed in the Scrollsheet) but it will still be edited in this field.


Scrollsheet Edit Column Specs - Second Line

Enter the second line of the column heading here.  Again, the length is limited to the current column width and the column heading can contain any printable characters.


Scrollsheet Edit Column Specs - Format

Format the display of the column values.

Automatic:  This option will automatically line up all of the numbers in the column according to the largest number (whether positive or negative) so that the decimal point is in the same position in every cell in the column.

Optimal:  The column values will not be aligned by the decimal point if this option is selected, but instead each cell will be adjusted separately to be "optimally" displayed.  Based on the Global Width and Margin Width specifications, the column values will fill the width of the column.

Float:  When this option is selected you can specify the number of decimal points for the values in that column.  The minimum number of decimal points is 1 and the maximum number is 15.

Integer:  This option will round off any decimal values to integers.  Specify the width (minimum = 1, maximum = current column width) to define the display of the integer values.


Scrollsheet Edit Column Specs - Global Width

The value entered here (minimum = 1, maximum = 80) determines the width of every column in the Scrollsheet.  (This is a global operation, i.e., whatever value you specify here will be applied to every column in the Scrollsheet.)  This option can also be accessed in the Customize Width dialog.


Scrollsheet Edit Column Specs - Margin Width

The values in each column can have a pre-specified margin on both sides in order to separate the values in one column from those in another.  This option will allow you to specify the width of the margin (minimum = 0, maximum = 10) for every column in the Scrollsheet.  (This is a global operation, i.e., whatever value you specify here will be applied to every column in the Scrollsheet.)  This option can also be accessed in the Customize Width dialog.


Scrollsheet Edit Row Names

Scrollsheet Edit Row Name

You can edit the currently highlighted Scrollsheet Row Name by selecting this option (or double-clicking on the Row Name in the Scrollsheet) to bring up the Scrollsheet Row Name dialog.

Keyboard Shortcut:  ALT+F2

Scrollsheet Row Name dialog

Name:  Enter/edit the Row Name here.  The Row Name can be up to 40 characters in length and can contain any printable characters.

Width:  Enter here a number (minimum = 1, maximum = 40) that will specify (globally) the width of the Row Names in the Scrollsheet.  You can also specify the global width of Row Names in the Customize Width dialog.


Scrollsheet Edit Titles

Edit Scrollsheet titles in the Scrollsheet Titles dialog, accessed either from the Edit pull-down menu or by double-clicking on the title area of the Scrollsheet.

Scrollsheet Titles dialog

Window Title:  By default, the Window Title will contain the name of the analysis performed as well as the data file name.  You can edit those entries here.

First Line:  In addition to the Window Title, you are allowed two more lines of Scrollsheet titles.  Enter the first title (up to 63 printable characters) for the Scrollsheet here.

Second Line:  Enter the second line (up to 63 printable characters) of the Scrollsheet title here.  You do not have to use two lines of titles for the Scrollsheet, however, the area reserved in the Scrollsheet for the titles will not be reduced if only one title line is used.  Note that when the Titles option of the View pull-down menu is unchecked (de-selected), then these two titles will not be displayed in the Scrollsheet.

Alignment:  Choose to Center the First and Second Titles, or Left- or Right-justify them in the Scrollsheet.


Scrollsheet Edit Info Box

The Info Box is an area to the left of the Titles (sometimes temporarily under the Continue button) in the Scrollsheet that can be used to further customize the Scrollsheet.  You can edit entries in the Info Box in the Scrollsheet Info Box dialog.

Scrollsheet Info Box dialog:

Enter the first of 4 lines of Scrollsheet information here.  Each of the 4 line entries can only be as long as the current row width (as specified in the Row Name Width dialog.

Line 1:  By default, STATISTICA records the statistics module that you are in on this line and continues it (if necessary) in Line 2.

Line 2:  This line is, by default, a continuation of the module name from Line 1.  Note that if the Scrollsheet title is suppressed (i.e., Titles is de-selected in the View pull-down menu), then Lines 1 and 2 are not displayed in the Info Box.

Line 3:  By default, this line is blank.

Line 4:  This last line is reserved (by default) for the Row Names heading:  e.g., Variables.

You may edit the text in each of the 4 lines.


Coordinating the Text/output Window (and file) Output from Multiple Modules

When the same text editor window (e.g., a Text/output Window or an SCL or STATISTICA BASIC program) is open in more than one module at the same time and you modify and save the contents of the window in one module, those changes will automatically be modified in the other module.  The following situations could also occur:

Reopen a file saved in another module

Save a modified file before opening it in another module


Text/output Window - Overview

When you select this option from the View pull-down menu, the Text/output Window will open.  All printed output (see Printing) will be directed to this window (regardless of whether or not you are also printing to the printer or disk file).  If you set any of the Auto Report options (e.g., Automatically Print All Scrollsheets), then the respective output (e.g., graphs or contents of each Scrollsheet displayed on the screen) will also be automatically directed to the Text/output Window.  You can also open the Text/output Window by selecting the Window option in the Page/Output Setup dialog.  Note that opening this window by either method will result in the printer output from analyses being sent to this window as well as optionally to the printer or file (whichever you choose in the Page/Output Setup dialog).

You can edit the text in this window as well as paste some additional information there [formatted (RTF) text and graphics either from STATISTICA or other Windows applications] using the standard Copy and Paste operations.  When running multiple analyses, any "new" results will be appended to the previous analysis results, producing a continuous log of the results of analyses. If you want to permanently store the text and/or graphs from the Text/output Window (including your notes or inserts pasted to the window), then use the Save As option.  You can also use the Text/output Window as a "notepad" (see Text/output Window) in order to maintain records or notes.

When the Text/output Window is open and active, it will have its own Toolbar and pull-down menus (see Text/output Window).  See also, Coordinating the Text/output Window (and file) Output from Multiple Modules.

Note:  When a spreadsheet or Scrollsheet is printed to the Text/output Window, the font that is defined in the Page/Output Setup dialog for spreadsheet and Scrollsheet output will be used as the default font in the Text/output Window.  Therefore, if you want to print the spreadsheet or Scrollsheet in the Text/output Window using a special font, you will need to set that font style in the Page/Output Setup dialog.  If you are pasting text from another application, select RTF as the format in the Paste Special dialog in order to paste the text into the Text/output Window using the source font style.


Text/output Window

Use this window as a "text editor" to take notes or to bring in a previously-saved text or report file.  Also, all output (text and graphs) can be directed to this window, in order to create a report (see, Text/output Window - Overview and Page/Output Setup).  The following pull-down menu options and Toolbar buttons are available for the Text/output Window.  Additional options are available when this window is used to process STATISTICA BASIC files, SCL (STATISTICA Command Language) files, MML (Megafile Manager Language) files, or SEPATH (Structural Equation Modeling) PATH1 language files.

Text/output Window Toolbar buttons, Ruler

File Menu

Edit Menu

View Menu

Character Menu

Paragraph Menu

Analysis Menu

Options Menu

Window Menu

Help Menu


Text/output Window File Menu

These options are available from the File pull-down menu.

New

Open Text

Open Other

New Data

Data File

Graph File

Scrollsheet

Text/Output

STATISTICA BASIC

Command Language (SCL)

Save

Save As

Print All

Print Selection

Page Layout

Print Files

Printer Setup

Exit


Text/output Window Edit Menu

  Undo	Find

  Cut	Find Next

  Copy	Replace

  Paste	Go To

Paste Special	Insert Bitmap from File

Clear	Object Size

Select All	Screen Catcher


Text/output Window - Paste Special

When you select this option, you will be able to choose the desired format (e.g., Rich Text Format, text, or picture) in which the Clipboard object will be pasted in the Text/output Window.


Text/output Window - Find Value

The Find dialog will enable you to search for a specific text or number in the Text/output Window.

Shortcut:  CTRL+F

Find dialog:

Find What:  Specify the text or number that you want to search for in the Text/output Window.

Direction:  Find will search either from the beginning of the file, or from the current cursor position (forward or backward).

Case Sensitive Search:  When you select this option, STATISTICA will search for the same upper/lowercase occurrance of the text.

Note:  A Find Next option is available from the Text/output Window Edit pull-down menu.  After STATISTICA has found the specified text or value, you can continue searching the Text/output Window by selecting the Find Next option from the Edit pull-down menu instead of re-opening the Find dialog and clicking on the Find Next button.


Text/output Window - Replace Value

The Replace dialog will enable you to search for a specific data value in the currently highlighted variable (or for a specific case name) and replace it with a different value, or search for a specific text or number in the Text/output Window, and replace it with a different text or number.

Shortcut:  CTRL+H

Replace dialog:

Find What:  Specify the text or number that you want to search for in the Text/output Window.

Replace:  Specify the text or number that will be used to replace the text or number that you are searching for.

Search:  You can choose to search the Entire Document or only the Selection highlighted by the cursor.

Verify Each Replace:  When you set this check box, STATISTICA will prompt you to verify the replacement.  The verification dialog allows you to skip the replacement (click No) or complete the replacement (click Yes) for each instance found, or Cancel the replacement procedure.  When this option is de-selected, then all occurrances of the text or number specified in the Find edit field will be replaced.


Text/output Window - Verify Replace

When you select the Verify Each Replace option in the Replace dialog, then for each time a specified value is found, STATISTICA will prompt you to verify the replacement via the Verify Replace dialog.  This dialog allows you to skip the replacement (click No) or complete the replacement (click Yes) for each instance found, or Cancel the replacement procedure.


Text/output Window - Select All

Click on this option in order to select all of the text and objects in the Text/output Window.

Shortcut:  CTRL+A


Text/output Window - Go To

Select this option in order to move to the specified location (Line Number) in the text.  After entering the desired line number, click OK to go to that line of the text.

Shortcut:  F5


Text/output Window - Insert Object from File

Text/output Window - Insert Bitmap from File

Selecting this option will allow you to insert a bitmap from file into the text document in the Text/output Window.  When you select this option, the File Open/Save As dialog will open in which you can choose the desired file.  When you click OK in that dialog, the bitmap will be placed in the text/output window at the current cursor position.

Shortcut:  F3


Text/output Window - Object Size

This option will allow you to change the size of the selected object in the Text/output Window.

Shortcut:  SHIFT+F3

Specify Picture Size dialog:

Picture Height/Width:  You can specify the height and width of the selected picture with these options.

Measure:  Choose to measure the picture size (height and width) in either inches or centimeters with these options.

Graphic object size and the minimum line setting.  Note that when you reduce the STATISTICA graph in the Text/output Window (for example to 2x3), then very thin lines may become unreadable.  Therefore, you may want to adjust the minimum line thickness setting in the Page/Output Setup dialog to a respectively larger setting.


Text/output Window - 2x3 Object Size

Select this option in order to change the size of the selected object to 2x3 (height x width) inches.

Graphic object size and the minimum line setting.  Note that when you reduce the STATISTICA graph in the Text/output Window (for example to 2x3), then very thin lines may become unreadable.  Therefore, you may want to adjust the minimum line thickness setting in the Page/Output Setup dialog to a respectively larger setting.


Text/output Window - 3x4.5 Object Size

Select this option in order to change the size of the selected object to 3x4.5 (height x width) inches.

Graphic object size and the minimum line setting.  Note that when you reduce the STATISTICA graph in the Text/output Window (for example to 2x3), then very thin lines may become unreadable.  Therefore, you may want to adjust the minimum line thickness setting in the Page/Output Setup dialog to a respectively larger setting.


Text/output Window - 4x6 Object Size

Select this option in order to change the size of the selected object to 4x6 (height x width) inches.

Graphic object size and the minimum line setting.  Note that when you reduce the STATISTICA graph in the Text/output Window (for example to 2x3), then very thin lines may become unreadable.  Therefore, you may want to adjust the minimum line thickness setting in the Page/Output Setup dialog to a respectively larger setting.


    Text/output Window - Deleting Tab Stops

To delete a single Tab stop, select the [image] Delete Tab Stop option from the right-mouse-button flying menu.  The Delete Tab Stop dialog will open in which you can select the desired Tab stop to delete.  Note that you can also delete a Tab stop by clicking on the Tab stop arrow on the Text/output Window Ruler.

To delete all Tab stops in the document, select the [image] Delete All Tab Stops option from the right-mouse-button flying menu.

See also, Setting Tab Stops in the Text/output Window.


Setting Tab Stops in the Text/output Window

You can set Tab stops in the Text/output Window by clicking on the Ruler with the left-mouse-button.  The Tab stop will be indicated by an arrow on the Ruler.

To delete a Tab stop, click on the arrow on the Ruler with the mouse or select the Delete Tab stop option from the right-mouse-button flying menu.


Text/output Window View Menu

Show Hidden (Paragraph Marker)

Ruler

Toolbar

Status Bar

Auto Task Buttons


Text/output Window - Paragraph Mark

Text/output Window - Paragraph Marker

This option toggles between displaying and hiding paragraph marks in the Text/output Window.  Alternatively, you can click on the [image] toobar button.


Text/output Window - Ruler

The option Ruler in the pull down menu View toggles between displaying and hiding the Ruler in the Text/output Window.  The Ruler is used as a measurement scale and and is displayed at the top of the Text/output Window.  You can click on the ruler with the mouse in order to set Tab stops (see, Setting Tab Stops in the Text/output Window).


Text/output Window Character Menu

Regular	  Superscript

  Bold	  Strikethrough

  Italic	Hidden

  Underline	Font

  Double Underline	  Color

  Subscript	Insert Page Break


Text/output Window - Font

The Font Selection dialog will allow you to change the font style (Face Name) and Size for either the highlighted text or new text.

Note that if the currently highlighted block of text in the Text/output Window contains different fonts, then the font type whose name is displayed in the Font field of the Text/output Window toolbar will be used if you insert new text or replace the block with new text.

Note also, when a spreadsheet or Scrollsheet is printed to the Text/output Window, the font that is defined in the Page/Output Setup dialog for spreadsheet and Scrollsheet output will be used as the default font in the Text/output Window.  Therefore, if you want to print the spreadsheet or Scrollsheet in the Text/output Window using a special font, you will need to set that font style in the Page/Output Setup dialog.  If you are pasting text from another application, select RTF as the format in the Paste Special dialog in order to paste the text into the Text/output Window using the source font style.  See also, Character Formatting.

Shortcut:  CTRL+F9


Text/output Window - Character Formatting

The following options control the format of characters in the Text/output Window.  These options are accessible from the Character pull-down menu or, in some cases, from the Text/output Window toolbar (see Text/output Window Toolbar Buttons).  The keyboard shortcuts for some of these options are given in parentheses.

Regular (CTRL+0):  Select this option to return the font to a regular character formatting (e.g., not italicized).

Bold (CTRL+B):  Select this option in order to make subsequent or highlighted characters bold.

Italic (CTRL+I):  Select this option in order to make subsequent or highlighted characters italics.

Underline (CTRL+U):  Select this option in order to underline subsequent or highlighted characters.

Double Underline (CTRL+D):  Select this option in order to double underline subsequent or highlighted characters.

Subscript:  Select this option in order to make subsequent or highlighted characters subscripted.

Superscript:  Select this option in order to make subsequent or highlighted characters superscripted.

Strikethrough:  Select this option in order to strikethrough subsequent or highlighted characters.

Hidden:  Select this option in order to make subsequent or highlighted characters hidden.

Font (CTRL+F9):  Select this option to open the Font Selection dialog in order to change the font style.  Note that if the currently highlighted block of text in the Text/output Window contains different fonts, then the font type whose name is displayed in the Font field of the Text/output Window toolbar will be used if you insert new text or replace the block with new text.

Color (SHIFT+F9):  Select this option in order to change the font color (via the standard Windows Color dialog).


Text/output Window - Page Break

Use this option in order to insert a manual (hard) page break whever you want in the Text/output Window.  This break will appear as a solid horizontal line in the Window.  You can use manual page breaks to force text or objects onto a new page, keep paragraphs together, place an object or text at the top of the page, etc.

Shortcut:  CTRL+ENTER


Text/output Window Paragraph Menu

Normal	  Double Space

  Left	  Left Indent

  Center	  Right Indent

  Right	Hanging Indent

  Single Space


Text/output Window - Paragraph Formatting

The following options will allow you to control the paragraph formatting of text in the Text/output Window.

Normal:  Select this option to return the paragraph formatting to the default style.

Left:  Select this option to align the paragraph at the left indent.

Center:  Select this option to center the paragraph in the middle of the page.

Right:  Select this option to align the paragraph at the right indent.

Single Space:  Select this option to set the paragraph spacing to one line.

Double Space:  Select this option to set the paragraph spacing to two lines.

Left Indent:  This option allows you to set the left indent in the paragraph.

Right Indent:  This option allows you to set the right indent in the paragraph.

Hanging Indent:  This option allows you to set the hanging indent (i.e., the indentention of the second and subsequent lines in the paragraph).


Text/output Window Analysis Menu

These general options are available from the Analysis pull-down menu.

Startup Panel

Resume Analysis

STATISTICA BASIC

Command Language (SCL)

Quick Basic Stats

  Descriptive Statistics

  Correlation Matrices

  Frequency Tables

  Probability Calculator

  More....

Other Statistics


Text/output Window Options Menu

Append Results	Display

Print	General

Macro

Command Langage (SCL)	Keyboard Macro

STATISTICA BASIC	Recorded Show Macro

Quick Open File	Customize Auto Task Buttons


Text/output Window Window Menu

These options are available from the Window pull-down menu.

Scrollsheet Manager

Graph Manager

Cascade

Tile Horizontally

Tile Vertically

Arrange Icons

Close All but Data File


Text/output Window Help Menu

These options are available from the Help pull-down menu.

Index	Search Help On

Spreadsheet	Glossary

Scrollsheet	Keyboard

Graph	Advisor

Text/Output	About


Text/output Window Toolbar Buttons

The following is a list of toolbar buttons specific to the Text/output Window.  For more information about this window, see Text/output Window Overview, see also, Ruler.

For more information on specific dialogs or options, click on the [image] button in the upper-right corner of the dialog.  For more general information, see STATISTICA Index.

  Change Show

  STATISTICA Module Switcher

  Workbook Management

  Startup Panel

  Resume Analysis

  Font

  Bold

  Italic

  Underline

  Double Underline

  Subscript

  Superscript

  Strikethrough

  Center

  Color

  Right

  Left

  Single Space

  Double Space

  Paragraph Mark

  Open Text File

  Save Text As

  Print

  Cut

  Copy

  Paste

  Undo

  Electronic Manual


New Window

Select this option from the Text/output Window File pull-down menu in order to clear all text in this window.


  Printing the Text/output Window

Unlike the printing options available when printing a Scrollsheet or spreadsheet (see Printing), clicking on the Print button [image] or selecting the Print All option from the Text/output Window File pull-down menu will automatically send all of the text and graphs in this window to the printer (i.e., there will be no intermediate dialogs).  To print only a highlighted block of text from the Text/output Window, see the Print Selection option.

Shortcut:  CTRL+P


Text/output Window - Print Selection

Use this option from the Text/output Window File pull-down menu to print only the selected (highlighted) block of text in the Text/output Window.  To print all of the text, use the Print All option from the File pull-down menu.


  Text/output Window Undo Option

Click on this option in order to reverse (undo) the last specific command or action.  This option applies to the following actions:

•  Cut, Paste, Clear

•  The last entry (text or numeric) typed into the Text/output Window

Shortcut:  CTRL+Z (or ALT+Bksp)


Appending Results

When checked, this option (available from the Output Window Options pull-down menu) will append (add) the results of analyses to the end of any existing text in the Output Window.  This is useful if you want a continuous log of output from analyses.  However, sometimes you may want to use this Output Window as a "notepad" in which you can keep notes.  If this is the case, then you can temporarily disable the Append mode of operation by de-selecting the Append Results option (click on this option once again in order to return to the Append mode of operation.


Scrollsheet View Menu

These options are available from the Scrollsheet View pull-down menu.

Width	Text/output Window

Font	Titles

Zoom In	Toolbar

Zoom Out	Change Show

Colors	Status Bar

Mark Selection	Auto Task Buttons


  Mark Selection

This option (available also from the Toolbar and the pop-up right-mouse button menu from every cell) allows you to mark (or un-mark) individual values or a block of values in the Scrollsheet to make them stand out from the rest.  Highlight the cells in the Scrollsheet with the cursor and then select the Mark Selection option from the View pull-down menu.  The marked Scrollsheet values will be identified by a color other than the default data value color (by default, marked values appear red, see Customize Color) in the STATISTICA window and when printed, by default, will be identified with an  *  (asterisk) next to the value (other options to handle marked cells in printed or saved reports are available and can be selected in the Print Scrollsheet dialog).

Specific cells or blocks appear already marked in many Scrollsheets (at the point when they are initially generated) in order to "highlight" statistically significant results (e.g., correlation coefficients).  Such Scrollsheets usually offer an option to change the criterion used to select the cells to be highlighted (e.g., the significance level) via the Options button on the Scrollsheet Toolbar.

Note:  This option is also available from the right-mouse-button pop-up menu.


  Options Scrollsheet Toolbar button

This Scrollsheet Toolbar button will allow you to change (or select) a specific option (depending on the STATISTICA module you are using) that will affect the results in the Scrollsheet.  For example, in some correlation matrices, this button will open a dialog allowing you to set the threshold significance level for correlation coefficients which will be marked in the Scrollsheet (by default p = .05).


  Scrollsheet View Width

Selecting this option from the View pull down-menu will open the Customize Width dialog in which you can edit the Scrollsheet Column Width, Row Name Width, and Margin Width.  These options are global operations (i.e., the selections you make here will effect every column, row, or margin in the Scrollsheet).  The Column Width and Margin Width can also be edited in the Scrollsheet Column Specs dialog.

Customize Width dialog:

Column Width:  The value entered here (minimum = 1, maximum = 80) determines the width of every column in the Scrollsheet.

Row Name Width:  Enter here a number (minimum = 1, maximum = 40) that will specify (globally) the width of the Row Names in the Scrollsheet.  The Row Name width can also be specified in the Scrollsheet Row Name dialog.

Margin Width:  The values in each column can have a pre-specified margin on both sides in order to separate the values in one column from those in another.  This option will allow you to specify the width of the margin (minimum = 0, maximum = 10) for every column in the Scrollsheet.

Note that the column width can also be adjusted interactively by dragging the border between column names or by pressing the [image] and [image] toolbar buttons.


Scrollsheet Increase Font

  Scrollsheet Zoom In

This option allows you to increase the Scrollsheet font (in increments defined by the font type) by clicking the Scrollsheet Toolbar button (see below) to incrementally increase the font size.  When you first click on this button, the Zoom Options dialog may open (depending on the type of font in the Scrollsheet), warning you that the current font may not zoom (scale) continuously and offering you the option to change to a different font.

You can also decrease the font (see Scrollsheet Zoom Out) in the Scrollsheet in the same increments by which it was increased.


Scrollsheet Decrease Font

  Scrollsheet Zoom Out

This option allows you to decrease the Scrollsheet font (in increments defined by the font type) by clicking the Scrollsheet Toolbar button (see below) to incrementally decrease the font size.  When you first click on this button, the Zoom Options dialog may open (depending on the type of font in the Scrollsheet), warning you that the current font may not zoom (scale) continuously and offering you the option to change to a different font.

You can also increase the font size (see Scrollsheet Zoom In) in the Scrollsheet in the same increments by which it was decreased.


 Scrollsheet View Titles

With this option, you can choose to display the Scrollsheet (or Graph Data Editor) with a title (when checked, a one- or two-line title will be included in the display), or without a title (Title will appear unchecked in the View pull-down menu).  De-selecting the titles will only suppress the display (i.e., it will not delete the title information).  You can edit the Scrollsheet title by double-clicking on the title area of the Scrollsheet (or select the Titles option from the Edit pull-down menu) to open the Scrollsheet Edit Titles dialog.  You can edit the Graph Data Editor title by double-clicking on the title area of the Graph Data Editor to open the appropriate General Layout dialog.


Analysis Menu

These general options (as well as options specific to the STATISTICA module that you are using) are available from the Analysis pull-down menu.

Startup Panel

Resume Analysis

STATISTICA BASIC

Command Language (SCL)

Quick Basic Stats

  Descriptive Statistics

  Correlation Matrices

  Frequency Tables

  Probability Calculator

  More....

STATISTICA Module Switcher/Other Statistics


  Startup Panel

When you select this option from the Analysis pull-down menu, a window will open in which you can select an analysis from those available in the active STATISTICA module.  Select the analysis by highlighting it and then clicking the OK button.  Other options available in this window are discussed below.

Keyboard Shortcut:  CTRL+T

Toolbar button (in Text/output Window):

Startup Panel window:

Open Data button:  Clicking on this button will open the standard Open Data File dialog, from which you can select a data file for the analysis.

Select Cases button:  This button will bring up the standard Case Selection Conditions dialog.  Use this dialog to specify a subset of cases in the open data file on which to perform the analysis.

Define Weight (W) button:  Click on this button to open the Define Weight dialog, from which you can specify the case weighting conditions for the open data file.


  Resume Analysis

When the analysis that you are performing is still active, but the current analysis control dialog is minimized (the analysis icon appears in the lower left-hand corner of the screen), select this option to resume the analysis (open the analysis dialog) from the last dialog.  Alternatively, you can double-click on the icon to resume the analysis, click on the Text/output Window Resume Analysis Toolbar button, or (in most cases) click on the Continue button in the upper left corner of the current Scrollsheet or graph window.

Keyboard Shortcut:  CTRL+R

Toolbar button (in Text/output Window):


  Quick Basic Stats

The Quick Basic Stats options are available from either the spreadsheet or Scrollsheet right-mouse-button flying menu or from the Analysis pull-down menu of any module of STATISTICA.  Quick Basic Statistics can be used at any point of your data analysis (e.g., to provide supplementary information when you review output from any STATISTICA module).

These procedures include a selection of basic statistics which can be performed on long lists of variables (e.g., correlation indices for all variables in the data set), and all analyses can be performed by groups, for every value (i.e., code) of a selected grouping variable.

If Quick Basic Stats are called from the pull-down menu Analysis, then the variables to be analyzed are selected via subsequent variable selection dialogs.

Analysis pull-down menu options:

  Descriptive Statistics

  Correlation Matrices

  Frequency Tables

  Probability Calculator

  More....

If Quick Basic Stats are called from a right-mouse-button flying menu, then STATISTICA will not ask for variables to be analyzed because the selection of variables to be analyzed depends on the current cursor/block location in the spreadsheet or Scrollsheet; STATISTICA will ask for variables only if the option More.... is chosen, or if the currently selected block does not contain enough variables (e.g., if it contains only one variable for Correlation Matrices, or one list of variables for an analysis to be performed by... groups).

Right-mouse-button flying menu options:

  Descriptives of ...	  Correlations by ...

  Correlations of ...	  Frequencies by ...

  Frequencies of ...	  Probability Calculator

  Descriptives by ...	  More....

Use the More... option to customize the computations, for example, to select casewise deletion of missing data, the display of long variable names, the computation of medians and quartiles, etc. (the choices that you make on that dialog will remain in effect the next time that you compute Quick Basic Stats without going through the Extended Options dialog).


  Quick Basic Stats - Descriptive Statistics

This option from the Analysis pull-down menu, will allow you to compute a wide selection of  descriptive statistics for the selected variables in the current data set.  A sequential table of "descriptives" for the consecutive variables will be generated (one row per variable) for each level of a grouping variable (if one is selected).

The descriptive statistics available via this option are: valid n, mean, 95% confidence limits of the mean, sum, minimum, maximum, range, variance, standard deviation, standard error of the mean, skewness, kurtosis, and the standard errors of the skewness and kurtosis.  For more information, see Descriptive Statistics Overview; for additional statistics see Quick Basic Stats - More... or Basic Statistics - Descriptive Statistics.

To compute medians and quartiles, use the Quick Basic Stats option More.....

When you first select this option, the Select Variables (and optional grouping variable) dialog will open in which you can select the variables (up to 4092 variables can be selected) for the analysis and (optionally) a single grouping variable by which the descriptive statistics will be calculated.  If you do not select a grouping variable, then clicking OK in this dialog will produce the descriptive statistics Scrollsheet.  If you select a grouping variable, then clicking OK in this dialog will bring up the Select codes for grouping variable dialog in which you can select the codes. (i.e., groups) by which the descriptive statistics will be calculated.  After selecting the desired codes for the groups, the Select a group dialog will open.  In this dialog, you can choose to display the series of descriptive statistics Scrollsheets for all groups (press OK to select this default option) or only for specific groups (one Scrollsheet per group).  Click OK to complete the analysis.

Casewise deletion of missing data, can be requested in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

Long variable names can be included in the output Scrollsheets by setting a global option in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

For more information on other Quick Basic Stats options, see:

Correlation Matrices

Frequency Tables

Probability Calculator

More....


  Quick Basic Stats - Correlation Matrices

This option from the Analysis pull-down menu, will allow you to compute correlations between the selected variables for each level of a grouping variable (if one is selected).  Correlation matrices will be computed with casewise deletion of missing data unless pairwise deletion is requested in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.  The size of the correlation matrix is restricted only by the amount of memory in your computer.  For more detailed information see Correlations - Overview, for more options see Quick Basic Stats - More... or Correlation Matrices.

In order to display p-levels in the correlation Scrollsheet, select the p-levels option in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

When you first select this option, the Select Variables (and optional grouping variable) dialog will open in which you can select the variables for the analysis and (optionally) a grouping variable by which the correlations will be calculated.  If you do not select a grouping variable, then clicking OK in this dialog will display the correlation matrix in a Scrollsheet.  If you select a grouping variable, then clicking OK in this dialog will bring up the Select codes for grouping variable dialog in which you can select the codes. (i.e., groups) by which the correlations will be calculated.  After selecting the desired codes for the groups, the Select a group dialog will open.  In this dialog, you can choose to display the correlation matrices for all groups or only for specific groups (one Scrollsheet per group).  Click OK to complete the analysis.

Pairwise deletion of missing data, can be requested in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

Long variable names can be included in the output Scrollsheets by setting a global option in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

For more information on other Quick Basic Stats options, see:

Descriptive Statistics

Frequency Tables

Probability Calculator

More....


  Quick Basic Stats - Frequency Tables

This option from the Analysis pull-down menu, will compute a cascade of frequency tables for the selected variables, one Scrollsheet per variable for each level of a grouping variable (if one is selected).  For more detailed information see Frequency Tables - Overview, for more options see Quick Basic Stats - More... or Frequency Tables.

To compute Normal expected frequencies and other statistics, use the options in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

When you first select this option, the Select Variables (and optional grouping variable) dialog will open in which you can select the variables (up to 4092 variables can be selected) for the analysis and (optionally) a single grouping variable by which the frequencies will be calculated.  If you do not select a grouping variable, then clicking OK in this dialog will display the frequency Scrollsheets.  If you select a grouping variable, then clicking OK in this dialog will bring up the Select codes for grouping variable dialog in which you can select the codes. (i.e., groups) by which the frequencies will be calculated.  After selecting the desired codes for the groups, the Select a group dialog will open.  In this dialog, you can choose to display the frequency Scrollsheets for all groups or only for specific groups (one Scrollsheet per group).  Click OK to complete the analysis.

Casewise deletion of missing data, can be requested in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

Long variable names can be included in the output Scrollsheets by setting a global option in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

For more information on other Quick Basic Stats options, see:

Descriptive Statistics

Correlation Matrices

Probability Calculator

More....


  Quick Basic Stats - More...

This Quick Basic Stats option from the Analysis pull-down menu, offers more descriptive statistics, correlations, and frequency tables options as well as graphing options.  See below for a description of each of those options.  (For more detailed information see Basic Statistics - Overview.)

Quick Basic Statistics - Extended Options dialog:

Variables

Codes

Global options

Descriptive Statistics

Correlations

Distribution, Normality

Categorization

Graphs

For more information on other Quick Basic Stats options, see:

  Descriptive Statistics

  Correlation Matrices

  Frequency Tables

  Probability Calculator


  Quick Basic Stats Extended Options - Categorization

The options selected in this box will only affect the frequency tables and histograms produced via the options in the Distribution, Normality box (to the left).  This categorization option has only two modes of categorizing the values of selected variables for the frequency table; a number of additional options, graphs, and statistics are available via the Frequency tables option (on the Basic Statistics and Tables startup panel).  You can also use the Recode option which allows you to categorize data (i.e., create values for a grouping variable) based on user-defined criteria of practically unlimited complexity.

Number of intervals:  If this radio button is set, then the range of values will for the selected variables will be divided into approximately the requested number of intervals for subsequent Frequency tables Scrollsheets or Histograms.  This option is appropriate when the variables to be tabulated are continuous in nature.  The tests of normality (Normal expected frequencies and KS and Lilliefors test) are only available if this option is chosen.  Note that the actual number of categories that will be produced may sometimes differ from the number of intervals requested.  STATISTICA will produce "neat" intervals; that is, interval boundaries and widths with the last digit being 1, 2, or 5 (e.g., 10.5, 11.0, 11.5, etc.).  Such "simple" or "neat" intervals are more easily interpreted than interval boundaries defined by many significant digits (e.g., 10.12423, 10.13533, etc.).  Full control over the method of categorization of variables is available via the Basic Statistics and Tables Frequency tables option.

Integer intervals:  Chose this method of categorization if the variables to be tabulated can be interpreted as integer categories, or contain only integer values.  If this method is chosen, all non-integer values will be ignored when producing Frequency tables or Histograms via the Distribution, Normality option; the choice of Categorization in this box will not affect other computations (e.g., of Descriptive Statistics).


Quick Basic Stats Extended Options - Casewise (Listwise) Deletion of Missing Data

If casewise deletion of missing data is selected, then STATISTICA will ignore all cases that have missing data for any of the variables selected in the list.  If this check box is not selected, then all valid data points will be included in the analyses for the respective variables (pairwise deletion of missing data, resulting possibly in unequal valid n per variable).


Quick Basic Stats Extended Options - Display Long Variable Names

If this check box is set, then long variable names (if any, see Spreadsheet Edit Specs) will be displayed along with the short names in the first column or the title of the Scrollsheet.  If no long variable names have been specified for any of the selected variables, then the setting of this check box will have no effect.


  Quick Basic Stats Extended Options - Descriptive Statistics

These options allow you to compute specific descriptive statistics for the selected variables (up to 4092 variables can be selected).  A sequential table of "descriptives" for the consecutive variables will be generated (one row per variable) for each level of a grouping variable (if one is selected).  The descriptive statistics available via this option are: valid n, mean, 95% confidence limits of the mean, sum, minimum, maximum, range, variance, standard deviation, standard error of the mean, skewness, kurtosis, and the standard errors of the skewness and kurtosis.  For more information on these and other options, see Descriptive Statistics Overview.

Descriptive Statistics button:  When you click on this button, the Select a group dialog will open.  In this dialog, you can choose to compute the descriptive statistics for all groups or only for specific groups (one Scrollsheet per group).  Click OK in this dialog to complete the analysis.

Compute medians & quartiles:  If checked, then in addition to the above statistics, the descriptive statistics Scrollsheets will contain the median (50th percentile), quartiles (25th and 75th percentiles), and quartile range for all variables.  The median is defined as the value that divides the distribution of all values in half; that is, 50% of all values for the respective variable (within the respective group) will fall below the median and 50% will be greater than the median.  The 25th and 75th percentiles (quartiles) are defined accordingly.  Note that you can also calculate percentiles in the Basic Statistics & Tables module and user-specified percentiles can be calculated in the Nonparametrics module.  For these two modules, you can specify the method of computing percentiles in the STATISTICA Defaults: General dialog.


  Quick Basic Stats Extended Options - Correlations

These options allow you to compute correlations between the selected variables for each level of a grouping variable (if one is selected).  The size of the correlation matrix is restricted only by the amount of memory in your computer.  For more information on these and other options, see Correlations - Overview.

Correlations button:  When you click on this button, the Select a group dialog will open.  In this dialog, you can choose to compute the correlations for all groups or only for specific groups (one Scrollsheet per group).  Click OK in this dialog to complete the analysis.

Save button:  Use this option to first compute the correlation matrix (without displaying it) and then save it in a file.  When you click on this button, the Save Matrix As dialog will open in which you can specify a name under which the matrix will be saved.  If a grouping variable was previously selected, then multiple correlation matrices (i.e., correlations "by group") will be produced and saved in a single file (for use in such procedures as Structural Equation Modeling which can use multiple correlation matrices for input).

p-levels:  Set this checkbox in order to display the p-level along with the correlation coefficient in the Scrollsheet.   NOTE:  The significance levels reported in correlation matrices for individual coefficients should be interpreted with caution (for example, at alpha=.05, one can expect by chance correlations to be significant for 5% of the pairs of variables).

Casewise MD del.:  Unlike the Casewise (listwise) deletion of MD option (which is a global option), this option applies only to Correlations.  If this check box is set, then only the cases that have complete (valid) data for all variables that are currently selected for the analysis (i.e., casewise deletion of missing data) will be included in the computation of the correlations.  If this check box is not set (i.e., pairwise deletion of missing data), then each correlation will be computed from all cases that have complete (valid) data for the respective pair of variables, possibly resulting in unequal n for different correlations.


  Quick Basic Stats Extended Options - Distribution, Normality

These options will compute a cascade of frequency tables for the selected variables, one Scrollsheet per variable for each level of a grouping variable (if one is selected).  For more information on these and other options, see Frequency Tables - Overview.

Frequency tables button:  When you click on this button, the Select a group dialog will open.  In this dialog, you can choose to compute frequency tables for all groups or only for specific groups (one Scrollsheet per group).  Click OK in this dialog to complete the analysis.

Histograms button:  When you click on this button, the Select a group dialog will open.  In this dialog, you can choose to compute frequency histograms for all groups or only for specific groups (one Scrollsheet per group).  Click OK in this dialog to display the histograms.

Normal expected frequencies:  If this check box is set then for each category in the frequency table, the expected frequencies are computed based on the normal distribution.

K-S and Lilliefors test:  If this check box is set, then the Kolmogorov-Smirnov one-sample D statistic will be computed and Lilliefors probabilities will be reported (see Lilliefors, 1976).  If the Kolmogorov-Smirnov D statistic is significant, then the hypothesis that the respective distribution is normal should be rejected.  The probability values that will be reported are based on those tabulated by Massey (1951); those probability values are valid when the mean and standard deviation of the normal distribution are known a priori and not estimated from the data.  However, usually those parameters are computed from the actual data.  In that case, the test for normality involves a complex conditional hypothesis ("how likely is it to obtain a D statistic of this magnitude or greater, contingent upon the mean and standard deviation computed from the data"), and thus the Lilliefors probabilities should be interpreted (Lilliefors, 1967).


Quick Basic Stats Extended Options - Graph Options

For more information on these types of graphs, see Stats Graphs.

Box & whisker plot for all variables:  This option will produce a box and whisker plot for the selected variables by group (if a grouping variable was selected), one graph for each group.  This box and whisker plot will summarize each variable by three components:

(1)	A central line to indicate central tendency or location;

(2)	A box to indicate variability around this central tendency;

(3)	Whiskers around the box to indicate the range of the variable.

After clicking on this button you can choose to plot for each variable:

(1)	Medians (central line), quartiles (box), and ranges (whiskers);

(2)	Means, standard errors of the means, and standard deviations;

(3)	Means, standard deviations, and 1.96 times the standard deviations (95% normal confidence interval for individual observations around the mean);

(4)	Means, standard errors of the means, and 1.96 times the standard errors of the means (95% normal confidence interval for means).

Box & whisker plot by group:  This option will produce a box and whisker plot for each selected variable categorized by each of the groups in the previously selected grouping variable, one graph per variable.  (If a grouping variable has not been previously selected, you will be prompted to select one when you click on this button.)  This box and whisker plot will summarize each group by three components:

(1)	A central line to indicate central tendency or location;

(2)	A box to indicate variability around this central tendency;

(3)	Whiskers around the box to indicate the range of the variable.

After clicking on this button you can choose to plot for each variable:

(1)	Medians (central line), quartiles (box), and ranges (whiskers);

(2)	Means, standard errors of the means, and standard deviations;

(3)	Means, standard deviations, and 1.96 times the standard deviations (95% normal confidence interval for individual observations around the mean);

(4)	Means, standard errors of the means, and 1.96 times the standard errors of the means (95% normal confidence interval for means).

Categorized histograms button:  This option will produce a cascade of categorized histograms for the selected variables, one plot per selected variable.  For each selected variable, STATISTICA will produce a histogram, broken down (categorized) by the levels of the grouping variable (e.g., separately for males and females).  (If a grouping variable has not been previously selected, you will be prompted to select one when you click on this button.)

2D scatterplot (/with names) button:  This option will produce a cascade of scatterplots for selected pairs of variables and for each selected level of the grouping variable.  (If a grouping variable has not been previously selected, you will be prompted to select one when you click on this button.)  If the 2D scatterplot option is chosen, then the plot will show the regression line and the 95% confidence interval bands for the regression line.  If the /w names button is used, then the scatterplot will identify the points in the scatterplot with the case numbers or names (if case names are specified in the respective data file).

(2D scatterplot) Matrix button:  This option will produce a scatterplot matrix for the selected variables, one scatterplot matrix for each selected level of the grouping variable.

3D scatterplot (/with names) button:  This option will produce a 3D scatterplot for a selected triplet of variables and for each selected level of the grouping variable.  (If a grouping variable has not been previously selected, you will be prompted to select one when you click on this button.)  If the /w names button is used, then the points in the scatterplot will be identified by the case numbers or names (if case names are specified in the respective data file).

Surface button:  This option will produce a 3D scatterplot for a selected triplet of variables and for each selected level of the grouping variable and fit a quadratic surface to the data.

Normal probability plots:  This option will produce a cascade of normal probability plots for the selected variables by group (if a grouping variable was selected), one plot per selected variable per group.  For more information, see Normal Probability Plots.

Half-normal probability plots:  This option will produce a cascade of half-normal probability plots for the selected variables by group (if a grouping variable was selected), one plot per selected variable per group.  For more information, see Half-Normal Probability Plots.

Detrended normal probability plots:  This option will produce a cascade of detrended normal probability plots for the selected variables by group (if a grouping variable was selected), one plot per selected variable per group.  For more information, see Detrended Normal Probability Plots.

Categorized normal probability plots button:  This option will produce a cascade of normal probability plots for the selected variables (one plot per variable), categorized by the levels of the grouping variable.  (If a grouping variable has not been previously selected, you will be prompted to select one when you click on this button.)

Categorized scatterplots button:  This option will produce a cascade of categorized scatterplots for selected pairs of variables, one plot per pair.  After clicking on this button, the user will be prompted to select two lists of variables (from the list of dependent variables).  Scatterplots will be produced for each variable in the first list with each variable in the second list, categorized by the levels of the grouping variable.  (If a grouping variable has not been previously selected, you will be prompted to select one when you click on this button.)

If the /w names button is used, then the scatterplot will identify the points in the categorized scatterplot with the case numbers or names (if case names are specified in the respective data file).

3D bivariate distribution histogram:  This option will produce a cascade of 3D histograms for selected pairs of variables by group (if a grouping variable was selected).  After clicking on this button, the user is first prompted to select the groups by which the 3D histogram will be produced.  Once selected, you will then be prompted to select two lists of variables (from among those originally selected via the Variables option).  3D histograms will be produced for each variable in the first list with each variable in the second list for each previously selected level of the grouping variable.

Note:  In order to produce histograms, normal probability plots, or box plots representing the distribution of the values in cases (and not variables), use the Block Stats Graphs options available from the flying menu, Graphs pull-down menu, or in the Graphs Gallery (instead of transposing your data file).


Quick Basic Stats Extended Options - Variables

Click on this button to open the Select Variables (and optional grouping variable) dialog.  In this dialog you can select the variables for the analysis and (optionally) a grouping variable by which the analysis will be performed.  (Note that the name of the grouping variable will be displayed below this button.)


Quick Basic Stats Extended Options - Codes

Click on this button to open the Select codes for grouping variable dialog in which you can select the codes (i.e., groups) by which the desired analysis will be performed.

For more information, see Selecting Codes.


Quick Basic Stats Extended Options - Global Options

With the exception of casewise deletion of missing data for correlations (which is specified independently of this option, see Correlations), the following two options apply globally to all of the other options described in this dialog.

Casewise (listwise) deletion of MD

Display long variable names


  Quick Basic Stats - Descriptives of ...

Selecting this Quick Basic Stats option will display a descriptive statistics Scrollsheet of the values of the currently highlighted variable(s).  The descriptive statistics available via this option are: valid n, mean, 95% confidence limits of the mean, sum, minimum, maximum, range, variance, standard deviation, standard error of the mean, skewness, kurtosis, and the standard errors of the skewness and kurtosis.  For more information, see Descriptive Statistics Overview; for additional statistics see Quick Basic Stats - More... or Basic Statistics - Descriptive Statistics.

To compute medians and quartiles, use the Quick Basic Stats option More.....

Casewise deletion of missing data, can be requested in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

Long variable names can be included in the output Scrollsheets by setting a global option in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

For information on other Quick Basic Stats options, see:

  Correlations of ...

  Frequencies of ...

  Descriptives by ...

  Correlations by ...

  Frequencies by ...

  Probability Calculator

  More....


  Quick Basic Stats - Correlations of ...

Select this Quick Basic Stats option to produce a square matrix of correlations between the currently highlighted variable(s).  The size of the correlation matrix that you can compute is restricted only by the amount of memory in your computer.  For more information see Correlations - Overview.

In order to display p-levels in the correlation Scrollsheet, select the p-levels option in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

Pairwise deletion of missing data, can be requested in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

Long variable names can be included in the output Scrollsheets by setting a global option in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

For information on other Quick Basic Stats options, see:

  Descriptives of ...

  Frequencies of ...

  Descriptives by ...

  Correlations by ...

  Frequencies by ...

  Probability Calculator

  More....


  Quick Basic Stats - Frequencies of ...

Selecting this Quick Basic Stats option will display frequency Scrollsheets of the values of the currently highlighted variable(s), one Scrollsheet per variable.

To compute Normal expected frequencies and other statistics, use the options in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

Casewise deletion of missing data, can be requested in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

Long variable names can be included in the output Scrollsheets by setting a global option in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

For information on other Quick Basic Stats options, see:

  Descriptives of ...

  Correlations of ...

  Descriptives by ...

  Correlations by ...

  Frequencies by ...

  Probability Calculator

  More....


  Quick Basic Stats - Descriptives by ...

This Quick Basic Stats option will allow you to calculate descriptive statistics for the values of the currently highlighted variable(s) as categorized by the levels of a grouping variable.  When you select this option from the spreadsheet right-mouse-button flying menu, the Select codes for grouping variable dialog will open in which you can select the codes (i.e., groups) by which the descriptive statistics will be calculated (optionally, you can select or deselect variables for the analysis in this dialog; up to 4092 variables can be selected).  Clicking OK in this dialog will bring up the Select a group dialog.  In this dialog, you can choose to display the series of descriptive statistics Scrollsheets for all groups (press OK to select this default option) or only for specific groups (one Scrollsheet per group).  Click OK to complete the analysis.

If you click on a Scrollsheet with the right-mouse-button and a grouping variable or a secondary variable was used in the analysis, then that grouping variable will automatically be selected and displayed in the Quick Basic Stats flying menu.  In this case, selecting this option will bring up the Select a group dialog in which you can choose to display the descriptive statistics Scrollsheets for all groups or only for specific groups (one Scrollsheet per group).  Click OK in this dialog to complete the analysis.

The descriptive statistics available via this option are: valid n, mean, 95% confidence limits of the mean, sum, minimum, maximum, range, variance, standard deviation, standard error of the mean, skewness, kurtosis, and the standard errors of the skewness and kurtosis.  For more information, see Descriptive Statistics Overview; for additional statistics see Quick Basic Stats - More... or Basic Statistics - Descriptive Statistics.  To compute medians and quartiles, use the Quick Basic Stats option More.....

Casewise deletion of missing data, can be requested in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

Long variable names can be included in the output Scrollsheets by setting a global option in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

For information on other Quick Basic Stats options, see:

  Descriptives of ...

  Correlations of ...

  Frequencies of ...

  Correlations by ...

  Frequencies by ...

  Probability Calculator

  More....


  Quick Basic Stats - Correlations by ...

This Quick Basic Stats option will allow you to produce a square matrix of correlations between the currently highlighted variable(s) as categorized by the levels of a grouping variable.  Correlation matrices will be computed with casewise deletion of missing data unless pairwise deletion is requested in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

In order to display p-levels in the correlation Scrollsheet, select the p-levels option in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

When you select this option from the spreadsheet right-mouse-button flying menu, the Select grouping Variable dialog will open in which you can select a single grouping variable by which the correlations will be calculated (optionally, you can select or deselect variables for the analysis in this dialog; the size of the correlation matrix that you can compute is restricted only by the amount of memory in your computer).  Clicking OK in this dialog will bring up the Select a group dialog.  In this dialog, you can choose to display the correlation Scrollsheets for all groups or only for specific groups (one Scrollsheet per group).  Click OK to complete the analysis.

If you click on a Scrollsheet with the right-mouse-button and a grouping variable or a secondary variable was used in the analysis, then that grouping variable will automatically be selected and displayed in the Quick Basic Stats flying menu.  In this case, selecting this option will bring up the Select a group dialog in which you can choose to display the correlations for all groups or only for specific groups (one Scrollsheet per group).  Click OK in this dialog to complete the analysis.

Pairwise deletion of missing data, can be requested in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

Long variable names can be included in the output Scrollsheets by setting a global option in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

For more information see Correlations - Overview.

For information on other Quick Basic Stats options, see:

  Descriptives of ...

  Correlations of ...

  Frequencies of ...

  Descriptives by ...

  Frequencies by ...

  Probability Calculator

  More....


  Quick Basic Stats - Frequencies by ...

This Quick Basic Stats option will allow you to calculate frequencies for the values of the currently highlighted variable(s) as categorized by the levels of a grouping variable.  When you select this option from the spreadsheet right-mouse-button flying menu, the Select grouping Variable dialog will open in which you can select a single grouping variable by which the frequencies will be calculated (optionally, you can select or deselect variables for the analysis in this dialog; up to 4092 variables can be selected).  Clicking OK in this dialog will bring up the Select a group dialog.  In this dialog, you can choose to display the frequency tables for all groups or only for specific groups (one Scrollsheet per group).  Click OK to complete the analysis.

To compute Normal expected frequencies and other statistics, use the options in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

If you click on a Scrollsheet with the right-mouse-button and a grouping variable or a secondary variable was used in the analysis, then that grouping variable will automatically be selected and displayed in the Quick Basic Stats flying menu.  In this case, selecting this option will bring up the Select a group dialog in which you can choose to display the frequency tables for all groups or only for specific groups (one Scrollsheet per group).  Click OK in this dialog to complete the analysis.

Casewise deletion of missing data, can be requested in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

Long variable names can be included in the output Scrollsheets by setting a global option in the Quick Basic Stats - Extended Options dialog accessible by selecting the More... option in the Quick Basic Stats menu.

For information on other Quick Basic Stats options, see:

  Descriptives of ...

  Correlations of ...

  Frequencies of ...

  Descriptives by ...

  Correlations by ...

  Probability Calculator

  More....


Other Statistics

  STATISTICA Module Switcher/Other Statistics

Selecting the Other Statistics option will bring up the STATISTICA Module Switcher dialog.  This dialog contains a list of all the STATISTICA modules to which you can transfer.  Whenever you highlight a module, a brief description of that module appears in the dialog.  This dialog also contains options described below.  For information on each of the modules from the list, see Statistics (Index of all Modules).

Shortcut:  Click the right-mouse-button on the application background in order to bring up this global flying menu.  You can also double-click on the application background (analogous to double-clicking on the desktop in order to open the Windows Task Switcher).

STATISTICA Module Switcher dialog:

Switch To button:  After you have selected (highlighted) the module to which you want to transfer, click on this button to switch to that module.  Depending on your selection of single or multiple application mode in the STATISTICA Defaults: General dialog, the currently open module (if there is one) will either remain open (de-select the Single Application Mode), or will close (select the Single Application Mode) when the desired module opens.  Alternatively, you can double-click on the module name in this dialog in order to switch to it (keeping the current module open or closing it, see the above explanation of single and multiple application modes).

End & Switch To button:  Use this button to close the module that you are currently using and switch to the module highlighted in this dialog.

Customize List button:  This button will open the Customize List of Modules dialog from which you can customize (rearrange, or reduce) the list of modules.  In the Customize List of Modules dialog, you can either Replace the entire list of modules with only selected modules (most likely the modules that you would use the most) or Append selected modules to the end of the Module Switcher list (essentially rearranging the list by moving the modules that you use the least to the end of the list).


Customize List of Modules

The Customize List of Modules dialog is used to customize the selection of modules available from the STATISTICA Module Switcher.  The Customize List of Modules dialog contains a list of all of the modules that have been installed in STATISTICA and three other options listed below.

Customize List of Modules dialog:

Append:  In this mode, the module(s) highlighted in the list will be appended to the end of the Module Switcher list.

Replace:  In this mode, all modules currently selected in the list will replace the list in the Module Switcher.

Add/Remove:  Press this button to change the STATISTICA configuration.  This button starts the Reinst.exe program (located in your STATISTICA program directory).  This utility allows you to install any modules of STATISTICA which were not selected during a previous installation, to remove (delete) any previously installed modules, or if you are on a workstation and will use STATISTICA from a network file server, you may create your own customized working directory for STATISTICA.

In order to create a new, specific order of modules in the Module Switcher list, Replace the first module (this will also remove the previous selection in the Module Switcher); then Append subsequent modules in the desired order (one at a time).


Spreadsheet and Scrollsheet Graphs Menu

These options are available from the spreadsheet or Scrollsheet Graphs pull-down menu.

  Quick Stats Graphs

Stats Graphs

  Stats 2D Graphs

  2D Histograms	  2D Box Plots

  2D Scatterplots	  Bar/Column Plots

  Scatterplots w/Histograms	  2D Line Plots (Variables)

  Scatterplots w/Box Plots	  2D Line Plots (Case Profiles)

  Probability Plots	  Sequential/Stacked Plots

  Quantile-Quantile Plots	  Pie Charts

  Probability-Probability Plots	  Missing/Range Data Points

  2D Range Plots	  2D Custom Function Plots

  Stats 3D Sequential Graphs:

  Raw Data Plots	  Range Plots

  Bivariate Histograms	  Box Plots

  Stats 3D XYZ Graphs:

  Scatterplots	  Ternary Plots

  Surface Plots	  Categorized Plots

  Contour Plots	  Categorized Ternary Plots

  Trace Plots	  Custom Function Plots

  Stats Matrix Plots

  Stats Icon Plots

  Stats Categorized Graphs:

  Histograms	  Box Plots

  Scatterplots	  Pie Charts

  Probability Plots	  Missing/Range Data Plots

  Quantile-Quantile Plots	  3D XYZ Plots

  Probability-Probability Plots	  3D Ternary Plots

  Line Plots

  Multiple Graph Layouts:

  Wizard

  Templates

  Blank Graph:

  Default Proportion

  Page/Printer Proportion

  Custom Graphs:

  2D Graphs	  Matrix Plots

  3D Sequential Graphs	  Icons Plots

  3D XYZ Graphs	  Ternary Plots

  Block Stats Graphs

  Histograms	  Box Plot/Medians

  Box Plot/Means	  Normal Prob. Plots

  Stats User-defined Graphs

  Graph Data Links


Get Plotted Values From...

Get Plotted Values From

This dialog is accessed from any Scrollsheet or spreadsheet Custom graph dialog.  To open the Get Plotted Values From dialog, double-click on the displayed variable (or Scrollsheet column or row) name in the edit field.  Use this dialog to choose the source of values to be plotted.

Get Plotted Values From dialog:

Get From:  Select the source of values to be plotted in the graph.  The choices offered here will depend on the axis (X or Y) or type of graph for which you are selecting values.

Col:  Click on this option if you want to select a column of values to be used in the plot.  When you click on Col, a list of column names (or variable names in the spreadsheet) will be displayed in a list in this dialog.  Choose a set of values to be plotted by highlighting the name of the column that contains those values.

Row:  When you click on this option, the row names (or case names in the spreadsheet) will be displayed in a list.  Choose a set of row values in this window by highlighting the name of the row containing the values.

Col Names:  When you select this option, STATISTICA will use the actual column names (or variable names in the spreadsheet) as values in the plot.  The display window will be dimmed when you select this option since all of the column names (corresponding to the selected values, see the option Values in any of the Custom Graphs dialogs) will be used.

Row Names:  Row names (or case names in the spreadsheet) will be used as values in the plot when you select this option.  The display window will be dimmed when you select this option since all of the row names (corresponding to the selected values) will be used.


Custom Graphs

Custom Graphs allow you to visualize any custom-defined combination of values from Scrollsheets and spreadsheets (from rows, columns, or both, and/or their subsets).  When you select one of the global categories of these graphs (Custom 2D Graphs, Custom 3D Sequential Graphs, Custom 3D XYZ Graphs, Custom Martix Plots, or Custom Icon Plots), a respective dialog will open allowing you to specify the parts of the current Scrollsheet or spreadsheet to be plotted.  The layout of this dialog depends on the global category of the Custom graph which you have selected (e.g., Custom 2D Graphs).  The initial selection of the data to be plotted (suggested in that dialog) depends on the current block (or cursor) position in the current Scrollsheet or spreadsheet.  Each of these Custom graph definition dialogs allow you to select the specific types of graph (within the global category).  However, as described below, the graph type can also be adjusted later, after the graph is created (via the General Layout or Plot Layout dialogs accessible by clicking on the graph background or from the graph pull-down menu Layouts).

For information on specific Custom Graphs, click on the graph name below.

  Custom 2D Graphs	  Matrix Plots

  Custom 3D Sequential Graphs	  Icons Plots

  Custom 3D Scatterplots and Surfaces	  Ternary Plots


  Custom Ternary Graphs

This type of Custom Graph (accessible from the Graphs pull-down menu or the Graphs Gallery button) allows you to examine relations between four or more dimensions where three of those dimensions represent components of a mixture (i.e., the relations between them is constrained such that the values of the three variables add up to the same constant for each case).  One typical application of this graph is when the measured response(s) from an experiment depends on the relative proportions of three components (e.g., three different chemicals) which are varied in order to determine an optimal combination of those components (e.g., in mixture designs).  In this type of ternary plot, the triangular coordinate systems are used to plot four (or more) variables (the components X, Y, and Z, and the responses V1, V2, etc.) in three dimensions (e.g., 3D scatterplots).  In order to produce a Custom Ternary Graph, the relative proportions of each component (within each case) are plotted (i.e., the values are recoded such that they add up to 1).  (Options to manage cases with invalid sums are available via the Stats Graphs Ternary Plots or Categorized Ternary Plots dialogs.)

Custom Ternary Graphs dialog:

Graph Type:  Choose the type of 3D ternary plot here (the type can also be changed later from within the graph via the General Layout dialog).  To select the plot type, click on its name.  See below for a list of plots in this dialog (click on each name for a brief description of the plot type).

  2D Scatterplot	  Trace Plot

  3D Scatterplot	  Surface Plot

  Space Plot	  Contour/Lines

  Deviation Plot	  Contour/Areas

Data Type:  You can choose from four regression functions to fit to the data in a ternary plot.  Click on a function name for more information about that function.  See also Fitting Options for Ternary Plots.

  Linear Smooth	  Special Cubic Smooth

  Quadratic Smooth	  Custom Function

  Full Cubic Smooth

Note:  User-defined functions can be specified in the Plot Layout dialog.  These functions are plotted over (i.e., overlaid) and not fitted to the data.  In order to fit (and plot) user-defined functions to the data, use the Nonlinear Estimation module.

Variables

  Graphs Gallery

Values


  Custom Ternary Graphs - Variables

Select the variables that you want to be plotted here.  You can have up to three overlaid XYZV plots which share the X, Y, and Z variables; you will need to select at least one (maximum of 3) V variable.  To select variables, either type in the variable name, or double-click on the variable edit field to open the Get Plotted Values From dialog.  In this dialog, you will be able to select the source of values (choose from column values or row values) to be plotted.


  Custom Ternary Graphs - Graphs Gallery

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Custom Ternary Graphs - Values

Designate the range of the values here (i.e., From what value, To what value).  If you have a highlighted block of values in the spreadsheet, then by default STATISTICA will include the range of that block here.

For example, designate the range as From:  10, To:  15.  Now if you obtain the first set of values to be plotted from column 3 and the second set of values to be plotted from column 4, then STATISTICA will plot only the 10th through the 15th values of column 3 vs. the 10th through the 15th values of column 4.


  Custom 2D Graphs

This type of Custom Graph is available from either the Scrollsheet or spreadsheet Toolbars or the Graphs pull-down menu); see Custom Graphs vs. Stats Graphs.  This option will allow you to custom-define a two-dimensional graph with up to four different plots (using any combination of values from rows and/or columns of the current Scrollsheet/spreadsheet, or subsets of those values).  When you select this option, the 2D Graphs dialog will open from which you can specify the type of each of the four plots as well as where to get each set of values to be plotted.

2D Graphs dialog:

Type:  Choose the type of plot here (the type can also be changed later from within the graph via the General Layout dialog).  Choose up to 4 different plots; you can include more plots by merging graphs, adding more series of data to the Graph Data Editor via the Clipboard, or by defining graphs of practically any complexity in Graphics.  To designate the plot type, select it from the list in the combo box.  See below for a list of plots in this dialog (click on each name for a brief description of the plot type).

  Scatterplot	  Bar Right Y

  Line Plot	  Bar Top

  Step Plot	  Bar Dev

  Min-Max X	  Pie

  Min-Max Y	  MPatt Bar

  Bar X	  Voronoi

  Bar Left Y	  Ignore

Note:  The Min-Max type plots require that you designate a third variable as the Y-Max (or X-Max) variable.  STATISTICA will prompt you to do this in the Get Variable For Min-Max Plot dialog.  The Bar Dev plot will require you to specify a deviation level in the Define Deviation Level dialog.

X and Y

Values

  Graphs Gallery


  Custom 2D Graphs - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Custom 2D Graphs - X and Y

Double-click on the variable name in either of these fields to open the Get Plotted Values From dialog.  In this dialog, you will be able to select the source of values (choose from column values, row values, row names or column names) to be plotted.


  Custom 2D Graphs - Values

Designate the range of the values here (i.e., From what value, To what value).  If you have a highlighted block of values in the Scrollsheet or spreadsheet, then by default STATISTICA will include the range of that block here.  For example, designate the range as From:  10, To:  15.  Now if you obtain the first set of values to be plotted from column 3 and the second set of values to be plotted from column 4, then STATISTICA will plot only the 10th through the 15th values of column 3 vs. the 10th through the 15th values of column 4.


Custom 3D Sequence Graphs

  Custom 3D Sequential Graphs

This type of Custom Graph is available from either the Scrollsheet or spreadsheet Toolbars or the Graphs pull-down menu); see Custom Graphs vs. Stats Graphs.  This option will allow you to custom-define a three-dimensional graph (using any combination of values from rows and/or columns of the current Scrollsheet/spreadsheet, or subsets of those values) in order to visualize one or more sequence of values in the form of 3D displays (see the list of 3D graph types below).  In general, these graphs represent each series of data (e.g., each selected column or its subset) as one plot (e.g., a ribbon).  The consecutive values of the series are plotted along the X-axis, and these values are represented as "heights" of the plot (as measured on the Z-axis).  The contour and surface types integrate all individual plots into one structure.  (See also, Calculating Contour Levels and Distance.)

3D Sequential Graphs dialog:

Type:  Choose the type of plot here (the type can also be changed later from within the graph via the General Layout dialog).  To select the plot type, click on its name.  See below for a list of plots in this dialog (click on each name for a brief description of the plot type).

  Box Plot	  Spikes

  Block Plot	  Contour/Discrete

  Ribbons	  Surface Plot

  Lines	  Contour Plot

Plots

Values

  Graphs Gallery


Custom 3D Sequence Graphs - Graphs Gallery button

  Custom 3D Sequential Graphs - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


Custom 3D Sequence Graphs - Plots

  Custom 3D Sequential Graphs - Plots

You can select variables (for up to 12 plots) for the 3D graph here.  You can include more plots by merging graphs, adding more series of data to the Graph Data Editor via the Clipboard, or by defining graphs of practically any complexity in Graphics.  Either type in the variable name, or double-click on the variable edit field to open the Get Plotted Values From dialog.  In this dialog you will be able to select the source of values (choose from column values or row values) to be plotted.


Custom 3D Sequence Graphs - Values

  Custom 3D Sequential Graphs - Values

Designate the range of the values here (i.e., From what value, To what value).  If you have a highlighted block of values in the Scrollsheet or spreadsheet, then by default STATISTICA will include the range of that block here.


  Custom 3D Scatterplots and Surfaces

This type of Custom Graph is available from either the Scrollsheet or spreadsheet Toolbars or the Graphs pull-down menu); see Custom Graphs vs. Stats Graphs.  This option will allow you to custom-define a three-dimensional scatterplot or surface plot (using any combination of values from rows and/or columns of the current Scrollsheet/spreadsheet, or subsets of those values) in order to visualize complex interactive relationships between variables.  Unlike the Custom 3D Sequential Graphs which merely offer an alternative way to display simple individual series of data, in these graphs, each data point is defined by 3 values (x, y, z) and is visualized in 3D space according to its x-y-z coordinates.  Several graph and data types (i.e., transformations of data to be performed before the data are plotted) are available when you select this option and bring up the 3D Scatterplots and Surfaces dialog.

3D Scatterplots and Surfaces dialog:

Graph Type:  Choose the type of 3D plot here (the type can also be changed later from within the graph via the General Layout dialog).  To select the plot type, click on its name.  See below for a list of plots in this dialog (click on each name for a brief description of the plot type).

  Scatterplot	  Trace Plot

  Space Plot	  Surface Plot

  Spectral Plot	  Contour Plot

  Deviation Plot

Data Type:  Instead of plotting raw data (default), you may choose to display a surface (or contour) representing a smoothed image of the data following one of the available transformation/fitting procedures (click on each name below for a brief description of the data type).

  Linear	  Negative Exponential

  Quadratic	  Spline Smooth

  Least Squares	  Custom Function

Variables

Values

  Graphs Gallery


Custom 3D Scatterplots and Surfaces - Graph Type

  Custom 3D Scatterplots and Surfaces - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Custom 3D Scatterplots and Surfaces - Variables

Select the variables that you want to be plotted here.  You can have up to four overlaid XYZ plots which share the X and Y variables; you will need to select at least one (maximum of 4) Z variable.  You can include more plots by merging graphs, adding more series of data to the Graph Data Editor via the Clipboard, or by defining graphs of practically any complexity in Graphics.  To select variables, either type in the variable name, or double-click on the variable edit field to open the Get Plotted Values From dialog.  In this dialog, you will be able to select the source of values (choose from column values or row values) to be plotted.


  Custom 3D Scatterplots and Surfaces - Values

Designate the range of the values here (i.e., From what value, To what value).  If you have a highlighted block of values in the Scrollsheet or spreadsheet, then by default STATISTICA will include the range of that block here.


  Custom Icon Graphs

This type of Custom Graph is available from either the Scrollsheet or spreadsheet Toolbars or flying menus or the Graphs pull-down menu; see Custom Graphs vs. Stats Graphs.  This option will allow you to custom-define icon graphs (using any combination of values from rows and/or columns of the current Scrollsheet/spreadsheet, or subsets of those values) by selecting the appropriate graph type in the Custon Icon Graphs dialog.

Icon plots represent individual units of observation as particular graphical objects (i.e., Chernoff faces, stars, sun rays, polygons, pies, columns, lines, and profiles) where values of up to 12 variables are assigned to specific features or dimensions of the objects (one case = one object).  You can include more plots by merging graphs, adding more series of data to the Graph Data Editor via the Clipboard, or by defining graphs of practically any complexity in Graphics.  Examining such icons may help to discover specific clusters of both simple relationships and interactions between variables.  (Many other types of icon plots are available in Graphics.)

Custom Icon Graphs dialog:

Graph Type:  Choose here the type of icon plot.  To select the plot type, click on its name (the type can also be changed later from within the graph via the General Layout dialog).  See below, for a list of plots in this dialog (click on each name for a brief description of the plot type).

  Chernoff Faces	  Pies

  Stars	  Columns

  Sun Rays	  Lines

  Polygons	  Profiles

Variables

Values

  Graphs Gallery


Custom Icon Graphs - Graphs Gallery Button

  Custom Matrix and Icon Graphs - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Custom Icon Graphs - Variables

Select the variables that you want plotted here.  To select variables, either type in the variable name, or double-click on the variable edit field to open the Get Plotted Values From dialog.  In this dialog, you will be able to select the source of values (choose from column values or row values) to be plotted.


  Custom Icon Graphs - Values

Designate the range of cases (i.e., From what case, To what case, inclusive) to be plotted here.  If you have a highlighted block of values in the Scrollsheet or spreadsheet, then by default STATISTICA will present here the range of cases for that block.


  Custom Matrix Graphs

This type of Custom Graph is available from either the Scrollsheet or spreadsheet Toolbars or flying menu, or the Graphs pull-down menu); see Custom Graphs vs. Stats Graphs.  This option will allow you to custom-define matrix graphs (using any combination of values from rows and/or columns of the current Scrollsheet/spreadsheet, or subsets of those values) by selecting the appropriate graph type in the Custom Matrix Graphs dialog.

Matrix graphs (multiple XY graphs resulting from "crossing" the values of two rows, two columns, or a row and column in the matrix) represent relationships between variables (you can select up to 12 rows or columns to cross).  You can include more plots by merging graphs, adding more series of data to the Graph Data Editor via the Clipboard, or by defining graphs of practically any complexity in Graphics.

STATISTICA matrix graphs feature histograms (placed on the diagonal of the matrix) representing the distributions of the respective plotted values.  By default, the vertical scales of those histograms (i.e., those representing frequencies) are independent; specifically, they are standardized for the values of each row or column to take advantage of the entire plot area of each small graph (you can force all histograms to a common scale by selecting the Histograms-Common option in the matrix graph General Layout dialog).  Independent scaling means that the scales are adjusted to the distributions of the row or column values in order to provide the best conditions for exploring the individual shapes of distributions.  When you select this option, you will be able to choose from three types of matrix plots (Scatterplot, Line and Column) to display the individual X-Y data sets.  (Many other types of matrix graphs are available in Graphics.)

Custom Matrix Graphs dialog:

Graph Type:  Choose here the type of matrix plot.  To select the plot type, click on its name (the type can also be changed later from within the graph via the General Layout dialog).  See below, for a list of plots in this dialog (click on each name for a brief description of the plot type).

  Scatterplot (matrix)

  Line (matrix)

  Column (matrix)

Variables

Values

  Graphs Gallery


Custom Matrix Graphs - Graphs Gallery Button

  Custom Matrix and Icon Graphs - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Custom Matrix Graphs - Variables

Select the variables that you want plotted here.  To select variables, either type in the variable name, or double-click on the variable edit field to open the Get Plotted Values From dialog.  In this dialog, you will be able to select the source of values (choose from column values or row values) to be plotted.


  Custom Matrix Graphs - Values

Designate the range of cases (i.e., From what case, To what case, inclusive) to be plotted here.  If you have a highlighted block of values in the Scrollsheet or spreadsheet, then by default STATISTICA will present here the range of cases for that block.


Get Variable for Min-Max Plot

Each "data unit" in the Min-Max type of plot must consist of a triplet of values:  x, y-Min, and y-Max for Min-Max Y plots, and x-Min, x-Max, and y for Min-Max X plots.  When you select either of the Min-Max plot options from the Custom 2D Graphs dialog, you will be asked to select the variable that contains the maximum values in the Get Variable for Min-Max Plot dialog.

Enter the variable name containing the maximum values either by typing it into the edit window or by double-clicking on this window to open the Get Plotted Values From dialog.  In this dialog, you will be able to select the source of the maximum values (choose from column variables or row values) to be plotted.


Define Deviation Level

The Define Deviation Level dialog will open whenever you select the Bar Dev plot from the Custom 2D Graphs dialog.  You can adjust the base of the bars (columns) in this plot.  That is, if the base value is set to a different value than the minimum of the Y axis, then individual bars are directed either up or down depending on the direction of the "deviation" of individual data points from the base line.  Enter the deviation level in the edit window of this dialog.


Scrollsheet Continue Button/Option

Data analysis sometimes results in several Scrollsheets of results.  When the number of Scrollsheets produced is greater than the Scrollsheet queue (see Scrollsheet Manager) a Continue button will appear on the last Scrollsheet displayed.  Clicking this button will continue the queue and open the next Scrollsheet of results.

If only one Scrollsheet is produced from an analysis (or if it is the last Scrollsheet in the queue), clicking on the Continue button will bring up the previous analysis dialog.  (Note that you can also re-open the analysis dialog by double-clicking on the analysis icon in the lower corner of the STATISTICA window.)


Box-Whisker Plot Types

Median/Quart./Range:  This box plot describes the central tendency of the variable in terms of the median of the values (represented by the smallest box in the plot).  The spread (variability) in the variable values is represented in this plot by the quartiles (the 25th and 75th percentiles, larger box in the plot) and the minimum and maximum values of the variable (the "whiskers" in the plot).  Note that you can select the desired method of computing percentiles in the STATISTICA Defaults:  General dialog.

Mean/SE/SD:  Here, the smallest box in the plot represents the mean (central tendency) of the variable, while the dispersion (variability) is represented by ± 1 times the standard error (large box) and ± 1 times the standard deviation about the mean ("whiskers").

Mean/SD/1.96*SD:  This plot will show the mean (small box in the plot) of the variable surrounded by a larger box (± 1 times the standard deviation).  If the distribution is normal, then the "whiskers" in this plot represent a "95% confidence interval" defined as the variable mean ± 1.96 times the variable standard deviation.

Mean/SE/1.96*SE:  Once again, this plot will show the mean (small box in the plot) of the variable surrounded by a larger box.  However, in this plot, the larger box represents ± 1 times the standard error.  If the distribution is normal, then the "whiskers" in this plot represent a "95% confidence interval" defined as the variable mean ± 1.96 times the variable standard error.

Many other graphic options (such as graph customizations or variable selections) or types of graphs are available in the pull-down menu Graphs (or by pressing the Graphs Gallery toolbar button [image].  In order to produce box plots representing the distribution of the values in cases (and not variables), use either the Block Stats Graphs - Box Plot/Means of Rows or Block Stats Graphs - Box Plot/Medians of Rows option from the Graphs pull-down menu (instead of transposing your data file).


Variables Selection for Analyses

When you need to select one or more variables for an analysis in STATISTICA, a variable selection dialog will open.  There are three types of variable selection dialogs (see below) that may open, depending upon the analysis.  Variables can be selected either by highlighting them in the dialog list or by entering their variable number in the dialog edit window.  In most cases (where applicable), when you mark a block of data in the spreadsheet and then enter into either the Selecting a Variable from a Single List or Selecting a Variable from a Double (or Multiple) List dialog for the first time, the highlighted variables in the block will be suggested to you in the dialog (i.e., pre-selected).

For specific information on each dialog, choose the dialog name below.

Selecting a Single Variable from a List

Selecting a Variable from a Single List

Selecting a Variable from a Double (or Multiple) List


Selecting Variables from a Single List

NOTE:  For information on the respective analysis (or graph) designs and the way in which the selected variables are used in the respective procedures, refer to the help topic for the dialog from which this variable selection window originated.

This dialog opens whenever you are requested to select variables from a single list.  If the list of variables is too large for the display window, then the list will be scrollable.

Selecting Variable dialog:

Selecting Variables

De-selecting Previously Selected Variables

Select All

Spread/Shrink

Zoom

Shortcut method to select one variable and exit:  When you need to select only one variable in the list, simply double-click on the variable name to select it and close the dialog box.

Note that in most cases (where applicable), when you mark a block of data in the spreadsheet and enter into this dialog for the first time, then the highlighted variables in the block will be suggested to you (i.e., "pre-selected").  The range of the block of variables will be displayed and highlighted in the dialog edit window.  In order to edit the variable number in the edit window, simply type over the highlighted numbers (you do not have to delete the numbers first).


Selecting Variables from a Single List - Selecting Variables

Select variables in this dialog either by highlighting them or entering the variable number in the edit window and then clicking on the OK button.

If you choose to select the variables by highlighting them in the list, you can select a continuous block of variables by holding down the left-mouse-button and dragging the cursor over the variables that you want to highlight.  You can also highlight a continuous block of variables by clicking on the first variable name that you want to select, and while holding down the SHIFT key, clicking on the last variable name that you want to select.  This method will select (highlight) the first and last variables and all variables in-between.  You can select discontinuous blocks of variables by holding down the CTRL key and then clicking on each variable that you want to select.


Selecting Variables from a Single List - De-selecting Previously Selected Variables

You can de-select discontinuous or continuous blocks of previously selected variables by holding down the CTRL key and then clicking on each variable that you want to de-select.  Alternatively, you can de-select variables by deleting the variable number(s) from the list of variables in the edit window.


Selecting Variables from a Single List - Select All

Click this button to automatically select all of the variables in the list.  Alternatively, you can enter an  *  (asterisk) in the edit window to select the entire list of variables.


Selecting Variables from a Single List - Spread/Shrink

When you click on this button, any long variable names associated with each variable will be displayed.  Click on this button again to remove the long variable names from the list.


Selecting Variables from a Single List - Zoom

Clicking this button will open the Variable Values Window (for the first of the highlighted variables) in which you can browse through a sorted list of the data values (numeric and text equivalents).


Selecting Variables from a Double (or Multiple) List

NOTE:  For information on the respective analysis (or graph) designs and the way in which the selected variables are used in the respective procedures, refer to the help topic for the dialog from which this variable selection window originated.

Some analyses may require you to select variables from more than one list of variables (e.g., one list for independent variables and another for dependent variables).  When this is the case, a dialog will open displaying two (or more) lists of variables from which you can select all or only specific variables in each list.

Selecting Variable dialog:

Selecting Variables

De-selecting Previously Selected Variables

Select All

Spread/Shrink

Zoom

Shortcut method to select one variable and exit:  Double-clicking in a variable selection dialog with more than one selection list will not change the previously selected variables, therefore, when you need to select only one variable in one of the lists, first select all of the other variables in the other lists, then simply double-click on the single variable name in the last list to select all of the highlighted variables and close the dialog box.

Note that in most cases (where applicable), when you mark a block of data in the spreadsheet and enter into this dialog for the first time, then the highlighted variables in the block will be suggested to you (i.e., "pre-selected").  The range of the block of variables will be displayed and highlighted in the dialog edit window.  In order to edit the variable number in the edit window, simply type over the highlighted numbers (you do not have to delete the numbers first).


Selecting Variables from a Double (or Multiple) List - Selecting Variables

Select variables by highlighting in each list the desired variables or by entering the variable numbers in the edit window of each list and then clicking on the OK button.

If you choose to select the variables by highlighting them, you can select a continuous block of variables by holding down the left-mouse-button and dragging the cursor over the variables that you want to highlight in each list.  You can also highlight a continuous block of variables by clicking on the first variable name that you want to select, and while holding down the SHIFT key, clicking on the last variable name that you want to select.  This method will select (highlight) the first and last variables and all variables in-between.  You can select discontinuous blocks of variables by holding down the CTRL key and then clicking on each variable that you want to select.


Selecting Variables from a Double (or Multiple) List - De-selecting Previously Selected Variables

You can de-select discontinuous or continuous blocks of previously selected variables by holding down the CTRL key and then clicking on each variable that you want to de-select.  Alternatively, you can de-select variables by deleting the variable number(s) from the list of variables in the edit window.


Selecting Variables from a Double (or Multiple) List - Select All

Click this button in the appropriate list to automatically select all of the variables in that list.  Alternatively, you can enter an  *  (asterisk) in the edit window to select all of variables in a particular list.


Selecting Variables from a Double (or Multiple) List - Spread/Shrink

When you click on this button, any long variable names associated with each variable will be displayed.  Click on this button again to remove the long variable names from the list.


Selecting Variables from a Double (or Multiple) List - Zoom

Clicking this button will open the Variable Values Window (for the first of the highlighted variables) in which you can browse through a scrollable, sorted list of the data values (numeric and text equivalents).


Selecting a Single Variable from a List

NOTE:  For information on the respective analysis (or graph) designs and the way in which the selected variables are used in the respective procedures, refer to the help topic for the dialog from which this selection window originated.

This dialog opens whenever you are requested to select one variable from a list of variables.  (If the list of variables is too large for the display window, then the list will be scrollable.)

Selecting Variable dialog:

Selecting Variables:  Select a variable in this dialog either by double-clicking on the variable name or by highlighting it (clicking once on the variable name) and then clicking on the OK button.

Spread/Shrink button:  When you click on this button, the long variable names (if there are any) associated with each variable in the list will be displayed.  Click on this button again to remove the long variable names from the list.

Zoom button:  Clicking this button will open the Variable Values Window in which you can browse through a scrollable, sorted list of the data values (numeric and text equivalents).


Reviewing Variables from a List

This dialog opens whenever you request to review the names of variables as well as other variable attributes.  (If the list of variables is too large for the display window, then the list will be scrollable.)

Reviewing Variables dialog:

Spread/Shrink button:  When you click on this button, the long variable names (if there are any) associated with each variable in the list will be displayed.  Click on this button again to remove the long variable names from the list.

Zoom button:  Clicking this button will open the Variable Values Window in which you can browse through a scrollable, sorted list of the data values (numeric and text equivalents).


Variable Values Window

This window allows you to examine the values of a variable, as well as its name, missing data value, format and long variable name (if there is one), and some descriptive statistics for that variable (see below).

Variable Values:  The variable values are presented in a sorted list through which you can browse.  If the variable has any text values, then these are displayed next to their numeric equivalents in the list.  If this dialog is accessed by pressing the Zoom button in a variable list (or variable selection) dialog, then you can return to that dialog by clicking OK.

Descriptive Statistics:  The descriptive statistics for the variable include the sample size (n), mean, and standard deviation.  You can copy the variable name and these statistics to the clipboard (press on the Copy button in this part of the dialog) in order to paste it into a graph, Text/output Window, or use it in another Windows application (e.g., a word processor).

Copy to Clipboard button:


Variable Codes Window

To select a code and enter it in the respective edit field, you can either double-click on it, or highlight it and click OK to close the dialog.

This window allows you to examine the values of a grouping variable, as well as the variable name, missing data value, format and long variable name (if there is one).  The codes for the grouping variable are presented in a sorted list through which you can browse.  If the code values have any text equivalents, then these are displayed next to the numeric values in the list.

For more information, see Selecting Codes.


Selecting Codes

The Codes dialog will open whenever you have to select codes for grouping variables (i.e., specific values of a variable to be used to identify group membership of cases or observations).  The dialog will display the grouping variable name and then prompt you to enter the codes for that variable (e.g., 1, Male, "#52").

You may either type specific codes in the window, or enter an  *  (asterisk) to accept all of the codes available for the variable.  When entering text codes in this window, you can save time by typing the codes in the edit field with lower case letters and STATISTICA will automatically convert them to upper case letters (e.g., smith will be converted to SMITH).  However, since STATISTICA distinguishes between lower and upper case letters in codes, be sure to place any code that needs to remain in lower case letters in single or double quotes (e.g., 'Smith', "Pepsi", "StatSoft", see below).

The following conventions apply when entering code names:

•	If codes consist of only uppercase letters and numbers (e.g., ITEM9, MALE) but not starting with a number, then the code will be displayed in the edit field without single or double quotes around them.

•	Codes which have been entered in the spreadsheet in upper and lower case or only lower case letters (e.g., 'Male', "test1") need to be displayed in quotes (single or double) in this edit window in order to preserve the upper and lower case character formatting.

•	Codes which start with a number or a character other than a letter (e.g., "=shift3", '39lbs', "49°C", "15-Apr") need to be displayed in quotes (single or double).

•	Date values will be displayed in quotes (single or double) if the variable's format is set to Date (see Current Specs).

See also:	Using code values greater than 32,000

Using dates as codes

Shortcut:  If you leave all fields in this dialog empty (blank) and click OK, then STATISTICA will identify and automatically use all available codes (for the previously specified grouping variables).  Also, the same effect will be achieved if you do not enter this dialog but click the OK button in the previous (design specification) dialog, without explicitly specifying any codes.

Codes dialog:

All

View

Select All


Selecting Codes - Edit Window

Specify the variable values (to be used as codes) here.  You may either type specific codes in the window, or enter an  *  (asterisk) to accept all of the codes available for the variable.  When entering text codes in this window, you can save time by typing the codes in the edit field with lower case letters and STATISTICA will automatically convert them to upper case letters (e.g., smith will be converted to SMITH).  However, since STATISTICA distinguishes between lower and upper case letters in codes, be sure to place any code that needs to remain in lower case letters in single or double quotes (e.g., 'Smith', "Pepsi", "StatSoft", see below).

The following conventions apply when entering code names:

•	If codes consist of only uppercase letters and numbers (e.g., ITEM9, MALE) but not starting with a number, then the code will be displayed in the edit field without single or double quotes around them.

•	Codes which have been entered in the spreadsheet in upper and lower case or only lower case letters (e.g., 'Male', "test1") need to be displayed in quotes (single or double) in this edit window in order to preserve the upper and lower case character formatting.

•	Codes which start with a number or a character other than a letter (e.g., "=shift3", '39lbs', "49°C", "15-Apr") need to be displayed in quotes (single or double).

•	Date values will be displayed in quotes (single or double) if the variable's format is set to Date (see Current Specs).


Selecting Codes - All

Select all of the variable's values by clicking the All button.  When you click on this button, STATISTICA will automatically search the variable values (taking into account any case selection conditions) and enter all the variable's codes in the edit window.  Alternatively, to select all codes for a variable, click the OK button (leaving the edit window blank) or enter an  *  (asterisk) in the edit window.


Selecting Codes - View

If you would like to view the values of the variable before selecting specific codes, press the View button to open the Variable Values Window.  You can browse through a table of sorted variable values in this window (all values will be shown regardless of any currently specified case selection conditions).


Selecting Codes - Select All

This button is available when you have more than one variable listed in this dialog.  If you want to automatically enter all of the codes for each of the variables listed (taking into account any case selection conditions), then click on the Select All button.  You may also select all codes for each variable by clicking the OK button before entering any codes or clicking any other buttons.


  System Menu

Use the System Menu options to perform various Window functions.

Restore:  This option restores the window to its previous size after it has been maximized or minimized.

Move:  This option will enable you to use the keyboard to move the window to another position.

Size:  With this option you can enable the keyboard to change the size of the window.

Minimize:  This option reduces the window to an icon.

Maximize:  Selecting this option will enlarge the window to its maximize size.

Close:  Selecting this option will close the current STATISTICA module.

Switch To:  This option will open the Task List dialog from which you can select between running applications and rearrange their windows and icons.


Keyboard Interface

Keyboard combinations can be used as Hot Keys in order to access various STATISTICA procedures.  These system procedures Hot Keys are given below.  To assign a Hot Key to a macro (Auto Task Button), see Hot Keys and Hot Keys in Use.

Click on a Window name in order to view the keyboard shortcuts which are specific for that window:

Spreadsheet	Graph

Scrollsheet	Graph Data Editor

Text/Output Window	Megafile Manager

STATISTICA BASIC	SCL

Common Keys (available in all windows)

File I/O:	Open	CTRL+O
Save	CTRL+S
Save As	F12

Open Other 	New Data	CTRL+N
Data File	CTRL+F12
Graph File	SHIFT+F3
Scrollsheet	CTRL+F11

Toolbars:	Auto Task Buttons (on/off)	CTRL+M

Printing:	Print	CTRL+P, F4
Page/Output Setup	SHIFT+F4

Edit:	Undo	CTRL+Z or ALT+Backspace
Select All	CTRL+A  (See the note about the Graph window, below).
Clear Selection	DEL

Clipboard:	Cut	CTRL+X
Copy	CTRL+C
Paste	CTRL+V
Screen Catcher	ALT+F3

Analyses:	Startup Panel	CTRL+T
Resume Analysis	CTRL+R
Case Selection Conditions	F8
Weighting Variable	F7

Macros:	Record macro	CTRL+F3
Run macro	CTRL+letter

Windows:	Cascade	SHIFT+F6
Tile Horizontally	ALT+F6
Tile Vertically	ALT+SHIFT+F6
Help	F1
Close	CTRL+F4
Close all but data file	CTRL+L
Exit	ALT+F4
Switch to	CTRL+ESC

Note:  In the Graph window, all contents of the window are always "selected" in that the entire graph will be copied to the Clipboard when you press CTRL+C.  Pressing CTRL+A (the global "select all" hot key) will select consecutive, custom objects; pressing SHIFT+ CTRL+A will go back down the list of objects.


Keyboard Interface - Spreadsheet Window

In addition to the common keys available in every window, the following keyboard combinations are specific to the spreadsheet window.

Convert:	Convert to Scrollsheet	F11

Recalculate:	Recalculate All Formulas	F9

Edit:	Undo	CTRL+Z or ALT+Backspace
Edit Cell	F2
Edit Current Specs	CTRL+F2

Expanding Blocks	SHIFT-cursor [or position the cursor in one corner of the block to be selected, scroll to the location of the opposite (diagonal) corner and click in that corner location while holding down the SHIFT key].

Customization:	View Font dialog	CTRL+F9
Customize Colors	SHIFT+F9

Graphs:	Quick Stats Graphs	F3


Keyboard Interface - Scrollsheet Window

In addition to the common keys available in every window, the following keyboard combinations are specific to the Scrollsheet window.

Edit:	Edit Cell	F2
Column Specs	CTRL+F2
Row Name	ALT+F2

Expanding Blocks	SHIFT-cursor [or position the cursor in one corner of the block to be selected, scroll to the location of the opposite (diagonal) corner and click in that corner location while holding down the SHIFT key].

Customization:	View Font dialog	F9
Customize Colors	SHIFT+F9

Graphs	Quick Stats Graphs	F3


Keyboard Interface - Text/output Window, STATISTICA BASIC Window, SCL Window

Keyboard Interface - Text/output Window, STATISTICA BASIC Window, or SCL Window

In addition to the common keys available in every window, the following keyboard combinations are specific to the Text/output Window, STATISTICA BASIC window, or SCL window.

Undo:	Undo	CTRL+Z or ALT+Backspace

Edit:	Find	CTRL+F
Find Next	CTRL+ALT+F
Replace	CTRL+H
Go To	F5
Insert Bitmap from File	F3
Object Size	SHIFT+F3
Colors	SHIFT+F9
Insert page break	CTRL+ENTER

Characters:	Regular	CTRL+0 (zero)
Bold	CTRL+B
Italic	CTRL+I
Underline	CTRL+U
Double Underline	CTRL+D
Font	CTRL+F9

Wizard:	Wizard	ALT+I (applicable to SCL and
 STATISTICA BASIC)


Keyboard Interface - Graph Window

In addition to the common keys available in every window, the following keyboard combinations are specific to the Graph window.

Edit:	Undo	CTRL+Z

Object Properties:	Object Properties	ALT+ENTER

Object Alignment:	View Alignment Grid (on/off)	CTRL+G
Snap to Grid	hold TAB

Moving and resizing objects using cursor keys	Select an object and position the cursor on the object (to resize or move it), then use the keyboard cursor keys to drag a shadow of the selected graph object to a new position.  Hold down the CTRL key for fine (1 pixel only) dragging movements.  Press ENTER to complete the action.

Select All	CTRL+A  Note:  In the Graph window, all contents of the window are always "selected" in that the entire graph will be copied to the Clipboard when you press CTRL+C.  Pressing CTRL+A (the global "select all" hot key), will select individual, consecutive, custom objects; pressing SHIFT+CTRL+A will go back down the list of objects.

Text Rotation	Page Up/Down  Select the added text and use the PAGE DOWN and PAGE UP hot keys to rotate text objects selected in the graph clockwise or counterclockwise, respectively, in 5° increments.  To rotate in 1° increments, hold down the CTRL key while pressing PAGE DOWN and PAGE UP.


Keyboard Interface - Graph Data Editor Window

In addition to the common keys available in every window, the following keyboard combinations are specific to the Graph Data Editor window.

Edit:	Edit Cell	F2

Customization:	View Font dialog	F9
Customize Colors	SHIFT+F9


Keyboard Interface - Megafile Manager Window

In addition to the common keys available in every window, the following keyboard combinations are specific to the Megafile Manager window.

Edit:	Edit Cell	F2

Customization:	View Font dialog	F9
Customize Colors	SHIFT+F9


Mouse Conventions

In addition to the standard, Windows-system related applications, the mouse provides shortcuts to specific features in STATISTICA.  See below for an overview of these mouse conventions and functions.

Right- and Left-Mouse-Buttons

Left-mouse-button:  The left-mouse-button is used for selecting (e.g., an option in a dialog), highlighting (e.g., a block of data in a spreadsheet), and dragging (e.g., dragging a block in a spreadsheet or dragging an object in a graph; see below).  Double-clicking on an object with the left-mouse-button provides a direct shortcut to some of the most commonly used dialogs in STATISTICA.  For example, double-clicking with the left-mouse-button on a spreadsheet or Scrollsheet cell, header, column name, etc., will bring up a dialog allowing you to edit the respective feature, while double-clicking with the left-mouse-button on a graph object, title, point marker, etc., will bring up the respective dialog allowing you to edit that part of the graph.  In this way, you save a step whenever you want to access a commonly-used option.  In addition, double-clicking on the background of STATISTICA, will bring up the Module Switcher.

Right-mouse-button:  When you click on an object (e.g., a cell in a spreadsheet) with the right-mouse-button, a dynamic flying menu will come up.  These flying menus allow easy access to some commonly-used options in every window in STATISTICA (e.g., graph window, spreadsheet window, Text/output Window, etc.).  For example, if you click with the right-mouse-button on a spreadsheet cell, a flying menu of graph options, statistics options, Clipboard operations, and others will come up, allowing you to quickly perform the desired operation.  Clicking on the background of STATISTICA with the right-mouse-button will bring up the Module Switcher.

Selecting Items from Multiple-Selection Lists

You can select items in a multiple-selection list in the following manners:

•	Click on an item to select (highlight) it.  Clicking OK in the dialog will accept the selection.

•	Double-click on an item to select it and accept the selection (close the dialog).

•	In order to select a continuous list of items, you can (1) hold down the left-mouse-button and drag the cursor over the items that you want to highlight or (2) highlight the first item and then while holding down the SHIFT key, click on the last item that you want to select.

•	In order to select a discontinuous list of items, hold down the CTRL key and click on the desired items.

Using the SHIFT and CTRL Keys with the Mouse

For some applications of the mouse, holding down the CTRL or SHIFT key will modify the default mouse actions.  For example,

•	You can quickly highlight a block of values in a spreadsheet or Scrollsheet by clicking on a cell to define the beginning of the block and then (e.g., after scrolling with the scrollbars) while holding down the SHIFT key, click on a cell that will define the end of the block.  All of the values in-between will be highlighted.

•	Holding down the CTRL key when you click on an Auto Task Button will open the respective dialog for editing the contents of the button.

•	Holding down the CTRL key while pressing either the Graphics window [image] Increase Font or [image] Decrease Font toolbar buttons will achieve a small (4% instead of the default 16%) increase or decrease in the mapping base.

•	Holding down the CTRL key while pressing on the spreadsheet window [image] toolbar button will switch to the value label display in the spreadsheet (see Spreadsheet View Text and Numeric Values and Value Labels.

•	Hold down on the SHIFT key while you are dragging the mouse in the Graphics window in order to make a square, squared rounded rectangle, circle, or quarter arc (see Graphics Drawing Tools).

Specific applications are given below.

Other Applications

In addition to the applications mentioned above, you can perform the following using the mouse:

•	Drag-and-Drop:  Provides mouse shortcuts for moving, copying, deleting, inserting, extrapolating, etc. a block of values in the spreadsheet or Scrollsheet.

•	Increase/decrease column width:  Adjusts the spreadsheet or Scrollsheet column width by dragging the right column border to the desired width.

•	Split Scrolling (in spreadsheets and Scrollsheets):  Splits the spreadsheet or Scrollsheet window (i.e., split scrolling) by dragging the split box (the black rectangle at the top of the vertical scrollbar or to the left of the horizontal scrollbar).

•	Variable-speed Scrolling:  Controls the speed at which you scroll (1 line at a time by moving the cursor a short distance away or one page at a time by moving the cursor further away) when you extend a block outside the spreadsheet or Scrollsheet.

•	MicroScrolls [image]:  Enables you to increase or decrease the value in a numeric edit field incrementally, by either the last digit (click on the micro scroll with the left-mouse-button, e.g., 1.11, 1.12, 1.13, ...) or the last digit by a factor of 10 (click on the micro scroll with the right-mouse-button, e.g., 1.11, 1.21, 1.31, ...).

•	Toolbar configuration:  Double-clicking on the space between the buttons of the toolbar will toggle between four toolbar configurations (1 line, 2 lines, right & top, and left & top).

•	Auto Task Buttons:  Holding down the CTRL key while clicking on an Auto Task Button will open a dialog allowing you to edit the Auto Task Buttons contents.

•	Auto Task Buttons toolbar:  Double-clicking on the space between the buttons of the Auto Task Buttons toolbar with the left-mouse-button will resize it (alternatively, you can drag this toolbar's border with the mouse to resize it).  Clicking with the right-mouse-button will bring up a flying menu of options.  You can "dock" the toolbar by dragging it to an area of the STATISTICA window (above the toolbar, below the status bar, or to either side of the window) where the toolbar will change configuration and remain in that position until you drag it to a different area of the window.

•	Reordering items in a list:  You can reorder items in a list (e.g., Workbook, Auto Task Buttons, Multiple-Graph AutoLayout Wizard, etc.) by highlighting one or more (in a continuous or dis-continuous list) items and then moving the mouse cursor to the desired position (the cursor will change to a [image]).  Clicking the left-mouse-button will then move the highlighted item(s) to the insertion point.

Graph Applications

The following applications apply to the Graphics window in STATISTICA.  Note that the current mouse coordinates (or angle of rotation, see below) will be displayed in the Change Show window of the Graphics toolbar.

•	OLE:  Links or embeds foreign document files to STATISTICA documents by dragging them with the mouse directly from File Manager (across application windows) and dropping them onto STATISTICA graphs.

•	Brushing:  Highlights data points from the graph by clicking on them with the brushing tool.

•	Zoom in and Zoom out tools:  Zooms in (magnifies) or zooms out ("shrinks") respectively, the selected area of the graph.

•	Drawing tools:  Adds rectangles, ovals (or circles), polylines and free-hand drawings, arrows, etc. to a graph.  Hold down on the SHIFT key while you are dragging the mouse in order to make a square, squared rounded rectangle, circle, or quarter arc.

•	Resizing and Moving:  Resizes (drag on a "black selection square," [image]) or moves (drag the entire object, [image]) selected graph objects.  For fine adjustments, see Controlling the mouse with the keyboard in graphs, below.

•	Editing polyline objects:  Reshapes individual segments of the polyline drawing by dragging with the mouse on either the object area black selection squares or any of the black selection squares that mark the line segments.  For fine adjustments, see Controlling the mouse with the keyboard in graphs, below.

•	Rotating text:  You can interactively rotate custom text by selecting it in the graph and then dragging one of the object handles (small black squares) in the desired direction [the angle (in degrees) will be displayed in the Change Show window of the Graphics toolbar].  For fine adjustments (1 degree movements), see Controlling the mouse with the keyboard in graphs, below.

•	Snap to Grid [image] (in graphs):  Aligns drawing objects with the drawing grid, an invisible network of lines that covers the drawing area.

•	Graph Mapping Base:  Clicking on the [image] or [image]  toolbar buttons will change the value of the Graph Mapping Base by ±16%, respectively.  Holding down the CTRL key while pressing either of these buttons will achieve a smaller (4%) increase or decrease in the mapping base.

•	Controlling the mouse with the keyboard in graphs:  You can also emulate the mouse with the keyboard in order to move or resize an object by selecting the object, placing the mouse over the object, and then using the keyboard cursor keys to move or resize the object.  Hold down the CTRL key for fine (1 pixel only) movements and press ENTER to complete the action.

Note that the mouse cursor will change to the appropriate tool to match the application for which it is being used.  Clicking on the ESC key will return the mouse to the default mode.

Interrupt/Break Current Action.  You can also use the mouse (press on the left-mouse-button) to interrupt a current action (e.g., redrawing of a graph, processing of an SCL program, etc.; for more information, see Breaking, Stopping, or Interrupting the Current Action.


Date Operations

You can create a single date variable from two or three variables (containing the month and year, day and month, or month, day, and year) or split a single date variable into two or three variables (one each for the month and year, day and month, or month, day, and year) using the Date Operations dialog.  (See below for examples, see also, Dates.)

Date Operations dialog:

Create Date from 2 or 3 Variables

Split Date into 2 or 3 Variables

Text Values/Dates

Source Variables

Destination Variables

Example 1 (Create a single date)

Example 2 (Split a date variable)


Date Operations - Create Date from 2 or 3 Variables

Select this option if you want to create single date values (in a new variable) from day, month, and year values in three existing variables or from the month and year values or day and month values in two existing variables.


Date Operations - Split Date into 2 or 3 Variables

Select this option if you want to split single date values (from an existing variable) into separate values for the day, month, and year, in three (previously created) new variables or into separate values for either the month and year or day and month, in two (previously created) new variables.


Date Operations - Text Values/Dates

Click on this button to open the Text Values/Dates dialog.  In this dialog, you can change the dates to text labels (e.g., in order to use the date variable as a categorical variable) and vice versa.


Date Operations - Source Variables

The variable(s) that you select here will depend on whether you are creating a single date, or splitting a single date.

Create Date from 2 or 3 Variables:  When you select this option, you will need to specify as the Source Variables, the three variables containing the Day, Month, and Year values (see, Example 1, below) or the two variables containing either the Day and Month (STATISTICA will enter the current year as the year value) or the Month and Year (STATISTICA will enter the first day of the month as the day value).

Split Date into 2, or 3 Variables:  When you select this option, you will need to specify as the Source Variable, the variable containing the single date values.


Date Operations - Destination Variables

The variable(s) that you select here will depend on whether you are creating a single date, or splitting a single date.

Create Date from 2 or 3 Variables:  When you select this option, you will need to specify as the Destination Variable, a single variable name in which the new date values will be placed (see Example 1, below).  You will also need to specify the date format by selecting the desired format from the Format combo box.

Split Date into 2, or 3 Variables:  When you select this option, you will need to specify as the Destination Variables, the previously created variables in which the Day, Month, and Year values ( for 3 variables, see Example 2, below), or the the Day and Month or Month and Year values (for 2 variables) will be placed.


Creating a Single Date

In this example, lets create a single date variable from three variables using the STATISTICA example data file Heart.sta.  You can access the Date Operations dialog by selecting the Vars - Date Values option from the Edit pull-down menu or by clicking on the Vars Toolbar button and selecting the Date Values option.

Step 1:	You will first need to create a new variable that will contain the single dates.  To do this, select the Vars-Add option from the Edit pull-down menu and specify 1 new variable to be added to the data file.  (For more information on adding variables, see Add Variables; for more information on changing the variable name and other specifications, see Current Specs.)

Step 2:	Now, open the Date Operations dialog (see above) and select the option Create Date from 3 Variables.

Step 3:	In the Date Operations dialog, specify the 3 variables with the dates (Source Variables) by double-clicking on the Day, Month, and Year variable edit fields and then selecting the appropriate variable from the list of variables in the data file (for more information on selecting variables, see Selecting a Single Variable from a List).

Step 4:	Specify the variable name in which the single date values will be placed (the Destination Variable) and also the value format for the single dates.  First, double-click on the variable edit field and select the new variable that you previously created as the destination file.  Next, select the desired value format from the Format combo box (you can later change the date value format in the Current Specs dialog).

Step 5:	Click OK in the Date Operations dialog to complete the creation of one date variable from the three variables.


Splitting a Date Variable

In this example, we will create three variables with the month, day and year from a single date variable using the STATISTICA example data file Heart.sta and the new date variable that was created in Example 1.  You can access the Date Operations dialog by selecting the Vars - Date Values option from the Edit pull-down menu or by clicking on the Vars Toolbar button and selecting the Date Values option.

Step 1:	You will need to create three new variables that will be used as the Destination Variables (see below) and will contain the day, month, and year values, respectively.  To do this, select the Vars-Add option from the Edit pull-down menu and specify 3 new variables to be added to the data file.  (For more information on adding variables, see Add Variables; for more information on changing the variable name and other specifications, see Current Specs.)

Step 2:	Open the Date Operations dialog (see above) and select the option Split Date into 3 Variables.

Step 3:	In the Date Operations dialog, the Source Variable is now a single variable (instead of three as in Example 1).  Double-click on this variable edit field to select the variable with the date values from a list of variables in the data file (for more information on selecting variables, see Selecting a Single Variable from a List).

Step 4:	Specify the Destination Variables by double-clicking on the Day, Month, and Year variable edit fields and selecting each of the previously created variables (see Step 1).

Step 5:	Click OK in the Date Operations dialog to complete the splitting of the single date variable into three variables.


Dates

STATISTICA internally stores date values of variables in Julian format.  This type of date format presents the date as a single integer value that represents the number of days that have passed since Jan. 1, 1900; for example a date entered as 1/21/1968 will be stored as the Julian date 24858).  Date values stored in this manner can be used in subsequent analyses (e.g., in Survival Analysis in order to calculate survival times, see below).

Julian date values can be displayed in the spreadsheet in numeric (Julian) format or in one of several pre-defined date display formats.  To change the date display format, select the Date format option in the Current Specs dialog (accessible by double-clicking on the variable name in the spreadsheet or from the spreadsheet Edit pull-down menu) and choose one of the pre-defined display formats from the combo box.

When entering dates into a new variable, you will first need to change the variable display format from Decimal (the default format) to Date in the Current Specs dialog and select the desired date display format.  Now, you can enter the dates in any of the pre-defined date display formats (i.e., enter the dates in the format that is easiest to key in, even if it is different than the desired display format) and STATISTICA will recognize those formats, convert the display to the desired date format, and internally store the date values in Julian format.  Note the following when entering dates:

•	If you enter a date in the month-year format (e.g., Mar-1987), then STATISTICA will interpret the missing day entry to be the first day of the month (e.g., 1-Mar-1987) in order to store the date in Julian format.

•	For dates entered in the day-month format (e.g., 6-Mar), STATISTICA will interpret the missing year entry to be the current year (e.g., 6-Mar-1993) in order to store the date in Julian format.

•	If you enter a date without any separators (e.g., as 2855 instead of 2/8/55) then STATISTICA will interpret that number to be a Julian date and convert it accordingly to the desired date format, resulting in an incorrect date (e.g., 2855 would become 10/25/07 instead of 2/8/55).

You can copy dates from a STATISTICA spreadsheet and paste them into other Windows applications (e.g., MS Word, Excel) as well as paste dates copied from another Windows application into a STATISTICA spreadsheet.  Note that if Decimal format is selected for the current variable (see, Current Specs), then the dates will be displayed in Julian format when pasted to the STATISTICA spreadsheet, otherwise, they will be displayed in the selected date format when pasted into the spreadsheet.

You can create a single date variable from two (month, year or day, month) or three (day, month, year) variables as well as split a single date variable into two or three variables in the Date Operations dialog.

Example

Dates as Text Values:

In some circumstances it may be useful to create text values with date information (e.g., when using a date variable as a coding variable).  In this case, you can transform the date variable into a variable containing date text values with numeric equivalents in a range that will allow STATISTICA to use them as codes (i.e., numeric values less than 32,000), in the Text Values/Dates dialog.


Using Dates in STATISTICA

The Survival Analysis module in STATISTICA utilizes date variables in order to compute survival times.  These date variables can be specified in one of two ways:

•	Survival times can be computed from two variables containing dates.  These variables will contain the month, day, and year when the observation began and ended, respectively, but the month, day, and year is now specified in a single variable instead of three (see below).

•	Survival times can also be computed from six variables containing dates.  Specifically, these variables contain the month, day, and year when the particular observation began (e.g., when the patient was admitted to the hospital), and the month, day, and year when the observation was terminated (due to death/failure or censoring, for example when a patient was dismissed from the hospital).  While processing the data, Survival Analysis will compute the number of days that elapsed between dates, and perform the analysis on this measure.

For either of the two methods given above, while processing the data, Survival Analysis will compute the number of days that elapsed between dates, and perform the analysis on this measure.  Survival times can also be specified in a single variable as the number of weeks, days, years, etc. surviving.


Text Values/Dates

In some circumstances it may be useful to create text values with date information (e.g., when using a date variable as a coding variable).  In this dialog, you can transform the date variable into a variable containing date text values with numeric equivalents in a range that will allow STATISTICA to use them as codes (i.e., numeric values less than 32,000).  You can also transform a variable containing date text values into a date variable with the desired date format.

Text Values/Dates dialog:

Transform:  Select the type of variable transformation here.

Date Variable to Variable with Text Values:  Select this option if you want to transform a date variable (see Date Operations) into a variable containing dates as text values.  The resulting date text values will be of the format MMMDD_YY.  For example, the date value 6-Jan-68 (with the Julian value of 24843) will be transformed to the text value JAN06_68 (with the numeric equivalent of 4843).

Variable with Text Values to Date Variable:  This option allows you to transform variables with dates as text values into date variables.  For example, the date text value MAY25_80 will be transformed into the pre-specified date format of 05/25/80.  In order for STATISTICA to recognize the date text value, it must be entered in the MMMDD_YY format.  When you transform this text value into a date value, you will be able to select the desired date format (see below).

Source Variable:  The variable that you select here will depend on the type of transformation that you are performing:

If you are transforming a Date Variable to a Variable with Text Values, then select here, the variable with the formatted date values.

If you are transforming a Variable with Text Values to a Date Variable, then select here, the variable containing the date text values.

Destination Variable:  You can select as the destination variable (where the transformed values will be placed) either the source variable (i.e., the transformed values will replace the original values) or a different variable in which the transformed variables will be placed.

Format:  When you are transforming a variable with text date values into a variable containing date values, you will be able to select the format for the resulting transformed dates from this combo box.


Reopen File Saved in Another Module

This dialog box is displayed when you run two (or more) STATISTICA modules simultaneously, modify the same file (e.g., data file or text window) in both modules, and then try to save it in one of the modules.

For example:

1. You are using and have modified the file A.STA in Basic Statistics and Tables.

2. You are using and have modified the file A.STA in Data Management.

3. You request "Save" in Data Management.

In such a case, after saving the file in Data Management, the program will ask you if you wish to reopen the new (saved) version of A.STA in Basic Statistics and Tables.

If you answer Yes, the file will be reopened to reflect the result of the "Save" operation performed in Data Management. If you answer No, then the changes you made in Basic Statistics and Tables will be maintained.

Note that a similar situation will occur when in one module you perform a "Save As" operation and specify the name of a file that has been modified but not saved in another module.

For example:

1. You are using and have modified the file A.STA in Basic Statistics and Tables.

2. You are using file B.STA in Data Management.

3. You request "Save As" in Data Management, and specify A.STA as a new name for the saved file.

In such a case, STATISTICA will first warn you that A.STA already exists and will be overwritten.  Then, after saving the file in Data Management, the program will ask you if you wish to reopen the new (saved) version of A.STA in Basic Statistics and Tables.

If you answer Yes, the file will be reopened to reflect the result of the "Save As" operation performed in Data Management. If you answer No, the changes you made in Basic Statistics and Tables will be maintained.


Save Modified File before Opening It in Another Module

This dialog box is displayed when you run two (or more) STATISTICA modules simultaneously and in one module try to open a file (e.g., data file or text window) that is currently in use and has been modified (but not saved) in another module.

For example:

1. You are using and have modified the file A.STA in Basic Statistics and Tables.

2. You request "Open" in Data Management and specify A.STA as the file to be opened.

In such a case, the program will ask if you want to save the changes you made in Basic Statistics and Tables before opening the file in Data Management.

If you answer Yes, Basic Statistics and Tables will automatically save the file, and the new version will be opened in Data Management. If you answer No, Data Management will open the original version of A.STA.

Note that a similar situation will occur when you use and modify (but not save) a file in one module and then try to run another STATISTICA module.

For example:

1. You are using and have modified file A.STA in Basic Statistics and Tables.

2. You bring up STATISTICA Module Switcher and select Data Management.

When Data Management is starting, it tries to open A.STA as its data file. After determining that A.STA has been modified but not saved in Basic Statistics and Tables, the program will perform the same action as described in the example above.


Print Graph and Scrollsheet Files

This option (available from the File pull-down menu) allows you to print previously-saved graphs and Scrollsheets in batch.  This option is useful if you want to batch print graphs and Scrollsheets at a later time.  You simply save the graphs or Scrollsheets (via the Scrollsheet Save or Save Graph options) after you make them, then at a later time open this dialog, select the desired graphs and Scrollsheets (see below) and click OK to begin the batch printing process.

When you click OK in this dialog, all of the selected graphs will be printed first (on separate pages, in the order in which they are selected) and then all of the Scrollsheets will be printed together (in the order in which they are selected).

Print Graph and Scrollsheet Files dialog:

List of Files to be Printed:  This area of the dialog displays the list of files to be printed.  You can add or remove files from this list using the buttons described below.  Once a graph or Scrollsheet file is sent to the printer, its file name is removed from the List of Files to be Printed.

Add Files buttons:  When you click on this button, the Select Files to be Printed dialog will open in which you can select the graph or Scrollsheet files to be printed.  Press on the CTRL button in order to select multiple files (continuously or discontinuously) from the list of files.  Once selected, the name of the files will be placed in the List of Files to be Printed (see above).

Remove button:  Click on this button to remove the highlighted file from the List of Files to be Printed.

Cancel button:  When you click OK in this dialog, the printing begins but the dialog will continue to be displayed in the background.  All of the buttons will be dimmed except this Cancel button.  You can interrupt the batch printing by clicking on the Cancel button.  When you click on the Cancel button, the batch printing will stop after printing of the last graph or Scrollsheet sent to the printer buffer is complete.

You can also interrupt the printing of an individual graph or Scrollsheet (rather than interrupting the batch printing) by clicking on the Cancel button in the Windows Printing status dialog.


Auto Task Buttons

The Auto Task Buttons is a floating, user-defined toolbar that allows you to quickly access most of STATISTICA's task automation facilities.  You can define the buttons on the Auto Task Buttons toolbar by assigning them to:

•	 macros created by recording keystrokes and mouse actions;

•	 macros created by entering sequences of keystrokes (or by editing pre-recorded macros);

•	 batches of STATISTICA procedures specified using SCL (STATISTICA Command Language);

•	 user-defined procedures and programs written in STATISTICA BASIC (e.g., new graphs, new computational procedures, data transformations, etc.);

•	 specific STATISTICA files (data, graphs, reports, etc.) to which you need quick access.

Procedures assigned to Auto Task Buttons can also be invoked with user-specified Hot Keys.  In addition, Auto Task Buttons can be utilized when a dialog is open.  For example, you can create a keyboard macro that will select specific options in a commonly-used dialog (e.g., a Stats Graph dialog).  Then when that dialog is open, all you have to do is press the Auto Task Button (or optionally use the user-specified Hot Key combination) to run the macro that will select the options for that dialog.  (See Hints for some useful hints for entering keyboard macros.)

The contents of the Auto Task Buttons toolbar can be customized by modifying, (e.g., reassigning), adding or removing buttons and also by resizing the menu (drag the toolbar border with the left-mouse-button or double-click on the toolbar) and can be saved.  Auto Task Buttons toolbars can be global (available to all modules) or local (associated with specific modules or specific projects).

You can toggle on/off the display of this toolbar using the keystrokes CTRL+M.  Double-clicking on the toolbar will change the toolbar configuration (i.e., resize the toolbar, see above).  You can "dock" the toolbar by dragging it to an area of the STATISTICA window (above the toolbar, below the status bar, or to either side of the window) where the toolbar will change configuration and remain in that position until you drag it to a different area of the window.

The following options are available when you click on the Customize button on the Auto Task Buttons toolbar.

Customize Auto Task Buttons dialog:

View Auto Task Buttons (Buttons List and Description)

Display Toolbar

Edit/Reassign Button

Remove Button(s)

Add Buttons

Auto Task Files

Auto Save Changes

Display button Icons

Display Hot Keys

Keyboard Shortcut:  CTRL+M.


Auto Task Buttons - View Auto Task Buttons (Buttons List and Description)

This area of the dialog displays the names of the buttons available to the current Auto Task Buttons toolbar.  Only those buttons which are checked in this list (see View, below) are displayed in the Toolbar.  When a button is highlighted in this list, the associated file name, type of file, Hot Key (if applicable), and previously entered description of the button is displayed below this area of the dialog.

View:  You can select the buttons to be displayed in the Auto Task Buttons toolbar by checking the respective check box in this area of the dialog.  Un-checked buttons will not be displayed on the toolbar but will remain in this list and their actions can still be accessible using the respective Hot Keys (if assigned).  In this way, you can further customize the Auto Task Buttons toolbar by displaying only the desired buttons.

Changing the order of buttons:  To change the order of the buttons in the toolbar, first highlight one or more of the button names in this area of the dialog, then move the cursor to the desired position in the list and when the cursor changes to a [image], click on the left-mouse-button to complete the move.

Editing a button:  To edit the button name, description, Hot Key, or contents, you can highlight the button name and then click Edit/Reassign Button, double-click on the button name in this list.  Alternatively, outside this dialog you can hold down on the CTRL key when you click on the button in the Auto Task Buttons toolbar.


Auto Task Buttons - Display Toolbar

De-elect this option in order to hide the Auto Task Buttons toolbar.  Alternatively, you can toggle the toolbar on/off by pressing CTRL+M or via the View pull-down menu option Auto Task Buttons.

Note that if you assign Hot Keys to specific buttons, their respective actions can still be accessed with the keyboard even if the Auto Task Buttons toolbar is not displayed.


Auto Task Buttons - Edit/Reassign Button

In order to edit the button name, description, file name, Hot Key, and and other options, highlight the desired button name in the buttons list and then click on the Edit/Reassign button to open the appropriate dialog for editing the button.

Shortcut:  Outside this dialog, double-click on the button name in the list of buttons or hold down on the CTRL key and click on the desired button on the Auto Task Buttons toolbar to open the appropriate dialog.


Auto Task Buttons - Remove Button(s)

When you click on this button, all of the highlighted buttons in the Auto Task Buttons area of the dialog will be removed from the list of Auto Task Buttons.  Note that this option only removes the highlighted buttons from the list and does not delete the associated files.


Auto Task Buttons - Add Buttons

This area of the dialog provides options for adding new buttons to the Auto Task Buttons toolbar.  Clicking on each of these buttons opens the appropriate dialog (see below) in which you can define a new button and select the desired action to be assigned to the new button.

Command Language (SCL) Program:  When you click on this button, the Edit the Auto Task Buttons dialog will open in which you can assign an SCL program file (file name extension *.scl) to an Auto Task Button.  For more information on other options in this dialog, see Edit the Auto Task Buttons Item.

STATISTICA BASIC Program:  This button brings up the Edit the Auto Task Buttons Item dialog in which you can select a previously saved STATISTICA BASIC file (file name extension *.stb).  For more information on other options in this dialog, see Edit the Auto Task Buttons Item.

Quick Open File (data, graph, report, ...):  This button opens the Edit the Auto Task Buttons Item dialog which allows you to select a file from many types of STATISTICA files (e.g., a graph file, data file, Scrollsheet file, text file, RTF file, etc.); the selected file will then be easily available by pressing the respective Auto Task Button.

Keyboard Macro (Recorded and/or Edited):  Click on this button to open the Record or Enter/Edit a Keyboard Macro dialog in which you can open, enter, or record a keyboard macro.  A keyboard macro is an editable macro that is either entered directly (using the standard Microsoft Sendkeys conventions) or recorded.  You can also open a text file containing a previously-saved sequence of keystrokes.  For more information on editable macros and the Sendkeys syntax, see the Record or Enter/Edit a Keyboard Macro dialog.

Recorded Show (with Mouse Movements):  When you click on this button, the Recorded Show Macro dialog will open in which you can define and initiate recording mouse movements as well as keystrokes.  When you play back the Recorded Show macro, the recorded mouse movements and/or keystrokes will be replayed (the recorded macros can be played back at the speed at which they were recorded or in the Fast Playback mode).

Note that macros containing recorded mouse movements are "context-dependent" and they may not produce the same results if the size of the window or its position on the screen changes.  Use keystroke-based macros whenever possible for better reproducibility (all menu and dialog box buttons in STATISTICA have their own keyboard equivalents).

Note also that recorded mouse movements in macros are not editable.  However, if you record any keystrokes using the Recorded Show option, you can edit those keystrokes in the Record or Enter/Edit a Keyboard Macro dialog.

For more information, see Recorded Show Macro.


Auto Task Buttons - Auto Task Files

The following options allow you to change or save the Auto Task Buttons configuration file.  The name of the current Auto Task Buttons file is given in the title area of this dialog.  Note that you can also quickly switch between configuration files via the right-mouse-button flying menu option Change Auto Task Buttons Toolbar.

Open:  Click on this button in order to open the Open an Auto Task Buttons File dialog and select a previously-saved Auto Task Buttons configuration file.  When the selected configuration file (file name extension *.atb) is opened, it becomes assigned to the current module in the Statist.ini file and the name of the current module is removed from the module assignment for the previous configuration file (if one was established).  Note that you can also open a previously-saved Auto Task Buttons toolbar configuration file by clicking on the toolbar with the right-mouse-button and selecting Change Auto Task Buttons Toolbar from the flying menu.

Save As:  Click on the Save As button in order to open the Save an Auto Task Buttons File dialog and save the Auto Task Buttons configuration under the default name (Default.atb) or a new name (file name extension *.atb).  When you save the Auto Task Buttons configuration, the file name, path, and associated module will be specified in the Statist.ini file.

Global vs. local Auto Task Buttons:  An Auto Task Buttons configuration file can be assigned to several modules (i.e., global; each time you open the respective file in a module, it becomes assigned to that module in the Statist.ini file), however, each module can have only one Auto Task Buttons configuration associated with it (i.e., local; either save the configuration in the current module or open a previously-saved configuration file in a module in order for it to be assigned to that module).

For example, the Default.atb configuration file will open in every module with which it is associated in the Statist.ini file [by default it is (globally) associated with every module in STATISTICA].  If you make changes to this default file and save it under the same path and name, then it will still be associated with each of the modules with which it was previously associated.  Now, if you make changes to the Default.atb configuration and save it under a different name or path (e.g., New.atb), then the new configuration file will be assigned (locally) to the current module and the current module's name will be removed from the list of modules associated with Default.atb.  However, Default.atb will still be assigned to the remaining modules in STATISTICA.

Restore Default:  When you click on this button, the Default.atb (Auto Task Buttons) configuration file will be opened and reassigned to the current module.


Auto Task Buttons - Auto Save Changes

Select this option in order to skip the default confirmation request (issued by STATISTICA) and automatically save any changes to the current Auto Task Buttons configuration file.


Auto Task Buttons - Display Button Icons

When you de-select this option, icons representing the type of Auto Task Button will not be displayed on the buttons to the left of the button names (this option can be used if you wish to save space covered by the Auto Task Buttons toolbar, and, for example, identify buttons by single letters).


Auto Task Buttons - Display Hot Keys

Select this option in order to display Hot Keys (which may have been assigned to an Auto Task Button) after the name on the button.  Note that the Hot Keys can be used regardless of their display setting.


Edit the Auto Task Buttons Item

This dialog is used to create new Auto Task Buttons (see Customize Auto Task Buttons) or to edit existing buttons.  Here, you can assign an previously saved file (e.g., an SCL or STATISTICA BASIC program file, or a data, Scrollsheet, graph, or report file) to an Auto Task Button.  The STATISTICA BASIC and SCL program files can also be edited from this dialog (see Edit the Program File, below).

Edit the Auto Task Buttons Item dialog:

Button name

Type

Description

File name

Hot Key

Edit the Program File

Shortcuts:	Double-click on the appropriate button name in the list of Auto Task Buttons in the Customize Auto Task Buttons dialog.

Hold down the CTRL key and click on the appropriate button on the  Auto Task Buttons toolbar.


Edit the Auto Task Buttons Item - Button Name

Enter/edit the name of the Auto Task Button (up to 30 characters) here.


Edit the Auto Task Buttons Item - Type

This area shows the type of Auto Task Button that you have selected.  You can enter or edit the button name, description, Hot Key, etc., in this dialog for the following three types of Auto Task Buttons:

•	SCL;

•	STATISTICA BASIC program files;

•	Quick open files (e.g., data, Scrollsheet, graph, RTF, etc.).


Edit the Auto Task Buttons Item - Description

You can edit the description of the button (up to 128 characters) in this edit field.  The description that you enter here is displayed in the description area of the Customize Auto Task Buttons dialog when the respective button name is highlighted.


Edit the Auto Task Buttons Item - File Name

Click on the File Name button in order to change the file associated with this Auto Task Button.


Edit the Auto Task Buttons Item - Hot Key

If desired, you can assign a Hot Key to this Auto Task Button.  If you specify a currently assigned Hot Key here [i.e., a system Hot Key (see below) or one currently assigned to an Auto Task Button], STATISTICA will detect it and will give you the opportunity to either change the Hot Key or override the current assignment.

System global Hot Keys (using the CTRL+character key combinations):

Open, Save, Print, New Data	CTRL+O, S, P, N

Clipboard, Undo	CTRL+C, V, X, Z

Startup Panel, Resume	CTRL+T, R

Auto Task Buttons (on/off)	CTRL+M

Select All (table, text)	CTRL+A

Close All Output Windows	CTRL+L

System local Hot Keys (using the CTRL+character key combinations)

Find, Replace (data, text)	CTRL+F, H

Font Attributes (in text editors)	CTRL+0 (zero), B, I, U, D

Graph Alignment Grid (on/off)	CTRL+G

See also, Keyboard Commands.


Edit the Auto Task Buttons Item - Edit the Program File

Click on this button in order to edit an SCL or STATISTICA BASIC program file (this option is dimmed when the current button is assigned to a quick open file).  When you click on this button, a respective type of the Text/output Window will open with the respective file for editing.


Record or Enter/Edit a Keyboard Macro

This dialog allows you to enter, record, edit and save (in a text file) a sequence of keystrokes (an editable macro) that can later be executed by clicking on the designated button in the Auto Task Buttons toolbar.  You can enter/record a new keyboard macro in this dialog by clicking on the Keyboard Macro (Recorded and/or Edited) button.  To edit an existing keyboard macro, highlight the respective button name and click on the Edit/Reassign button in the Customize Auto Task Buttons dialog.  You can also use this dialog to open a previously recorded show macro file (file name extension *.stm), or a previously entered or recorded macro for editing.

Example

Record or Enter/Edit a Keyboard Macro dialog:

Button Name/Type

Description

Hot Key

Enter a Sequence of Keystrokes (or press Record)

Quick Entry Buttons

Syntax Reference

Open

Save

Clipboard Operations (Cut, Copy, Paste buttons)

Shortcuts:	Double-click on the appropriate button name in the list of Auto Task Buttons in the Customize Auto Task Buttons dialog.

Hold down the CTRL key and click on the appropriate button on the  Auto Task Buttons toolbar.


Record or Enter/Edit a Keyboard Macro - Button Name/Type

The Button Name edit field allows you to enter or edit (up to 30 characters) the name of this Auto Task Button.  Immediately below this edit field is displayed the type of Auto Task Button.


Record or Enter/Edit a Keyboard Macro - Description

You can enter a description (up to 128 characters) for this button in the Description area of the dialog.  The description that you enter here is displayed in the description area of the Customize Auto Task Buttons dialog when the respective button name is highlighted.


Record or Enter/Edit a Keyboard Macro - Hot Key

If desired, you can assign a Hot Key to this Auto Task Button.  If you specify a currently assigned Hot Key here [i.e., a system Hot Key (see below) or one currently assigned to an Auto Task Button], STATISTICA will detect it and will give you the opportunity to either change the Hot Key or override the current assignment.

System global Hot Keys (using the CTRL+character key combinations):

Open, Save, Print, New Data	CTRL+O, S, P, N

Clipboard, Undo	CTRL+C, V, X, Z

Startup Panel, Resume	CTRL+T, R

Auto Task Buttons (on/off)	CTRL+M

Select All (table, text)	CTRL+A

Close All Output Windows	CTRL+L

System local Hot Keys (using the CTRL+character key combinations)

Find, Replace (data, text)	CTRL+F, H

Font Attributes (in text editors)	CTRL+0 (zero), B, I, U, D

Graph Alignment Grid (on/off)	CTRL+G

See also, Keyboard Commands.


Record or Enter/Edit a Keyboard Macro - Enter a Sequence of Keystrokes (or press Record)

In this area of the dialog, you can enter, record, or edit a sequence of keystrokes (editable macro) which will be executed whenever you click on the respective button in the Auto Task Buttons toolbar.  The Microsoft Sendkeys conventions are used to represent the keystrokes in this macro.  You can enter the keystrokes manually or by recording the keystrokes via the Record button.  Both of these methods are discussed below.

Entering/editing a sequence of keystrokes:  You can directly enter or edit the keystrokes using the Sendkeys syntax in this edit field.  Several Quick Entry Buttons are available in order to quickly add commonly-used keystrokes to the sequence.  A quick keystroke syntax reference is given in this dialog.  For a complete syntax reference of the keystrokes (which closely follow that of the Microsoft Sendkeys conventions), see Syntax Reference.  Note that if you are editing a sequence of keystrokes, any additional keystrokes will be inserted at the current cursor position in this edit field.  If you highlight a series of keystrokes and enter, record, or insert from a file additional keystrokes, then those keystrokes will replace the highlighted keystrokes.

Record:  Instead of manually entering the keystrokes, you can click on the Record button in order to begin recording a series of keystrokes (to record mouse movements, use the Recorded Show Macro option in the Customize Auto Task Buttons dialog).  When you click on this button, REC will flash in the Status Bar to remind you that you are recording.  To stop recording, press CTRL+F3.  This recorded macro can be edited as described above (the keystrokes will be displayed in the edit field).  Note that if the recording is executed in order to produce a sequence of keystrokes for future editing, you should not use the mouse while recording (because recorded mouse movements cannot be edited).


Record or Enter/Edit a Keyboard Macro - Quick Entry Buttons

Use the quick entry buttons in the Record or Enter/Edit a Keyboard Macro dialog to quickly enter the respective keystrokes in the macro.  The quick entry buttons (shown below next to the respective keyboard character) and the codes used to represent specific keyboard characters are listed below (note that the curly brackets {} are part of the code).

Quick Entry	Keyboard

Buttons	Characters	Code

ALT	%

CTRL 	^

Down	{Down}

ENTER	~ or {Enter}

Escape 	{Esc}

Left 	{Left}

Page Down	{Pgdn}

Page Up	{Pgup}

Right	{Right}

SHIFT	+

TAB 	{Tab}

Up	{Up}


Record or Enter/Edit a Keyboard Macro - Syntax Reference

The syntax described here follows the same logic as that used in other Windows applications (e.g., Excel, Word for Windows).  Note that you can use the Quick Entry Buttons to quickly enter some of the commonly-used keystrokes

Entering Regular Characters:  Each keyboard key is represented by one or more characters.  To specify a single keyboard character, use the character by itself.  For example, to specify the text "ABC", type ABC in the edit field.  The keyboard characters + (plus sign), ^ (caret), % (percent), ~ (tilde), and () (parentheses) are used as short-cuts for specific keys (see below).  To use these characters as part of a sequence of keystrokes, enclose the character in curly brackets {}.  For example, to specify the plus sign as part of the "ABC" text string, type ABC{+}.  To use a curly bracket ({}) as part of a sequence of keystrokes, enclose them in curly brackets as well (i.e., use {{} and {}}).

Entering Special Keyboard Keys.  The syntax for keyboard macros allows you to specify keyboard keys that are not displayed when you press on them (e.g., ENTER or TAB) and keys that represent actions rather than characters (e.g., UP or RIGHT).  For those keys, use the Sendkeys code shown below (note that the curly brackets are part of the code).

Keyboard

Characters	Code

ALT	%

Backspace	{Backspace}

BREAK	{Break}

CapsLock	{Capslock}

Clear	{Clear}

CTRL 	^

Delete	{Del}

Double quotes	"  "

Down	{Down}

END 	{End}

ENTER	~ or {Enter}

ESCape 	{Esc}

F1, ..., F12  	{Fnumber} (e.g., {F11})

Help	{Help}

Home	{Home}

Insert	{Insert}

Keyboard
Character	type in that key (e.g., abc@!)

Left 	{Left}

Page Down	{Pgdn}

Page Up	{Pgup}

Print Screen	{Prtsc}

Right	{Right}

SHIFT	+

Single quotes	'  '

TAB 	{Tab}

Up	{Up}

Order of Keystrokes:  The keystrokes will be processed in the order in which you type them into the editor.  For example, if you enter the keystrokes +EC, then STATISTICA will first press shift followed by the letters E and C.  You can use parentheses, brackets, or curly brackets to define the order of keystrokes.  For example, if you want to hold down the ctrl key while pressing the shift and c keys, specify this "string" as:  ^(+C).  To hold down the shift and ctrl keys while pressing two other keys, specify this string as: +(^(AB)).

Repeating Keystrokes:  You can instruct STATISTICA to repeat specific key sequences by specifying the number of times that you want it repeated (use the form {key number}).  For example {LEFT 42} means press the left arrow key 42 times, {h 10} means press the H key 10 times.  (Note:  be sure to leave a space between the code word and the number.)

Wait Command:  You can use the {WAIT} command in order to pause the keyboard macro for the specified number of milliseconds (1 second = 1,000 milliseconds).  For example, entering {WAIT 15000} will cause the macro to "wait" for 15 seconds before processing the next keystrokes.  If no parameter is entered here, then by default, the macro will "wait" for 1 second.

Hints for Entering Keyboard Macros:  The following hints may be useful when entering a keyboard macro (see the following example for an illustration of most of these hints).

•	Use {Esc} at the beginning of the macro if you intend to exit any open dialog boxes.  (Note that you should not include this keystroke if you want to perform a keyboard macro from within an open dialog.)

•	Use the Window pull-down menu to bring the spreadsheet or another type of window to the top to make it current.

•	Use the underlined letters in dialog boxes (i.e., so-called accelerators) to specify the option you wish to select instead of "moving" down, right, etc.

•	In list boxes, use {Home} in dialog list boxes in order to position the cursor at the beginning of the list each time, then specify the number of positions {Down} to select the desired option.

•	Use %o to accept and close dialog boxes (i.e., click OK).


Record or Enter/Edit a Keyboard Macro - Open

Click on this button in order to open the Open an Auto Task Buttons File dialog in which you can select a previously saved text file (*.txt) or a recorded macro file (*.stm) containing a sequence of keystrokes (editable macro).  If you open a Recorded Show Macro file, then only the keystrokes will be displayed in this editor (mouse movements will be ignored).


Record or Enter/Edit a Keyboard Macro - Save

Click on this button in order to open the Save an Auto Task Buttons File dialog in which you can save the sequence of keystrokes (editable macro) in a text file (*.txt).


Entering a Sequence of Keystrokes Macro - Example

You can execute the following keystrokes in the spreadsheet window in order to make a 2D Scatterplot by entering them in the Record or Enter/Edit a Keyboard Macro dialog.  The keystrokes and their descriptions are given below.  Note that you can use the Quick Entry Buttons to enter some of the keystrokes used below (see Quick Entry Buttons and Syntax Reference for more information), also note that often the easiest method to create editable macro is to record it.

Step 1 (Enter the Keystrokes):  {ESC 3}%w1%g2{DOWN}~v1{TAB}2~f{HOME}{DOWN 5}%o

{ESC 3}	Pressing esc at the beginning of the macro will ensure that any open dialogs will be closed.

%w1	alt+w  followed by 1 opens the Window pull-down menu and selects the current data file (to ensure that the spreadsheet is on top; note that the spreadsheet is always the first window file listed in this menu).

%g	alt+g pulls down the Graphs menu.

2	Selects the Stats 2D Graphs option in this pull-down menu.

{DOWN}	Moves down 1 line to select the 2D Scatterplots sub-option in this menu.

~	Presses enter to bring up the 2D Scatterplots dialog.

v	Opens the Variables dialog so that you can specify the variables for the plot.

1	Selects variable 1 by entering 1 in the variable selection edit field of the dialog.

{TAB}	tabs to the second list.

2	Selects variable 2 by entering 2 in the variable selection edit field of the dialog.

%o	Presses alt+o to exit this dialog (i.e., click OK) and returns to the 2D Scatterplots dialog.

f{HOME}	Moves to the Fit area of the dialog and places the cursor to the top of the list,

{DOWN 5}	and moves 5 lines down to select the Polynomial fit).

%o	Presses alt+o to exit this dialog (i.e., click OK) and create the graph.

Step 2:  If you have not already done so, enter a name for this button and description and then save these keystrokes in a text file (file name extension *.txt).

Step 3:  Click OK in this dialog to return to the Customize Auto Task Buttons dialog.  Click OK in this dialog to place the button on the Auto Task Buttons toolbar.  Now, click on this button to create the graph.


Record or Enter/Edit a Keyboard Macro - Clipboard Operations (Cut, Copy, Paste)

You can use these buttons to perform the Clipboard operations cut ( [image]), copy ( [image]), and paste ( [image]) in this editor.


Recorded Show Macro

This dialog is accessible by clicking on the Recorded Show (with Mouse Movements) button (to record a new macro) or the Edit/Reassign button (if the name of an Auto Task Button of this type is highlighted) in the Customize Auto Task Buttons dialog.  Here, you can specify a button name, description, and optionally, a Hot Key for the macro.

This type of macro can record mouse movements (which can be played back at a rate at which they were recorded or fast speed) and keystrokes (which can later be edited in the Record or Enter/Edit a Keyboard Macro dialog).  However, note that macros containing recorded mouse movements are "context-dependent" and they may not produce the same results if the size of the window or its position on the screen changes.  Therefore, use keystroke-based macros whenever possible for better reproducibility (all menu and dialog box buttons in STATISTICA have their own keyboard equivalents).

Recorded Show Macro dialog:

Button Name/Type

Description

File Name

Hot Key

Fast Playback

Record

Shortcuts:	Double-click on the appropriate button name in the list of Auto Task Buttons in the Customize Auto Task Buttons dialog.

Hold down the CTRL key and click on the appropriate button on the  Auto Task Buttons toolbar.


Recorded Show Macro - Button Name/Tyoe

Recorded Show Macro - Button Name/Type

The Button Name edit field allows you to enter or edit (up to 30 characters) the name of this Auto Task Button.  Immediately below this edit field is displayed the type of Auto Task Button.


Recorded Show Macro - Description

You can enter/edit the description of the Auto Task Button (up to 128 characters) in this edit field.  The description that you enter here is displayed in the description area of the Customize Auto Task Buttons dialog when the respective button name is highlighted.


Recorded Show Macro - File Name

Click on this button to open the Add a Recorded Show Macro dialog in which you can select a file name (*.stm) under which to save the macro.


Recorded Show Macro - Hot Key

If desired, you can assign a Hot Key to this Auto Task Button.  If you specify a currently assigned Hot Key here [i.e., a system Hot Key (see below) or one currently assigned to an Auto Task Button], STATISTICA will detect it and will give you the opportunity to either change the Hot Key or override the current assignment.

System global Hot Keys (using the CTRL+character key combinations):

Open, Save, Print, New Data	CTRL+O, S, P, N

Clipboard, Undo	CTRL+C, V, X, Z

Startup Panel, Resume	CTRL+T, R

Auto Task Buttons (on/off)	CTRL+M

Select All (table, text)	CTRL+A

Close All Output Windows	CTRL+L

System local Hot Keys: (using the CTRL+character key combinations)

Find, Replace (data, text)	CTRL+F, H

Font Attributes (in text editors)	CTRL+0 (zero), B, I, U, D

Graph Alignment Grid (on/off)	CTRL+G

See also, Keyboard Commands.


Recorded Show Macro - Fast Playback

You can designate the speed of the macro playback here.  When you select this option, the macro will be played back very quickly (i.e., with no recorded delays or pauses), otherwise, it is played back at the same rate that you record it.  Note that Recorded Show Macros executed at a rate at which they were recorded (i.e., de-select Fast Playback) can be used for demonstration purposes.

Note:  To break the macro playback, click on the mouse button, or press the ESC or BREAK keys.


Recorded Show Macro - Record

When you click on the Record button, the program will start recording your mouse movements (and associated keystrokes).  While the program is recording, REC will flash in the last field of the Status Bar.  Press CTRL+F3 to stop the recording.

Note that macros containing recorded mouse movements are "context-dependent" and they may not produce the same results if the size of the window or its position on the screen changes.  Use keystroke-based macros (see Record or Enter/Edit a Keyboard Macro) whenever possible for better reproducibility (all menu and dialog box buttons in STATISTICA have their own keyboard equivalents).


Auto Task Buttons - Arrange Horizontally

This right-mouse-button flying menu option will arrange the Auto Task Buttons horizontally in the toolbar.  Alternatively, you can double-click on the Auto Task Buttons toolbar title area or drag the borders of the toolbar to change the display format.


Auto Task Buttons - Arrange Vertically

This right-mouse-button flying menu option will arrange the Auto Task Buttons vertically in the toolbar.  Alternatively, you can double-click on the Auto Task Buttons toolbar title area or drag the borders of the toolbar to change the display format.


Auto Task Buttons - Change Auto Task Buttons Toolbar

When you click on this option from the right-mouse-button flying menu, the Open an Auto Task Buttons File dialog will open in which you can select a different Auto Task Buttons toolbar to open (file name extension *.atb).

See also, Auto Task Files.


Macro - Command Language (SCL)

Select this option from the Options pull-down menu to open the Edit the Auto Task Buttons Item dialog.  Here you can select a STATISTICA Command Language (SCL) file to assign to an Auto Task Button.


Macro - STATISTICA BASIC

When you select this option from the Options pull-down menu, the Edit the Auto Task Buttons Item dialog will open in which you can select a STATISTICA BASIC file to assign to an Auto Task Button.


Macro - Quick Open File

When you select this option from the Options pull-down menu, the Edit the Auto Task Buttons Item dialog will open in which you can select a spreadsheet, Scrollsheet, graph, or report file to assign to an Auto Task Button.


Macro - Keyboard Macro

Select this option from the Options pull-down menu to open the Record or Enter/Edit a Keyboard Macro dialog.  Here you can enter or record a new keyboard macro or open a previously saved keyboard macro file and assign it to an Auto Task Button.


Macro - Recorded Show Macro

When you select this option from the Options pull-down menu, the Recorded Show Macro dialog will open in which you can record a new macro or open a previously saved macro file and assign it to an Auto Task Button.


Macro - Hot Keys in Use

Hot Keys in Use

The Hot Key that you have selected is currently assigned either to a system operation (see below) or another Auto Task Button.  Click Yes to reassign the specified Hot Key to the current Auto Task Button (overriding any previous assignment).  If you do not want to override the existing assignment, click No and you will be returned to the previous dialog where you can change the Hot Key.

System global Hot Keys (using the CTRL+character key combinations):

Open, Save, Print, New Data	CTRL+O, S, P, N

Clipboard, Undo	CTRL+C, V, X, Z

Startup Panel, Resume	CTRL+T, R

Auto Task Buttons (on/off)	CTRL+M

Select All (table, text)	CTRL+A

Close All Output Windows	CTRL+L

System local Hot Keys: (using the CTRL+character key combinations)

Find, Replace (data, text)	CTRL+F, H

Font Attributes (in text editors)	CTRL+0 (zero), B, I, U, D

Graph Alignment Grid (on/off)	CTRL+G

See also, Keyboard Commands.


Pearson Product Moment Correlation Distribution

Pearson Product-Moment Correlation Distribution

This option allows you to compute the p value for a given correlation coefficient or you can enter a desired p value and determine the correlation coefficient (based on a specified sample size).

Pearson Product-Moment Correlation Distribution dialog:

Parameters:  The parameters in this dialog are N (the sample size), r (the correlation coefficient), p (the significance level), and Fisher Z (the critical value of the distribution).  These parameters can be specified or computed (see below).

Two-tailed:  You can choose to perform a one-tailed (de-select this option) or two-tailed (select this option) test via this option.

Compute p from r:  Select this option in order to compute the p level and Z value based on a specified correlation coefficient r and sample size N.

Compute r from p:  Select this option in order to compute r and the Z value based on a specified p level and sample size N.

Compute r from Z:  Select this option in order to compute r and the p level based on a specified Z value and sample size N.

Print:  Set this check box if you want to print (send to the printer, file, and/or Text/output Window whichever output destination you selected in the Page/Output Setup dialog) the results of the computation.  These values will be printed when you click on the Compute button, and not when you change the parameters with the micro scrolls.  Therefore, you can edit the parameters using the micro scrolls and review the results in the edit fields in the dialog, then when you are ready, click on the Compute button to print the resulting values.

Compute button:  Click on this button to perform the computations and Print the results (if the Print check box is set (see above).


Functions or Command Wizard

This dialog will allow you to select pre-defined parts of formulas (e.g., for spreadsheet formulas), STATISTICA BASIC commands, or SCL commands depending on where you called the dialog.  In each of these cases, you can highlight a Category in the first list which will then give the Name of the item (function or command) available under that Category in the second list.  When you highlight a Name in the second list, the item will appear in the edit field and a brief description of that item will be given in the lower part of this dialog.  If it is necessary to enter specific parameters (e.g., a variable name) for the item, you can do so in this edit field before it is inserted into the window or dialog.  You can use the Clipboard operation buttons (Copy, Cut, and Paste) in order to combine more than one item in this edit field.  Once you have selected the desired function or command, click on the Insert button to insert it in the current cursor position of the window (for STATISTICA BASIC or SCL) or edit field (for Spreadsheet Formulas).

Spreadsheet Formulas:  Function Wizard.  This dialog is called by clicking on the [image] button in the Current Specs dialog.  When you click Insert in this dialog, the selected item will be pasted in the current cursor position in the edit field of the Current Specs dialog (for more information on specific formula items available in this dialog, see Summary of STATISTICA Formula Syntax).

STATISTICA BASIC and SCL Wizards:  You can call the Wizard by clicking on the [image] on the STATISTICA BASIC toolbar or the [image] button on the SCL toolbar, respectively.  Clicking Insert will paste the selected item in the current cursor position (see New Line, below) in the respective text window (for more information on specific commands available in the Wizard, see BASIC - Syntax Reference and SCL - Syntax Reference).

New Line:  When this option is selected, the cursor will move to a new line after the inserted function or command is placed at the current cursor position.  In the case of STATISTICA BASIC functions, when this option is checked, a semicolon will be added to the end of the selected command.

When this option is de-selected, then the cursor will remain at the end of the pasted command or function (and in the case of STATISTICA BASIC functions, a semicolon will not be placed at the end of the function).

Keyboard Shortcut:  Press ALT+I while in either the STATISTICA BASIC or SCL window to open the respective Wizard.


References

Citing STATISTICA:  The proper citation for the STATISTICA program/documentation is:

StatSoft, Inc. (1995). STATISTICA for Windows [Computer program manual].  Tulsa, OK: StatSoft, Inc., 2300 East 14th Street, Tulsa, OK, 74104-4442, (918) 749-1119, fax: (918) 749-2217, e-mail: info@statsoft.com, WEB: http://www.statsoft.com.

Note: StatSoft, Inc. is the author and publisher of the program and manuals.

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Zupan, J. (1982). Clustering of large data sets. New York: Research Studies Press.

Zwick, W. R., & Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99, 432-442.


Using the ? in STATISTICA

The question mark (?) can be used in two ways in STATISTICA.

•	Pressing the question mark button in the upper right hand corner of the dialog box (or in a toolbar) allows context-sensitive access to the relevant help topics in the Electronic Manual.

•	In some STATISTICA BASIC function calls, you can ignore the value of a parameter by placing a "?" before any word in place of the parameter (for text parameters, a "$" must be used at the end of the word).  For more information on using the "?" in STATISTICA BASIC, see How to Set (or Leave Unchanged) Default Values of Function Parameters.


Allows you to select a file from a list of supplementary files (e.g., graph files, Scrollsheet files, import/export files, etc.) associated with the current data file (a log of all supplementary files associated with the current data file is maintained in the STATISTICA Workbook).

For easy access to a desired file, this list is sorted by file type (e.g., *.scr, *.stg, etc.) that you would like to open/save.  Files which are not relevant for the current open/save operation are dimmed (they are included for reference only).


Allows you to save the contents of the Text/output Window (including STATISTICA BASIC program files, Command Language (SCL) program files, and SEPATH command files) in the standard ASCII text format (file name extension *.txt) instead of the default RTF file format.

If you save it as text, the file can be processed by virtually any program, however, not all formatting information (and no graphs) will be preserved.


Glossary - ?

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

? - Electronic Manual

? in STATISTICA BASIC


Glossary - 2D

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

2D Bar/Column Plots (Multiple)

2D Bar/Column Plots (Regular)

2D Bar Dev Plot(Custom Graph)

2D Bar Left Y Plot (Custom Graph)

2D Bar Right Y Plot (Custom Graph)

2D Bar Top Plot (Custom Graph)

2D Bar X Plot (Custom Graph)

2D Box Plot/Medians (Block Stats Graphs)

2D Box Plot/Means (Block Stats Graphs)

2D Box Plots

2D Box Plots - Box Whiskers

2D Box Plots - Boxes

2D Box Plots - Columns

2D Box Plots - Error Bars

2D Box Plots - Multiple (Format) Box Plots

2D Box Plots - Regular (Format) Box Plots

2D Box Plots - Whiskers

2D Categorized Detrended Probability Plots

2D Categorized Half-Normal Probability Plots

2D Categorized Line Plot of Medians with Quantiles and Min-Max Range Bars

2D Categorized Normal Probability Plots

2D Categorized Probability-Probability Plots

2D Categorized Quantile-Quantile Plots

2D Categorized Scatterplot Matrix

2D Categorized Scatterplot (Ternary graph)

2D Custom Graph - Bar Dev Plot

2D Custom Graph - Bar Left Y Plot

2D Custom Graph - Bar Right Y Plot

2D Custom Graph - Bar Top Plot

2D Custom Graph - Bar X Plot

2D Custom Graph - Line Plot

2D Custom Graph - Min-Max X Plot

2D Custom Graph - Min-Max Y Pot

2D Custom Graph - MPatt Bar Plot

2D Custom Graph - Scatterplot

2D Custom Graph - Step Plot

2D Custom Graph - Ternary Scatterplot

2D Custom Graph - Voronoi

2D Detrended Probability Plots

2D Detrended Probability Plots - Categorized

2D Histograms

2D Histograms (Block Stats Graphs)

2D Histograms - Double-Y

2D Histograms - Hanging Bars

2D Histograms - Multiple

2D Histograms - Regular

2D Half-Normal Probability Plots

2D Half-Normal Probability Plots - Categorized

2D Icon Plots - Chernoff Faces

2D Icon Plots - Columns

2D Icon Plots - Lines

2D Icon Plots - Pies

2D Icon Plots - Polygons

2D Icon Plots - Profiles

2D Icon Plots - Stars

2D Icon Plots - Sun Rays

2D Line Plot of Means with "Error Bars"

2D Line Plot of Medians with Quantiles and Min-Max Range Bars

2D Line Plots

2D Line Plots - Aggregrated

2D Line Plots - Double-Y

2D Line Plots - Multiple

2D Line Plots - Regular

2D Line Plots - XY Trace

2D Line Plots (Case Profiles)

2D Matrix Plots - Columns

2D Matrix Plots - Lines

2D Matrix Plots - Scatterplot

2D Min-Max X Plot (Custom Graph)

2D Min-Max Y Pot (Custom Graph)

2D MPatt Bar Plot (Custom Graph)

2D Multiple Normal Probability Plot

2D Normal Probability Plots

2D Normal Probability Plots - Categorized

2D Pie Chart (Custom Graph)

2D Pie Chart - Counts (Stats Graph)

2D Pie Chart - Multi-pattern Bar (Stats Graph)

2D Pie Chart - Values (Stats Graph)

2D Probability Plots - Detrended

2D Probability Plots - Normal

2D Probability Plots - Half-Normal

2D Probability-Probability Plots

2D Probability-Probability Plots - Categorized

2D Quantile-Quantile Plots

2D Quantile-Quantile Plots - Categorized

2D Range Plots - Boxes

2D Range Plots - Columns

2D Range Plots - Error Bars

2D Range Plots - Whiskers

2D Scatterplot

2D Scatterplot - Categorized Matrix

2D Scatterplot - Categorized Ternary Graph

2D Scatterplot - Double-Y

2D Scatterplot - Frequency

2D Scatterplot - Multiple

2D Scatterplot - Regular

2D Scatterplot - Ternary Graph

2D Scatterplot - Voronoi

2D Sequential/Stacked Plots - Area

2D Sequential/Stacked Plots - Column

2D Sequential/Stacked Plots - Lines

2D Sequential/Stacked Plots - Mixed Line

2D Sequential/Stacked Plots - Mixed Step

2D Sequential/Stacked Plots - Step

2D Sequential/Stacked Plots - Step Area

2D Step Plot (Custom Graph)

2D Ternary Plots - Scatterplot

2D Voronoi (Custom Graph)


Glossary - 3D

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

3D Bivariate Histogram

3D Box Plots - Border-style Ranges

3D Box Plots - Double Ribbon Ranges

3D Box Plots - Error Bars

3D Box Plots - Flying Blocks

3D Box Plots - Flying Boxes

3D Box Plots - Points

3D Categorized Plots - Contour/Line

3D Categorized Plots - Contour/Areas

3D Categorized Plots - Deviation Plot

3D Categorized Plots - Scatterplot

3D Categorized Plots - Space Plot

3D Categorized Plots - Spectral Plot

3D Categorized Plots - Surface Plot

3D Categorized Scatterplot (Ternary graph)

3D Categorized Space Plot (Ternary Graph)

3D Categorized Surface Plot (Ternary graph)

3D Categorized Trace Plot (Ternary Graph)

3D Deviation Plot, Scatterplot

3D Deviation Plot (Ternary Graph)

3D Histogram by... - Continuous by Continuous

3D Histogram by... - Discrete by Discrete

3D Histogram by... - Continuous by Discrete

3D Histogram by... - Discrete by Continuous

3D Histograms, Bivariate

3D Histograms, Bivariate - Box Plots

3D Histograms, Bivariate - Contour/Discrete

3D Histograms, Bivariate - Contour Plot

3D Histograms, Bivariate - Spikes

3D Histograms, Bivariate - Surface Plot

3D Range Plot - Border-style Ranges

3D Range Plot - Double Ribbon Ranges

3D Range Plot - Error Bars

3D Range Plot - Flying Blocks

3D Range Plot - Flying Boxes

3D Range Plot - Points

3D Raw Data Plots

3D Raw Data Plots - Block Plot

3D Raw Data Plots - Box Plot

3D Raw Data Plots - Contour/Discrete

3D Raw Data Plots - Contour Plot

3D Raw Data Plots - Lines

3D Raw Data Plots - Ribbons Plot

3D Raw Data Plots - Spikes

3D Raw Data Plots - Surface Plot

3D Scatterplots

3D Scatterplots - Contour Plot

3D Scatterplots - Deviation Plot

3D Scatterplots - Raw Data

3D Scatterplots - Space Plot

3D Scatterplots - Spectral Plot

3D Scatterplots - Surface Plot

3D Scatterplots - Ternary Graph

3D Scatterplots - Trace Plot

3D Surface Plot

3D Surface Plot (Ternary graph)

3D Surface Plot (Ternary graph), Categorized

3D Ternary Plots

3D Ternary Plots - Categorized Scatterplot

3D Ternary Plots - Categorized Space

3D Ternary Plots - Categorized Surface

3D Ternary Plots - Categorized Trace

3D Ternary Plots - Contour (Custom Graph)

3D Ternary Plots - Contour/Areas

3D Ternary Plots - Contour/Lines

3D Ternary Plots - Deviation

3D Ternary Plots - Space

3D Ternary Plots - Surface

3D Ternary Plots - Trace

3D Trace Plot (Scatterplot)


Glossary - A

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Abrupt Temporary Impact

Abrupt Permanent Impact

Action

Additive Season, Damped Trend

Additive Season, Exponential Trend

Additive Season, Linear Trend

Additive Season, No Trend

Adjusted means

Aggregrated Line Plots

Animated Stratification

Anisotropic

Apply Common Value

Arrow (in SEPath)

Asymmetrical Distribution

Augmented Product Moment Matrix

AutoFill (Extrapolating Values in Blocks)

Auto Task Buttons


Glossary - B

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Bar Dev Plot

Bar Left Y Plot

Bar Right Y Plot

Bar Top Plot

Bar X Plot

Bartlett Window

BASIC (STATISTICA BASIC)

Beta Distribution

Binomial Distribution

Bitmap Format

Bivariate Normal Distribution

Block Stats

Boldface in Graph Text

Boundary Case

Box Plot/Medians (Block Stats Graphs)

Box Plot/Means (Block Stats Graphs)

Box Plots, 2D

Box Plots, 2D - Box Whiskers

Box Plots, 2D - Boxes

Box Plots, 2D - Columns

Box Plots, 2D - Multiple (Format) Box Plots

Box Plots, 2D - Regular (Format) Box Plots

Box Plots, 2D - Whiskers

Box Plots 3D - Border-style Ranges

Box Plots 3D - Double Ribbon Ranges

Box Plots 3D - Error Bars

Box Plots 3D - Flying Blocks

Box Plots 3D - Flying Boxes

Box Plots 3D - Points

Boxes (Range Plots)

Box-Ljung Q Statistic

Breaking, Stopping, or Interrupting the Current Action

Brushing Terms

Burt Table


Glossary - C

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

*.cmd Extension

Calculating Contour Levels and Distance

Cartesian Coordinates

Case Profiles 2D Line Plots

Casewise MD Deletion

Categorized Plots, 2D - Detrended Probability Plots

Categorized Plots, 2D - Half-Normal Probability Plots

Categorized Plots, 2D - Line Plot of Medians with Quantiles and Min-Max Range Bars

Categorized Plots, 2D - Normal Probability Plots

Categorized Plots, 2D - Probability-Probability Plots

Categorized Plots, 2D - Quantile-Quantile Plots

Categorized Plots, 2D - Scatterplot Matrix

Categorized Plots, 2D - Scatterplot (Ternary graph)

Categorized Plots, 3D - Contour/Line

Categorized Plots, 3D - Contour/Areas

Categorized Plots, 3D - Deviation Plot

Categorized Plots, 3D - Scatterplot

Categorized Plots, 3D - Space Plot

Categorized Plots, 3D - Spectral Plot

Categorized Plots, 3D - Surface Plot

Categorized 3D Scatterplot (Ternary graph)

Categorized 3D Space Plot (Ternary Graph)

Categorized 3D Surface Plot (Ternary graph)

Categorized 3D Trace Plot (Ternary Graph)

Categorized Contour/Areas (Ternary graph)

Categorized Contour/Lines (Ternary graph)

Categorized Detrended Probability Plot

Categorized Half-Normal Probability Plot

Categorized Normal Probability Plot

Categorized Scatterplot Matrix

Categorized Scatterplot (Ternary graph)

Cauchy Distribution

Chernoff Faces (Icon Plots)

Chi-square Distribution

Circumplex

Client Mode

Clipboard

Codes (Values of Grouping Variables)

Coefficient of Determination

Column Sequential/Stacked Plot

Color Palette

Columns (Box Plot)

Columns (Icon Plot)

Columns (Matrix Plot)

Columns (Range Plots)

Communality

Complex Numbers

Compound Graphs

Computation Note for Normal Probability Plots

Confidence Interval

Contour/Discrete Raw Data Plot

Contour/Areas

Contour/Areas (Ternary graph)

Contour/Areas (Ternary graph), Categorized

Contour/Lines

Contour/Lines (Ternary graph)

Contour/Lines (Ternary graph), Categorized

Contour Plot

Contour Plot (Custom Ternary Graph)

Control Characters (Text Formatting) - Part I

Control Characters (Text Formatting) - Part II

Correlation

Correlation (Pearson r)

Crossed Factors

Cubic Polynomial, Full (Ternary Plots)

Cubic Polynomial, Special (Ternary Plots)

Custom Function

Custom Graphs vs. Stats Graphs


Glossary - D

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Daniell (or Equal Weight) Window

Deviation Plot

Deviation Plot (Ternary Graph)

Dependent vs. Independent Variables

De-selecting Points (in Brushing)

Detrended Probability Plots

Differencing (in Time Series)

Discrepancy Function

Double-Y Histograms

Double-Y Line Plots

Double-Y Scatterplot

Drag-and-Drop

Dynamic Data Exchange (DDE Link)


Glossary - E

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Editing Graph Data for Box and Whisker Format Graphs

Ellipse, (Confidence)

Endogenous Variable

Eps

Error Bars (2D Box Plots)

Error Bars (2D Range Plots)

Error Bars (3D Box Plots)

Error Bars (3D Range Plots)

Exogenous Variable

Exponential Function

Exponential Distribution

Exponentially Weighted Moving Average Line

Extrapolating Values in Blocks (AutoFill)

Extreme Value Distribution


Glossary - F

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

F Distribution

First Degree Polynomial (Ternary Plots)

Fitting Options for Ternary Plots

Fixed Legends

Fixed Size Font

Free Parameter

Frequency Scatterplot

Full Cubic Polynomial (Ternary Plots)


Glossary - G

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Gamma Distribution

Geometric Distribution

Geometric Mean

Glossary of Brushing Terms

Gradient

Gradual Permanent Impact

Graph Handle

Group Control Charts

Grouping Variable


Glossary - H

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Half-Normal Probability Plots

Half-Normal Probability Plots - Categorized

Hamming Window

Handle, Graph

Handle, Object

Handle, Scrollsheet

Hanging Bars Histogram

Harmonic Mean

Hazard Rate

Heywood Case

High-Low Close

Highlighting Points (in Brushing)

Histogram by..., 3D - Continuous by Continuous

Histogram by..., 3D - Discrete by Discrete

Histogram by..., 3D - Continuous by Discrete

Histogram by..., 3D - Discrete by Continuous

Histograms, 2D

Histograms, 2D - Double-Y

Histograms, 2D - Hanging Bars

Histograms, 2D - Multiple

Histograms, 2D - Regular

Histograms, 3D Bivariate

Histograms, 3D - Box Plots

Histograms, 3D - Contour/Discrete

Histograms, 3D - Contour Plot

Histograms, 3D - Spikes

Histograms, 3D - Surface Plot

Hot Keys

How to Stop, Break, or Interrupt the Current Action


Glossary - I

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Icon Plots

Icon Plots - Chernoff Faces

Icon Plots - Columns

Icon Plots - Lines

Icon Plots - Pies

Icon Plots - Polygons

Icon Plots - Profiles

Icon Plots - Stars

Icon Plots - Sun Rays

Ignore Graph

Independent vs. Dependent Variables

Inertia

Internal STATISTICA Representation

Interrupting, Breaking, or Stopping the Current Action

Interval Scale

Invariance Under a Constant Scale Factor (ICSF)

Invariance Under Change of Scale (ICS)

Isotropic

Italics in Graph Text


Glossary - J

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Johnson Curves

Jump (in Help)

Jump (in STATISTICA BASIC)


Glossary - K

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Kurtosis


Glossary - L

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Labels in STATISTICA BASIC

Lambda Prime

Laplace Distribution

Latent Variable

Layered Compression

Least Squares (2D graphs)

Least Squares (3D graphs)

Least Squares Estimator

Legends

Legend Symbols in Graph Text

Line Plot of Means with "Error Bars"

Line Plot of Medians with Quantiles and Min-Max Range Bars

Line Plots, 2D

Line Plots, 2D - Aggregrated

Line Plots, 2D (Case Profiles)

Line Plots, 2D - Double-Y

Line Plots, 2D - Multiple

Line Plots, 2D - Regular

Line Plots, 2D - XY Trace

Line Point Pattern for High-Low Close Graphs

Linear (2D graphs)

Linear (3D graphs)

Lines (Icon Plot)

Lines (Matrix Plot)

Lines Sequential/Stacked Plot

Logarithmic Function

Logistic Distribution

Log-normal Distribution


Glossary - M

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Macro

Manifest Variable

Mapping Base

Marked Points (in Brushing)

Marked Points (in Multiple Subset Graphs)

Mass

Matching Moments Method

Matrix Ill-Conditioning

Matrix Plots - Columns

Matrix Plots - Lines

Matrix Plots - Scatterplot

Maximum Likelihood Method

Mean

Mean, Geometric

Mean, Harmonic

Mean Substitution of Missing Data

Means, Adjusted

Means, Unweighted

Median

Metafile Format

Method of Matching Moments

Micro Scrolls

Missing Data

Mixed Line Sequential/Stacked Plot

Mixed Step Sequential/Stacked Plot

Mode

Monte Carlo

Movable Legends

MPatt Bar

Multiple Histogram

Multiple Graph Layout Wizard

Multiple Line Plots

Multiple Scatterplot

Multiple R

Multiple Normal Probability Plot

Multiple Stream (Group) Control Charts

Multiple Subset Graphs

Multiplicative Season, Damped Trend

Multiplicative Season, Exponential Trend

Multiplicative Season, Linear Trend

Multiplicative Season, No Trend


Glossary - N

? 2D  3D A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

n Point Moving Average Line

Negative Correlation

Negative Exponential (2D graphs)

Negative Exponential (3D graphs)

Nested Factors

Nested Compound Documents

Nested Sequence of Models

Nominal Scale

Non-normal distribution fitting

Non-outlier range

Nonseasonal, Damped Trend

Nonseasonal, Exponential Trend

Nonseasonal, Linear Trend

Nonseasonal, No Trend

Normal Coordinates

Normal Distribution

Normal Distribution, Bivariate

Normal Fit

Normal Probability Plots (Computation Note)

Normal Probability Plots

Normal Probability Plots - Categorized


Glossary - O

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Object Handle

ODBC

Odds Ratio

"One-sided" Ranges or Error Bars in Range Plots

Order of SCL Statements

Ordinal Scale

Outliers


Glossary - P

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

p-level (Statistical Significance)

Pairwise Deletion of Missing Data vs. Mean Substitution

Pairwise MD Deletion

Palette, Color

Pareto Distribution

Parzen Window

Pearson Correlation

Pearson Curves

Percentiles

Pie Chart (Custom Graph)

Pie Chart - Counts

Pie Chart - Multi-pattern Bar

Pie Chart - Values

Pies (Icon Plots)

Point (a unit of measurement)

Point Pattern, Line

Poisson Distribution

Polar Coordinates

Polygons (Icon Plots)

Polynomial

Positive Correlation

Predictive Mapping

Printing Objects with Filled Background

Probability Plots - Detrended

Probability Plots - Normal

Probability Plots - Half-Normal

Probability-Probability Plots

Probability-Probability Plots - Categorized

Profiles (Icon Plots)

Pseudo-components


Glossary - Q

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Quadratic

Quality

Quantiles

Quantile-Quantile Plots

Quantile-Quantile Plots - Categorized

Quartile Range

Quartiles

Queue (of Scrollsheets or graphs)

Quick Basic Stats

Quick MML

Quick Stats Graphs


Glossary - R

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

r (Pearson Correlation Coefficient)

Range Plots - Boxes

Range Plots - Columns

Range Plots - Whiskers

Ratio Scale

Raw Data, 3D Scatterplot

Raw Data Plots, 3D

Raw Data Plots, 3D - Block Plot

Raw Data Plots, 3D - Box Plot

Raw Data Plots, 3D - Contour/Discrete

Raw Data Plots, 3D - Contour Plot

Raw Data Plots, 3D - Lines

Raw Data Plots, 3D - Ribbons Plot

Raw Data Plots, 3D - Spikes

Raw Data Plots, 3D - Surface Plot

Rayleigh Distribution

Rectangular Coordinates

Regular Histogram

Regular Line Plots

Regular Scatterplot

Relative Function Change Criterion

Residual

RTF Files


Glossary - S

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Scatterplot, 2D

Scatterplot, 2D - Categorized Matrix

Scatterplot, 2D - Categorized Ternary Graph

Scatterplot, 2D - Double-Y

Scatterplot, 2D - Frequency

Scatterplot, 2D - Multiple

Scatterplot, 2D - Regular

Scatterplot, 2D - Ternary Graph

Scatterplot, 2D - Voronoi

Scatterplot, 3D

Scatterplot, 3D - Contour Plot

Scatterplot, 3D - Deviation Plot

Scatterplot, 3D - Raw Data

Scatterplot, 3D - Space Plot

Scatterplot, 3D - Spectral Plot

Scatterplot, 3D - Surface Plot

Scatterplot, 3D - Ternary Graph

Scatterplot, 3D - Trace Plot

Scatterplot (Matrix Plot)

Screen Catcher

Scrollsheet

Scrollsheet Handle

Second Degree (Quadratic) Polynomial (Ternary Plots)

Selected Points

SEPath Wizard

Sequential Contour Plot (3D)

Sequential Raw Data Plots, 3D

Sequential Raw Data Plots, 3D - Block Plot

Sequential Raw Data Plots, 3D - Box Plot

Sequential Raw Data Plots, 3D - Contour/Discrete

Sequential Raw Data Plots, 3D - Contour Plot

Sequential Raw Data Plots, 3D - Lines

Sequential Raw Data Plots, 3D - Ribbons Plot

Sequential Raw Data Plots, 3D - Spikes

Sequential Raw Data Plots, 3D - Surface Plot

Sequential/Stacked Plots, 2D - Area

Sequential/Stacked Plots, 2D - Column

Sequential/Stacked Plots, 2D - Lines

Sequential/Stacked Plots, 2D - Mixed Line

Sequential/Stacked Plots, 2D - Mixed Step

Sequential/Stacked Plots, 2D - Step

Sequential/Stacked Plots, 2D - Step Area

Sequential Surface Plot (3D)

Server Mode

Short Run Control Charts

Skewness

Space Plot

Space Plot (Ternary Graph)

Space Plot, Categorized (Stats Ternary Graph)

Special Cubic Polynomial (Ternary Plots)

Spectral Plot

Spikes (3D)

Spline (2D graphs)

Spline (3D graphs)

SQL

Standard Deviation

Standard Error

Stars (Icon Plots)

Stationary Series (in Time Series)

STATISTICA BASIC

STATISTICA Graph Format

Statistical Significance (p-level)

Stats Graphs vs. Custom Graphs

Steepest Descent Iterations

Step Area Sequential/Stacked Plot

Step Sequential/Stacked Plot

Stiffness Parameter (in Fitting Options)

Stopping, Breaking, or Interrupting the Current Action

Student's t Distribution

Subscripts in Graph Text

Sun Rays (Icon Plots)

Superscripts in Graph Text

Suppressor Variable

Surface Plot

Surface Plot (from Raw Data)

Surface Plot (Ribbons)

Surface Plot (Ternary graph)

Surface Plot (Ternary graph), Categorized

Symmetric Matrix

Symmetrical Distribution


Glossary - T

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Tapering

Task in SCL (STATISTICA Command Language)

Ternary Plots, Fitting Options

Ternary Plots, 2D - Scatterplot

Ternary Plots, 3D

Ternary Plots, 3D - Categorized Scatterplot

Ternary Plots, 3D - Categorized Space

Ternary Plots, 3D - Categorized Surface

Ternary Plots, 3D - Categorized Trace

Ternary Plots, 3D - Contour (Custom Graph)

Ternary Plots, 3D - Contour/Areas

Ternary Plots, 3D - Contour/Lines

Ternary Plots, 3D - Deviation

Ternary Plots, 3D - Space

Ternary Plots, 3D - Surface

Ternary Plots, 3D - Trace

Text Values

Time-Dependent Covariates

ToolTips

Trace Plot

Trace Plot (Ternary Graph)

Trace Plot, Categorized (Ternary Graph)

Trimmed Means

Tukey Window


Glossary - U

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Underline in Graph Text

Uniform Distribution

Unwieghted Means

User-defined Functions in Graphs

Using Dynamic (Coordinate) Mode in Categorized and Matrix Graphs


Glossary - V

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Value Labels

Variance

Voronoi

Voronoi Scatterplot


Glossary - W

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

Wald Statistic

Weibull Distribution

Whiskers (Box Plot)

Whiskers (Range Plots)

Window Handle

Wire (in SEPath)


Glossary - X

? 2D  3D  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X

X11 output: A 1.  Original Series

X11 output: A 2.  Prior Monthly Adjustment Factors

X11 output: A 3.  Original Series Adjusted by Prior Monthly Adjustment Factors

X11 output: A 4.  Prior Trading Day Adjustment Factors

X11 output: B 1.  Prior Adjusted Series or Original Series

X11 output: B 2.  Trend-cycle

X11 output: B 3.  Unmodified S-I Differences or Ratios

X11 output: B 4.  Replacement Values for Extreme S-I Differences (Ratios)

X11 output: B 5.  Seasonal Factors

X11 output: B 6.  Seasonally Adjusted Series

X11 output: B 7.  Trend-cycle

X11 output: B 8.  Unmodified S-I Differences (Ratios)

X11 output: B 9.  Replacement Values for Extreme S-I Differences (Ratios)

X11 output: B 10.  Seasonal Factors

X11 output: B 11.  Seasonally Adjusted Series

X11 output: B 13.  Irregular Series

X11 output: B 14.  Extreme Irregular Values Excluded from Trading-day Regression

X11 output: B 15.  Preliminary Trading-day Regression

X11 output: B 16.  Trading-day Adjustment Factors Derived from Regression Coefficients

X11 output: B 17.  Preliminary Weights for Irregular Component

X11 output: B 18.  Trading-day Factors Derived from Combined Daily Weights

X11 output: B 19.  Original Series Adjusted for Trading-day and Prior Variation

X11 output: C 1.  Original Series Modified by Preliminary Weights and Adjusted for Trading-day and Prior Variation

X11 output: C 2.  Trend-cycle

X11 output: C 4.  Modified S-I Differences (Ratios)

X11 output: C 5.  Seasonal Factors

X11 output: C 6.  Seasonally Adjusted Series

X11 output: C 7.  Trend-cycle

X11 output: C 9.  Modified S-I Differences (Ratios)

X11 output: C 10.  Seasonal Factors

X11 output: C 11.  Seasonally Adjusted Series

X11 output: C 13.  Irregular Series

X11 output: C 14.  Extreme Irregular Values Excluded from Trading-day Regression

X11 output: C 15.  Final Trading-day Regression

X11 output: C 16.  Final Trading-day Adjustment Factors Derived from Regression X11 output: Coefficients

X11 output: C 17.  Final Weights for Irregular Component

X11 output: C 18.  Final Trading-day Factors Derived From Combined Daily Weights

X11 output: C 19.  Original Series Adjusted for Trading-day and Prior Variation

X11 output: D 1.  Original Series Modified by Final Weights and Adjusted for Trading-day and Prior Variation

X11 output: D 2.  Trend-cycle

X11 output: D 4.  Modified S-I Differences (Ratios)

X11 output: D 5.  Seasonal Factors

X11 output: D 6.  Seasonally Adjusted Series

X11 output: D 7.  Trend-cycle

X11 output: D 8.  Final Unmodified S-I Differences (Ratios)

X11 output: D 9.  Final Replacement Values for Extreme S-I Differences (Ratios)

X11 output: D 10.  Final Seasonal Factors

X11 output: D 11.  Final Seasonally Adjusted Series

X11 output: D 12.  Final Trend-cycle

X11 output: D 13.  Final Irregular

X11 output: E 1.  Modified Original Series

X11 output: E 2.  Modified Seasonally Adjusted Series

X11 output: E 3.  Modified Irregular Series

X11 output: E 4.  Differences (Ratios) of Annual Totals

X11 output: E 5.  Differences (Percent Changes) in Original Series

X11 output: E 6.  Differences (Percent Changes) in Final Seasonally Adjusted Series

X11 output: F 1.  MCD (QCD) Moving Average

X11 output: F 2.  Summary Measures

X11 output: G 1.  Chart

X11 output: G 2.  Chart

X11 output: G 3.  Chart

X11 output: G 4.  Chart

"X-ray" Facility to Explore Layers of Graphs

X, Y Coordinates


Short Run Control Charts

The short run quality control chart, for short production runs, plots transformations of the observations of variables or attributes for multiple parts, each of which constitutes a distinct "run," on the same chart.  The transformations rescale the variable values of interest such that they are of comparable magnitudes across the different short production runs (or parts).  The control limits computed for those transformed values can then be applied to determine if the production process is in control, to monitor continuing production, and to establish procedures for continuous quality improvement.

See also the description of the quality control module for additional details.


Group Control Charts
Group Control Charts (Multiple Stream Group Charts)

The group quality control chart plots multiple streams of observations or attributes on the same chart.  Two points are plotted for each of the samples for which measurements are collected, producing two plotted lines across samples.  The upper line is a plot of the highest mean values from the multiple streams or attributes measured for each of the samples, and the lower line is a plot of the lowest mean values from the multiple streams or attributes for each of the samples.  These upper and lower plotted points represent the maximum and minimum mean values across the multiple streams or attributes for each sample, and if these extreme values are within the specified control limits, then obviously all other mean values are also within the control limits.  The multiple stream group chart therefore allows one to quickly determine whether many process streams or characteristics are under control without necessarily inspecting each and every measurement.

See also the description of the quality control module for additional details.


Text Values

All values in STATISTICA may have two identities:  text (e.g., Male) and numeric (e.g., 1). Text values can be up to 8 characters long and may contain any keyboard character.  The program does differentiate between upper and lowercase letters entered in text values (e.g., "Smith" is not equivalent to "SMITH").  You can switch between viewing text values or their numeric equivalents in the Spreadsheet by pressing the [image] button on the spreadsheet toolbar or via the Text Values option from the View pull-down menu (see also, Text Values Manager and Data Values (Numeric, Text) and Labels).


Value Labels

Each value of a variable can have a label assigned to it.  Value labels can be up to 40 characters long and contain any printable characters.  To display value labels in the spreadsheet, press the [image] button while holding down the CTRL key or select the Text Values - Value Labels option in the spreadsheet View pull-down menu.  For more information, see Text Values Manager and Data Values (Numeric, Text) and Labels).


Euler's Constant

This is the base of the natural logarithm (numerical value: 2.71828182834905...), named after the Swiss mathematician Leonhard Euler (1707-1783).


Block Stats

The Block Stats options provide easy access (via a flying menu) to statistical procedures and graphs for each row or column in a selected block in the spreadsheet or Scrollsheet.  The selected statistics will be computed and added to (i.e., appended to the end of) the spreadsheet or Scrollsheet as additional rows or columns.  Selecting Block Stats/Rows will append the resulting statistic in a new column and the variable name will contain the name of the selected statistic and the long name will include the range description.  Selecting Block Stats/Columns will append the resulting statistic in a new row and the case name will include the name of the selected statistic and the range description.  For more information, see:

Block Stats/Columns

Block Stats/Rows

Block Stats Graphs


Ellipse, Confidence

The following confidence ellipses are available in STATISTICA 2D graphs.

Confidence Area Ellipse:  This type of ellipse is based on the assumption that the two variables follow the bivariate normal distribution.  The orientation of this ellipse is determined by the sign of the linear correlation between two variables (the longer axis of the ellipse is superimposed on the regression line).  The probability that the values will fall within the area marked by the ellipse is determined by the value of the Coefficient (e.g., see Stats Graphs 2D Scatterplots).

Range Ellipse:  This type of ellipse is a fixed size ellipse such that the length of its horizontal and vertical projection onto the X- and Y-axis (respectively) is equal to the mean ± (Range * I) where the mean and range refer to the X or Y variable, and I is the current value of the coefficient field.


Pseudo-Components

Pseudo-components are transformed values of the components (plotted in Ternary graphs) where:

x'  = (x -L )/(Total-L)

  i     i  i

Here, x'i stands for the ith pseudo-component, xi stands for the original component value, Li stands for the lower constraint (limit) for the ith component, L stands for the sum of all lower constraints (limits) for all components in the design, and Total stands for the mixture total.  This transformation makes the coefficients for different factors comparable in size.

See Ternary Graphs (and Cornell, 1993, Chapter 3).


Scrollsheet Handle

When you perform operations on Scrollsheets in STATISTICA BASIC, you need a way to identify specific Scrollsheet windows.  The Scrollsheet handle is a number which is used to identify a specific Scrollsheet in STATISTICA BASIC.  This number is assigned for you and is returned in the functions which create or open a new Scrollsheet.  When using the functions which operate on Scrollsheets, you may need to refer to this Scrollsheet handle to tell STATISTICA BASIC which Scrollsheet you want to affect.  In order to do this, the Scrollsheet handle is stored in a STATISTICA BASIC variable and that variable is later used as a parameter to a Scrollsheet function.  For instance, the following program segment opens a Scrollsheet and stores the Scrollsheet handle in the variable my_scrollsheet.  Then, that same Scrollsheet handle is used in the function PrintScrollsheet to print the Scrollsheet which was just opened.

my_scrollsheet := OpenScrollsheet('c:\stat\examples\results.scr');

PrintScrollsheet(my_scrollsheet);

See also, STATISTICA BASIC - Scrollsheet Library.


Window Handle

The Window Handle is a unique identifier associated with each individual window in the Microsoft Windows environment.  You can obtain window handles by calling Microsoft Windows API functions (such as FindWindow).  After retrieving the window handle, programs may use it in Microsoft Windows API function calls to refer to that window.

For instance, the following program segment opens the topmost Scrollsheet and stores the Scrollsheet handle in the variable my_scrollsheet.  Then, that same Scrollsheet handle is used in the function PrintScrollsheet to print the Scrollsheet.

my_scrollsheet := GetScrollsheet(0);

PrintScrollsheet(my_scrollsheet);

For more information, please refer to the Microsoft Windows SDK documentation.

See also, STATISTICA BASIC - Scrollsheet Library.


Graph Handle

When you perform operations on graphs in STATISTICA BASIC, you need a way to identify specific graphs.  The graph handle is a number which is used to identify a specific graph in STATISTICA BASIC.  This number is assigned for you and is returned in the functions which create or open a new graph.  When using the functions which operate on graphs, you may need to refer to this graph handle to tell STATISTICA BASIC which graph you want to affect.  In order to do this, the graph handle is stored in a STATISTICA BASIC variable and that variable is later used as a parameter to a graph function.  For instance, the following program segment opens a graph and stores the graph handle in the variable my_graph.  Then, that same graph handle is used in the function PrintGraph to print the graph which was just opened.

my_graph := OpenGraph('c:\stat\examples\bwplot.stg');

PrintGraph(my_graph);

See also, STATISTICA BASIC - Graphics Library.


Object Handle

When you perform operations on objects within graphs in STATISTICA BASIC, you need a way to identify specific objects.  The object handle is a number which is used to identify a specific object within a graph in STATISTICA BASIC.  This number is assigned for you and is returned in the functions which create new graph objects.  When using the functions which operate on graphs, you may need to refer to this object handle to tell STATISTICA BASIC which object within the graph you want to affect.  In order to do this, the object handle is stored in a STATISTICA BASIC variable and that variable is later used as a parameter to a graph object function.  For instance, the following program segment opens a graph, creates a graph object and stores the object handle in the variable new_object.  Then, that same object handle is used in the function GraphSetObjectLineStyle to change the line style of the object which was just created.

my_graph := OpenGraph('c:\stat\examples\bwplot.stg');

new_object := GraphDrawShape(my_graph, SHAPE_RECTANGLE, 21, 88, 44, 71, ?DYNAMIC);

GraphSetObjectLineStyle(my_graph, new_object, ON, L_LONG_DASH, 5, RED);

See also, STATISTICA BASIC - Graphics Library.


Color Palette

The color palette contains a set of colors which will define such graph elements as lines, points, borders and surface levels.  You can specify a set of colors in the Edit Palette dialog and save the custom color palette under the file name extension *.pal.  Previously-saved color palettes can also be opened in this dialog for use in the current graph.


Hot Keys

Keyboard combinations can be used as Hot Keys in order to quickly access various STATISTICA procedures (e.g., CTRL+M to toggle on/off the display of the Auto Task Buttons toolbar).  These system procedures Hot Keys are given in Keyboard Interface.  User-defined Hot Keys can also be assigned to a macro (see Auto Task Buttons; see also Hot Keys and Hot Keys in Use).


2D Range Plots - Error Bars

In this style of Stats 2D Range Plot, the ranges or error bars are defined by the raw values in the selected variables.  The midpoints are represented by point markers.  One range or error bar is plotted for each case.  In the simplest instance, three variables need to be selected, one representing the mid-points, one representing the upper limits and one representing the lower limits.

See also "One-sided" Ranges or Error Bars in Range Plots.


2D Box Plots - Error Bars

In this style of Stats 2D Box plots, the ranges or error bars are calculated from the data.  The central tendency (e.g., median or mean), and range or variation statistics (e.g., min-max values, quartiles, standard errors, or standard deviations) are computed for each variable and the selected values are presented as error bars.


2D Line Plot (or Categorized Line Plot) of Means with "Error Bars"

You can create a 2D line plot of means with "error bars" via the Stats 2D Box Plots dialog.  In this dialog, select Mean as the Middle Point and then select the Connect Middle Points option in order to "draw" a line connecting the means in the graph.

Similarily, you can create a categorized 2D line plot of means with "error bars" via the same options in the Stats Categorized Box Plots dialog


2D Line Plot (or Categorized Line Plot) of Medians with Quantiles and Min-Max Range Bars

You can create a 2D line plot of medians with quantiles and min-max range bars via the Stats 2D Box Plots dialog.  In this dialog, select Median as the Middle Point, Percentiles (with a coefficient of 25) as the Box, and Min-Max as the Whisker.  Finally, select the Connect Middle Points option in order to "draw" a line connecting the medians in the graph.

Similarily, you can create a categorized 2D line plot of medians with quantiles and min-max range bars via the same options in the Stats Categorized Box Plots dialog.


How to Stop, Break, or Interrupt the Current Action

Sometimes it may be necessary to stop, break, or interrupt the current action or analysis.  In this case, you can do so in the following manners:

Analysis.  Click on the CANCEL button on the Progress Bar to interrupt the task in progress.

Graph Redraw.  Graph redraw may be interrupted by a click of the mouse (anywhere on the screen) or by pressing any key.

Brushing (in a graph).  You can deactivate the brushing tool by clicking on the Point Tool [image] toolbar button or by pressing the ESC key.

Printing:  You can interrupt the printing of spreadsheets, Scrollsheets, graphs, text output, etc., by clicking on the CANCEL button on the Printing dialog.

STATISTICA BASIC.  Click on the ESC key or the Cancel button on the Progress Bar in order to interrupt the execution of the STATISTICA BASIC program.

SCL.  You can interrupt execution of the SCL program at any point by clicking the mouse or pressing the ESC or CTRL+BREAK keys.

MML.  Click on the ESC key or the Cancel button on the Progress Bar in order to interrupt the execution of the MML program.

Macros.  To stop recording a macro, press CTRL+F3.  To break a macro playback, click on the mouse button, or press the ESC or CTRL+BREAK keys.


Using Dynamic (Coordinate) Mode in Categorized and Matrix Graphs

In categorized and matrix graphs (see Stats Graphs, Quick Stats Graphs, and Custom Graphs), when an object (in dynamic mode) is inserted outside of the component graphs, STATISTICA will beep and then automatically adjust the mode to fixed in order to anchor the position of the object against fixed window coordinates (since dynamic anchoring against X-Y coordinates can only occur within the component graphs).


Jump (in STATISTICA BASIC)

A STATISTICA BASIC command that allows you to "jump" a specified case in the data file (e.g., JUMP 100 would jump to case number 100).  This command is used in the Sequential mode only; in the (default) RandomAccess mode, all data reside in the predefined data array DATA(c,v) and all cases are available by referencing the respective rows of the array (c).


2D Line Plots (Case Profiles)

Unlike in the regular line plots where the values of one variable are plotted as one line (individual data points are connected by a line), in case profile line plots, the values of the selected variables in a case (row) are plotted as one line (i.e., one line plot will be generated for each of the selected cases).  Case profile line plots provide a simple way to visually present the values in a case (e.g., test scores for several tests).  Note that you can use the Block Stats/Columns option from the Analysis pull-down menu to perform some statistics on the cases [e.g., sum the values or take the mean of the values for each test (variable)] and then plot those statistics along with the cases in the block for comparison purposes.

For more information, see Stats Graphs - 2D Line Plots (Case Profiles).


Maximum Likelihood Method

The method of maximum likelihood (the term first used by Fisher, 1922a) is a general method of estimating parameters of a population by values that maximize the likelihood (L) of a sample.  The likelihood L of a sample of n observations x1, x2, ..., xn, is the joint probability function p(x1, x2, ..., xn) when x1, x2, ..., xn are discrete random variables.  If x1, x2, ..., xn are continuous random variables, then the likelihood L of a sample of n observations, x1, x2, ..., xn, is the joint density function f(x1, x2, ..., xn).

Let L be the likelihood of a sample, where L is a function of the parameters θ1, θ2, ... θk.  Then the maximum likelihood estimators of θ1, θ2, ... θk are the values of θ1, θ2, ... θk that maximize L.

Let θ be an element of Ω.  If Ω is an open interval, and if L(θ) is differentiable and assumes a maximum on Ω, then the MLE will be a solution of the following equation:  (dL(θ))/dθ = 0.  For more information, see Mendenhall and Sincich (1984), Bain and Engelhardt (1989), and Neter, Wasserman, and Kutner (1989).

See also, Nonlinear Estimation.


Least Squares Estimation

In the most general terms, least squares estimation is aimed at minimizing the sum of squared deviations of the observed values for the dependent variable from those predicted by the model.  Technically, the least squares estimator of a parameter θ is obtained by minimizing Q with respect to θ where:

                2

Q = Σ[Y - f (θ)]

       i   i

Note that fi(θ) is a known function of θ, Yi = fi(θ) + εi where i = 1 to n, and the εi are random variables, and usually assumed to have expectation of 0.

For more information, see Mendenhall and Sincich (1984), Bain and Engelhardt (1989), and Neter, Wasserman, and Kutner (1989).  See also, Basic Statistics, Multiple Regression, and Nonlinear Estimation.


Bivariate Normal Distribution

Two variables follow the bivariate normal distribution if for each value of one variable, the corresponding values of another variable are normally distributed.  The bivariate normal probability distribution function for a pair of continuous random variables (X and Y) is given by:

                       1/2                 2             2

f(x) = {1/[2πσ σ *(1-ρ)   ]} * e^{-1/2(1-ρ )*[(x-μ )/σ ]  -

              1 2                                  1   1

                                               2

       2ρ[(x-μ )/σ ]*[(y-μ )/σ ] + [(y-μ )/σ ]  }

              1   1       2   2           2    2

-∞<x<∞, -∞<y<∞,-∞<μ1<∞, -∞<μ2<∞, σ1>0, σ2>0, and -1<ρ<1

where

μ1, μ2	are the respective means of the random variables X and Y

σ1, σ2	are the respective standard deviations of the random variables X and Y

ρ	is the correlation coefficient of X and Y

e	is Euler's constant (2.71...)

π	is the constant Pi (3.14...)

See also, Normal Distribution, Elementary Concepts (Normal Distribution), Basic Statistics - Tests of Normality, Distribution Fitting - Normal Distribution, Q-Q Plots - Normal Distribution, P-P Plots - Normal Distribution.


Suppressor Variable

A suppressor variable (in Multiple Regression) has zero (or close to zero) correlation with the criterion but is correlated with one or more of the predictor variables, and therefore, it will suppress irrelevant variance of independent variables.  For example, you are trying to predict the times of runners in a 40 meter dash.  Your predictors are Height and Weight of the runner.  Now, assume that Height is not correlated with Time, but Weight is.  Also assume that Weight and Height are correlated.  If Height is a suppressor variable, then it will suppress, or control for, irrelevant variance (i.e., variance that is shared with the predictor and not the criterion), thus increasing the partial correlation.  This can be viewed as ridding the analysis of noise.

Let t = Time, h = Height, w - Weight, rth = 0.0, rtw = 0.5, and rhw = 0.6.

Weight in this instance accounts for 25% (Rtw**2 = 0.5**2) of the variability of Time.  However, if Height is included in the model, then an additional 14% of the variability of Time is accounted for even though Height is not correlated with Time (see below):

Rt.hw**2 = 0.5**2/(1 - 0.6**2) = 0.39

For more information, please refer to Pedhazur, 1982.


Point (a unit of measurement)

A point (pt) is a unit of measurement used to define the size of font, point markers, line widths, or other components of STATISTICA graphs.  1 point is equal to 1/72 of an inch.

In order to print output in which the physical size of the fonts (and other components of the graph specified in points) is equal to their specified size (in points), set the absolute value of the mapping base in the Graph Mapping Options or Graph Mapping Defaults dialog equal to the diagonal of the output.


Anisotropic

In this mapping mode, the X- and Y-axes of the transformed object (e.g., an embedded graph) are arbitrarily (i.e., disproportionately) scaled.  This mode depends on the graph aspect ratio.  In this mode, the embedded/linked graph or object is vertically and/or horizontally "stretched" in order to fit into the defined space.  For an illustration, see Graph Mapping Mode.

See also, Isotropic, Fixed Size Font.


Isotropic

In this mapping mode, one unit on the X-axis is equal to one unit on the Y-axis and the output is created proportionately, with equally scaled axes.  The size of the object will be changed proportionately when the size of the plot is changed (regardless of whether or not you are maintaining the graph aspect ratio).  For an illustration, see Graph Mapping Mode.

See also, Anisotropic, Fixed Size Font.


Fixed Size Font

In fixed size font mode, physical sizes of fonts (as well as point markers, and other graph components defined in points) in embedded or linked graphs will be the same size as objects in the graph in which they are embedded.  When you select the Fixed Size Font option, you can use the [image] Increase Font and [image] Decrease Font toolbar buttons to globally and proportionally increase or decrease the font size (as well as markers and all distances and spacing defined in points or related to font and marker sizes), incrementally, for each font style and size represented in the current graph.  Each click of these toolbar buttons will change the value of the Graph Mapping Base by 16% (e.g., one click on the bmc gfontinc.bmp} button will increase the font size and decrease the mapping base by 16%).  Hold down the CTRL key while pressing either of these buttons to achieve a smaller (4%) increase rate.  For an illustration, see Graph Mapping Mode.

See also, Anisotropic, Isotropic.


Pearson Correlation

The most widely-used type of correlation coefficient is Pearson r (Pearson, 1896), also called linear or product-moment correlation (the term correlation was first used by Galton, 1888).  It is the basic type of correlation that is offered in Quick Basic Stats (in every module; see Block Stats) and the Basic Statistics and Tables module; the Pearson Product Moment Correlation Distribution option is also available from the Analysis - Quick Basic Stats - Probability Calculator - Corr option in every module of STATISTICA.  Using non technical language, one can say that the correlation coefficient determines the extent to which values of two variables are "proportional" to each other.  The value of the correlation (i.e., correlation coefficient) does not depend on the specific measurement units used; for example, the correlation between height and weight will be identical regardless of whether inches and pounds, or centimeters and kilograms are used as measurement units.  Proportional means linearly related; that is, the correlation is high if it can be approximated by a straight line (sloped upwards or downwards).  This line is called the regression line or least squares line, because it is determined such that the sum of the squared distances of all the data points from the line is the lowest possible.  Pearson correlation assumes that the two variables are measured on at least interval scales.  The Pearson product moment correlation coefficient is calculated as follows:

           Σ(Y  - Y-bar )*(Y  - Y-bar )

r  =          i1       1    i2       2

 12  [Σ(Y  - Y-bar )^2*Σ(Y  - Y-bar )^2]^(1/2)

         i1       1       i2       2

See also, Correlations - Overview.


Pearson Curves

A system of distributions proposed by Karl Pearson (e.g., see Hahn and Shapiro, 1967, pages 220-224) consists of seven solutions (of 12 originally enumerated by Pearson) to a differential equation which approximate a wide range of distributions of different shapes.  Gruska, Mirkhani, and Lamberson (1989) describe in detail how the different Pearson curves can be fit to an empirical distribution.  A method for computing specific Pearson percentiles is also described in Davis and Stephens (1983).  For a comparison between Pearson and Johnson distributions, please refer to the Technical Notes section of Process Analysis.

See also, Johnson Curves.


Johnson Curves

Johnson (1949) described a system of frequency curves that represents transformations of the standard normal curve (see Hahn and Shapiro, 1967, for details).  By applying these transformations to a standard normal variable, a wide variety of non-normal distributions can be approximated, including distributions which are bounded on either one or both sides (e.g., U-shaped distributions).  The advantage of this approach is that once a particular Johnson curve has been fit, the normal integral can be used to compute the expected percentage points under the respective curve.  Methods for fitting Johnson curves, so as to approximate the first four moments of an empirical distribution, are described in detail in Hahn and Shapiro, 1967, pages 199-220; and Hill, Hill, and Holder, 1976.  For a comparison between Pearson and Johnson distributions, please refer to the Technical Notes section of Process Analysis.

See also, Pearson Curves.


Matching Moments, Method of

This method can be employed to determine parameter estimates for a distribution (see Quantile-Quantile Plots, Probability-Probability Plots, and Process Analysis).  The method of matching moments sets the distribution moments equal to the data moments and solves to obtain estimates for the distribution parameters.  For example, for a distribution with two parameters, the first two moments of the distribution (the mean and variance of the distribution, respectively, e.g., μ and σ, respectively) would be set equal to the first two moments of the data (the sample mean and variance, respectively, e.g., the unbiased estimators x-bar and s**2, respectively) and solved for the parameter estimates.  Alternatively, you could use the Maximum Likelihood Method to estimate the parameters.  For more information, see Hahn and Shapiro, 1994.


Auto Task Buttons

You can place customized Auto Task Buttons on the floating Auto Task Buttons toolbar which will allow you to execute Command Language (SCL) programs, STATISTICA BASIC programs, and open supplementary files (e.g., report, graph, or Scrollsheet files), or excute commands entered in the format of editable sequences of keystrokes.  The contents of the Auto Task Buttons toolbar can be customized by adding or removing buttons and also by resizing the menu (drag the toolbar border with the left-mouse-button); for more information, see Auto Task Buttons.


Micro Scrolls

Numeric edit fields in STATISTICA dialogs contain micro scrolls [image] which enable you to increase or decrease the value in the edit field incrementally, by either the last digit (click on the micro scroll with the left-mouse-button, e.g., 1.11, 1.12, 1.13, ...) or the last digit by a factor of 10 (click on the micro scroll with the right-mouse-button, e.g., 1.11, 1.21, 1.31, ...).


ToolTips

ToolTips are a balloon-style Help for Toolbar buttons in STATISTICA.  Simply point to a Toolbar button with the mouse cursor and after a brief delay, the respective ToolTips Help will appear, briefly describing that button.  If a more detailed description of a button is required, you can click on the button with the left-mouse-button, but instead of releasing the mouse-button, hold it down and a description of that button will appear in the comment area of the Status Bar.  To obtain detailed descriptions of all the buttons on the respective Toolbar, click on the [image] button on the Toolbar.


Mapping Base

Graphic objects (e.g., fonts, point markers) of a specified logical size (as set in points) will be printed at the same physical size if the diagonal of the output is equal to the absolute value of the mapping base.  If the diagonal of the output is larger or smaller than the absolute value of the mapping base (as specified in points in the Graph Mapping Defaults dialog), then the graphic objects will be proportionally larger or smaller, respectively.  You can set the mapping base in the Graph Mapping Options or Graph Mapping Defaults dialog.

1 point = 1/72 inch


Quick MML

Quick MML (QMML) is a programming language which was supported in STATISTICA/w up to version 4.5.  In release 5.0, QMML was replaced with a much more comprehensive (but downward compatible) programming language STATISTICA BASIC.  In addition to support for all QMML features, STATISTICA BASIC offers many new facilities such as text values management, sequential and random access modes of operation, data arrays, support for external DLLs (Dynamic Link Libraries of procedures written in other programming languages), matrix operations, user-interface controls, Scrollsheets, and extensive support for STATISTICA graphics procedures.  For more detailed information on these and other capabilities of STATISTICA BASIC, see STATISTICA BASIC Language.


BASIC (STATISTICA BASIC)

STATISTICA BASIC is a programming language similar to BASIC in terms of its general syntax conventions (e.g., variables do not have to be declared).  STATISTICA BASIC can be used to perform a variety of operations from simple data transformations such as executing a list of formulas (which can include distribution functions), to advanced applications (such as developing custom computational algorithms and graphics procedures that can later be used as special extensions to STATISTICA).  STATISTICA BASIC supports nested loops, conditional compound instructions, and offers specialized facilities such as user-defined recoding functions, random number generators that follow theoretical distributions, special functions that automatically handle missing data, random access to specific records in the file, and others.  Also, STATISTICA BASIC offers comprehensive support for STATISTICA graphics procedures allowing the user to develop custom graphics applications (including the creation of compound graphics documents with linked or embedded objects).  STATISTICA BASIC can also be used to call functions and/or subroutines from external DLLs (Dynamic Link Library files), thus allowing the user to "integrate" custom STATISTICA BASIC procedures with other applications.  Applications developed in STATISTICA BASIC can be assigned to Auto Task Buttons for quick access from the customizable floating toolbar.  For more information on these and other capabilities of STATISTICA BASIC, see STATISTICA BASIC Language.


3D Histogram by... - Continuous by Continuous

Select this Quick Stats Graphs - 3D Histogram by... option if both currently highlighted variables in the spreadsheet or Scrollsheet are continuous and/or you want STATISTICA to perform an automatic categorization on the values of the variables for this bivariate histogram.  Each variable's values will be categorized according to the following automatic categorization conventions.

Automatic categorization conventions:  Both selected variables will be divided into categories for this bivariate histogram.  When a selected variable is categorical (usually 10 or fewer categories), STATISTICA will use those categories as the histogram intervals for that variable.  If a variable has either more than 10 categories or its values are non-integers (continuous), then STATISTICA will divide the values into approximately 10 to 12 intervals based on the range of the values.


3D Histogram by... - Discrete by Discrete

Select this Quick Stats Graphs - 3D Histogram by... option when you have highlighted a discrete variable in the spreadsheet or Scrollsheet and you want to plot another discrete variable on the second axis of the bivariate histogram.  After you have selected the second variable, the Select Codes dialog will open in which you will designate the codes for each variable.  (Click on the OK button to accept all of the codes for both variables.)


3D Histogram by... - Continuous by Discrete

This Quick Stats Graphs - 3D Histogram by... option will allow you to plot a continuous (or to-be-categorized automatically) variable (the currently highlighted variable) against a discrete variable.  The values of the first variable will be categorized according to the STATISTICA automatic categorization conventions (see below), however, you will be given the option to specify the codes for the discrete variable in the Select Codes dialog.

Automatic categorization conventions:  Both selected variables will be divided into categories for this bivariate histogram.  When a selected variable is categorical (usually 10 or fewer categories), STATISTICA will use those categories as the histogram intervals for that variable.  If a variable has either more than 10 categories or its values are non-integers (continuous), then STATISTICA will divide the values into approximately 10 to 12 intervals based on the range of the values.


3D Histogram by... - Discrete by Continuous

This Quick Stats Graphs - 3D Histogram by... option is similar to the Continuous by Discrete option, except that the first (highlighted) variable in the spreadsheet or Scrollsheet is the discrete (or to be manually categorized) variable for the bivariate histogram.  STATISTICA will automatically categorize (see below) the values of the continuous variable that you have selected in the Select Single Variable dialog, and the Select Codes dialog will allow you to specify the codes for the discrete variable.

Automatic categorization conventions:  Both selected variables will be divided into categories for this bivariate histogram.  When a selected variable is categorical (usually 10 or fewer categories), STATISTICA will use those categories as the histogram intervals for that variable.  If a variable has either more than 10 categories or its values are non-integers (continuous), then STATISTICA will divide the values into approximately 10 to 12 intervals based on the range of the values.


3D Sequential Raw Data Plots

These options allow you to plot sequences of raw data from selected variables in a 3-dimensional display.  The selected variables are represented on the Y-axis, the consecutive cases on the X-axis, and the values are plotted against the Z-axis.  The contour and surface types integrate all individual plots into one structure.

You can create a 3D Sequential Raw Data Plot via the Custom Graph 3D Sequential Graphs or Stats Graphs 3D Sequential Graphs - Raw Data Plots options.

For more information on the styles of raw data plots available in STATISTICA, see:

Block Plot	Lines

Box Plot	Ribbons Plot

Contour/Discrete	Spikes

Contour Plot	Surface Plot


2D Histograms

2D histograms (the term was first used by Pearson, 1895) present a graphical representation of the frequency distribution of the selected variable(s) in which the columns are drawn over the class intervals and the heights of the columns are proportional to the class frequencies.

You can create 2D Histograms via the Stats Graph - 2D Histogram, Stats Graph - Categorized Histograms, Quick Stats Graph - Histogram of..., Quick Stats Graph - 2D Histogram by..., or Block Stats Graphs - Histograms options.  See also Scatterplots w/Histograms.

For more information on the styles of histograms available in STATISTICA, see:

Double-Y	Multiple

Hanging Bars	Regular


Matrix Plots

Matrix plots summarize the relationships between several variables in a matrix of true X-Y plots.  The most common type of matrix plot is the scatterplot matrix, which can be considered to be the graphical equivalent of the correlation matrix.  If one list of variables is selected when defining the matrix plot, then a square matrix plot will be produced and the histograms of frequency distributions of the respective variables are plotted on the diagonal.  If you select variables in two lists, then a rectangular matrix plot will be produced.  In this style of matrix plot, the histograms for the respective variables will be displayed in the first row and column of the matrix.

You can create matrix plots via the Custom Graphs Matrix Plots, Stats Graph Matrix Plots, or Quick Stats Graph Matrix Scatterplot options.  In addition, Scatterplot Matrices can be created via options available as a part of a particular analysis (e.g., in ANOVA).  In order to produce a scatterplot matrix for each of the selected groups in a grouping variable, see Categorized Scatterplot Matrix.

For more information on the styles of matrix plots available in STATISTICA, see:

Columns

Lines

Scatterplot


Icon Plots

One of the potentially powerful general techniques of exploratory data analysis are multidimensional icon graphs.  The basic idea of icon plots is to represent individual units of observation as particular graphical objects where values of variables are assigned to specific features or dimensions of the objects (usually one case = one object).  The assignment is such that the overall appearance of the objects changes as a function of the configuration of values.  Thus, the objects are given visual "identities" that are unique for configurations of values and that can be identified by the observer.  Examining such icons may help to discover specific clusters of both simple relations and interactions between variables.

You can create icon plots via the Custom Graphs Icon Plots or Stats Graph Icon Plots options.

For more information on the styles of icon plots available in STATISTICA, see:

Chernoff Faces	Polygons

Columns	Profiles

Lines	Stars

Pies	Sun Rays


2D Histograms (Block Stats Graphs)
2D Histogram (Block Stats Graphs)

This type of Block Stats Graph will produce a 2D histogram with a fitted normal curve for each column/row of the block (depending on the option that you select from the spreadsheet or Scrollsheet flying menu, Graphs pull-down menu, or Graphs Gallery dialog), and plotted in one graph (a multiple histogram) to allow for comparisons between the frequency distributions of values in block columns.  (You can create a univariate histogram by selecting a block containing only one column.)

For more information, see Block Stats Graphs - Histogram.


2D Box Plot/Medians (Block Stats Graphs)

This type of Block Stats Graph will produce a box plot of medians (and min/max values and 25th and 75th percentiles) for the columns or rows of the block (depending on the option that you select from the spreadsheet or Scrollsheet flying menu, Graphs pull-down menu, or Graphs Gallery dialog).  Each box will represent data from one column or row.

For more information, see Block Stats Graphs - Box Plot/Medians.


2D Box Plot/Means (Block Stats Graphs)

This type of Block Stats Graph will produce a box plot of means (and standard errors and standard deviations) for the columns or rows of the block (depending on the option that you select from the spreadsheet or Scrollsheet flying menu, Graphs pull-down menu, or Graphs Gallery dialog).  Each box will represent data from one column or row.

For more information, see Block Stats Graphs - Box Plot/Means.


2D Box Plots

In Box Plots (this term was first used by Tukey, 1970), ranges or distribution characteristics of values of a selected variable (or variables) are plotted separately for groups of cases defined by values of a categorical (grouping) variable.  The central tendency (e.g., median or mean), and range or variation statistics (e.g., quartiles, standard errors, or standard deviations) are computed for each group of cases and the selected values are presented in the selected box plot style.  Outlier data points can also be plotted (see Outliers and Extremes).

You can create a Box Plot via the Stats Graph (2D Box Plots, Scatterplots w/Box Plots), Quick Stats Graph, Block Stats Graph (Box Plot/Means, Box Plot/Medians) options, or a Categorized Box Plot via the Stats Graph or Quick Stats Graph options.

For more information on the style of box plots, see:

Box Whiskers	Columns

Boxes	Whiskers


Extrapolating Values in Blocks (AutoFill)

STATISTICA provides an intelligent AutoFill facility which allows you to extrapolate a series of numbers (sequentially or linearly), dates, or text names of months, days, or quarters of the year.  A block of values can be extrapolated up or down or to the left or right of the block.  For more complete information, see Drag-and-Drop - Extrapolate.

Note that you can use the Fill Block commands on the pop-up menu or Edit pull-down menu to copy a cell or range of cells to adjacent cells within the currently selected block.

See also, Time Series.


Multiple Normal Probability Plot

Unlike Categorized Normal Probability Plots which produce a series of standard 2D probability plots (one for each category of cases identified by the X- and Y-axis category variables or identified by the Multiple Subset criteria), Block Stats Graphs - Normal Prob. Plots allow you to evaluate the normality of the distributions of one or more variables or cases in one multiple probability plot (in order to allow for comparisons between the block columns or rows).  The values and line for each column/row will be represented by different point markers and line patterns, respectively, in the multiple normal probability plot.

For more information, see:

Stats Probability Plots

Normal Probability Plots

Normal Probability Plots (Computational Notes)


  Histogram, 3D Bivariate

Three-dimensional histograms are used to visualize crosstabulations of values in two variables.  They can be considered to be a conjunction of two simple (i.e., univariate) histograms, combined such that the frequencies of co-occurrences of values on the two analyzed variables can be examined.  In a most common format of this graph, a 3D bar is drawn for each "cell" of the crosstabulation table and the height of the bar represents the frequency of values for the respective cell of the table.

You can create 3D Bivariate Distribution Histograms via the Stats 3D Sequential Graphs - Bivariate Histograms or the Quick Stats Graphs - 3D Histogram by... options.

For more information on the style of 3D bivariate histograms, see:

3D Histogram - Box Plots	3D Histogram - Spikes

3D Histogram - Contour/Discrete	3D Histogram - Surface Plot

3D Histogram - Contour Plot


Wald Statistic

The results Scrollsheet with the parameter estimates for the Cox proportional hazard regression model includes the so-called Wald statistic, and the p level for that statistic.  This statistic is a test of significance of the regression coefficient; it is based on the asymptotic normality property of maximum likelihood estimates, and is computed as:

W = β * 1/Var(β) * β

In this formula, β stands for the parameter estimates, and Var(β) stands for the asymptotic variance of the parameter estimates.  The Wald statistic is tested against the Chi-square distribution.


Adjusted Means

These are the means that one would get after removing all differences that can be accounted for by the covariate in an analysis of variance design (see ANOVA).


Unweighted Means

If the cell frequencies in a multi-factor ANOVA design are unequal, then the unweighted means (for levels of a factor) are calculated from the means of sub-groups without weighting, that is, without adjusting for the differences between the sub-group frequencies.


ODBC

ODBC (Open DataBase Connectivity) is a set of conventions introduced by Microsoft which allows access to information from a wide range of data bases (e.g., MS Access, Oracle) and performing queries via SQL.

See, Import Data - ODBC.


SQL

SQL (Standard Query Language) enables you to query an outside data source about the data it contains.  You can use SQL in order to specify a subset of rows to import (see Import Data - ODBC).  For information on SQL syntax, please consult an SQL manual.

See also, ODBC.


Fitting Options for Ternary Plots

The following four regression functions can be fit to the data in a Stats, Categorized, or Custom ternary plot.  Note that these functions are derived from the equations for the respective standard polynomial functions, using the restriction that the sum of the values of the component (X, Y, Z) variables for each case is equal to a constant (e.g., 1.0).  For example, the simple first-degree model:

V = a + b1*X + b2*Y + b3*Z

with the constraint X+Y+Z=1, can be adjusted by multiplying the intercept coefficient a by 1=X+Y+Z:

V = a*X + a*Y + a*Z + b1*X + b2*Y + b3*Z

This expression can be simplified to:

V = (a+b1)*X + (a+b2)*Y + (a+b3)*Z

or:  V = b1'*X + b2'*Y + b3'*Z

The available "canonical" form polynomial regression functions are listed below (note that in these equations, the parameters are simply referred to as b1, b2, etc., and not b1', b2', etc.):

Linear Smooth (1st degree polynomial):	V = b1*X + b2*Y + b3*Z

Quadratic Smooth (2nd degree polynomial):	V = b1*X + b2*Y + b3*Z +
b12*X*Y + b13*X*Z + b23*Y*Z

Full Cubic Smooth:	V = b1*X + b2*Y + b3*Z + b12*X*Y +
b13*X*Z + b23*Y*Z + b12*X*Y*(X-Y) +
b13*X*Z*(X-Z) + b23*Y*Z*(Y-Z) + b123*X*Y*Z

Special Cubic Smooth:	V = b1*X + b2*Y + b3*Z + b12*X*Y +
b13*X*Z + b23*Y*Z + b123*X*Y*Z

For more information about ternary representation of data, see Ternary Plots.


  Ternary Plots - 2D Scatterplot

In this type of ternary graph, the triangular coordinate systems are used to plot three (or more) variables [the components X, Y, and Z] in two dimensions.  Here, the points representing the proportions of the component variables (X, Y, and Z) are plotted.

For more information about ternary representation of data, see Ternary Plots.

See also, Stats Ternary Plots, Custom Ternary Plots


  Ternary Plots - 3D Scatterplot

In this type of ternary graph, the triangular coordinate systems are used to plot four (or more) variables (the components X, Y, and Z, and the responses V1, V2, etc.) in three dimensions (ternary 3D scatterplots or surface plots).  Here, the responses (V1, V2, etc.) associated with the proportions of the component variables (X, Y, and Z) in a ternary graph are plotted as the heights of the points.

For more information about ternary representation of data, see Ternary Plots.

See also, Stats Ternary Plots, Custom Ternary Plots


Ternary Plots - Space Plot

This type of ternary graph offers a distinctive method of representing 3D scatterplot data through the use of an X-Y-Z plane (defined via a triangular coordinate system) positioned at a user-selectable level of the vertical V-axis (which "sticks up" through the middle of the plane).  The level of the X-Y-Z plane can be adjusted in order to divide the X-Y-Z- space into meaningful parts (e.g., featuring different patterns of the relation between the three variables).  The V-axis value defining the level of the base plane can be adjusted in the 3D Graphs/More Options dialog accessible from the More Options button in the General Layout dialog.

For more information about ternary representation of data, see Ternary Plots.

See also, Stats Ternary Plots

Custom Ternary Plots


Ternary Plot - Deviation Plot
Ternary Plots - Deviation Plot

This type of ternary graph allows you to examine the relations between four or more dimensions (X, Y, Z, and V1, V2, etc.) as "deviations" from a specified base-level of the V-axis (see Ternary Space Plot and 3D Graphs/More Options) where three of those dimensions (X, Y, and Z) represent components of a mixture (i.e., the relations between them is constrained such that the values of the three variables add up to the same constant for each case).

For more information about ternary representation of data, see Ternary Plots.

See also, Stats Ternary Plots

Custom Ternary Plots


Ternary Plots - Trace Plot
Ternary Plots - Stats Trace Plot

This type of ternary graph allows you to examine the relations between four or more dimensions (X, Y, Z, and V1, V2, etc.) as a 3D trace plot where three of those dimensions (X, Y, and Z) represent components of a mixture (i.e., the relations between them is constrained such that the values of the three variables add up to the same constant for each case).  Data points in this graph are positioned as in regular 3D scatterplots, however, individual data points are connected with a line (in the order in which they were read from the data file), visualizing a "trace" of sequential values.

For more information about ternary representation of data, see Ternary Plots.

See also, Stats Ternary Plots.

Custom Ternary Plots


Ternary Plots - Surface
  Ternary Plots - Surface Plot

A surface is fit (see Fitting Options for Ternary Plots) to a four-coordinate data set in this 3-dimensional ternary graph.

First degree polynomial

Second degree (quadratic) polynomial

Full cubic polynomial

Special cubic polynomial

For more information about ternary representation of data, see Ternary Plots.

See also, Stats Ternary Plots.

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


Ternary Plot - Custom Contour Plot
Ternary Plots - Custom Contour Plot

This Custom Graph option allows you to examine the relations between four dimensions (X, Y, Z, and V) as a contour plot where three of those dimensions (X, Y, and Z) represent components of a mixture (i.e., the relations between them is constrained such that the values of the three variables add up to the same constant for each case).  Here, the 3-dimensional surface (fitted to a four-coordinate data set) is projected onto a 2-dimensional plane as a contour.

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.

See also, Calculating Contour Levels and Distance.

For more information about ternary representation of data, see Ternary Plots.


Quartile Range

The quartile (this term was first used by Galton, 1882) range of a variable is calculated as the value of the 75th percentile minus the value of the 25th percentile.  Thus it is the width of the range about the median that includes 50% of the cases.

For more information, see Nonparametrics.


Ternary Plots

A ternary plot can be used to examine relations between four or more dimensions where three of those dimensions represent components of a mixture (i.e., the relations between them is constrained such that the values of the three variables add up to the same constant).  One typical application of this graph is when the measured response(s) from an experiment depends on the relative proportions of three components (e.g., three different chemicals) which are varied in order to determine an optimal combination of those components (e.g., in mixture designs).

Ternary plots can be created via the Stats Ternary Plots, Stats Categorized Ternary Plots, or Custom Ternary Plots options.

For more information on the style of ternary plots available, see:

  2D Scatterplot	  Surface

  3D Scatterplot	  Contour/Lines

  Space Plot	  Contour/Areas

  Trace Plot	  Deviation Plot

  Categorized 2D Scatterplot	  Categorized Trace Plot

  Categorized 3D Scatterplot	  Categorized Surface

  Categorized Space Plot	  Categorized Contour/Lines

  Categorized Contour/Areas


  Ternary Plots - Contour/Lines

In this type of ternary graph, the 3-dimensional surface (fitted to a four-coordinate data set) is projected onto a 2-dimensional plane as a line contour.

First degree polynomial

Second degree (quadratic) polynomial

Full cubic polynomial

Special cubic polynomial

See also: Fitting Options for Ternary Plots

Stats Ternary Plots.

For more information about ternary representation of data, see Ternary Plots.

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.  See also, Calculating Contour Levels and Distance.


  Ternary Plots - Contour/Areas

In this type of ternary graph, the 3-dimensional surface (fitted to a four-coordinate data set) is projected onto a 2-dimensional plane as an area contour.

First degree polynomial

Second degree (quadratic) polynomial

Full cubic polynomial

Special cubic polynomial

See also: Fitting Options for Ternary Plots.

Stats Ternary Plots.

For more information about ternary representation of data, see Ternary Plots.

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.  See also, Calculating Contour Levels and Distance.


  Ternary Plots - Stats Categorized 2D Scatterplot

The points representing the proportions of the component variables (X, Y, and Z) in a ternary graph are plotted in a 2-dimensional display for each level of the grouping variable (or user-defined subset of data).  One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).

For more information about ternary representation of data, see Ternary Plots.

See also, Stats Ternary Plots.


  Ternary Plots - Stats Categorized 3D Scatterplot

The responses associated with the proportions of the component variables (X, Y, and Z) in a ternary graph are plotted in a 3-dimensional display for each level of the grouping variable (or user-defined subset of data).  One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).

For more information about ternary representation of data, see Ternary Plots.

See also, Stats Ternary Plots.


Ternary Plots - Stats Categorized Space Plot

In this type of ternary graph, 3D scatterplot data are represented through the use of an X-Y-Z plane (defined via a triangular coordinate system) positioned at a user-selectable level of the vertical V-axis (which "sticks up" through the middle of the plane) and categorized by each level of the grouping variable (or user-defined subset of data).  One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).

The level of the X-Y-Z plane can be adjusted in order to divide the X-Y-Z-V space into meaningful parts (e.g., featuring different patterns of the relation between the three variables).  The V-axis value defining the level of the base plane can be adjusted in the 3D Graphs/More Options dialog accessible from the More Options button in the General Layout dialog.

For more information about ternary representation of data, see Ternary Plots.

See also, Stats Ternary Plots

Stats Categorized Ternary Plots.


Ternary Plots - Stats Categorized Trace Plot

In this type of ternary graph, you can examine the relations between four or more dimensions (X, Y, Z, and V1, V2, etc.) as a 3D trace plot categorized by each level of the grouping variable (or user-defined subset of data).  One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).

For more information about ternary representation of data, see Ternary Plots.

See also, Stats Ternary Plots

Stats Categorized Ternary Plots.


  Ternary Plots - Stats Categorized Surface

A surface is fit to a four-coordinate data set in this 3-dimensional ternary graph categorized by each level of the grouping variable (or user-defined subset of data).  One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).  See also:

First degree polynomial

Second degree (quadratic) polynomial

Full cubic polynomial

Special cubic polynomial

See also: Fitting Options for Ternary Plots

Stats Categorized Ternary Plots.

For more information about ternary representation of data, see Ternary Plots.

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


  Ternary Plots - Stats Categorized Contour/Lines

In this type of ternary graph, the 3-dimensional surface (fitted to a four-coordinate data set) is projected onto a 2-dimensional plane as a line contour for each level of the grouping variable (or user-defined subset of data).  One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).

For more information about ternary representation of data, see Ternary Plots.

See also: Fitting Options for Ternary Plots

Calculating Contour Levels and Distance

Stats Categorized Ternary Plots.

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


  Ternary Plots - Stats Categorized Contour/Areas

In this type of ternary graph, the 3-dimensional surface (fitted to a four-coordinate data set) is projected onto a 2-dimensional plane as an area contour for each level of the grouping variable (or user-defined subset of data).  One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).

For more information about ternary representation of data, see Ternary Plots.

See also: Fitting Options for Ternary Plots

Calculating Contour Levels and Distance

Stats Categorized Ternary Plots.

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


Marked Points (in Brushing)

Specific points in graphs can be marked (i.e., assigned different -- by default, filled -- point markers) by using the interactive Brushing Tool (available from the Graphics window View pull-down menu or toolbar button [image], see also Brushing Glossary).  Points marked via Brushing can be managed in the Graph Data Editor.

See also Marked Points (in Multiple Subset Graphs).


Marked Points (in Multiple Subset Graphs)

Specific points in graphs can be marked (i.e., assigned different point markers) by using the Specify Multiple Subsets dialog.  This dialog (accessible from the respective graph definition dialogs) allows you to specify selection conditions that will subset (i.e., categorize) the cases in one plot and "mark" each defined subset in the graph by a different point marker.  For more detailed information about multiple subset graphs, see Mark Selected Subsets.

See also Marked Points (in Brushing).


Odds Ratio

The odds ratio is useful in the interpretation of the results of Logistic regression (see Neter, Wasserman, and Kutner, 1989) and is computed from a 2x2 classification table which displays the predicted and observed classification of cases for a binary dependent variable:

(f  *f  )/(f  *f  )

  11  22    12  21

where fij represents the respective frequencies in the 2x2 table.


Time-Dependent Covariates

Time-dependent covariates occur when the effect of the covariate on survival is dependent on time (i.e., the conditional hazard at each point in time is a function of the covariate and time).  You can specify time-dependent covariates in the Survival Analysis module of STATISTICA.


3D Categorized Contour/Line

This Stats Graphs - 3D Categorized Plot projects a 3-dimensional surface onto a 2-dimensional plane as line contour plots for each level of the grouping variable.  One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).

See also, Calculating Contour Levels and Distance.

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


3D Categorized Contour/Areas

This Stats Graphs - 3D Categorized Plot projects a 3-dimensional surface onto a 2-dimensional plane as area contour plots for each level of the grouping variable.  One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).

See also, Calculating Contour Levels and Distance.

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


Quartiles

The lower and upper quartiles (this term was first used by Galton, 1882; also referred to as the .25 and .75 quantiles) are the 25th and 75th percentiles of the distribution (respectively).

The 25th percentile of a variable is a value such that 25% of the values of the variable fall below that value.

Similarly, the 75th percentile is a value such that 75% of the values of the variable fall below that value and is calculated accordingly.  You can specify the method of computing percentiles in the STATISTICA Defaults: General dialog.  User-specified percentiles can be calculated in Nonparametrics.


Percentiles

The percentile (this term was first used by Galton, 1885a) of a distribution of values is a number xp such that a percentage p of the population values are less than or equal to xp.  For example, the 25th percentile (also referred to as the .25 quantile or lower quartile) of a variable is a value (xp) such that 25% (p) of the values of the variable fall below that value.

Similarly, the 75th percentile (also referred to as the .75 quantile or upper quartile) is a value such that 75% of the values of the variable fall below that value and is calculated accordingly.  You can specify the method of computing percentiles in the STATISTICA Defaults: General dialog.  User-specified percentiles can be calculated in Nonparametrics.


Quantile-Quantile Plots

You can visually check for the fit of a theoretical distribution to the observed data by examining the quantile-quantile (or Q-Q) plot (also called Quantile Plot, see Stats Quantile-Quantile Plots).  In this plot, the observed values of a variable are plotted against the theoretical quantiles.  A good fit of the theoretical distribution to the observed values would be indicated by this plot if the plotted values fall onto a straight line.  To produce a Q-Q plot, the program will first sort the n observed data points into ascending order, so that:

x  ≤ x  ≤ ... ≤ x

 1    2          n

These observed values are plotted against one axis of the graph; on the other axis the plot will show:

 -1

F  ((i-r   )/(n+n   ))

        adj      adj

where i is the rank of the respective observation, radj and nadj are adjustment factors (≤ 0.5) and F**-1 denotes the inverse of the probability integral for the respective standardized distribution.  The resulting plot is a scatterplot of the observed values against the (standardized) expected values, given the respective distribution.  Note that, in addition to the inverse probability integral value, STATISTICA will also show the respective cumulative probability values on the opposite axis, that is, the plot will show not only the standardized values for the theoretical distribution, but also the respective p-values.  Note also that the adjustment factors radj and nadj ensure that the p-value for the inverse probability integral will fall between 0 and 1, but not including 0 and 1 (see Chambers, Cleveland, Kleiner, and Tukey, 1983; in STATISTICA, the default value for both adjustment factors is 1/3=.333).


Categorized Quantile-Quantile Plots

In this Stats Graph, you can visually check for the fit of a theoretical distribution to the observed data by examining each quantile-quantile (or Q-Q) plot (also called Quantile Plot, see Stats Quantile-Quantile Plots) for the respective level of the grouping variable (or user-defined subset of data).  In this plot, the observed values of a variable are plotted against the theoretical quantiles.  A good fit of the theoretical distribution to the observed values would be indicated by this plot if the plotted values fall onto a straight line.  One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).  (See Quantile-Quantile Plots for more details on how to produce a Q-Q plot.)


Probability-Probability Plots

You can visually check for the fit of a theoretical distribution to the observed data by examining the probability-probability plot (also called Probability Plot, see also Stats Probability-Probability Plots).  In probability-probability plots (or P-P plots for short) the observed cumulative distribution function is plotted against the theoretical cumulative distribution function.  As in the Quantile-Quantile plot, the values of the respective variable are first sorted into ascending order.  The ith observation is plotted against one axis as i/n (i.e., the observed cumulative distribution function), and against the other axis as F(x(i)), where F(x(i)) stands for the value of the theoretical cumulative distribution function for the respective observation x(i).  If the theoretical cumulative distribution approximates the observed distribution well, then all points in this plot should fall onto the diagonal line.


Categorized Probability-Probability Plots

In this Stats Graph, you can visually check for the fit of a theoretical distribution to the observed data by examining each probability-probability plot (also called Probability Plot, see also Stats Probability-Probability Plots) for the respective level of the grouping variable (or user-defined subset of data).  In probability-probability plots (or P-P plots for short) the observed cumulative distribution function is plotted against the theoretical cumulative distribution function.  As in the Categorized Quantile-Quantile plot, the values of the respective variable are first sorted into ascending order.  The ith observation is plotted against one axis as i/n (i.e., the observed cumulative distribution function), and against the other axis as F(x(i)), where F(x(i)) stands for the value of the theoretical cumulative distribution function for the respective observation x(i).  If the theoretical cumulative distribution approximates the observed distribution well, then all points in this plot should fall onto the diagonal line.  One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).


Internal STATISTICA Representation

Whenever you copy a STATISTICA graph or graph object to the Clipboard, one format in which the Clipboard contents can then be pasted in STATISTICA (via Paste Special) is Internal STATISTICA Representation.  This is the default format for STATISTICA graphs and graphic objects within STATISTICA modules.  This format contains all specifications of the graph or graphic object (including its location in the graph) and is used internally in STATISTICA to transfer STATISTICA graphs or graphic objects between STATISTICA graphs or compound graphs.

See also STATISTICA Graph Format.


Multiple Subset Graphs

You can create multiple subset graphs via the Specify Multiple Subsets dialog.  This dialog allows you to specify selection conditions that will subset (i.e., categorize) the cases in one plot.  Each defined subset will be represented in the graph by a different point marker.  For more detailed information about multiple subset graphs, see Mark Selected Subsets.


Polar Coordinates

Polar coordinates (r, θ) represent the location of a point (in 2D space) by its distance (r) from a fixed point on a fixed line (polar axis) and the angle (θ, in radians) from that fixed line.

  Polar plots are used to visualize functions.  They also offer an intuitive way to present relations involving a variable representing direction.

See also, General Layout - 2D Graphs.


Cartesian Coordinates

Cartesian coordinates (x, y, or x, y, z; also known as rectangular coordinates) are directed distances from two (or three) perpendicular axes.  The location of a point in space is established by the corresponding coordinates on the X-and Y-axes (or X-, Y-, and Z-axes).

See also, General Layout - 2D Graphs.


Layered Compression

In 2D graphs, layered compression is an exploratory data analysis technique that may facilitate the identification of otherwise obscured trends and patterns in 2-dimensional data sets.  To obtain the layered effect, the main graph plotting area is reduced in size to leave space for Margin Graphs in the upper and right side of the display (and a miniature graph in the corner).  These smaller Margin Graphs represent vertically and horizontally compressed images (respectively) of the main graph.  In order to produce a layered 2D graph, select the Layered option from either the General Layout dialog or from the respective 2D graph dialog (when the graph is created; e.g., Stats 2D Scatterplot).

See also, General Layout - 2D Graphs.


Glossary of Brushing Terms

The following terms describe the use of Brushing in STATISTICA graphs.

Highlighting

Action

Mark

Label

Turn OFF

De-select

Reverse

Selected

De-selecting


Glossary of Brushing Terms - Highlighting (in Brushing)

The initial state of selected data points prior to the occurrence of some brushing Action.  Highlighting data points in the graph works like in word processors where highlighting is a precursor to performing an Action on the highlighted text (e.g., applying a font attribute such as boldface or italic).  If no Action is taken and you exit the brushing mode, the highlighted status of a point is hidden (not displayed), but preserved internally (e.g., is saved with the graph) and the points will be highlighted once again whenever you re-enter the brushing mode for the graph.

Note that you cannot highlight any points when you are in the Auto Update mode because then, every application of the brushing tool will result directly in the execution of the current action (e.g., labeling of the point).

For other Brushing terms, see Glossary of Brushing Terms.

See also, Brushing in STATISTICA graphs.


Glossary of Brushing Terms - Action (in Brushing)

An Action is an operation performed on highlighted data points.  Actions are executed when you press the Update button in the Brushing dialog (or after every operation of pointing to a data point with the mouse when you are in the Auto Update mode).  The following operations are available in the Brushing dialog.

Mark (in Brushing)	De-select (in Brushing)

Label (in Brushing)	Reverse (in Brushing)

Turn OFF (in Brushing)

For other Brushing terms, see Glossary of Brushing Terms.

See also, Brushing in STATISTICA graphs.


Brushing - Mark Points

When you select Mark Points via brushing and the Action is updated, then the selected points will be identified with a different point marker.  The marker can be specified by pressing the Point Pattern button in the Brushing - Extended Options dialog, or by double-clicking on the point (after exiting the brushing mode).

For other Brushing terms, see Glossary of Brushing Terms.

See also, Brushing in STATISTICA graphs.


Brushing - Label Points

When you select Label Points via brushing and the Action is updated, then the selected points will be identified with the respective data point labels (e.g., the case names, text label, or specific type of data point coordinates, depending on the current setting in the Data Point Labels dialog).  The labels can be edited by pressing on the Labels button in the Brushing - Extended Options dialog, or by double-clicking on the label (after exiting the brushing mode).  An individual data point label can also be edited in the Graph Data Editor (see also Graph Data Point ID Info).  If you want to label specific points in the graph, use the Brushing facility (note that the current setting in this dialog will affect the "labels" that will be generated via Brushing).

For other Brushing terms, see Glossary of Brushing Terms.

See also, Brushing in STATISTICA graphs.


Brushing - Turn OFF Points
Brushing - Turn OFF

This operation temporarily removes the selected points from the display and fitted function calculations.  The point values remain visible in the Graph Data Editor.  Turned off points are not displayed in the graph, thus they cannot be easily selected and turned on again with the Point brush, however, they can be turned on by:

(1)	pressing the Reverse button to change the Turn OFF action to Turn ON, then using the Rectangle or Lasso brush to select a region of points,

(2)	clicking on the Edit pull-down menu (or flying menu) option De-select Block in the Graph Data Editor in order to remove the Turn OFF attribute from the block of data points (selected data points are displayed in a different color in the Graph Data Editor),

(3)	using the De-select All option in the Brushing dialog.

For other Brushing terms, see Glossary of Brushing Terms.

See also, Brushing in STATISTICA graphs.


Brushing - De-select Points
Brushing - De-select

This operation removes all attributes (marked, labeled, turned off, or highlighted) due to previous actions performed on the selected points for the plot specified in the Plot combo box.

For other Brushing terms, see Glossary of Brushing Terms.

See also, Brushing in STATISTICA graphs.


Brushing - Reverse

Pressing this button inverts all Actions; allowing you to Un-Mark, Un-Label, or Turn ON highlighted points.

For other Brushing terms, see Glossary of Brushing Terms.

See also, Brushing in STATISTICA graphs.


Glossary of Brushing Terms - Selected (in Brushing)

A state in which points have been Highlighted or further identified by execution of some Action. The selected status of a point is saved with the graph.  Four selection attributes are available:

Mark (in Brushing)	Turn OFF (in Brushing)

Label (in Brushing)	Highlight (in Brushing)

For other Brushing terms, see Glossary of Brushing Terms.

See also, Brushing in STATISTICA graphs.


Brushing - Highlight

The initial state of selected data points prior to the occurrence of some brushing Action.  Highlighting data points in the graph works like in word processors where highlighting is a precursor to performing an Action on the highlighted text (e.g., applying a font attribute such as boldface or italic).  If no Action is taken and you exit the brushing mode, the highlighted status of a point is hidden (not displayed), but preserved internally (e.g., is saved with the graph) and the points will be highlighted once again whenever you re-enter the brushing mode for the graph.

Note that you cannot highlight any points when you are in the Auto Update mode because then, every application of the brushing tool will result directly in the execution of the current action (e.g., labeling of the point).

See also, Brushing in STATISTICA graphs.


Glossary of Brushing Terms - De-selecting (in Brushing)

Removal of all attributes (marked, labeled, turned off, and highlighted); this is the default status of all points when a graph is created.

For other Brushing terms, see Glossary of Brushing Terms.

See also, Brushing in STATISTICA graphs.


Contour/Discrete Raw Data Plot

This sequential plot (see Stats 3D Sequential Raw Data Plots) can be considered to be a 2D projection of the 3D Ribbons plot.  Each data point in this plot is represented as a rectangular region, with different colors and/or patterns corresponding to the values (or range of values of the data points (the ranges are described in the legend).  Values within each series are presented along the X-axis, with each series plotted along the Y-axis.  (See also, Calculating Contour Levels and Distance.)

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


Surface Plot (from Raw Data)

This sequential plot (see Stats 3D Sequential Raw Data Plots) fits a spline-smoothed surface to each data point.  Successive values of each series are plotted along the X-axis, with each successive series represented along the Y-axis.  The smoothness of the surface can be adjusted using the stiffness control in the 3D Graphs-More Options dialog.

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


Multiple Graph AutoLayout Wizard

You can use the Multiple Graph AutoLayout Wizard to create compound graphs (graphs that contain linked or embedded OLE objects).  STATISTICA supports a comprehensive selection of facilities to insert OLE-compliant objects in STATISTICA graphics documents (see Exchanging Information (Data, Graphs) with other Applications).  This Wizard provides two ways of creating multiple graph layouts:

•	In order to create a multiple graph layout in which pre-selected graphs will be placed on the same page, use the Graph AutoLayout - Wizard option.  The AutoLayout Wizard assists you (in two steps) in selecting graphs to be placed on the same page (graphs may be selected from currently open windows or from graph files previously saved to disk).

•	In order to create a multiple graph template into which Clipboard objects may be pasted (using Paste Replace), use the Graph AutoLayout - Template option.


SEPATH Wizards

The SEPATH Path Wizards are a preprogrammed sequences of dialog boxes that guide you, step by step, through the construction of the most common kinds of structural models.  The Wizards do most of the work (they generate the necessary code of the PATH1 language necessary to estimate the models), and they structure the problem for you so that the chances of making a mistake in specifying a model are greatly reduced when a Wizard is guiding you.

The Structural Modeling module contains two Wizards.  Click on the names below for details on these Wizards.

Confirmatory Factor Analysis Wizard

General Structural Model Wizard


Missing Data

In cases where there is no data available for some variables, then those cells in the spreadsheet are displayed as blanks.  Those missing data are marked in the spreadsheet by a reserved value (by default it is -9999; this value can be changed separately for each variable in the Spreadsheet Edit Current Specs dialog and viewed in the spreadsheet toolbar Show Field when a blank cell is highlighted in the spreadsheet).  Values of a variable that are assigned such Missing data codes are ignored in all analyses (i.e., either Pairwise MD Deleted, or Casewise MD Deleted is used).  See also, Casewise vs. pairwise deletion of missing data.

Alternatively, you can use mean substitution of missing data (replacing all missing data in a variable by the mean of that variable) in order to eliminate missing data in the data file.  This way of handling missing data can be requested in many modules; you can also use this method to permanently "remove" the missing data from your data set (via the Data Management module).  For more information on the advantages and disadvantages of mean substitution, see Pairwise Deletion of Missing Data vs. Mean Substitution.


Pairwise Deletion of Missing Data vs. Mean Substitution

In order to avoid loosing data due to casewise deletion of missing data, you can use one of two other methods.  These are (1) the so-called mean substitution of missing data (replacing all missing data in a variable by the mean of that variable) and (2) pairwise deletion of missing data.  These methods of handling missing data can be requested in many modules; you can also use the mean substitution method to permanently "remove" missing data from your data set (via the Data Management module).  Mean substitution offers some advantages and some disadvantages as compared to pairwise deletion.  Its main advantage is that it produces "internally consistent" sets of results ("true" correlation matrices).  The main disadvantages are:

(a) Mean substitution artificially decreases the variation of scores, and this decrease in individual variables is proportional to the number of missing data (i.e., the more missing data, the more "perfectly average scores" will be artificially added to the data set).

(b) Because it substitutes missing data with artificially created "average" data points, mean substitution may considerably change the values of correlations.


Server Mode (OLE)

When an application is in OLE Server Mode, it is acting as the creator or source of the OLE object.  When a linked or embedded object is edited in the client application (see Client Mode), then the source application (i.e., server) is opened in the Server Mode and the object is automatically loaded for editing.

STATISTICA can perform as either the OLE client or server application, or both simultaneously.

See also, Overview of Object Linking and Embedding (OLE)


Client Mode (OLE)

When an application is in OLE Client Mode, it is acting as the recipient of an OLE object (OLE container) from a server application (see Server Mode).  In order to edit the OLE object in the client application, you can either double-click on the object or select Object from the Edit pull-down menu to launch the source application (i.e., server) and automatically open the the object for editing.

STATISTICA can perform as either the OLE client or server application, or both simultaneously.

See also, Overview of Object Linking and Embedding (OLE)


Nested Compound Documents

Compound documents are those that contain linked or embedded (OLE) objects (e.g., see Compound Graphs).  STATISTICA supports nested compound documents (up to the fourth order), that is, STATISTICA documents with embedded documents can be embedded in other STATISTICA documents.


Compound Graphs

Compound graphs are those that contain linked or embedded OLE objects.  Unlike categorized or matrix graphs which consist of multiple but unseparable graphs (controlled by a single General Layout set of characteristics), compound graphs consist of several completely independent, stand-alone STATISTICA graphics objects placed on a single display.

Customizing.  The component graphs are customizable as separate (OLE) objects in the master (blank graph) document.  In order to customize any detail of a component graph (in a compound graph), double-click on it and STATISTICA will open it in a separate window where its attributes can be accessed directly.

Creating.  STATISTICA can automatically create compound graphs (e.g., see the Scatterplot w/ Histograms and Scatterplots w/ Box Plots Stats Graphs, or the Quality Control module where one display contains 4 different types of graphs) or you can use the Multiple Graph AutoLayout Wizard to create them yourself.  STATISTICA supports a comprehensive selection of facilities to insert OLE-compliant objects in STATISTICA graphics documents (see Exchanging Information (Data, Graphs) with other Applications).  In order to create a multiple graph template into which Clipboard objects may be pasted (using Paste Replace), use the Graph AutoLayout - Template option.


Drag-and-Drop

STATISTICA supports all standard spreadsheet (Excel-style) block Drag-and-Drop operations (copy, move, insert, etc.) and block extension operations, as well as mouse-controlled column width, split scrolling, etc.  The Drag-and-Drop conventions are also supported for inserting files from the File Manager directly into STATISTICA graphics documents (the files can be dragged across application windows).

For more information on these operations, see Drag-and-Drop Overview.


RTF Files

Standard, formatted text and graphics files used in STATISTICA to store reports (i.e., output from the Text/output Window).  When files are saved in Rich Text Format (*.rtf), all of the file formatting is preserved so that it can be read and interpreted by other RTF-compatible applications (e.g., MS Word).

The Rich Text Format (RTF) is a Microsoft standard method of encoding formatted text and graphics for easy transfer between applications.


Quantiles

The quantile (this term was first used by Kendall, 1940) of a distribution of values is a number xp such that a proportion p of the population values are less than or equal to xp.  For example, the .25 quantile (also referred to as the 25th percentile or lower quartile) of a variable is a value (xp) such that 25% (p) of the values of the variable fall below that value.

Similarly, the .75 quantile (also referred to as the 75th percentile or upper quartile) is a value such that 75% of the values of the variable fall below that value and is calculated accordingly.  You can specify the method of computing percentiles in the STATISTICA Defaults: General dialog.  User-specified percentiles can be calculated in Nonparametrics.

See also, Quantile-Quantile Plots and Stats 2D Scatterplot - Quantile


Categorized Scatterplot Matrix

If a grouping variable is specified, then the Matrix (graph) option in the Quick Basic Stats - Extended Options dialog will produce a cascade of scatterplot matrices for the selected variables, one scatterplot matrix for each selected level of the grouping variable.  Note that the Multiple-Graph AutoLayout Wizard can be used to arrange the cascade of graphs on one page.


Labels in STATISTICA BASIC

A label specifies the place in the program where you can jump to using a GOTO statement.  A label can be any combination of characters that starts with a letter and ends with a colon; however, each label must be unique.  Labels can be placed anywhere in the program, and they are not case-sensitive.


Lambda Prime

Lambda is defined as the geometric sum of 1 minus the squared canonical correlation, where lambda is Wilk's lambda.  The squared canonical correlation is an estimate of the common variance between two canonical variates, thus 1 minus this value is an estimate of the unexplained variance.  Lambda is used as a test of significance for the squared canonical correlation and is distributed as Chi-square (see below).

  2

χ  = [-N - 1 - {.5(p+q+1)}] *  log λ

                                  e

where

N	is the number of subjects

p	is the number of variables on the right

q	is the number of variables on the left


Quick Basic Stats

Quick Basic Stats procedures are available (1) by pressing the [image] toolbar button, (2) from the spreadsheet or Scrollsheet right-mouse-button flying menu, or (3) from the Analysis pull-down menu of any module of STATISTICA.  These options allow you to compute descriptive statistics, correlations, or frequency tables for the desired variables (up to 4,092 variables can be selected); all analyses can be performed by group if an (optional) grouping variable is specified.  Variables for the analysis are selected either via the standard variable selection dialog (if Quick Basic Stats is selected from the Analysis pull-down menu or the More... option is used) or are automatically selected from the currently highlighted block in the Scrollsheet or spreadsheet (if Quick Basic Stats is selected from the right-mouse-button flying menu or the toolbar).

For more details, see Quick Basic Stats.


Quick Stats Graphs

"Quick Stats Graphs" are one of two general categories of graphs accessible from all Scrollsheets and spreadsheets in STATISTICA; see the Graphics Overview.  Unlike "Custom Graphs" (which provide a general tool to visualize numerical output and allow you to custom-define graphs by specifying any subsets or combinations of rows, columns, or both to be represented in a graph), "Quick Stats Graphs" are predefined statistical graphs.  They represent either standard methods to graphically summarize raw data (e.g., various scatterplots, histograms, or plots of central tendencies such as medians) or standard graphical analytic techniques (e.g., categorized normal probability plots, detrended probability plots, or plots of confidence intervals of regression lines).  For information about differences between Quick Stats Graphs and Stats Graphs see Graphics Overview.

For more information, see Quick Stats Graphs.


Codes (Values of Grouping Variables)

Codes are values of a grouping variable (e.g., 1, 2, 3, ... or MALE, FEMALE) which identify the levels of the grouping variable in an analysis.  Codes can either be text values (STATISTICA automatically assigns to them integer equivalents or you can assign/edit those integer values, see Text Values Manager) or integer values.  In some cases (this does not apply to Stats Graphs, Quick Stats Graphs, Quick Basic Stats, Quality Control, Process Analysis, Experimental Design, and other procedures) the actual integer value for the code must be less than 32,000.  Since Julian values of dates may exceed 32,000 (e.g., the Julian value for the date 4/6/94 is 34,430), if you want to use dates as codes, first transform the dates to text values via the Text Values/Dates dialog (e.g., the date 4/6/94 would be transformed into the text value APR06_94 with the numeric equivalent 14430 which could then be used as a code).

See Selecting Codes for upper/lower case and special character conventions.


Grouping Variable

In STATISTICA, a grouping variable is used to identify group membership for individual cases in the data file.  Typically, the grouping variable is categorical (i.e., contains either discrete values, e.g., 1, 2, 3, ..., or a few text values, e.g., MALE, FEMALE) and the values are referred to as codes (they can be integer values or integer values with text value equivalents).  However, the grouping variable does not have to be a categorical variable (e.g., contain codes) in some instances (e.g., in Categorized Stats Graphs where you can use one of the Methods of Categorization options to categorize a continuous variable).  You can also recode a continuous variable into some discrete values (via the Recode facility, Spreadsheet Formulas, or STATISTICA BASIC) and then, if desired, assign text values to those recoded values in order to categorize the continuous variable and use it as a grouping variable.


Task in SCL (STATISTICA Command Language)

A STATISTICA Command Language program consists of one or more tasks.  A task is some particular statistical technique or operation.  For example, DESCRIPTIVES is a task, that is, it will compute descriptive statistics.

Each task often requires additional necessary or optional specifications, such as the specification of a variable list.

For example, this is a complete SCL task:

DESCRIPTIVES VARS = ALL

For more information on the tasks available in SCL, see the description of SCL Syntax.  See also, Global SCL Options.


Normal Probability Plots (Computation Note)
Normal Probability Plots (Computational Note)

The following formulas are used to convert the ranks into expected normal probability values, that is, the respective normal z values.

Normal probability plot.  The normal probability value zj for the jth value (rank) in a variable with N observations is computed as:

      -1

z  = Φ  [(3*j-1)/(3*N+1)]

 j

where Φ**-1 is the inverse normal cumulative distribution function (converting the normal probability p into the normal value z).

Half-normal probability plot.  Here, the half-normal probability value zj for the jth value (rank) in a variable with N observations is computed as:

      -1

z  = Φ  [(3*N+3*j-1)/(6*N+1)]

 j

where Φ**-1 is again the inverse normal cumulative distribution function.

Detrended normal probability plot.  In this plot each value (xj) is standardized by subtracting the mean and dividing by the respective standard deviation (s).  The detrended normal probability value zj for the jth value (rank) in a variable with N observations is computed as:

      -1

z  = Φ  [(3*j-1)/(3*N+1)] - (x  -mean)/s

 j                             j

where Φ**-1 is again the inverse normal cumulative distribution function.

See also:  Multiple Normal Probability Plots


  X-11 Output: A 1.  Original Series

This X-11 table will show the original series, prior to any initial user-defined or trading-day adjustment.  Note that for quarterly series, no prior adjustment factors can be specified, and the original series will be shown as table B 1.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: A 2.  Prior Monthly Adjustment Factors

For X-11 monthly series, the user may specify a second series that contains prior monthly adjustment factors, for example, in order to adjust for an unusual holiday etc.  The factors specified here will be subtracted from the original series for additive models, or will be used to divide the original series if multiplicative seasonal adjustment was requested (thus, the values in this series must be unequal to zero in that case).

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: A 3.  Original Series Adjusted by Prior Monthly Adjustment Factors

In this X-11 monthly series, the factors specified in A 2 will be subtracted from the original series (additive adjustment) or they will be used to divide the values in the original series (multiplicative adjustment).  The resulting adjusted series is shown in this table.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: A 4.  Prior Trading Day Adjustment Factors

This X-11 table is only available (applicable) when prior trading-day adjustment factors and a multiplicative model were specified.  The user may specify a weight for each day (Monday through Friday); those weights are then proportionately adjusted so that they add to 7.  The series (A 1 or A 3) is then divided by monthly calendar factors that are computed based on the number of the respective days in the respective month.  Note that by default, the calendar factors are also adjusted for different lengths of different months; however, the length of month variability can also be included in the calendar factors (in which case a constant length of month of 30.4375 is used).

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: B 1.  Prior Adjusted Series or Original Series

This X-11 table shows the original series, or the initial adjusted series, depending on whether or not prior monthly adjustment factors and/or trading day adjustment factors where specified (for quarterly X-11, B 1 is always the original series).

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: B 2.  Trend-cycle

The For more information, see X-11 Census Method II Seasonal Adjustment.

initial trend-cycle estimate is computed as a centered 12-term moving average of B 1.


  X-11 Output: B 3.  Unmodified S-I Differences or Ratios

An initial estimate of the combined irregular and seasonal component is obtained by subtracting B 2 from B 1 (additive model) or dividing B 1 by B 2 (multiplicative model).

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: B 4.  Replacement Values for Extreme S-I Differences (Ratios)

First a preliminary estimate of the X-11 seasonal component is computed by applying a weighted 5-term moving average separately to the B 3 values for each month.  Then a centered 12-term moving average of the preliminary factors for the entire series is computed, and the resulting values are adjusted to sum to zero (additive model) or 12.0 (multiplicative model) within each year.  Next an initial estimate of the irregular component is obtained by subtracting from the S-I differences (additive model) or dividing the S-I ratios by the initial estimate for the seasonal component.  For the resulting initial estimate of the irregular component, a 5-year sliding standard deviation (σ, sigma) is computed, and extreme values in the central year that are beyond 2.5*σ are removed.  The 5-year sliding σ is then recomputed and the process repeated; however, this time a zero weight is assigned to irregular values beyond 2.5*σ, a full weight is assigned for values within 1.5*σ, and linearly graduated weights between zero and one are assigned for values between 1.5 and 2.5 * σ.  Values receiving less than full weights are then recomputed as the average of the respective value times its weight and the nearest two full-weight values preceding and following the respective value in that month.  Table B 4 shows the final replaced (re-computed) values, and the sliding 5-year σ's.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: B 5.  Seasonal Factors

The extreme values in the B 3 series are replaced by the values shown in B 4.  From this X-11 series, preliminary seasonal factors are derived by applying a 5-term moving average to each month separately; then a 12-term moving average is computed for the entire series, and the resulting values adjusted to sum to zero (additive model) or 12.0 (multiplicative model) within each year.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: B 6.  Seasonally Adjusted Series

The preliminary seasonally adjusted series is obtained by subtracting from B 1 (additive model) or dividing B 1 (multiplicative model) by the seasonal factors in B 5.

For more information, see X-11 Census Method II Seasonal Adjustment.


X-11 Output: B 7.  Trend cycle
  X-11 Output: B 7.  Trend-cycle

The X 11 seasonally adjusted series (B 6) is smoothed via a variable moving average procedure (see Shiskin, Young, & Musgrave, 1967, for details).  Optionally, extremes can be removed from the smoothed series by a process analogous to that described under B 4.  In general, the so-called Henderson curve moving average is applied, which is a weighted moving average with the magnitudes of the weights following a bell-shaped curve (see, for example, Makridakis and Wheelwright, 1978, or Shiskin, Young, and Musgrave, 1967).  The choice of the appropriate length of the moving average is an important issue in the seasonal decomposition (i.e., the computation of the trend-cycle component).  The general idea is to choose a longer moving average when there is a lot of random fluctuation in the data relative to the trend-cycle component, and to choose a shorter moving average when there is only relative little random fluctuation.  By default the program will select a moving average transformation automatically.  Specifically, first a preliminary 13-term Henderson (weighted) moving average of the seasonally adjusted series is computed (without extending to the ends of the series).  A preliminary estimate of the irregular component is then computed by subtracting this series from (additive model) or dividing it into (multiplicative model) the seasonally adjusted series.  Next, the average month-to-month difference (percent change) without regard to sign is computed for both the estimated irregular and trend-cycle components.  The ratio of the average month-to-month differences (percent changes) in the two series reflects the relative importance of the irregular variations relative to the movements in the trend-cycle component.  Depending on the value of this ratio, either a 9-term Henderson moving average is selected (if the ratio is between 0.0 and .99), a 13-term Henderson moving average is selected (if the ratio is between 1.0 and 3.49) or a 23-term Henderson moving average is selected (if the ratio is greater than 3.5).

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: B 8.  Unmodified S-I Differences (Ratios)

This X-11 table is the same as B 3 except that it is based on the trend-cycle values computed in B 7.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: B 9.  Replacement Values for Extreme S-I Differences (Ratios)

This X-11 table is the same as B 4 except that the differences (ratios) in B 8 are used to which a 7 term moving average is applied (to estimate the seasonal factors).

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: B 10.  Seasonal Factors

After replacing extreme values by the corresponding B 9 values, a 7-term weighted moving average is applied to the S-I differences (ratios) in B 8.  The resulting estimate of the seasonal factors is then adjusted so that the sum for each year is equal to zero (additive model) or 12.0 (multiplicative model).

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: B 11.  Seasonally Adjusted Series

This X-11 table is the same as B 6, except that the seasonal factors in B 10 are used.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: B 13.  Irregular Series

The trend-cycle estimates in B 7 are subtracted from the seasonally adjusted series in B 11 (additive model), or the B 7 values are used to divide the series in B 11 (multiplicative model).  The resulting series is an improved estimate of the irregular series.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: B 14.  Extreme Irregular Values Excluded from Trading-day Regression

The months in the series are sorted into different groups, depending on the particular day when the month begins (30-day, 31-day months, and Februarys are treated separately).  Then extreme values (beyond 2.5 * σ; different σ values can also be specified) are identified within each type of month in a two-step procedure.  The final extreme values that will be excluded are shown in this X-11 table.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: B 15.  Preliminary Trading-day Regression

After removing the B 14 extreme values from B 13, least squares estimates for the seven daily weights are computed.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: B 16.  Trading-day Adjustment Factors Derived from Regression Coefficients

From the trading-day regression weights, monthly adjustment factors are computed based on the number of particular trading days (i.e., Mondays, Tuesdays, etc.) in the respective months.  These factors are printed in this X-11 table, and are then used to adjust (i.e., subtracted from or divided into) the B 13 irregular series for trading-day variation.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: B 17.  Preliminary Weights for Irregular Component

The estimates of the irregular component (in B 13 or adjusted by B 16, depending on whether or not a trading-day adjustment was performed) are further refined by computing graduated weights for extreme values, depending on their relative (in terms of a sliding 5-year σ) distance from 0.  Specifically, a process analogous to that described in B 4 above is used.  This X-11 table (B17) contains the resulting adjustment factors.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: B 18.  Trading-day Factors Derived from Combined Daily Weights

This X-11 table contains the final trading day adjustment factors, computed from the least squares trading-day weights in B 15 and/or the prior trading-day weights in A 4.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: B 19.  Original Series Adjusted for Trading-day and Prior Variation

The values in B 18 are used to adjust the original (adjusted) series (in A 1, A 3, or B 1, depending on whether or not prior adjustment factors were specified).  Specifically, the values in B 18 are subtracted from (additive model) or divided into (multiplicative model) the original series.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: C 1.  Original Series Modified by Preliminary Weights and Adjusted for Trading-day and Prior Variation

The series in B 19 (or B 1 if no trading-day adjustment was requested) is adjusted for extreme values by the weights computed in B 17  The resulting modified series in shown in this X-11 table (C 1).

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: C 2.  Trend-cycle

An estimate of the combined trend-cycle component is computed from C 1 by applying a centered 12-term moving average.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: C 4.  Modified S-I Differences (Ratios)

To obtain the refined S-I differences (ratios), the values in C 2 are subtracted from (additive model) or divided into (multiplicative model) the modified series in C 1.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: C 5.  Seasonal Factors

These values are the same as those in B 5, except that the C 4 differences (ratios) are used.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: C 6.  Seasonally Adjusted Series

The preliminary seasonally adjusted series is computed by subtracting C 5 from (or dividing C 5 into) C 1.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: C 7.  Trend-cycle

The seasonally adjusted series (C 6) is smoothed via a variable moving average procedure (the same procedure used for B 7, see also Shiskin, Young, & Musgrave, 1967, for details) to derive the preliminary estimate of the trend-cycle component.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: C 9.  Modified S-I Differences (Ratios)

The modified S-I differences (ratios) are computed by subtracting C 7 from (additive models) or dividing C 7 into (multiplicative models) the C 1 series.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: C 10.  Seasonal Factors

The seasonal factors are computed analogously to B 10, but based on the C 9 S-I differences (ratios).

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: C 11.  Seasonally Adjusted Series

The refined seasonally adjusted series is computed by subtracting from B 1 (additive model) or dividing B 1 by (multiplicative model) the values in C 10.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: C 13.  Irregular Series

The refined estimate of the irregular (random) component is computed by subtracting from C 11 (additive model) or dividing C 11 by (multiplicative model) the values in C 7.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: C 14.  Extreme Irregular Values Excluded from Trading-day Regression

This table is analogous to table B 14, and it shows the extreme irregular values (usually beyond 2.5 * σ) after re-applying the trading-day routine (based on the monthly trading-day factors shown in B 16).

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: C 15.  Final Trading-day Regression

This X-11 table is the same as B 15, except that the computations are based on the values from table C 13.

For more information, see X-11 Census Method II Seasonal Adjustment.


C 16. Final Trading-day Adjustment Factors Derived from Regression Coefficients
  X-11 Output: C 16.  Final Trading-day Adjustment Factors Derived from Regression Coefficients

This X-11 table is analogous to B 16, except that the factors are subtracted from (additive case) or divided into (multiplicative case) the values from table C 13.

For more information, see X-11 Census Method II Seasonal Adjustment.


C 17. Final Weights for Irregular Component
  X-11 Output: C 17.  Final Weights for Irregular Component

This table is analogous to table B 17, except that it is computed based on the values in C 16 (or C 13 if no trading day adjustment is requested).

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: C 18.  Final Trading-day Factors Derived From Combined Daily Weights

This X-11 table is analogous to B 18, except that the final weights shown in C 15 are used in the computations.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: C 19.  Original Series Adjusted for Trading-day and Prior Variation

The values in C 18 are used to adjust the original (adjusted) series (in A 3 or B 1).  Specifically, the values in C 18 are subtracted from (additive model) or divided into (multiplicative model) the original series.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: D 1.  Original Series Modified by Final Weights and Adjusted for Trading-day and Prior Variation

This X-11 table is analogous to C 1, except that the C 17 weights and C 19 adjusted series are used in the computations.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: D 2.  Trend-cycle

A 12-term moving average of D 1 is computed to estimate the trend-cycle component.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: D 4.  Modified S-I Differences (Ratios)

The modified S-I differences (ratios) are computed by subtracting D 2 from (additive model) or dividing D 2 into (multiplicative model) the values in D 1.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: D 5.  Seasonal Factors

This X-11 table is computed analogously to B 5, except that the computations are based on the values in D 4.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: D 6.  Seasonally Adjusted Series

The values in this table are computed by subtracting D 5 from D 1 (additive model) or dividing D 1 by D5 (multiplicative model).

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: D 7. Trend-cycle

The values in this X-11 table are computed analogously to those in B 7, except that the computations are based on the values in D 6.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: D 8.  Final Unmodified S-I Differences (Ratios)

The values in the D 7 series are subtracted from (additive model) or divided into (multiplicative case) the values in C 19 (or B 1 if no adjustment for trading-day variation is applied).  Then an analysis of variance by month (or quarter) is performed on this series, in order to test for the presence of stable significant seasonality.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: D 9.  Final Replacement Values for Extreme S-I Differences (Ratios)

The values in D 7 are subtracted from (additive model) or divided into (multiplicative model) D 1; values that are not identical to the corresponding entries in D 8 are then reported.  Also, for each month, the year-to-year difference (additive model) or percent change (multiplicative mode) in the estimates of the irregular and the seasonal components and their ratio (called MSR, moving seasonality ratio) are computed.  The MSR may be useful in order to determine the amount of moving seasonality present in each month.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: D 10.  Final Seasonal Factors

This X-11 table is computed analogously to the values in B 10, except that it is computed based on the values reported in D 8 and D 9.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: D 11.  Final Seasonally Adjusted Series

The final seasonally adjusted series is computed by subtracting D 10 from C 19 (additive model) or dividing C 19 by D 10 (multiplicative model).

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: D 12.  Final Trend-cycle

These values are computed by subtracting D 10 from D 1 (additive model), or by dividing D 1 by D 10 (multiplicative model).

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: D 13.  Final Irregular

These values are computed by subtracting D 12 from D 11 (additive model), or by dividing D 11 by D 12 (multiplicative model).

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: E 1.  Modified Original Series

The values in this X-11 table are computed by replacing in the original series extreme values (identified by a zero weight in C 17) by the values predicted from the final trend-cycle, seasonal, trading-day (if applicable), and prior adjustment (if applicable) components.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: E 2.  Modified Seasonally Adjusted Series

These values are computed by replacing in the final seasonally adjusted series (D 11) extreme values (identified by a zero weight in C 17) with the D 12 final trend-cycle values.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: E 3.  Modified Irregular Series

The values in this X-11 table are computed by replacing the values in D 13 with zero (additive model) or 1.0 (multiplicative model) if they were identified as extremes (i.e., assigned zero weight) in C 17.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: E 4.  Differences (Ratios) of Annual Totals

These values are computed as the differences (additive model) or ratios (multiplicative model) of the annual totals of (a) the original series B 1 and the final seasonally adjusted series D 11, (b) the modified original series E 1 and the modified seasonally adjusted series E 2.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: E 5.  Differences (Percent Changes) in Original Series

The values in this X-11 table are computed as the month-to-month (quarter-to-quarter) differences (additive model) or percent changes (multiplicative model) in B 1.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: E 6.  Differences (Percent Changes) in Final Seasonally Adjusted Series

These values are the month-to-month (quarter-to-quarter) differences (additive model) or percent changes (multiplicative model) in D 11.

For more information, see X-11 Census Method II Seasonal Adjustment.


  X-11 Output: F 1.  MCD (QCD) Moving Average

The values in this series are computed by applying an unweighted moving average to the final seasonally adjusted series (D 11).  The width of the smoothing window is determined by the month (quarter) for cyclical dominance, or MCD (QCD) for short.  The MCD (QCD) is computed as the average span at which the changes in the random component are equal to the changes in the trend-cycle component

For more information, see X-11 Census Method II Seasonal Adjustment.


  F 2. Summary Measures

Several final summary X-11 tables are computed:

(1)  The average differences (additive model) or percent changes (multiplicative model) are computed without regard to sign across spans 1, 2, 3 ..., 12 months (or four quarters) for the following series: Original series A 1 (B 1), final seasonally adjusted series (D 11), final irregular series (D 13), final trend-cycle (D 12), final seasonal factors (D 10), final prior monthly adjustment factors (A 2, monthly X-11 only), final trading-day adjustment factors (C 18, monthly X-11 only), modified original series (E 1), modified seasonally adjusted series (E 2), modified irregular series (E 3).

(2)  Next a table of relative contributions of the different components to the differences (additive model) or percent changes (multiplicative model) in the original series are computed.

(3)  The next table reports the average duration of run (the average number of consecutive monthly changes in the same direction; "no change" is counted as a change in the same direction) for the following series: Final seasonally adjusted series (D 11), final irregular series (D 13), final trend-cycle (D 12), and the MCD (QCD) moving average (F 1).

(4)  Finally, the means and standard deviations of differences (additive model) or percent changes (multiplicative model) are computed across different spans for each of the series mentioned above.

For more information, see X-11 Census Method II Seasonal Adjustment.


  G 1. Chart

This line graph will show the final seasonally adjusted series and final trend-cycle components (D 11 and D 12, respectively).

For more information, see X-11 Census Method II Seasonal Adjustment.


  G 2. Chart

This line graph will show the final S-I differences (additive model) or ratios (multiplicative model) with the extremes, the final S-I differences (ratios) without extremes, and the final seasonal factors (i.e., D 8, D 9, and D 10, respectively), categorized by month (X-11 monthly) or quarter (X-11 quarterly).

For more information, see X-11 Census Method II Seasonal Adjustment.


  G 3. Chart

This plot shows the same values as G 2; however, this line plot shows those values in chronological order.

For more information, see X-11 Census Method II Seasonal Adjustment.


  G 4. Chart

This is a line graph of the final irregular and final modified irregular series (D 13 and E 3, respectively).

For more information, see X-11 Census Method II Seasonal Adjustment.


Multiple R

The coefficient of multiple correlation (Multiple R) is the positive square root of R-square (the coefficient of multiple determination, see Residual Variance and R-Square).  This statistic is useful in multivariate regression (i.e., multiple independent variables) when you want to describe the relationship between the variables.


  Stationary Series (in Time Series)

In Time Series analysis, a stationary series has a constant mean, variance, and autocorrelation through time (i.e., seasonal dependencies have been removed via Differencing).

For more information, see Identifying Patterns in Time Series Data.


  Differencing (in Time Series)

In this Time Series transformation, the series will be transformed as: X=X-X(lag).  After differencing, the resulting series will be of length N-lag (where N is the length of the original series).


Complex Numbers

Complex numbers are the superset that includes all real and imaginary numbers.  A complex number is usually represented by the expression a + ib where a and b are real numbers and i is the imaginary part of the expression where i has the property that i**2=-1.

See also, Cross-spectrum Analysis in Time Series.


  Tapering

The so-called process of split-cosine-bell tapering in Time Series is a recommended transformation of the series prior to the spectrum analysis.  It usually leads to a reduction of leakage in the periodogram.  The rational for this transformation is explained in detail in Bloomfield (1976, p. 80-94).  In essence, a proportion (p) of the data at the beginning and at the end of the series is transformed via multiplication by the weights:

w  = ½*(1-cosine(π*(t-½)/m)) (for t=0 to m-1)

 t

w  = ½*(1-cosine(π*(N-t+½)/m)) (for t=N-m to N-1)

 t

where m is chosen so that 2*m/N is equal to the proportion of data to be tapered (p).


  Daniell (or Equal Weight) Window

In Time Series, the Daniell window (Daniell 1946) is a weighted moving average transformation used to smooth the periodogram values.  This transformation amounts to a simple (equal weight) moving average transformation of the periodogram values, that is, each spectral density estimate is computed as the mean of the m/2 preceding and subsequent periodogram values.  Note also that the Time Series module will standardize the weights so that they sum to 1.

See also, Basic Notations and Principles.


  Tukey Window

In Time Series, the Tukey window is a weighted moving average transformation used to smooth the periodogram values.  In the Tukey (Blackman and Tukey, 1958) or Tukey-Hanning window (named after Julius Von Hann), for each frequency, the weights for the weighted moving average of the periodogram values are computed as:

w  = 0.5+0.5*cosine(π*j/p) (for j=0 to p)

 j

w   = w  (for j≠0)

 -j    j

where p = (m-1)/2x

This weight function will assign the greatest weight to the observation being smoothed in the center of the window, and increasingly smaller weights to values that are further away from the center.  Note also that the Time Series module will standardize the weights so that they sum to 1.

See also, Basic Notations and Principles.


  Hamming Window

In Time Series, the Hamming window is a weighted moving average transformation used to smooth the periodogram values.  In the Hamming (named after R. W. Hamming) window or Tukey-Hamming window (Blackman and Tukey, 1958), for each frequency, the weights for the weighted moving average of the periodogram values are computed as:

w  = 0.54+0.46*cosine(π*j/p) (for j=0 to p)

 j

w   = w  (for j≠0)

 -j    j

where p = (m-1)/2

This weight function will assign the greatest weight to the observation being smoothed in the center of the window, and increasingly smaller weights to values that are further away from the center.  Note also that the Time Series module will standardize the weights so that they sum to 1.

See also, Basic Notations and Principles.


  Parzen Window

In Time Series, the Parzen window is a weighted moving average transformation used to smooth the periodogram values.  In the Parzen window (Parzen, 1961), for each frequency, the weights for the weighted moving average of the periodogram values are computed as:

              2        3

w  = 1-6*(j/p) +6*(j/p)  (for j=0 to p/2)

 j

              3

w  = 2*(1-j/p)  (for j=p/2+1 to p

 j

w   = w  (for j≠0)

 -j    j

where p = (m-1)/2

This weight function will assign the greatest weight to the observation being smoothed in the center of the window, and increasingly smaller weights to values that are further away from the center.  Note also that the Time Series module will standardize the weights so that they sum to 1.

See also, Basic Notations and Principles.


  Bartlett Window

In Time Series, the Bartlett window is a weighted moving average transformation used to smooth the periodogram values.  In the Bartlett window (Bartlett, 1950) the weights are computed as:

w  = 1-(j/p) (for j=0 to p)

 j

w   = w  (for j≠0)

 -j    j

where p = (m-1)/2

This weight function will assign the greatest weight to the observation being smoothed in the center of the window, and increasingly smaller weights to values that are further away from the center.  Note also that the Time Series module will standardize the weights so that they sum to 1.

See also, Basic Notations and Principles.


Order of SCL Statements

The order of keywords and options (i.e., all statements) in STATISTICA Command Language programs is important.  If the statements are entered out of logical order (see the appropriate STATISTICA Command Language topic for the logical order of statements), then STATISTICA will give a syntax error and the program will not be processed.


  Nonseasonal, No Trend

This Time Series model is equivalent to the simple exponential smoothing model.  Note that, by default, the first smoothed value will be computed based on an initial S0 value equal to the overall mean of the series.


  Additive Season, No Trend

This Time Series model is partially equivalent to the simple exponential smoothing model; however, in addition, each forecast is "enhanced" by an additive seasonal component that is smoothed independently (see The seasonal smoothing parameter δ).  This model would, for example, be adequate when computing forecasts for monthly expected amount of rain.  The amount of rain will be stable from year to year, or change only slowly.  At the same time, there will be seasonal changes ("rainy seasons"), which again may change slowly from year to year.

To compute the smoothed values for the first season, initial values for the seasonal components are necessary.  By default, the Time Series module will estimate those values (for all models including a seasonal component) from the data via Classical seasonal decomposition.  The initial smoothed value S0 will by default be computed as the mean for all values included in complete seasonal cycles.


  Multiplicative Season, No Trend

This Time Series model is partially equivalent to the simple exponential smoothing model; however, in addition, each forecast is "enhanced" by a multiplicative component that is smoothed independently (see The seasonal smoothing parameter δ).  This model would, for example, be adequate when computing forecasts for monthly expected sales for a particular toy.  The level of sales may be stable from year to year, or change only slowly; at the same time, there will be seasonal changes (e.g., greater sales during the December holidays), which again may change slowly from year to year.  The seasonal changes may affect the sales in a multiplicative fashion, for example, depending on the respective overall level of sales, December sales may always be greater by a factor of 1.4.

To compute the smoothed values for the first season, initial values for the seasonal components are necessary.  By default, the Time Series module will estimate those values (for all models including a seasonal component) from the data via Classical seasonal decomposition.  The initial smoothed value S0 will by default be computed as the mean for all values included in complete seasonal cycles.


Nonseasonal, Linear Trend (Holt's Two-Parameter Method)
  Nonseasonal, Linear Trend

(Holt's Two-Parameter Method)

In this Time Series model, the simple exponential smoothing forecasts are "enhanced" by a linear trend component that is smoothed independently via the γ (gamma) parameter (see discussion of trend smoothing parameters).  This model is also referred to as Holt's two parameter method.  This model would, for example, be adequate when producing forecasts for spare parts inventories.  The need for particular spare parts may slowly increase or decrease over time (the trend component), and the trend may slowly change as different machines etc. age or become obsolete, thus affecting the trend in the demand for spare parts for the respective machines.

In order to compute the smoothed value (forecast) for the first observation in the series, both estimates of S0 and T0 (initial trend) are necessary.  By default, these values are computed as:

T  = (X -X )/(N-1)

 0     n  1

where

N	is the length of the series,

and

S  = X -T /2

 0    1  0


  Additive Season, Linear Trend

In this Time Series model, the simple exponential smoothing forecasts are "enhanced" both by a linear trend component (independently smoothed with parameter γ) and an additive seasonal component (smoothed with parameter δ).  For example, suppose we were to predict the monthly budget for snow-removal in a community.  There may be a trend component (as the community grows, there is a steady upward trend for the cost of snow removal from year to year).  At the same time, there is obviously a seasonal component, reflecting the differential likelihood of snow during different months of the year.  This seasonal component could be additive, meaning that a particular fixed additional amount of money is necessary during the winter months, or (see below) multiplicative, that is, given the respective budget figure, it may increase by a factor of, for example, 1.4 during particular winter months.

To compute the smoothed values for the first season, initial values for the seasonal components are necessary.  By default, the Time Series module will estimate those values (for all models including a seasonal component) from the data via Classical seasonal decomposition.  Also, to compute the smoothed value (forecast) for the first observation in the series, both estimates of S0 and T0 (initial trend) are necessary.  By default, these values are computed as:

T  = (M -M )/((k-1)*p)

 0     k  1

where

k	is the number of complete seasonal cycles

Mk	is the mean for the last seasonal cycle

M1	is the mean for the first seasonal cycle

p	is the length of the seasonal cycle

and

S  = M -T /2

 0    1  0


  Multiplicative Season, Linear Trend

(Triple Exponential Smoothing or Winter's Three-Parameter Trend and Seasonality Method)

In this Time Series model, the simple exponential smoothing forecasts are "enhanced" both by a linear trend component (independently smoothed with parameter γ) and a multiplicative seasonal component (smoothed with parameter δ).  For example, suppose we were to predict the monthly budget for snow-removal in a community.  There may be a trend component (as the community grows, there is an upward trend for the cost of snow removal from year to year).  At the same time, there is obviously a seasonal component, reflecting the differential likelihood of snow during different months of the year.  This seasonal component could be multiplicative, meaning that given a respective budget figure, it may increase by a factor of, for example, 1.4 during particular winter months; or it may be additive (see above), that is, a particular fixed additional amount of money is necessary during the winter months.  To compute the smoothed values for the first season, initial values for the seasonal components are necessary.  By default, the Time Series module will estimate those values (for all models including a seasonal component) from the data via Classical seasonal decomposition.  Also, to compute the smoothed value (forecast) for the first observation in the series, both estimates of S0 and T0 (initial trend) are necessary.  By default, these values are computed as:

T  = (M -M )/((k-1)*p)

 0     k  1

where

k	is the number of complete seasonal cycles

Mk	is the mean for the last seasonal cycle

M1	is the mean for the first seasonal cycle

p	is the length of the seasonal cycle

and  S  = M -T /2

      0    1  0


  Nonseasonal, Exponential Trend

In this Time Series model, the simple exponential smoothing forecasts are "enhanced" by an exponential trend component (smoothed with parameter γ).  For example, suppose we wanted to predict the overall monthly costs of repairs to a production facility.  There could be an exponential trend in the cost, that is, from year to year the costs of repairs may increase by a certain percentage or factor, resulting in a gradual exponential increase in the absolute dollar costs of repairs.

To compute the smoothed value (forecast) for the first observation in the series, both estimates of S0 and T0 (initial trend) are necessary.  By default, these values are computed as:

T  = (X /X )

 0     2  1

and

S  = X /√T

 0    1   0


  Additive Season, Exponential Trend

In this Time Series model, the simple exponential smoothing forecasts are "enhanced" both by an exponential trend component (independently smoothed with parameter γ) and an additive seasonal component (smoothed with parameter δ).  For example, suppose we wanted to forecast the monthly revenue for a resort area.  Every year, revenue may increase by a certain percentage or factor, resulting in an exponential trend in overall revenue.  In addition, there could be an additive seasonal component, for example a particular fixed (and slowly changing) amount of added revenue during the December holidays.

To compute the smoothed values for the first season, initial values for the seasonal components are necessary.  By default, the Time Series module will estimate those values (for all models including a seasonal component) from the data via Classical seasonal decomposition.  Also, to compute the smoothed value (forecast) for the first observation in the series, both estimates of S0 and T0 (initial trend) are necessary.  By default, these values are computed as:

T  = exp((log(M )-log(M ))/p)

 0             k       1

where

k	is the number of complete seasonal cycles

Mk	is the mean for the last seasonal cycle

M1	is the mean for the first seasonal cycle

p	is the length of the seasonal cycle

and

S  = exp((log(M )-p*log(T )/2)

 0             1         0


  Multiplicative Season, Exponential Trend

In this Time Series model, the simple exponential smoothing forecasts are "enhanced" both by an exponential trend component (independently smoothed with parameter γ) and a multiplicative seasonal component (smoothed with parameter δ).  For example, suppose we wanted to forecast the monthly revenue for a resort area.  Every year, revenue may increase by a certain percentage or factor, resulting in an exponential trend in overall revenue.  In addition, there could be an multiplicative seasonal component, that is, given the respective annual revenue, each year 20% of the revenue is produced during the month of December, that is, during Decembers the revenue grows by a particular (multiplicative) factor.

To compute the smoothed values for the first season, initial values for the seasonal components are necessary.  By default, the Time Series module will estimate those values (for all models including a seasonal component) from the data via Classical seasonal decomposition.  Also, to compute the smoothed value (forecast) for the first observation in the series, both estimates of S0 and T0 (initial trend) are necessary.  By default, these values are computed as:

T  = exp[(log(M )-log(M )]/p)

 0             k       1

where

k	is the number of complete seasonal cycles

Mk	is the mean for the last seasonal cycle

M1	is the mean for the first seasonal cycle

p	is the length of the seasonal cycle

and

S  = exp[(log(M )-p*log(T )/2]

 0             1         0


  Nonseasonal, Damped Trend

In this Time Series model, the simple exponential smoothing forecasts are "enhanced" by a damped trend component (independently smoothed with parameters γ for the trend, and φ for the damping effect).  For example, suppose we wanted to forecast from month to month the percentage of households that own a particular consumer electronics device (e.g., a VCR).  Every year, the proportion of households owning a VCR will increase, however, this trend will be damped (i.e., the upward trend will slowly disappear) over time as the market becomes saturated.

To compute the smoothed value (forecast) for the first observation in the series, both estimates of S0 and T0 (initial trend) are necessary.  By default, these values are computed as:

T  = (1/φ)*(X  -X  )/(N-1)

 0            n   1

where

N  is the number of cases in the series,

φ   is the smoothing parameter for the damped trend

and

S  = X -T /2

 0    1  0


  Additive Season, Damped Trend

In this Time Series model, the simple exponential smoothing forecasts are "enhanced" both by a damped trend component (independently smoothed with the single parameter φ, this model is an extension of Brown's one-parameter linear model, see Gardner, 1985, p. 12-13) and an additive seasonal component (smoothed with parameter δ).  For example, suppose we wanted to forecast from month to month the number of households that purchase a particular consumer electronics device (e.g., VCR).  Every year, the number of households that purchase a VCR will increase, however, this trend will be damped (i.e., the upward trend will slowly disappear) over time as the market becomes saturated.  In addition, there will be a seasonal component, reflecting the seasonal changes in consumer demand for VCR's from month to month (demand will likely be smaller in the summer and greater during the December holidays).  This seasonal component may be additive, for example, a relatively stable number of additional households may purchase VCR's during the December holiday season.  To compute the smoothed values for the first season, initial values for the seasonal components are necessary.  By default, the Time Series module will estimate those values (for all models including a seasonal component) from the data via Classical seasonal decomposition.  Also, to compute the smoothed value (forecast) for the first observation in the series, both estimates of S0 and T0 (initial trend) are necessary.  By default, these values are computed as:

T  = (1/φ)*(M -M )/[(k-1)*p]

 0           k  1

where

φ	is the smoothing parameter

k	is the number of complete seasonal cycles

Mk	is the mean for the last seasonal cycle

M1	is the mean for the first seasonal cycle

p	is the length of the seasonal cycle

and  S  = M -p*T /2

      0    1    0


  Multiplicative Season, Damped Trend

In this Time Series model, the simple exponential smoothing forecasts are "enhanced" both by a damped trend component (independently smoothed with the single parameter φ; this model is an extension of Brown's one-parameter linear model, see Gardner, 1985, p. 12-13) and a multiplicative seasonal component (smoothed with parameter δ).  For example, suppose we wanted to forecast from month to month the number of households that purchase a particular consumer electronics device (e.g., VCR).  Every year, the number of households that purchase a VCR will increase, however, this trend will be damped (i.e., the upward trend will slowly disappear) over time as the market becomes saturated.  In addition, there will be a seasonal component, reflecting the seasonal changes in consumer demand for VCR's from month to month (demand will likely be smaller in the summer and greater during the December holidays).  This seasonal component may be multiplicative, for example, sales during the December holidays may increase by factor of 1.4 (or 40%) over the average annual sales.  To compute the smoothed values for the first season, initial values for the seasonal components are necessary.  By default, the Time Series module will estimate those values (for all models including a seasonal component) from the data via Classical seasonal decomposition.  Also, to compute the smoothed value (forecast) for the first observation in the series, both estimates of S0 and T0 (initial trend) are necessary.  By default, these values are computed as:

T  = (1/φ)*(M -M )/[(k-1)*p]

 0           k  1

where

φ 	is the smoothing parameter

k	is the number of complete seasonal cycles

Mk	is the mean for the last seasonal cycle

M1	is the mean for the first seasonal cycle

p	is the length of the seasonal cycle

and  S  = M -p*T /2

      0    1    0


  Abrupt Permanent Impact

In Time Series, a permanent abrupt impact pattern simply implies that the overall mean of the times series shifted after the intervention; the overall shift is denoted by ω (omega).


  Gradual Permanent Impact

In Time Series, the gradual permanent impact pattern implies that the increase or decrease due to the intervention is gradual, and that the final permanent impact becomes evident only after some time.  This type of intervention can be summarized by the expression:

Impact  = δ*Impact   +ω

      t           t-1

(for all t  time of impact, else = 0).

Note that this impact pattern is defined by the two parameters δ (delta) and ω (omega).  If δ is near 0 (zero), then the final permanent amount of impact will be evident after only a few more observations; if δ is close to 1, then the final permanent amount of impact will only be evident after many more observations.  As long as the δ parameter is greater than 0 and less than 1 (the bounds of system stability), the impact will be gradual and result in an asymptotic change (shift) in the overall mean by the quantity:

Asymptotic change in level = ω/(1-δ)

The Time Series module will automatically compute the asymptotic change for gradual permanent impacts.  Note that, when evaluating a fitted model, it is important that both parameters are statistically significant; otherwise one could reach paradoxical conclusions.  For example, suppose the ω parameter is not statistically significant from 0 (zero) but the δ parameter is; this would mean that an intervention caused a significant gradual change, the final result of which was not significantly different from zero.


  Abrupt Temporary Impact

In Time Series, the abrupt temporary impact pattern implies an initial abrupt increase or decrease due to the intervention which then slowly decays, without permanently changing the mean of the series.  This type of intervention can be summarized by the expressions:

Prior to intervention:	Impactt = 0

At time of intervention:	Impactt = ω

After intervention:	Impactt = δ*Impactt-1

Note that this impact pattern is again defined by the two parameters δ (delta) and ω (omega).  As long as the δ parameter is greater than 0 and less than 1 (the bounds of system stability), the initial abrupt impact will gradually decay.  If δ is near 0 (zero) than the decay will be very quick, and the impact will have entirely disappeared after only a few observations.  If δ is close to 1 then the decay will be slow, and the intervention will affect the series over many observations.  Note that, when evaluating a fitted model, it is again important that both parameters are statistically significant; otherwise one could reach paradoxical conclusions.  For example, suppose the ω parameter is not statistically significant from 0 (zero) but the δ parameter is; this would mean that an intervention did not cause an initial abrupt change, which then showed significant decay.


3D Range Plots - Points

In this style of Stats 3D Sequential Range Plot, the ranges are not calculated from data but defined by the raw values in the selected variables and represented by point markers (connected by a line).  One range is plotted for each case.  The range variables can be interpreted either as absolute values or values representing deviations from the midpoint depending on the current setting of the Mode option in the graph definition dialog.  Single or multiple variables can be represented in the graph.  See also "One-sided" Ranges or Error Bars in Range Plots.  3D Range plots differ from 3D Box plots in that for Range plots, the ranges are the values of the selected variables (e.g., one variable contains the minimum range values and another variable contains the maximum range values) while for Box plots, the ranges are calculated from variable values (e.g., standard deviations, standard errors, or min-max values).


3D Range Plots - Border-style Ranges

In this style of Stats 3D Sequential Range Plot, the ranges are not calculated from data but are defined by the raw values in the selected variables and represented by two continuous lines (upper and lower ranges).  The midpoints are represented by point markers connected with a line.  The range variables can be interpreted either as absolute values or values representing deviations from the midpoint depending on the current setting of the Mode option in the graph definition dialog.  Single or multiple variables can be represented in the graph.  See also "One-sided" Ranges or Error Bars in Range Plots.  3D Range plots differ from 3D Box plots in that for Range plots, the ranges are the values of the selected variables (e.g., one variable contains the minimum range values and another variable contains the maximum range values) while for Box plots, the ranges are calculated from variable values (e.g., standard deviations, standard errors, or min-max values).


3D Range Plots - Error Bars

In this style of Stats 3D Sequential Range Plot, the error bars are not calculated from data but defined by the raw values in the selected variables.  The midpoints are represented by point markers.  One error bar is plotted for each case.  The range variables can be interpreted either as absolute values or values representing deviations from the midpoint depending on the current setting of the Mode option in the graph definition dialog.  Single or multiple variables can be represented in the graph.  See also "One-sided" Ranges or Error Bars in Range Plots.  3D Range plots differ from 3D Box plots in that for Range plots, the ranges are the values of the selected variables (e.g., one variable contains the minimum range values and another variable contains the maximum range values) while for Box plots, the ranges are calculated from variable values (e.g., standard deviations, standard errors, or min-max values).


3D Range Plots - Double Ribbon Ranges

In this style of Stats 3D Sequential Range Plot, the ranges are not calculated from data but defined by the raw values in the selected variables and represented by two ribbons (upper and lower ranges).  The range variables can be interpreted either as absolute values or values representing deviations from the midpoint depending on the current setting of the Mode option in the graph definition dialog.  Single or multiple variables can be represented in the graph.  See also "One-sided" Ranges or Error Bars in Range Plots.  3D Range plots differ from 3D Box plots in that for Range plots, the ranges are the values of the selected variables (e.g., one variable contains the minimum range values and another variable contains the maximum range values) while for Box plots, the ranges are calculated from variable values (e.g., standard deviations, standard errors, or min-max values).


3D Range Plots - Flying Boxes

In this style of Stats 3D Sequential Range Plot, the ranges are not calculated from data but defined by the raw values in the selected variables and represented by "flying" boxes.  The range variables can be interpreted either as absolute values or values representing deviations from the midpoint depending on the current setting of the Mode option in the graph definition dialog.  Single or multiple variables can be represented in the graph.  See also "One-sided" Ranges or Error Bars in Range Plots.  3D Range plots differ from 3D Box plots in that for Range plots, the ranges are the values of the selected variables (e.g., one variable contains the minimum range values and another variable contains the maximum range values) while for Box plots, the ranges are calculated from variable values (e.g., standard deviations, standard errors, or min-max values).


3D Range Plots - Flying Blocks

In this style of Stats 3D Sequential Range Plot, the ranges are not calculated from data but defined by the raw values in the selected variables and represented by "flying" blocks.  The range variables can be interpreted either as absolute values or values representing deviations from the midpoint depending on the current setting of the Mode option in the graph definition dialog.  Single or multiple variables can be represented in the graph.  See also "One-sided" Ranges or Error Bars in Range Plots.  3D Range plots differ from 3D Box plots in that for Range plots, the ranges are the values of the selected variables (e.g., one variable contains the minimum range values and another variable contains the maximum range values) while for Box plots, the ranges are calculated from variable values (e.g., standard deviations, standard errors, or min-max values).


3D Box Plot - Points

In this style of Stats 3D Sequential Box Plot, the ranges of values of selected variables are plotted separately for groups of cases defined by values of a categorical (grouping) variable.  The central tendency (e.g., median or mean), and range or variation statistics (e.g., quartiles, standard errors, or standard deviations) are computed for each variable and for each group of cases and the selected values are presented as point markers connected by a line.  3D Range plots differ from 3D Box plots in that for Range plots, the ranges are the values of the selected variables (e.g., one variable contains the minimum range values and another variable contains the maximum range values) while for Box plots, the ranges are calculated from variable values (e.g., standard deviations, standard errors, or min-max value).


Box Plots - Border-style Ranges
3D Box Plots - Border-style Ranges

In this style of Stats 3D Sequential Box Plot, the ranges of values of selected variables are plotted separately for groups of cases defined by values of a categorical (grouping) variable.  The central tendency (e.g., median or mean), and range or variation statistics (e.g., quartiles, standard errors, or standard deviations) are computed for each variable and for each group of cases and the selected values are presented as points with "whiskers," and the ranges marked by the "whiskers" are connected with lines (i.e., range borders) separately for each variable.  3D Range plots differ from 3D Box plots in that for Range plots, the ranges are the values of the selected variables (e.g., one variable contains the minimum range values and another variable contains the maximum range values) while for Box plots, the ranges are calculated from variable values (e.g., standard deviations, standard errors, or min-max value).


3D Box Plot - Error Bars

In this style of Stats 3D Sequential Box Plot, the ranges of values of selected variables are plotted separately for groups of cases defined by values of a categorical (grouping) variable.  The central tendency (e.g., median or mean), and range or variation statistics (e.g., min-max values, quartiles, standard errors, or standard deviations) are computed for each variable and for each group of cases and the selected values are presented as error bars.  3D Range plots differ from 3D Box plots in that for Range plots, the ranges are the values of the selected variables (e.g., one variable contains the minimum range values and another variable contains the maximum range values) while for Box plots the ranges are calculated from variable values (e.g., standard deviations, standard errors, or min-max value).


Box Plots - Double Ribbon Ranges
3D Box Plots - Double Ribbon Ranges

In this style of Stats 3D Sequential Box Plot, the ranges of values of selected variables are plotted separately for groups of cases defined by values of a categorical (grouping) variable.  The range or variation statistics (e.g., quartiles, standard errors, or standard deviations) are computed for each variable and for each group of cases and the selected values are presented as double ribbons.  3D Range plots differ from 3D Box plots in that for Range plots, the ranges are the values of the selected variables (e.g., one variable contains the minimum range values and another variable contains the maximum range values) while for Box plots the ranges are calculated from variable values (e.g., standard deviations, standard errors, or min-max value).


Box Plots - Flying Boxes
3D Box Plots - Flying Boxes

In this style of Stats 3D Sequential Box Plot, the ranges of values of selected variables are plotted separately for groups of cases defined by values of a categorical (grouping) variable.  The central tendency (e.g., median or mean), and range or variation statistics (e.g., quartiles, standard errors, or standard deviations) are computed for each variable and for each group of cases and the selected values are presented "flying" boxes.  3D Range plots differ from 3D Box plots in that for Range plots, the ranges are the values of the selected variables (e.g., one variable contains the minimum range values and another variable contains the maximum range values) while for Box plots the ranges are calculated from variable values (e.g., standard deviations, standard errors, or min-max value).


Box Plots - Flying Blocks
3D Box Plots - Flying Blocks

In this style of Stats 3D Sequential Box Plot, the ranges of values of selected variables are plotted separately for groups of cases defined by values of a categorical (grouping) variable.  The central tendency (e.g., median or mean), and range or variation statistics (e.g., quartiles, standard errors, or standard deviations) are computed for each variable and for each group of cases and the selected values are presented as "flying" blocks.  3D Range plots differ from 3D Box plots in that for Range plots, the ranges are the values of the selected variables (e.g., one variable contains the minimum range values and another variable contains the maximum range values) while for Box plots the ranges are calculated from variable values (e.g., standard deviations, standard errors, or min-max value).


"One-sided" Ranges on Error Bars in Range Plots
"One-sided" Ranges or Error Bars in Range Plots

In order to display a "one-sided" range (relative to the mid-point) or an error bar which extends in only one direction, set the respective values of the variable defining the range boundary to 0 (when the Relative to the Mid-point style is selected) or the mid-point (when the Absolute style is selected).


2D Histograms - Regular

This simple histogram will produce a column plot of the frequency distribution for the selected variable (if more than one variable is selected, then one graph will be produced for each variable in the list).

See also, Stats 2D Histograms.


2D Histograms - Multiple

Multiple histograms present frequency distributions of more than one variable in one 2D graph.  Unlike the Double-Y Histograms, the frequencies for all variables are plotted against the same left-Y axis.  Also, the values of all examined variables are plotted against a single X-axis, which facilitates comparisons between analyzed variables.  This axis is determined by the first variable selected in the list.

See also, Stats 2D Histograms.


2D Histograms - Double-Y

The Double-Y histogram can be considered to be a combination of two separately scaled multiple histograms.  Two different series of variables can be selected.  A frequency distribution for each of the selected variables will be plotted but the frequencies of the variables entered into the first list (called Left-Y variables) will be plotted against the left-Y axis, whereas the frequencies of the variables entered into the second list (called Right-Y variables) will be plotted against the right-Y axis.  The names of all variables from the two lists will be included in the legend followed by a letter L or R, denoting the Left-Y and Right-Y axis, respectively.  This graph is useful to compare distributions of variables with different frequencies.

See also, Stats 2D Histograms.


2D Histograms - Hanging Bars
2D Histogram - Hanging Bars

The hanging bars histogram offers a "visual test of normality" of the distribution that helps identify the areas of the distribution where the discrepancies (between the observed and expected normal frequencies) occur.  While the standard way of presenting the normal distribution fitted to an observed distribution is to overlay the best-fitting normal curve over a histogram, the hanging bars histogram does just the opposite:  it suspends the bars representing the observed frequencies for consecutive ranges of values from the best-fitting normal curve.  If the investigated distribution can be well approximated by the normal curve, then the bottoms of all bars should form a straight, horizontal line.  If more than one variable is selected, then one graph will be produced for each variable selected.

See also, Stats 2D Histograms.


2D Bar/Column Plots - Regular

This graph will produce a simple bar/column plot for the selected variable (if more than one variable is selected, then a separate graph will be produced for each variable in the list).

See also, Multiple Bar/Column Plots, Stats 2D Bar/Column Plots.


2D Bar/Column Plots - Multiple

Multiple bar/column plots present (in one 2D graph) multivariate clusters of bars/columns (one case = one cluster); one bar/column within each cluster represents one of the selected variables.  The values of all examined variables are plotted against a single y-axis (or x-axis if the horizontal orientation is selected), which facilitates comparisons between analyzed variables.  This axis scaling is determined by the first variable selected in the list.

See also, Regular Bar/Column Plots, Stats 2D Bar/Column Plots.


Normal Fit

The normal/observed histogram represents the most common graphical test of normality.  When you select this fit, a normal curve will be overlaid on the frequency distribution.  The curve is drawn as a Custom Function (the equation can be reviewed or edited in the User-Defined Function dialog, or automatically placed in a title via Control Characters).

The normal function fitted to histograms is defined as:

f(x) = NC * step * normal(x, mean, std.dev.)

The normal function fitted to cumulative histograms is defined as:

f(x) = NC * inormal(x, mean, std.dev.)

where

NC	is the number of cases.

step	is the categorization step size (e.g., the integral categorization step size is 1).

normal	is the normal function.

inormal	is the integral of the normal function.

See also, Stats 2D Histograms, Normal Distribution, and Bivariate Normal Distribution.


2D Scatterplot - Regular Scatterplot
2D Scatterplot - Regular

The regular scatterplot visualizes a relation between two variables X and Y ( e.g., weight and height).  Individual data points are represented by point markers in two-dimensional space, where axes represent the variables.  The two coordinates (X and Y) which determine the location of each point, correspond to its specific values on the two variables.  If the two variables are strongly related, then the data points form a systematic shape (e.g., a straight line or a clear curve).  If the variables are not related, then the points form an irregular "cloud."

See also, Stats 2D Scatterplots.


2D Scatterplot - Multiple Scatterplot
2D Scatterplot - Multiple

Unlike the regular scatterplot in which one variable is represented by the horizontal axis and one by the vertical axis, the multiple scatterplot consists of multiple plots and represents multiple correlations: one variable (X) is represented by the horizontal axis, and several variables (Y's) are plotted against the vertical axis.  A different point marker and color is used for each of the multiple Y-variables and referenced in the legend so that individual plots representing different variables can be discriminated in the graph.  The Multiple scatterplot is used to compare images of several correlations by overlaying them in a single graph that uses one common set of scales (e.g., to reveal the underlying structure of factors or dimensions in Discriminant Function Analysis).

See also, Stats 2D Scatterplots.


2D Scatterplot - Double-Y Scatterplot
2D Scatterplot - Double-Y

This type of scatterplot can be considered to be a combination of two multiple scatterplots for one X-variable and two different sets (lists) of Y-variables.  A scatterplot for the X-variable and each of the selected Y-variables will be plotted, but the variables entered into the first list (called Left-Y) will be plotted against the left-Y axis, whereas the variables entered into the second list (called Right-Y) will be plotted against the right-Y axis.  The names of all Y-variables from the two lists will be included in the legend followed either by the letter (L) or (R), denoting the left-Y and right-Y axis, respectively.  The Double-Y scatterplot can be used to compare images of several correlations by overlaying them in a single graph.  However, due to the independent scaling used for the two list of variables, it can facilitate comparisons between variables with values in different ranges.

See also, Stats 2D Scatterplots.


2D Scatterplot - Frequency Scatterplot
2D Scatterplot - Frequency

Frequency scatterplots display the frequencies of overlapping points between two variables in order to visually represent data point weight or other measurable characteristics of individual data points.  The program counts the frequencies of the overlapping points and categorizes those frequencies according to the number specified in the No of Freq option in the dialog (min=2, max=16).  The sizes of the point markers in the plot are then adjusted to represent the frequencies.  Note that if you are using a variable as a case weight (see Weight), then the point markers will automatically reflect those weights in the scatterplot.  The point marker patterns can be changed in the Select Point Patterns dialog.  The default point marker patterns and styles used in this graph can be adjusted in the Specific Plots Default Patterns dialog.

See also, Stats 2D Scatterplots.


2D Scatterplot - Quantile Scatterplot
2D Scatterplot - Quantile

In quantile scatterplots, the quantiles of one variable are plotted against the quantiles of another variable in order to assess the similarity of the empirical distributions of the two variables.  If the data points fall on the regression line, then it can be concluded that the two variables follow the same distribution.

See also, Stats 2D Scatterplots, Quantile-Quantile Plots, and Probability-Probability Plots.


2D Scatterplot - Voronoi Scatterplot
2D Scatterplot - Voronoi

This specialized univariate scatterplot is more an analytic technique than just a method to graphically present data.  The solutions it offers, help to model a variety of phenomena in natural and social sciences (e.g., Coombs, 1964; Ripley, 1981).  The program divides the space between the individual data points represented by XY coordinates in 2D space.  The division is such that each of the data points is surrounded by boundaries including only the area that is closer to its respective "center" data point than to any other data point.  The particular ways in which this method is used depends largely on specific research areas, however, in many of them, it is helpful to add additional dimensions to this plot by using the marked subset (select points) and categorization options in this dialog.  Note:  The pattern of the line used to draw the Voronoi divisions can be adjusted via the Patterns - Lines button in the 2D Plot Layout dialog.

See also, Stats 2D Scatterplots.


Normal Probability Plots

This type of graph is used to evaluate the normality of the distribution of a variable, that is, whether and to what extent the distribution of the variable follows the normal distribution.  The selected variable will be plotted in a scatterplot against the values "expected from the normal distribution."  The standard normal probability plot is constructed as follows.  First, the deviations from the mean (residuals) are rank ordered.  From these ranks the program computes z values (i.e., standardized values of the normal distribution) based on the assumption that the data come from a normal distribution (see Computation Note).  These z values are plotted on the Y-axis in the plot.  If the observed residuals (plotted on the X-axis) are normally distributed, then all values should fall onto a straight line.  If the residuals are not normally distributed, then they will deviate from the line.  Outliers may also become evident in this plot.  If there is a general lack of fit, and the data seem to form a clear pattern (e.g., an S shape) around the line, then the variable may have to be transformed in some way (e.g., a log transformation to "pull-in" the tail of the distribution, etc., see Edit Variable Specs or STATISTICA BASIC).

See also, Stats Probability Plots	Multiple Normal Probability Plots

Quick Stats Graphs - Probability Plot of...	Normal Probability Plots (Computation Note)

Block Stats Graph - Normal Prob. Plot

See also, Stats Graphs - Quantile-Quantile Plots and Stats Graphs - Probability-Probability Plots.


Half-Normal Probability Plots

This type of graph is used to evaluate the normality of the distribution of a variable, that is, whether and to what extent the distribution of the variable follows the normal distribution.  The selected variable will be plotted in a scatterplot against the values "expected from the normal distribution."  The half-normal probability plot is constructed in the same way as the standard normal probability plot, except that only the positive half of the normal curve is considered.  Consequently, only positive normal values will be plotted on the Y-axis.  This plot is used when one wants to ignore the sign of the residual, that is, when one is mostly interested in the distribution of absolute residuals, regardless of the sign.

See also, Stats Probability Plots.

Quick Stats Graphs - Probability Plot of...

See also, Stats Graphs - Quantile-Quantile Plots and Stats Graphs - Probability-Probability Plots.


Detrended Probability Plots

This type of graph is used to evaluate the normality of the distribution of a variable, that is, whether and to what extent the distribution of the variable follows the normal distribution.  The selected variable will be plotted in a scatterplot against the values "expected from the normal distribution."  This plot is constructed in the same way as the standard normal probability plot, except that before the plot is generated, the linear trend is removed.  This often "spreads out" the plot, thereby allowing the user to detect patterns of deviations more easily.

See also, Stats Probability Plots.

Quick Stats Graphs - Probability Plot of...

See also, Stats Graphs - Quantile-Quantile Plots and Stats Graphs - Probability-Probability Plots.


Categorized Normal Probability Plots

This type of probability plot is constructed as follows.  First, within each category, the values (observations) are rank ordered.  From these ranks one can compute z values (i.e., standardized values of the normal distribution) based on the assumption that the data come from a normal distribution (see Computation Note).  These z values are plotted on the Y-axis in the plot.  If the observed values (plotted on the X-axis) are normally distributed, then all values should fall onto a straight line.  If the values are not normally distributed, then they will deviate from the line.  Outliers may also become evident in this plot.  If there is a general lack of fit, and the data seem to form a clear pattern (e.g., an S shape) around the line, then the variable may have to be transformed in some way (e.g., a log transformation to "pull-in" the tail of the distribution, etc.) before some statistical techniques that are affected by non-normality can be used.

See also, Stats Categorized Probability Plots	Multiple Normal Probability Plots

Quick Stats Graphs - Probability Plot by...	Normal Probability Plots (Computation Note)

See also, Stats Graphs - Quantile-Quantile Plots and Stats Graphs - Probability-Probability Plots.


Categorized Half-Normal Probability Plots

The categorized half-normal probability plot is constructed in the same manner as the standard normal probability plot, except that only the positive half of the normal curve is considered.  Consequently, only positive normal values will be plotted on the Y-axis.  This plot is often used in plots of residuals (e.g., in multiple regression), when one wants to ignore the sign of the residuals, that is, when one is interested in the distribution of absolute residuals, regardless of the sign.

See also, Stats Categorized Probability Plots.

Quick Stats Graphs - Probability Plot by...

See also, Stats Graphs - Quantile-Quantile Plots and Stats Graphs - Probability-Probability Plots.


Categorized Detrended Probability Plots

This categorized plot is constructed in the same way as the standard normal probability plot for the categorized values, except that before the plot is generated, the linear trend is removed.  This often "spreads out" the plot, thereby allowing the user to detect patterns of deviations more easily.

See also, Stats Categorized Probability Plots.

Quick Stats Graphs - Probability Plot by...

See also, Stats Graphs - Quantile-Quantile Plots and Stats Graphs - Probability-Probability Plots.


2D Range Plots - Whiskers

In this style of range plot, the range is represented by "whiskers" (i.e., as a line with a serif on both ends).  The midpoints are represented by point markers.  For more information and examples on input data arrangement for this graph see Stats Graphs - 2D Range Plots.  See also "One-sided" Ranges or Error Bars in Range Plots.

Editing graph data for box and whisker format graphs: see Editing Graph Data for Box and Whisker Format Graphs


2D Range Plots - Boxes

In this style of range plot, the range is represented by a "box" (i.e., as a rectangular box where the top of the box is the upper range and the bottom of the box is the lower range).  The midpoints are represented either as point markers or horizontal lines that "cut" the box.  For more information and examples on input data arrangement for this graph see Stats Graphs - 2D Range Plots.  See also "One-sided" Ranges or Error Bars in Range Plots.

Editing graph data for box and whisker format graphs: see Editing Graph Data for Box and Whisker Format Graphs


2D Range Plots - Columns

In this style of range plot, a column represents the mid-point (i.e., the top of the column is at the mid-point value) and the range (represented by "whiskers") is overlaid in the column.  For more information and examples on input data arrangement for this graph see Stats Graphs - 2D Range Plots.  See also "One-sided" Ranges or Error Bars in Range Plots.

Editing graph data for box and whisker format graphs: see Editing Graph Data for Box and Whisker Format Graphs


2D Box Plots - Box-Whiskers

This type of box plot will place a box around the midpoint (i.e., mean or median) which represents a selected range (i.e., standard error, standard deviation, min-max, or constant) and whiskers outside of the box which also represent a selected range (see above).  The default box and whisker patterns used in this graph can be adjusted in the Specific Plots Default Patterns dialog.

Editing graph data for box and whisker format graphs: see Editing Graph Data for Box and Whisker Format Graphs.

See also:	Quick Stats Graphs - Box-Whisker of ...	Block Stats Graphs - Box Plot/Medians

Stats Graphs - Scatterplots w/Box Plots	Stats Graphs  - Categorized Box Plots

Stats Graphs - 2D Box Plots	Quick Stats Graphs - Box-Whisker by...

Block Stats Graphs - Box Plot/Means


2D Box Plots - Whiskers (Box Plot)
2D Box Plots - Whiskers

In this style of box plot, the range (i.e., standard error, standard deviation, min-max, or constant) is represented by "whiskers" (i.e., as a line with a serif on both ends).  The default whisker patterns used in this graph can be adjusted in the Specific Plots Default Patterns dialog.

Editing graph data for box and whisker format graphs: see Editing Graph Data for Box and Whisker Format Graphs

See also:	Stats Graphs - Scatterplots w/Box Plots

Stats Graphs - 2D Box Plots

Stats Graphs  - Categorized Box Plots


2D Box Plots - Boxes

This type of box plot will place a box around the midpoint (i.e., mean or median) which represents the selected range (i.e., standard error, standard deviation, min-max, or constant).  The default box patterns used in this graph can be adjusted in the Specific Plots Default Patterns dialog.

Editing graph data for box and whisker format graphs: see Editing Graph Data for Box and Whisker Format Graphs

See also:	Stats Graphs - Scatterplots w/Box Plots

Stats Graphs - 2D Box Plots

Stats Graphs  - Categorized Box Plots


2D Box Plots - Columns

In this type of box plot, vertical columns are used to represents the variable's midpoint (i.e., mean or median).  The whiskers superimposed on each column mark the selected range (i.e., standard error, standard deviation, min-max, or constant) around the midpoint.

Editing graph data for box and whisker format graphs: see Editing Graph Data for Box and Whisker Format Graphs

See also:	Stats Graphs - Scatterplots w/Box Plots

Stats Graphs - 2D Box Plots

Stats Graphs  - Categorized Box Plots


High-Low Close

In this type of box or range plot, the "serifs" on the whiskers are not symmetrical but point to the left of the bar, representing the traditional "stock price graph" style.  Note that you can change the whisker style (i.e., Hi/Lo Left, Hi/Lo Right, or regular Whiskers) in the Plot Layout dialog, for example:

Editing graph data for box and whisker format graphs: see Editing Graph Data for Box and Whisker Format Graphs

See also:	Stats Graphs - 2D Box Plots

Stats Graphs - Categorized Box Plots

Stats Graphs - 2D Range Plots

Line Point Patternfor High-Low Close Graphs


Line Point Pattern
Line Point Pattern for High-Low Close Graphs

When you are selecting a point pattern for High-Low Close graphs in the Points, Lines, Area Patterns dialog, you can choose to center, left-justify, or right-justify the line point marker with respect to the point position (see below).

See also High-Low Close.


2D Line Plots - Regular

Regular line plots are used to examine and present the sequences of values (usually when the order of the presented values is meaningful).  Another typical application for line sequence plots is to plot continuous functions, such as fitted functions or theoretical distributions.  Note that an empty data cell (i.e., missing data) "breaks" the line.

See also, Stats Graphs - 2D Line Plots.


2D Line Plots - Multiple

Unlike regular line plots in which a sequence of values of one variable is represented, the multiple line plot represents multiple sequences of values (variables).  A different line pattern and color is used for each of the multiple variables and referenced in the legend.  This type of line plot is used to compare sequences of values between several variables (or several functions) by overlaying them in a single graph that uses one common set of scales (e.g., comparisons between several simultaneous experimental processes, social phenomena, stock or commodity quotes, shapes of operating characteristics curves, etc.).

See also, Stats Graphs - 2D Line Plots.


2D Line Plots - Double-Y

The Double-Y line plot can be considered to be a combination of two separately scaled multiple line plots.  A separate line pattern is plotted for each of the selected variables, but the variables selected in the Left-Y list will be plotted against the left-Y axis, whereas the variables selected in the Right-Y list will be plotted against the right-Y axis.  The names of all variables will be identified in the legend with the letter (R) for the variables associated with the right-Y axis and with the letter (L) for the variables associated with the left-Y axis.  The Double-Y line plot can be used to compare sequences of values of several variables by overlaying their respective line representations in a single graph.  However, due to the independent scaling used for the two axes, it can facilitate comparisons between otherwise "incomparable" variables (i.e., variables with values in different ranges).

See also, Stats Graphs - 2D Line Plots.


2D Line Plots - XY Trace

In trace plots, a scatterplot of two variables is first created, then the individual data points are connected with a line (in the order in which they are read from the data file).  In this sense, trace plots visualize a "trace" of a sequential process (movement, change of a phenomenon over time, etc.).

See also, Stats Graphs - 2D Line Plots, Stats 3D XYZ Graphs - Trace Plots.


2D Line Plots - Aggregated

Aggregated line plots display a sequence of means for consecutive subsets of a selected variable.  You can select the number of consecutive observations from which the mean will be calculated (Aggr. Index option) and if desired, the range of values in each subset will be marked by the whisker-type markers (Value Range Bars option).  Aggregated line plots are used to explore and present sequences of large numbers of values.  A large selection of data smoothing and filtering procedures (e.g., moving average, moving median, 4253 filters, and others) are available in the Time Series module.

See also, Stats Graphs - 2D Line Plots.


2D Sequential/Stacked Plots - Line

The sequence of values from each selected variable will be represented by consecutive lines stacked on one another in this type of Stats Graphs.

See also, Stats Graphs - Sequential/Stacked Plots, Stats Graphs - 2D Line Plots (Variables), and Stats Graphs - 2D Line Plots (Case Profiles).


2D Sequential/Stacked Plots - Area

The sequence of values from each selected variable will be represented by consecutive areas stacked on one another in this type of Stats Graphs.

See also, Stats Graphs - Sequential/Stacked Plots.


2D Sequential/Stacked Plots - Mixed Line

In this type of Stats Graphs, the sequences of values of variables selected in the first list will be represented by consecutive areas stacked on one another while the sequences of values of variables selected in the second list will be represented by consecutive lines stacked on one another (over the area representing the last variable from the first list).

See also, Stats Graphs - Sequential/Stacked Plots.


2D Sequential/Stacked Plots - Step

The sequence of values from each selected variable will be represented by consecutive step lines stacked on one another in this type of Stats Graphs.

See also, Stats Graphs - Sequential/Stacked Plots.


2D Sequential/Stacked Plots - Step Area

The sequence of values from each selected variable will be represented by consecutive step areas stacked on one another in this type of Stats Graphs.

See also, Stats Graphs - Sequential/Stacked Plots.


2D Sequential/Stacked Plots - Mixed Step

In this type of Stats Graphs, the sequences of values of variables selected in the first list will be represented by consecutive step areas stacked on one another while the sequences of values of variables selected in the second list will be represented by consecutive step lines stacked on one another (over the step area representing the last variable from the first list).

See also, Stats Graphs - Sequential/Stacked Plots.


2D Sequential/Stacked Plots - Column

The sequence of values from each selected variable will be represented by consecutive segments of vertical columns stacked on one another in this type of Stats Graphs.

See also, Stats Graphs - Sequential/Stacked Plots.


Pie Chart - Counts

Unlike the values pie chart, this type of pie (this term was first used by Haskell, 1922) chart (sometimes called frequency pie chart) interprets data like a histogram.  It categorizes all values of the selected variable following the selected categorization technique (see Stats Graphs - Pie Charts) and then displays the relative frequencies as pie slices of proportional sizes.  The default pie slice patterns and colors used in this graph can be adjusted in the Specific Plots Default Patterns dialog.

See also, Stats Pie Charts.


Pie Chart - Values

The sequence of values from the selected variable will be represented by consecutive slices of the pie (this term was first used by Haskell, 1922); the size of each slice will be proportional to the respective value.  The values should be greater than 0 (0's and negative values cannot be represented as slices of the pie).  This simple type of pie chart (sometimes called data pie chart) interprets data in the most straightforward manner:  one case = one slice.  The default pie slice patterns and colors used in this graph can be adjusted in the Specific Plots Default Patterns dialog.

See also, Stats Pie Charts.


Pie Chart - Multi-pattern Bar

The multi-pattern bar plot is designed to display the same type of data as the values pie chart (see Pie Chart - Values or 2D Histograms), however, the consecutive values are represented by the height of vertical bars (of different colors and patterns) and not areas of pie slices.  Their advantage over pie charts is that they may allow for more precise comparisons between presented values (e.g., small pie slices may be difficult to compare if they are not adjacent).  This type of graph may also have advantages over regular histograms (where one fill pattern and color is used for all columns), in cases when quick identification of specific columns is desired.

See also, Stats Pie Charts.


2D Scatterplot

The scatterplot visualizes a relation (correlation) between two variables X and Y (e.g., weight and height).  Individual data points are represented in two-dimensional space, where axes represent the variables (X on the horizontal axis and Y on the vertical axis).  The two coordinates (X and Y) that determine the location of each point correspond to its specific values on the two variables.

You can create a Scatterplot via the Custom 2D Graphs, Stats Graphs - 2D Scatterplots, Stats Graphs - Categorized Scatterplots, or Quick Stats Graphs - Scatterplot by... options.

For more information on the style of scatterplots, see:

Double-Y	Regular

Frequency	Voronoi

Multiple

See also, 3D XYZ Scatterplots, Ternary Scatterplots.


2D Line Plots

In line plots, individual data points are connected by a line.  Line plots provide a simple way to visually present a sequence of values.  XY Trace-type line plots can be used to display a trace (instead of a sequence).  Line plots can also be used to plot continuous functions, theoretical distributions, etc.

You can create a Line Plot via the Custom 2D Graphs or Stats Graphs - 2D Line Plots options.

For more information on the style of line plots available in STATISTICA, see:

Aggregrated	Regular

Double-Y	XY Trace

Multiple


2D Step Plot

In this plot, the values of one variable X are plotted against the values of another variable Y (as in a regular scatterplot), with individual data points connected by a step-style line (points are connected in the order of their sequential position in the data file or Scrollsheet).

See also, Custom 2D Graphs.


2D Min-Max X

This vertical range plot represents individual ranges of data.  For each value of X (representing horizontal position on the X-axis), a vertical bar (or a pair of "whiskers" or a line segment) is drawn from the respective values of Y-Min to Y-Max, representing the range from Y-Min to Y-Max at that level of X.  Select the X and Y-Min variables in the Custom 2D Graphs dialog, and the Y-Max variable in the subsequent Get Variable for Min-Max Plot dialog.

See also, Custom 2D Graphs.


2D Min-Max Y

This horizontal range plot represents individual ranges of data.  For each value of Y (representing vertical position on the Y-axis), a horizontal bar (or a pair of "whiskers" or a line segment) is drawn from the respective values of X-Min to X-Max, representing the range from X-Min to X-Max at that level of Y.  Select the Y and X-Min variables in the Custom 2D Graphs dialog, and the X-Max variable in the Get Variable for Min-Max Plot dialog.

See also, Custom 2D Graphs.


Bar X

In this plot, one vertical bar is drawn for each data point (i.e., each pair of XY coordinates), connecting the data point and the lower X-axis.  The horizontal position of the bar is determined by the data point's X value, and its height by the respective Y value.  The width of the bars can be adjusted in the respective 2D Plot Layout dialog accessible from the Layout pull-down menu or from the flying menu (called by clicking the right-mouse-button on the specific plot).

See also, Custom 2D Graphs.


Bar Left Y

In this plot, one horizontal bar is drawn for each data point (i.e., each pair of XY coordinates), connecting the data point and the left Y-axis.  The vertical position of the bar is determined by the data point's Y value, and its length by the respective X value.  The width of the bars can be adjusted in the respective 2D Plot Layout dialog accessible from the Layout pull-down menu or from the flying menu (called by clicking the right-mouse-button on the specific plot).

See also, Custom 2D Graphs.


Bar Right Y

In this plot, one horizontal bar is drawn for each data point (i.e., each pair of XY coordinates), connecting the data point and the right Y-axis.  The vertical position of the bar is determined by the data point's Y value, and its length by the respective X value.  The width of the bars can be adjusted in the respective 2D Plot Layout dialog accessible from the Layout pull-down menu or from the flying menu (called by clicking the right-mouse-button on the specific plot).

See also, Custom 2D Graphs.


Bar Top

(Also known as "hanging" column plots.)  In this plot, one vertical bar is drawn for each data point (i.e., each pair of XY coordinates), connecting the data point and the upper X-axis.  The horizontal position of the bar is determined by the data point's X value, and its length by the respective Y value.  The width of the bars can be adjusted in the respective 2D Plot Layout dialog accessible from the Layout pull-down menu or from the flying menu (called by clicking the right-mouse-button on the specific plot).

See also, Custom 2D Graphs.


Bar Dev

The "bar deviation" plot is similar to the Bar X plot, in that individual data points are represented by vertical bars, however, the bars connect the data points to a user-selectable baseline (see Deviation Level option in the 2D Plot Layout dialog).  If the baseline value is different than the plot's Y-axis minimum, then individual bars will extend either up or down, depending on the direction of the "deviation" of individual data points from the baseline.  The width and the box line can be adjusted in the respective 2D Plot Layout dialog accessible from the Layout pull-down menu or from the flying menu (called by clicking the right-mouse-button on the specific plot).

See also, Custom 2D Graphs.


2D Pie

Pie charts (the term first used by Haskell, 1922) are useful for representing proportions.  Individual data values of the X variable are represented as the "wedges" of the pie.

See also, Custom 2D Graphs.


MPatt Bar

Multi-pattern bar plots may be used to represent individual data values of the X variable (the same type of data as in pie charts), however, consecutive data values of the X variable are represented by the heights of sequential vertical bars, each of a different color and pattern (rather than as pie wedges of different widths).

See also, Custom 2D Graphs.


Voronoi

The Voronoi tessellation graph plots values of two variables X and Y in a scatterplot, then divides the space between individual data points into regions such that the boundaries surrounding each data point enclose an area that is closer to that data point than to any other neighboring points.

See also, Custom 2D Graphs.


3D Histogram - Box Plot
3D Histograms - Box Plot

This type of bivariate histogram represents the frequencies as a series of 3D bars ("rectangular boxes").  This is the default representation of 3D histograms.  The "height" of each bar on the Z-axis corresponds to the frequency of the respective combination of levels for the two variables.  The "margins" (distances between the boxes) and other freatures of the boxes can be adjusted in the 3D Graphs/More Options dialog accessible from the More Options button in the General Layout dialog.

See also, Stats Sequential 3D Bivariate Histograms


3D Box Plot

This type of graph represents the individual values of one or more series of data along the X-axis as a series of 3D bars ("rectangular boxes").  Each series to be plotted is spaced along the Y-axis.  The "height" of each bar on the Z-axis corresponds to the value of the respective data point.  The "margins" (distances between the boxes) and other freatures of the boxes can be adjusted in the 3D Graphs/More Options dialog accessible from the More Options button in the General Layout dialog.

See also, Custom 3D Sequential Graphs.


3D Block Plot

This sequential plot represents individual values of one or more series of data along the x-axis  as a series of "3D blocks".  Each series to be plotted is spaced along the Y-axis.  The "height" of the beginning of each block on the Z-axis corresponds to the value of the respective data point.  The "margins" (distances between the blocks) and other features of the blocks can be adjusted in the 3D Graphs/More Options dialog accessible from the More Options button in the General Layout dialog.

See also, Custom 3D Sequential Graphs.


3D Ribbons

This plot represents the individual values of one or more series of data along the X-axis as a series of "ribbons" in 3D space.  Each series to be plotted is spaced along the Y-axis.  The "height" of the beginning of each ribbon segment on the Z-axis corresponds to the value of the respective data point.  The "margins" (distances between the ribbons) and other features of the ribbons can be adjusted in the 3D Graphs/More Options dialog accessible from the More Options button in the General Layout dialog.

See also, Custom 3D Sequential Graphs.


3D Lines

This sequential plot represents the individual values of one or more series of data along the X-axis as a series of continuous lines in 3D space.  Each series to be plotted is spaced along the Y-axis.  The "height" of the beginning of each line segment on the Z-axis corresponds to the value of the respective data point.

See also, Custom 3D Sequential Graphs.


3D Histograms - Spikes
3D Histogram - Spikes

In this type of bivariate histogram, the frequencies are represented as a series of "spikes" (point symbols with lines descending to the base plane).  The "height" of each spike is determined by the frequency for the respective combination of levels of the two variables.  The level of the base plane (i.e., the respective Z-value) can be adjusted in the 3D Graphs/More Options dialog.

See also, Stats Sequential 3D Bivariate Histograms


3D Spikes

In this type of graph, individual values of one or more series of data are represented along the X-axis as a series of "spikes" (point symbols with lines descending to the base plane).  Each series to be plotted is spaced along the Y-axis.  The "height" of each spike is determined by the the respective value of each series.  The level of the base plane (i.e., the respective Z-value) can be adjusted in the 3D Graphs/More Options dialog.

See also, Custom 3D Sequential Graphs.


3D Histogram - Contour/Discrete

This contour plot represents a discrete projection of the 3D (smoothed) histogram.  (See also, Calculating Contour Levels and Distance.)

See also, Stats Sequential 3D Bivariate Histograms

Bivariate histogram

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


3D Histogram - Surface Plot

In this representaion of the 3D bivariate histogram, a spline-smoothed surface is fit to the frequency data.  Smoothness of the surface can be adjusted using the stiffness control in the 3D Graphs/More Options dialog accessible from the More Options button in the General Layout dialog.

See also, Stats Sequential 3D Bivariate Histograms

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


3D Sequential Surface Plot

In this sequential plot, a spline-smoothed surface is fit to each data point.  Successive values of each series are plotted along the X-axis, with each successive series represented along the Y-axis.  Smoothness of the surface can be adjusted using the stiffness control in the 3D Graphs/More Options dialog accessible from the More Options button in the General Layout dialog.

See also, Stats Sequential 3D Bivariate Histograms

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


3D Histogram - Contour Plot

This contour plot presents a projection of the spline-smoothed surface fit to the frequency data (see 3D Sequential Surface Plot.  Successive values of each series are plotted along the X-axis, with each successive series represented along the Y-axis.  .  (See also, Calculating Contour Levels and Distance.)

See also, Stats Sequential 3D Bivariate Histograms

Bivariate histogram

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


3D Sequential Contour Plot

This contour plot (see Stats 3D Sequential Raw Data Plots) presents a 2-dimensional projection of the spline-smoothed surface fit to the data (see 3D Sequential Surface Plot).  Successive values of each series are plotted along the X-axis, with each successive series represented along the Y-axis.  (See also, Calculating Contour Levels and Distance.)

See also, Stats Sequential 3D Bivariate Histograms

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


3D Scatterplot

3D Scatterplots visualize a relationship between three or more variables, representing the X, Y, and one or more Z (vertical) coordinates of each point in 3-dimensional space.

A 3D Scatterplot can be created via the Custom Graph, Stats Graph - 3D Scatterplot, or Stats Graphs - 3D Scatterplots options.

For more information on the style of 3D scatterplots available in STATISTICA, see:

Deviation Plot	Surface Plot

Space Plot	Trace Plot

Spectral Plot	Contour Plot

See also:	3D Scatterplot - Custom Ternary Graph

3D Scatterplot - Stats Ternary Graph


Space Plot

This Custom Graph or Stats Graph - 3D Scatterplot option offers a distinctive method of representing 3D scatterplot data through the use of an X-Y plane positioned at a user-selectable level of the vertical Z-axis (which "sticks up" through the middle of the plane).  The level of the X-Y plane can be adjusted in order to divide the X-Y-Z- space into meaningful parts (e.g., featuring different patterns of the relation between the three variables).  The Z-axis value defining the level of the base plane can be adjusted in the 3D Graphs/More Options dialog accessible from the More Options button in the General Layout dialog.


Spectral Plot

The original application of this type of plot was in the context of spectral analysis in order to investigate the behavior of non-stationary time series.  On the horizontal axes one can plot the frequency of the spectrum against consecutive time intervals, and indicate on the Z-axis the spectral densities at each interval (see for example, Shumway, 1988, page 82).  STATISTICA offers a flexible implementation of spectral plots for various types of data.  For example, it allows you to explore patterns of relations between 3 variables by "compressing" the data into a requested number of planes.

This version of the Custom Graph or Stats Graph - 3D Scatterplot divides the 3D space into sections and then "compresses" the data points from consecutive sections into consecutive spectral planes.  Values of variables X and Z are interpreted as the X- and Z-axis coordinates of each point, respectively; values of variable Y are clustered into equally-spaced values, corresponding to the locations of the consecutive spectral planes.  The number of spectral planes can be adjusted in the 3D Graphs/More Options dialog.


Deviation Plot

Data points (representing the X, Y and Z coordinates of each point) in the Custom Graph or Stats Graph - 3D Scatterplot options are represented in 3D space as "deviations" from a specified base-level of the Z-axis (see 3D Graphs/More Options).


Trace Plot

Data points in the Custom Graph or Stats Graph - 3D Scatterplot option are positioned as in regular 3D scatterplots (the values of the variables represent the X, Y, and Z coordinates of each point), however, individual data points are connected with a line (in the order in which they were read from the data file), visualizing a "trace" of sequential values.


Surface Plot

When you select Surface Plot, a surfaceis fitted (defined by a smoothing technique) to the data (variables corresponding to sets of XYZ coordinates).

See also, Custom 3D Scatterplots and Surfaces.

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


Categorized 3D Surface Plot

In this type of Stats Graphs - 3D Categorized Plots, a surface (defined by a smoothing technique or user-defined mathematical expression) is fitted to the categorized data (variables corresponding to sets of XYZ coordinates, for subsets of data determined by the selected categorization method) arranged in one display to allow for comparisons between the subsets of data (categories).

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


Categorized 3D Scatterplot

This type of Stats Graphs - 3D Categorized Plot visualizes a relationship between three variables (representing the X, Y, and one or more Z [vertical] coordinates of each point in 3-dimensional space) categorized by a grouping variable (or a user-defined categorization method).  One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).


Categorized 3D Space Plot

This type of Stats Graphs - 3D Categorized Plot offers a distinctive means of representing 3D scatterplot data through the use of a separate X-Y plane positioned at a user-selectable level of the vertical Z-axis (which "sticks up" through the middle of the plane).  The level of the X-Y plane can be adjusted in order to divide the X-Y-Z- space into meaningful parts (e.g., featuring different patterns of the relation between the three variables).  The Z-axis value defining the level of the base plane can be adjusted in the 3D Graphs/More Options dialog accessible from the More Options button in the General Layout dialog.  One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).


Categorized 3D Spectral Plot

This type of Stats Graphs - 3D Categorized Plot produces multiple spectral plots (for subsets of data determined by the selected categorization method) arranged in one display to allow for comparisons between the subsets of data.  Values of variables X and Z are interpreted as the X- and Z-axis coordinates of each point, respectively; values of variable Y are clustered into equally-spaced values, corresponding to the locations of the consecutive spectral planes.  The number of spectral planes can be adjusted in the 3D Graphs/More Options dialog.  For more information, see Spectral Plots.


Categorized 3D Deviation Plot

Data points (representing the X, Y and Z coordinates of each point) in this Stats Graphs - 3D Categorized Plot are represented in 3D space as "deviations" from a specified base-level of the Z-axis (the Z-axis value defining the level of the base plane can be adjusted in the 3D Graphs/More Options dialog).  One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).


3D Contour Plot

A contour plot is the projection of a 3-dimensional surface onto a 2-dimensional plane.  (See also, Calculating Contour Levels and Distance.)

See also, Custom 3D Scatterplots and Surfaces.

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


Contour/Lines

A contour plot is the projection of a 3-dimensional surface onto a 2-dimensional plane.  This contour plot is displayed as a series of lines.  (See also, Calculating Contour Levels and Distance.)

See also, Overview of Graphic Options in STATISTICA.

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


Contour/Areas

A contour plot is the projection of a 3-dimensional surface onto a 2-dimensional plane.  This contour plot is displayed as a series of areas.  (See also, Calculating Contour Levels and Distance.)

See also, Overview of Graphic Options in STATISTICA.

In order to change the range of values and number of levels used to define the contour or surface, see Specify Contour Levels.


3D Scatterplot - Raw Data

An unsmoothed surface (no smoothing function is applied) is drawn through the points in the 3D scatterplot.

See also, Overview of Graphic Options in STATISTICA.


Linear (3D graphs)

A linear function (e.g., Z = a + bX + cY) is fitted to the points in the 3D scatterplot.

See also, Overview of Graphic Options in STATISTICA.


Linear (2D graphs)

A linear function (e.g., Y = a + bX) is fitted to the points in the 2D scatterplot.

Confidence bands can be requested in the Plot Layout dialog.

See also, Overview of Graphic Options in STATISTICA.


Quadratic

Fits a second-order polynomial function to the points in the 3D scatterplot.

See also, Overview of Graphic Options in STATISTICA.


Least Squares (3D graphs)

A surface is fitted to the XYZ coordinate data according to the distance-weighted least squares smoothing procedure (the influence of individual points decreases with the horizontal distance from the respective points on the surface); the stiffness of the fit can be controlled in the 3D Graphs/More Options dialog, accessible from the graph.  For more information, see Distance-Weighted Least Squares.

See also, Overview of Graphic Options in STATISTICA.


Least Squares (2D graphs)

A curve is fitted to the XY coordinate data according to the distance-weighted least squares smoothing procedure (the influence of individual points decreases with the horizontal distance from the respective points on the curve).  The stiffness of the fit can be controlled in the Fitting Options dialog.  For more information, see Distance-Weighted Least Squares.

See also, Overview of Graphic Options in STATISTICA.


Negative Exponential (3D graphs)

A surface is fitted to the XYZ coordinate data according to the negative exponentially-weighted smoothing procedure (the influence of individual points decreases exponentially with the horizontal distance from the respective points on the surface); the stiffness of the fit can be controlled in the 3D Graphs/More Options dialog, accessible from the graph.  For more information, see Negative Exponentially-Weighted Fitting.

See also, Overview of Graphic Options in STATISTICA.


Negative Exponential (2D graphs)

A curve is fitted to the XY coordinate data according to the negative exponentially-weighted smoothing procedure (the influence of individual points decreases exponentially with the horizontal distance from the respective points on the curve).  The stiffness of the fit can be controlled in the Fitting Options dialog.  For more information, see Negative Exponentially-Weighted Fitting.

See also, Overview of Graphic Options in STATISTICA.


Spline (3D graphs)

A surface is fitted to the XYZ coordinate data using the bicubic spline smoothing procedure; the stiffness of the fit can be controlled in the 3D Graphs/More Options dialog, accessible from the graph.  For more information, see Spline Fitting.

See also, Overview of Graphic Options in STATISTICA.


Spline (2D graphs)
Spline (2D graphs)  [image],

A curve is fitted to the XY coordinate data using the bicubic spline smoothing procedure.  The stiffness of the fit can be controlled in the Fitting Options dialog.  For more information, see Spline Fitting.

See also, Overview of Graphic Options in STATISTICA.


2D Matrix Plots - Scatterplot

In this type of Matrix Plot, 2D Scatterplots are arranged in a matrix format (values of the column variable are used as X coordinates, values of the row variable represent the Y coordinates).  Histograms representing the distribution of each variable are displayed along the diagonal of the matrix (in square matrices) or along the edges (in rectangular matrices).  The default matrix scatterplot points patterns used in this graph can be adjusted in the Specific Plots Default Patterns dialog.

In order to produce a scatterplot matrix for each of the selected groups in the grouping variable, see Categorized Scatterplot Matrix.

See also, Stats Graphs Matrix Plots.

Custom Graphs Matrix Plots

Quick Stats Graphs Matrix Scatterplot


2D Matrix Plots - Lines

In this type of Matrix Plot, a matrix of X-Y (i.e., nonsequential) line plots (similar to a scatterplot matrix) is produced in which individual points are connected by a line in the order of their appearance in the data file.  Histograms representing the distribution of each variable are displayed along the diagonal of the matrix (in square matrices) or along the edges (in rectangular matrices).

See also, Stats Graphs Matrix Plots.

Custom Graphs Matrix Plots


2D Matrix Plots - Columns

In this type of Matrix Plot, columns represent projections of individual data points onto the X-axis (showing the distribution of the maximum values), arranged in a matrix format.  Histograms representing the distribution of each variable are displayed along the diagonal of the matrix (in square matrices) or along the edges (in rectangular matrices).  The default matrix plot area patterns used in this graph can be adjusted in the Specific Plots Default Patterns dialog.

See also, Stats Graphs Matrix Plots.

Custom Graphs Matrix Plots


2D Icon Plots - Chernoff Faces

Chernoff faces is the most "elaborate" type of icon plot.  A separate "face" icon is drawn for each case; relative values of the selected variables for each case are assigned to shapes and sizes of individual facial features (e.g., length of nose, angle of eyebrows, width of face).  The assignment of variables represented in the graph to specific facial features is controlled in the Chernoff Face Definition dialog.

See also, Stats Icon Plots.

Custom Graphs Icons Plots


2D Icon Plots - Stars

In this type of icon plot, a separate star-like icon is plotted for each case; relative values of the selected variables for each case are represented (clockwise, starting at 12:00) by the relative length of individual rays in each star.  The ends of the rays are connected by a line.

See also, Stats Icon Plots.

Custom Graphs Icons Plots


2D Icon Plots - Sun Rays

In this type of icon plot, a separate sun-like icon is plotted for each case; each ray represents one of the selected variables (clockwise, starting at 12:00), and the length of the ray represents 4 standard deviations.  Data values of the variables for each case are connected by a line.

See also, Stats Icon Plots.

Custom Graphs Icons Plots


2D Icon Plots - Polygons

In this type of icon plot, a separate polygon icon is plotted for each case; relative values of the selected variables for each case are represented by the distance from the center of the icon to consecutive corners of the polygon (clockwise, starting at 12:00).

See also, Stats Icon Plots.

Custom Graphs Icons Plots


2D Icon Plots - Pies

In this type of icon plot, data values for each case are plotted as a pie chart (clockwise, starting at 12:00); relative values of selected variables are represented by the size of the pie slices.

See also, Stats Icon Plots.

Custom Graphs Icons Plots


2D Icon Plots - Columns

In this type of icon plot, an individual column graph is plotted for each case; relative values of the selected variables for each case are represented by the height of consecutive columns.

See also, Stats Icon Plots.

Custom Graphs Icons Plots


2D Icon Plots - Lines

In this type of icon plot, an individual line graph is plotted for each case; relative values of the selected variables for each case are represented by the height of consecutive break points of the line above the baseline.

See also, Stats Icon Plots.

Custom Graphs Icons Plots


2D Icon Plots - Profiles

In this type of icon plot, an individual area graph is plotted for each case; relative values of the selected variables for each case are represented by the height of consecutive peaks of the profile above the baseline.

See also, Stats Icon Plots.

Custom Graphs Icons Plots


Pairwise Missing Data Deletion

When pairwise deletion of missing data is selected, then cases will be excluded from any calculations involving variables for which they have missing data.  In the case of correlations, the correlations between each pair of variables are calculated from all cases having valid data for those two variables.

See also, Pairwise Deletion of Missing Data vs. Mean Substitution

Casewise vs. pairwise deletion of missing data


Casewise Missing Data Deletion

When casewise deletion of missing data is selected, then only cases that do not contain any missing data for any of the variables selected for the analysis will be included in the analysis.  In the case of correlations, all correlations are calculated by excluding cases that have missing data for any of the selected variables (all correlations are based on the same set of data).

See also, Casewise vs. pairwise deletion of missing data


Mean Substitution of Missing Data

When you select Mean Substitution, the missing data will be replaced by the means for the respective variables during an analysis.

See also, Casewise vs. pairwise deletion of missing data


Ignore Graph

This setting suppresses the display of data from the current plot.

See also Plot Layout.


Asymmetrical Distribution

If you split the distribution in half at its mean (or median), then the distribution of values on the two sides of this central point would not be the same (i.e., not symmetrical) and the distribution would be considered "skewed."

See also, Descriptive Statistics Overview.


Symmetrical Distribution

If you split the distribution in half at its mean (or median), then the distribution of values would be a "mirror image" about this central point.

See also, Descriptive Statistics Overview.


Negative Correlation

The relationship between two variables is such that as one variable's values tend to increase, the other variable's values tend to decrease.  This is represented by a negative correlation coefficient.

See also, Correlations - Introductory Overview.


Positive Correlation

The relationship between two variables is such that as one variable's values tend to increase, the other variable's values also tend to increase.  This is represented by a positive correlation coefficient.

See also, Correlations - Introductory Overview.


Coefficient of Determination

This is the square of the product-moment correlation between two variables (r²).  It expresses the amount of common variation between the two variables.

See also, Hays, 1988.


Nominal Scale

This is a categorical (i.e., quantative and not qualitative) scale of measurement where each value represents a specific category that the variable's values fall into (each category is "different" than the others but cannot be quantitatively compared to the others).

See also, Elementary Concepts.


Ordinal Scale

The ordinal scale of measurement represents the ranks of a variable's values.  Values measured on an ordinal scale contain information about their relationship to other values only in terms of whether they are "greater than" or "less than" other values but not in terms of "how much greater" or "how much smaller."

See also, Elementary Concepts.


Interval Scale

This scale of measurement allows you to not only rank order the items that are measured, but also to quantify and compare the sizes of differences between them (no absolute zero is required).

See also, Elementary Concepts.


Ratio Scale

This scale of measurement contains an absolute zero point, therefore it allows you to not only quantify and compare the sizes of differences between values, but also to interpret both values in terms of absolute measures of quantity or amount (e.g., time; 3 hours is not only 2 hours more than 1 hour, but it is also 3 times more than 1 hour).

See also, Elementary Concepts.


Custom Function

Custom functions take the form:  dependent variable = expression.  The expression (entered in the User-Defined Functions dialog) may contain constants, operators, functions and arguments (x in 2D functions, x and y in 3D functions, and x, y, and z in ternary graphs).  For example:

y = x^2+x

z = 2*x+3*y+12

z = 2*sin(2*sqrt(x^2+y^2))/sqrt(x^2)

v = 5*x - y**3 + 1/z


Logarithmic

This fits to the data, a logarithmic function of the form:

y = q*[log (x)]+b

          n

where the logarithm base (n) is selected by the user (by default, the natural logarithm log (base e) is selected, where e = 2.718...).  The base of the log function can be changed in the Fitting Options dialog.


Exponential Function

This fits to the data, an exponential function of the form:

y = b*exp(q*x)


Polynomial

This fits to the data, a polynomial function of the form:

                 2     3         n

y = b + b x + b x + b x +...+ b x

     0   1     2     3         n

where n is the order of the polynomial (1<n<6).  The order of the polynomial function can be changed in the Fitting Options dialog.


Uniform Distribution

The discrete Uniform distribution (the term first used by Uspensky, 1937) has density function:

f(x) = 1/N            x = 1, 2, ..., N

The continuous Uniform distribution has density function:

f(x) = 1/(b-a)        a < x < b

where

a	is the lower limit of the interval from which points will be selected

b	is the upper limit of the interval from which points will be selected


Cauchy Distribution

The Cauchy distribution (the term first used by Upensky, 1937) has density function:

                         2

f(x) = 1/(θπ*{1+[(x-η)/θ] })

0 < θ

where

η 	is the location parameter (median)

θ 	is the scale parameter

π 	is the constant Pi (3.1415...)

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


F Distribution

The F distribution (for x > 0) has density function (for ν = 1, 2, ...; ω = 1, 2, ...):

                                         ν/2

f(x) = {Γ[(ν+ω)/2]}/[Γ(ν/2)*Γ(ω/2)]*(ν/ω)    *

 (ν/2)-1                -(ν+ω)/2

x        * {1+[(ν/ω)*x]}

0 ≤ x < ∞

ν=1,2,..., ω=1,2,...

where

ν and ω 	are the degrees of freedom

Γ 	(gamma) is the Gamma function

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


Laplace Distribution

The Laplace (or Double Exponential) distribution has density function:

                -|x-a|/b

f(x) = 1/(2b) * e             -∞<x<∞

where

a	is the mean of the distribution

b 	is the scale parameter

e 	is Euler's constant (2.71...)

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


Logistic Distribution

The Logistic distribution has density function:

             -(x-a)/b     -(x-a)/b  -2

f(x) = (1/b)*e       *[1+e         ]

-∞<x<∞, 0<b

where

a	is the mean of the distribution

b	is the scale parameter

e 	is Euler's constant (2.71...)

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


Pareto Distribution

The standard Pareto distribution has density function (for positive parameter c ):

          c+1

f(x) = c/x         1 ≤ x, c < 0

where

c	is the shape parameter of the distribution

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


Student's t Distribution

The Student's t distribution has density function (for ν = 1, 2, ...):

                                -1/2

f(x) = Γ[(ν+1)/2]/ Γ(ν/2) * (ν*π)     *

              2    -(ν+1)/2

       [1 + (x /ν)]

where

ν 	is the degrees of freedom

Γ 	(gamma) is the Gamma function

π 	is the constant Pi (3.1415...)

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


Weibull Distribution

The Weibull distribution (Weibull, 1939, 1951; see also Lieblein, 1955) has density function (for positive parameters b, c, and θ):

                    c-1                c

f(x) = c/b*[(x-θ)/b]    * e^{-[(x-θ)/b]  }

θ < x, b > 0, c > 0

where

b	is the scale parameter of the distribution

c	is the shape parameter of the distribution

θ 	is the location parameter of the distribution

e 	is Euler's constant (2.71...)

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


Beta Distribution

The beta distribution (the term first used by Gini, 1911) is defined as:

                            ν-1       ω-1

f(x) = Γ(ν+ω)/(Γ(ν)Γ(ω)) * x   * (1-x)

0 ≤ x ≤ 1

ν > 0, ω > 0

where

Γ	(gamma) is the Gamma function

ν, ω	are the shape parameters

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


Binomial Distribution

The binomial distribution (the term first used by Yule, 1911) is defined as:

                         x    n-x

f(x) = [n!/(x!*(n-x)!)]*p  * q

for x = 0,1,2,...,n

where

p	is the probability of success at each trial

q	is equal to 1-p

n	is the number of independent trials

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


Chi-square Distribution

The Chi-square distribution is defined by:

            ν/2                (ν/2)-1    -x/2

f(x) = {1/[2    * Γ(ν/2)]} * [x        * e    ]

ν = 1, 2, ..., 0 < x

where

ν	is the degrees of freedom

e	is Euler's constant (2.71...)

Γ	(gamma) is the Gamma function

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


Exponential Distribution

The exponential distribution function is defined as:

          -λx

f(x) = λ*e

0 ≤ x < ∞

λ > 0

where

λ	(lambda) is an exponential function parameter (an alternative parameterization is scale parameter b=1/λ)

e	is Euler's constant (2.71...)

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


Gamma Distribution

The Gamma distribution (the term first used by Weatherburn, 1946) is defined as:

            c-1  (-x/b)

f(x) = (x/b)   *e      *[1/bΓ(c)]

0 ≤ x, b > 0, c > 0

where

Γ	(gamma) is the Gamma function

b	is the scale parameter

c	is the so-called shape parameter

e	is Euler's constant (2.71...)

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


Geometric Distribution

The geometric distribution (the term first used by Feller, 1950) is defined as:

              x-1

f(x) = p*(1-p)

where

p	is the probability that a particular event (e.g., success) will occur

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


Lognormal Distribution

The lognormal distribution (the term first used by Gaddum, 1945) has the probability density function:

                                   2   2

                1/2     -[log(x)-μ] /2σ

f(x) = 1/[xσ(2)   ] * e

0 ≤ x < ∞

μ > 0

σ > 0

where

μ	is the scale parameter

σ	is the shape parameter

e	is Euler's constant (2.71...)

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


Normal Distribution

The normal distribution (the term first used by Galton, 1889) function is determined by the following formula:

               1/2                         2

f(x) = 1/[(2*π)   * σ] * e**{-1/2*[(x-μ)/σ] }

-∞ < x < ∞

where

μ	is the mean

σ	is the standard deviation

e	is Euler's constant (2.71...)

π	is the constant Pi (3.14...)

See also, Bivariate Normal Distribution, Elementary Concepts (Normal Distribution), Basic Statistics - Tests of Normality, Distribution Fitting - Normal Distribution, Q-Q Plots - Normal Distribution, P-P Plots - Normal Distribution.

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


Poisson Distribution

The Poisson distribution (the term first used by Soper, 1914) is defined as:

         x    -λ

f(x) = (λ  * e   )/x!

for x = 0,1,2,..., 0 < λ

where

λ	(lambda) is the expected value of x (the mean)

e	is Euler's constant (2.71...)

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


Rayleigh Distribution

The Rayleigh distribution has the probability density function:

                  2   2

          2    -(x /2b )

f(x) = x/b  * e

0 ≤ x < ∞

b > 0

where

b	is the scale parameter

e	is Euler's constant (2.71...)

See also, Process Analysis.

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


Extreme Value Distribution
Extreme Value Distribution (Type I, Gumbel)

The extreme value (Type I) distribution (the term first used by Lieblein, 1953) has the probability density function:

                           -(x-a)/b

              -(x-a)/b   -e

f(x) = 1/b * e        * e

-∞ < x < ∞

b > 0

where

a	is the location parameter

b	is the scale parameter

e	is Euler's constant (2.71...)

This distribution is also sometimes referred to as the distribution of the largest extreme.

See also, Process Analysis.

For a complete listing of all distribution functions, see Distribution Functions, their Integrals and Inverse Distribution Functions


Printing Objects with Filled Background

Some printer drivers, by default, will change the order in which different graph components will be printed, and therefore, would override the "not transparent" options (e.g., the Filled Background option set in the Graphic Text Editor or in the Link/Embed Files dialog).  For example, this will result in the horizontal text under the embedded or linked object "showing through" the object.  To avoid this, select the Print TrueType Font as Graphics option in your Print Setup dialog.


Residual

The ith residual (ei) is equal to:

         ^

e = (y - y )

 i    i   i

where

yi	is the ith observed value

yi-hat	is the corresponding predicted value

See also, Multiple Regression


Symmetric Matrix

A matrix is symmetric if the transpose of the matrix is itself (i.e., A = A').  In other words, the lower triangle of the square matrix is a "mirror image" of the upper triangle with 1's on the diagonal (see below).

|1 2 3 4|

|2 1 5 6|

|3 5 1 7|

|4 6 7 1|


Custom Graphs vs. Stats Graphs

In addition to the specialized graphs which are available from the output dialogs of all statistical procedures, there are two general types of graphs accessible from the Graphs Gallery, pull-down menu Graphs, and toolbar and flying menus of all Scrollsheets and spreadsheets:

•	Stats Graphs (see Stats Graphs and Quick Stats Graphs), and

•	Custom Graphs.

The most important difference between these two types is that Stats Graphs produce statistical summaries or other representations of raw data in the selected variables of the current data file, whereas Custom Graphs provide a general tool to visualize numeric values in the currently highlighted block (which may contain values from custom defined subsets of numerical output or arbitrarily selected subsets of raw data).

See also,

Block Stats Graphs

Multiple Graph Layouts (Wizards, Templates)

Blank Graphs

Stats User-defined Graphs

  Graphs gallery

See also Customizing Graphs.


Stats Graphs vs. Custom Graphs

In addition to the specialized graphs which are available from the output dialogs of all statistical procedures, there are two general types of graphs accessible from the Graphs Gallery, pull-down menu Graphs, and toolbar and flying menus of all Scrollsheets and spreadsheets:

•	Stats Graphs (see Stats Graphs and Quick Stats Graphs), and

•	Custom Graphs.

The most important difference between these two types is that Stats Graphs produce statistical summaries or other representations of raw data in the selected variables of the current data file, whereas Custom Graphs provide a general tool to visualize numeric values in the currently highlighted block (which may contain values from custom defined subsets of numerical output or arbitrarily selected subsets of raw data).

See also,

Block Stats Graphs

Multiple Graph Layouts (Wizards, Templates)

Blank Graphs

Stats User-defined Graphs

  Graphs gallery

See also Customizing Graphs.


Scrollsheet

A Scrollsheet is a spreadsheet-like, scrollable table used in STATISTICA for displaying the results of analyses.  Results from consecutive analyses (or steps of an analysis) are presented in queues of Scrollsheets which are automatically closed on a "first in-first out" basis (see Window Manager).  The values presented in Scrollsheets can be converted into graphs via the right-mouse-button flying menu options.  These dynamic, flexable tables can also be customized (via the options available from the Scrollsheet Edit Menu) and the Scrollsheet contents can be saved as data for use as input in subsequent analyses.

For more information, see Scrollsheet Window Overview.  See also, STATISTICA BASIC - Scrollsheet Functions.


Bitmap Format

This format (filename extension*.bmp) is similar to another standard Windows graph file format--metafile in that it does not include the graph data and other analytic information (fitted equations, scaling options, etc.) supported by STATISTICA Graph graphics format.  However, unlike metafile (which stores dynamic representations ("definitions") of all graph components, allowing selective modifications of lines, text, etc., in other Windows applications), the bitmap format stores only a passive representation of pixels which form the graph.  Bitmaps can be opened by other Windows applications, but the customization or editing options of such graph representations will usually be limited to stretching/shrinking, cutting/pasting, and drawing "over" the graph.


STATISTICA Graph Format

Unlike other graphics formats such as metafiles and bitmaps, this (STATISTICA-specific) format not only stores the "image" of the current graph but also all information necessary to continue graph customization or graphical data analysis (including all data represented in the graph, fitted equations, links to and linked artwork, etc.).  Graphs stored in this format (filename extension *.stg) can be opened later (in any module of STATISTICA) allowing you to continue graphical data analysis (e.g., fit equations, add or merge new data series, etc.) or graph customization.  This format is recommended whenever you intend to use the graph again in the STATISTICA system or embed it or link it to other application documents using the MS Windows OLE conventions.


Metafile Format

The Windows Metafile format (filename extension*.wmf) stores a picture as a set of descriptions or definitions of all components of the graph and their attributes (e.g., segments of lines, specific fill patterns, text and text attributes, etc.).  Therefore, as compared to bitmaps, metafiles offer more flexible options for modification and customization in other Windows applications.  For example, when you open a metafile in the Microsoft Draw program, you can "disassemble" the graph, select and modify individual lines, fill patterns, colors, edit text and change its attributes, etc.  Note that not all applications which support the metafile graphics format support all graphics attributes supported by the Windows metafile standard (e.g., some applications do not support rotated text and thus all vertical axis labels saved in STATISTICA in metafile format will appear unrotated when opened in such applications).  Graphs saved in metafile format can also be dynamically linked to documents of other MS Windows applications using the OLE conventions.


Kurtosis

Kurtosis (the term first used by Pearson, 1905) measures the "peakedness" of a distribution.  If the kurtosis is clearly different than 0, then the distribution is either flatter or more peaked than normal; the kurtosis of the normal distribution is 0.  Kurtosis is computed as:

                                                            4

Kurtosis = [n*(n+1)*M  - 3*M *M *(n-1)]/[(n-1)*(n-2)*(n-3)*σ  ]

                     4      2  2

where:

Mj	is equal to:  Σ(xi-Meanx)**j

n	is the valid number of cases

σ**4	is the standard deviation (sigma) raised to the fourth power

See also, Descriptive Statistics Overview.


Skewness

Skewness (this term was first used by Pearson, 1895) measures the deviation of the distribution from symmetry.  If the skewness is clearly different from 0, then that distribution is asymmetrical, while normal distributions are perfectly symmetrical.

                              3

Skewness = n*M /[(n-1)*(n-2)*σ  ]

              3

where

M**3	is equal to:  Σ(xi-Meanx)**3

σ**3	is the standard deviation (sigma) raised to the third power

n	is the valid number of cases.

See also, Descriptive Statistics Overview.


Standard Deviation

The standard deviation (this term was first used by Pearson, 1894) is a commonly-used measure of variation.

The standard deviation of a population of values is computed as:

σ = √[Σ(x -μ)**2 / N]

         i

where

μ	is the population mean

N	is the population size.

The sample estimate of the population standard deviation is computed as:

s = √[Σ(x - xbar)**2 / n-1]

         i

where

xbar	is the sample mean

n	is the sample size.

See also, Descriptive Statistics Overview.


Variance

The variance (this term was first used by Fisher, 1918a) of a population of values is computed as:

σ**2 = Σ(x -μ)**2 / N

          i

where

μ	is the population mean

N	is the population size.

The unbiased sample estimate of the population variance is computed as:

s**2 = Σ(x - xbar)**2 / n-1

          i

where

xbar	is the sample mean

n	is the sample size.

See also, Descriptive Statistics Overview.


Standard Error

The standard error (this term was first used by Yule, 1897) is the standard deviation of a mean and is computed as:

std.err. = √(s**2/n)

where

s**2	is the sample standard deviation

n	is the sample size.

See also, Descriptive Statistics Overview.


Mode

A measure of central tendency, the mode (the term first used by Pearson, 1895) of a sample is the value which occurrs most frequently in the sample.

See also, Descriptive Statistics Overview, Ordinal Descriptive Statistics.


Median

A measure of central tendency, the median (the term first used by Galton, 1882) of a sample is the value for which one-half (50%) of the observations (when ranked) will lie above that value and one-half will lie below that value.  When the number of values in the sample is even, the median is computed as the average of the two middle values.

See also, Descriptive Statistics Overview, Ordinal Descriptive Statistics.


Harmonic Mean

The Harmonic Mean is a "summary" statistic used in analyses of frequency data; it is computed as:

H = n * 1/Σ(1/x )

               i

where

n	is the sample size.

See also, Ordinal Descriptive Statistics.


Geometric Mean

The Geometric Mean is a "summary" statistic useful when the measurement scale is not linear; it is computed as:

G = (x *x *...*x )**1/n

      1  2      n

where

n	is the sample size.

STATISTICA calculates the geometric mean via the logarithm (log):

log(G) = {Σ[log(x )]}/n

                 i

where

n	is the sample size.

See also, Ordinal Descriptive Statistics.


Crossed Factors

Some experimental designs are completely crossed (factorial designs), that is, each level of each factor appears with each level of all others.  For example, in a 2 (types of drug) x 2 (types of virus) design, each type of drug would be used with each type of virus.

See also, ANOVA/MANOVA.


Nested Factors

In nested designs the levels of a factor are nested (the term was first used by Ganguli, 1941) within the levels of another factor.  For example, if one were to administer four different tests to four high school classes (i.e., a between-groups factor with 4 levels), and two of those four classes are in high school A, whereas the other two classes are in high school B, then the levels of the first factor (4 different tests) would be nested in the second factor (2 different high schools).

See also, ANOVA/MANOVA.


n Point Moving Average Line

Each point on this moving average line represents the average of the respective sample and the n-1 number of preceding samples.  Thus, this line will smooth the pattern of means across samples, allowing the quality control engineer to detect trends.  You can specify the number of samples (n) that are to be averaged for each point in the plot.


Exponentially Weighted Moving Average Line

This type of moving average can be considered to be a generalization of the simple moving average.  Specifically, we could compute each data point for the plot as:

z  = λ*x-bar  + (1-λ)*z

 t          t          t-1

In this formula, each point zt is computed as λ (lambda) times the respective mean x-bart, plus one minus λ times the previous (computed) point in the plot.  The parameter λ (lambda) here should assume values greater than 0 and less than 1.  You may recognize this formula as the common exponential smoothing formula.  Without going into detail (see Montgomery, 1985, p. 239), this method of averaging specifies that the weight for historically "old" sample means decreases geometrically as one continues to draw samples.  This type of moving average line also smoothes the pattern of means across samples, and allows the engineer to detect trends more easily.


Independent vs. Dependent Variables

The terms dependent and independent variable apply mostly to experimental research where some variables are manipulated, and in this sense they are "independent" from the initial reaction patterns, features, intentions, etc. of the subjects.  Some other variables are expected to be "dependent" on the manipulation or experimental conditions.  That is to say, they depend on "what the subject will do" in response.  Independent variables are those that are manipulated whereas dependent variables are only measured or registered.

Somewhat contrary to the nature of this distinction, these terms are also used in studies where we do not literally manipulate independent variables, but only assign subjects to "experimental groups" based on some preexisting properties of the subjects.  For example, if in an experiment, males are compared with females regarding their white cell count (WCC), Gender could be called the independent variable and WCC the dependent variable.


Statistical Significance (p-level)

The statistical significance of a result is an estimated measure of the degree to which it is "true" (in the sense of "representative of the population").  More technically, the value of the p-level represents a decreasing index of the reliability of a result.  The higher the p-level, the less we can believe that the observed relation between variables in the sample is a reliable indicator of the relation between the respective variables in the population.  Specifically, the p-level represents the probability of error that is involved in accepting our observed result as valid, that is, as "representative of the population."  For example, the p-level of .05 (i.e.,1/20) indicates that there is a 5% probability that the relation between the variables found in our sample is a "fluke."  In other words, assuming that in the population there was no relation between those variables whatsoever, and we were repeating experiments like ours one after another, we could expect that approximately in every 20 replications of the experiment there would be one in which the relation between the variables in question would be equal or stronger than in ours.  In many areas of research, the p-level of .05 is customarily treated as a "border-line acceptable" error level.

See also, Elementary Concepts.


Macro

A Macro contains recorded keystrokes or mouse movements that are named and stored in a file.  You can later execute a specific macro and STATISTICA will perform each keystroke or mouse movement in the sequence in which they were recorded.

See also, Record Macro.


Dynamic Data Exchange (DDE Link)

A DDE (Dynamic Data Exchange) link between a "source" (or server) file (e.g., an Excel spreadsheet) and a STATISTICA data file (the "client" file), links the files in such a way that when changes are made to the data in the source file, the data will automatically be updated in the STATISTICA spreadsheet (client file).  DDE links can also be used in macro within a source file in order to open a channel to STATISTICA so that STATISTICA programs can be run (using STATISTICA Command Language) from within the source application.

See also, Creating Links (Dynamic Data Exchange).


Communality

In Principal Components and Factor Analysis, communality is the proportion of variance that each item has in common with other items.  The proportion of variance that is unique to each item is then the respective item's total variance minus the communality.  A common starting point is to use the squared multiple correlation of an item with all other items as an estimate of the communality (refer to Multiple Regression for details about multiple regression).  Some authors have suggested various iterative "post-solution improvements" to the initial multiple regression communality estimate; for example, the so-called MINRES method (minimum residual factor method; Harman & Jones, 1966) will try various modifications to the factor loadings with the goal to minimize the residual (unexplained) sums of squares.  Refer to the description of the Extraction dialog for the different methods available in the Factor Analysis module.


Matrix Ill-Conditioning

When STATISTICA needs to invert a correlation matrix (i.e., in Factor Analysis) and in this correlation matrix there are variables that are 100% redundant, then the inverse of the matrix cannot be computed.  In this case, STATISTICA will issue a respective warning and then artificially lower all correlations in the correlation matrix by adding a small constant to the diagonal of the matrix, and then restandardize it.  This procedure will usually yield a matrix that can be inverted.


Mean

The mean is a particularly informative measure of the "central tendency" of the variable if it is reported along with its confidence intervals.  Usually we are interested in statistics (such as the mean) from our sample only to the extent to which they are informative about the population.  The larger the sample size, the more reliable its mean.  The larger the variation of data values, the less reliable the mean (see also Elementary Concepts).

Mean = (Σx )/n

          i

where

n	is the sample size.

See also, Descriptive Statistics Overview.


Confidence Interval

The confidence intervals for the mean give us a range of values around the mean where we expect the "true" (population) mean is located (with a given level of certainty, see also Elementary Concepts).  In Basic Statistics you can request confidence intervals for any p-level; for example, if the mean in your sample is 23, and the lower and upper limits of the p=.05 confidence interval are 19 and 27 respectively, then you can conclude that there is a 95% probability that the population mean is greater than 19 and lower than 27.  If you set the p-level to a smaller value, then the interval would become wider thereby increasing the "certainty" of the estimate, and vice versa; as we all know from the weather forecast, the more "vague" the prediction (i.e., wider the confidence interval), the more likely it will materialize.  Note that the width of the confidence interval depends on the sample size and on the variation of data values.  The calculation of confidence intervals is based on the assumption that the variable is normally distributed in the population.  This estimate may not be valid if this assumption is not met, unless the sample size is large, say n = 100 or more.


Correlation

Correlation is a measure of the relation between two or more variables.  Correlation coefficients can range from −1.00 to +1.00.  The value of −1.00 represents a perfect negative correlation while a value of +1.00 represents a perfect positive correlation.  A value of 0.00 represents a lack of correlation.

See also, Correlation Overview

Pearson Correlation


Outliers

Outliers are atypical (by definition), infrequent observations.  Because of the way in which the regression line is determined in Multiple Regression (especially the fact that it is based on minimizing not the sum of simple distances but the sum of squares of distances of data points from the line), outliers have a profound influence on the slope of the regression line and consequently on the value of the correlation coefficient.  A single outlier is capable of considerably changing the slope of the regression line and, consequently, the value of the correlation.  Typically, we believe that outliers represent a random error that we would like to be able to control.  Needless to say, outliers may not only artificially increase the value of a correlation coefficient, but they can also decrease the value of a "legitimate" correlation.

The Brushing tool can be used to interactively remove outliers by pointing to them in the graph (to explore their influence on a linear or nonlinear function fitted to the data).


Hazard Rate

In Survival Analysis the hazard rate is defined as the probability per time unit that a case that has survived to the beginning of the respective interval will fail in that interval.  Specifically, it is computed as the number of failures per time units in the respective interval, divided by the average number of surviving cases at the mid-point of the interval.


Queue
Queue (of Scrollsheets or graphs)

The queue is the number of (unlocked) Scrollsheets or graphs that can be displayed on the screen at one time.  In STATISTICA, Scrollsheets and graphs are automatically managed in separate "queues" on a "first in-first out" basis.  For example, if the Scrollsheet queue depth is set to 3, then when the fourth Scrollsheet is created, the first one will close automatically.  There is no one recommended depth of the queue; the number of entries should be adjusted according to the type of analysis, size of the screen and individual preferences.  You can change the depth of the queue in the Window Manager dialog; you can also control the numbers of windows (Scrollsheets or graphs) in the screen by either locking them (in the Window Manager) or closing them manually.


Screen Catcher

The "Screen Catcher" is a STATISTICA utility which allows you to select any rectangular area of the screen (or the entire screen) and copy it as bitmap to the Clipboard.  The copied area may contain graphs, Scrollsheets, spreadsheets, or even screens from other applications (if they are currently displayed on the screen).  The copied bitmap may then be pasted into STATISTICA graphs, or any other application which supports bitmaps.


Clipboard

The Clipboard is used to temporarily "hold" cut or copied information (text or graphics) until the information is pasted into a specific application or until some other text or graph is cut or copied (replacing the previous contents of the Clipboard).  For more information on copying text, see Copy and Copy Raw; for information on Clipboard operations in graphs, see Paste Special.


Jump
Jump (in Help)

STATISTICA's hypertext based, on-line help enables you to "jump" to or change help topics by clicking on the name of the topic which is underlined with a solid line (you can return to the previous point by pressing the Go Back button on the Help toolbar).  When a topic is underlined with a dotted or broken line, then if you click on that topic, a pop-up window containing more information on that topic will appear.


User-defined Functions
User-defined Functions in Graphs

All user-defined function equations in STATISTICA graphs are of the same form, e.g., dependent variable = expression.  On the left side of the equation you may specify the dependent variable; for example:  y = x^2 + x.  However, the left side of the equation is optional (e.g., you can enter the equation as:  = x^2 + x or simply as:  x^2 + x.  On the right side of the equation, the expression may contain Constants, Operators, Functions (including Distributions and their Integrals), and Arguments.  For more information on user-defined functions in STATISTICA, see User-Defined Functions.  Note that user-defined functions which can be specified in graph Plot Layout dialogs are plotted over (i.e., overlaid) and not fitted to the data.  In order to fit (and plot) user-defined functions to the data, use the Nonlinear Estimation module.

See also, Eps.


Superscripts in Graph Text

Superscripts can be placed in graphic text by using the appropriate Control Characters wherever you can edit the desired text (e.g., edit titles in the Titles dialog, text scale values in the Scale Options dialog, etc.) or enter new text (e.g., in the Graphic Text dialog).

To create a superscript, use the Control Characters @U before the text string to enable the superscript text and the Control Characters @E at the end of the text string to disable the superscript text and return to normal text (note, it is not necessary to enter @E to disable the superscript if no more text follows the superscript text).  Superscripts and Subscripts can be nested in many levels.  The @E Control Characters will disable only one level of the nested superscripts or subscripts at a time.  You will need to enter the Control Characters @E for each level that you want to disable (e.g., the Control Characters @U(a+bx)@U2@E@E will place the two-level superscript (a+bx)**2 in the desired text and any text following these superscripts will be "normal" text).  Alternatively, you can use the Control Characters @H instead of multiple @E's to end all levels of the superscripts and subscripts in one step.


Subscripts in Graph Text

Subscripts can be placed in graphic text by using the appropriate Control Characters wherever you can edit the desired text (e.g., edit titles in the Titles dialog, text scale values in the Scale Options dialog, etc.) or enter new text (e.g., in the Graphic Text dialog).

To create a subscript, use the Control Characters @D before the text string to enable the subscript text and the Control Characters @E at the end of the text string to disable the subscript text and return to normal text (note, it is not necessary to enter @E to disable the subscript if no more text follows the subscript text).  Superscripts and Subscripts can be nested in many levels.  The @E Control Characters will disable only one level of the nested superscripts or subscripts at a time.  You will need to enter the Control Characters @E for each level that you want to disable (e.g., the Control Characters @D(a+bx)@U2@E@E will place the subscript (a+bx) with its superscript 2 in the desired text and any text following this will be "normal" text).  Alternatively, you can use the Control Characters @H instead of multiple @E's to end all levels of the superscripts and subscripts in one step.


Boldface in Graph Text

Graphic text can be made bold by using the appropriate Control Characters wherever you can edit the desired text (e.g., edit titles in the Titles dialog, text scale values in the Scale Options dialog, etc.) or enter new text (e.g., in the Graphic Text dialog).  To make the desired text bold, place the Control Characters @B at the beginning of the text string to enable the bold text and again at the end of the text string to disable the bold font style (note, it is not necessary to enter @B at the end of the text string if you want all of the remaining text to be bold).  You can end all font attributes (i.e., bold, italics, underline) in the text using the Control Characters @Z at the end of the text string instead of the individual Control Characters for each attribute.


Underline in Graph Text

You can underline specific Graphic text by using the appropriate Control Characters wherever you can edit the desired text (e.g., edit titles in the Titles dialog, text scale values in the Scale Options dialog, etc.).  To underline the desired text, place the Control Characters @X at the beginning of the text string to enable the underline and again at the end of the text string to disable the underline font style (note, it is not necessary to enter @X at the end of the text string if you want all of the remaining text to be underlined).  You can end all font attributes (i.e., bold, italics, underline) in the text using the Control Characters @Z at the end of the text string instead of the individual Control Characters for each attribute.


Italics in Graph Text

You can italicize specific Graphic text by using the appropriate Control Characters wherever you can edit the desired text (e.g., edit titles in the Titles dialog, text scale values in the Scale Options dialog, etc.) or enter new text (e.g., in the Graphic Text dialog).  To underline the desired text, place the Control Characters @I at the beginning of the text string to enable the underline and again at the end of the text string to disable the underline font style (note, it is not necessary to enter @I at the end of the text string if you want all of the remaining text to be underlined).  You can end all font attributes (i.e., bold, italics, underline) in the text using the Control Characters @Z at the end of the text string instead of the individual Control Characters for each attribute.


Legend Symbols in Graph Text

Legend symbols for individual plots (numbered 1 through 8) can be inserted in Graphic text using the appropriate Control Characters wherever you can edit the desired text (e.g., edit titles in the Titles dialog, text scale values in the Scale Options dialog, etc.) or enter new text (e.g., in the Graphic Text dialog).  The Control Characters for plot legend symbols are:

@L[plot number, select number]:  Specify the plot number (1 through 64) and optionally the selection number (applicable to multiple-subset graphs).  In the case of 2D and matrix multiple-subset plots, when you specify the selection number, the program will place the point marker for that subset next to the text.  For multiple-subset icon plots, when you specify the selection number, the specified subsetted icon border pattern will be placed next to the text.

@C[level number]:  Specify the level number in order to insert the line or surface pattern for that level of the contour or surface plot next to some text.

@V[level value]:  Alternatively, you can specify the level value in order to insert the line or surface pattern for that level of the contour or surface plot next to some text.

@N[level number]:  The Z-axis of 3D surface or contour plots is divided into a specified number of surface or contour levels (via the Surface Levels option in the 3D Graphs-More Options dialog) which is reflected in the number of surface colors or line patterns in the plot.  Specify here the number of the contour or surface plot level in order to place the upper-bound value for that Z-axis level, next to the respective line or surface pattern.  Whenever you change the number of surface levels in the 3D Graphs-More Options dialog (i.e., change the scale of the Z-axis), the program will automatically adjust these values to reflect the change.


Control Characters (Text Formatting) - Part I

Control Characters are specific characters that can be entered in graphic text in order to customize the text (see Control Characters).  A partial list of available Control Characters is displayed below, for more Control Characters, see also Control Characters (Text Formatting) - Part II.

@D	Subscript.  Makes the text following this code subscripts.

@U	Superscript.  Makes the text following this code superscripts.

@E	Ends one level of super- or subscript.

@H	Ends all levels of the superscripts and subscripts and returns to the default text level.

@I	Italics.  Toggles on (place Control Character before text string) and off (place Control Character after text string) italicized text.

@B	Boldface.  Toggles on (place Control Character before text string) and off (place Control Character after text string) bold text.

@X	Underline.  Toggles on (place Control Character before text string) and off (place Control Character after text string) underlined text.

@K	Begins a custom font definition for a selected portion of text.

@Z	Returns all italicized, bold and/or underlined text to the default format and ends the custom font definition.

@A	Inserts a line break (alternatively, click CTRL+ENTER when you are in the Graphic Text Editor).


Control Characters (Text Formatting) - Part II

Control Characters are specific characters that can be entered in graphic text in order to customize the text (see Control Characters).  A partial list of available Control Characters is displayed below, for more Control Characters, see also Control Characters (Text Formatting) - Part I.

@L[plot number, select number]  Inserts the plot symbol (for plots 1 - 64).

@F	Inserts the equation for the fitted function (default: plot #1).

@C[level number]  Inserts the line or surface pattern for the specified legend.

@V[level value]  Inserts the line or surface pattern for the specified level of the contour or surface plot.

@N[level number]  Places the upper-bound value for the specified contour or surface plot level next to the respective contour line or surface pattern.

@T[4] or @T  Tabs over 4 characters (the default value).

@T[8]  Tabs over 8 characters.

@S[point value]  Changes the line spacing (default: increase by 4 points)


Fixed Legends

By default, when a graph is created, the legend is fixed (unmovable), which means that its position is automatically determined and the graph is moved to the left in the window to leave space for the legend.  You can make the graph legend movable so that you can reposition it in the graph and customize the text (e.g., add text beyond the 20 character limit, adjust line spacing and the distance between the legend symbols and the text, etc.) and other attributes of the graph legend by selecting the Move Legend option from the right-mouse-button menu (click on the fixed legend with the right-mouse-button).


Movable Legends

Unlike fixed legends, graph legends which have been made movable (via the Move Legend option from the legend right-mouse-button menu) can be repositioned in the graph and the text can be customized (e.g., text can be added beyond the 20 character limit, the line spacing and distance between the legend symbols and the text can be adjusted, etc.) as well as other attributes of the graph legend.


Legends

Legends can be treated in two ways in STATISTICA graphs: either as fixed legends or movable legends.  By default, when a graph is created, the legend is fixed (unmovable), which means that its position is automatically determined and the graph is moved to the left in the window to leave space for the legend.  You can make the graph legend movable so that you can reposition it in the graph and customize the text (e.g., add text beyond the 20 character limit, adjust line spacing and the distance between the legend symbols and the text, etc.) and other attributes of the graph legend by selecting the Move Legend option from the right-mouse-button menu (click on the fixed legend with the right-mouse-button).  Fixed legends can be temporarily removed from the graph by selecting the Fixed Graph Legend OFF option from the right-mouse-button flying menu.  The fixed legend can then be placed back into the graph (in its default position) by selecting the Fixed Graph Legend ON option available from the "long" flying menu accessible by click the right-mouse-button anywhere in the empty space outside the graph region.  Both fixed and movable legends can be included in the same graph (see Legends for details).


Calculating Contour Levels and Distance (Default Setting:  Automatic)

STATISTICA offers a selection of facilities to custom define the levels for contour and surface plots (see Specify Contour Levels); also, custom contour/surface specifications can be saved and applied to new graphs.

If no custom definition of levels is specified (the option Automatic is enabled in the 3D Graphs/More Options dialog), then the values of the contour levels are calculated as follows:

(1)  Distance between contours = (Zmax - Zmin)/(n + Mode coeff.)

(2)  First Level (for line contour plot) = Zmin + .05*(Distance between contours)

First Level (for area contour plot) = Zmin

where

n 	is the number of levels (as specified in the No. of Levels field, default = 16)

Mode coeff. 	is the type of contour plot; 1=line contour, 0=area contour

Zmin 	is the minimum value on the Z-axis

Zmax 	is the maximum value on the Z-axis

For 3D surface graphs, you can choose to also display the surface contour in the graph via the 3D Graphs/More Options dialog.

The default number of levels (n), as well as the default fill and line patterns used to represent the levels, can be adjusted in the Global Defaults - Contour Definition dialog.

Additionally, the surface contour distance can be specified.  The distance value that you specify in the 3D Graphs/More Options dialog is interpreted as the distance between the contour and the Zmin value (see above) in percentiles of (Zmax - Zmin).  This number can be between 0% and 255% (the default distance value is 20%).


Trimmed Means

For certain Stats Graphs (e.g., 2D Box Plots, 3D Box Plots, Categorized Box Plots), an option is available to trim the extreme values from the distribution of values of a variable.  For example, you can trim (i.e., remove) the lowest 5% and the highest 5% from the distribution of values.  The mean of the trimmed distribution of values is referred to as a "trimmed mean" (this term was first used by Tukey, 1962).


2D Box Plots - Regular (Format) Box Plots

Regular box plots are used to examine and present the ranges of values of a variable as categorized by another variable.  When more than one Y-variable is selected, a sequence of graphs will be produced (one for each Y-variable selected).

See also, Stats 2D Box Plots.


2D Box Plots - Multiple (Format) Box Plots

Unlike regular box plots in which the ranges of values of one variable is represented, the multiple box plot represents ranges of values of multiple variables.  A different point marker, fill pattern, and color is used for each of the multiple variables and referenced in the legend.  This type of box plot is used to compare ranges of values between several variables (or several functions) by overlaying them in a single graph that uses one common set of scales (e.g., comparisons between several simultaneous experimental processes, social phenomena, stock or commodity quotes, shapes of operating characteristics curves, etc.).

See also, Stats 2D Box Plots.


Editing Graph Data for Box and Whisker Format Graphs

For box and whisker type graphs, the data are organized in the Graph Data Editor, in triplets of values for the box (X, Box 2, Box 1) and/or whiskers (X, Whisker 2, Whisker 1) and in pairs of values for the midpoint (X, middlepoint).  The X values in this editor, are integrated, in that if you edit (for example) the X value for the Midpoint, then the respective X values for the Box and/or Whiskers will also be changed accordingly.


Non-outlier Range

The non-outlier range is the range of values in the 2D Box Plots, 3D Sequential Graphs - Box Plots, or Categorized Box Plots, which fall below the upper outlier limit (for example, +1.5 * the height of the box) and above the lower outlier limit (for example, -1.5 * the height of the box).  For more information on how outliers are determined in box plots, see Outliers and Extremes.


Eps

In fitted function equations, eps stands for epsilon (ε), the random error associated with measurement.


Box-Ljung Q Statistic

In Time Series analysis, you can shift a series by a given lag k.  For that given lag, the Box-Ljung Q statistic is defined by:

                  2

Q  = n*(n+2)*Sum(r /(n-l))

 k                i

(for i = 1 to k)

When the number of observations is large, then the Q statistic has a Chi-square distribution with k-p-q degrees of freedom, where p and q are the number of autoregressive and moving average parameters, respectively.


Apply Common Value

This edit field is available in all dialogs for entry of multiple parameter values.  You can enter specific values individually for each of the parameters in this dialog or enter one Common Value and then click on the Apply button to transfer this value to each parameter field.


Animated Stratification

When you select the Animated Stratification option from the View pull-down menu or click on the [image] toolbar button, the Animated Stratification dialog will open allowing you to interactively view the graph layer by layer (applicable to 3D Sequential Graphs such as surface plots, ribbon/line plots, box plots, block plots, etc.).  When you select this option, STATISTICA will generate the graph in layers representing consecutive cross-sections corresponding to variables in the graph (e.g., ribbons, blocks, etc.), levels of variables (e.g., in 3D histograms) or determined by the current settings of the X: and Y: values in the Number of Cuts option in the General Layout:  3D Sequence Graphs dialog.  After each "slice" is generated, STATISTICA will pause until you click on either the Continue button, the Break button, or close the dialog (Cancel).  When you click on the Continue button, the next (sequential) "slice" of the graph will be displayed.  Clicking on the Break button will close the Animated Stratification dialog and complete the axes and titles of the graph without completing the missing layers.  Using the Break button, you can create complete (labeled) graphs that represent each or selected "slices" of the original graph.


"X-ray" Facility to Explore Layers of Graphs

In the default pointing mode (when the point tool [image] is enabled), you can selectively highlight individual plots in the graph by pressing the left-mouse-button anwhere on the selected plot.

For example, in sequntial 3D plots, this option allows you to temporarily highlight complete series of data even if the respective plots are almost entirely covered by other plots (as if you were "X-raying" a plot).  If the plot of interest is covered entirely, click on the respective row of the legend to achieve the same result.  This facility is also useful in examining other types of 2D and 3D graphs, as it allows you to uncover invisible areas of specific plots or discriminate between different plots (e.g., in multiple scatterplots).  In 3D histograms, which belong to a "one-plot only" category of graphs, the selection facility can also be useful to review the hidden layers of the graph, because in those specific graphs (3D histograms), the tool is automatically set to highlight individual layers and not separate plots.


Const in STATISTICA BASIC

Const - declares the value of a numeric or string constant.  Once defined, the value of the constant cannot be changed within the STATISTICA BASIC program.

Example:

Const Pie = 3.14;                 {declares value of numeric constant Pie}

Const Cake$ = 'Pie are Square';   {declares value of string constant Cake$}


Burt Tables

Multiple correspondence analysis expects as input (i.e., the program will compute prior to the analysis) a so-called Burt table.  The Burt table is the result of the inner product of a design or indicator matrix.  If you denote the data (design or indicator matrix) as matrix X, then matrix product X'X is a Burt table); shown below is an example of a Burt table that one might obtain in this manner.

                  SURVIVAL         AGE              LOCATION

                  ---------   -------------   ----------------------

                  NO   YES    <50 50-69 69+   TOKYO  BOSTON GLAMORGN

                  ---------   -------------   ----------------------

SURVIVAL:NO       210    0     68   93   49     60     82     68

SURVIVAL:YES        0  554    212  258   84    230    171    153

AGE:UNDER_50       68  212    280    0    0    151     58     71

AGE:A_50TO69       93  258      0  351    0    120    122    109

AGE:OVER_69        49  84       0    0  133     19     73     41

LOCATION:TOKYO     60  230    151  120   19    290      0      0

LOCATION:BOSTON    82  171     58  122   73      0    253      0

LOCATION:GLAMORGN  68  153     71  109   41      0      0    221

Overall, the data matrix is symmetrical.  In the case of 3 categorical variables (as shown above), the data matrix consists 3 x 3 = 9 partitions, created by each variable being tabulated against itself, and against the categories of all other variables.  Note that the sum of the diagonal elements in each diagonal partition (i.e., where the respective variables are tabulated against themselves) is constant (equal to 764 in this case).  The off-diagonal elements in each partition in this example are all 0.  If the cases in the design or indicator matrix are assigned to categories via fuzzy coding, then the off-diagonal elements of the diagonal partitions are not necessarily equal to 0.

For more information, refer to the description of Correspondence Analysis, and to the description of Burt tables in the context of that module.


Inertia (in Correspondence Analysis)

The term inertia in correspondence analysis is used by analogy with the definition in applied mathematics of "moment of inertia," which stands for the integral of mass times the squared distance to the centroid (e.g., Greenacre, 1984, p. 35).  Inertia is defined as the total Pearson Chi-square for a two-way frequency table (e.g., as can also be computed in the Basic Statistics  or Log-Linear modules) divided by the total sum of all observations in the table.

For more information, see the the Correspondence Analysis module.


Quality (in Correspondence Analysis)

The term Quality in the context of correspondence analysis pertains to the quality of representation of the respective row point in the coordinate system defined by the respective numbers of dimensions, as chosen by the user.  The quality of a point is defined as the ratio of the squared distance of the point from the origin in the chosen number of dimensions, over the squared distance from the origin in the space defined by the maximum number of dimensions (remember that the metric in the typical correspondence analysis is Chi-square).  By analogy to Factor Analysis, the quality of a point is similar in its interpretation to the communality for a variable in factor analysis.

Note that the Quality measure reported by STATISTICA is independent of the chosen method of standardization, and always pertains to the default standardization (i.e., the distance metric is Chi-square, and the quality measure can be interpreted as the "proportion of Chi-square accounted for" for the respective row, given the respective number of dimensions).  A low quality means that the current number of dimensions does not represent well the respective row (or column).

For more information, see the description of the Correspondence Analysis module.


Predictive Mapping

One application of multiple correspondence analysis is to perform the equivalent of a Multiple Regression for categorical variables, by adding supplementary columns to a design matrix (see also Burt tables).  For example, suppose you had a design matrix containing various categorical indicators of health related behaviors (e.g., whether or not the individual smoked, exercised, etc.).  You could add two columns to indicate whether or not the respective subject had or had not been ill over the past year (i.e., you could add one column Ill and another column Not ill, and enter 0's and 1's to indicate each subject's health status).  If in a simple correspondence analysis of the design matrix, you added those columns as supplementary columns to the analysis, then (1) the summary statistics for the quality of representation (see the Correspondence Analysis Introductory Overview) for those columns would give you an indication of how well you can "explain" illness as a function of the other variables in the design matrix, and (2) the display of the column points in the final coordinate system would provide an indication of the nature (e.g., direction) of the relationships between the columns in the design matrix and the column points indicating illness.  This technique (adding supplementary points to a multiple correspondence analysis) is also called predictive mapping.

For more information, see the description of the Correspondence Analysis module.


? - Electronic Manual

Pressing the question mark [image] found in the upper right hand corner of a dialog box, allows the user to access the relevant help topics for the dialog in the Electronic Manual (alternatively, press F1).  Pressing the toolbar question mark [image] button (the last button on every toolbar) will bring up the section of the Electronic Manual related to that toolbar and the currently active window.


? in  STATISTICA BASIC

Some parameter values in STATISTICA BASIC function calls can be ignored (i.e., left at their default values) by replacing them by a question mark (?) or placing a "?" before the parameter name (for text parameters, a "$" must be used at the end of the word).

For more information on using the "?" in STATISTICA BASIC, see How to Set (or Leave Unchanged) Default Values of Function Parameters.


Stiffness Parameters (in Fitting Options)
Stiffness Parameter (in Fitting Options)

The function that controls the weight (see Distance-Weighted Least Squares Fitting) is determined by the Stiffness parameter which can be modified on the Fitting Options dialog.  Thus, the stiffness parameter determines the degree to which the fitted curve depends on local configurations of the analyzed values.

The lower the coefficient, the more the shape of the curve is influenced by individual data points (i.e., the curve "bends" more to accommodate individual values and subsets of values).

The range of the stiffness parameters is 0 < s < 1.  Large values of the parameter produce smoother curves that adequately represent the overall pattern in the data set at the expense of local details.  See also Negative Exponentially-Weighted Fitting and Spline Fitting.

See also, McLain, 1974.


Mass (in Correspondence Analysis)

The term mass in correspondence analysis is used to denote the entries in the two-way table of relative frequencies (i.e., each entry is divided by the sum of all entries in the table).  Note that the results from correspondence analysis are still valid if the entries in the table are not frequencies, but some other measure of correspondence, association, similarity, confusion, etc.  Since the sum of all entries in the table of relative frequencies is equal to 1.0, one could say that the table of relative frequencies shows how one unit of mass is distributed across the cells of the table.  In the terminology of correspondence analysis, the row and column totals of the table of relative frequencies are called the row mass and column mass, respectively.

For more information, see the description of the Correspondence Analysis module.


Graph Window

The graphics window displays the graph created from a Scrollsheet, spreadsheet, or via a menu option (see also, Graphics Overview).

Graphics Window Toolbar Buttons

File Menu

Edit Menu

View Menu

Insert Menu

Layouts Menu

Analysis Menu

Graphs Menu

Options Menu

Window Menu

Help Menu


Graphics Window Analysis Menu

These general options are available from the Analysis pull-down menu.

Startup Panel

Resume Analysis

STATISTICA BASIC

Command Language (SCL)

Quick Basic Stats

  Descriptive Statistics

  Correlation Matrices

  Frequency Tables

  Probability Calculator

  More....

Other Statistics


Graphics Window Toolbar Buttons

The following is a list of toolbar buttons specific to the graph window.  For quick access to information about this window, see Overview of Graphics Options in STATISTICA.

For more information on specific dialogs or options, click on the [image] button in the upper-right corner of the dialog.

For more general information, see STATISTICA Index.

  Change Show Window

 / [image]  Dynamic Mode/Fixed Mode

  STATISTICA Module Switcher

  Workbook Management

  3D Graph Rotation

  Animated Stratification (3D Sequential Graphs only)

  Edit Graph Data (Graph Data Editor)

  Brushing Tool (in the first order graphs only; not in linked/embeded graphs)

  Fixed Graph Proportion (Maintain Graph Aspect Ratio)

  Change Graph Proportion

  Adjust Graph Margins, Plot Area

  Snap to Grid

  Graphics Zoom In Tool

  Graphics Zoom Out Tool

  Selection Mode

  Enter Text (Graphic Text Editor)

  Draw Rectangles, Squares

  Draw Rounded Rectangles, Squares

  Draw Ovals, Circles

  Draw Arc

  Freehand/Polyline

  Draw Arrow, Error Bars

  Insert Object

  Line Attributes

  Fill Attributes

  Bring to Front

  Send to Back

  Increase All Fonts by 16% (CTRL - 4%)

  Decrease All Fonts by 16% (CTRL - 4%)

  Graphs Gallery

  Open Graph File

  Save Graph File

  Print Graph

  Print Preview

  Cut

  Copy

  Paste

  Electronic Manual


    Dynamic and Fixed Toolbar Buttons

When you select an object for editing (i.e., click on an object), the current status of that object (i.e., Dynamic or Fixed mode) is displayed by the status Toolbar button.  You can change the status of the object from Fixed to Dynamic modes or from Dynamic to Fixed modes by clicking on the respective Toolbar button (see below).

Dynamic Mode

Fixed Mode

See also, Using Dynamic (Coordinate) Mode in Categorized and Matrix Graphs


  Dynamic and Fixed Toolbar Buttons - Dynamic Mode

When the Dynamic mode is selected, the object that you are inserting or adding to the graph will be anchored against the X and Y axis scales of 2D graphs and not the physical window coordinates; thus its position will be dynamically adjusted as you make changes to the graph.  (Note that when you insert or add an object in 3D graphs, the Dynamic option cannot be used due to the lack of fixed 2D graph coordinates.  Thus, the object positioned on the screen of a 3D or 4D graph may lose its relation to the specific elements of the graphs when you change the graph, e.g., resize, rescale, or rotate it.)


  Dynamic and Fixed Toolbar Buttons - Fixed Mode

When the status Toolbar button is depressed, the object will be assigned to a Fixed window location and its respective position in the graph will remain unchanged when you make adjustments to the graph (e.g., when you rescale the graph); thus it will be unrelated to any specific parts of the graph.

Depending on the current status (Dynamic or Fixed), the cursor coordinates displayed in the Toolbar Show window represent either the X- and Y-axis scale coordinates (respectively) or window coordinates as percentages of the total window width and height (the lower left corner is [0%, 0%] the upper right corner is [100%, 100%]).


Dynamic Graph Data Links - Overview

Dynamic Graph Data Links are links between STATISTICA spreadsheet data and the graph (i.e., the graph data) in Stats Graphs, Quick Stats Graphs, Block Stats Graphs, Custom Graphs, or embedded graphs (e.g., Scatterplots w/Histograms, Scatterplots w/Box Plots, embedded graphs created with the Multiple-Graph AutoLayout Wizard, or compound graphs created in the Quality Control module) which have been created from that spreadsheet.  Links in the currently open graphs can be managed in the Graph Data Links dialog (accessible from the pull-down menu Graphs).

How Auto Update Works.  When the data are linked (by default, the respective Graph Data Links (Auto Update) option is enabled in the STATISTICA Defaults:  General dialog), you can make changes to the spreadsheet data and the respective graph(s) will automatically be updated to reflect those changes.  By default, the link is restricted to the specific data file from which the graph was produced, but this setting can be changed to the "current data file" (allowing for easy "replacement" of data in a graph, see below).  Note that the entire Auto Update option can be disabled.  You can do so by de-selecting the Graph Data Links (Auto Update) option in the STATISTICA Defaults:  General dialog.

Management of Links.  Links between the spreadsheet and graph(s) can be managed in the Graph Data Links dialog (accessible via the Graphs pull-down menu).  Note that if you are about to change more than just a single value in the spreadsheet, you may want to temporarily disable the links (or close the graphs) in order to avoid delays caused by graph updates after every edit action.  If you do not want to establish any links between the spreadsheet data and graphs (before the graphs are created), you can de-select the Graph Data Links (Auto Update) option in the STATISTICA Defaults:  General dialog.

Applying Links to New Data Files.  Instead of a specific data file, a graph can be linked to the "current data file" (see the dialog Change Graph Data Link).  Also, note that the links maintained between STATISTICA data files and graphs are stored in terms of specific variable and case numbers and not names (e.g., for a simple scatterplot, it will store the variable numbers 1 and 2 instead of the variable names MEASUR1 and MEASUR2).  This allows you to re-create a graph (or a set of graphs) for a new data set simply by changing the data file (as long as the respective variable numbers and case numbers are present in the new data set).  For example, while a graph (linked to the "current data set") is currently open, you can quickly open consecutive data sets (e.g., from the list of recently used data files in the File menu), and watch the current graph automatically update for each new data set.

Technical Note:  Updating Customized Graphs.  The Auto Update operation will recreate the graph (with updated data) as it was originally defined from the respective variable(s) in the current data file.  Any inserted objects (e.g., drawn arrows, lines, pictures) will be preserved during the updating of the graph.  However, customization of the graph point markers, axes, gridlines, etc., customizations made via Brushing or in the General Layout, Plot Layout, or Scale Options dialogs after the graph was created will revert to the default styles, colors, etc. used to create a new graph (see the respective options in the Graph Data Links).


  Graph Data Links

This dialog allows you to manage links between the data spreadsheet and Stats Graphs, Quick Stats Graphs, Custom Graphs, Block Stats Graphs, or embedded graphs (e.g., Scatterplots w/Histograms, Scatterplots w/Box Plots, embedded graphs created with the Multiple-Graph AutoLayout Wizard, or compound graphs created in the Quality Control module)

For more information, see Dynamic Graph Data Links Overview.

Graph Data Links dialog:

Graph/Linked to

Update

Ask before performing automatic updates of modified graph

Don't update graphs embedded into this one

Update Now

Change Link

Break Link


  Graph Data Links - Don't Ask before performing automatic updates of modified graph

Deselecting this option enables the user to preserve any changes made to the graph that may be overwritten when the graph is automatically updated.  In those cases where some edits may be overwritten (e.g., changes to scale values, edited titles, point labels made via brushing, etc.), then before the graph is automatically updated, a dialog would come up, warning you that you may lose those edits when the graph is updated.


This graph window is about to be Auto Updated

This dialog box will open when STATISTICA is about to auto update a customized graph.  If you select Continue, the graph will auto update and you may lose some customizations (e.g., titles).  If you press the Don't Update Now button, the graph will not be updated at this time.

If you check the box marked Perform future updates without asking this dialog will be suppressed (for the current graph) and when the graph is auto-updated some of your editing or graph customizations may be lost without warning.  Checking this box would be equivalent to checking Don't ask before performing automatic updates of modified graphs in the Graph Data Links dialog.


  Graph Data Links - Don't update graphs embedded into this one

Select this option in order to prevent the embedded graph(s) in a compound graph (e.g., in Quality Control, scatterplot w/histogram, scatterplot w/box plot, multiple graph layout, etc.) from being automatically updated when the parent graph is updated.


  Graph Data Links - Update

This area of the dialog displays the current status of each graph created in the current session.  The link status of a graph can be changed by first highlighting the graph name and then clicking on one of the radio buttons described below.  (Note that in cases where the graph is not linked, then the buttons in this dialog will be dimmed.)

Automatic:  This is the default link status.  When Automatic is selected, you can make changes to the spreadsheet data and the respective graph will automatically be updated to reflect those changes.

Manual:  When you select Manual, then the link between the spreadsheet and graph will only be updated when you click on the Update Now button (see below) or the Update Graph option from the graph window File pull-down menu.

Locked (temporary):  Click on this option in order to lock the highlighted graph (i.e., temporarily break the link between the spreadsheet and graph) so that it will not be updated automatically or manually.  This option is useful when you intend to preserve the contents (i.e., protect from updating data) of one or more graphs embedded in another (master) graph, when that master graph is auto updated or manually updated.  (Note that, by default, data in all unlocked graphs embedded in a master graph are updated when the master graph is updated.)  In order to permanently break the link, use the Break Link option.


  Graph Data Links - Graph/Linked to

Graph:  The type and/or name of graph is displayed in this area of the dialog.

Linked to:  This area shows to which data file the graph is linked.


  Graph Data Links - Update Now

Click on this button in order to update a manually linked graph.


  Graph Data Links - Break Link

Click on this button in order to permanently break the link between the spreadsheet and graph.  If you only want to temporarily break the link, then change the status of the link to Lock.


  Graph Data Links - Change Graph Data Link

In this dialog you can either link the graph to a specific data file or you can set the link to "Current Data File."

Current Data File:  By setting the link to "Current Data File" you can recreate a graph (or a set of graphs) for a new data set simply by changing the data file (as long as the respective variable numbers and case numbers are present in the new data set).

Specific File:  This option can be used to select (or change) the specific data file to which the current graph is linked (the Browse button can be used to locate the desired file).  For example, a graph created from data in DATA1.STA, can be now linked to the corresponding block of values (if they exist) in DATA2.STA.


Update Graph

When a graph is manually linked with the STATISTICA spreadsheet data (see Graph Data Links), you can use this option to manually update a graph after the data have been edited.

For more information, see:

Graph Data Links

Dynamic Graph Data Links Overview


  Edit Data (via the Graph Data Editor) Overview

When you select the Edit Data option from the Graphics Layouts pull-down menu or click on the Edit Data Toolbar button [image], the Graph Data Editor will open.  This editor is a special kind of Scrollsheet which contains the actual data that are plotted in the current graph.  They may represent the raw data values (e.g., in Scatterplots of raw data), or calculated or "derived" values (e.g., in Normal Probability Plots, Histograms, or plots of residuals).  In STATISTICA, the graph data are organized in pairs of X and Y values for each 2D plot, in triplets of X, Y, and Z values for each 3D plot, and in quadruplets of X, Y, Z, and V values for each 4D plot, representing the coordinates of individual data points.  Each "double" (or "triple" or "quadruple") column in the editor represents one plot; its legend and type (icon) are displayed in the column header.  The title of the current graph is displayed in the title area of the editor.  The Graph Data Editor will allow you to perform many editing operations on the data as well as Brushing of the data (see below).

Editing

Brushing

Auto-Updating Data Values

Click on the column name or on the Plot Layout [image] Toolbar button to open the appropriate Plot Layout dialog (see Plot Layout:  2D Graphs, 3D Scatterplots and Surfaces, or 3D Sequence Graphs) in order to make adjustments to the attributes of a specific plot (e.g., change the plot type, legend, font, etc.) before the graph is redrawn.

Click on the title area of the editor or on the General Layout [image] Toolbar button to open the General Layout dialog (see General Layout:  2D Graphs, 3D Scatterplots and Surfaces, or 3D Sequence Graphs) in order to make global adjustments to the graph (e.g., change the global graph type, titles, scales, etc.) before the graph is redrawn.

When you have completed editing the plot values or brushing, click on the [image] Toolbar button to redraw and update the graph displaying all of the changes (the Graph Data Editor will remain open).  You can also click on the [image] Toolbar button to close the Graph Data Editor and redraw and update the graph.

Shortcut:  Click the right-mouse-button on any part of a plot (e.g., point marker, line, bar) and select the Edit This Plot/Series Data option from the flying menu.

See also:

Graph Data Editor Toolbar Buttons

Graph Data Editor - Brushing

Graph Data Point ID Info


  Editing Data in the Graph Data Editor

Data can be edited in the Graph Data Editor in the following manners:

•	You can edit individual plot values.

•	You can use the Copy and Paste operations to transfer data from another Windows application (e.g., MS Excel, Lotus) to the Graph Data Editor in order to plot it along with the values from STATISTICA.

•	Standard Clipboard-based and Drag-and-Drop-based editing and global restructuring operations can be performed on graph data in the Graph Data Editor.

•	You can add variables to be plotted to the Graph Data Editor by using the New Plot option (or by adding new rows to the existing plots).

•	You can leave some cells empty (delete the contents of the cell) in order to break a line plot into several segments.

•	Data point labels can be edited in the first column of the Graph Data Editor; if different plots have different labels, then the contents of the first column will change, depending on the cursor position, so that the labels for the currently highlighted plot are displayed.  Also, you can edit the labels in the Graph Data Point ID Info dialog, accessible by double-clicking on the respective label.  NOTE:  Use the Brushing tools to turn off individual (or all) data point labels that were created using the Brushing tools.


  Brushing in the Graph Data Editor

•	The attributes (Marked, Labeled, Turned off, or Highlighted, see the Glossary of Brushing terms) of designated points can be managed in the Graph Data Editor via specific toolbar buttons or menu options.

•	Data points (values) which are selected via brushing (i.e., Marked, Labeled, Turned off, or Highlighted, see the Glossary of Brushing terms) are displayed in a different color in the Graph Data Editor.


  Auto-Updating Graph Values in the Graph Data Editor

When a Quick Stats Graph, Stats Graph, or Custom Graph is created, the data points in the Graph Data Editor will remain linked to the data in the respective STATISTICA spreadsheet.  Therefore, if data values are changed in the spreadsheet, then those changes will automatically be reflected in the graph and the Graph Data Editor.

For more information, see Options Graph Data Links - Overview.


  Graph Data Editor - Toolbar Buttons

The following toolbar buttons are available when you open the Graph Data Editor window in order to view and/or edit the actual data that are plotted in the current graph.

For more information on specific dialogs or options, click on the [image] button in the upper-right corner of the dialog.

  Redraw Graph and Leave the Graph Data Editor Open

  Exit (Close) the Graph Data Editor and Redraw Graph

  Opens the Plot Layout dialog for the Current Plot

  Opens the General Layout dialog for the Current Graph

  Zoom In Tool

  Zoom Out Tool

  Increase Column Width (also available by dragging)

  Decrease Column Width (also available by dragging)

  Scrollsheet Global Width (also available by dragging)

  Increase Decimal Tool

  Decrease Decimal Tool

  Mark data points (a brushing attribute)

  Label data points (a brushing attribute)

  Turn off (temporarily) data points (a brushing attribute)

  Highlight data points (this brushing attribute is visible in the graph only when the graph is in brushing mode)

  De-selects data points (i.e., removes all brushing attributes)

  Graph Data Point ID/Info dialog

  Save File As

  Cut

  Copy

  Paste

  Electronic Manual


  Graph Data Editor - Brushing

Overview

Brushing can be accomplished two ways in STATISTICA:  by using the Graph window Brushing Tool or by using the brushing options and/or toolbar buttons available in the Graph Data Editor.  When data points (values) are selected via the Brushing Mode (that is, Marked, Labeled, Turned off, or Highlighted, see the Glossary of Brushing terms) then the coordinates of those points are displayed in a different color in the Graph Data Editor.

The Graph Data Editor provides a "command driven" environment where points may be assigned attributes (i.e., Marked, Labeled, Turned off, or Highlighted) directly (i.e., without first highlighting them), using the toolbar buttons, the Graph Data Point ID Info dialog, the flying menu options, or Edit pull-down menu options.  Thus, these brushing options have the same status as Auto Update in the Brushing Mode.  This status will execute the current Action after each selection of an attribute and the points defined by the cursor (either a single point or a block of points) will be immediately marked, labeled, highlighted, etc.

Note that graph data points can have more than one attribute assigned to them (e.g., Marked and Highlighted), they will only be identified by a different color in the Graph Data Editor and they will be displayed in the updated graph (click on the Redraw or Exit and Redraw button) accordingly.

Several options are available to assign attributes or manage selected points in the Graph Data Editor.  For more information, see:

  Point Label/ID Info	  Turn Off Block

  Mark Block	  Highlight Block

  Label Block	  De-select Block

Selected Data (All)


  Graph Data Editor - Point Label/ID Info

The Graph Data Point ID Info dialog is available by selecting Point Label/ID from the Edit pull-down menu or the right-mouse-button flying menu, or by pressing the [image] toolbar button in the Graph Data Editor.  In this dialog, the label, subgroup membership (by category or subset) and attributes of selected points are displayed and can be changed.

Graph Data Point ID Info dialog:

Label:  Edit the data point label for the current plot in this edit field.

1st/2nd Categories:  These respective combo boxes allow you to change the categorization assignment for the current point by selecting a category from the list of categories in the categorized graph.

Selected Subset:  Select the desired subset (in multiple subset graphs) on which the selections made in this dialog will be applied.

Data Point:  You can select one or more of the following attributes to apply to the currently selected (by the cursor) point in the Graph Data Editor.  After clicking OK in this dialog, the point will be identified by a different color in the Graph Data Editor.

Marked:  Select this attribute in order to identify the selected point by displaying an alternative point symbol in the graph.

Labeled:  Select this attribute in order to identify the selected point by displaying its respective data point label in the graph.

Turned off:  Select this attribute in order to temporarily remove the selected point from the graph.

Highlighted:  Select this attribute in order to identify the selected point by highlighting it in the graph.


  Graph Data Editor - Mark Block

When you select this option from the Graph Data Editor Edit pull-down menu, flying menu, or [image] toolbar button, the data points selected by the block will be identified by a different color in the Graph Data Editor and a different point marker in the graph (when you update the action via the Redraw or Exit and Redraw toolbar buttons).  When you click on any point in the graph, the Point Pattern dialog will open in which the patterns for the marked and unmarked points can be modified.

For more information on Brushing in the Graph Data Editor, see Brushing Overview.


  Graph Data Editor - Label Block

When you select this option from the Graph Data Editor Edit pull-down menu, flying menu, or [image] toolbar button, the data points selected by the block will be identified by a different color in the Graph Data Editor and with the respective data point label (e.g., the case name) in the graph (when you update the action via the Redraw or Exit and Redraw toolbar buttons).  These labels have a different status than labels displayed via the Data Labels option in the respective Plot Layout or General Layout dialogs.  Data point labels displayed by brushing can only be turned off via the brushing tool.

For more information on Brushing in the Graph Data Editor, see Brushing Overview.


  Graph Data Editor - Turn Off Block

When you select this option from the Graph Data Editor Edit pull-down menu, flying menu, or [image] toolbar button, the data points selected by the block will be identified by a different color in the Graph Data Editor and temporarily removed from the display and fitted function calculations in the graph (when you update the action via the Redraw or Exit and Redraw toolbar buttons).

For more information on Brushing in the Graph Data Editor, see Brushing Overview.


  Graph Data Editor - Highlight Block

When you select this option from the Graph Data Editor Edit pull-down menu, flying menu, or [image] toolbar button, the data points selected by the block will be identified by a different color in the Graph Data Editor and will be highlighted in the graph (when you update the action via the Redraw or Exit and Redraw toolbar buttons).

For more information on Brushing in the Graph Data Editor, see Brushing Overview.


  Graph Data Editor - De-select Block

When you select this option from the Graph Data Editor Edit pull-down menu, flying menu, or [image] toolbar button, the previously selected data points defined by the block will be de-selected (i.e., all previously assigned attributes will be removed) in the graph (when you update the action via the Redraw or Exit and Redraw toolbar buttons).

For more information on Brushing in the Graph Data Editor, see Brushing Overview.


  Graph Data Editor - Selected Data (All)

These options allow you to selectively manage the data points selected via Brushing.

By choosing the Selected Data (All) option from the Edit pull-down menu or the flying menu, all points in the current plot of the Graph Data Editor which have been selected by brushing (either in the Graph Data Editor or via the Brushing Mode) in the graph may be copied to the Clipboard (option Copy to Clipboard), copied to a new plot within the Graph Data Editor (option Copy to New Plot), moved (i.e., deleted from their location in the original plot and pasted) to a new plot (option Move to New Plot), Deleted, or De-selected.

When you choose either the Copy to New Plot or Move to New Plot options, STATISTICA will automatically add a new plot (of the same number of columns and type as the current plot) in the Graph Data Editor.


  Graph Data Editor - Redraw

When you have completed editing the plot values in the Graph Data Editor, you can select the Redraw option from the Graph Data Editor File pull-down menu or click on the [image] Toolbar button to redraw the graph displaying all of the changes and leave the Graph Data Editor open in the background.


  Graph Data Editor - Exit and Redraw

When you have completed editing the plot values in the Graph Data Editor, you can select the Exit + Redraw option from the Graph Data Editor File pull-down menu or click on the [image] Toolbar button to redraw the graph displaying all of the changes and close the Graph Data Editor.


Graph Data Editor - Add Rows

When you click on the Add Rows option from the Edit pull-down menu, you can add a specified number of rows after the last row of the Graph Data Editor.  This option is useful if you want to increase the number of data points in a plot (by entering or pasting the coordinates of the data points in the Graph Data Editor).  Once you have entered the new data points, click on either the Redraw or Exit & Redraw Toolbar buttons to redraw the graph with the additional data (see also, Add Columns).


Pie Labels

Pie chart labels can be customized in two ways in STATISTICA, either globally for all plots in the graph (resulting in the same type of labels for each plot) or individually for each plot in the graph (resulting in different or no labels for each plot).  When you double-click on a pie chart label, the Labels: Plot (number) dialog will open.  This dialog is plot dependent (as indicated by the plot number in the dialog title, see below) and will allow you to place labels next to individual slices of the pie chart for that plot.  You can also specify the type of pie chart labels for a specific plot in the Pie Options dialog.  This dialog is also plot dependent and can be accessed by clicking on the Pie Options button in the appropriate Plot Layout dialog.

To change the display of the pie chart labels globally, across all plots (i.e., every slice of the pie chart will be labeled in the manner selected in this dialog), click on the Data Point Labels button in the General Layout dialog to open the Pie Labels dialog.  The options for this and the Labels: Plot (number) dialog are discussed below.

Shortcut:  Double-click on any pie chart label.

Pie Labels or Labels: Plot (number) dialog:

Off

Percent

Value

Text Values

Text and Percent

Text and Value

Plot Dependent


Pie Labels - Off

Select this option to remove the pie chart labels either from the current plot (when selected in the Labels: Plot or Pie Options dialog) or globally for each plot (when selected in the Pie Labels dialog).

NOTE:  Use the Brushing tools to turn off individual (or all) data point labels that were created using the Brushing tools.


Pie Labels - Percent

Labels each pie slice with the proportion of the pie slice in percentages with this option.


Pie Labels - Value

Labels each pie slice with the appropriate value with this option.


Pie Labels - Text Values

Labels each pie slice with the appropriate case name with this option.


Pie Labels - Text and Percent

Selecting this option will label each pie slice with the appropriate case name and the proportion of the pie slice in percentages.


Pie Labels - Text and Value

Selecting this option will label each pie slice with the appropriate case name and value.


Pie Labels - Plot Dependent

The Plot Dependent option is a global option that when selected, indicates that plot specific pie chart labels are selected.  This global option is available only when the Pie Labels dialog is called from the General Layout dialog and is dimmed in the Labels: Plot(number) dialog.  When you select pie chart labels for individual plots in the graph (i.e., plot dependent pie chart labels), then this option will automatically be selected when you open the Pie Labels dialog from the General Layout dialog, indicating that the data point labels are currently different for each plot in the graph.

NOTE:  Use the Brushing tools to turn off individual (or all) data point labels that were created using the Brushing tools.


  Brushing Mode

Click on this option or the [image] toolbar button to activate the Brushing mode and bring up the interactive Brushing dialog.  When this mode is activated, the cursor changes to a "gunsight-style" cross-hair [image] (rectangle and lasso brushes are also available, see below) and the program will allow you to highlight data points from the graph by clicking on them with the cross-hair (or enclosing them in the rectangle or lasso).  STATISTICA features a comprehensive selection of brushing facilities, including a variety of tools for manipulation of data points on screen, as well as the management of brushed (selected) data points (see also Graph Data Editor - Brushing).

How Brushing works: the difference between highlighting data and Updating the Action

Applications

Brushing dialog:

Update

Quit

De-select All

Auto Update

Plot number

Action

Brush

Animation

More...

Brushing tool button:

See also:

Brushing - Extended Options

Animation

Glossary of Brushing Terms


  Brushing Mode - How Brushing Works:  the Difference between Highlighting Data and Updating the Action

Highlighting data points in a graph is a precursor to performing an Action.  This is analogous to highlighting in word processors, where highlighting text is a precursor to performing an action (e.g., applying a font attribute such as boldface or italic).  In a similar fashion, "pointing to" (highlighting) specific data in a graph amounts to "telling the program" on which data points you will execute the specified Action.  No changes are made to the graph as long as you do not Update the graph (i.e., execute the currently specified Action).  When the desired points are highlighted, pressing the Update button in the Brushing dialog will execute the current brushing Action (as requested in the Action section of the dialog).  As a result of the Action, the highlighted points can be Marked (with a different marker), Labeled, or Turned OFF (that is, temporarily eliminated from the graph e.g., to explore the influence of outliers on a fitted function).  One more action that is available, De-Select, allows you to remove all attributes (marked, labeled, turned off, or highlighted) due to previous actions performed on the selected points.

Note that highlighting is not available when you are in the Auto Update mode; then, the current action is executed automatically, after each application of the brushing tool.

The Brushing tool is deactivated by pressing Quit in the Brushing dialog, clicking on the Point Tool ( [image], the default mode), or by pressing the ESC key.  Note that when you exit the Brushing mode, highlighting of points on which an Action has not been executed (i.e., which have not been marked, labeled, etc.) will not be displayed until you re-enter the Brushing mode for this graph.


  Brushing Mode - Applications

Brushing is typically used in exploratory data analysis (EDA) to interactively explore the contribution of specific data points to patterns of relations between variables (e.g., in scatterplot matrices) or to identify (e.g., label) outliers.  However, it is often necessary to manage the selected data points (for example, to selectively copy them to the Clipboard or to create a new column of data consisting of the selected data points).  These operations can be performed in the Graph Data Editor.  A "typical" illustration of the use of brushing in exploratory data analysis is the examination of the contribution of data points representing different ranges or different levels of one variable to correlations between other variables, which can be visually inspected using a scatterplot matrix.

Typical applications of Animated Brushing (available from the Brushing dialog whenever the rectangle or lasso brush and the Animation options are selected) are in exploratory data analysis using matrix plots, where instead of brushing consecutive ranges of a variable (to explore the influence of various sections of its distribution), you can invoke an automatic movement of a brush (a rectangle or lasso brush) and watch the "results."  Specifically, a brushing region is defined in one subgraph in the matrix and is automatically moved across the subgraph (horizontally, vertically, or both).  As the brushing region passes over groups of points in the subplot, corresponding points in all other plots are highlighted.  The speed and direction of the movement can be interactively controlled in the Animation dialog.


  Brushing Mode - Update

Press the Update button in order to (manually) execute an Action (i.e., operations such as marking, labeling, or turning off which are performed on highlighted points).  Actions can be automatically updated via the Auto Update option.


  Brushing Mode - Quit

The Brushing tool is deactivated by pressing Quit, clicking on the Point Tool ( [image], the default mode), or by pressing the ESC key.  Note that when you exit the Brushing mode, highlighting of points on which an Action has not been executed (i.e., which have not been marked, labeled, etc.) will not be displayed until you re-enter the Brushing mode for this graph.


  Brushing Mode - De-select All

Pressing this button will remove all attributes (e.g., marked, labeled, turned off, or highlighted) from all selected points (no matter which plot is specified in the Plot combo box) and restore their default, un-selected status.

Note that the De-select action (see Action), de-selects only the data that belong to the plot which is specified in the Plot combo box.


  Brushing Mode - Auto Update

Selecting the Auto Update option will cause the graph to automatically update (i.e., execute the current Action) after each application of the brushing tool.  This mode saves time for graphs which are redrawn quickly because you do not have to highlight the data points first (they immediately become marked, labeled, etc.).


  Brushing Mode - Plot Number

Select either the desired plot or All Plots on which to perform the Brushing.  This option allows you to limit the data points that will respond to brushing only to those which belong to a particular plot (e.g., to avoid unintended selection of data from other plots when using the lasso or rectangle brush).


  Brushing Mode - Action

An Action is an operation performed on highlighted points.  Actions are executed when you press the Update button in the Brushing dialog (or after every operation of pointing to a data point with the mouse when you are in the Auto Update mode).  The following operations are available in the Brushing dialog.

Mark:  When you select this option and the Action is updated, then the selected points will be identified with a different point marker.  The marker can be specified by pressing the Point Pattern button in the Brushing - Extended Options dialog, or by double-clicking on the point (after exiting the brushing mode).

Label:  When you select this option and the Action is updated, then the selected points will be identified with the respective data point label (e.g., the case name, text label, or specific type of data point coordinates, depending on the current setting in the Data Point Labels dialog).  The labels can be edited by pressing on the Labels button in the Brushing - Extended Options dialog, the Data Labels button in the respective General Layout pr Plot Layout dialog, or by double-clicking on the label (after exiting the brushing mode).  An individual data point label can also be edited in the Graph Data Editor (see also Graph Data Point ID Info).

Turn OFF:  This operation temporarily removes the selected points from the display and fitted function calculations.  The point values remain visible in the Graph Data Editor.  Turned off points are not displayed in the graph, thus they cannot be easily selected and turned on again with the Point brush, however, they can be turned on by (1) pressing the Reverse button to change the Turn OFF action to Turn ON, then using the Rectangle or Lasso brush to select a region of points, (2) clicking on the Edit pull-down menu (or flying menu) option Deselect Block in the Graph Data Editor in order to remove the Turn OFF attribute from the block of data points (selected data points are displayed in a different color in the Graph Data Editor), (3) using the De-select All option in the Brushing dialog in order to remove all brushing attributes from the data points.

De-select:  This operation removes all attributes (marked, labeled, turned off, or highlighted) due to previous actions performed on the selected points for the plot specified in the Plot combo box.

Reverse.  Pressing this button inverts all Actions; allowing you to Un-Mark, Un-Label, or Turn ON highlighted points.


  Brushing Mode - Brush

Three types of "brushes" are available in this dialog.  Either the Rectangle and Lasso brush must be used when the animated brushing mode is enabled (check the Animation box)

Point:  When you select this brush, the cursor will change to a "gunsight-style" cross-hair [image] and the program will allow you to highlight individual data points from the graph by clicking on them with the cross-hair.

Rectangle:  Selecting this option will allow you to draw a rectangle around a continuous set of points in the graph in order to highlight all of the points within the rectangle.

Lasso:  Selecting this option will allow you to draw (free-hand) a line around the desired points (either continuous or discontinuous) in the graph in order to highlight all of the lassoed points.


  Brushing Mode - Animation

If the current brush type is Rectangle or Lasso (see Brush), then the animated brushing mode can be enabled (check the Animation box).  This option will automatically move the brush over the graph under interactive control of the Animation dialog settings.  This technique is particularly useful in exploratory data analyses using matrix plots (see Applications).


  Brushing Mode - More...

Pressing the More... button in the initial Brushing dialog will bring up the Brushing - Extended Options dialog containing options to select points by specifying the value range coordinates of selected variables, or by reference to attributes of previously selected points.  That dialog also allows you to change the Point Pattern and Labels for the selected points with those attributes.  Points Highlighted via the Extended Options dialog will have the Action specified in the Brushing dialog applied to them when the Update button in that dialog is pressed.  The extended methods can also be used in the Auto Update mode.

Example:  You may choose to Highlight points which have previously been Marked (i.e., had their point markers changed) by checking Marked Points in the Extended Options and clicking Highlight; you may then temporarily remove them from the display (and from fitted functions) by selecting Turn OFF in the Brushing dialog.


  Brushing - Extended Options

This dialog will open when you press on the More... button in the Brushing dialog.  This dialog offers additional methods of highlighting points for selection by specifying the value range coordinates of selected variables or by reference to attributes of previously selected points (i.e., without using the mouse).  The layout of this dialog depends on the type of current graph.  All Extended Options in this dialog work in conjunction, that is, points may be highlighted by ranges of values and by attributes and/or combinations of attributes.  For example, you may choose to highlight points which have been marked and labeled and are within a specified range of values.

Points Highlighted via the Extended Options dialog will have the Action specified in the Brushing dialog applied to them when the Update button in the Brushing dialog is pressed.  For example, you may choose to Highlight points which have previously been Marked (i.e., had their point markers changed) by checking Marked Points in the Extended Options dialog and clicking Highlight; you may then return to the Brushing dialog and temporarily remove those points from the display (and from fitted functions) by selecting the Action Turn OFF in the Brushing dialog.

When the Auto Update option in the Brushing dialog is enabled, then the Highlight and De-highlight buttons in the Extended Options dialog are not available (dimmed) and pressing the OK button will execute the currently specified Action directly (i.e., without highlighting the data points first).  Note that if no Action is specified, then pressing OK will execute the Action specified in the Brushing dialog to all points in the graph.

Brushing - Extended Options dialog:

Category

Selection by Ranges of Values

X/Y Variables

Selection by Sets

OK / Swap

Highlight

De-highlight

Point Pattern

Labels

See also:

Brushing

Animation

Glossary of Brushing Terms


  Brushing Extended Options - Category

This option is available when the current graph is a categorized graph.  Select the desired category class or All Classes for the specified variable(s).  When this option is used alone, then Highlighting or the current Action will be executed on all points from the selected class(es).  When used in conjunction with the Selection by Sets and/or Selection by Ranges of Values options, then only those points which meet each of the specified conditions (e.g., a specific category class within a specified range of values) will be affected.


  Brushing Extended Options - Selection by Ranges of Values

When you click on the Selection by Ranges of Values option, you can specify the points within a range of values that will be selected or (when used in conjunction with other options in this dialog) the range of values from which the points specified in the Selection by Sets and/or Category options will be selected.

The options available in the Selection by Ranges of Values box will depend on the current graph type.

X Variable/Y Variable:  For matrix plots, you can select the X and Y variables to which the range of values (see below) will be applied.  Those points which meet these specifications will be selected in the matrix plot.

Min/Max Values:  Specify in the respective edit fields a range of values (minimum and maximum, inclusive) from which the points will be selected.  In the case of matrix plots, the range specified here will apply to the designated variables (see above).  In the case of categorized graphs, this range will apply only to the designated categories.


  Brushing Extended Options - Selection by Sets

When you click on the Selection by Sets option, you can specify which previously Selected points to select here.  You can select more than one set of points (see below) in order to select only those points which meet all the specified conditions (e.g., Marked and Labeled) and these options can be used in conjunction with the Selection by Ranges of Values and/or Category options in order to select a specific subset of points.

The following attributes of points are available in this dialog to specify the sets (i.e., conjunctions of conditions):

Marked Points:  These are previously Selected points which are displayed with an alternative point symbol.

Labeled Points:  These are previously Selected points which are displayed with their respective data point labels.

Turned Off Points:  These are previously Selected points which have been temporarily removed from display in the graph.

Other Points:  These are the points which do not meet any of the above conditions (e.g., points which have not been previously selected).


  Brushing Extended Options - Highlight

Click on this button in order to highlight the points which meet the criteria specified in this dialog (see Selection by Sets, Selection by Ranges of Values, and Category).  Note that the currently highlighted data points will remain highlighted (see also OK).


  Brushing Extended Options - De-Highlight

Click on this button in order to de-highlight the points which meet the criteria specified in this dialog (see Selection by Sets, Selection by Ranges of Values, and Category).  Note:  data points that are currently not highlighted will remain not highlighted (see also OK).


  Brushing Extended Options - Swap (or OK)

The function on this button in the top right corner of the dialog (Swap or OK) depends on the Auto Update status in the Brushing dialog.

  Auto Update de-selected:  When the Auto Update option is de-selected in the Brushing dialog, then clicking Swap will apply highlighting to the specified points in the same way as if you clicked on each of them with the mouse, that is, all those points which are not highlighted will become highlighted, and those which are highlighted will become de-highlighted.  Note that all specified points can be highlighted or de-highlighted regardless of their previous status by using the Highlight and De-highlight buttons (respectively).

  Auto Update selected:  If the Auto Update is currently enabled in the Brushing dialog, then pressing the OK button will apply the current action directly (note that then the Highlight and De-highlight buttons are not available).  Note that if no Action is specified, then pressing OK will execute the Action specified in the Brushing dialog to all points in the graph.


  Brushing Extended Options - Point Pattern

Click on this button in order to open the Points Pattern dialog in which you can select a different point marker for the Marked points in the graph.  After selecting a different point marker in this dialog, click on the Update button in the Brushing dialog in order to implement the change.

Shortcut:  Double-click on the point to open the Point Patterns dialog


  Brushing Extended Options - Labels

Click on this button in order to open the Data Point Labels dialog in which you can edit the data point labels (e.g., case name, text label, or specific type of data point coordinates, depending on the current setting in the Data Point Labels dialog) for the Labeled points in the graph.  After editing the labels in this dialog, click on the Update button in the Brushing dialog in order to implement the changes.

The same dialog for editing data point labels can be accessed by double-clicking on the label in the graph.  The labels can also be edited in the Graph Data Editor by double-clicking on the label or by clicking on the Point Label/ID Info ( [image]) toolbar button.  You can also edit labels by clicking on the Data Labels button in the respective General Layout pr Plot Layout dialog.


  Animated Brushing

The Animation option is available from the Brushing dialog whenever a rectangle or lasso brush are selected.  Typical applications of Animated Brushing are in exploratory data analysis using matrix plots, where instead of brushing consecutive ranges of a variable (to explore the influence of various sections of its distribution), you can invoke an automatic movement of a brush (typically a rectangle brush selected in the Brushing dialog) and watch the "results."  Specifically, a brushing region is defined in one subgraph in the matrix and is automatically moved across the subgraph (horizontally, vertically, or both).  As the brushing region passes over groups of points in the subgraph, corresponding points in all other subgraphs are highlighted.  The speed and direction of the movement can be interactively controlled in the Animation dialog (see below).

Animation dialog:

OK

Cancel

Pause/Continue

Reset

X Step

Y Step

Waiting Time

See also:

Brushing

Brushing - Extended Options

Glossary of Brushing Terms


  Animated Brushing - OK

Click on this button in order to highlight the points currently in the rectangle or lasso and exit this dialog, returning to the Brushing dialog.


  Animated Brushing - Cancel

Click on this button in order to exit this dialog (withough highlighting any points) and return to the Brushing dialog.


  Animated Brushing - Pause/Continue

Click on the Pause button in order to temporarily stop the animated brushing process and examine the display.  The process can be restarted by clicking on the Continue button in this dialog.


  Animated Brushing - Reset

Click on this button in order to restart the animated brushing region from the original location of the rectangle or lasso.


  Animated Brushing - X, Y Steps

You can determine the direction in which the animated brushing region will move and the movement step size with these options.

Direction:  In order to move the brush in the direction of the X-axis (horizontally) only, set the Y Step to 0%, then set the desired step size (see below) for the X Step.  Similarly, to brush vertically only, set the X step to 0% and then set the desired step size (see below) for the Y Step.  By adjusting the percentages of the X and Y Steps, you can control the direction of the animated brushing region (e.g., diagonally, or in a zig-zag movement).

, [image] buttons:  You can change the direction in which the animated brushing region is moving by clicking on these buttons.  For example, if the region is moving horizontally, you can simply click on the [image] button to reverse the direction of the brushing.

Step Size:  As explained above, you can adjust the X and Y movement coordinates in order to control the resulting direction of the movement.  These settings will also affect the smoothness and, in a sense, the "speed" of the animation.


  Animated Brushing - Waiting Time

This option allows you to adjust the amount of time (in seconds) between steps while using the animated brushing tool.  Note that the overall "speed" of the movement depends also on the step size (e.g., small settings of the Waiting Time in conjunction with small Step Size settings will result in slow and "smooth" movements.


Point Patterns

This dialog will open whenever you double-click on a point in the graph which has been marked by Brushing.  Here you can change the default point pattern for the marked and unmarked points.

Point Patterns dialog:

Point Pattern:  Click on this button in order to open the Point Pattern dialog in which you can change the point pattern and color for un-marked points in the graph.

Marked Point Pattern:  Click on this button in order to open the Point Pattern dialog in which you can change the point pattern and color for marked points (via Brushing) in the graph.

Points:  These options allow you to turn On or Off the points in the graph.


Ignore Marked Points

Select this option from the Graphics window View pull-down menu in order to set the mode for the Brushing tool.  If the Ignore Marked Points option is checked, then the point selected with the Brushing tool will be temporarily removed from the graph and its coordinate values will be identified by a color other than the default coordinate value's color (by default, marked values appear red, see Customize Color) in the Graphics window Graph Data Editor and when printed, by default, will be identified with an  *  (asterisk) next to those values.  If Ignore Marked Points is unchecked, then the graph points selected by the Brushing tool will only be marked in the Graph Data Editor and not removed from the graph.


      Graph Proportions and Margins Toolbar Buttons

You can resize the graph proportionally or disproportionally and adjust the position of the graph in the window with these three mutually exclusive Toolbar buttons (alternatively, you can use the options available in the Graph Mapping Options dialog).  In order to restore the original graph proportions and margins (as well as the graph position and magnification ratio) use the Restore Original Settings option from the Graphics View pull-down menu.

Hint:  For best results, first reduce the size of the graph window and place it in the middle of the screen, then adjust the position of the graph in its window using the Adjust Graph Margins option.  The scroll-buttons will appear in the middle of each scrollbar, allowing you to scroll the graph in each direction (this arrangement will also allow you to expand the graph window in any of the four directions).

  Fixed Proportion

  Change Proportion

  Adjust Graph Margins


  Graph Proportions and Margins Toolbar Buttons - Fixed Proportion

In this mode, you will be able to resize the graph proportionally (e.g., maintain the current graph aspect ratio).  In other words, when you "stretch" or "shrink" the graph window, the graph and all graph objects will "stretch" or "shrink" proportional to the window size (i.e., maintain the height-to-width ratio of the window).

Fix Proportion Toolbar button:


  Graph Proportions and Margins Toolbar Buttons - Change Proportion

You can resize the graph (and graph objects) disproportionally (i.e., change the aspect ratio of the graph window) when you press on this Toolbar button.  Now when you return to the Fixed Proportion setting, the new aspect ratio will be "frozen" and maintained when you resize the graph.

Change Proportion Toolbar button:


  Graph Proportions and Margins Toolbar Buttons - Adjust Graph Margins

When you press on this Toolbar button, Scrollbars will appear in the graph window.  Now you will be able to reposition the graph (and graph objects) by using the scrollbars to move the graph up, down, left or right in the graph window, "add space" to the graph window by increasing the window size (e.g., to make room for embedded objects), etc.

The position of the graph in the STATISTICA window and the relative size of the graph will determine the size of the scrolling area (i.e., the amount of the area available on each side of the graph).  For example, if the graph is positioned in the upper-left-corner of the screen, then when you click on the Adjust Graph Margins Toolbar button, you will not be able to scroll the graph very far to the right (the buttons on the scrollbars will appear close to the lower-right-corner of the graph window).

Alternatively, you can use the Graph Area option from either the Graph Mapping Options or Graph Mapping Defaults dialog to specify the graph viewing area.

Adjust Graph Margins Toolbar button:


  Graphics Zoom In Tool

When you select this option, the mouse cursor will become a magnifier, enabling you to proportionally enlarge the current graph.  Place the magnifier over the area of the graph that you want to view and click once on the left-mouse-button.  This will result in a magnified view of the specified area; the point where you click (the focal point of magnification) will become the center of the new graph window.  Each time when you press the Zoom In tool, the graph area will be magnified by a factor of approximately 2; you may press it up to 5 times to achieve the magnification ratio of approximately 32:1.

Zoom operation in Auto mode:  The Zoom In tool can operate in one of 3 modes (Auto, Fixed Font Size, or Variable Font Size, see Graph Mapping Options).  When the default Auto mode is used, this tool offers more than just "mechanical stretching" of the picture.  Specifically, it provides a logical magnification of the selected area while maintaining the sizes of point markers, fonts, and width of all lines.  Thus, the Zoom In tool effectively increases the "functional resolution" of the display, allowing you to inspect areas of the graph which in normal (1:1) mode were not readable due to overlapping markers or point labels.  In contrast, if the zoom was "mechanical" and not logical, and the size of point markers was increased with the magnification ratio, then one would not be able to see the details (e.g., overlapping points).

Drawing in Zoom mode:  Because the Zoom In tool provides logical magnification (see above), the black editing/resizing squares will maintain their size independent of the zoom ratio; therefore, the zoom mode can be used to make precise modifications to freehand drawings.

Scrolling the graph in Zoom mode:  Because the zoom mode in STATISTICA is based on a virtual plot area technology (and not "partial redrawing"), you can use the Zoom In tool in conjunction with the graph area and margins adjusting mode.  By enabling that mode (press the [image] toolbar button}, you will place scrollbars around the graph, allowing you to scroll the magnified area in the graph window.  This way of examining a graph resembles moving a "magnifying glass" over the graph.

Reversing the Zoom operation:  You can also decrease the graph "size" (in the same increments that you increased it) using the Zoom Out tool.  Note that unless you selected exactly the same focal points for the Zoom Out operation as those you had used for the Zoom In, the original location of the graph in the window will not be restored.  In order to restore the original graph position (as well as margins and the magnification ratio) use the Restore Original Settings option from the Graphics View pull-down menu.


  Graphics Zoom Out Tool

When you select this option, the mouse cursor will become a magnifier, enabling you to proportionally "shrink" the current graph.  Place the magnifier over the area of the graph that you want to reduce and click once on the left-mouse-button.  This will result in a reduced view of the specified area; the point where you click (the focal point of reduction) will become the center of the new graph window.  Each time when you press the Zoom Out tool, the graph area will be reduced by a factor of approximately 2; you may press it up to 5 times to achieve the reduction ratio of approximately 32:1.

Zoom operation in Auto mode:  The Zoom Out tool can operate in one of 3 modes (Auto, Fixed Font Size, Variable Font Size, see Graph Mapping Options).  By default (Auto mode), the size of fonts, markers, and spacing between the components of the graph will remain the same as you Zoom In (to allow for truly "logical zooming" -- revealing more details, and not mechanical stretching).  However, the size of fonts, markers, and spacings will be proportionately reduced as you Zoom Out, to allow for true reduction of the entire graph area.  This can be adjusted in the Graph Mapping Options dialog from the View pull-down menu, and fonts, markers, and spacing may be forced to rescale or to stay the same for both Zoom In and Zoom Out.

Reversing the zoom operation.  You can also increase the graph "size" (in the same increments that you decreased it) using the Zoom In tool.  Note that unless you selected exactly the same focal points for the Zoom In operation as those you had used for the Zoom Out, the original location of the graph in the window will not be restored.  In order to restore the original graph position (as well as margins and the magnification ratio) use the Restore Original Settings option from the Graphics View pull-down menu.


    Selection Mode Toolbar Button

The default mode for graph windows is the selection mode (the Selection Mode Toolbar button will be depressed).  This default mode will allow you to use the left-mouse-button to select graph objects (e.g., arrows, embedded or linked objects, etc.) or different parts of the graph (e.g., titles, scales, gridlines, etc.) for customization or editing (see also the Object Selection option).  You will temporarily exit from this selection mode whenever you choose one of the graph customization options (e.g., Mark Selection, add Text, Arrows, or various Drawing Objects, or Embed Objects) or the Data Selection ("brushing") tool from the Graphics Toolbar or Edit pull-down menu.  Clicking on the Selection Mode Toolbar button will return STATISTICA to the default selection mode of operation.

Toolbar button (non-selection mode):

Toolbar button (selection mode):


Object Selection

De-selecting this option from the Graphics View pull-down menu disables the left-mouse-button for all graph windows so that you cannot "select" graph objects (e.g., arrows, embedded or linked objects, etc.) by clicking on them or open various dialogs by double-clicking on different graph components (e.g., titles, scales, gridlines, etc.).  Deselecting this option will save system memory, and may speed up processing extremely large graphics displays (e.g., very large matrix plots).


Graphics Drawing Tools

STATISTICA provides several drawing tools, via the Graphics Toolbar, for customizing graphs.  You can add Rectangles, Rounded Rectangles, Ovals (or circles), Polylines and free-hand drawings (see below), arrows (see Arrow Objects Style), and text (see Graphic Text) to a graph.

    Line/Fill Attributes

      Draw Rectangle, Rounded Rectangle, Oval

  Arc

  Polyline

  Arrow

Once added, the objects can be repositioned (see Moving a Graph Object) or resized within the graph and can have either a dynamic or fixed status (see Dynamic [image] and Fixed [image] Mode Toolbar buttons).  Note that you can change an object's status by first clicking on the object to select it (the current status [i.e., either Dynamic or Fixed] will be reflected by the status Toolbar button) and then clicking on the status Toolbar button to change it from Dynamic to Fixed or from Fixed to Dynamic.


    Graphics Drawing Tools - Line/Fill Attributes

You can change an object's line and/or fill pattern (if applicable) by selecting the object with the mouse (the black selection squares will appear around the object) and then using the Fill Attributes ( [image]) and Line Attributes ( [image]) Toolbar buttons or Edit pull-down menu options.  The Fill Attributes ( [image]) Toolbar button (or Fill pattern option from the Edit pull-down menu) will allow you to "fill" selected objects with a patterned or solid color and the Line Attributes ( [image]) Toolbar button (or Line pattern option from the Edit pull-down menu) will allow you to adjust the width, pattern or color of the selected object's lines.  (See also, Selecting Point/Lines/Area Patterns.)

In order to change the default line/fill pattern or color (for new objects), select the desired patterns or colors from the respective Object Properties dialog.

For examples, see:

Resizing a Graph Object

Moving a Graph Object


      Graphics Drawing Tools - Draw Rectangle, Rounded Rectangle, Oval

Place rectangles ( [image]), rounded rectangles ( [image]), or ovals ( [image]) in the graph by clicking on the respective Toolbar buttons.  To create a rectangle, rounded rectangle, oval, press on the appropriate Toolbar button or select the appropriate option from the Graphics Insert pull-down menu and move the mouse to the current graph window where the cursor will change into cross-hairs; press the left-mouse-button to select the starting point (upper left corner of the object) and then drag the mouse and release it when the object is the shape and size that you want.

Drawing Squares and Circles:  In order to make a square, squared rounded rectangle, or circle, hold down on the SHIFT key while you are dragging the mouse.

Command-driven drawing:  The graphics library of STATISTICA BASIC includes commands that specify custom graphics objects and place them in graphs; for more informations, see Graphics Library of STATISTICA BASIC.

See also:

Resizing a Graph Object

Moving a Graph Object


  Graphics Drawing Tools - Polyline

You can create Polylines and free-hand drawings in the graph using the Polyline [image] Toolbar button or the Polyline option from the Insert pull-down menu.  Once you have selected this option, the cursor will change into a "paint brush" and you can begin drawing by clicking once on the left-mouse-button.  To "anchor" the drawing (and stop drawing), double-click on the left-mouse-button.

For examples, see:

Drawing a Polyline in a Graph

Drawing Free-hand in a Graph

In addition to the usual object modification facilities which apply to added objects (e.g., rectangles, ovals, arrows, etc., see above), there is also a "second level" of editing free-hand drawings available in order to reshape individual segments of the drawing (e.g., pull-in the sides of an apple-shaped drawing to make it look more like a pear).  You can either drag the object area black selection squares (to change the global properties of the object) or any of the black selection squares that mark the line segments (to make local segment adjustments to the drawing).  If the line contains many break points, and the black selection squares overlap, use the zoom tool to enlarge the object.

See also:

Resizing a Graph Object

Moving a Graph Object


  Graphics Drawing Tools - Arc

Click on the [image] button or select the Arc option from the Insert pull-down menu to enter the arc drawing mode.  After pressing the button, the cursor will change into a cross-hair allowing you to draw arcs by dragging the mouse on the graph.  The arc is drawn as one-quarter of an ellipse and can be controlled as illustrated below.

Specifically, the proportions of the ellipse depend on the angle of mouse movement (45° will produce a quarter-circle arc; hold down the SHIFT key while drawing); the orientation of the arc (concave vs. convex) will depend on the direction of the movement (up or down, respectively).

Command-driven drawing:  The graphics library of STATISTICA BASIC includes commands that specify custom graphics objects and place them in graphs; for more informations, see Graphics Library of STATISTICA BASIC.

See also:

Resizing a Graph Object

Moving a Graph Object


Resizing a Graph Object

You can resize an added graph object by clicking on it with the left-mouse-button (to activate the editing mode) and then (when the black selection squares appear) dragging one of the black selection squares to "stretch" or "shrink" the object.

Mouse emulation with keyboard:  To resize an object using cursor keys, first select the object and position the cursor over one of the black selection squares, then use the keyboard cursor keys to drag a shadow of the selected graph object to "stretch" or "shrink" the object.  Hold down the CTRL key for fine (1 pixel only) dragging movements.  Press ENTER to complete the action.


Moving a Graph Object

Moving a Graph Object - Overview

Once added, graphic objects (e.g., added text, embedded or linked objects, arrows, free-hand drawings, a previously saved graph, etc.) can be repositioned in the graph in the following ways.

Using the mouse.  You can change an object's location by dragging it to a new position on the graph.  To do this using the mouse, click on the object with the left-mouse-button (to activate the editing mode; note that the cursor changes to a four-arrow icon when you place it on the body of the object) and then (when the black selection squares appear) grab it anywhere on the body of the object and drag it to a different area of the graph (avoid dragging on the black selection squares).

Mouse emulation with keyboard.  To do this using the keyboard cursor keys, first click on the object to select it and then with the four-arrow icon on the body of the object, use the keyboard cursor keys to drag a shadow of the graph to a new position).  Now, press ENTER to move the object to the new position (where the shadow is displayed) or ESC to cancel the move (and remove the shadow).

Fine adjustments.  Note that if you hold down the CTRL key while using the cursor keys to drag the graph object, then the dragging movements will be very small (1 pixel only).  This may be userful when very fine adjustments of the object position are necessary.

Using cursor coordinates.  When the object is placed in fixed mode (click on the object to select it and then click on the Dyn/Fix toolbar button so that it shows [image]), you can use the cursor coordinates displayed in the Toolbar Show window to align the object in a precise fixed position.  These coordinates are the percentages of the total window width and height (the lower left corner is [0%, 0%] the upper right corner is [100%, 100%]) and will not change as the graph is resized.

Using the Snap to Grid and/or Alignment Grid.  You can use the Snap to Grid and/or Alignment Grid facilities to aid in repositioning the object.  The "snap to grid" facility (enabled by clicking the [image] toolbar button or the Snap to Grid option in the View pull-down menu) aligns drawing objects with the drawing grid, an invisible network of lines that covers the drawing area (the grid may be displayed by pressing CTRL+G or by selecting the option Alignment Grid from the View pull-down menu).  When this facility is enabled, inserted objects are always pulled into alignment with gridlines or intersections of gridlines (the "snap to grid" effect).  The Alignment Grid (a a visible representation of the grid specified via the Snap to Grid dialog) aids in the placement and alignment of graphic objects; however, the grid will not be printed when you print the graph and can be turned on or off by clicking on the Alignment Grid option in the View pull-down menu or by pressing CTRL+G.  These options are especially useful when arranging and aligning objects (for example, an embedded object) in Blank Graphs.

Note.  For some video drivers, when you move an object, some residue from the selected object (i.e., shades of color or small pieces of the object) may remain on the screen.  This residue will not be displayed in the graph when printed and will disappear from the screen when the graph is redrawn (e.g., after resizing the graph or repositioning the graph in the window via the Adjust Graph Margins toolbar button).


Drawing a Polyline in a Graph

Once you have selected this option and the cursor changes into a "paint brush," move the cursor to an area of the graph that you want to be the starting point for the polyline.  Click once on the left-mouse-button to anchor the beginning of the polyline.  Now, release the button and move the cursor to a different part of the graph and click once on the left-mouse-button to anchor that segment of the line.  Repeat until the polyline is complete and then double-click on the left-mouse-button to place the final anchor and stop drawing that polyline.

See also:

Resizing a Graph Object

Moving a Graph Object


Free-hand Drawing in a Graph

When the cursor changes into a "paint brush," move the cursor to an area of the graph that you want to be the starting point for your free-hand drawing.  While holding down the left-mouse-button, move the cursor around to create the drawing.  Double-click on the left-mouse-button to stop drawing.

See also:

Resizing a Graph Object

Moving a Graph Object


    Line, Fill Attributes

You can use the Line Attributes and/or  Fill Attributes Toolbar buttons or Edit pull-down menu options to customize selected objects in the graph (e.g., rectangles, ovals, arrows, etc.).  (See also, Selecting Point, Lines, Area Patterns.)

In order to change the default line/fill pattern or color (for new objects), select the desired patterns or colors from the respective Object Properties dialog.

  Line Attributes

  Fill Attributes


  Line Attributes

Use this option to change the line color, width, and pattern of selected objects in the graph.  When you select an existing graph object and click on this toolbar button (or the Line Pattern option in the Edit pull-down menu), the appropriate Line Pattern dialog will open.  If an object is not highlighted, then the Edit pull-down menu option will be dimmed.  In order to change the default line pattern or color (for new objects), select the desired patterns or colors from the respective Object Properties dialog.

See also:

Resizing a Graph Object

Moving a Graph Object


  Fill Attributes

This option will allow you to "fill" the selected object's background area with a colored pattern or a solid color.  When you select an existing graph object and click on this toolbar button (or the Fill Pattern option in the Edit pull-down menu), then the appropriate Area Pattern dialog will open.  If an object is not highlighted, then the Edit pull-down menu option will be dimmed.  In order to change the default fill pattern or color (for new objects), select the desired patterns or colors from the respective Object Properties dialog.

See also:

Resizing a Graph Object

Moving a Graph Object


    Graphic Object Placement Toolbar Buttons

These Toolbar buttons allow you to rearrange the order of overlapping objects (e.g., ovals, rectangles, arrows, embedded or linked objects, etc.) in the graph.  Click on the Bring to Front tool to move the selected object to the top of the group of objects.  Click on the Send to Back tool to move the selected object to the bottom of the group of objects.

Bring to Front Toolbar button:

Send to Back Toolbar button:


    Graphics Increase, Decrease All Font by 16 % (CTRL - 4%) Toolbar Buttons

Use the Increase Font and Decrease Font Graphics Toolbar buttons to globally and proportionally increase or decrease the font size (as well as markers and all distances and spacing defined in points or related to font and marker sizes), incrementally, for each font style and size represented in the current graph.  Pressing the [image] button will increase all those sizes by 16%; hold down the CTRL key while pressing this button to achieve a smaller (4%) increase rate.  Analogously, when you press the [image], the sizes will decrease by 16% (or 4% if you hold down the CTRL key while pressing this button).

Pressing either of these buttons is equivalent to opening the Graph Mapping Options dialog and increasing or decreasing the Mapping Base by 16% (or 4% if you hold down the CTRL key when pressing these buttons).

You can change the font size and style of individual graph text (titles, scales, etc.), by double-clicking on the individual text to open the appropriate dialog where you can select the Font option.

See also Logical vs. Physical Font Sizes (Mapping Font Sizes onto Plot Regions of Different Sizes).

Increase All Font by 16% (CTRL - 4%) Toolbar button:

Decrease All Font by 16% (CTRL - 4%) Toolbar button:


Logical vs. Physical Font Sizes (Mapping Font Sizes onto Plot Regions of Different Sizes)

In STATISTICA, all graph displays and printouts can be continuously scaled along with their fonts.  Unless you change the Graph Mapping Base factor (as provided by the current [image] or [image] button), the fonts will appear printed in their actual physical size (as set in points; 1 point = 1/72 of an inch) if letter-size paper is used, in portrait orientation with the default (1 inch) margins on all sides, and if the default graph proportions are not modified (this setting can be modified in the Graph Mapping Options dialog).  Technically speaking, the Graph Mapping Base value is the length of the diagonal (in points) of the output at which fonts will be printed at the same physical font size as their logical definition in the graph.

The shortcut font size adjustment enabled by pressing either of these buttons allows you to effectively increase or decrease all fonts (both on the screen and in graph printouts) not by changing the specific font size settings (e.g., not by changing a 12-point setting into a 14-point setting) but by globally adjusting the manner in which the logical font sizes are mapped into the plot region of the screen or the printout (i.e., Graph Mapping Base).  Thus, after you press this button, a text in the graph which was set to size 10 (points) will remain set to 10, but this size (10) will now be represented by approximately 16% larger letters when displayed or printed, as determined by the new Graph Mapping Base factor.

Embedded or linked graphs.  Note that if the mapping mode in an embedded or linked graph is set to Fixed Size Font (i.e., it is tied to the Mapping Base setting of the master document, see the Object Properties dialog for the child graph), then clicking on the [image] or [image] buttons will also affect font sizes in the embedded or linked graph.


Graphics Font Dialog

Clicking on the Font button (where applicable in a graphics dialog, e.g., in the Titles dialog) will bring up the graphics Font dialog where you can edit the type of font, the font style, and the font size of the graph text component (e.g., titles, scale values, labels, added text, etc.).  As you make your selections, you can view a sample text in the Sample window of this dialog.

All graphs in STATISTICA are saved along with their specific font settings which can be different for every text component of the graph.

Font dialog:

Font

Font Style

Size

Effects

Set as Common Font

Use Common Font


Graphics Font Dialog - Font

Specify the name of the font that you want to use here; the selection depends on the fonts installed on your computer.  Click on the font type to select it.


Graphics Font Dialog - Font Style

There are four font styles to choose from; regular, italic, bold and bold italic.  Click on the font style that you want to select.


Graphics Font Dialog - Size

The available font sizes depend on the type of font that you select.  First select the font type, then click on the font size that you want to select.  If the specific size you need is not listed in the list box, enter it into the Size edit box.


Graphics Font Dialog - Effects

You can add emphasis to the text in graphs by selecting either the Strikeout (e.g., text) or Underline (e.g., text) effects.  You can also choose a different color for the text in the Color combo box.


Graphics Font Dialog - Set as Common Font

This option (where applicable) will allow you to use the font style and size that you have selected as the common font throughout the application (e.g., graph).


Graphics Font Dialog - Use Common Font

When you select this option (where applicable), the font style and size throughout the application (e.g., graph) will return to the default font (see Global Default).


Graphics File Menu

These options are available from the graphics window File pull-down menu.

Open Graph

Merge Graph

Open Other

New Data

Data File

Graph File

Scrollsheet

Text/Output

STATISTICA BASIC

Command Language (SCL)

Close Graph

Close and Return to Graph...

Update Graph...

Save

Save As

Save Metafile

Save Bitmap

Print Graph

Print Preview

Print Files

Page/Output Setup

Printer Setup

Update Graph

Exit


Close Graph

Close Graph:  Select this option in order to close the current graph.

Close and Return to Graph...:  This option is available when a component graph (of a Compound Graph) is the current graph.  When you click on this option, you may be prompted to update the Compound Graph before closing the component graph (if the component graph had previously been edited).  In order to update the Compound Graph while leaving the component graph open, use the Update Graph... option from the File pull-down menu.


Update Graph...

This option is available when a component graph (of a Compound Graph) is the current graph.  Clicking on this option will update the Compound Graph while leaving the component graph open.  In order to update the Compound Graph while closing the component graph, use the Close and Return to Graph.. option from the File pull-down menu.


Merge Graph

Use this option from the Graphics File pull-down menu to merge a STATISTICA graph (*.stg extension) with the current graph.  When you select this option, the Open Graph File dialog will open from which you can select the graph file to merge with the current graph.


  Save Graph

Use this option from the Graphics File pull-down menu or from the Graphics Toolbar to save the current graph in the STATISTICA graph format (file name extension *.stg).  Unlike other graphics formats such as metafiles and bitmaps (see Save Metafile, Save Bitmap), this format not only stores the "image" of the current graph but also all information necessary to continue graph customization or graphical data analysis (including all data represented in the graph, fitted equations, links to and linked artwork, etc.).  Graphs stored in this format can be opened later (in any module of STATISTICA) allowing you to continue graphical data analysis (e.g., fit equations, add or merge new data series, etc.) or graph customization.  This format is recommended whenever you intend to use the graph again in the STATISTICA system or link it to other application documents using the MS Windows OLE conventions.

If the graph has been not previously-saved when you select this option, then the File Save dialog will open from which you can specify the name under which the graph will be saved.  Once you have designated the file name, selecting this option later will automatically save the graph under that name (i.e., you will not be prompted with any further dialogs).

Workbook Files:  In this area of the File Save dialog, a list of supplementary files (e.g., graph files, *.ini files, import/export files, Scrollsheet files, etc.) associated with the current data file is displayed (a log of all supplementary files associated with the current data file is maintained in the STATISTICA Workbook).  For easy access to a desired file, this list is sorted by file type (e.g., *.stg file) that you would like to save.  Files which are not relevant for the current save operation are dimmed (they are included for reference only).


Save As Graph

This option from the Graphics File pull-down menu will allow you to save the graph under a different file name in the STATISTICA graph format (file name extension *.stg), or in a different directory or drive.  Unlike other graphics formats such as metafiles and bitmaps (see Save Metafile, Save Bitmap), this format not only stores the "image" of the current graph but also all information necessary to continue graph customization or graphical data analysis (including all data represented in the graph, fitted equations, links to and linked artwork, etc.).  Graphs stored in this format can be opened later (in any module of STATISTICA) allowing you to continue graphical data analysis (e.g., fit equations, add or merge new data series, etc.) or graph customization.  This format is recommended whenever you intend to use the graph again in the STATISTICA system or link it to other application documents using the MS Windows OLE conventions.

When you select this option, the File Save dialog will open from which you can specify a name, directory or drive under which the graph will be saved.

Workbook Files:  In this area of the File Save dialog, a list of supplementary files (e.g., graph files, *.ini files, import/export files, Scrollsheet files, etc.) associated with the current data file is displayed (a log of all supplementary files associated with the current data file is maintained in the STATISTICA Workbook).  For easy access to a desired file, this list is sorted by file type (e.g., *.stg file) that you would like to save.  Files which are not relevant for the current save operation are dimmed (they are included for reference only).


Save Metafile

This option will allow you to save the graph in the Windows graphics metafile format (file name extension *.wmf).  The resulting graph file can then be directly accessed by most Windows applications (depending on the current setting of the Metafile Mode Screen/Printer Resolution option in the Page/Output Setup dialog, see the technical note Limitations of the Metafile Format).  In this respect this format is similar to another standard Windows graph file format--bitmap (see Save Bitmap); however, unlike bitmaps (which store only a "passive" representation of pixels which form the graph), the Windows metafile format stores the picture as a set of descriptions or definitions of all components of the graph and their attributes (e.g., segments of lines, specific fill patterns, text and text attributes, etc.).  Therefore, as compared to bitmaps, metafiles offer more flexible options for modification and customization in other Windows applications.  For example, when you open a metafile in the Microsoft Draw or another drawing programs, you can "disassemble" the graph, select and modify individual lines, fill patterns, colors, edit text and change its attributes, etc.

When you select this option, the Save Metafile dialog will open in which you can specify a name and directory under which the graph will be saved.

Technical Notes:

Saving STATISTICA Graphs as Metafiles

Limitations of the Metafile Format


Saving STATISTICA Graphs as Metafiles (Technical Note)

STATISTICA uses optimized graph resizing procedures with resolution enhancement, in order to achieve the optimum display precision (e.g., when you resize the graph, all graph components will maintain the desired line thickness).  Metafiles (and Bitmaps) use more simple ("mechanical") resizing procedures and thus the effect will not always be "clean" (e.g., the thickness of the gridlines may not be the same and some gridlines may not appear in the graph window if the metafile-graph area is small).  Some Windows applications (e.g., Microsoft Draw) do not support 3D font transformations or rotated text in graph metafiles, thus if a STATISTICA graph (saved in metafile format) is opened in such applications, then the rotated text will appear horizontal.  For best effects, paste STATISTICA graphs to other applications (e.g., word processor documents) using the STATISTICA Graph format (via the OLE).  This will allow STATISTICA to continue controlling the display and printing of the exported graphs.  To paste the graph in the other application use the Paste Special (instead of Paste) option and then, from the list of available paste formats, select the STATISTICA format.

Limitations of the Metafile Format

The Windows graphics Metafile format is well-suited for representing small to moderate size (i.e., complexity) graphics images.  However, when the file size exceeds 1-2 megabytes (depending on its contents) the Windows system may interpret the graph incorrectly (e.g., the Clipboard mechanisms may malfunction or the graph file will be distorted).  STATISTICA will beep or issue an error message when the metafile to be created would exceed the Metafile format limitations (see the Advanced option in the Page/Output Setup - Graphs dialog).  STATISTICA may generate graphs of size and complexity which exceed by far the capacity of the metafile representation; if you need to transfer such graphs to other applications, use the Screen Resolution option for Metafile Mode (in the Page/Output Setup - Graphs dialog), which will produce smaller metafile representations (both in the Clipboard and when saving to the metafile format), or use the Bitmap representation (either via the Clipboard  use Paste Special in the target application, or disk files  use the Save Bitmap option) which does not impose any file size limitations.


Save Bitmap

This option from the Graphics File pull-down menu will allow you to save the graph in bitmap format (file name extension *.bmp).  Unlike the STATISTICA Graph file format (see Save Graph or Save As), this option saves only the image of the current graph (with no data and STATISTICA-specific analytic information).  The resulting graph file can then be directly accessed by most Windows applications.  In this respect this format is similar to another standard Windows graph file format--metafile (see Save Metafile); however, unlike the metafile (which stores dynamic representations ("definitions") of all graph components, allowing selective modifications of lines, text, etc., in other Windows applications), the bitmap format stores only a passive representation of pixels which form the graph.  Bitmaps can be opened by other Windows applications, but the customization or editing options of such graph representations will be limited to stretching/shrinking, cutting /pasting, and drawing "over" the graph (see also Save Metafile).

When you select this option, the Save Bitmap dialog will open in which you can specify a name and directory under which the graph will be saved.

Technical Note


Saving STATISTICA Graphs as Bitmaps (Technical Note)

STATISTICA uses optimized graph resizing procedures with resolution enhancement, in order to achieve the optimum display precision (e.g., when you resize the graph, all graph components will maintain the desired line thickness).  Bitmaps (and Metafiles) use more simple ("mechanical") resizing procedures and thus the effect will not always be "clean" (e.g., the thickness of the gridlines may not be the same and some gridlines may not appear in the graph window if the metafile-graph area is small).  For best effects, paste STATISTICA graphs to other applications (e.g., word processor documents) using the STATISTICA Graph format (via the OLE).  This will allow STATISTICA to continue controlling the display and printing of the exported graphs.  To paste the graph in the other application use the Paste Special (instead of Paste) option and then, from the list of available paste formats, select the STATISTICA format.


Graphics Edit Menu

Cut	Delete

Copy	Screen Catcher

Paste	Object Properties

Paste Special	Links

Paste Link	Object

Paste Replace All

Undo, Undo Paste Replace, Undo Selected Object, Undo Edit


Edit Object

When a graph object is selected, this option will offer an appropriate object related action.  For example, if you highlight a rectangle drawn in the graph and select this option, then the Line pattern - Custom Graphic Object: Rectangle dialog will open in which you can edit the line pattern, size, etc., or if you select a linked object, you may be given options to edit it, convert it to embedded or static.  For more information, see Object.

Note that you can use the Undo Selected Object option from the Edit pull-down menu in order to reverse the edit or object conversion.


Paste Replace All

Select this option in order to replace the entire contents of the current graph with the contents of the Clipboard.  This action can be reversed by selecting the Undo Paste Replace option from the Edit pull-down menu.


Change Links

Change Link

This dialog (accessible from the Links dialog) allows you to edit the currently selected link.

Change Link dialog:

File Name

Type of File

Item

Directory

Drive

Network

Get Item from File


Change Links - File Name

Change Link - File Name

Select from the list or enter the file name to which you want to link information.


Change Links - Type of File

Change Link - Type of File

Choose to list in the File Name section all the files of a specific type (i.e., STATISTICA graph files, MS Excel files, metafiles, bitmaps, etc.).


Change Links - Item

Change Link - Item

This edit box displays an identifier for the linked item.  If the currently linked file contains more than one object, then you can select the object to be displayed (e.g., specific cells from a spreadsheet); consult the documemtation for the respective server application for information about how to identify and reference components of its files.  STATISTICA graphs are treated as single objects and the Item field can be used to edit their names.


Change Links - Directory

Change Link - Directory

Specify the Directory in which the file is located.


Change Links - Drive

Change Link - Drive

Specify the Drive in which the file is located.


Change Links - Network

Change Link - Network

Click on this button in order to open the Connect Network Drive dialog so that you can make a connection to a network source for the link.


Change Links - Get Item from File

Change Link - Get Item from File

This option is dimmed unless STATISTICA graph is specified as the Type of File (see above).


Links

This option opens the Links dialog from which you can edit the link(s) between the source application and the linked object(s) in the current STATISTICA graph.  You can establish a link using either the Paste Link or Paste Special options.

Links dialog:

Links (Source File, Item, Type, Update)

Update

Update Now

Open Source

Change Source

Break Link

Undo Changes


Links - Links (Source File, Item, Type, Update)

This window displays information concerning the source, item, type, and update status of all the linked objects in the current STATISTICA graph.  You can edit a link by highlighting it in this window and then clicking on the Change Source button.


Links - Update

These radio buttons allow you to specify how you want to update the object (by highlighting the link and then selecting either Automatic or Manual update).  Linked objects can be either "hot" (automatic status) or "cold" (manual status).  Automatic status means that the linked object in the STATISTICA graph will automatically be updated whenever any changes are made to the object in the source application.  Manual status means that the link is temporarily disabled and that you will have to manually update the object using the Update Now button or by changing the status back to "hot."


Links - Update Now

Click on this button to manually update the currently highlighted link(s) in the STATISTICA graph.


Links - Open Source

Click on this button in order to open the source application for the linked object which is currently highlighted in the window.


Links - Change Source

Click on this button to open the Change Link dialog in which you can edit the currently highlighted link.


Links - Break Link

Click on this button to convert the linked object into an embedded object (the same as the ... Object - Convert to Embedded option in the pull-down menu Edit).  You can resume the link by clicking on the Undo Changes button.


Links - Undo Changes

Click on this button in order to undo any changes made to the currently highlighted link.


Undo, Undo Paste Replace, Undo Selected Object/Undo Edit

Undo, Undo Paste Replace, Undo Selected Object, Undo Edit

This multi-level undo option (available from the Edit pull-down menu) maintains separate queues of previously performed operations for separate objects.  The undo operation works on the currently highlighted object; therefore, if you press CTRL+Z, STATISTICA will undo the last operation performed on the currently selected object and not merely the last operation on an object.  Note that this option can also be used to undo operations on linked or embedded objects.

Keyboard shortcut:  CRTL+Z


Object

This option from the Edit pull-down menu is available when you select an object which has been pasted or inserted into the graph.  When a graph object is selected, appropriate object related actions will be offered here.  These object related actions depend on the type of object that you have selected (e.g., a linked or embedded STATISTICA graph, Excel Worksheet object, Word object, etc.) and the source application.

Object:  This object related action will bring up the Object Properties dialog in which you can edit properties specific to that object (e.g., object frame, lock the object, etc.).

Edit:  Click on this object related action in order to edit the selected object.

Convert to Embedded:  When you select this object related action, the link to the source application will be broken and the linked object will be embedded in the graph.  You will be able to double-click on the object to open the source application in order to edit it (or select the Edit option, above).  You can click on the Undo Selected Object option in the Edit pull-down menu in order to undo this action and re-establish the link to the source application.

Convert to Static:  When you select this object related action, the object status of linked or embedded objects will become static (i.e., all links to the source application will be broken) and double-clicking on the object will not bring up the source application.  You can click on the Undo Selected Object option in the Edit pull-down menu in order to undo this action.


Remove Object - Del

Use this option to remove (delete) the selected object (e.g., arrow, rectangle, oval, embedded or linked object, etc.) from the graph.  To delete an object, click on the object to select it and then choose the Remove Object - Del option from the Edit pull-down menu.


Delete Text

Click on this option to delete the selected title from the graph.


Paste Special

The Paste Special option from the Graphics Edit pull-down menu will allow you to select the display format for the Clipboard object when it is pasted in a STATISTICA graph.

Paste Special dialog:

Source

Paste

Paste Link

As

Paste Replace Object

Put in Default Place

Object Properties

Clipboard Viewer


Paste Special - Source

Specifies the source of the Clipboard object.


Paste Special - Paste

Select this option and then specify the desired format (see As, below) in order to paste the Clipboard object into the current graph.  Selecting Paste and accepting the default format selection is the same as selecting Paste from the Edit pull-down menu (or pressing CTRL+V).


Paste Special - Paste Link

Select this option and then specify the desired format (see As) in order to paste the Clipboard object into the current graph while maintaining a link to the source document.  Selecting Paste Link and accepting the default format selection is the same as selecting Paste Link from the Edit pull-down menu.


Paste Special - As

Specify the type of information you want to paste from the Clipboard.  Usually several format options [e.g., Internal STATISTICA Representation, STATISTICA Graph object, Picture (i.e., Windows metafile), Bitmap] will be displayed in this area of the dialog, depending upon which formats are available (i.e., depending upon the current Clipboard contents).  The order of the available formats listed in this menu depends upon the priority of each format, as set in the Clipboard by the application from which the Clipboard contents were copied [e.g., STATISTICA assigns the highest priority to its own (STATISTICA Graph object or Internal STATISTICA Representation) formats, thus when the current Clipboard content is a STATISTICA graph or object, then a STATISTICA format will be listed first].


Paste Special - Paste Replace Object

Select this option in order to paste over (i.e., replace) the currently selected object in the STATISTICA graph (this option is available only when there is currently a selected object in the graph; then, the name of the object is listed below).


Paste Special - Put in Default Place

When this option is selected, the Clipboard object will be pasted in the upper-left-hand corner of the graph (the default location).  You can then click on the object to select it and move it to the desired location in the graph or resize it.  If you deselect this option and click OK, then you will be able to specify with the cursor the exact location and size of graph area in which to paste the Clipboard object.


Paste Special - Object Properties

Click on this button in order to bring up the appropriate Object Properties dialog.  In this dialog, you will be able to select from several options (e.g., frame options, mapping mode) for the newly pasted object.  This option is not available (dimmed) for STATISTICA internal objects (e.g., arrows, rectangle, graphic text) because those objects contain options which can be adjusted at any point.


Paste Special - Clipboard Viewer

When you click on this button, the Clipboard Viewer will be displayed allowing you to preview the current Clipboard object.


Object Properties

This option will allow you to pre-specify (select the appropriate option from the Insert pull-down menu) or change (highlight the object and select the Object Properties option from the Edit pull-down menu) certain properties for specific graph objects (e.g., text, pictures, bitmaps).  When you select this option (either from the Paste Special dialog or the Edit pull-down menu), the appropriate Style dialog will open.  For more information on each of the dialogs, see below:

Object Properties Dialogs:

Text Objects Style Dialog

Shape Objects Style Dialog

Arrow Objects Style Dialog

Picture and Complex Objects Style Dialog


Text Objects Style

This option will allow you to pre-specify (select the Object Styles - Texts option from the Insert pull-down menu) or change (highlight the object and select the Object Properties option from the Edit pull-down menu) certain properties for added text in the graph (e.g., movable legends, custom text, or unformatted text).

Text Objects Style dialog:

Patterns

Borders

Filled Background

Orientation (and Rotation)

Alignment

Dynamic Scale

Locked Position

Set as default style

Remove

Font button

See also, Using Dynamic (Coordinate) Mode in Categorized and Matrix Graphs


Object Properties - Orientation (and Rotation)

Orientation:  Select the orientation (Horizontal, Vertical Left, or Vertical Right) for the text in the graph.

Rotation:  You can also choose to rotate the text by specifying the custom rotation angle (from 0 to 359° or 0 to -359°) in the Angle edit field.  Alternatively, you can interactively rotate the text by selecting it in the graph and then dragging one of the object handles (small black squares) in the desired direction or by using the hot keys PAGE DOWN and PAGE UP to rotate text objects selected in the graph clockwise or counterclockwise, respectively, in 5° increments.  To rotate in 1° increments, hold down the CTRL key while pressing PAGE DOWN and PAGE UP.  The rotation of text objects takes place around the object's anchor point, which is visible as a "cross-hair" when the object is rotated.

Note that the angle (in degrees) will be displayed in the Change Show window of the Graphics toolbar.

Shortcut:  Select the text in the graph and use the hot keys PAGE DOWN and PAGE UP to rotate text in 5° increments.  Fine rotation can be achieved by holding down the CTRL key while pressing PAGE DOWN and PAGE UP.

Note also that some fonts may not support rotation and some fonts may support only limited rotation and will approximate rotation to the nearest angle to which it may be rotated.  When these fonts are used, misalignment between the frame around the text and the font may occur.  In this case, do not place a frame around the text.  Also note that some printer drivers may not support rotation of some fonts (even though the text may appear properly rotated on the screen).


Text Objects Style - Alignment

Justification:  This option will allow you to left-, center-, or right-justify the text against the respective margins.

Text in graph (anchor point):  Select the anchor point for the custom text.  When you select the text object in the graph, the selected anchor point location is displayed as a black selection square inside the outline of the selected text.

Moving selected text:  When you drag the text in the graph, the anchor changes to a cross-hair at the anchor location.  You can use this point to aid in the alignment of the text in the graph (e.g., this anchor point will be pulled into alignment with gridlines or intersections of gridlines when using the snap to grid option).  For example:

A Horizontal-Left and Vertical-Top alignment:

A Horizontal-Right and Vertical-Bottom alignment:

Rotating selected text:  The anchor point is also used as the point around which the text is rotated (see Orientation).  When the anchor point is used as the "pivot point" during rotation, it changes to a cross-hair at the anchor location.


Object Properties - Font

Click on the Font button to open the Font dialog from which you can select a global font style and size for the text.  Note that this setting will affect all of the text except for sections formatted using a local font (see the Graphic Text Editor).


Shape Objects Style

This option will allow you to pre-specify (select the Object Styles - Shapes option from the Insert pull-down menu) or change (highlight the object and select the Object Properties option from the Edit pull-down menu) certain properties for shape objects in the graph (e.g., squares, circles, polylines, see Graph Drawing Tools).

Shape Objects Style dialog:

Dynamic Scale

Locked Position

Patterns

Outline

Filled Background

Remove

Set as default style

See also, Using Dynamic (Coordinate) Mode in Categorized and Matrix Graphs


Object Properties - Outline

This option allows you to change the line pattern of the outline of the object.  Click on the Line Pattern button to open the Line Pattern dialog from which you can select the pattern, width, and color of the outline.  (See also, Selecting Point, Lines, Area Patterns.)


Picture and Complex Objects Style

This option will allow you to pre-specify (select the Object Styles - Pictures option from the Insert pull-down menu) or change (highlight the object and select the Object Properties option from the Edit pull-down menu) certain properties for pictures and other complex objects in the graph (e.g., bitmaps, linked or embedded objects, see Insert Object).

Picture and Complex Objects dialog:

Object Properties

Dynamic Scale

Locked Position

Original Proportions

Borders

Filled Background

Remove

Set as default style

Mapping Mode

See also, Using Dynamic (Coordinate) Mode in Categorized and Matrix Graphs


Object Properties - Dynamic Scale

When you select this option, the object will be dynamically anchored against the X- and Y-axis scales of 2D graphs and not the physical window coordinates, thus its position will be dynamically adjusted as you make changes to the graph and the positions of the dynamic object will always correspond to the respective coordinates of the plots (e.g., point markers, lines. bars, etc.).  When you de-select this option, the object will be assigned to a Fixed window location and its respective position in the graph will remain unchanged when you make adjustments to the graph (e.g., when you rescale the graph), thus it will be unrelated to any specific parts of the graph.  (Note that in 3D graphs, the Dynamic option cannot be used due to the lack of fixed 2D graph coordinates.  Thus, the object positioned on the screen of a 3D or 4D graph may lose its relation to the specific elements of the graphs when you change the graph, e.g., resize, rescale, or rotate it.)

You can change between fixed and dynamic modes using the respective Toolbar button (see below) by first highlighting the object (click on it once) and then clicking on the Toolbar button to toggle between modes.

Fixed Mode:

Dynamic Mode (when depressed):

See also, Using Dynamic (Coordinate) Mode in Categorized and Matrix Graphs


Object Properties - Original Proportions

Click on this option to maintain the original proportion of the object.  When this option is selected, you will be able to resize the object proportionately (i.e., maintain the aspect ratio of the object).  When this option is de-selected, you will be able to resize the object disproportionately (e.g., elongate the object by stretching it in one direction).  For more information on resizing an object, see Resizing an Object.


Object Properties - Borders

When selected, this option will place a border around the object.  Once you have selected this option, the Border Pattern button will no longer be dimmed.  Click on this button to open the Line Pattern dialog from which you can select the pattern, width, and color of the frame line.  (See also, Selecting Point, Lines, Area Patterns.)


Object Properties - Filled Background

Selecting this option will cause the background and foreground of the object to be displayed in the graph (i.e., the object will cover-up what is underneath it).  When you de-select this option, the background of the object will become transparent, allowing you to view the current graph background instead of the object's background.  (See also, Printing Objects with Filled Background.)


Object Properties - Remove

This button is dimmed when no objects are currently selected.  Clicking on the Remove button will allow you to remove (delete) the currently selected (highlighted) object from the current graph.  Note that you can also delete an object from the graph by clicking once on the object (to highlight it, or highlight it by pressing CTRL+A) and then pressing Delete on the keyboard.


Object Properties - Locked Position

Once you have positioned the object in the graph, you can use this option to lock it into place in the graph.  If the object is moved or resized after it is locked, then STATISTICA will prompt you to either unlock it (so the action can be completed) or to cancel the action.


Graphics View Menu

Fixed Proportions	Object Selection

Change Proportions	Display Filters

Adjust Graph Margins	Toolbar

Page/Printer Proportion	Change Show

Restore Original Settings	Status Bar

Brushing Mode	Alignment Grid

Rotate	Snap to Grid

Animated Stratification	Auto Task Buttons


Graphics Insert Menu

Text	Polyline

Rectangle	Arrow

Round Rectangle	Line Attributes

Oval	Fill Attributes

Arc	Object


Page/Printer Proportion

Select this option when you want the graph window to have the same proportions as the current printer/page proportions (as specified in the Print Preview, Margins, and Printer Setup dialogs).  This option will automatically adjust the proportion of the graph to fill the physical size of the printed page.  This is especially useful when pasting more than one graph into a Blank Graph (in order to place more than one graph on a page).


Alignment Grid

When you select this option, a grid will be placed over the current graph.  This grid is a visible representation of the grid specified via the Snap to Grid option and the spacing of the gridlines are dependent on the Horizontal and Vertical Spacing settings in the Snap to Grid dialog.  The alignment grid aids in the placement and alignment of graphic objects (e.g., added text, embedded or linked objects, arrows, free-hand drawings, a previously saved graph, etc.); however, the grid will not be printed when you print the graph and can be turned on or off by clicking on this option in the View pull-down menu or by pressing CTRL+G.  This option is especially useful when using the Blank Graph option from the Graphs pull-down menu.  In this case, a blank graph will open, and the Alignment Grid can be used to arrange and align the objects (for example, an embedded object) in the blank graph.

Note that for more precise placement of graphic objects, place the object in fixed mode and use the cursor coordinates displayed in the Toolbar Show window to align the object.  These coordinates are the percentages of the total window width and height (the lower left corner is [0%, 0%] the upper right corner is [100%, 100%]) and will not change as the graph is resized.

Shortcut:  Use CTRL+G to toggle the Alignment Grid on and off.

See also:

Moving a Graph Object


  Snap to Grid

The "snap to grid" facility, enabled by clicking the [image] toolbar button or the Snap to Grid option in the View pull-down menu, aligns drawing objects with the drawing grid, an invisible network of lines that covers the drawing area (the grid may be displayed by pressing CTRL+G or selecting the option Alignment Grid from the View pull-down menu).  When this facility is enabled, inserted objects are always pulled into alignment with gridlines or intersections of gridlines (the "snap to grid" effect).  The default spacing of gridlines is 5% of the display; the vertical and horizontal spacing between gridlines can be changed.  Initially, the grid begins at the 0,0 point in the upper-left corner of the graph window, but you can change the location from which gridlines are measured by editing the Horizontal and Vertical Origin values.

When placing objects, you may toggle the Snap to Grid effect on and off by holding down the TAB key.  In addition, you may specify whether the Snap to Grid alignment will apply only to objects placed in Fixed mode, or to all objects, regardless of drawing mode.

Snap to Grid dialog:

Horizontal/Vertical Spacing:  You can specify the vertical and horizontal spacing of the gridlines with this option.

Horizontal/Vertical Origin:  Specify here, the location (horizontal and/or vertical) in the graph at which STATISTICA will begin to draw the gridlines.

Snap to Grid:  These options set the default action of the Snap to Grid.

Off:  When you select this option, the Snap to Grid effect will be turned off.  Holding down on the TAB key while dragging an object will temporarily enable or disable the Snap to Grid depending on this setting.

On (Fixed Only):  When you select this option, the Snap to Grid effect will be enabled only for objects placed in Fixed mode.

On (Fixed and Dynamic): When you select this option, the Snap to Grid effect will be enabled for objects placed in either Fixed or Dynamic mode.

Shortcut:  Hold down the TAB key.

See also:

Moving a Graph Object


  Blank Graph

When you select this option from the Graphs pull-down menu (or the Graphs Gallery dialog), a blank graph will open in which you can add new or existing graph objects (e.g., added text, embedded or linked objects, arrows, free-hand drawings, previously saved graphs, etc.).  The Alignment Grid can be used to aid in the placement and alignment of the graph objects in the blank graph.  Blank graphs are also used as a master document for the components of compound graphs (for example, see Quality Control or Multiple AutoLayout Graph).

  Default Proportion:  When you select this option, the proportions of the blank graph window will follow the default graph window proportions (i.e., they will not necessarily be the same as the current printer/page proportions, e.g., portrait/landscape, margins, etc., see Print Preview).  The graph proportion can later be adjusted via the Page/Printer Proportion option from the View pull-down menu (so that the graph will fill the physical size of the printed page) or the Change Proportions option in the View pull-down menu.

  Page/Printer Proportions:  Selecting this option will open a blank graph window which is proportional to the current printer page proportions, as specified in the Print Preview, Margins, and Printer Setup dialogs (e.g., portrait or landscape).  The blank graph proportion will automatically be adjusted so that the graph will fill the physical size of the printed page.  This is especially useful when pasting more than one graph into the blank graph (in order to place more than one graph on a page).  The graph proportions can later be adjusted to the default proportions via the Restore Original Settings option in the View pull-down menu.


Restore Original Settings

When you make changes to the graph proportions or margins (i.e., "stretch" or "shrink" the graph proportionately or disproportionately, or move the graph around in the graph window) using the Fixed Proportions, Change Proportions, Adjust Graph Margins, Zoom In, or Zoom Out options, selecting the Restore Original Settings option from the View pull-down menu will return the graph to its original (at the point when the graph was created or the previously-saved graph settings) window proportions and margins.


Filters

Display Filters

When data points or text (such as scale values or data point labels) overlap in the graph, you can use this option from the Graphics View pull-down menu to open the Display Filters dialog in order to select the degree of filtering (removal of overlapping points or text) in the current graph.  STATISTICA examines each point or text and does not draw the overlapping points or text within a designated radius (determined by the degree of filtering), in order to increase the readability of the graph speed up the graph drawing process.

Display Filters dialog:

Points, Text Filters:  Select for Points and Text one of four degrees of filtering.

Off:  Selecting this option will turn off the filtering process (i.e., STATISTICA will draw all points or text).

Level 1 through Level 3:  Indicate the size of radius around the points (or text) in the graph in which the overlapping points will be "filtered out," by selecting the appropriate Level (i.e., Level 1 indicates the smallest radius and Level 3 indicates the largest radius).

Set as Default:  Set this checkbox in order to make your selections here the default selections for subsequent graphs.

See also:  If Data Point Labels Overlap

NOTE:  Use the Brushing tools to turn off individual (or all) data point labels that were created using the Brushing tools.


Graphics Layout Menu

Graphics Layouts Menu

This menu will be displayed when you open the Layouts pull-down menu while a graph is currently active.

General Layout

Plot 1, . . . 10

New Plot

Edit Data

The length of the menu (the number of Plot ... options) depends on the number of plots in the current graph.  The specific contents of the options available from this menu depend on the general category of the graph (see Overview of Graphic Options in STATISTICA).


General Layout

There are two main graph customization dialogs in STATISTICA:  General Layout (controlling the global attributes and components of the entire graph, e.g., titles, gridlines) and Plot Layout (controlling attributes of individual plots, i.e., series of data represented in the graph).  Selecting this option will open the appropriate General Layout dialog for the current graph.  The General Layout dialogs for the various general types of graphs available in STATISTICA are listed below:

2D Graphs	Icon Plots

3D Scatterplots and Surfaces	Matrix Plots

3D Sequence Graphs	Ternary Scatterplots and Surfaces

3D Histograms


Plot Layout

There are two main graph customization dialogs in STATISTICA:  General Layout (controlling the global attributes and components of the entire graph, e.g., titles, gridlines) and Plot Layout (controlling attributes of individual plots, i.e., series of data represented in the graph).  Selecting this option will open the appropriate Plot Layout dialog for the current graph.  The Plot Layout dialogs for the various general types of graphs available in STATISTICA are listed below:

2D Graphs

3D Scatterplots and Surfaces

3D Sequence Graphs

Note that for 3D Histograms, Icon Plots, and Matrix Plots, the customization options controlling the patterns and colors of individual plots are included in their respective General Layout dialogs.


Graphics Options Menu

Global Defaults	General

Save Defaults	Display

Save Defaults As	Print

Retrieve Defaults	Stats Graphs

Retrieve Defaults From	User Graphs

General Layout Dialog

Macro

Command Langage (SCL)	Keyboard Macro

STATISTICA BASIC	Recorded Show Macro

Quick Open File	Customize Auto Task Buttons


Graphics Window Graphs Menu

These options are available from the graphics window Graphs pull-down menu.

  Stats 2D Graphs:

  2D Histograms	  2D Range Plots

  2D Scatterplots	  2D Box Plots

  Scatterplots w/Histograms	  2D Line Plots

  Scatterplots w/Box Plots	  Sequential/Stacked Plots

  Probability Plots	  Pie Charts

  Quantile-Quantile Plots	  Missing/Range Data Points

  Probability-Probability Plots	  2D Custom Function Plots

  Stats 3D Sequential Graphs:

  Raw Data Plots	  Range Plots

  Bivariate Histograms	  Box Plots

  Stats 3D XYZ Graphs:

  Scatterplots	  Ternary Plots

  Surface Plots	  Categorized Plots

  Contour Plots	  Categorized Ternary Plots

  Trace Plots	  Custom Function Plots

  Stats Matrix Plots

  Stats Icon Plots

  Stats Categorized Graphs:

  Histograms	  Box Plots

  Scatterplots	  Pie Charts

  Probability Plots	  Missing/Range Data Plots

  Quantile-Quantile Plots	  3D XYZ Plots

  Probability-Probability Plots	  3D Ternary Plots

  Line Plots

  Multiple Graph Layouts:

  Wizard

  Templates

  Blank Graph:

  Default Proportion

  Page/Printer Proportion

  Custom Graphs:

  2D Graphs	  Matrix Plots

  3D Sequential Graphs	  Icon Plots

  3D XYZ	  Ternary Plots

  Block Stats Graphs

  Histograms	  Box Plot/Medians

  Box Plot/Means	  Normal Prob. Plots

  Stats User-defined Graphs

 Graph Data Links


2D Graph Fitted Functions

2D Graphs Fitted Functions

You can fit an equation to the data in 2D plots by selecting one of the predefined functions (see below), or by custom defining a function (by default, this option is set to Off) in the Plot Layout: 2D Graphs dialog.  To custom define a function (mathematical expression), select either the Custom Function option or click on the Custom Function button to bring up the User-Defined Functions dialog.

  Linear	  Polynomial

  Logarithmic	  Least Squares

  Exponential	  Negative Exponential

  Spline	  Custom Function


General Layout:  2D Graphs

The General Layout:  2D Graphs dialog contains options to control the global characteristics of the entire graph (scales, titles, gridlines, etc.).  Each of these options is discussed below.

Shortcuts:  Double-click on the outside graph background or click the right-mouse-button and select the Change General Layout option from the flying menu.

General Layout:  2D Graphs dialog:

Graph Icon

Titles

Scales

Graph Type:  The current setting of the global Graph Type is displayed in this option.  If there is more than one plot in the current graph, then the Graph Type setting will apply to all the plots.  If you want to change the type of each plot individually, then click the Plot Layout button to specify the type and other plot specifications in the Plot Layout dialog (see below).

  Scatterplot	  Bar Left Y

  Line Plot	  Bar Right Y

  Step Plot	  Bar Top

  Min-Max X	  Bar Dev

  Min-Max Y	  Pie

  Bar X	  MPatt Bar

  Voronoi

Layout

Categorization

Plot Layout

Gridlines

Data Labels

Borders

Control Limits

Background


General Layout:  2D Graphs - Graph Icons

General Layout:  2D Graphs - Graph Icon

The graph icon in the upper left-hand corner of the dialog, represents the current global Graph Type (see below), and several aspects of the current general graph specifications, such as scale lines, gridlines, major tickmark style, and types of scale lines.  The graph icon will preview any changes that you make in this dialog.  The amount of details displayed on the icon can be controlled in the General Layout Dialog Options dialog (e.g., you can simplify the icon to speed up the display when you routinely work with very complex graphs).  However, the redraw of the icon can always be stopped by pressing any key or clicking the mouse button.


General Layout:  2D Graphs - Titles

You can edit or enter up to 11 lines of text in the active graph.  Each of the 11 lines can be up to 80 characters long and are automatically positioned and centered against the plotting area.  These 11 lines of text include up to 5 titles (positioned on the top of the graph) and 6 labels (2 labels for the X-axis, 2 labels for the left-Y axis, and 2 labels for the right-Y axis).

Title text can be customized using Control Characters.  By entering the appropriate Control Characters, you can add superscripts and subscripts to the title text as well as change the font attributes for specific parts of the text in each title (see the topic Control Characters Reference, for a listing of the available codes).  If you wish, you can use the fitted function equation as a graph title by entering the appropriate Control Characters in the title edit box.  The Control Characters for the fitted function are @F[plot number, subgraph number] where you specify the desired plot number and optionally the subgraph number (for categorized graphs).  For example, if you enter the Control Characters @F[2], then STATISTICA will enter in that title position, the fitted function for the second plot in a multiple plot graph (i.e., a 2D line plot with 3 plots).  If you enter the Control Characters @F[1,3] in a title, then STATISTICA will place in that title position the fitted function for the third subgraph in a categorized graph.  (Note:  @F can be used instead of @F[1] or @F[1,1].)

Font:  Click on this button to bring up the Font dialog from which you can choose a different font for the titles and labels (the choice will affect only the title which is currently selected in the edit box).


General Layout:  2D Graphs - Scales

Change the scale of the X-axis, Y-left axis, Y-right axis, or Top axis by selecting one of these axes and then specifying the scaling type and other options (see below).

Max:, Step:, Min:  These fields determine the minimum, step, and maximum scaling values for the axis specified above.  They are available only if you choose a Manual scaling method (see below) and dimmed otherwise.

Scaling:  Choose one of four scaling methods.  The method you choose here determines whether the minimum, step, and maximum scaling values of each axis will be set automatically by the program (Auto or Auto/0) or manually by the user (Manual or Manual/0).  When you select Auto or Manual, the steps will be determined by "counting" from the current minimum (value of Min, see above).  The choice of Auto/0 or Manual/0, will determine the steps by "counting" from 0, even if 0 is not in the current range between the minimum and maximum scaling values.

Type:  Choose between three types of scaling (Linear, Logarithmic, or Log-decimal).  Note that if the Logarithmic or Log-decimal scale is selected, the scale minimum for that axis must be greater than 0.  Logarithmic scales appear like this:

When you select the Log-decimal scale, STATISTICA will use as major tickmarks only decimal logarithmic steps that represent consecutive powers of 10 (e.g., .1, 1, 10, 100, etc.).  The step size (i.e., width of the steps on the graph) will be determined by STATISTICA.

(Note that the display of some scale values placed close to each other in Logarithmic scales may be suppressed if the current setting of the Display Filters is other than Off.)

Scale Options:  Click on this button to open the Scale Options dialog.  This dialog contains many other scaling options for the currently highlighted axis (see above) such as:  changing from numeric to text scale values or turning the scale values off, or changing the axis tickmarks, or scale lines.


General Layout:  2D Graphs - Layout

Normal:  Select this option in order to display the graph using Cartesian coordinates.

Polar:  Select this option in order to convert the standard (Cartesian) coordinates into a graph with polar coordinates.  Categorized graphs with polar coordinates can also be produced.

Layered:  Selecting this option will reduce the main graph plotting area to leave space for Margin Graphs in the upper and right side of the display (and a miniature graph in the corner).  The Margin Graphs represent vertically and horizontally compressed images (respectively) of the main graph.  This so-called layered compression is an exploratory data analysis technique that may facilitate the identification of otherwise obscured trends and patterns in 2-dimensional data sets.


General Layout:  2D Graphs - Categorization

Click on this button to open the Categorization Options dialog.  Use this dialog to edit the type of categorization, category labels, and the scaling of the category-graphs (applicable to categorized graphs).


General Layout:  2D Graphs - Plot Layout

Click on this button to open the Plot Layout dialog from which you can edit the plot legend, choose another plot type (for each individual plot when more than one plot is represented in the graph), change the line patterns or bar style, etc..  By default, the Plot Layout dialog for the first plot will be displayed.  You can move to the next plot using the Next Plot >> button in that dialog, or by selecting the desired plot layout in the Layout pull-down menu.


General Layout:  2D Graphs - Gridlines

Choose from four types of gridlines (None, X, Y, and X+Y) when you click on this button and open the Gridline dialog.


General Layout:  2D Graphs - Data Labels

When you click on this button, the Data Point Labels dialog will open.  In this dialog you can specify whether the actual values (i.e., coordinates) of individual data points (or their text labels) are to be displayed above the respective data points in the graph.  Changing the data labels in this dialog is a global operation in that the selection for labels that you make here will be applied to each plot in the graph.  To change the labels for an individual plot, double-click on a label for a specific plot to open the Data Point Labels dialog in which you can make your selection for that plot.

See also:  If Data Point Labels Overlap

NOTE:  Use the Brushing tools to turn off individual (or all) data point labels that were created using the Brushing tools.


General Layout:  2D Graphs - Borders

In the dialog resulting from this button (Line Pattern-Borders), you can choose to have a border drawn around the graph as well as the color and thickness of the border.


General Layout:  2D Graphs - Control Limits

Click on this button to open the Control Limits dialog.  Here, you will be able to determine whether Control Limits will be drawn on the graph and also how the limits will be shown.


General Layout:  2D Graphs - Background

Click on the desired color to change the graph background colors (separately for the Inside and Outside area of the display).  If you choose Other, then the Colors dialog will open from which you can choose a color from the color palette or customize a color.  You can preview the color that you have selected in the graph icon (see above).

Outside:  Click on a color to specify it for the background on the Outside of the plot.

Inside:  Select a color for the background Inside of the graph.

Note that when printing graphs, by default, the background colors are ignored; in order to print them (e.g., on a color device or a monochrome printer capable of generating fine shades of gray) select the Use dithered color to fill background option in the Print Graph dialog.


General Layout:  Ternary Scatterplots and Surfaces

The General Layout:  Ternary Scatterplots and Surfaces dialog contains options to control the global characteristics of the entire graph (scales, titles, gridlines, etc.).  Each of these options is discussed below.

Shortcuts:  Double-click on the outside graph background (outside the axes) or click the right-mouse-button and select Change General Layout from the flying menu.

General Layout:  Ternary Scatterplots and Surfaces dialog

Graph Icon

Titles

Scales

3D Text

Fit:  You can choose from four regression functions to fit to the data in a ternary plot.  Click on a function name for more information about that function.  See also Fitting Options for Ternary Plots.  You can use the fitted equation as a title in the graph by entering the appropriate Control Characters (see Titles).

  Linear Smooth	  Full Cubic Smooth

  Quadratic Smooth	  Special Cubic Smooth

  Custom Function:  Choosing the Custom Function type of surface above, or clicking on the Custom Function button will open the User-Defined Functions dialog.  In the User-Defined Functions dialog, you can specify a mathematical expression to define the surface of the plot.  Note that the surface specified here will be overlaid and not fit to the data (use the Nonlinear Estimation module to fit user-defined models to the data; that module features a wide selection of techniques to fit functions of virtually unlimited complexity).

Fit Options:  Clicking on this button will open the Fitting Options dialog from which you can choose the stiffness level and order of polynomial for the surface that you chose above.  (For more information on these options, see Fitting Options.)

Number of Cuts

Raw Data Spike

Graph Type:  The current setting of the global Graph Type is displayed in this option.  You can change the type (select it from the list) to one of the graphs listed below (click on each name for a brief description of the plot type).

  2D Scatterplot	  Trace Plot

  3D Scatterplot	  Surface Plot

  Space Plot	  Contour Plot

  Deviation Plot

Categorization

Plot Layout

Axes

Gridlines

Data Labels

Borders

More Options

Background

Contour


Ternary Scatterplots and Surfaces - Graph Icon

General Layout:  Ternary Scatterplots and Surfaces - Graph Icon

The graph icon in the upper left-hand corner of the dialog, represents the current global 3D Graph Type, and several aspects of the current general graph specifications, such as scale lines, gridlines, major tickmark style, and types of scale lines.  The graph icon will preview any changes that you make in this dialog.  The amount of details displayed on the icon can be controlled in the General Layout Dialog Options dialog (e.g., you can simplify the icon to speed up the display when you routinely work with very complex graphs).  However, the redraw can always be stopped by pressing any key or clicking the mouse button.


Ternary Scatterplots and Surfaces - Titles

General Layout:  Ternary Scatterplots and Surfaces - Titles

You can edit or enter up to 13 lines of text in the active graph.  Each of the 13 lines can be up to 80 characters long and are automatically positioned and centered against the plotting area.  These 13 lines of text include up to 5 titles (positioned on the top of the graph) and 8 labels (2 labels for the X-axis, 2 labels for the Y-axis, 2 labels for the Z-axis, and 2 labels for the V-axis).  Title text can be customized using Control Characters.  By entering the appropriate Control Characters, you can add superscripts and subscripts to the title text as well as change the font attributes for specific parts of the text in each title (see the topic Control Characters Reference, for a listing of the available Control Characters).

If you wish, you can use the fitted function equation as a graph title by entering the appropriate Control Characters in the title edit box.  The Control Characters for the fitted function are @F[plot number, subgraph number] where you specify the desired plot number and optionally the subgraph number (for categorized graphs).  For example, if you enter the Control Characters @F[2], then STATISTICA will enter in that title position, the fitted function for the second plot in a multiple plot graph (e.g., a 3D scatterplot with 3 plots).  If you enter the Control Characters @F[1,3] in a title, then STATISTICA will place in that title position the fitted function for the third subgraph in a categorized graph.  (Note:  @F can be used instead of @F[1] or @F[1,1].)

Font:  Click on this button to bring up the Font dialog from which you can choose a different font for the titles and labels (the choice will affect only the title which is currently selected in the edit box).


Ternary Scatterplots and Surfaces - Scales

General Layout:  Ternary Scatterplots and Surfaces - Scales

Change the scale of the X, Y, Z, or V-axis by selecting one of them and then specifying the scaling type and other options (see below).

Max:, Step:, Min:  These fields determine the minimum, step, and maximum scaling values for each of the three foreground axes specified above.  They are available only if you choose a Manual scaling method (see below) and dimmed otherwise.

Scaling:  Choose one of four scaling methods.  The method you choose here determines whether the minimum, step, and maximum scaling values of each axis will be set automatically by the program (Auto or Auto/0) or manually by the user (Manual or Manual/0).  When you select Auto or Manual, the steps will be determined by "counting" from the current minimum (value of Min, see above).  The choice of Auto/0 or Manual/0 will determine the steps by "counting" from 0, even if 0 is not in the current range between the minimum and maximum scaling values.

Type:  Choose between three types of scaling (Linear, Logarithmic, or Log-decimal).  Note that if the Logarithmic or Log-decimal scale is selected, then the scale minimum for that axis must be greater than 0.  Logarithmic scales appear like this:

When you select the Log-decimal scale, STATISTICA will use as major tickmarks only decimal logarithmic steps that represent consecutive powers of 10 (e.g., .1, 1, 10, 100, etc.).  The step size (i.e., width of the steps on the graph) will be determined by STATISTICA.

(Note that the display of some scale values placed close to each other in Logarithmic scales may be suppressed if the current setting of the Display Filters is other than Off.)

Scale Options:  Click on this button to open the Scale Options dialog.  This dialog contains many other scaling options for the currently highlighted axis such as:  changing from numeric to text scale values or turning the scale values off, or changing the axis tickmarks, or scale lines.


Ternary Scatterplots and Surfaces - 3D Text

General Layout:  Ternary Scatterplots and Surfaces - 3D Text

When this option is selected, the axis labels will appear alongside the foreground axes in 3-dimensional perspective.  If de-selected, the axis labels will appear as in a two-dimensional graphics display.


Ternary Scatterplots and Surfaces - Number of Cuts

General Layout:  Ternary Scatterplots and Surfaces - Number of Cuts

Specify the number of cuts for the X-,Y-, and Z-axes (separately) in this option.  The number of cuts will affect the smoothness of the surface or contour (i.e., the larger the number, the smoother and more detailed the surface).


Ternary Scatterplots and Surfaces - Raw Data Spike

General Layout:  Ternary Scatterplots and Surfaces - Raw Data Spike

Select this option if you want the raw data to be overlaid on the graph surface.  If the points are not located directly on the surface, then they will be "connected" to the surface by "spikes," which help identify the location of points (e.g., below or above the surface).


Ternary Scatterplots and Surfaces - Categorization

General Layout:  Ternary Scatterplots and Surfaces - Categorization

Click on this button to open the Categorization Options dialog.  Use this dialog to edit the type of categorization, category labels, and the scaling of the category-graphs (applicable to 3D categorized graphs).


Ternary Scatterplots and Surfaces - Plot Layout

General Layout:  Ternary Scatterplots and Surfaces - Plot Layout

Click on this button to open the Plot Layout dialog from which you can edit the plot legend, change the line patterns or point marker style, and other options.


Ternary Scatterplots and Surfaces - Axes

General Layout:  Ternary Scatterplots and Surfaces - Axes

Click on this button to open the Display Axes dialog.  There are 9 axes in a 3D ternary graph (2 horizontal X-axes, 2 horizontal Y-axes, 2 horizontal Z-axes, and 3 vertical V-axes.


Ternary Scatterplots and Surfaces - Gridlines

General Layout:  Ternary Scatterplots and Surfaces - Gridlines

Choose from several types of gridlines (None, X, Y, Z, X+Y, X+Z, Y+Z, and X+Y+Z) for the respective planes of the 3D ternary graph (XYZ, the base plane, XYZ', the upper plane, and XV, YV, and ZV the foreground planes) when you click on this button to open the Gridline dialog.


Ternary Scatterplots and Surfaces - Data Labels

General Layout:  Ternary Scatterplots and Surfaces - Data Labels

When you click on this button, the Data Point Labels dialog will open.  In this dialog, you can specify whether the actual values (i.e., X, Y, X+Y, Z, X+Z, Y+Z, X+Y+Z, V, X+V, Y+V, X+Y+V, Z+V, X+Z+V, Y+Z+V, or X+Y+Z+V coordinates) of individual data points (or their text labels) are to be displayed above the respective data points in the graph.  Changing the data labels in this dialog is a global operation in that the selection for labels that you make here will be applied to each plot in the graph.  To change the labels for an individual plot, double-click on a label for a specific plot to open the Data Point Labels dialog in which you can make your selection for that plot.

See also:  If Data Point Labels Overlap

NOTE:  Use the Brushing tools to turn off individual (or all) data point labels that were created using the Brushing tools.


Ternary Scatterplots and Surfaces - Borders

General Layout:  Ternary Scatterplots and Surfaces - Borders

In the dialog resulting from selecting this button (Line Pattern-Borders), you can choose to have a border drawn around the graph, as well as specify the color and thickness of that border.


Ternary Scatterplots and Surfaces - More Options

General Layout:  Ternary Scatterplots and Surfaces - More Options

Clicking on this button will bring up the 3D Graphs/More Options dialog from which you can adjust the eye position and axis proportions of the graph, as well as all the specifications of the contour and/or surface (levels, patterns, etc., see Specify Contour/Surface Levels).


Ternary Scatterplots and Surfaces - Background

General Layout:  Ternary Scatterplots and Surfaces - Background

Click on the desired color to change the graph background color.  If you choose Other, then the Colors dialog will open from which you can choose a color from the color palette or customize a color.  You can preview the color that you have selected in the graph icon.

Outside:  Click on a color to specify it for the background on the Outside of the 3D graph.

Inside:  Select a color for the background Inside of the 3D graph.

Note that when printing graphs, by default, the background colors are ignored; in order to print them (e.g., on a color device or a monochrome printer capable of generating fine shades of gray) select the Use dithered color to fill background option in the Print Graph dialog.


Ternary Scatterplots and Surfaces - Contour

General Layout:  Ternary Scatterplots and Surfaces - Contour

This option controls the display of Contour plots.  You can display these plots with or without a Legend and you can choose to display the contour as a series of Lines or Areas.  (See also, Specify Contour/Surface Levels and Calculating Contour Levels and Distance.)   In the case when more than one variable is selected for the V-axis, two fixed legends will be displayed in the graph, one for the contour level and one for the point markers.  Each legend can be independently removed and/or converted into a movable legend by clicking on the legend with the right-mouse-button and selecting the appropriate option from the resulting flying menu (see Legends).


General Layout:  3D Scatterplots and Surfaces

The General Layout:  3D Scatterplots and Surfaces dialog contains options to control the global characteristics of the entire graph (scales, titles, gridlines, etc.).  Each of these options is discussed below.

Shortcuts:  Double-click on the outside graph background (outside the axes) or click the right-mouse-button and select Change General Layout from the flying menu.

General Layout:  3D Scatterplots and Surfaces dialog

Graph Icon

Titles

Scales

Fit:  The following Fit options (fitted functions and smoothing methods) are only applicable for Surface and Contour types of graphs (see below).  When you select one of these Graph Types, you can specify the type of surface fit as well as other options discussed below.  You can use the fitted equation as a title in the graph by entering the appropriate Control Characters (see Titles).

Type of Fit:  Choose from among the following surfaces for the Surface or Contour plots.

  Linear Smooth	  Negative Exp/Wght

  Quadratic Smooth	  Spline Smooth

  Least Squares	  Custom Function

Custom Function:  Choosing the Custom Function type of surface above, or clicking on the Custom Function button will open the User-Defined Functions dialog.  In the User-Defined Functions dialog, you can specify a mathematical expression to define the surface of the plot.  Note that the surface specified here will be overlaid and not fit to the data (use the Nonlinear Estimation module to fit user-defined models to the data; that module features a wide selection of techniques to fit functions of virtually unlimited complexity).

Fit Options:  Clicking on this button will open the Fitting Options dialog from which you can choose the stiffness level for the surface that you chose above.  (For more information on these options, see Fitting Options.)

Number of Cuts

Raw Data Spike

Graph Type:  The current setting of the global Graph Type is displayed in this option.  You can change the type (select it from the list) to one of the graphs listed below (click on each name for a brief description of the plot type).

  Scatterplot	  Trace Plot

  Space Plot	  Surface Plot

  Spectral Plot	  Contour Plot

  Deviation Plot

Categorization

Plot Layout

Axes

Gridlines

Data Labels

Borders

More Options

Background

Contour


3D Scatterplots and Surfaces - Graph Icon

General Layout:  3D Scatterplots and Surfaces - Graph Icon

The graph icon in the upper left-hand corner of the dialog, represents the current global 3D Graph Type (see below), and several aspects of the current general graph specifications, such as scale lines, gridlines, major tickmark style, and types of scale lines.  The graph icon will preview any changes that you make in this dialog.  The amount of details displayed on the icon can be controlled in the General Layout Dialog Options dialog (e.g., you can simplify the icon to speed up the display when you routinely work with very complex graphs).  However, the redraw can always be stopped by pressing any key or clicking the mouse button.


3D Scatterplots and Surfaces - Titles

General Layout:  3D Scatterplots and Surfaces - Titles

You can edit or enter up to 11 lines of text in the active graph.  Each of the 11 lines can be up to 80 characters long and are automatically positioned and centered against the plotting area.  These 11 lines of text include up to 5 titles (positioned on the top of the graph) and 6 labels (2 labels for the X-axis, 2 labels for the Y-axis, and 2 labels for the Z-axis).  Title text can be customized using Control Characters.  By entering the appropriate Control Characters, you can add superscripts and subscripts to the title text as well as change the font attributes for specific parts of the text in each title (see the topic Control Characters Reference, for a listing of the available Control Characters).

If you wish, you can use the fitted function equation (see below) as a graph title by entering the appropriate Control Characters in the title edit box.  The Control Characters for the fitted function are @F[plot number, subgraph number] where you specify the desired plot number and optionally the subgraph number (for categorized graphs).  For example, if you enter the Control Characters @F[2], then STATISTICA will enter in that title position, the fitted function for the second plot in a multiple plot graph (e.g., a 3D scatterplot with 3 plots).  If you enter the Control Characters @F[1,3] in a title, then STATISTICA will place in that title position the fitted function for the third subgraph in a categorized graph.  (Note:  @F can be used instead of @F[1] or @F[1,1].)

Font:  Click on this button to bring up the Font dialog from which you can choose a different font for the titles and labels (the choice will affect only the title which is currently selected in the edit box).


3D Scatterplots and Surfaces - Scales

General Layout:  3D Scatterplots and Surfaces - Scales

Change the scale of the X, Y, or Z axis by selecting one of them and then specifying the scaling type and other options (see below).

3D Text:  When this option is selected, the axis labels will appear alongside the foreground axes in 3-dimensional perspective.  If de-selected, the axis labels will appear as in a two-dimensional graphics display.

Max:, Step:, Min:  These fields determine the minimum, step, and maximum scaling values for each of the three foreground axes specified above.  They are available only if you choose a Manual scaling method (see below) and dimmed otherwise.

Scaling:  Choose one of four scaling methods.  The method you choose here determines whether the minimum, step, and maximum scaling values of each axis will be set automatically by the program (Auto or Auto/0) or manually by the user (Manual or Manual/0).  When you select Auto or Manual, the steps will be determined by "counting" from the current minimum (value of Min, see above).  The choice of Auto/0 or Manual/0 will determine the steps by "counting" from 0, even if 0 is not in the current range between the minimum and maximum scaling values.

Type:  Choose between three types of scaling (Linear, Logarithmic, or Log-decimal).  Note that if the Logarithmic or Log-decimal scale is selected, then the scale minimum for that axis must be greater than 0.  Logarithmic scales appear like this:

When you select the Log-decimal scale, STATISTICA will use as major tickmarks only decimal logarithmic steps that represent consecutive powers of 10 (e.g., .1, 1, 10, 100, etc.).  The step size (i.e., width of the steps on the graph) will be determined by STATISTICA.

(Note that the display of some scale values placed close to each other in Logarithmic scales may be suppressed if the current setting of the Display Filters is other than Off.)

Scale Options:  Click on this button to open the Scale Options dialog.  This dialog contains many other scaling options for the currently highlighted axis such as:  changing from numeric to text scale values or turning the scale values off, or changing the axis tickmarks, or scale lines.


3D Scatterplots and Surfaces - Number of Cuts

General Layout:  3D Scatterplots and Surfaces - Number of Cuts

Specify the number of cuts for the X and Y axes (separately) in this option.  If you want the same number of cuts for both axes, you can enter the number in the X axis and then click on the Next (>>) button (directly below these entries) to copy that number to the Y axis.  The number of cuts will affect the smoothness of the surface or contour (i.e., the larger the number, the smoother and more detailed the surface).


3D Scatterplots and Surfaces - Raw Data Spike

General Layout:  3D Scatterplots and Surfaces - Raw Data Spike

Raw Data Spike:  Select this option if you want the raw data to be overlaid on the graph surface.  If the points are not located directly on the surface, then they will be "connected" to the surface by "spikes," which help identify the location of points (e.g., below or above the surface).


3D Scatterplots and Surfaces - Categorization

General Layout:  3D Scatterplots and Surfaces - Categorization

Click on this button to open the Categorization Options dialog.  Use this dialog to edit the type of categorization, category labels, and the scaling of the category-graphs (applicable to 3D categorized graphs).


3D Scatterplots and Surfaces - Plot Layout

General Layout:  3D Scatterplots and Surfaces - Plot Layout

Click on this button to open the Plot Layout dialog from which you can edit the plot legend, change the line patterns or point marker style, and other options.


3D Scatterplots and Surfaces - Axes

General Layout:  3D Scatterplots and Surfaces - Axes

Click on this button to open the Display Axes dialog.  There are 12 axes in a 3D graph (4 horizontal X axes, 4 horizontal Y axes, and 4 vertical Z axes) and you can specify exactly which of these axes will be displayed in the graph.


3D Scatterplots and Surfaces - Gridlines

General Layout:  3D Scatterplots and Surfaces - Gridlines

Choose from four types of gridlines (None, X, Y, and X+Y) for the respective plane of the 3D box (XY, XZ, YX, the background planes and XY', XZ', YZ', the foreground planes) when you click on this button to open the Gridline dialog.


3D Scatterplots and Surfaces - Data Labels

General Layout:  3D Scatterplots and Surfaces - Data Labels

When you click on this button, the Data Point Labels dialog will open.  In this dialog, you can specify whether the actual values (i.e., X, Y, X and Y, Z, X and Z, Y and Z, or X, Y, and Z coordinates) of individual data points (or their text labels) are to be displayed above the respective data points in the graph.  Changing the data labels in this dialog is a global operation in that the selection for labels that you make here will be applied to each plot in the graph.  To change the labels for an individual plot, double-click on a label for a specific plot to open the Data Point Labels dialog in which you can make your selection for that plot.

NOTE:  Use the Brushing tools to turn off individual (or all) data point labels that were created using the Brushing tools.


3D Scatterplots and Surfaces - Borders

General Layout:  3D Scatterplots and Surfaces - Borders

In the dialog resulting from selecting this button (Line Pattern-Borders), you can choose to have a border drawn around the graph, as well as specify the color and thickness of that border.


3D Scatterplots and Surfaces - More Options

General Layout:  3D Scatterplots and Surfaces - More Options

Clicking on this button will bring up the 3D Graphs/More Options dialog from which you can adjust the eye position and axis proportions of the graph, as well as the display of surface lines and a surface contour.


3D Scatterplots and Surfaces - Background

General Layout:  3D Scatterplots and Surfaces - Background

Click on the desired color to change the graph background color.  If you choose Other, then the Colors dialog will open from which you can choose a color from the color palette or customize a color.  You can preview the color that you have selected in the graph icon.

Outside:  Click on a color to specify it for the background on the Outside of the 3D graph.

Inside:  Select a color for the background Inside of the 3D graph.

Note that when printing graphs, by default, the background colors are ignored; in order to print them (e.g., on a color device or a monochrome printer capable of generating fine shades of gray) select the Use dithered color to fill background option in the Print Graph dialog.


3D Scatterplots and Surfaces - Contour

General Layout:  3D Scatterplots and Surfaces - Contour

This option controls the display of Contour plots.  You can display these plots with or without a Legend and you can choose to display the contour as a series of Lines or Areas.  (See also, Specify Contour/Surface Levels and Calculating Contour Levels and Distance.)   In the case when more than one variable is selected for the Z-axis, two fixed legends will be displayed in the graph, one for the contour levels and one for the point markers.  Each legend can be independently removed and/or converted into a movable legend by clicking on the legend with the right-mouse-button and selecting the appropriate option from the resulting flying menu (see Legends).


General Layout:  3D Sequence Graphs

The General Layout: 3D Sequence Graphs dialog contains options to control the global characteristics of the entire graph (scales, titles, gridlines, etc.).  Each of these options is discussed below.

Shortcuts:  Double-click on the outside graph background or click the right-mouse-button and select Change General Layout from the flying menu.

General Layout:  3D Sequence Graphs dialog

Graph Icon

Titles

Scales

Number of Cuts

Graph Type:  The current setting of the global Graph Type is displayed in this option.  You can change the type (select it from the list) to one of the graphs listed below (click on each name for a brief description of the plot type).

  Box Plot	  Spikes

  Block Plot	  Contour/Discre

  Ribbons	  Surface Plot

  Lines	  Contour Plot

Plot Layout

Axes

Gridlines

Borders

More Options

Background

Contour Style


General Layout:  3D Sequence Graphs - Graph Icon

The graph icon in the upper left-hand corner of the dialog, represents the current global 3D Graph Type, and several aspects of the current general graph specifications, such as scale lines, gridlines, major tickmark style, and types of scale lines.  The graph icon will preview any changes that you make in this dialog.  The amount of detail displayed on the icon can be controlled in the General Layout Dialog Options dialog (e.g., you can simplify the icon to speed up the display when you routinely work with very complex graphs).  However, the redraw can always be stopped by pressing any key or clicking the mouse button.


General Layout:  3D Sequence Graphs - Titles

You can edit or enter up to 11 lines of text in the active graph.  Each of the 11 lines can be up to 80 characters long and are automatically positioned and centered against the plotting area.  These 11 lines of text include up to 5 titles (positioned on the top of the graph) and 6 labels (2 labels for the X-axis, 2 labels for the left Y-axis, and 2 labels for the Z-axis).  Title text can be customized using Control Characters.  By entering the appropriate Control Characters, you can add superscripts and subscripts to the title text as well as change the font attributes for specific parts of the text in each title (see the topic Control Characters Reference, for a listing of the available codes).

Font:  Click on this button to bring up the Font dialog from which you can choose a different font for the titles and labels (the choice will affect only the title which is currently selected in the edit box).


General Layout:  3D Sequence Graphs - Scales

Change the scale of the X-, Y-, or Z-axis by selecting one of them and then specifying the scaling type and other options (see below).

3D Text:  When this option is selected, the axis labels will appear alongside the foreground axes in 3-dimensional perspective.  If de-selected, the axis labels will appear as in a two-dimensional graphics display.

Max:, Step:, Min:  These fields determine the minimum, step, and maximum scaling values for each of the three foreground axes specified above.  They are available only if you choose a Manual scaling method (see below) and dimmed otherwise.

Scaling:  Choose one of four scaling methods.  The method you choose here determines whether the minimum, step, and maximum scaling values of each axis will be set automatically by the program (Auto or Auto/0) or manually by the user (Manual or Manual/0).  When you select Auto or Manual, the steps will be determined by "counting" from the current minimum (value of Min, see above).  The choice of Auto/0 or Manual/0, will determine the steps by "counting" from 0, even if 0 is not in the current range between the minimum and maximum scaling values.

Type:  Choose between three types of scaling (Linear, Logarithmic, or Log-decimal).  Note that if the Logarithmic or Log-decimal scale is selected, then the scale minimum for that axis must be greater than 0.  Logarithmic scales appear like this:

When you select the Log-decimal scale, STATISTICA will use as major tickmarks only decimal logarithmic steps that represent consecutive powers of 10 (e.g., .1, 1, 10, 100, etc.).  The step size (i.e., width of the steps on the graph) will be determined by STATISTICA.

(Note that the display of some scale values placed close to each other in Logarithmic scales may be suppressed if the current setting of the Display Filters is other than Off.)

Scale Options:  Click on this button to open the Scale Options dialog.  This dialog contains many other scaling options for the currently highlighted axis (see above) such as:  changing from numeric to text scale values or turning the scale values off, or changing the axis tickmarks, or scale lines.


General Layout:  3D Sequence Graphs - Graph Type

General Layout:  3D Sequence Graphs - Number of Cuts

This option applies if the Graph Type is set to Surface or Contour.  Specify the number of cuts for the X-and Y-axes (separately) in this option.  If you want the same number of cuts for both axes, you can enter the number in the X-axis and then click on the Next (>>) button (below these entries) to copy that number to the Y-axis.  The number of cuts will affect the smoothness of the graph surface (i.e., the larger the number, the smoother and more detailed the surface).


General Layout:  3D Sequence Graphs - Plot Layout

Click on this button to open the Plot Layout dialog from which you can change the patterns of points, lines, walls (the surfaces of the plot blocks, ribbons or boxes when those plots are selected) and borders.


General Layout:  3D Sequence Graphs - Axes

Click on this button to open the Display Axes dialog.  There are 12 axes in a 3D graph (4 horizontal X-axes, 4 horizontal Y-axes, and 4 vertical Z-axes) and you can specify exactly which of these axes will be displayed in the graph.


General Layout:  3D Sequence Graphs - Gridlines

Choose from four types of gridlines (None, X, Y, and X+Y) for the corresponding plane of the 3D box (XY, XZ, YX, the background planes and XY', XZ', YZ', the foreground planes) when you click on this button to open the Gridline dialog.


General Layout:  3D Sequence Graphs - Borders

In the dialog resulting from this button (Line Pattern-Borders), you can choose to have a border drawn around the graph as well as the color and thickness of that border.


General Layout:  3D Sequence Graphs - More Options

Clicking on this button will bring up the 3D Graphs/More Options dialog from which you can adjust the eye position and axes proportions of the graph, as well as display surface lines and a surface contour.


General Layout:  3D Sequence Graphs - Borders

General Layout:  3D Sequence Graphs - Background

Click on the desired color to change the graph background color.  If you choose Other, then the Colors dialog will open from which you can choose a color from the color palette or customize a color.  You can preview the color that you have selected in the graph icon.

Outside:  Click on a color to specify it for the background on the Outside of the 3D graph.

Inside:  Select a color for the background Inside of the 3D graph.

Note that when printing graphs, by default, the background colors are ignored; in order to print them (e.g., on a color device or a monochrome printer capable of generating fine shades of gray) select the Use dithered color to fill background option in the Print Graph dialog.


General Layout:  3D Sequence Graphs - Contour Style

This option controls the display of Contour plots.  You can display these plots with or without a Legend and you can choose to display the contour as a series of Lines or Areas.  (See also, Calculating Contour Levels and Distance.)


General Layout and Plot Layout:  3D Histograms

The General Layout and Plot Layout:  3D Histograms dialog contains options to control the global characteristics of the entire graph (scales, titles, gridlines, etc.).  Each of these options is discussed below.

Shortcuts:  Double-click on the outside graph background or click the right-mouse-button and select Change General Layout from the flying menu.

General Layout and Plot Layout:  3D Histogram dialog

Graph Icon

Titles

Scales

Number of Cuts

Graph Type:  The current setting of the global Graph Type is displayed in this option.  You can change the type (select it from the list) to one of the graphs listed below (click on each name for a brief description of the plot type).

  Box Plot	  Surface Plot

  Spikes	  Contour Plot

  Contour/Discrete

Axes

Gridlines

Borders

More Options

Background

Contour Style

Patterns


General Layout and Plot Layout:  3D Histograms - Graph Icon

The graph icon in the upper left-hand corner of the dialog, represents the current global 3D Graph Type, and several aspects of the current general graph specifications, such as scale lines, gridlines, major tickmark style, and types of scale lines.  The graph icon will preview any changes that you make in this dialog.  The amount of detail displayed on the icon can be controlled in the General Layout Dialog Options dialog (e.g., you can simplify the icon to speed up the display when you routinely work with very complex graphs).  However, the redraw can always be stopped by pressing any key or clicking the mouse button.


General Layout and Plot Layout:  3D Histograms - Titles

You can edit or enter up to 11 lines of text in the active graph.  Each of the 11 lines can be up to 80 characters long and are automatically positioned and centered against the plotting area.  These 11 lines of text include up to 5 titles (positioned on the top of the graph) and 6 labels (2 labels for the Bottom X-axis, 2 labels for the left Bottom Y-axis, and 2 labels for the Z-axis).  Title text can be customized using Control Characters.  By entering the appropriate Control Characters, you can add superscripts and subscripts to the title text as well as change the font attributes for specific parts of the text in each title (see the topic Control Characters Reference, for a listing of the available codes).

Font:  Click on this button to bring up the Font dialog from which you can choose a different font for the titles and labels (the choice will affect only the title which is currently selected in the edit box).


General Layout and Plot Layout:  3D Histograms - Scales

Change the scale of the X-, Y-, or Z- axis by selecting one of them and then specifying the scaling type and other options (see below).

3D Text:  When this option is selected, the axis labels will appear alongside the foreground axes in 3-dimensional perspective.  If de-selected, the axis labels will appear as in a two-dimensional graphics display.

Max:, Step:, Min:  These fields determine the minimum, step, and maximum scaling values for each of the three foreground axes specified above.  They are available only if you choose a Manual scaling method (see below) and dimmed otherwise.

Scaling:  Choose one of four scaling methods.  The method you choose here determines whether the minimum, step, and maximum scaling values of each axis will be set automatically by the program (Auto or Auto/0) or manually by the user (Manual or Manual/0).  When you select Auto or Manual, the steps will be determined by "counting" from the current minimum (value of Min, see above).  The choice of Auto/0 or Manual/0, will determine the steps by "counting" from 0, even if 0 is not in the current range between the minimum and maximum scaling values.

Type:  Choose between three types of scaling (Linear, Logarithmic, or Log-decimal).  Note that if the Logarithmic or Log-decimal scale is selected, then the scale minimum for that axis must be greater than 0.  Logarithmic scales appear like this:

When you select the Log-decimal scale, STATISTICA will use as major tickmarks only decimal logarithmic steps that represent consecutive powers of 10 (e.g., .1, 1, 10, 100, etc.).  The step size (i.e., width of the steps on the graph) will be determined by STATISTICA.

(Note that the display of some scale values placed close to each other in Logarithmic scales may be suppressed if the current setting of the Display Filters is other than Off.)

Scale Options:  Click on this button to open the Scale Options dialog.  This dialog contains many other scaling options for the currently highlighted axis such as:  changing from numeric to text scale values or turning the scale values off, or changing the axis tickmarks, or scale lines.


General Layout and Plot Layout:  3D Histograms - Number of Cuts

This option applies if the Graph Type is set to Surface or Contour.  Specify the number of cuts for the X-and Y-axes (separately) in this option.  If you want the same number of cuts for both axes, you can enter the number in the X-axis and then click on the Next (>>) button (in-between these entries) to copy that number to the Y-axis.  The number of cuts will affect the smoothness of the graph surface (i.e., the larger the number, the smoother and more detailed the surface).


General Layout and Plot Layout:  3D Histograms - Axes

Click on this button to open the Display Axes dialog.  There are 12 axes in a 3D graph (4 horizontal X-axes, 4 horizontal Y-axes, and 4 vertical Z-axes) and you can specify exactly which of these axes will be displayed in the graph.


General Layout and Plot Layout:  3D Histograms - Gridlines

Choose from four types of gridlines (None, X, Y, and X+Y) for the corresponding plane of the 3D box (XY, XZ, YX, the background planes and XY', XZ', YZ', the foreground planes) when you click on this button to open the Gridline dialog.


General Layout and Plot Layout:  3D Histograms - Borders

In the dialog resulting from this button (Line Pattern-Borders), you can choose to have a border drawn around the graph as well as specify the color and thickness of that border.


General Layout and Plot Layout:  3D Histograms - More Options

Clicking on this button will bring up the 3D Graphs/More Options dialog from which you can adjust the eye position and axis proportions of the graph, as well as the display of surface lines and a surface contour.


General Layout and Plot Layout:  3D Histograms - Background

Click on the desired color to change the graph background color.  If you choose Other, then the Colors dialog will open from which you can choose a color from the color palette or customize a color.  You can preview the color that you have selected in the graph icon (see above).

Outside:  Click on a color to specify it for the background on the Outside of the 3D graph.

Inside:  Select a color for the background Inside of the 3D graph.

Note that when printing graphs, by default, the background colors are ignored; in order to print them (e.g., on a color device or a monochrome printer capable of generating fine shades of gray) select the Use dithered color to fill background option in the Print Graph dialog.


General Layout and Plot Layout:  3D Histograms - Contour Style

This option controls the display of Contour plots.  You can display these plots with or without a Legend and you can choose to display the contour as a series of Lines or Areas.  (See also, Calculating Contour Levels and Distance.)


General Layout and Plot Layout:  3D Histograms - Patterns

Choose a pattern for the Top, X, or Y walls of the histogram bars in the 3-dimensional graph.  When you select a wall, the Area Pattern dialog will open from which you can choose a color and pattern for the specified wall.  Click on the Box Borders, Points and Spike Lines buttons in this option to bring up dialogs from which you can change the color, pattern and size of the border, points or lines (see Line Pattern).  (See also, Selecting Point/Lines/Area Patterns.)  The default histogram patterns (top, X, Y faces) used in this graph can be adjusted in the Specific Plots Default Patterns dialog.


General Layout and Plot Layout:  Icon Graphs

Icon graphs represent cases or other units of observations as multidimensional symbols.  The General Layout and Plot Layout:  Icon Graphs dialog contains options to control the global characteristics of the entire graph (patterns, legend, layout, icon, etc.).  Each of these options is discussed below.

Shortcuts:  Double-click on the outside graph background or click the right-mouse-button and select Change General Layout from the flying menu.

General Layout and Plot Layout:  Icon Graphs dialog

Graph Icon

Titles

Graph Type:  The current setting of the global Graph Type is displayed in this option.  You can change the type (select it from the list) to one of the graphs listed below (click on each name for a brief description of the plot type).

  Chernoff Faces	  Pies

  Stars	  Columns

  Sun Rays	  Lines

  Polygons	  Profiles

Layout

Legend

Case Names

Selection

Points

Lines

Areas

Borders

Icon Info

Background


General Layout and Plot Layout:  Icon Graphs - Graph Icon

The graph icon in the upper left-hand corner of the dialog, represents the current global Icon Graph Type, and several aspects of the current general graph specifications, such as layout of icons.  The graph icon will preview changes that you make in this dialog.  The amount of details displayed on the icon can be controlled in the General Layout Dialog Options dialog (e.g., you can simplify the icon to speed up the display when you routinely work with very complex graphs).  However, the redraw can always be stopped by pressing any key or clicking the mouse button.


General Layout and Plot Layout:  Icon Graphs - Titles

You can edit or enter up to 11 lines of text in the active graph.  Each of the 11 lines can be up to 80 characters long and are automatically positioned and centered against the plotting area.  These 11 lines of text include up to 5 titles (positioned on the top of the graph) and 6 labels (2 labels for the X-axis, 2 labels for the left-Y axis, and 2 labels for the right-Y axis).  Title text can be customized using Control Characters.  By entering the appropriate Control Characters, you can add superscripts and subscripts to the title text as well as change the font attributes for specific parts of the text in each title (see the topic Control Characters Reference, for a listing of the available codes).

Font:  Click on this button to bring up the Font dialog from which you can choose a different font for the titles and labels (the choice will affect only the title which is currently selected in the edit box).


General Layout and Plot Layout:  Icon Graphs - Layout

Change the layout and resolution of the icon plot by changing the number of Rows and Columns in which the icons are displayed (this may stretch or shrink the icons to fit the specified space).  You can also modify the assignment of the currently selected variables to the consecutive components of the icon (e.g., columns of the Column icon plot) in the plot when you click on the Var Order button to bring up the Order of Variables dialog.  (In the case of Chernoff Faces, clicking on the Var Order button will open the Chernoff Faces Definition dialog from which you can edit the dimensions of the icon facial characteristics.)


General Layout and Plot Layout:  Icon Graphs - Legend

Choose to display the icon plot with (On) or without (Off) the legend.  You can also change the font for the legend when you click on the Font button.  The legend consists of the names of variables used to define the consecutive components of the icons (or in the case of Chernoff Faces, the corresponding facial characteristics of the icons).  Edit the variable names in the Variable Names dialog when you click on the Edit button.


General Layout and Plot Layout:  Icon Graphs - Case Names

By default, case names are displayed under their respective icons in the icon plots.  You can turn off the case name display with this option.  The case names font can be changed by clicking on the Font button.  You can also edit the case names when you click on the Edit button to open the Data Point Labels dialog.

NOTE:  Use the Brushing tools to turn off individual (or all) data point labels that were created using the Brushing tools.


General Layout and Plot Layout:  Icon Graphs - Selection

Click on this button to select the Frame Pattern used to mark the selected icons.  This option is only available to icon plots in which cases have been "selected" via the Mark Icon option.


General Layout and Plot Layout:  Icon Graphs - Points

Click on this button to change the point size and pattern in the Points Pattern dialog (this option is applicable to icons that contain a "marked" center point, e.g., in polygons).


General Layout and Plot Layout:  Icon Graphs - Lines

When you select Chernoff Faces as the icon and click on this button, the Chernoff Face Patterns dialog will open from which you can change the pattern of each of the facial lines.  For all other types of icons, the Line Patterns dialog will open when you click on this button.  You can select a different line pattern in this dialog.


General Layout and Plot Layout:  Icon Graphs - Areas

Click on this button to open the Area Pattern dialog in which you can change the pattern and color of the filled in areas of the icons (such as for Profiles and Polygons).


General Layout and Plot Layout:  Icon Graphs - Borders

In the dialog resulting from this button (Line Pattern-Borders), you can choose to have a border drawn around the graph as well as the color and thickness of that border.


General Layout and Plot Layout:  Icon Graphs - Icon Info

Click on this button to display a summary description of the current icon graph (e.g., number of cases, variables, icon selection conditions, etc.).


General Layout and Plot Layout:  Icon Graphs - Background

Click on the desired color to change the graph background color.  If you choose Other, then the Colors dialog will open from which you can choose a color from the color palette or customize a color.  You can preview the color that you have selected in the graph icon (see above).

Outside:  Click on a color to specify it for the background on the Outside area of the graph where the icons are located.

Inside:  Select a color for the background Inside area of the graph where the icons are located.

Note that when printing graphs, by default, the background colors are ignored; in order to print them (e.g., on a color device or a monochrome printer capable of generating fine shades of gray) select the Use dithered color to fill background option in the Print Graph dialog.


General Layout and Plot Layout:  Matrix Graphs

Matrix graphs combine (in one display) multiple x-y graphs generated for all combinations of variables from one or two lists.  The General Layout and Plot Layout:  Matrix Graphs dialog contains options to control the global characteristics of the entire graph (titles, gridlines, patterns, etc.).  Each of these options is discussed below.

Shortcuts:  Double-click on the outside graph background or click the right-mouse-button and select Change General Layout from the flying menu.

General Layout and Plot Layout:  Matrix Graphs dialog

Graph Icon

Titles

Graph Type:  The current setting of the global Graph Type is displayed in this option.  You can change the type (select it from the list) to one of the graphs listed below.

  Square Scatter Matrix	  Rectangular Scatter Matrix

  Square Line Matrix	  Rectangular Line Matrix

  Square Column Matrix	  Rectangular Column Matrix

Layout

Fit:  Choose to fit an equation to the data in each of the matrix plots, by selecting one of the predefined functions (see below), or by custom defining a function (to be overlaid).  To custom define a function (mathematical expression), select either the Custom Function option or click on the Custom Function button to bring up the User-Defined Functions dialog.

  Linear	  Polynomial

  Logarithmic	  Least Squares

  Exponential	  Negative Exponential

  Spline	  Custom Function

You can also change the line pattern of the fitted function by clicking on the Pattern button to open the Line Patterns dialog.  Click on the Options button to open the Fitting Options dialog from which you can choose the stiffness level and order of polynomial as well as other options concerning the function that you chose above.

Histograms

Matrix Type

Points

Lines

Areas

Frame

Gridlines

Borders

Background


General Layout and Plot Layout:  Matrix Graphs - Graph Icon

The graph icon in the upper left-hand corner of the dialog, represents the current global Graph Type, and several aspects of the current general graph specifications, such as, gridlines, or matrix format.  The graph icon will preview any changes that you make in this dialog.  The amount of details displayed on the icon can be controlled in the General Layout Dialog Options dialog (e.g., you can simplify the icon to speed up the display when you routinely work with very complex graphs).  However, the redraw can always be stopped by pressing any key or clicking the mouse button.


General Layout and Plot Layout:  Matrix Graphs - Titles

You can edit or enter up to 11 lines of text in the active graph.  Each of the 11 lines can be up to 80 characters long and are automatically positioned and centered against the plotting area.  These 11 lines of text include up to 5 titles (positioned on the top of the graph) and 6 labels (2 labels for the X-axis, 2 labels for the left-Y axis, and 2 labels for the right-Y axis).  Title text can be customized using Control Characters.  By entering the appropriate Control Characters, you can add superscripts and subscripts to the title text as well as change the font attributes for specific parts of the text in each title (see the topic Control Characters Reference, for a listing of the available codes).

Font:  Click on the [image] button to bring up the Font dialog from which you can choose a different font for the titles and labels (the choice will affect only the title which is currently selected in the edit box).  To change the font for the Histogram titles, see Histograms.


General Layout and Plot Layout:  Matrix Graphs - Layout

Change the layout and "resolution" of the matrix of graphs by changing the number of Rows and Columns of graphs that are displayed.  You can also reorder the variables when you click on the Var Order button to bring up the Order of Variables dialog.


General Layout and Plot Layout:  Matrix Graphs - Histograms

Frequency histograms are placed on the diagonal of square matrix plots and in the first row and column of rectangular matrix plots.  Select Off in this option to remove the histograms from the matrix plot.  You can also choose the type of scaling for the histograms in this option.  When you select a Common scale, then the scale will be based on a common range of all of the histogram ranges and will allow you to compare the histograms.  However, if the individual histogram ranges vary widely (causing a very wide common scale), then some of the histograms may be unreadable.  When Independent scale is chosen, STATISTICA will plot each of the histograms based on their individual ranges.  If you select Independent, then comparing histograms would be difficult since they could all possibly have different scales, but they may be better defined than if a Common scale was used.

# of Bins:  This option allows you to control the number of bins in the histograms, that is, the number of (equal width) intervals represented by columns in the histograms (minimum = 2, maximum = 250).

  Click on this button to bring up the Font dialog from which you can choose a different font for the histogram titles.

  Click on this button to open the Area Pattern dialog in which you can change the pattern and color of the Histogram columns.


General Layout and Plot Layout:  Matrix Graphs - Matrix Type

Display a square matrix graph in either Full or Half matrix format.  In Full matrix format, each relation between the variables X and Y is represented twice (once as an "XY" and once as an "YX" plot), in a symmetrical array with histograms on the diagonal.  When a function is fitted to data in square matrix graphs, the functions fitted to the same graphs are different depending upon which variable is vertical and which is horizontal.


General Layout and Plot Layout:  Matrix Graphs - Points

Click on the [image] button to change the point size and pattern for the scatterplot matrix in the Points Pattern dialog.


General Layout and Plot Layout:  Matrix Graphs - Lines

Select a line pattern for the line plot matrix in the Line Patterns dialog by clicking on this button.


General Layout and Plot Layout:  Matrix Graphs - Areas

Click on the [image] button to open the Area Pattern dialog in which you can change the pattern and color of the columns in both types of column matrices.  To change the pattern for the Histogram columns, see Histograms.


General Layout and Plot Layout:  Matrix Graphs - Frame

Click on the [image] button to open the Line Pattern-Borders dialog from which you can select a different line pattern or color for the frame around the individual matrix plots.


General Layout and Plot Layout:  Matrix Graphs - Gridlines

When you click on this button, the Gridlines dialog will open from which you can select the style of gridlines (None, Auto, 3s, or 9s) in the background of the individual matrix plots.  The option 3s will divide each scale into 3 segments (i.e., 4 gridlines will be drawn for each axis); 9s will produce 9 segments (i.e., 10 gridlines will be drawn for each axis).  Note that when the Auto option is selected, then the resolution of gridlines (9s, 3s, or None) will depend on the display window size and the resolution of the device, thus, for example, the gridlines may appear in the 3s style on the screen and 9s style when printed on a high-resolution printer.


General Layout and Plot Layout:  Matrix Graphs - Borders

Click on this button to open the Line Patterns-Borders dialog in which you can choose the color, pattern, and thickness of a border around the graph.


General Layout and Plot Layout:  Matrix Graphs - Background

Click on the desired color to change the graph background color.  If you choose Other, then the Colors dialog will open from which you can choose a color from the color palette or customize a color.  You can preview the color that you have selected in the graph icon (see above).

Outside:  Click on a color to specify it for the background on the Outside of the matrix graph.

Inside:  Select a color for the background Inside of the matrix graph.

Note that when printing graphs, by default, the background colors are ignored; in order to print them (e.g., on a color device or a monochrome printer capable of generating fine shades of gray) select the Use dithered color to fill background option in the Print Graph dialog.


Plot Layout:  2D Graphs

Unlike the General Layout dialog (which contains the customization options which apply to the entire graph), the Plot Layout dialogs contain the customization options which apply to individual plots (one graph may consist of several plots - each representing one series of data).  The Plot Layout dialog will allow you to edit the plot legend, choose another plot type (for each individual plot when more than one plot is represented in the graph), change the plot patterns and style, as well as other options.

Shortcut:  Click the right-mouse-button on the graph and select Change Plot Layout(s) from the flying menu; click the right-mouse-button anywhere on the specific plot (e.g., if it is a scatterplot, click on any point marker) and select the Change This Plot/Series Layout option from the flying menu; or select the desired Plot Layout dialog (for the specific plot) from the Layout pull-down menu.

Plot Layout dialog:

Fixed Legend

Graph Type:  The current setting of the Graph Type is displayed in this option.  You can change the type (select it from the list) to one of the graphs listed below (click on each name for a brief description of the plot type). In order to change the Graph Type globally (i.e., change all plots to the same Graph Type), select the Graph Type in the General Layout: 2D Graphs dialog.

  Scatterplot	  Bar Right Y

  Line Plot	  Bar Top

  Step Plot	  Bar Dev

  Min-Max X	  Pie

  Min-Max Y	  MPatt Bar

  Bar X	  Voronoi

  Bar Left Y	  Ignore

Patterns

Bar Style

Fit:  Choose to fit an equation to the data in the plots, by selecting one of the predefined functions (see below), or by custom defining a function to be overlaid (by default, this option is set to Off).  To custom define a function (mathematical expression), select either the Custom Function option or click on the Custom Function button to bring up the User-Defined Functions dialog.

  Linear	  Polynomial

  Logarithmic	  Least Squares

  Exponential	  Negative Exponential

  Spline	  Custom Function

You can also change the line pattern of the fitted function by clicking on the Pattern button to open the Line Patterns dialog.  Click on the Options button to open the Fitting Options dialog from which you can choose the stiffness level and order of polynomial as well as other options concerning the function that you chose above.  You can use the fitted equation as a title in the graph using Control Characters (see Titles).  The Control Characters for the fitted function are @F[plot number, subgraph number] where you specify the desired plot number and optionally the subgraph number (for categorized graphs).  For example, if you enter the Control Characters @F[2], then STATISTICA will enter in that title position, the fitted function for the second plot in a multiple plot graph (i.e., a 2D line plot with 3 plots).  If you enter the Control Characters @F[1,3] in a title, then STATISTICA will place in that title position the fitted function for the third subgraph in a categorized graph.  (Note:  @F can be used instead of @F[1] or @F[1,1].)

Y-Axis

Ellipse

Confidence bands

General Layout

Previous Plot (<< button)

Next Plot (>> button)

Pie Options

Data Labels


Plot Layout:  2D Graphs - Fixed Legends

Enter up to two lines of text (up to 20 characters each) as a fixed legend for each plot.  You can change the font of the fixed legends by clicking on the Font button to open the Font dialog.  These settings will affect the default location and style of the fixed legend (on the right side of the graph); fixed legends which have been made movable (click the right-mouse-button on the legend and select Move Legend from the flying menu) may be customized and repositioned as on-screen custom text and their length can exceed 20 characters (see Legends).  The fixed (unmovable) legends can be temporarily removed from the graph by selecting the Fixed Graph Legend OFF option from the right-mouse-button flying menu.  The fixed legend can then be placed back into the graph (in its default position) by selecting the Fixed Graph Legend ON option available from the "long" flying menu accessible by clicking the right-mouse-button anywhere in the empty space outside the graph region.


Plot Layout:  2D Graphs - Patterns

You can change the basic appearance of the plot by selecting colors and patterns for the existing Points, Lines, or Areas of the plot or add points or lines to the graph by enabling the display of the points or lines.  (See also, Selecting Point, Lines, Area Patterns.)  For example, you can add points to the line in a Line Plot (see above) by clicking on the Points button and then turning on the Display of the points in the resulting dialog; you can add a line (that would connect the top of the bars) in a Bar X plot (see above) by clicking on the Lines button in this dialog and then turning on the Display of the line in the resulting dialog.  Note that this operation does not add a new plot to the graph, but only changes the display style of an existing plot.


Plot Layout:  2D Graphs - Bar Style

Select a bar style (Columns, Lines, Whiskers, or Rectangles) for all Min-Max and bar plots offered above.  If you select Whiskers as the Bar Style, you can choose from three types in the combo box:  Whiskers, HiLo/Left (the traditional stock price graph style), and HiLo/Right (a mirror image of the traditional stock price graph style).

You can also specify the Line Pattern, Width of the selected bar (or serif of the whiskers), and Deviation Level (for the Bar Dev plot) in this option.


Plot Layout:  2D Graphs - Y-Axis

Position the Y values on the Left- or Right-Y axis of the plot by selecting one of these axes.


Plot Layout:  2D Graphs - Ellipse

Superimpose an ellipse on the data in the plot with this option.  By default, the Off option is selected when you open this dialog.  However, you can choose to display one of two types of ellipses (Conf or Range, see below) in this option as well as change the pattern of the line defining the ellipse when you click on the Pattern button to open the Line Pattern dialog.  (See also, Selecting Point, Lines, Area Patterns.)

Confidence Area (Conf) Ellipse:  This option will produce an ellipse based on the the assumption that the two variables follow the bivariate normal distribution.  The orientation of the ellipse is determined by the sign of the linear correlation between the two variables (the longer axis of the ellipse is superimposed on the regression line).  The probability that the values will fall within the area marked by the ellipse is determined by the current setting of the Coefficient (see below).

Range Ellipse:  This option will produce a fixed size ellipse such that the length of its horizontal and vertical projection onto the X- and Y-axis (respectively) is equal to the mean ± (Range * I) where the mean and range refer to the X or Y variable, and I is the current value of the coefficient field.

Coeff:  Specify the coefficient that controls the ellipses described above.


Plot Layout:  2D Graphs - Confidence Bands

This option (applicable when Linear Fit or Polynomial Fit is selected, see above) will allow you to select (On) confidence bands around the fitted (regression) line.  You can enter the probability value (Level ) which represents the probability that the "true" fitted line (in the population) falls between the bands.  The standard error for the fitted line (which represents the predicted values, given the respective linear or polynomial fit) is computed based on the polynomial regression model (it is assumed that the data and their polynomial transformations are normally distributed, e.g., see Neter, Wasserman, & Kutner, 1985, p. 246).  You can also change the pattern of the line defining the confidence bands when you click on the Pattern button to open the Line Pattern dialog.  (See also, Selecting Point, Lines, Area Patterns.)


Plot Layout:  2D Graphs - General Layout

Click on this button to open the General Layout:  2D Graphs dialog from which you can control the global characteristics of the entire graph.


Plot Layout:  2D Graphs - Previous Plot (<< Button)

Clicking this button will return you to the previous Plot Layout dialog.


Plot Layout:  2D Graphs - Next Plot (>> Button)

Clicking on this button will bring up the next consecutive Plot Layout dialog.


Plot Layout:  2D Graphs - Pie Options

Click on this button to open the Pie Options dialog (applicable if the current plot type is Pie) from which you can customize the Pie chart (i.e., explode slices or change the pie position, style, shape, color and pattern).


Plot Layout:  2D Graphs - Data Labels

When you click on this button, the Data Point Labels dialog will open.  In this dialog, you can determine whether the actual values (i.e., coordinates) of individual data points (or their text labels) are displayed above the respective data points for the specific plot in the graph.

NOTE:  Use the Brushing tools to turn off individual (or all) data point labels that were created using the Brushing tools.


Plot Layout:  3D Scatterplots and Surfaces

Unlike the General Layout dialog (which contains the customization options which apply to the entire graph), the Plot Layout dialogs contain the customization options which apply to individual plots (one graph may consist of several plots - each representing one series of data).  The Plot Layout dialog will allow you to edit the plot legend, change the patterns of points, spikelines or tracelines, as well as other options.

Shortcut:  Click the right-mouse-button on the graph and select Change Plot Layout(s) from the flying menu; click the right-mouse-button anywhere on the specific plot (e.g., if it is a scatterplot, click on any point marker) and select the Change This Plot/Series Layout option from the flying menu; or select the desired Plot Layout dialog (for the specific plot) from the Layout pull-down menu.

Plot Layout dialog:

Fixed Legend

Patterns

Ignore this Plot

Previous Plot (<< button)

Next Plot (>> button)

General Layout

Data Labels


Plot Layout:  3D Scatterplots and Surfaces - Fixed Legends

Enter up to two lines of text (up to 20 characters each) as a fixed legend for each plot.  You can change the font of the fixed legends by clicking on the Font button to open the Font dialog.  These settings will affect the default location and style of the fixed legend (on the right side of the graph).  Note that for surface and contour plots, the shading (or line pattern) legend referencing the Z-axis levels is placed by default on the right side of the graph if there is no fixed legend specified or on the left side if there is one.

Fixed legends which have been made movable (click the right-mouse-button on the legend and select Move Legend from the flying menu) may be customized and repositioned as on-screen custom text and their length can exceed 20 characters (see Legends).  The fixed (unmovable) legends can be temporarily removed from the graph by selecting the Fixed Graph Legend OFF option from the right-mouse-button flying menu.  The fixed legend can then be placed back into the graph (in its default position) by selecting the Fixed Graph Legend ON option available from the background flying menu accessible by clicking the right-mouse-button anywhere in the empty space outside the graph region.


Plot Layout:  3D Scatterplots and Surfaces - Patterns

Change the basic appearance of the plot by selecting colors and patterns for the plot Points, Spikelines, or Tracelines.  (See also, Selecting Point, Lines, Area Patterns.)


Plot Layout:  3D Scatterplots and Surfaces - Ignore this Plot

Select this option to ignore (do not display) the current plot.


Plot Layout:  3D Scatterplots and Surfaces - Previous Plot (<< Button)

Clicking this button will bring up the previous Plot Layout dialog.


Plot Layout:  3D Scatterplots and Surfaces - Next Plot (>> Button)

Clicking on this button will bring up the next sequential Plot Layout dialog.


Plot Layout:  3D Scatterplots and Surfaces - General Layout

Click on this button to open the General Layout:  3D Scatterplots and Surfaces dialog from which you can control the global characteristics of the entire graph.


Plot Layout:  3D Scatterplots and Surfaces - Data Labels

When you click on this button, the Data Point Labels dialog will open.  In this dialog, you can determine whether the actual values (i.e., coordinates) of individual data points (or their text labels) are displayed above the respective data points for the specific plot in the graph.

See also:  If Data Point Labels Overlap

NOTE:  Use the Brushing tools to turn off individual (or all) data point labels that were created using the Brushing tools.


Plot Layout:  3D Sequence Graphs

Unlike the General Layout dialog (which contains the customization options which apply to the entire graph), the Plot Layout dialogs contain the customization options which apply to individual plots (one graph may consist of several plots - each representing one series of data).  The Plot Layout dialog will allow you to edit the plot legend, change the patterns of points, spikelines, borders, or tracelines, as well as other options.

Shortcut:  Click the right-mouse-button on the graph and select Change Plot Layout(s) from the flying menu; click the right-mouse-button anywhere on the specific plot (e.g., if it is a spike plot, click on any point marker) and select the Change This Plot/Series Layout option from the flying menu; or select the desired Plot Layout dialog (for the specific plot) from the Layout pull-down menu.

Plot Layout dialog:

Fixed Legend

Patterns

Previous Plot <<  button

Next Plot >>  button

General Layout button


Plot Layout:  3D Sequence Graphs - Fixed Legend

Enter up to two lines of text (up to 20 characters each) as a fixed legend for each plot.  You can change the font of the fixed legends by clicking on the Font button to open the Font dialog.  These settings will affect the default location and style of the fixed legend (on the right side of the graph); fixed legends which have been made movable (click the right-mouse-button on the legend and select Move Legend from the flying menu) may be customized and repositioned as on-screen custom text and their length can exceed 20 characters (see Legends).  The fixed (unmovable) legends can be temporarily removed from the graph by selecting the Fixed Graph Legend OFF option from the right-mouse-button flying menu.  The fixed legend can then be placed back into the graph (in its default position) by selecting the Fixed Graph Legend ON option available from the background flying menu accessible by clicking the right-mouse-button anywhere in the empty space outside the graph region.


Plot Layout:  3D Sequence Graphs - Patterns

Choose a pattern for the Top, Bottom, X, or Y walls (the surfaces of the plot blocks, ribbons or boxes when those plots are selected) of the 3-dimensional graph.  When you click on one of the wall buttons, the Area Pattern dialog will open from which you can choose a color and pattern for the specified wall.  Click on the Points, Borders, Tracelines and Spikelines buttons in this option to bring up dialogs from which you can change the color, pattern and size of the border, points or lines (see Line Pattern).  (See also, Selecting Point, Lines, Area Patterns.)


Plot Layout:  3D Sequence Graphs - Previous Plot <<  button

Clicking this button will return you to the previous Plot Layout dialog.


Plot Layout:  3D Sequence Graphs - Next Plot >>  button

Clicking on this button will bring up the next sequential Plot Layout dialog.


Plot Layout:  3D Sequence Graphs - General Layout

Click on this button to open the General Layout:  3D Sequence Graphs dialog from which you can control the global characteristics of the entire graph.


Scale Options

Select scale options for each of the graph axes (X-, Top, Y-right, and Y-left axes for 2D graphs, X-, Y-, Z-axes for 3D graphs, and X-, Y-, Z-, and V-axes for triangular axis surface graphs).  Separate options are available for each graph axis and the changes that you make for each axis are independent of one another (unless any of the Copy to ... options are selected to transfer the settings to other axes, see below).  Therefore, the following descriptions of the scale options will apply to each axis in the graph.

Shortcut (to access this dialog):  Double-click on an axis:  you can also click the right-mouse-button on the graph background and select General Plot Layout from the flying menu (or select General Layout from the Layouts pull-down menu), then click on the Scale Options button; alternatively, click the right-mouse-button on a specific scale value (e.g., if you want to edit the X-axis, click on any scale value on that axis) and select one of the following options from the flying menu:  Adjust Scaling/Style, Edit Scale Values, or Adjust Tickmarks.

Scale Options dialog:

Scale

Scale Values

Place a 'Scale Break' at:

Shift axis

Major Tickmarks

Minor Tickmarks

Copy to Other Axes

Copy to Opposite Axes

Scaling

Transfer

Scale Line


Scale Options - Scale

Although all of the options are the same for each axis, you can make changes to each axis independently of the other.  Select here the axis (X, Y-left, Y-right, or top axis for 2D graphs, X-, Y-, or Z-axes for 3D graphs, or X-, Y-, Z-, or V-axes for triangular axis surface graphs) to which you would like to make changes.


Scale Options - Scale Values

Scale values can be set to Off (no scale values are displayed), Numeric (use numeric values of the variable as the Scale Values), Dates (use the values of a date variable as the Scale Values) or Text Labels (use the text labels from the editable list box below, e.g., category names or text values, as the Scale Values).

Font button:  Click on this button to bring up the Font dialog from which you can choose a different font for the scale values of the currently selected axis.

Off:  Select this option if you do not want to display any scale values for the currently selected axis.

Numeric:  If you choose Numeric, then STATISTICA will automatically format those values for you (check the Auto option next to this option) or you can enter a specific format (de-select Auto and enter the desired format by specifying the number of digits before and after the decimal point).

Dates:  Date values of variables can be used as scale values in one of two ways:  either as true date values (select this option) or as text representations of Julian date values (select Text Labels).  When you select the Dates option, you will be able to choose the desired date format from a list of pre-defined formats.  Date values which are represented as Text Labels use the equivalent Julian date values to determine the location of the date text labels on the axis.  The date text labels can be individually edited in the list box directly below the Text Labels option (see below).

Text Labels:  If you want Text Labels as scale value labels (arbitrarily positioned on the scales and independent of the actual numeric Steps of the scale), then select this option and enter or edit a list of text strings in the editable list box directly below this option in the dialog.  In the first column of the text labels list box, enter numeric values which will determine the location of text labels on the axis.  In the second column, enter the actual text labels.  For example, if you enter the following:

then the names of the three cities will be placed on the axis in the location of the numeric values 1, 2, and 3, respectively.  Text scale values can be customized using Control Characters.  By entering the appropriate Control Characters, you can add superscripts and subscripts to the text scale values as well as change the font attributes for each text value or specific parts of the text scale values (see the topic Control Characters Reference, for a listing of the available codes).

Editable List Box:  Enter or edit numeric or text values in this editable list box.  Numeric values are entered or edited in the left half of the list box and text values in the right half of the list box.  Each text value must have a numeric value associated with it so that STATISTICA will know where to position the text value on the scale; the labels do not have to be spaced evenly.

Formatting mini-toolbar:  The Formatting mini-toolbar provides quick access to options for customizing scale values.  By placing the cursor in the desired position in the scale value (see Editable List Box, above) and using these buttons, you can easily add superscripts and subscripts, change the font attributes to bold or italics, etc.  You can also break the scale value into two lines using the [image] button.  A listing and brief description of each of these mini-toolbar buttons is given in Quick Reference (commonly used Control Characters).  For more information, see Control Characters.

You can place legend symbols in scale values by clicking on the legend buttons [image] (for legends for plots 1 through 6; for other plots, replace the number in the brackets with the desired number).  You can also specify a legend symbol for a graph in a multiple-subset graph by typing the selection number next to the plot number in Control Characters (i.e., @L[plot number, select number]).  (Note:  @L is equivalent to @L[1] and @L[1,1].)

Skip values:  Sometimes the scale values (numbers, dates, or labels) are so close together on the axis that they are hard to distinguish.  This option will allow you to skip values, displaying only the specified values (e.g., every fourth label).


Scale Options - Place a 'Scale Break' at:

When you select this option, STATISTICA will place a 'scale break' mark at the specified position on the respective axis (the default position is at the beginning of the scale).  When placed at the beginning of the scale, this 'scale break' indicaties that the scaling starts at an arbitrary level and not (for example) at absolute zero (see below).

In order to suppress displaying a scale value on the left side (or below for vertical axes) of the break, you can:

(1)	Set the Scaling to Manual/0 and specify a Min scale value above the minimum value displayed (e.g., 0).

(2)	Use text labels to label the scale values and leave the text label for the scale value to the right or below the scale break blank.


Scale Options - Shift Axis

This option will allow you to shift the current axis by a specified number of points (enter a positive value to shift the axis to the outside of the graph, enter a negative value to shift it inside).  For example:

When X is selected as the current Scale (see above), you can shift the X-axis up by specifying a negative number in the edit field.

In order to show that there is no causal relation between the X and Y variables, shift both variables by specifying a positive value in the edit field of the respective axes X and Y (causing a break where the X- and Y-axes meet).


Scale Options - Major Tickmarks

Customize the style and size of Major tickmarks for each of the axes with these options.

Style:  Selecting Off from this combo box will remove the major tickmarks from the axis.  When you select one of the Inside, Outside, or Crossed style settings, the tickmarks will be displayed on the inside, outside, or both sides of the axis (respectively).

Size:  Choose the relative length (from 0 to 9) of the tickmarks here.  The color and thickness of the tickmarks are determined by the current specifications of the respective scale line (see Scale Line, below).


Scale Options - Minor Tickmarks

Customize the style and size of Minor tickmarks for each of the axes with these options.

Style:  Selecting Off from this combo box will remove the minor tickmarks from the axis.  When you select one of the Inside, Outside, or Crossed style settings, the tickmarks will be displayed on the inside, outside, or both sides of the axis (respectively).

Size:  Choose the relative length (from 0 to 9) of the tickmarks here.  The color and thickness of the tickmarks are determined by the current specifications of the respective scale line (see Scale Line, below).

Number:  This option allows you to specify the number (from 1 to 15) of minor tickmarks that will be placed in-between the major tickmarks on the scale (if you do not want any minor tickmarks, select Off in the Style combo box, see above).  If you want STATISTICA to select the number of minor tickmarks, then choose Auto in this combo box.


Scale Options - Copy to Other Axes

Instead of manually selecting the same Font, Line Pattern, or Tickmarks specifications for each of the axes in each of their dialogs, select these options to automatically copy your selections to the remaining axes.


Scale Options - Copy to Opposite Axes

You can automatically copy your specifications for the Scale and Tickmarks to the opposite axis by selecting these options.  (For example, the settings for the Y-left axis will be copied to the Y-right axis.)


Scale Options - Scaling

Scaling Mode:  Choose one of four scaling methods.  The method you choose here determines whether the minimum, step, and maximum scaling values of each axis will be set automatically by the program (Auto or Auto/0) or manually by the user (Manual or Manual/0).  When you select Auto or Manual, the steps will be determined by "counting" from the current minimum (value of Min).  The choice of Auto/0 or Manual/0, will determine the steps by "counting" from 0, even if 0 is not in the current range between the minimum and maximum scaling values.

Type:  Choose between three types of scaling (Linear, Logarithmic, or Log-decimal).  Note that if the Logarithmic or Log-decimal scale is selected, then the scale minimum for that axis must be greater than 0.  Logarithmic scales appear like this:

When you select the Log-decimal scale, STATISTICA will use as major tickmarks only decimal logarithmic steps that represent consecutive powers of 10 (e.g., .1, 1, 10, 100, etc.).  The step size (i.e., width of the steps on the graph) will be determined by STATISTICA.

(Note that the display of some scale values placed close to each other in Logarithmic scales may be suppressed if the current setting of the Display Filters is other than Off.)

Value Layout:  This option affects the layout of the scale values with respect to their axis.  When you select Auto, STATISTICA will use either the Parallel, Normal, or Alternate layout, whichever is appropriate for the current graph.  The Normal layout option will position the scale values perpendicular (vertically) to their respective axis, while the Parallel option will position the scale values horizontally (parallel) to their respective axis.  The Alternate layout option will position the scale values in an alternating pattern (one above, one below) along the axis.

Max:, Step:, Min:  These fields determine the minimum, step, and maximum scaling values for the current axis.  They are available only if you choose a Manual scaling option (see above) and dimmed otherwise.

Reverse Scaling:  Click on this option in order to reverse the scale values (technically: set the step size to a respective negative value) for the currently selected axis.  When you click OK in this dialog, the graph will be redrawn with the scale values reversed for that axis (e.g., 100 to 0 instead of 0 to 100).


Scale Options - Transfer

It is often necessary to use identical scaling options in different graphs.  Because scales can be defined with many settings and parameters (which are time consuming to re-enter), the global Transfer options are provided to automate the task of re-using existing scale definitions, using either the Clipboard or disk files to store axis definitions.

Click on the desired radio button in order to apply the Transfer options (described below) to the Current axis or All axes of the current graph.  For example, when you use the Copy option (see below) when the All axes radio button is selected, then all axes of the current graph will be copied to the Clipboard and can be used to replace all axes in another graph by opening any Scale Options dialog for that graph and pressing the Paste button (note that the radio button All should also be selected in that dialog).

Current axis:  Click on this radio button in order to save, copy, or paste the scale options from or to the current axis in the graph.

All axes:  Click on this radio button in order to save, copy, or paste the scale options from or to all of the axes in the graph.

Open button:  When you click on this button, the Open Axis dialog will come up in which you can open a file (file name extension *.axd) containing previously saved scale options.

Save As button:  Click on this button in order to save the scale options for the Current axis or All axes (depending on the current setting of the radio buttons, see above) in a file (file name extension *.axd).

Copy button:  Click on this button in order to copy the scale options for the Current axis or All axes (depending on the current setting of the radio buttons, see above) to the Clipboard.

Paste button:  Click on this button in order to paste the previously copied scale options to the Current axis or All axes (depending on the current setting of the radio buttons, see above).


Scale Options - Scale Line

Click on this button to open the Line Pattern dialog from which you can select the scale line pattern, thickness, and color, or even turn off the scale line so that it is not displayed in the graph.


Titles

Edit or enter up to 13 lines of text in the active graph.  Each of the 13 lines can be up to 80 characters long and are automatically positioned and centered against the plotting area.  These 13 lines of text include up to 5 titles (positioned on the top of the graph) and 8 labels (2 labels for the X-axis, 2 labels for the left-Y axis, and 2 labels for the right-Y axis in 2D graphs or for the Z-axis in 3D graphs, and 2 labels for the V-axis in Ternary Plots).  Note that a title can be split at the current cursor location by using the @A Control Characters (click on the [image] mini-toolbar button}.

 buttons:  To edit the font for a particular title, click on the Font ( [image]) button next to that title in order to bring up the Font dialog.  Note that the current font selection can quickly be applied to all other titles and graph components by selecting either the Set as Common Font or the Use Common Font check boxes in the Font dialog.

Formatting mini-toolbar:  The Formatting mini-toolbar provides quick access to options for customizing the text in the titles.  By placing the cursor in the desired position in the text and using these buttons, you can easily add superscripts and subscripts, change the font attributes to bold or italics, add fitted function equations, etc.  You can also break the title into two lines using the [image] button (note that the title is limited to 80 characters).  A listing and brief description of each of these mini-toolbar buttons is given in Quick Reference (commonly used Control Characters).  For more information, see Control Characters.

If you wish, you can use the fitted function equation (see 2D Plot Layout or 3D Surfaces and Scatterplots) as a graph title.  To do this, click on the desired [image] button (for fitted functions 1 through 6; for other functions, replace the number in the brackets with the desired number).  You can also specify a fitted function for a subgraph (for categorized graphs) by specifying the subgraph number next to the plot number in brackets (i.e., @F[plot number, subgraph number]).  For example, in order to place the fitted function for the third subgraph in a categorized graph in a title, first click on the [image] button (STATISTICA will enter the Control Characters @F in the title), then type in the characters [1,3] after the @F so that the Control Characters will be @F[1,3].  (Note:  @F can be used instead of @F[1] or @F[1,1].)  Once the Control Characters for the fitted function have been entered and you exit this dialog, you can edit the fitted function by re-entering this dialog (double-click on the fitted function).  The fitted function will be displayed after the Control Characters in curly brackets (e.g., @F{PRICE = -0.145+0.152log10(x)+eps@}).  Now, delete the @F code, the curly brackets, and the @ symbol after the function (e.g., PRICE = -0.145+0.152log10(x)+eps) so that the edited function will be treated as regular text instead of as a fitted function.

You can place legend symbols in titles by clicking on the legend buttons [image] (for legends for plots 1 through 6; for other plots, replace the number in the brackets with the desired number).  You can also specify a legend symbol for a graph in a multiple-subset graph by typing the selection number next to the plot number in control characters (i.e., @L[plot number, select number]).  (Note:  @L is equivalent to @L[1] and @L[1,1].)

Shortcuts:  Double-click on any title to open the Titles dialog; click the right-mouse-button on a specific title (e.g., click on the first title above the graph) and select the Edit Text option from the flying menu; or, click the right-mouse-button on the graph background and select General Plot Layout from the flying menu (or select General Layout from the Layouts pull-down menu) to use the Titles option in the General Layout dialog.


Categorization Options

A categorized graph is a series of standard graphs (such as histograms, scatterplots, etc.), one for each category of cases identified by one level of a grouping variable (e.g., Male and Female respondents to a survey) or a combination of levels of two grouping variables (e.g., Male/Old, Male/Young, Female/Old, Female/Young).  The graphs are placed sequentially (or in the case of two grouping variables, they form a "crosstabulation" of graphs) in one display, allowing for comparisons between the patterns of data shown in the graphs for each of the requested groups (e.g., one for Males and one for Females).

Unlike Matrix Plots which produce graphs for all combinations of variables from one or two lists, categorized plots require only the selection of variables that are included in a single graph.  For example, only one "variable to be plotted" is entered for a categorized histogram, two variables for a categorized scatterplot, etc.  However, in categorized plots, you also need to specify a grouping variable (at least one) that contains information on group membership of each case (e.g., Low, Medium, or High).  That grouping variable will not be included in the graph directly (i.e., it will not be plotted) but it will serve as a criterion for dividing all analyzed cases into separate graphs.  One graph will be created for each group (category) identified by the grouping variable (or by each group identified by combinations of values of two grouping variables).

When you create a categorized graph, the Categorization Options dialog (accessible from the Categorization button in either the 2D General Layout or the 3D Scatterplots and Surfaces General Layout dialogs) offers specific customizing options described below.

Categorization Options dialog:

Categories

Class Names

Scale

First Category

Second Category


Categorization Options - Categories

When you open this dialog, First Category will be displayed if the graph is only categorized by one variable and Two Categories will be displayed if the graph is categorized by two or more variables.  Regardless of how the graph is categorized (by one or more variables), you can choose to turn off the categorization by selecting Off (one graph combining all graphs will be produced).  If the data are categorized by more than one variable (Two Categories), then you can change the categorization so that the data will be categorized only by the First Category variable or by the Second Category variable.  Note that eliminating one (or two) categorical variables will result in concatenation (overlaying) of the contents of the respective category graphs (and not in reprocessing the raw data).  Thus, the usefulness of such options will depend on the graph type (e.g., the result will be meaningful in the case of scatterplots but usually not informative in the case of histograms).


Categorization Options - Class Names

Class names can be edited and customized using Control Characters in this dialog.  By entering the appropriate Control Characters, you can add superscripts and subscripts to the class names as well as change the font attributes for each name that is customized (see the topic Control Characters, for a listing of the available Control Characters).


Categorization Options - Scale

Choose to scale the graphs using Common or Independent scales.

Common:  A common scale will be used for all category graphs when you select this option.  The range of the common scales will be wide enough to accommodate all of the values in all of the category graphs.  Choosing this option will allow you to make visual comparisons of ranges and distributions of values among categories.  However, if the ranges of values in graph categories are considerably different (causing a very wide common scale), then some of the graphs may be unreadable.

Independent:  When Independent scale is chosen, STATISTICA will plot each of the category graphs based on their individual ranges.  If you select Independent, then it may be difficult to make comparisons of ranges of values among categories, but easier to spot trends and specific patterns within categories.  When you select Independent scale, only those scales which have been set to Automatic scaling in the Scale Options dialog will be affected.  In this way, only the axes that you want (i.e., those that have been set to Automatic scaling) will be set to Independent, thereby giving you more customization abilities.  For example, all component graphs in a categorized graph may have Manual scaling on the X-axes (and thus remain constant across the component graphs) and Automatic scaling on the Y-axes (select these settings in the Scale Options dialog).  Now, when you select Independent in the Categorization Options dialog, the Y-axes will be adjusted by the program separately for each graph while the X-axis for each component graph will remain constant.


Categorization Options - First Category

In this area of the Categorization Options dialog, the variable name for the first categorization variable is listed along with its class names (category labels, e.g., Male, Female).  You can edit these names or change the font (independently for the variable name and class names) by clicking on the appropriate Font button.


Categorization Options - Second Category

When the graph is categorized by a second variable, the variable name for the second categorization variable is listed along with its class names (category labels, e.g., Male, Female).  You can edit these names or change the font (independently for the variable name and class names) by clicking on the appropriate Font button.


Fitting Options

When you fit a function to the data in a STATISTICA graph, several options are available from the Fitting Options dialog to customize the fit.

Fitting Options dialog:

Stiffness

Optimize

Order of Polynomial

Base of Logarithm

Fit Line Resolution


Fitting Options - Fit Line Resolution

This option allows you to control the resolution of the fitted function in the graph.  Once the fitted function has been determined, the fit is approximated by points on the X-axis.  To control the resolution, you can choose to approximate the fit with a small number of points - 200 (select Normal), a large number of points - 3200 (select Perfect) or somewhere in-between (select High (400 points) or Very High (800 points)).  Selecting a higher number of points will result in a smoother appearance of the fitted function in the graph; however, selecting a higher number of points will also slightly slow down the graphing procedure.

Note that the default (Normal) setting will produce smooth function lines in most cases; the higher settings will make a difference only when you either zoom in on part of the graph or use logarithmic scaling (to "stretch" a part of the scale).


Fitting Options - Stiffness

The function that controls the weight (see Distance-Weighted Least Squares Fitting) is determined by the Stiffness parameter which can be modified on the Fitting Options dialog.  Thus, the stiffness parameter determines the degree to which the fitted curve depends on local configurations of the analyzed values.

The lower the coefficient, the more the shape of the curve is influenced by individual data points (i.e., the curve "bends" more to accommodate individual values and subsets of values).

The range of the stiffness parameters is 0 < s < 1.  Large values of the parameter produce smoother curves that adequately represent the overall pattern in the data set at the expense of local details.  See also Negative Exponentially-Weighted Fitting and Spline Fitting.

See also, McLain, 1974.


Fitting Options - Optimize

When you have selected either the Least Squares or Negative Exponentially-Weighted smoothing functions, you can speed up fitting the data with this option (by enabling the data image reduction procedure).  When you select On, you will need to enter an integer value less than or equal to the number of cases in the data file (n).  The proportion between this value and the number of valid cases in the data file will control the degree to which the data set will be reduced (by random selection) to speed up fitting the function.  This option is useful if you have a large number of data points.


Fitting Options - Order of Polynomial

When you select the Polynomial fitting function, you can select the order for the fitted polynomial (choose either a second, third, fourth or fifth order polynomial).


Fitting Options - Base of Logarithm

When you select the Logarithmic function, you can select either the natural log (base e) or the base 10 logarithmic function.


Data Point Labels

The Data Point Labels dialog will allow you to place labels (either the coordinates of the points or text labels) over individual data points in the graph.  Accessing the Data Point Labels dialog from the General Layout dialog will allow you to change the display of the point labels globally, across all plots (i.e., every point in the graph will be labeled in the manner selected in this dialog).  Note that the Edit button will be dimmed when the Data Point Labels dialog is accessed from the General Layout dialog, since STATISTICA will not know for which plot the data point labels will be edited.  If you want to adjust labels for only the points in a specific plot or label the points in each plot differently (i.e., Plot Dependent, see below), then click on the Data Labels button in the appropriate Plot Layout dialog (the resulting Data Point Labels dialog will apply only to the points in the current plot).  If you want to label specific points in the graph, use the Brushing facility (note that the current setting in this dialog will affect the "labels" that will be generated via Brushing).

Shortcut:  Double-click on any point label.

Data Point Labels dialog:

None

Coordinates

Font

Text Labels

Plot Dependent

NOTE:  Use the Brushing tools to turn off individual (or all) data point labels that were created using the Brushing tools.


Data Point Labels - None

When this option is selected, no point labels are displayed.  You can use this option to turn off any point labels present in the graph.


Data Point Labels - Coordinates

You can use point coordinates as point labels with this option.  Select one of the following coordinates as point labels:

•	For 2D graphs:  X, Y, or X and Y.

•	For 3D graphs:  X, Y, X and Y, Z, X and Z, Y and Z, or X, Y, and Z.


Data Point Labels - Font

Click on this button to bring up the Font dialog from which you can choose a different font for the text labels.


Data Point Labels - Text Labels

Select this option to use strings of text for the point labels.  By default, the strings of text used will be the numbered cases (e.g., Case 1, Case 2, . . .) in the plot.  Click on the Edit button to open the Edit Text Labels dialog from which you can edit the text labels for the plot so that they are more meaningful (the standard Control Characters can be used to enter sub/superscripts and other text format attributes).  Note that the Edit button will be dimmed when the Data Point Labels dialog is accessed from the General Layout dialog, since STATISTICA will not know for which plot the data point labels will be edited.  To edit the labels, click on the Data Point Labels button in the Plot Layout dialog (for the respective plot), or double-click in the graph, on a data point label for a specific plot and then click on the Edit button.

See also:  If Data Point Labels Overlap

NOTE:  Use the Brushing tools to turn off individual (or all) data point labels that were created using the Brushing tools.


Data Point Labels - Plot Dependent

When the data points for at least one plot in a multiple plot graph (e.g., as in a multiple scatterplot) are labeled differently from the rest, then when the Data Point Labels dialog is called by clicking on the Data Labels option in the General Layout dialog, the Plot Dependent option will be automatically selected.  This global Plot Dependent option indicates that plot-specific data point labels are selected.  Therefore, if you change the labels in this Data Point Labels dialog (called from the General Layout dialog), those changes will be applied globally to all plots in the graph.  In order to add or change the labels for a specific plot, go to the respective Plot Layout dialog and click on the Data Labels button or double-click on an existing data point label in the graph.  (Note that the Plot Dependent option will be dimmed in the Data Point Labels dialogs which are called in these ways.)


Data Point Labels for Ternary Plots

The Data Point Labels dialog will allow you to place labels (either the coordinates of the points or text labels) over individual data points in the graph.  Accessing the Data Point Labels dialog from the General Layout dialog will allow you to change the display of the point labels globally, across all plots (i.e., every point in the graph will be labeled in the manner selected in this dialog).  Note that the Edit button will be dimmed when the Data Point Labels dialog is accessed from the General Layout dialog, since STATISTICA will not know for which plot the data point labels will be edited.  If you want to adjust labels for only the points in a specific plot or label the points in each plot differently (i.e., Plot Dependent, see below), then click on the Data Labels button in the appropriate Plot Layout dialog (the resulting Data Point Labels dialog will apply only to the points in the current plot).

Shortcut:  Double-click on any point label.

Data Point Labels dialog:

None

Coordinates

Font

Text Labels

Plot Dependent

See also:  If Data Point Labels Overlap

NOTE:  Use the Brushing tools to turn off individual (or all) data point labels that were created using the Brushing tools.


Data Point Labels for Ternary Plots - None

When this option is selected, no point labels are displayed.  You can use this option to turn off any point labels present in the graph.


Data Point Labels for Ternary Plots - Coordinates

You can use point coordinates as point labels with this option.  Select one of the following coordinates as point labels:  X, Y, X+Y, Z, X+Z, Y+Z, X+Y+Z, V, X+V, Y+V, X+Y+V, Z+V, X+Z+V, Y+Z+V, or X+Y+Z+V.

See also:  If Data Point Labels Overlap


Data Point Labels for Ternary Plots - Font

Click on this button to bring up the Font dialog from which you can choose a different font for the text labels.


Data Point Labels for Ternary Plots - Text Labels

Select this option to use strings of text for the point labels.  By default, the strings of text used will be the numbered cases (e.g., Case 1, Case 2, . . .) in the plot.  Click on the Edit button to open the Edit Text Labels dialog from which you can edit the text labels for the plot so that they are more meaningful (the standard Control Characters can be used to enter sub/superscripts and other text format attributes).  Note that the Edit button will be dimmed when the Data Point Labels dialog is accessed from the General Layout dialog, since STATISTICA will not know for which plot the data point labels will be edited.  To edit the labels, click on the Data Point Labels button in the Plot Layout dialog (for the respective plot), or double-click in the graph, on a data point label for a specific plot and then click on the Edit button.

See also:  If Data Point Labels Overlap

NOTE:  Use the Brushing tools to turn off individual (or all) data point labels that were created using the Brushing tools.


Data Point Labels for Ternary Plots - Plot Dependent

The Plot Dependent option is a global option that when selected, indicates that plot specific data point labels are selected.  This global option is available only when the Data Point Labels dialog is called from the General Layout dialog and is dimmed if it is called from the Plot Layout dialog or by double-clicking on a plot label in the graph.  When you select data point labels for individual plots in the graph (i.e., plot dependent data point labels), then this option will automatically be selected when you open the Data Point Label dialog from the appropriate General Layout dialog, indicating that the data point labels are currently different for each plot in the graph.


Edit Text Labels

This dialog will allow you to enter or edit text labels assigned to points (or icons) in a graph (see Data Point Labels or Data Point Labels for Ternary Plots).  You can edit these labels or enter new text labels (up to 20 characters long).  You can also delete text labels so that only specific points (or icons) in the graph will be labeled.

See also:  If Data Point Labels Overlap

Formatting mini-toolbar:  The Formatting mini-toolbar provides quick access to options for customizing text labels.  By placing the cursor in the desired position in the text label and using these buttons, you can easily add superscripts and subscripts, change the font attributes to bold or italics, etc.  You can also break the label into two lines using the [image] button.  A listing and brief description of each of these mini-toolbar buttons is given in Quick Reference (commonly used Control Characters).  For more information, see Control Characters.

You can place legend symbols in the text labels by clicking on the legend buttons [image] (for legends for plots 1 through 6; for other plots, replace the number in the brackets with the desired number).  You can also specify a legend symbol for a graph in a multiple-subset graph by typing the selection number next to the plot number in control characters (i.e., @L[plot number, select number]).  (Note:  @L is equivalent to @L[1] and @L[1,1].)

Note:  Use the Brushing tools to turn off individual (or all) data point labels that were created using the Brushing tools.


Selected Point Patterns

This option applies to multiple-subset graphs whose individual data points belong to previously specified subsets (classes).  In the Selected Points Patterns dialog, you can change the point size and style as well as edit legends for each of the classes represented in the graph.  The new patterns and text  will be used to identify the specific subsets in the graph.

Selected Points Patterns dialog:

Legend:  For each class, you can enter one line (24 characters) of text in the edit box.  This text will be used as a legend in the graph to briefly describe the selected class (by default the case selection condition used to define the class are used as the legend).  In order to enter texts longer than the capacity of the fixed legend, convert the legend to movable (see Legends) and double-click on it to use the Graphic Text Editor.

Point Pattern:  Click on an individual point button to open the Point Patterns dialog from which you can choose a different color, size or style of point.  (See also, Selecting Point, Lines, Area Patterns.)

Points (On or Off):  Choose to identify (select On) or not identify (select Off) the selected points in the current graph.

Marked Point:  Click on this button to open the Point Patterns dialog from which you can choose a different color, size or style of point for the points which have been marked via Brushing.


Edit Palette

You can specify a set of colors in the Edit Palette dialog for graph elements such as lines, points, borders and surface levels.  This dialog contains a comprehensive set of options to control all features of a palette; in order to make the two most common types of adjustments (change a color and create a new palette), follow the steps outlined in the following two examples.

Example 1:  Changing colors in the current palette.

Example 2:  Creating a new palette.

Edit Palette dialog:

Colors in Palette

Custom Buffer

Single Color Operations

Global Operations

Save Palette

Get Palette


Edit Palette - Colors in Palette

This display shows the current colors in the palettes.  You can Add or Delete or Change colors from the Colors in Palette display.


Edit Palette - Custom Buffer

When the Edit Palette dialog is called up (from any dialog option or pop-up menu; e.g., from the area or lines patterns boxes), the colors in the Custom Buffer will be the same.  To change colors in the Custom Buffer, click on the Custom Colors and select some colors from the Color Palette.  Now, these "new" colors in the Custom Buffer will become the default colors for the buffer whenever the Edit Palette dialog is opened or until you change the buffer colors.  You can add colors from the Custom Buffer to the Colors in Palette by highlighting a color square in the Custom Buffer and then clicking on the Add button.


Edit Palette - Single Color Operations

Delete:  Delete a color from the Colors in Palette by highlighting the color square and then clicking on the Delete button.

Change: This option will change a color in the Colors in Palette without adding more colors to the palette.  You can change a color by first clicking on the desired color square in the Custom Buffer, then click on the color square that you want to replace in the Colors in Palette.  Finally, click on the Change button to complete the transfer.

Insert:  Click on this button to Insert a color from the Custom Buffer in front of a highlighted color square in the Colors in Palette.  To Insert a color, first highlight the desired color square in the Custom Buffer, then click on the color square in the Colors in Palette before which you want to insert the desired color.  Finally, click on the Insert button to complete the transfer.

Add:  Click on this button to Add a highlighted color from the Custom Buffer after the last color square in the Colors in Palette.


Edit Palette - Global Operations

Custom Colors:  Click on this button to open the Color Palette dialog from which you can select other colors to replace the colors in the Custom Buffer.  After you have made your selections in the Color Palette, you will need to click on the Copy to Buffer button (see below) to transfer those selections to the Custom Buffer.

Copy to Buffer:  This button is used to replace the Custom Buffer colors with selected colors from the Colors in Palette (i.e., all of the colors in the Custom Buffer will be replaced with 16 consecutive colors, starting with the highlighted color, from the Colors in Palette).

Solid Palette:  Colors in STATISTICA can be solid (no pattern in the background) or have a patterned background.  Click on this button to replace the colors in the Colors in Palette with the system default solid colors.

Default Palette:  Click on this button to replace the colors in the Colors in Palette with the system default colors (solid and patterned).


Edit Palette - Save Palette

Use this option to save the customized Colors in Palette.  When you click on this button the Palette Save dialog will open, allowing you to specify the name of the file under which these color selections will be saved.  By default, STATISTICA color palette selection files are saved under the file name extension *.pal.


Edit Palette - Get Palette

You can use previously saved color palette selections with this option.  When you click on this button the Open Palette File dialog will open, allowing you to specify the name of the file (file name extension *.pal) in which the color palette selections are saved.


Creating a New Palette

Changing Colors in the Current Palette

Step 1.	Click on the color square in the Custom Buffer that you want to add to the current palette.

Step 2.	Highlight a color square (that you want to replace) in the Colors in Palette and then click on the Change button to replace it with the pre-selected color from the Custom Buffer, or click on the Insert button to place the pre-selected color in front of the highlighted color square in the Colors in Palette, or click on the Add button to add the pre-selected color to the Colors in Palette.

Step 3.	Now when you click OK, if you are editing the colors for Background/Foreground color palettes, then they will be displayed in the Background/Foreground list boxes (see Background or Points, Lines, Area Patterns Dialog), or if you are editing the colors for a surface palette (see 3D Surfaces and Scatterplots or 3D Sequence Graphs), your colors will be applied to the surface.


Changing Colors in the Current Palette

Creating a New Palette

Step 1.	Click on the Custom Colors button to open the Color Palette dialog.

Step 2.	In the Color Palette dialog, highlight the desired color square in the Basic Color Palette (or specify a customized color in the Color Refiner Box) and then click on the Add to Custom Colors button to add this color to the Custom Colors palette.  You can continue this process until you have filled the Custom Colors palette with up to 16 selected colors.

Step 3.	Once you have finished your selections, click on the OK button to transfer the selected colors to the Custom Buffer in the Edit Palette dialog.  Now you can Add, Change, Insert the new colors in the Custom Buffer into the Colors in Palette (see Example 1).


Color Palette

You can select from a palette of basic colors or customize a color in this dialog.

Color dialog:

Basic Color Palette:  Select a basic color in this palette by clicking on the color square and then clicking the OK button.  You can also add a color from the Basic Color Palette to the Custom Colors palette by highlighting the color and then clicking on the Add to Custom Colors button.

Custom Colors:  Click the Define Custom Colors button to bring up the Color Refiner Box from which you can create a customized color and add it to the Custom Colors Palette.  You can create a color by adjusting its Hue, saturation (Sat) and luminosity (Lum) manually, or by specifying its Red, Green and Blue values manually, or by dragging the cursor to the desired color in the Color Refiner Box and adjusting the Luminosity Bar.  Once you have defined the custom color, click on the Add to Custom Colors button to add the new color to the selected square in the Custom Colors Palette.


Distance-Weighted Least Squares Fitting

Distance-Weighted Least Squrares Fitting

Unlike some other fitting procedures, the distance-weighted least squares procedure does not fit to the data one function that can be easily described by a single formula and plotted independently from the data.

The distance-weighted least squares method fits a curve to the data by using the following procedure.  A polynomial (second-order) regression is calculated for each value on the X variable scale to determine the corresponding Y value such that the influence of the individual data points on the regression (i.e., the weight, see Fitting Options - Stiffness) decreases with their distance from the particular X value (an algorithm similar to the one used by this procedure is described by McLain, 1974).

Applications

There are two general classes of applications for this and similar (e.g., spline, negative exponentially-weighted) smoothing procedures.  First, it provides a sensitive method for revealing non-salient overall patterns of data.  Due to measurement error, such patterns can be hard to identify by simply looking at the scatterplot, although if revealed, they may turn out to be interpretable and reliable.

Another type of application is to use the identified pattern to develop quantitative models of the investigated phenomenon.  Specifically, the curve revealed by the smoothing procedure often consists of segments that cannot easily be described by one function (e.g., such as a particular polynomial or logarithmic function).  However, the segmentation, and the nature of the component curves (in the consecutive segments) may contain interpretable information about the investigated phenomenon, and a linear or nonlinear piecewise regression function can be developed to account for (and predict) the process in question.  The model suggested by the results of such analyses can then be quantitatively verified in a nonlinear estimation analysis (note that the Nonlinear Estimation module offers flexible facilities to estimate user-defined piecewise regression and other models).


Negative Exponentially-Weighted Fitting

The negative exponentially-weighted fitting (smoothing) procedure is based on a polynomial regression algorithm similar to the one used in the Distance-Weighted Least Squares procedure.  However, the weights that determine the influence of individual data points on consecutive segments of the curve (depending on their distance from the given segment) are calculated according to a negative (decreasing) exponential function.

The choice of that function is not entirely arbitrary because research experience confirms that, in many circumstances, exponential weighting offers an adequate balance between preventing points at remote subregions from biasing the curve while not ignoring them entirely.  McLain (1974) argues that negative exponential weighting receives "some slight theoretical support" from the fact that in cubic splines (which are proven to provide adequate approximations of real-life sequential data sets) the effect of remote data points decreases approximately exponentially with distance.

Applications

There are two general classes of applications for this and similar (e.g., spline, distance-weighted least squares) smoothing procedures.  First, it provides a sensitive method for revealing non-salient overall patterns of data.  Due to measurement error, such patterns can be hard to identify by simply looking at the scatterplot, although if revealed, they may turn out to be interpretable and reliable.

Another type of application is to use the identified pattern to develop quantitative models of the investigated phenomenon.  Specifically, the curve revealed by the smoothing procedure often consists of segments that cannot easily be described by one function (e.g., such as a particular polynomial or logarithmic function).  However, the segmentation, and the nature of the component curves (in the consecutive segments) may contain interpretable information about the investigated phenomenon, and a linear or nonlinear piecewise regression function can be developed to account for (and predict) the process in question.  The model suggested by the results of such analyses can then be quantitatively verified in a nonlinear estimation analysis (note that the Nonlinear Estimation module offers flexible facilities to estimate user-defined piecewise regression and other models).

See also Fitting Options - Stiffness.


Spline Fitting

It can be demonstrated that curves of any complexity can be described by a sequence of segments defined as polynomials.  In practice, most real-life curves can be reliably approximated by a sequence of third-order (cubic) polynomials.

For bivariate data sets (correlations that involve two variables), to determine the curve, the spline procedure solves cubic equations for every point at a regular interval (for more information on cubic interpolation, see de Boor, 1978; Johnson and Ries, 1982; Dahlquest and Bjorck, 1976; and Gerald and Wheatley, 1989).

A minimum of at least 3 data points are necessary to perform a spline fit; the algorithm ignores overlapping data points.

See also Fitting Options - Stiffness.


Points, Lines, Area Patterns Dialog

This dialog will allow you to change the size, color and style of points, lines, or plot areas, in the graph.  (See also, Selecting Point, Lines, Area Patterns.)  The default patterns, colors and modes of display of consecutive plots and other components of the graphs are determined by the current selections in the Options pull-down menu.  (You can use that menu to change the defaults.)

Shortcut:  Double-click on a point, line, axis, or area (e.g., a column bar or a wall of a 3D Sequence Plot); click on the appropriate button in the Plot Layout dialog or the General Layout dialog.

Patterns dialog:

Display

Size

Background/Foreground

Palette

Opaque/Transparent

Pattern:  Area

Pattern:  Line

Pattern: Point Marker

Hints:  Two-color patterns can be created by using combinations of the background and foreground colors (for example: ).  New ("reversed") patterns can be created by setting the foreground color to the current color of the graph background and thus assigning the "foreground status" to the original background of the pattern.  (See also, Selecting Point, Lines, Area Patterns.)


Points, Lines, Area Patterns Dialog - Display

Choose to display (On) or not display (Off) the lines, borders, etc., for a specific plot in the graph (this option does not apply to area patterns).  To re-activate the display of the removed plot items, click on the appropriate button in the General Layout or Plot Layout dialog to open the respective Line, Area Patterns Dialog and then select On.


Points, Lines, Area Patterns Dialog - Size

You can change the size of the plot item based on either Pixels (this type of measurement is device dependent, i.e., the items may look different on different monitors or may print differently depending on the printer type) or Points (one Point is 1/72nd of an inch, this type of measurement is device independent).  Line width increments of a quarter of a point (1/288 of an inch) are supported.  (This option does not apply to area patterns.)


Points, Lines, Area Patterns Dialog - Background/Foreground

You can select a different color for the item Foreground (i.e., the main component or the "outside" of the item, e.g., the outline of the hollow point markers, "dashes" of the dashed lines) and Background (the "inside" of the item, e.g., the inside of the hollow point markers or spaces between "dashes" in the dashed lines) with these options.  When you click on the combo box arrow, a list of colors will appear from which you can select the desired color.  If you select the Other option from the list of colors, the Color Palette will open.  Here, you will be able to select a single color to be added to the list of colors.  Click on the Palette button in order to add, delete or change more than one color in the list.


Points, Lines, Area Patterns Dialog - Palette

Click on this button to open the Edit Palette dialog from which you can select different colors for the palette.


Points, Lines, Area Patterns Dialog - Opaque/Transparent

Whenever you are using a background color, you can turn on (select Opaque) or off (select Transparent) the display of the background color in the pattern (i.e., line, area or point).  When you select Transparent, you will be able to see the default graph background in-between the pattern.  The option to use transparent patterns is particularly useful when you intend to precisely show the points or areas of overlap between items (i.e., their respective patterns).  For example, if a dashed line was not set to transparent (i.e., select Opaque) and its cross-section with a solid line would fall in the space between the "dashes," then the solid line would appear broken at the point of cross-section.  (See also, Printing Objects with Filled Background.)


Points, Lines, Area Patterns Dialog - Pattern

Select a pattern for a plot item with this option (see Points, Lines, Area Patterns Dialog).  The following patterns are available in this dialog:


Background

This dialog will allow you to change the color of the Inside or Outside of the graph background.  (See also, Selecting Point, Lines, Area Patterns.)  A specialized palette of 24 light colors is provided; you can also select other colors (see Palette button, below).  Note that in order to print the graph background color, you will need to select the Use Dithered Color to Fill Background option from the Graph Print Options dialog.

Shortcut:  Double-click on the inside graph background; click on the right-mouse-button and select the Set Background Colors option from the flying menu.

Background dialog:

Inside/Outside:  You can select a different color for the Inside (the inside of the graph) or Outside (the outside of the graph) with these options.  When you click on the arrow, a list of 24 suggested "background colors" will appear from which you can select the desired color.  Click on the Palette button (see below) in order to add, delete or change colors in the list.

Palette button:  Click on this button to open the Edit Palette dialog from which you can select different colors for the palette of Inside or Outside colors.

Note that the default graph background colors can be adjusted in the Options pull-down menu.


User-Defined Functions

To define a function (mathematical expression) to be plotted, select the Custom Function option (from the list of predefined options) and then click on the Custom Function button to bring up the User-Defined Functions dialog.  This dialog consists of syntax help and an edit window in which to enter the function.  The equation you enter will be checked for formal correctness (syntax) at the point of exiting this dialog.  If a math error (e.g., division by zero or square root of a negative number) is detected during the evaluation of an equation, then the appropriate error message will be issued, the graph will not be plotted, and STATISTICA will ask you to change the equation.

The general rules for this syntax are described as follows:

•	All user-defined function equations are of the same form, e.g., dependent variable = expression.

•	On the left side of the equation you may specify the dependent variable (y in 2D functions or z in 3D functions); for example:  y = x^2 + x.  However, the left side of the equation is optional (e.g., you can enter the equation as:  = x^2 + x or simply as:  x^2 + x.

•	On the right side of the equation, the expression may contain Constants, Operators, Functions (including Distributions and their Integrals), and Arguments (see below):

Arguments

Constants

Operators

Functions

Ifgraph function

Distributions and their integrals

You can fit an equation to the data in 2D Plots, Matrix Graphs, or 3D Scatterplots and Surfaces by selecting one of the predefined functions or you can overlay a custom-defined function.  If you wish, you can use the fitted function or equation defined here as a graph title in 2D Plots and 3D Scatterplots and Surfaces by entering the appropriate Control Characters in the title edit box.  The Control Characters for the fitted function are @F[plot number, subgraph number] where you specify the desired plot number and optionally the subgraph number (for categorized graphs).  For example, if you enter the Control Characters @F[2], then STATISTICA will enter in that title position, the fitted function for the second plot in a multiple plot graph (i.e., a 2D line plot with 3 plots).  If you enter the Control Characters @F[1,3] in a title, then STATISTICA will place in that title position the fitted function for the third subgraph in a categorized graph.  (Note:  @F can be used instead of @F[1] or @F[1,1].)


User-Defined Functions - Arguments

Arguments are:

x in 2D functions (e.g., y = 2x);

x and y in 3D functions (e.g., z = 2*x + 3*y + 12);

x, y, and z in 4D functions (e.g., v = x**2 + y**3 + z; see Ternary Plots)


User-Defined Functions - Constants

Constants can be:

Integers

Floating point numbers (numbers with a decimal point)

Pi (3.1415. . .)

Euler (e = 2.7182. . .)


User-Defined Functions - Operators

The following operators are allowable in user-defined functions:

Arithmetic:  +, -, *, /, ** or ^ (exponentiation), ( )

Relational:  <, >, >=, <=, <>

Logical:

AND (equivalent to &)

OR (equivalent to |)

NOT (equivalent to ~)


User-Defined Functions - Functions

abs	Absolute Value

acos	Arc Cosine Function

asin	Arc Sine Function

atan	Arc Tangent Function

cos	Cosine Function

cosh	Hyperbolic Cosine Function

exp	Exponentiation to base e

hypot(x,y)	Equivalent to sqrt(x^2+y^2)

log 	Natural Logarithm to Base e

log10	Logarithm to Base 10

max(a,b)	a if a ≥ b, or b if a < b

min(a,b) 	a if a ≤ b, or b if a > b

sin 	Sine Function

sinh	Hyperbolic Sine Function

sqrt	Square Root Function

tan	Tangent Function

tanh	Hyperbolic Tangent Function

trunc	Truncate to Integer


User-Defined Functions - Ifgraph

The ifgraph function allows you to display different functions for each component graph in Categorized Graphs.  The parameters of the ifgraph function identify individual component graphs; for a particular component graph, the function evaluates to 1 if the parameters identify the current component graph; otherwise the function evaluates to 0.  You can use this function in the following manner:

If the graphs are categorized by 1 category, use ifgraph(graphnumber).  For example, the following ifgraph functions will display two separate functions:

ifgraph(1)*x**2 + ifgraph(2)*sin(x)

y=x**2 will be displayed in the first of the categorized graphs and y=sin(x) will be displayed in the second of the categorized graphs.

If the graphs are categorized by 2 categories, use ifgraph(row,column).  For example:

ifgraph(1,1)*x**2 + ifgraph(2,1)*sin(x) + ifgraph(1,2)*(x+sqrt(x)) + ifgraph(2,2)*5

These ifgraph functions will display y=x**2 in the graph in row 1, column 1; y=sin(x) in the graph in row 2, column 1; y=sqrt(x) in the graph in row 1, column 2; and y=5 in the graph in row 2, column 2.


User-Defined Functions - Distributions, their Integrals and Inverse Distribution Functions

Distribution functions can be used in custom functions like all other functions.  For example, in general, in 2D custom functions they would be entered as:

y=distrib(x, parameter1, parameter2)

The value of y will be computed for the range of the values of x.  Instead of x, an expression involving x can also be used (as in all functions); for example:

y=normal(log(x), 1, 2)

The default plot is a unit distribution plot, i.e., the area under the curve is equal to 1.  When plotting a distribution curve against a histogram, you may need to increase the area under the curve to be equivalent to that of the histogram.  To do this, multiply the desired distribution function by a "scaling factor" whose value equals the histogram category width times the total number of cases plotted (e.g., y = 10*20*normal(x,95,15), where 10 is the category width and 20 is the number of cases).

Note that the meaning of the parameters, as well as the number of parameters, depends on the respective distribution function.  Here is a listing of all available functions.

Density or	Inverse

Probability	Distribution	Distribution

Distribution	Function	Function	Function

Beta Distribution	beta(x,ν,ω)	ibeta(x,ν,ω)	vbeta(x,ν,ω)

Binomial Distribution	binom(x,p,n)	ibinom(x,p,n)

Cauchy Distribution	cauchy(x,η,θ)	icauchy(x,η,θ)	vcauchy(x,η,θ)

Chi-square Distribution	chi2(x,ν)	ichi2(x,ν)	vchi2(x,ν)

Exponential Distribution	expon(x,λ)	iexpon(x,λ)	vexpon(x,λ)

Extreme Distribution	extreme(x,a,b)	iextreme(x,a,b)	vextreme(x,a,b)

F Distribution	F(x,ν,ω)	iF(x,ν,ω)	vF(x,ν,ω)

Gamma Distribution	gamma(x,c)	igamma(x,c)	vgamma(x,c)

Geometric Distribution	geom(x,p)	igeom(x,p)

Laplace Distribution	laplace(x,a,b)	ilaplace(x,a,b)	vlaplace(x,a,b)

Logistic Distribution	logis(x,a,b)	ilogis(x,a,b)	vlogis(x,a,b)

Lognormal Distribution	lognorm(x,μ,σ)	ilognorm(x,μ,σ)	vlognorm(x,μ,σ)

Normal Distribution	normal(x,μ,σ)	inormal(x,μ,σ)	vnormal(x,μ,σ)

Pareto Distribution	pareto(x,c)	ipareto(x,c)	vpareto(x,c)

Poisson Distribution	poisson(x,λ)	ipoisson(x,λ)

Rayleigh Distribution	rayleigh(x,b)	irayleigh(x,b)	vrayleigh(x,b)

Student's t Distribution 	student(x,df)	istudent(x,df)	vstudent(x,df)

Weibull Distribution	weibull(x,b,c,θ)	iweibull(x,b,c,θ)	vweibull(x,b,c,θ)


Change Gridlines Layout

When you click on this option, the appropriate Gridline dialog will open (see below) allowing you to change the format and patterns for gridlines in the graph.  For information on a specific gridline dialog, click on one of the options below.

Gridlines - 2D Graphs

Gridlines - 3D Graphs

Gridlines - Matrix Graphs

Gridlines - Ternary Plots


Gridlines - 2D Graphs

You can specify the format and pattern for gridlines in 2D Graphs in the Gridlines dialog.

Gridlines dialog

Format:  Select either no gridlines in the graph (None), only horizontal gridlines (select X), only vertical gridlines (select Y) or both horizontal and vertical gridlines (select X and Y).

Pattern button:  Click on this button to open the Line Pattern-Gridline dialog from which you can select the pattern, color and thickness of the gridlines.  (See also, Selecting Point, Lines, Area Patterns.)


Gridlines - 3D Graphs

You can specify the format and pattern for gridlines in 3D Sequential Graphs or 3D Scatterplots and Surfaces in the Gridlines dialog.

Gridlines dialog

Format:  This option allows you to specify the gridline format for each of the 6 planes (XY, XZ, YZ, XY', XZ', and YZ') in the 3D box.  You can select either no gridlines in the graph, only horizontal gridlines, only vertical gridlines, or both horizontal and vertical gridlines in the plane.

Pattern button:  Click on this button to open the Line Pattern-Gridline dialog from which you can select the pattern, color and thickness of the gridlines (the choices that you make here will apply to the gridlines in each of the planes).  (See also, Selecting Point, Lines, Area Patterns.)


Gridlines - Ternary Plots

You can specify the format and pattern for gridlines in Ternary Plots in the Gridlines dialog.

Gridlines dialog

Format:  This option allows you to specify the gridline format (or no gridlines via option None) for each of the 5 planes (XYZ, XYZ', XV, YV', and ZV') in the 3D triangle.

Vertical Planes (XV, YV, ZV): This option allows you to specify the gridline format (or no gridlines via option None) for each of the 5 planes (XYZ, XYZ', XV, YV', and ZV') in the 3D triangle.  Specify here whether you want the vertical planes to be displayed in the Background Only or turned On (i.e., displayed in the graph).

Pattern button:  Click on this button to open the Line Pattern-Gridline dialog from which you can select the pattern, color and thickness of the gridlines (the choices that you make here will apply to the gridlines in each of the planes).  (See also, Selecting Point, Lines, Area Patterns.)


Gridlines - Matrix Graphs

You can specify the format and pattern for gridlines in Matrix Graphs in the Gridlines dialog.

Gridlines dialog

Format:  You can remove the gridlines from the plots (select None), use the gridlines to partition each plot into either 9 squares (select 3s) or 81 squares (select 9s), or choose to have STATISTICA automatically select the best gridline option for the plots (select Auto).  Note that if set at Auto, the gridline style will depend on the size of the graph (on the screen or when printed) and the resolution of the device; therefore, for example, the lines may not be displayed on the screen, but they will appear when printed.

Pattern button:  Click on this button to open the Line Pattern-Gridline dialog from which you can select the pattern, color and thickness of the gridlines (the choices that you make here will apply to the gridlines in each of the plots).  (See also, Selecting Point, Lines, Area Patterns.)


Display Axes

In a 3D graph, there are four (horizontal) X-axes (x1 through x4), four (horizontal) Y-axes (y1 through y4), and four (vertical) Z-axes (Z1 through Z4).  By default, 3D graphs in STATISTICA display the foreground axes (X1, Y1, and Z1) and the rest of the axes are "turned off" (de-selected in this dialog).  The Display Axes dialog will allow you to display (select the axes that you want to display) or not display (de-select the axes) any of the axes in the 3D plot.  The line pattern and tickmarks for each axis selected in this dialog are determined by the settings in the appropriate Scale Options dialog.


Display Axes (in Ternary Plots)

There are 9 axes in a 3D ternary graph:  2 horizontal X-axes (X1 and X2), 2 horizontal Y-axes (Y1 and Y2), 2 horizontal Z-axes (Z1 and Z2), and 3 vertical V-axes (V1, V2, and V3).  By default, 3D graphs in STATISTICA display the foreground axes (X1, Y1, and V3) and the rest of the axes are "turned off" (de-selected in this dialog).  The Display Axes dialog will allow you to display (select the axes that you want to display) or not display (de-select the axes) any of the axes in the 3D plot.  The line pattern and tickmarks for each axis selected in this dialog are determined by the settings in the appropriate Scale Options dialog.


Control Limits

The quickest way to add custom control (or range) limit lines or boxes is to use the drawing tools; by default, they will be Dynamic (not Fixed, seeDynamic and Fixed Toolbar buttons) and thus their specific location will be related to scales and need no adjustment when the graph is modified.  However, this method is less convenient for categorized graphs when the user may need to place the same limits in many component graphs.  To automate the process of drawing multiple control lines or boxes, the Control Limits facility is provided.  You can use this technique to place control limits or boxes in 2D graphs in order to define simple and data-independent limit ranges or in categorized graphs as a common point of reference.  When you select this option, the Control Limit dialog will open.

Control Limit dialog:

Limits

Value

Pattern

Get All Patterns From the First


Control Limits - Limits

Select Off to turn off this option and any existing control limits in the graph.  You can also choose between displaying the control limits as intersecting Lines or as a Box (the box would be drawn at the intersection of the control limit lines).


Control Limits - Value

You will need to specify for each of the four limits (X1, X2, Y1, and Y2), whether you want the limit displayed in the graph (select On), and also the exact coordinate of the limit on the respective axis (i.e., its Value) that will determine its position in the graph.


Control Limits - Patterns

Control Limits - Pattern

Click on this button to open the Line Pattern dialog from which you can select the pattern, color, and thickness of the control limit lines.  The pattern, color, and thickness can be different for each line in the control limit (i.e., a separate dialog will open for each limit), however, you can use the selections that you made in the first dialog for all of the limit when you select the Get All Patterns From the First option.  (See also, Selecting Point, Lines, Area Patterns.)


Control Limits - Get all Patterns from the First

Selecting this option will allow you to transfer the pattern, color, and thickness selections from the Line Pattern dialog for the Y1 limit to the rest of the limits.


Pie Options

Pie Charts are one of the most common graph formats used for representing proportions or frequencies (see Custom 2D Plots).  When you create a Pie Chart, you will be able to customize it by using the options in the Pie Options dialog.

Shortcut:  Double-click on the pie (in the graph).

Pie Options dialog:

Pie Position

Pie Style

Pie Shape

Pie Labels

Border

Patterns

Explode


Pie Options - Pie Position

You can change the position of the pie icon in the graph by specifying the location of the center of the pie with the Center X and Center Y options.  By default, the center of the pie is located in the center of the graph at the X,Y position 0,0 (note that if the pie chart is produced as one of the plots in a mixed type graph, then the coordinates of the center of the graph will typically be different from 0,0).  The units of a negative or positive shift in the X- or Y-axis is based on the units used on the X or Y scale, respectively.  For example, if you enter -1 for the Center X: value and -1 for the Center Y: value, then the center of the pie would be moved 1 unit down (this unit would depend on the Y-axis scale) and 1 unit to the left (this unit would depend on the X-axis scale) in the graph.  (Note that the X and Y coordinates can be referenced even if the display of the actual scales is suppressed; the current X- and Y-axis minimum and maximum can be reviewed and adjusted in the Scale Options dialog.)

When you select the Ellipse pie shape option, you can change the size of the pie ellipse by adjusting the X and Y Radii (represented in terms of % of the X- and Y-axis, respectively).  The Starting Angle option allows you to rotate the pie in order to change the starting position for the first slice of the pie (i.e., change the Starting Angle in degrees; by default 0° = "12 o'clock").


Pie Options - Pie Style

You can change the appearance of the pie by choosing either the 2-dimensional (2D) or 3-dimensional (3D) display in this option.


Pie Options - Pie Shape

The pie shape can be either circular (select Circle) or elliptical (select Ellipse).  However, choosing the Ellipse option may cause the slices to be disproportionate in size (i.e., the slices that follow radii close to the vertical axis of the screen or paper will look relatively larger than their real size as compared to the "horizontal" slices which will be "squeezed" in perspective and will appear smaller).


Pie Options - Pie Labels

You can choose from several labeling options for the individual pie slices, or if you prefer, remove the labels from the pie chart (select Off).  The available labels are:

%:  Labels each pie slice with the proportion of the pie slice in percentages.

Value:  Labels each pie slice with the appropriate value.

Text Values:  Labels each pie slice with the appropriate case name.

Text & %:  Labels each pie slice with the appropriate case name and the proportion of the pie slice in percentages.

Text & Value:  Labels each pie slice with the appropriate case name and value.


Pie Options - Border

Click on this button to open the Line Pattern-Border dialog from which you can de-activate the border or select a pattern, color and thickness for the border line outlining the "edges" of the slices of the pie (e.g., you could set it to a dark color to make the shape of a 3D pie more salient).


Pie Options - Patterns

Each pie slice is represented by a numbered color square (the first slice is in the "12 o'clock" position) in this dialog.  You can change the pattern and color of a slice area by clicking on its color square to open the Areas dialog.  (See also, Selecting Point, Lines, Area Patterns.)


Pie Options - Explode

This option will allow you to "explode" (check the Explode box under each slice number) some or all of the slices of the pie.


3D Graphs/More Options

The 3D Graph/More Options dialog offers several options for customizing 3D graphs.  This dialog is available for either 3D Scatterplots and Surfaces, 3D Histograms, or 3D Sequence Graphs by clicking on the More Options button in each of the respective General Layout dialogs.

3D Graph/More Options dialog:

Eye Position

Axis Proportions

Surface Style

Surface Lines

Surface Contour

Surface/Contour Levels

Box Margins

Deviation Level

Number of Spectral Planes


3D Graphs/More Options - Eye Position

This option allows you to expose specific aspects of the 3D display for analytic purposes and also to create special presentation effects by changing the perspective of the graph.  The Eye Position parameters determine the location of the "view point" of the graph separately for each of the three axes X, Y, and Z.  The absolute value of each parameter determines the distance between the eye and the respective axis (i.e., the degree of the perspective transformation for the respective plane).  The sign of the parameter determines the side from which the axis is viewed (i.e., a value of 0 represents the "facing position" and no perspective transformation; negative and positive values represent left and right or up and down shifts of the viewpoint, respectively).

Shortcut:  Use the interactive Perspective and Rotation control facility accessible by clicking the Rotate [image] button on the Graphics Toolbar (or from the Graphics View pull-down menu).


3D Graphs/More Options - Axis Proportions

You can control the proportions of the axes in the graph in order to adjust the frame of reference for the graph (axes) to its shape (i.e., in order to expose or explore a particular aspect of the data).  The three fields, X, Y, and Z determine the relative length of the axes.  The default proportions of the axes are 1:1:1 (i.e., the proportions of the X, Y, and Z sides are of equal length and form a regular cube).  By changing the respective values, you can "flatten" (e.g., increase the proportions of the X- and Y-axes compared to the Z-axis:  1:1:.5) or "stretch" (e.g., increase the relative length of just the Z-axis:  1:1:2) the 3D box in any direction.  The proportions of the box will not change when you change the graph window aspect ratio.


3D Graphs/More Options - Surface Style

This option allows you to change the style of the top and bottom of surfaces of Surface Plots.  (See also, Calculating Contour Levels and Distance.)

Shaded:  Instead of using a single solid color for the plot surface, you can select a different color for each level of the surface from a predefined palette of colors or from a custom-defined color palette.  To do this, select Shaded and then click the OK button to accept the default palette colors, or click on the Get Palette button in the Specify Contour Levels dialog to open the Edit Palette dialog from which you can custom-define the colors in the palette.

Solid:  Instead of using a combination of colors (e.g., a specific palette of shades) for the plot surfaces, you can select a single color for the top or bottom of surfaces of the plot by choosing Solid and then selecting the individual colors for the Top and Bottom surfaces from the respective lists in this option.


3D Graphs/More Options - Surface Lines

These options allow you to control the display of the "wire frame" which outlines the cuts of a Surface Plot.  By default, this wire frame is not transparent and a "patch work" of colors makes up the contour surface of the plot.  You can suppress the surface color or pattern shading and display a transparent wire frame representation of the surface by selecting Show Hidden.  You can also select the pattern and color of the lines in the wire frame by clicking on the X Line button or Y Line button to open the respective Line Pattern dialog.  (See also, Selecting Point, Lines, Area Patterns.)


3D Graphs/More Options - Surface Contour

This option allows you to control the projection (select Display) of the contour of the surface onto the XY plane.  In this area of the dialog, you can also specify the Distance from the surface to the contour (the contour does not have to be projected onto the XY plane at the level of "minimum Z value").  (See also, Calculating Contour Levels and Distance.)


3D Graphs/More Options - Surface/Contour Levels

The following options allow you to define the number of color levels (from the color palette) to be used in the surface plot or contour as well as the range of values which define each level of the surface or contour; see also, Calculating Contour Levels and Distance.

Automatic:  If you select this option, STATISTICA will define the levels of the surface or contour based on either the default number (10) of levels or a specified No. of levels (see below).

No. of Levels:  If you select Automatic (see above), then you can specify here the number of levels to be used in the surface plot or contour.  If you request more levels than are in the current color palette, then STATISTICA will cycle through those colors until the surface or contour is complete.  You can add more colors to the palette or open a different palette in order to use more than the default number of color levels (see the Edit Palette dialog accessible by pressing the Get Palette button in the Specify Contour Levels dialog).

User-defined:  Select this option if you want to specify the values used to define the levels of the surface or contour (see Specify Contours, below).

Specify Contours:  After you select the User-defined option (see above), the Specify Contours button will become available.  Click on this button in order to open the Specify Contour Levels dialog.  Here, you can define the levels of the contour or surface and change the colors associated with each level for the current graph.  You can change the level colors globally in the Specify Default Contour Attributes dialog (available from the Global Defaults option of the pull-down menu Options).


3D Graphs/More Options - Box Margins

This option (applicable to Box, Block, and Ribbon plots) allows you to specify the width of the X and Y margins (in percent) between the boxes, blocks and ribbons, relative to the maximum width of the box, block or ribbon in the plot (e.g., if in a Ribbon Plot both margins are more than 0%, then a "broken line" graph will be created, i.e., there will not only be breaks between the ribbons but also between consecutive segments of the same ribbon).


3D Graphs/More Options - Deviation Level

This option (applicable to Deviation and Space plots) allows you to specify a value on the Z-axis that determines the level from which deviations are derived; or in the case of Space Plots, this value determines the Z-level of the XY plane.


3D Graphs/More Options - Number of Spectral Planes

This option will allow you to specify the number of spectral planes into which the data are segmented (compressed) in Spectral Plots.


Specify Contour Levels

The options in this dialog will allow you to change the range of values and number of levels used to define the contour or surface.  You can also change the color and pattern for each level.  In order to change the color and number of levels globally, use the Specify Default Contour Attributes dialog (available from the Global Defaults option of the pull-down menu Options).

Specify Contour Levels dialog:

Style

Level

Cont. Line

Area Line

Area

Open

Save As

Get Palette

Restore Defaults

Interval Levels

Uniform Levels

Insert Level

Append Level

Delete Level

Draw Lines


Specify Contour Levels - Style

You can choose to display the contour as a series of Lines or Areas with this option.


Specify Contour Levels - Level

For each level of the contour or surface plot, a value (lower limit) is specified in the edit field to the right.  You can change the value of each level or Insert, Append, or Delete levels from this list.


Specify Contour Levels - Contour Line

Click on the contour line button next to the desired Level in order to change the line pattern for that level of the line contour plot.


Specify Contour Levels - Area Line

Click on the area line button next to the desired Level in order to change the line pattern for that level of the area contour plot.  Note that these line patterns will apply when you select the option Draw Lines.


Specify Contour Levels - Area

Click on the area button next to the desired Level in order to change the color and pattern for that level of the area contour plot or surface.


Specify Contour Levels - Open

Click on this button to open the Retrieve Contour Definition dialog.  In this dialog you can select a previously saved initialization file (*.ini) with the desired contour definition (see also STATISTICA initialization files).


Specify Contour Levels - Save As

Click on this button to open the Save Contour Definition dialog.  Here you can save the contour definitions in a new STATISTICA initialization file (*.ini).


Specify Contour Levels - Get Palette

Click on this button in order to open a previously saved color palette (file name extension *.pal; see Edit Palette) or to edit the current color palette.


Specify Contour Levels - Restore Defaults

Clicking on this button will restore the STATISTICA default colors and line patterns.


Specify Contour Levels - Interval Levels

When you click on this button the Specify Interval Levels dialog will open in which you can request a new set of levels by specifying the number of levels, the minimum value, and step size.


Specify Contour Levels - Uniform Levels

When you click on this button the Specify Uniform Level dialog will open in which you can specify the number of levels for the contour or surface (the entire range of values of the Z variable will be divided into the requested number of levels).  This option is similar to the Automatic option in the 3D Graphs/More Options dialog.  However, using the Uniform Levels option in this dialog will allow you to change the line and area color and pattern for each level.


Specify Contour Levels - Insert Level

Click on this button in order to insert a new contour or surface level after the current level.


Specify Contour Levels - Append Level

Click on this button in order to append a new contour or surface level after the last level.


Specify Contour Levels - Delete Level

Click on this button in order to delete the current level.


Specify Contour Levels - Draw Lines

When you select this option, the contour lines defining the levels of contour will be drawn in Area contour plots or surface plots.  These line patterns can be edited via the Area Line option.


Specify Interval Levels

Unlike the Specify Uniform Levels option, where the contour/surface levels are determined depending on the current range of values of the Z variable, this contour definition facility allows you to define levels independent of the current values of the Z variable (e.g., in order to produce a series of contour plots from different data sets to be compared).  The requested No. of Levels for the surface or contour plot will be created, starting with the specified Minimum level value and following the requested Step size.


Specify Uniform Level

Specify Uniform Levels

Specify in this dialog, the number of levels for the contour or surface.  The entire range of Z values will be divided into the requested number of equal length intervals.  This option is similar to the Automatic option in the 3D Graphs/More Options dialog, however, using the Uniform Levels option from the Specify Contour Levels dialog will allow you to change the line and area color and pattern for each level.


Specify Default Contour/Surface Attributes

The options in this dialog will allow you to globally change the range of values and number of levels used to define the contour or surface.  You can also change the color and pattern for each level.  In order to change the color and number of levels in the current graph only, use the Specify Contour Levels dialog (available from the 3D Graphs/More Options dialog).

Specify Default Contour Attributes dialog:

Cont. Line

Area Line

Area

Open

Save As

Get Palette

System Defaults

Get from Graph

Insert Level

Append Level

Delete Level

Draw Lines


Specify Default Contour Attributes - Style

You can choose to display the contour as a series of Lines or Areas with this option.  (See also, Calculating Contour Levels and Distance.)


Specify Default Contour Attributes - Line

Click on the Line button next to the desired Level in order to change the line pattern for that level of the contour plot.


Specify Default Contour Attributes - Area

Click on the Area button next to the desired Level in order to change the color and pattern for that level of the contour plot or surface.


Specify Default Contour Attributes - Open

Click on this button to open the Retrieve Contour Definition dialog.  In this dialog you can select a previously saved initialization file (*.ini) with the desired contour definition (see also STATISTICA initialization files).


Specify Default Contour Attributes - Save As

Click on this button to open the Save Contour Definition dialog.  Here you can save the contour definitions in a new STATISTICA initialization files (*.ini).


Specify Default Contour Attributes - Get Palette

Click on this button dialog in order to open a previously saved color palette (file name extension *.pal; see Edit Palette) or to edit the current color palette.


Specify Default Contour Attributes - System Defaults

Click on this button to replace all of the changes that you have made in the Specify Default Contour Attributes dialog with STATISTICA's system defaults.


Specify Default Contour Attributes - Get from Graph

Click on this button in order to transfer the settings from the current graph to the Specify Default Contour Attributes dialog in order to use them as defaults.  The advantage of this option is that you can experiment with different settings in the graph in order to visually inspect the outcome.  Once you have decided upon the appropriate settings, you can open the Specify Default Contour Attributes dialog (click on the Contour Definition button in the Global Defaults dialog) in order to make those settings the defaults for subsequent graphs or save them in a file.


Specify Default Contour Attributes - Insert Level

Click on this button in order to insert a new contour or surface level after the current level.


Specify Default Contour Attributes - Append Level

Click on this button in order to append a new contour or surface level after the last level.


Specify Default Contour Attributes - Delete Level

Click on this button in order to delete the current level.


Specify Default Contour Attributes - Draw Lines

When you select this option, the contour lines defining the levels of contour will, by default, be drawn in Area contour plots.


Variable Names

Variable names used in icon plot legends to define the consecutive components of the icons (or in the case of Chernoff Faces legends, of the variables represented by specific facial characteristics of the icons), can be edited in the Variable Names dialog.  The variable names are presented in an editable list box.  To edit a name, highlight it (click on the respective number) and then type in the edited name.  Variable names can be customized using Control Characters.  By entering the appropriate Control Characters, you can add superscripts and subscripts to the variable names as well as change the font attributes for each name (see the topic Control Characters Reference, for a listing of the available codes).

Shortcut:  Double-click on the legend text to bring up the General Layout and Plot Layout - Icon Graphs dialog from which you can click on the Legend-Edit button.


Selected Icons Border Patterns

This option applies to multiple-subset icon plots, where individual icons belong to previously specified subsets (classes).  In the Selected Icons Border Patterns dialog, you will be able to change the line size and style as well as add legends for each of the selected classes of icons in the icon plot.  The line borders will be used to identify specific classes of cases in the icon plot.

Selected Icons Border Patterns dialog:

Legend:  For each line border, you can enter one line of text in the edit box.  This text will be used as a legend in the icon plot to briefly describe the selected (bordered) class of cases (by default the case selection conditions used to define the class is used as the legend).

Line (Border) Pattern:  Click on an individual line button to open the Line Patterns dialog from which you can choose a different color, size or style of line.  (See also, Selecting Point, Lines, Area Patterns.)


Chernoff Face Definition

Chernoff faces represent the most elaborate type of icon plot.  Cases are visualized by schematic faces such that the relative values of variables selected for the graph are represented by the variations of specific facial features.  The Chernoff Face Definition dialog not only allows you to modify the specific assignment of variables to individual features of the Chernoff faces, but also to change the Default settings for each facial feature (the Default values are used when a feature has not been assigned to a specific variable).  The Default values are useful because Chernoff faces are always "complete" (i.e., in order to look like faces, they always need to have all 20 features, even if fewer than 20 variables were selected), thus some features may have to remain constant.  The range of variation (from:to) for each facial feature is displayed to provide a reference point for setting the Defaults (values for constant features).  The Variables column lists the column or row numbers according to the order in which they were entered into the Custom Icon Plots dialog or variable numbers according to the order in which they were selected in the Icon Plots definition dialog.  The original names can be reviewed and edited in the Variable Names dialog.


Order of Variables

An important part of exploring relations between variables via Icon Plots or Matrix Plots is to reorder the variables (i.e., reassign them to different aspects of the icon or reorder the display of matrices).  You can rearrange the order of variables for each type of icon or for each type of matrix plot in the Order of Variables dialog (accessible by clicking on the Var. Order button in the General Layout and Plot Layout - Icon Graphs or the General Layout and Plot Layout -Matrix Graphs dialog).  To reorder a variable, first select a position for the variable in the number order list (No.), and then select the variable name (from the list of variables) that will be placed in that position (repeat these steps until the variables are ordered the way that you want).  Note that the names of variables here may also be the names of rows or columns in Scrollsheets or other identifiers of variables in the graph.  You can always restore the list of variables to the original (default) order (designated by the order of variables in the Custom Matrix Plots or Icon Plots dialog) by clicking on the Original button.


Chernoff Face Patterns

This dialog allows you to customize the default colors and patterns of the lines used to draw the main components of the Chernoff Faces.  Note that a comprehensive selection of options to customize the appearance of Chernoff Faces icons is accessible from the General Layout and Plot Layout - Icon Graphs dialog for this graph by pressing the button Definition.

You can change the line color, pattern, or width for each of the main Chernoff facial components (Face, Nose, Mouth, Eyes, Eyebrows, and Pupils) in the Chernoff Face Patterns dialog (accessible by clicking on the Lines button in the General Layout and Plot Layout - Icon Graphs dialog).  When you click on one of the facial characteristics in the dialog, the Line Patterns dialog will open in which you can choose a different line color, pattern, or width for that component.  (See also, Selecting Point, Lines, Area Patterns.)


Icon Information

This window contains information about the number of cases and number of variables in the current icon plot design.


  Insert Object

When you select the Object option from the Insert pull-down menu, the Insert dialog will open, allowing you to combine into one display different objects, graphs, metafiles, or bitmaps.

Example

Insert dialog:

New Object

Object from File

Picture from File

Object Type

Type of File

File Name

Directory

Drive

Set as Default Style

Link to File

Put in Default Place

Object Properties

Graph Mapping Mode


  Insert Object - New Object

Select this radio button if you want to create a new object (in another application or a new STATISTICA graph) to be inserted into the current graph.


  Insert Object - Object from File

Select this radio button if you want to embed or link (using the OLE facilities) a previously saved object (e.g., STATISTICA graph, Paintbrush picture, etc.) into the current graph.  You can embed the current graph into itself either by copying it and then pasting back or by first saving the graph using the Save option from the File pull-down menu, and then selecting that graph name when you choose the Object Type.


  Insert Object - Picture from File

Select this radio button in order to embed or link objects saved in Windows metafile format (file name extension *.wmf) or bitmap format (file name extension *.bmp).  Unlike using the previous option (Object from File), the OLE facilities will not be used, thus this option can be used to insert non-OLE-compliant graphs into STATISTICA graphics windows.  Linked pictures will maintain manual only (i.e., not automatic) links to their respective files.


  Insert Object - Object Type

When you click on the New Object radio button, you will be able to choose the type of object that you want to create from a list of Windows applications which support OLE.  When you select the object type and click OK in this dialog, the application will open allowing you to create the new object.

When you click on the Object from File radio button, this option will allow you to select the type of object that you want to insert from a list of Windows applications which support OLE.  Select the appropriate object type in order to display all of the previously saved files for that application (see File Name).


  Insert Object - Type of File

This option (available when you select Picture from File) will allow you to insert either a Windows metafile (file name extension *.wmf) or a bitmap (file name extension *.bmp) with this option.


  Insert Object - File Name

Once you have selected the Object Type or Type of File and the appropriate Drive and Directory, all of the previously saved files of this type will be displayed here.  Select the desired file to be embedded or linked into the current STATISTICA graph.


  Insert Object - Directory

Select the directory in which the desired file resides.


  Insert Object - Drive

Select the drive in which the desired file resides.


  Insert Object - Link to File

You can choose between Linking (select this option) or Embedding (de-select this option) the object, metafile, or bitmap in the current graph.

  When checked, this option will link the selected object in the current graph with the original object file created by the source application.  In other words, unlike with embedded objects, when you make changes to the object in the source application, the changes will appear in the linked object in the STATISTICA graph.  By double-clicking on the linked object, you can start the application that was used to create the object while remaining in STATISTICA.

  When unchecked, a copy of the selected object will be embedded in the current graph.  In order to make changes to the embedded object, you can double-click on it to start the application that was used to create it while remaining in STATISTICA.


  Insert Object - Put in Default Place

When this option is selected ( [image]), the Clipboard object will be pasted in the upper-left-hand corner of the graph (the default location).  You can then click on the object to select it and move it to the desired location in the graph or resize it.  If you de-select this option ( [image]) and click OK, then you will be able to specify with the cursor (by dragging a rectangle) the exact location and size of graph area in which to paste the Clipboard object.


  Insert Object - Object Properties

Dynamic Scale:  When you select Dynamic Scale, the object that you are pasting will be anchored against the X- and Y-axis scales of 2D graphs and not the physical window coordinates, thus their position will be dynamically adjusted as you make changes to the graph.  When you de-select this option, the objects will be assigned to a Fixed window location and their respective position in the graph will remain unchanged when you make adjustments to the graph (e.g., when you rescale the graph), thus they will be unrelated to any specific parts of the graph.  (Note that when you paste objects in 3D graphs, the Dynamic option cannot be used due to the lack of fixed 2D graph coordinates.  Thus, the object positioned on the screen of a 3D or 4D graph may lose its relation to the specific elements of the graphs when you change the graph, e.g., resize, rescale, or rotate it.)

You can change between fixed and dynamic modes using the respective Toolbar button (see below) by first highlighting the object (click on it once) and then clicking on the Toolbar button to toggle between modes.

Fixed Mode:

Dynamic Mode (when depressed):

See also, Using Dynamic (Coordinate) Mode in Categorized and Matrix Graphs

Locked Position:  Select ( [image]) this option in order to lock the inserted object in the graph location to which it is pasted (see Put in Default Place).  Before repositioning or resizing the object, it must first be unlocked [double-click on the object or press ALT+ENTER (when the object is selected) in the graph to bring up the Object Properties dialog in which the locked status can be changed].  See Inserting Objects into a STATISTICA Graph for an example using the Locked Position option.

Original Proportion:  Click on this option to maintain the original proportion of the pasted object.  When this option is selected, you will be able to resize the object proportionally.  When this option is de-selected, you will be able to resize the graph disproportionately (e.g., elongate the object by stretching it in one direction).  For more information on resizing an object, see Resizing an Object.

Borders:  When selected, this option will place a border around the pasted object.  Once you have selected this option, the Border Pattern button will no longer be dimmed.  Click on this button to open the Line Pattern dialog from which you can select the pattern, width, and color of the frame line.  (See also, Selecting Point, Lines, Area Patterns.)

Filled Background:  Selecting this option will cause the background and foreground of the metafile or graph file to be displayed in the graph (i.e., the object will cover-up what is underneath it).  When you de-select this option, the background of the embedded or linked metafile or graph file will become transparent, allowing you to view the current graph instead of the embedded/linked object's background.  (See also, Printing Objects with Filled Background.)


Inserting Objects into a STATISTICA Graph

The following example will describe the necessary steps to embed a graph file into the current graph.  To link a graph file, follow the same steps outlined below, except select the Link to File option.

Step 1:	Click on the Insert Object Toolbar button or select the Insert option from the Edit pull-down menu to open the Insert dialog.

Step 2:	In the Insert dialog, click on the Object from File radio button.  Select STATISTICA Graph (*.stg) as the Object Type and then select the desired file.

Step 3:	De-select the Link to File option in order to embed the graph file into the current graph.  Also for this example, let's select (click on the option to check the boxes) the options Dynamic Scale and Original Proportion (see Insert for a discussion of each option).  Deselect the option Put in Default Place and select the option Locked Position; accept all other defaults, and click OK in this dialog.

Step 4:	Now, place the mouse cursor in the area of the graph that you want the graph file embedded, and while holding down on the left-mouse-button, drag the cursor across the graph until the box outline is the dimension that you desire.  When you release the mouse button, the graph file will fill the area inside the box outline and be locked in this position.  (Note that the embedded graph can be repositioned or resized by clicking on it once and then dragging it or stretching it with the mouse cursor.)

Note that for some video drivers, when you move an object, some residue from the selected object (i.e., shades of color or small pieces of the object) may remain on the screen.  This residue will not be displayed in the graph when printed and will disappear from the screen when the graph is redrawn (e.g., after resizing the graph or repositioning the graph in the window via the Adjust Graph Margins toolbar button).


Graph Mapping Mode

The mapping mode setting (applicable only to linked or embeded STATISTICA graph objects) specifies the manner in which the logical sizes of the components of the graph are mapped (transformed) onto the physical space of the current device (e.g., a printer or a display window).  Three modes are specified:

Fixed size font:  In fixed size font mode, physical sizes of fonts (as well as point markers, and other graph components specified in points) in embedded or linked graphs will be the same size as objects in the graph in which they are embedded.  For example, in the Master Document graph shown above, the mapping mode for the embedded graph on the left was set to Fixed Size Font.  Therefore, the font in this child graph can be increased or decreased along with the font in the Master Document via the [image] Increase Font and [image] Decrease Font toolbar buttons.

Isotropic:  In this mapping mode, one unit on the X-axis of the transformed object (e.g., an embedded graph) is equal to one unit on the Y-axis and the output is created proportionately, with equally scaled axes.  The size of the object will be changed proportionally when the size of the plot is changed (regardless of whether or not you are maintaining the graph aspect ratio).  For example, in the Master Document graph shown above, the mapping mode for the middle child document is set to isotropic.  Therefore, the embedded graph is scaled proportionally and if it is resized, it will resize proportionally.

Anisotropic:  In this mapping mode, the X- and Y-axes of the transformed object (e.g., an embedded graph) are arbitrarily (i.e., disproportionately) scaled.  This mode depends on the graph aspect ratio.  For example, in the Master Document graph shown above, the mapping mode for the child graph on the right is set to anisotropic.  Here, the embedded graph is vertically "stretched" in order to fit into the space provided for the embedded graph.

Note:  When you select the Fixed Size Font option, you can use the [image] Increase Font and [image] Decrease Font toolbar buttons to globally and proportionally increase or decrease the font size (as well as markers and all distances and spacing specified in points or related to font and marker sizes), incrementally, for each font style and size represented in the current graph.  Each click of these toolbar buttons will change the value of the Graph Mapping Base by 16% (e.g., one click on the [image] button will increase the font size and decrease the mapping base by 16%).  Hold down the CTRL key while pressing either of these buttons to achieve a smaller (4%) increase rate.

See also, Mapping Base.


Resizing an Object

Inserted objects can be resized in the following ways:

Resize While Maintaining the Original Aspect Ratio:  You can resize the inserted object while maintaining the original aspect ratio (resize proportionally) when the Original Proportion option is selected in the Insert dialog.  When you click once on the object with the left-mouse-button, four black selection squares will appear around the object (see below).

Original Proportion Selected (four selection squares):

Now you can drag on one of the corner black selection squares to either "stretch" or "shrink" the object.

Resize Without Maintaining the Original Aspect Ratio:  You can change the aspect ratio of the inserted object (i.e., resize disproportionately) if the Original Proportion option is de-selected in the Insert dialog.  When this option is de-selected and you click once on the object with the left-mouse-button, eight black selection squares will appear around the object (see below).

Original Proportion De-selected (eight selection squares):

Now you can drag on one of the side black selection squares to either "stretch" or "shrink" the object in one direction (depending on which black selection square that you drag).

See also:

Moving a Graph Object


  Graphic Text

In STATISTICA graphs, you can enter additional text (other than titles, fixed legends, category values, category names, data labels, or scale values) by clicking on the Graphic Text Toolbar button ( [image]) or selecting the Text option from the Insert pull-down menu in order to open the Graphic Text Editor dialog.  Legends which have been made movable (see Legends) can also be edited in this dialog (double-click on the movable legend in order to open the Graphic Text Editor dialog).

Text can be formatted by highlighting it in the Editor and then clicking on an option button (e.g., click on the superscript button, see below).  STATISTICA will automatically insert the Control Characters to enable and disable that option around the highlighted text.  In other words, the option will only apply to the highlighted text.  Control Characters can also be added directly to the text (see Control Characters).

The Graphic Text Editor dialog contains options relating to the position, display, and format of the text (or movable legend) in the graph (see below).

Shortcut:  Double-click on the added text (or movable legend) to re-open the Graphic Text Editor dialog.

Example:  How to Change the Font for a Part of the Custom Text.

Graphic Text Editor dialog:

Custom Text

Mini-toolbars

  Plot Legend

  Plot Fitted Function

  New Line

  Tab

  Default Tab

  Line Spacing

 and [image]  Sub/Superscript

 and [image]  End Sub/Superscript

  Local Font

, [image], and [image]  Font Attributes

  Return to Default Font

 and [image]  Clipboard Operations (keyboard shortcuts: CTRL+C and CTRL+V)

  Undo (keyboard shortcut: CTRL+Z)

Displaying Control Characters

Borders

Fill

Set as Default Style

Orientation (and Rotation)

Dynamic Scale

Locked Position

Alignment

Remove

  (Default) Font

  Symbols

Put in Default Place

Command-driven placement of text:  The graphics library of STATISTICA BASIC includes commands that define custom graphics objects and place them in graphs; for more information, see Graphics Library of STATISTICA BASIC.  (Note that STATISTICA BASIC contains functions that allow you to anchor objects, including custom text, not only in 2D but also in 3D and 4D coordinates).


  Graphic Text - Put in Default Place

When this option is selected, the custom text will be placed in the upper-left-hand corner of the graph (the default location).  You can then click on the text to select it and move it to the desired location in the graph (see Alignment).  If you deselect this option and click OK, then you will be able to specify with the cursor the exact location in which to place the custom text.


  Graphic Text - Custom Text

For added text, enter the text string that will be added to the graph in the edit box.  For movable legends, you can edit the existing text or add new text to the legend.  Several options are available for customizing the new or existing text.  You can utilize these options either by clicking on the appropriate button in this dialog to automatically enter the Control Characters or by manually entering the appropriate Control Characters.

Note that if you place the cursor in the text in this editor and then press the [image] Local Font button, then the resulting Font dialog will display the currently selected text and not the global text type.  Click on the (Default) Font button in order to view or edit the global font.


  Graphic Text - Plot Legend Buttons

When you click on any of these plot legend buttons [1 through 8 (for plots above number 8, enter the number manually)], then the plot symbol for the respective plot will be added to the text at the point in the text that you place the Control Character (for example in legends, this Control Character is placed at the beginning of the text).  These options are especially useful when you want to associate a specific text string with a specific plot (as in legends).  The Control Characters for plot legend symbols are:

@L[plot number, select number]:  Specify the plot number (1 through 64) and optionally the selection number (applicable to multiple-subset graphs).  In the case of 2D and matrix multiple-subset plots, when you specify the selection number, the program will insert the point marker for that subset.  For multiple-subset icon plots, when you specify the selection number, the specified subsetted icon border pattern will be inserted.

@C[level number]:  Specify the level number in order to insert the line or surface pattern for that level of the contour or surface plot.

@V[level value]:  Alternatively, you can specify the level value in order to insert the line or surface pattern for that level of the contour or surface plot.

@N[level number]:  The Z-axis of 3D surface or contour plots is divided into a specified number of surface or contour levels (via the Surface Levels option in the 3D Graphs-More Options dialog) which is reflected in the number of surface colors or line patterns in the plot.  Specify here the number of the contour or surface plot level in order to place the upper-bound value for that Z-axis level, next to the respective line or surface pattern.  Whenever you change the number of surface levels in the 3D Graphs-More Options dialog (i.e., change the scale of the Z-axis), the program will automatically adjust these values to reflect the change.  Note that once the Control Characters for this Z-axis level have been entered and you exit this dialog, you can edit this value by re-entering this dialog (double-click on the Z-axis level value).  The value of the Z-axis level will be displayed after @N in curly brackets (e.g., @N{  5.356@}.  Now, delete the @N code, the curly brackets, and the @ symbol after the value (e.g., 5.356) so that the edited value will be treated as regular text.


  Graphic Text - Plot Fitted Function Buttons

When you click on any of these plot fitted function buttons (1 through 8 [for plots above number 8, enter the number manually]), then the fitted function equation (either selected from the list of functions or customized, see 2D Plot Layout or 3D Surfaces and Scatterplots) will be added to the text at the point in the text that you place the Control Characters.  Once the Control Characters for the fitted function have been entered and you exit this dialog, you can edit the fitted function by re-entering this dialog (double-click on the fitted function).  The fitted function will be displayed after the Control Characters in curly brackets (e.g., @F{PRICE = -0.145+0.152log10(x)+eps@}.  Now, you can delete the @F code, the curly brackets, and the @ symbol after the function (e.g., PRICE = -0.145+0.152log10(x)+eps) so that the edited function can be treated as regular text instead of a fitted function.  The Control Characters for fitted functions are:

@F[plot number, subgraph number]:  Specify the plot number (1 through 64) and optionally the number of the subgraph in categorized graphs.  For example, @F[2] can be used to insert the equation for plot number 2; the following Control Characters can be used to enter the plot fitted functions for the first three subgraphs in a categorized graph:  @F[1,1] @F[1,2] @F[1,3].  (Note:  @F can be used instead of @F[1] or @F[1,1].)


  Graphic Text - New Line Button

Use this button to insert a new line characters (the text following this Control Character will be displayed in a new line), alternatively, type @A in the text where you want the line break to occur.  In the Graphic Text Editor, press ENTER while holding down the CTRL key (CTRL + ENTER).


    Graphic Text - Tab Buttons

  This button will insert a tab of 8 characters at the point in the text where the cursor is located.  The Control Character for this tab is @T[8], you can replace the value 8 by another value.

  This button will insert a "default" tab of 4 characters at the point in the text where the cursor is located.  The Control Character for this tab is @T.


  Graphic Text - Line Spacing Button

Use this button to modify the default (i.e., font size dependent) spacing between the lines of text.  The default setting of this Control Character is 4 points, but you can specify a negative or positive number of points to be used to modify (i.e., increase or decrease) the default line spacing.  The Control Character for this option is @S[point value], @S (with no value setting) is equivalent to @S[4] and will increase the line spacing by 4 points.


    Graphic Text - Sub/Superscript Buttons

These buttons allow you to place subscripts and superscripts, respectively, into the text.  Subscripts and superscripts can be nested in many levels (e.g., @D@D2 will place the value 2, two levels below the normal text; @D2@D3 will place the value 2 below the normal text and the value 3 below the level of value 2; see also, Control Characters).  The Control Characters are:

@D:  Makes the text following this Control Character subscripts.

@U:  Makes the text following this Control Character superscripts.


    Graphic Text - End Sub/Superscript Buttons

These buttons allow you to end or disable the super- or subscript text either one level at a time or for all levels (i.e., return to default text), respectively.  These Control Characters are entered after the super- or subscript text string in the edit box (i.e., at the point when you want to end the super- or subscripts and begin normal text).  The Control Characters are:

@E:  Ends one level of super- or subscript.  Note, to end more than one level without ending all levels, enter the Control Character once for each level that you want to end (this Control Character refers to the most recent super- or subscript code entered); e.g., @E@E will end two levels of the nested super- and subscripts.

@H:  Ends all levels of the superscripts and subscripts and returns to the default text level.


  Graphic Text - Local Font Button

You can place the cursor in the text or highlight some of the text in this editor and click on the [image] Local Font button in order to open the Font dialog in which you can display and edit the local font for the current text.

When a custom font is selected for part of the text, an additional font description is added to the internal structure of the custom text object and assigned a sequential number.  The control characters surrounding the custom text refer to this internal "font list."  For example, @K[1] would refer to the first additional font in the list.  A previous font selection in the same custom text object may be repeated by referencing the same control character font number. @Z is used to end the local font.  For an example of inserting a symbol in the text and of changing the font style, see How to Change the Font for a Part of the Custom Text.


      Graphic Text - Font Attributes Button

These buttons toggle on (place Control Character before text string) and off (place Control Character after text string) the font attributes:  italicize text, bold text, and underline text, respectively.  The Control Characters for these options are:

@I:  Italics font attribute.

@B:  Bold font attribute.

@X:  Underline font attribute.


  Graphic Text - Return to Default Font Button

This button will enter a Control Character that ends all italicized, bold, and/or underlined text, or local font and returns to the default font.  The Control Character for this option is @Z.


    Graphic Text - Clipboard Operations Buttons

Utilizing the Clipboard, these buttons allow you to copy and paste, respectively, while you are adding or editing text in the Graphic Text Editor edit box (alternatively, press CTRL+C and/or CTRL+V, respectively).  In order to cut highlighted text, press CTRL+X.


  Graphic Text - Displaying Control Characters

Note that in order to enter and display a string of characters that represent a control character (i.e., make the program ignore its special control status and display the string as regular characters), precede the control character text with an @ symbol (e.g., enter @@B in order to display the string as @B and not as @ followed by the beginning of the Bold mode).


  Graphic Text - Alignment

Justification:  This option will allow you to left-, center-, or right-justify the text against the respective margins.

Text in graph (anchor point):  Select the Horizontal (Left, Right, or Center) and Vertical (Top, Bottom, or Center) anchor point positions for the custom text.  When you select the text object in the graph, the selected anchor point location is displayed as a black selection square inside the outline of the selected text.

Moving selected text:  When you drag the text in the graph, the anchor changes to a cross-hair at the anchor location.  You can use this point to aid in the alignment of the text in the graph (e.g., this anchor point will be pulled into alignment with gridlines or intersections of gridlines when using the snap to grid option).

Rotating selected text:  The anchor point is also used as the point around which the text is rotated (see Orientation).  When the anchor point is used as the "pivot point" during rotation, it changes to a cross-hair at the anchor location.


Graphic Text - Border

  Graphic Text - Borders

When selected, this option will place a border around the text string or movable legend.  Once you have selected this option, the Border Pattern button will no longer be dimmed.  Click on this button to open the Line Pattern dialog from which you can select the pattern, width, and color of the border line.  (See also, Selecting Point, Lines, Area Patterns.)


  Graphic Text - Fill

Select this option to fill the text or movable legend background with a different color or pattern than the graph.  Once you have selected this option, the Fill Pattern button will no longer be dimmed.  Click on this button to open the Area Pattern dialog from which you can select the pattern and color of the background area.  (See also, Printing Objects with Filled Background.)


  Graphic Text - Remove

This button is dimmed until you re-open the Text dialog by double-clicking on an added text string or movable legend.  Clicking on the Remove button will allow you to remove (delete) the selected text string or movable legend from the current graph.  Note that you can also delete a text item from the graph by clicking once on it (to highlight it) and then pressing Delete on the keyboard.  If you remove or delete a movable legend, you can place the fixed legend back in the graph by selecting the Fixed Graph Legend ON option in the graph "long" right-mouse-button flying menu accessible by double-clicking anywhere in the empty space outside the graph region.


  Graphic Text - Default Font

Click on the [image] Default Font button to open the Font dialog from which you can select a font style and size for the default text that you are adding or for the default text in the movable legend.  Note that this setting will affect the entire contents of the Graphic Text Editor except for the sections formatted using a Local Font.


  Graphic Text - Inserting Symbols

Pressing the {bmp symbol.bmp} Symbols button will bring up the Windows Character Map utility (by default, the Symbol font is selected).  You can use the Windows Character Map to insert into documents, extended characters not found on most keyboards. These include special characters provided in symbol fonts.  The character(s) selected in the Windows Character Map are copied to the Clipboard when you press Copy; they may then be pasted into STATISTICA (or another application).  Note that the Windows Character Map transfers only the ASCII representation of the character to the Clipboard; therefore, after pasting the characters into the Graphic Text Editor, you need to use the Local Font button [image], and set them to the same font (e.g., TrueType Symbol) in order to properly display the characters in the graph.  For more information on the Windows Character Map, press Help while you are in that utility.  For an example of inserting symbols in custom text, see How to Change the Font for a Part of the Custom Text.


  Graphic Text - Orientation (and Rotation)

This option allows you to select the orientation (Horizontal, Vertical Left, or Vertical Right) for the text or movable legend in the graph.  You can also choose to rotate the text by specifying the rotation angle (from 0 to 359° or 0 to -359°) in the Angle edit field.  Alternatively, you can interactively rotate the text by selecting it in the graph and then dragging one of the object handles (small black squares) in the desired direction or by using the hot keys PAGE DOWN and PAGE UP to rotate text objects selected in the graph clockwise or counterclockwise, respectively, in 5° increments.  To rotate in 1° increments, hold down the CTRL key while pressing PAGE DOWN and PAGE UP.  The rotation of text objects takes place around the object's anchor point, which is visible as a "cross-hair" when the object is rotated.

Note that the angle (in degrees) will be displayed in the Change Show window of the Graphics toolbar.

Shortcut:  Select the text in the graph and use the hot keys PAGE DOWN and PAGE UP to rotate text in 5° increments.  Fine rotation can be achieved by holding down the CTRL key while pressing PAGE DOWN and PAGE UP.

Note also that some fonts may not support rotation and some fonts may support only limited rotation and will approximate rotation to the nearest angle to which it may be rotated.  When these fonts are used, misalignment between the frame around the text and the font may occur.  In this case, do not place a frame around the text.  Also note that some printer drivers may not support rotation of some fonts (even though the text may appear properly rotated on the screen).


  Graphic Text - Dynamic Scale

The movable legend or text entered into the graph via the Text dialog can have either Dynamic (select this option) or Fixed (de-select this option) status (see Dynamic/Fixed Toolbar buttons).  Fixed texts and movable legends are assigned to the fixed screen locations and they remain unchanged when you rescale the graph.  Dynamic texts and movable legends are anchored against the scales of the graph, thus their position will be dynamically adjusted as you make changes to the graph (e.g., resize or rescale the graph).  Texts that annotate specific points or objects in the graph should be entered in dynamic mode so that they will maintain their position in relation to that object or point if the graph is changed.

See also, Using Dynamic (Coordinate) Mode in Categorized and Matrix Graphs


  Graphic Text - Locked Position

Select this option in order to lock the graphic text into its present or default position in the graph.  If the object is moved or resized after it is locked, then STATISTICA will prompt you to either unlock it (so the action can be completed) or to cancel the action.


Graphic Text - How to Change the Font for a Part of the Custom Text

Example 1

Changing the font of selected text:  In order to change the font of selected text, follow the steps outlined below:

Step 1:	In the Graphic Text Editor, select the desired text by highlighting it, then press the local font [image] button.

Step 2:	In the resulting Font dialog select the desired font size, style or other attributes.

Step 3:	Click OK to exit the Font dialog.  Upon exiting the Font dialog, the Control Characters @K and @Z will be added before and after the selected text.  When you click OK in the Graphic Text Editor, the desired font will be displayed in the custom text.  The specified text will not be affected by changing the default font (see Default Font) for the text.

Technical Note:  When a custom font is selected for part of the text, an additional font description is added to the internal structure of the custom text object and assigned a sequential number.  The control characters surrounding the custom text refer to this internal "font list."  For example, @K[1] would refer to the first additional font in the list.  A previous font selection in the same custom text object may be repeated by referencing the same control character font number

Example 2

Inserting symbols.  In order to insert the character β into the text in the Graphic Text Editor, follow the steps outlined below:

Step 1:	Click on the Symbols button and in the resulting Windows Character Map facility, select TrueType Symbol as the font, highlight the β character, click on the Select button, and then on the Copy button in this utility in order to copy the character to the Clipboard.  Click OK to exit this dialog.

Step 2:	In the Graphic Text Editor, position the cursor in the text and press CTRL+V to paste an ASCII representation of the character to the Editor.  Now, highlight that character and click on the Local Font [image] button.  In the resulting Font dialog, select the TrueType Symbol font; when you click OK in the Font dialog, the control characters @K and @Z will be added before and after (respectively) the selected text.  Now when you click OK in the Graphic Text Editor, the β symbol will be displayed in the graph.

For more information on the Windows Character Map, press Help while you are in that utility.


Control Characters

Control Characters are specific characters that can be entered in graphic text (e.g., titles, legends, scale values, added text, category values, category names) in order to customize the text.

If the text is entered via the Graphic Text Editor dialog, then specific customizations (e.g., attributes of text) can be entered by highlighting the respective part of the text and then pressing one of the mini-toolbar buttons.  Some of the most commonly used buttons are shown below:

STATISTICA will then automatically insert the respective Control Characters into the text.  Both in the Graphic Text Editor window and in all other instances where the graphic text can be entered, the Control Characters can by typed directly into the text.

For a listing of commonly used Control Characters, see Quick Reference (commonly used Control Characters).

For a complete listing of available Control Characters, see Control Characters (Text Formatting) Reference.

Control Characters that define a specific customization option always begin with an @ symbol which is followed by a letter designating the option, optionally with values for that option in brackets (e.g., @T[4] specifies a tab of four spaces).  If you enter just the @ symbol and a letter without any value assigned to it, then the default value will be assigned (see below for each default value).  In most cases, placing the Control Character before the text will affect all of the text following that code (see below for specific details).  You can also highlight some text and then click on an option button (e.g., click on the superscript button, see below) and STATISTICA will automatically insert the Control Characters to enable and disable that option around the highlighted text.  In other words, the option will only apply to the highlighted text.

For example, @B turns on/off the bold font style, therefore, the text entered as:

This is @BBOLD@B style

will appear as:

This is BOLD style

The control character for the legend pattern symbol for plot number 1 is @L[1], and @U starts the superscript style and @E ends the superscript style, therefore, the text entered as:

@L[1]   X@U2@E values

will appear as:

(in the last example, the specific legend pattern symbol depends on the current plot number 1).

Note that in order to enter and display a string of characters that represent a control character (i.e., make the program ignore its special control status and display the string as regular characters), precede the control character text with an @ symbol (e.g., enter @@B in order to display the string as @B and not as @ followed by the beginning of the Bold mode).

For a detailed description of the Control Characters, see below.

Control Characters:

Plot Legend Symbols

Tab

Line Spacing

Superscripts and Subscripts

End Superscripts and Subscripts

Local Font

Format Styles

Return to Default Format

Fitted function

Specific Applications


Control Characters (Text Formatting) Reference

Control Characters are specific characters that can be entered in graphic text in order to customize the text (see Control Characters).

@A	Inserts a line break (alternatively, press CTRL+ENTER when you are in the Graphic Text Editor).

@T[4] or @T  Tabs over 4 characters (the default value).

@T[8]  Tabs over 8 characters (alternatively press CTRL+TAB when you are in the Graphic Text Editor).

@S[point value]  Changes the line spacing (default: increase by 4 points)

@D	Subscript.  Makes the text following this code subscripts.

@U	Superscript.  Makes the text following this code superscripts.

@E	Ends one level of super- or subscript.

@H	Ends all levels of the superscripts and subscripts.

@K	Begins a custom (local) font definition.

@I	Italics.  Toggles on (place Control Character before text string) and off (place Control Character after text string) italicized text.

@B	Boldface.  Toggles on (place Control Character before text string) and off (place Control Character after text string) bold text.

@X	Underline.  Toggles on (place Control Character before text string) and off (place Control Character after text string) underlined text.

@Z	Ends the bold/italic/underline or other local font attributes.

Copies the highlighted text to the Clipboard.

Pastes the contents of the Clipboard at the current cursor position.

Undoes the most recent operation (keyboard shortcut: CTRL+Z).

@L	Inserts the legend (pattern) symbol.

@F	Inserts the fitted function equation.

@C[level number]  Inserts the line or surface pattern for the specified legend.

@V[level value]  Inserts the line or surface pattern for the specified level of the contour or surface plot.

@N[level number]  Places the upper-bound value for the specified contour or surface plot level next to the respective contour line or surface pattern.


Control Characters - Specific Applications

For custom text that you are adding to the graph, you can use any of the Control Characters in order to customize the text string in the Graphic Text Editor edit box.  For movable legends, you can customize the existing text and any new text via the Graphic Text Editor dialog.  In this dialog, you can enter the Control Characters automatically by clicking on the appropriate button or manually by entering the appropriate Control Characters.  Fixed legends can be customized in the appropriate Plot Layout dialog.

For graph titles, double-click on the title to open the Titles dialog in which you can use Control Characters to customize up to 11 titles in the graph (note that you are still limited to 80 characters for each title).  Now, you can add superscripts and subscripts as well as plot legend symbols to the text, change the font style for specific parts of the title text, and other customization options listed above.

Plot scale values can be customized in the Scale Options dialog using the appropriate Control Characters.  Note that you are limited to 20 characters in this edit box (including the Control Characters) when you add text or symbols to the scale values.

The text used to define the categorization options in graphs can also be customized using Control Characters.  You can add superscripts and subscripts as well as change the font attributes of the text in the Categorization Options dialog.


Control Characters - Quick Reference (Commonly Used Control Characters)

  @B	Bold font attribute (on/off).

  @I	Italic font attribute (on/off).

  @X	Underline font attribute (on/off).

  @Z	Ends the bold/italic/underline font attributes.

  @U	Starts the superscript (one level).

  @D	Starts the subscript (one level).

  @H	Ends all levels of the superscripts and subscripts.

  @A	Inserts a line break (alternatively, click CTRL+ENTER in the Graph Text Editor).

  @T	Tab (default: 4 characters).

  @T[8]	Tabs over 8 characters (you can enter any other value here).

  @L	Inserts the legend (pattern) symbol.

  @F	Inserts the equation for a fitted function.

Copies the highlighted text to the Clipboard.

Pastes the contents of the Clipboard at the current cursor position.

Undoes the most recent pasting operation.


Control Characters - Plot Legend Symbols

Plot legend symbols can be placed in graphic text  by entering the appropriate Control Characters for the plot.  The Control Characters for plot legend symbols are:

@L[plot number, select number]:  Specify the plot number (1 through 64) and optionally the selection number (applicable to multiple-subset graphs).  In the case of 2D and matrix multiple-subset plots, when you specify the selection number, the program will insert the point marker for that subset.  For multiple-subset icon plots, when you specify the selection number, the specified subsetted icon border pattern will be inserted.

@C[level number]:  Specify the level number in order to insert the line or surface pattern for that level of the contour or surface plot.

@V[level value]:  Alternatively, you can specify the level value in order to insert the line or surface pattern for that level of the contour or surface plot.

@N[level number]:  The Z-axis of 3D surface or contour plots is divided into a specified number of surface or contour levels (via the Surface Levels option in the 3D Graphs-More Options dialog) which is reflected in the number of surface colors or line patterns in the plot.  Specify here the number of the contour or surface plot level in order to place the upper-bound value for that Z-axis level, next to the respective line or surface pattern.  Whenever you change the number of surface levels in the 3D Graphs-More Options dialog (i.e., change the scale of the Z-axis), the program will automatically adjust these values to reflect the change.  Note that once the Control Characters for this Z-axis level have been entered and you exit this dialog, you can edit this value by re-entering this dialog (double-click on the Z-axis level value).  The value of the Z-axis level will be displayed after @N in curly brackets (e.g., @N{  5.356@}.  Now, delete the @N code, the curly brackets, and the @ symbol after the value (e.g., 5.356) so that the edited value will be treated as regular text.


Control Characters - Tabs

You can specify a tab of 4 characters (the default value) or of any number of characters at the point in the text where the cursor is located.  The Control Characters are:

  or @T[4] or @T Tabs over 4 characters.

@T[20] Tabs over 20 characters.


Control Characters - Line Spacing

Use this button to modify the default (i.e., font size dependent) spacing between the lines of text.  The default setting of this Control Character is 4 points, but you can specify a negative or positive number of points to be used to modify (i.e., increase or decrease) the default line spacing.  The Control Character for this option is @S[point value], @S (with no value setting) is equivalent to @S[4] and will increase the line spacing by 4 points.


Control Characters - Superscripts and Subscripts

These Control Characters allow you to place subscripts and superscripts, respectively, into the text.  Subscripts and superscripts can be nested in many levels (e.g., @D@D2 will place the value 2, two levels below the normal text; @U2@Dn will cause the superscript 2 to have the "footnote" n).  The Control Characters for superscripts and subscripts are:

@D	Makes the text following this code subscripts.

@U	Makes the text following this code superscripts.


Control Characters - Ends Superscripts and Subscripts

These codes allow you to end or disable the super- or subscript text either one level at a time or for all levels (i.e., return to the default text).  These Control Characters are entered after the super- or subscript text string in the edit box (i.e., at the point when you want to end the super- or subscripts and begin normal text).  The Control Characters are:

@E	Ends one level of super- or subscript (e.g., @D@D2@E3 will place the value 2, two levels below the normal text and the value 3 one level below the normal text).  Note, to end more than one level without ending all levels, enter the Control Character once for each level that you want to end (this Control Character refers to the most recent super-or subscript code entered); e.g., @E@E will end only two levels of the nested super-and subscripts.

@H	Ends all levels of the superscripts and subscripts and returns to the default text level (e.g., @D@D2@H3 will place the value 2, two levels below the normal text and the value 3 on the normal text level).


Control Characters - Format Styles

These codes toggle on (place Control Character before text string) and off (place Control Character after text string) the font attributes:  italicize text, bold text, and underline text.  For example, @IABCDEFG@I will italicize only the text string ABCDEFG.  The Control Characters for these options are:

  @I	Italics font attribute.

  @B	Bold font attribute.

  @X	Underline font attribute.

  @K	Begins a Local Font definition for a selected portion of text.


Control Characters - Return to Default Format

This Control Character will end all italicized, bold, and/or underlined text or custom font definition and return to the default font.  The Control Character for this option is @Z.


Control Characters - Fitted Functions

The Control Characters for the fitted function are @F[plot number, subgraph number] where you specify the desired plot number and optionally the subgraph number (for categorized graphs).  For example, if you enter the Control Characters @F[2], then STATISTICA will enter in that title position, the fitted function for the second plot in a multiple plot graph (i.e., a 2D line plot with 3 plots).  If you enter the Control Characters @F[1,3] in a title, then STATISTICA will place in that title position the fitted function for the third subgraph in a categorized graph.  (Note:  @F can be used instead of @F[1] or @F[1,1].)


Control Characters - Local Font

You can place the cursor in the text or highlight some of the text in this editor and click on the [image] Local Font button in order to open the Font dialog in which you can display and edit the local font for the current text.  When a custom font is selected for part of the text, an additional font description is added to the internal structure of the custom text object and assigned a sequential number.  The control characters surrounding the custom text refer to this internal "font list."  For example, @K[1] would refer to the first additional font in the list.  A previous font selection in the same custom text object may be repeated by referencing the same control character font number.  @Z is used to end the local font.  For an example of inserting a symbol in the text and of changing the font style, see How to Change the Font for a Part of the Custom Text.


Legends

Legends can be treated in two ways in STATISTICA graphs: either as fixed (unmovable) legends or movable legends.  By default, when a graph is created, the legend is fixed (unmovable), which means that its position is automatically determined and the graph is moved to the left in the window to leave space for the legend.  You can make the graph legend movable so that you can reposition it in the graph and customize the text (e.g., add text beyond the 20 character limit of the fixed legends, adjust line spacing and the distance between the legend symbols and the text, etc.) and other attributes of the graph legend by selecting the Move Legend option from the right-mouse-button menu (click on the fixed legend with the right-mouse-button).  When you select this option, the legend text will become like any other added text in the graph and you can double-click on it to open the Graphic Text Editor dialog (in order to edit the text), or you can reposition the movable legend in the graph (click on it once and then "grab" it with the mouse and drag it to the new position on the graph).  For example, you can delete the "new line" characters from the end of the lines and reformat the legend into one line (see below)

or you can split the legend into two or more pieces using the cut and paste operations.  For specific information on customizing the text, see the Graphic Text Editor.  Note that by default, the respective position of the movable legend in the graph will remain unchanged when you make adjustments to the graph (fixed position).  If you prefer to "attach" the movable legend to a particular part of the graph, select the dynamic option in the Graphic Text Editor dialog.

Fixed (unmovable) legends can be temporarily removed from the graph by selecting the Fixed Graph Legend OFF option from the right-mouse-button flying menu.  The fixed legend(s) can then be placed back into the graph (in its default position) by selecting the Fixed Graph Legend ON option available from the "long" flying menu accessible by clicking the right-mouse-button anywhere in the empty space outside the graph region.  Superscripts and subscripts can be added to fixed legends using Control Characters in the appropriate Plot Layout dialog, but (unlike the movable legend) are limited in the number of characters that can be added to the legend (20).  The fixed legend font can be changed by double-clicking on the fixed legend or by selecting the Change Font option in the right-mouse-button flying menu.  However, unlike movable legends, changing the font style will apply to all text in the fixed plot legends.

If you wish, you can include both fixed (unmovable) and movable legends in the same graph.  First, make the fixed legend movable by selecting the Move Legend option.  Reposition this legend and then double-click on the graph background and select the Fixed Graph Legend ON option from the right-mouse-button flying menu.  After you select this option, you will be asked if you want to remove (delete) the movable legend before placing the fixed legend in the graph.  If you answer No, then the movable legend will remain and the fixed legend will be placed in its default position in the graph.  If you answer Yes, then the movable legend will be deleted from the graph before the fixed legend is replaced.

Note that for some video drivers, when you move an object, some residue from the selected object (i.e., shades of color or small pieces of the object) may remain on the screen.  This residue will not be displayed in the graph when printed and will disappear from the screen when the graph is redrawn (e.g., after resizing the graph or repositioning the graph in the window via the Adjust Graph Margins toolbar button).


Fixed Graph Legend ON

Click on this option in order to return all of the fixed plot legends which have been turned off, to the graph.  You can temporarily remove fixed plot legends (e.g., contour plot legend, icon plot legend, etc.) from the graph by clicking on the Fixed Graph Legend OFF option in the legend right-mouse-button flying menu.  The plot legend can be made movable (not fixed) by selecting the Move Legend option from the right-mouse-button menu so that it can be edited in the Graphic Text.  For more information on fixed and movable plot legends, see Legends.


Fixed Graph Legend OFF

Click on this option in order to temporarily remove the selected fixed plot legend from the graph.  All of the fixed plot legends which have been removed can be returned to the graph by clicking on the Fixed Graph Legend ON option in the "long" right-mouse-button flying menu accessible by clicking on the graph outside-background area.  The plot legend can be made movable (not fixed) by selecting the Move Legend option from the right-mouse-button menu so that it can be edited in the Graphic Text.  For more information on fixed and movable plot legends, see Legends.


Move Legend

Legends can be treated in two ways in STATISTICA graphs: either as fixed (unmovable) legends or movable legends.  By default, when a graph is created, the legend is fixed (unmovable), which means that its position is automatically determined and the graph is moved to the left in the window to leave space for the legend.  Movable legends offer more customization options (see Legends).

In order to convert a fixed legend into a movable legend, click on it with the right-mouse-button and select the Move Legend option from the right-mouse-button flying menu.  Now, the plot legend is no longer fixed, but is movable and editable.  After you select this option, you can reposition the movable legend by clicking on it (to put it in selection mode) and then dragging it with the mouse to the desired position in the graph.  Double-click on the movable legend to open the Graphic Text Editor dialog in which you can edit the text, change the legend background and frame color and pattern, as well as other customization options.  Several Control Characters are available (via the Graphic Text Editor dialog buttons) so that you can edit the legend text (e.g., add superscripts or subscripts, place plot legend markers in the text, etc.).

Note that by default, the background of the movable legend is set to the current outside-background color, however, this background color will print only if you set the Use dithered color to fill background option in the Print Graph dialog.

Also by default, the respective position of the movable legend in the graph will remain unchanged when you make adjustments to the graph (fixed position).  If you prefer to "attach" the movable legend to a particular part of the graph, select the dynamic option in the Graphic Text Editor dialog.

Note that for some video drivers, when you move an object, some residue from the selected object (i.e., shades of color or small pieces of the object) may remain on the screen.  This residue will not be displayed in the graph when printed and will disappear from the screen when the graph is redrawn (e.g., after resizing the graph or repositioning the graph in the window via the Adjust Graph Margins toolbar button).


  Arrow Objects Style

In Arrow Objects Style dialog, you will be able to customize the currently selected arrow (or custom error bar), or specify an arrow that will be placed in the graph.  This dialog is accessible by clicking on the Arrow [image] toolbar button, double-clicking on an existing arrow on the graph, selecting the Object Properties option from the Edit pull-down menu (when an arrow is selected), or you can pre-specify an arrow by selecting the Object Styles - Arrow option from the Insert pull-down menu.  See below for examples on creating a new arrow and customizing an existing arrow.

Command-driven drawing:  The graphics library of STATISTICA BASIC includes commands to define custom graphics objects and place them in graphs; for more information, see Graphics Library of STATISTICA BASIC.

Shortcut:  Double-click on the arrow to re-open the Arrow Objects Style dialog.

Arrow Objects Styles dialog:

Arrow Combo Box

Customization Options

Dynamic Scale

Set as Default Style

Remove

Line

Custom Fill

Locked

See also, Using Dynamic (Coordinate) Mode in Categorized and Matrix Graphs

Example 1 (Creating a new arrow)

Example 2 (Customizing an existing arrow)

Double-headed arrow:  Note that you can create double-headed arrows by aligning two arrows.  To change the position of the arrow in the graph, click on the arrow to put it in "editing" mode and drag it with the mouse (hold down on the left-mouse-button and then release the button when the arrow is positioned appropriately).  If you drag the arrow shaft, then you can move it anywhere in the graph that you want (the angle and size of the arrow will not change).  If you drag on a black selection square (on either the tip of the tail or head), then you can rotate the arrow or stretch the arrow head or tail.


  Arrow Objects Style - Locked

Once you have positioned the arrow in the graph, you can use this option to lock it into place in the graph.  If the arrow is moved or resized after it is locked, then STATISTICA will prompt you to either unlock it (so the action can be completed) or to cancel the action.


Set as Default Style

Check this option in order to make the selections in this dialog the default style.

Note that this option is dimmed and cannot be de-selected when this dialog is called when an object is not selected, since then the only purpose for accessing this dialog is to specify new default settings.  Therefore, any changes to the settings in this dialog will become the default settings.


  Arrow Objects Style - Arrow Combo Box

From this combo box select the type of arrow (or error bar) that you want to place in the graph.  You can customize the arrow type and view the changes here before you exit this dialog.


  Arrow Objects Style - Dynamic

The arrows entered into the graph via the Arrow Objects Style dialog can have either Dynamic (select this option) or Fixed (de-select this option) status.  Fixed arrows are assigned to fixed screen locations and they remain unchanged when you rescale the graph.  Dynamic arrows are anchored against the scales of the graph, thus their position will be dynamically adjusted as you make changes to the graph (e.g., resize or rescale the graph).  Arrows that identify specific points or objects in the graph should be entered in dynamic mode so that they will maintain their position in relation to that object or point if the graph is changed.

Dynamic arrows in graphs with multiple coordinates.  Note that in graphs with multiple coordinate systems (e.g., categorized graphs or matrix graphs) the head and the tail of an arrow may be located in different coordinate systems.  In those instances, when the arrow has Dynamic status and the graph changes, the position of the arrow will be adjusted according to its head (and not tail) coordinates (in other words, the anchor point for arrows is the head and not the tail).

See also, Using Dynamic (Coordinate) Mode in Categorized and Matrix Graphs


  Arrow Objects Style - Customization Options

You can use the respective scrollbar to adjust the Size, Angle, and Style of the arrow head.  The size value of each option will be displayed immediately above the respective scrollbar (you can also enter/edit these values).  Note that the availability of some of these three options depends on the arrow type chosen in the Arrow Combo Box.  When an option is not available, it will be dimmed.


  Arrow Objects Style - Remove

This button is dimmed when you are creating a new arrow (i.e., until you re-open the Arrow Objects Style dialog by double-clicking on an existing arrow in the graph).  Clicking on the Remove button will allow you to remove (delete) the arrow from the current graph.  Note that you can also delete the arrow from the graph like any other graphic object by clicking once on it (to highlight it) and then pressing Delete on the keyboard.


  Arrow Objects Style - Line

Click on this button to open the Line Patterns dialog from which you can select a line pattern, width, and color for the shaft of the arrow.  (See also, Selecting Point, Lines, Area Patterns.)  The appearance of the arrow after making the line thickness (and other) adjustments can be previewed in the dialog before returning to the graph.


  Arrow Objects Style - Custom Fill

Select this option when you want to fill the arrow head area with a different color or pattern.  When you select this option, the Area button will no longer be dimmed.  Click on this button to open the Area Pattern dialog from which you can select the pattern and color for the filled area.  (See also, Selecting Point, Lines, Area Patterns.)


Creating a New Arrow

Step 1:	Click on the Arrow Toolbar button  [image]  to open the Arrow Objects Style dialog.  Here, you can choose the style, size, and other customization options for the arrow that will be placed in the graph.  Click OK when you are through making your selections.

Step 2:	Move the mouse to the current graph window and the cursor will change into cross-hairs; click and hold the left-mouse-button at the point where you want the head of the arrow to be.  Now, while holding down on the left-mouse-button, drag the cursor to the location for the end of the arrowhead and then release the button to draw the arrow (you can later adjust the arrow location by dragging the arrow or dragging its endpoints, see Example 2).


Customizing an Existing Arrow

Step 1:	Click once on the existing arrow in order to put it in the selection mode (black selection squares will appear at both ends of the arrow).

Step 2:	Move the arrow (without changing its length or direction) by grabbing it with the mouse in the middle of the arrow shaft (the cursor will change to a four arrow icon) and dragging it to the new location in the graph.

Step 3:	Resize the arrow by grabbing the arrow with the mouse on either of the selection boxes.  Drag the selection box in order to stretch the arrow shaft.

Step 4:	Rotate the arrow shaft by grabbing the black selection box on the end of the shaft (the arrowhead will remain anchored in the same position) and dragging it either up or down to rotate it.  You can also rotate the arrow by dragging the black selection box on the arrowhead while the tail remains anchored.

Step 5:	You can change the style, size, line pattern, or fill pattern of the existing arrow by double-clicking on the arrow or selecting the Object Properties option to open the Arrow Objects Style dialog.


  Animated Stratification

When you select the Animated Stratification option from the View pull-down menu or click on the [image] toolbar button, the Animated Stratification dialog will open allowing you to interactively view the graph layer by layer (applicable to 3D Sequential Graphs such as surface plots, ribbon/line plots, box plots, block plots, etc.).  When you select this option, STATISTICA will generate the graph in layers representing consecutive cross-sections corresponding to variables in the graph (e.g., ribbons, blocks, etc.), levels of variables (e.g., in 3D histograms) or determined by the current settings of the X: and Y: values in the Number of Cuts option in the General Layout:  3D Sequence Graphs dialog.  After each "slice" is generated, STATISTICA will pause until you click on either the Continue button, the Break button, or close the dialog (Cancel).  When you click on the Continue button, the next (sequential) "slice" of the graph will be displayed.  Clicking on the Break button will close the Animated Stratification dialog and complete the axes and titles of the graph without completing the missing layers.  Using the Break button, you can create complete (labeled) graphs that represent each or selected "slices" of the original graph.


  Rotation

You can use the interactive Perspective and Rotation control facility (accessible by clicking the Rotate [image] button on the Graphics Toolbar or from the Graphics View pull-down menu) to change the perspective or rotate 3D graphs.  Any changes that you make in the perspective or rotation of the graph can be previewed in the Perspective and Rotation control facility before making the final adjustments to the graph (click OK).  Note that when you click on the [image] button, a simplified representation of the graph data is displayed initially (to reduce the redrawing time).  All data points will be shown, however, if you request the Spin function, so that the complete pattern of data can be explored.

Perspective:  The perspective scrollbar (on the left side of the Perspective and Rotation control facility) can be adjusted to determine the location of the "viewpoint" for the graph.  (Note that you can also control the graph perspective by setting the numeric viewpoint parameters in the 3D Graphs/More Options dialog.)

Rotation:  You can rotate the 3D graph vertically (use the right scrollbar) and horizontally (use the bottom scrollbar) by adjusting the respective scrollbar.

 Spin:  Click on this button in order to perform continuous, horizontal rotation (spin) of the 3D graph at the current viewpoint (see Perspective, above).  When you click on this button, 4 additional buttons will become available:

   buttons:  These buttons allow you to control the direction (clockwise or counterclockwise, respectively) of the automatic spin.  You can click on these buttons at any point during the spin to change directions.

 button:  Click on this button to temporarily stop the spin so that you can use the scrollbars in order to manually rotate the image of the 3D graph.

  button:  Click on this button to stop the spin in the current position and return to the "manual" mode of rotating where you can click OK to update the current graph or Cancel to cancel the rotation of the graph.


Page Setup

Click on this option from the File pull-down menu in order to open the Page/Output Setup dialog.  Here you can click on the Margins/Setup button to open the Graph Margins dialog.  In this dialog, you can position the graph on the printed page by adjusting the margins (specify the Left, Top, Right, and Bottom margin widths) according to a specific measure (Percent, Centimeter, or Inch).

Click on the Printer Setup button in the Graph Margins dialog to display a dialog of printer options, specific to the printer you chose in the Select Printing Devices dialog.  Here, you can select the printer settings that will be used as default settings whenever you print a graph to that printer.  These printer settings will vary depending on the type of printer that you have chosen, therefore, the dialog resulting from the Printer Setup button will appropriately reflect your choice of printer.

Note that alternatively, you can adjust the margins by dragging the respective margin lines in the Print Preview dialog.


  Print Preview

Selecting this option from the File pull-down menu will open the Print Preview dialog displaying the graph as it would appear in the printout.  Note that this dialog is resizable and can be maximized to see small details in the graph as you adjust the position of the graph on the page (see below).

Print Preview dialog:

Margins

Printer Setup

Print

  Print toolbar button


  Print Preview - Margins

You can interactively adjust the position of the graph on the page by clicking on the Margins button to open a supplemental Graph Margins dialog (this dialog is also accessible from the Page Setup option of the File pull-down menu).  In this dialog, you can position the graph in the printout by adjusting the margins (specify the Left, Top, Right, and Bottom margin widths) according to a specific measure (Percent, Centimeter, or Inch).  Alternatively, you can adjust the margins by dragging the respective margin lines in the Print Preview dialog (when you do this, their position on the page is displayed in the Graph Margins dialog in the currently selected units, e.g., cm).


  Print Preview - Printer Setup

Click on the Printer Setup button to display a dialog of printer options, specific to the printer you chose in the Select Printing Devices dialog.  Here, you can select the printer settings that will be used as default settings whenever you print a graph to that printer.  These printer settings will vary depending on the type of printer that you have chosen, therefore, the dialog resulting from the Printer Setup button will appropriately reflect your choice of printer.


  Print Preview - Print

When you have completed your margin selections, you can print the graph using the Print button in the Print Preview dialog, or close the dialog using the Close button (in order to make further customizations) and later print the graph using the Print option from the File pull-down menu or the Print Toolbar button.


  Print Preview - Print Toolbar Button

Pressing this button will initiate printing with no intermediate dialogs, however, the printout will follow the current output settings adjusted in the Print Preview and Print Graph dialogs.


  Print Graph

When Printer is selected as the output channel in the Page/Output Setup dialog and you choose this option from the Graphics File pull-down menu, the Graph Print Options dialog will open allowing you to customize the conversion of the graph into a hard-copy printout or slide (e.g., minimum line width, representation of the background color, etc.).  Pressing OK in that dialog will initiate printing.  If Window is selected as the output channel in the Page/Output Setup dialog, then selecting this option will immediately print the graph to the Text/output Window.

Clicking on the Print Graph Toolbar button ( [image]) will immediately print the graph to the currently selected output channel (printer and/or Text/output Window) using the previous selections in the Page/Output Setup dialog or Graph Print Options dialog (see also, Automatically Print all Graphs).  In order to print non-transparent objects, some printer drivers require that the Print TrueType Font as Graphics option be selected in the Print Setup dialog (see, Printing Objects with Filled Background.)

Keyboard shortcut:  CTRL+P


  Print Graph Toolbar button

Clicking on this button will immediately print the graph without opening any intermediate dialogs (see Print).  The printing options previously selected in the Print Options dialog will be used to print the current graph (see also, Automatically Print all Graphs).  In order to print non-transparent objects, some printer drivers require that the Print TrueType Font as Graphics option be selected in the Print Setup dialog (see, Printing Objects with Filled Background.)


  Print Graph Options

When you click on the Print Graph option from the Graphics window File pull-down menu, the Print Options dialog will open.

Note:  In order to print non-transparent objects, some printer drivers require that the Print TrueType Font as Graphics option be selected in the Print Setup dialog (see, Printing Objects with Filled Background.)

Print Options dialog:

Printer

Use Dithered Color to Fill Background

Use Dithered Color for Solid Lines

Min. Line Thickness (printer pixels)

Print Quality

Print to File

Setup

Copies

Collate Copies


  Print Graph Options - Printer

The current (on line) printer is displayed here.  You can change the printer that STATISTICA will print to in the Print Setup dialog (see the Setup option, below).


  Print Graph Options - Use Dithered Color to Fill Background

When you select this option, STATISTICA will use a dithered color to fill the graph background and the background of custom text, legend, embedded objects, etc. (see Background).  If de-selected, then the graph will be printed without the specified colored background (i.e., the color of the paper will be the background color).  By default, this option is de-selected (i.e., the background color is not printed) to allow for the optimal appearance of the graph on the screen and when printed (a dithered background improves readibility of graphs on-screen but it often reduces readability of hard copies unless a very high resolution or a color printer is used).  (See also, Page/output Setup dialog.)


  Print Graph Options - Use Dithered Color for Solid Lines

Select this option if you want the colors of solid lines in the graph to appear dithered when printed, otherwise, the lines will appear solid in the printout (this option may be useful when the lines are thick, otherwise, the lines may appear "broken").  (See also, Page/output Setup dialog.)


Print Graph Options - Minimum Line Thickness

  Print Graph Options - Min. Line Thickness

Specify here the minimum line thickness (in printer or other device pixels).  Unless you change the default setting of this option (1 printer pixel), the width of all lines printed by STATISTICA is determined by the individual settings of the line width for specific graph components (by default .5 point, see Points, Lines, Area Patterns Dialog).  However, if you change some of those individual settings (or if you prefer to use the screen pixel instead of the point scale in the Points, Lines, Area Patterns dialog) and if your printer "pixel size" is very small (e.g., on a high resolution 600 d.p.i. printer), then some printed lines may appear too thin.  This option allows you to determine the minimum printed line thickness; e.g., if you set it to 2, then all printed lines might be at least 2 printer pixels wide even if they are set to a smaller setting in some Points, Lines, Area Patterns dialogs.


  Print Graph Options - Print Quality

This option displays the resolution levels for the current (on line) printer.  You may select the print resolution from the available levels here.


  Print Graph Options - Print to File

Select this option to "print" the graph to a printer file (this file will contain all of the specifications needed to later print the graph).  When you select this option, you will be asked to specify the output file name under which to store the graph.  You can later print the graph using the standard DOS copy command (i.e., copy the output file to the printer).  This option also allows you to create graphics files to be used by other applications, e.g., HPGL files or Postscript files.  Note that this setting is independent of whether or not you are directing the current text output (e.g., from Scrollsheets) to the printer or an output file.


  Print Graph Options - Setup

Click on this button to open the Printer Setup dialog in which you can designate a different printer, specify the paper size and source, the orientation, and other options.


  Print Graph Options - Copies

Enter the number of copies that you want to print.


Print Graph Options - Copies

  Print Graph Options - Collate Copies

Select this option to collate printed copies (applicable to multi-page printouts).


New Plot(s)

Choosing the New Plot option from the Layout pull-down menu or the flying menu in the Graph Data Editor will open the New Plot dialog.  In this dialog, you can specify the number of plots to add to the Graph Data Editor as well as the number of variables that will be plotted in the new plot(s).

New Plot dialog:

No. of plots

No. of Variables

No. of Points

Plot Layout


New Plot(s) - No. of Plots

Specify here the number of plots to add to the Graph Data Editor.  The number of variables and number of points that you specify in this dialog (see below) will apply to each of the plots that you specify here.


New Plot(s) - No. of Variables

This option will allow you to specify the number of variables that will be used to define the points in the new plot.  Choose to add either 2 (when adding a plot to a 2D graph) or 3 (when adding a plot to a 3D graph) variables.  When you click OK, the Graph Data Editor Scrollsheet will expand, allowing you to enter the variable values for the new plots.  Select the Weight option to add a column in the Graph Data Editor in which you can specify the weight of each point in the plot.  (See also, Add Rows for information about adding rows to the Graph Data Editor.)

The new variable columns will be displayed with the headings X, Y, and Z (if 3 was selected).  Here, you can enter the values for each variable that will be used to define the points in the new plot.  You can use the values of variables from a spreadsheet or Scrollsheet by highlighting the column name in the spreadsheet or Scrollsheet (this will select all of the values for that variable) and then copying the highlighted values to the Clipboard via the Copy option or the Copy Toolbar button.  Now, in the Graph Data Editor, highlight the column name that you want the values placed in and use the Paste operation to transfer the values to the Graph Data Editor.  You can also use the Copy and Paste operations to transfer data from another Windows application (e.g., Excel, Lotus) to the Graph Data Editor in order to plot it along with the values currently residing in the Graph Data Editor.


New Plot(s) - No. of Points

Specify in this option, the number of data points that will be plotted in the new plot.  If this number is greater than the number of existing data points (rows) in the Graph Data Editor, then STATISTICA will add enough rows to the Graph Data Editor to accommodate the additional data.


New Plot(s) - Plot Layout

Click on this button to open the appropriate Plot Layout dialog (the dialog that opens depends on the type of graph; i.e., 2D Graphs, 3D Surface and Scatterplots, or 3D Sequence Graphs).  In this dialog, you will be able to enter a plot legend, change the point size and color, and other options specific to the new plot.


Global Defaults

Selecting the Global Defaults option from the graph Options pull-down menu will open the Global Defaults dialog containing options that will apply to all types of graphs in STATISTICA.

Global Defaults dialog:

Background

Titles

Axes

Copy Options to Current Graph

Get Options from Current Graph

Restore System Defaults

Mapping Options

Border, Gridlines, Control Lines, Matrix Frame

Legend, Data Labels

Selected Points

Selected Icons

Chernoff Faces

Contour Definition

General Plots

Specific Plots

Save

Save As

Retrieve (Defaults)

Retrieve (Defaults) From

Example


Global Defaults - Mapping Options

Click on this button to open the Graph Mapping Defaults dialog in which you can select specific options which will determine how the graph will be mapped to the screen or printed output.


Global Defaults - Background

Select here the Outside and Inside default colors for the graph from a list of colors.  If you wish, you can custom-define a color (in the Color dialog) for the Outside or Inside of the graph by selecting the Other option from the predefined list of colors.  (See also, Selecting Point, Lines, Area Patterns.)


Global Defaults - Titles

Choose a default font for each of the graph titles listed below, by selecting a title in the combo box and then clicking on the Font button to open the Font dialog (see the above example).

•	5 top titles;

•	2D graphs:  2 X-axis, 2 Y-left axis, and 2 Y-right axis titles;

•	3D graphs:  2 X-axis, 2 Y-axis, and 2 Z-axis titles.

The font style and size that you choose in the Font dialog will be used as the default font (for that title) in subsequent graphs.


Global Defaults - Axes

You can specify the scale settings that will be used as default settings for each axis (2D graphs:  X, Y-right, Y-left, Top; 3D graphs:  X, Y, Z) by first highlighting the axis name in the list and then clicking on the Settings button to open the Default Scale Options dialog.  The scale settings (Tickmarks, Scale Line, etc.) that you choose in the Default Scale Options dialog will be used as the default settings (for that axis) in subsequent graphs.


Global Defaults - Copy Options to current Graph

You can press on the Copy Options to Current Graph button to replace all relevant settings in the current graph with the current settings from the Global Defaults dialog.


Global Defaults - Get Options from Current Graph

Use this option to transfer all relevant settings from the current graph to the Global Defaults dialog in order to use them as defaults.  The advantage of this option is that you can experiment with different settings in the graph in order to visually inspect the outcome.  Once you have decided upon the appropriate settings, you can open the Global Default dialog and click on this button in order to make those settings the defaults for subsequent graphs.


Global Defaults - Restore System Defaults

Click on this button to replace all of the changes that you have made in the Global Defaults dialog with STATISTICA's system defaults.


Global Defaults - Border, Gridlines, Control Lines, Matrix Frame

When you click on either of these buttons, the appropriate Line Pattern dialog will open, allowing you to make color and pattern selections (for the graph border, matrix border, control lines, or gridlines) to be used as default settings.


Global Defaults - Legend, Data Labels

Select the default font (in the Font dialog) for the graph Legends and Data Labels when you click on the respective buttons.


Global Defaults - Selected Points

Click on the Selected Points button to open the Selected Point Default Patterns dialog from which you can choose default patterns and colors for the point markers that will be used to identify selected data points in STATISTICA graphs (applicable to multiple-subset graphs; see Specify Multiple Subsets, 2D Scatterplots, 3D Scatterplots, 3D Trace Plots, Matrix Plots, and Stats Categorized Graphs).


Global Defaults - Selected Icons

Click on the Selected Icons button to open the Selected Icons Default Patterns dialog from which you can choose default line patterns and colors for the frames ("rectangles") that will be used to identify selected observations (cases) in the icons (applicable to multiple-subset icon plots, see Specify Multiple Subsets and nD Icon Plots).


Global Defaults - Chernoff Faces

You can choose the default color and pattern for each of the elements (eyes, nose, mouth, etc.) of Chernoff Faces when you click on the Chernoff Faces button to open the Chernoff Face Pattern dialog.


Global Defaults - Contour Definition

Click on this button to open the Specify Default Contour Attributes dialog in which you can choose the default colors and patterns for the levels of the contour or surface.  You can also change the default number of levels for the surface or contour by adding or deleting levels.


Global Defaults - General Plots

Click on this button to open the Plot Defaults dialog from which you can select the default colors and patterns for general plot components (i.e., point markers, lines, areas, fit lines, box top, box X-face, box Y-face, and box borders).  These selections apply to "general" plots, such as general types of scatterplots, line plots , bar graphs, etc., which do not have components which are specific for only one particular type of plot (see Specific Plots).


Global Defaults - Specific Plots

The Specific Plots Default Pattern dialog will open when you click on the Specific Plots button.  The default patterns and colors for components of specific plots (Pie Chart, Frequency Scatterplot, Box and Whisker plot, 3D Histogram and Matrix plot) can be changed in the Specific Plots Default Pattern dialog.


Global Defaults - Save

In order to use the selections that you made in the Global Defaults dialog as defaults for subsequent sessions of STATISTICA, you will need to save them in STATISTICA's default initialization file (STATIST.ini).  You can do this by clicking on the Save button, or by selecting the Save Defaults option from the Graph Options pull-down menu.


Global Defaults - Save As

If you prefer, you can save the defaults in a file other than STATIST.ini.  Click on the Save As button to open the Save Defaults dialog in which you can choose the file name under which to save the global defaults (STATISTICA will suggest the file name extension *.ini).  This option allows you to create specific graph "style sheets" which can later be used (i.e., retrieved via Retrieve From) to replace the default graph configuration.

Note that after it is saved, each *.ini file is automatically added to the Workbook list of files associated with the current data set and thus later it can easily be retrieved (a Workbook combo box containing the list of all supplementary files associated with the current data set is available in every Open/Save dialog in STATISTICA).


Global Defaults - Retrieve (Defaults)

Click on this button to retrieve the defaults saved in the initialization file STATIST.ini.  The defaults retrieved from this file will apply only to subsequent graphs (and not to those already displayed). Alternatively, you can also select the Retrieve Defaults From option from the Graph Options pull-down menu; note that if you use this alternative method, then the settings from the STATIST.ini initialization file will automatically be applied to the currently-displayed graph.Note that you can use the Copy Options to Current Graph option to apply these defaults to the currently displayed graph.


Global Defaults - Retrieve (Defaults) From

When you click on this button, the Retrieve Defaults dialog will open from which you can select an file containing previously saved defaults (i.e., a custom graph "style sheet").  Alternatively, you can also select the Retrieve Defaults From option from the Graph Options pull-down menu; note that if you use this alternative method, then the settings from the specified initialization file will automatically be applied to the currently-displayed graph.

Note that any previously saved defaults for the current data file are listed in the Workbook combo box in the Retrieve Defaults dialog (the Workbook combo box contains the list of all supplementary files associated with the current data set is available in every Open/Save dialog in STATISTICA).


Changing Global Defaults:  Example

When you want all of the graphs that you create to have the first two titles in a different font and font size than the other titles, follow the steps outlined below.

Step 1:	After opening the Global Defaults dialog, select Title 1 in the Titles option and then click on the Font button.

Step 2:	Select the font and font size in the Font dialog and then click OK to exit the Font dialog and return to the Global Defaults dialog.

Step 3:	Repeat steps 1 and 2 for Title 2.

Step 4:	Click on the Save button in the Global Defaults dialog in order to save your selections as the default graph settings.

Now, whenever you create a graph in STATISTICA, the first two titles will be written in the font and font size that you designated in the Global Defaults dialog.


Plot Defaults

Graphs in STATISTICA consist of one or more plots (i.e., they may represent one or more series/sets of data).  By default, a different set of colors and patterns is used for each consecutive plot.  You can select for each plot (of the first 10 plots), the default point, line, area colors and patterns of specific plot components (Point Markers, Lines, Areas, and Fit Line for 2D graphs, and Box Top, X-Face, Y-Face and Border for 3D Sequential graphs) in the Plot Defaults dialog (accessed by clicking on the General Plots button in the Global Defaults dialog).  Click on a (numbered) plot component to open the appropriate Point, Line, Area dialog from which you can select the default color and pattern for the component.  (See also, Selecting Point, Lines, Area Patterns.)


Selected Point Default Patterns

Selected Points Default Patterns

The settings in this dialog allow you to customize default point marker patterns used in multiple-subset graphs to represent custom-defined subsets of data points.  The Selected Point Default Patterns dialog (accessed by clicking on the Selected Points button in the Global Defaults dialog) will allow you to select the default patterns and colors for the point markers (up to 16) that will be used as identifiers of the selected subsets.  When you click on a (numbered) point, the Point Patterns dialog will open from which you can select the default color and pattern for the point.  (See also, Selecting Point, Lines, Area Patterns.)


Specific Plots Default Patterns

You can change the default patterns and colors for components of specific plots (such as Pie Charts, Frequency Scatterplots, Box and Whisker plots, 3D Histogram and Matrix plots) in the Specific Plots Default Pattern dialog (accessible by clicking on the Specific Plots button in the Global Defaults dialog).  To change a pattern, click on the point, line, or area pattern button to open the appropriate pattern dialog (see Points, Lines, Area Patterns Dialog).  (See also, Selecting Point, Lines, Area Patterns.)


Selected Icons Default Patterns

The settings in this dialog allow you to customize the default patterns used to mark icons in the multiple-subset icon plots where subsets of cases are defined by the user (using the Multiple-Subset Specifications dialog) before the plot is processed.  The Selected Icons Default Patterns dialog (accessed by clicking on the Selected Icons button in the Global Defaults dialog) will allow you to select the default patterns and colors for the frames ("rectangles") used to mark cases (icons) which are members of specific subsets.  When you click on a (numbered) frame line, the Line Patterns dialog will open from which you can select the default color and pattern for the line.  (See also, Selecting Point, Lines, Area Patterns.)


Default Scale Options

You can adjust the default scale settings in the Default Scale Options dialog for each of the graph axes (X-, Top, Y-right, and Y-left axes for 2D graphs and X-, Y-, and Z-axes for 3D graphs).  A separate dialog (accessible from the Global Defaults dialog) is available for each graph axis and the changes that you make for each axis are independent of one another.  Therefore, the following descriptions of the scale options will apply to each individual Default Scale Options dialog.

Default Scale Options dialog:

Scale Values

Scale >>  button

Scale <<  button

Tickmarks

Scale Line

Copy to Other Axes


Default Scale Options - Scale Values

You can choose the default numeric scaling format with this option.  If you check Auto, then STATISTICA will automatically format the numeric scale values for you.  If you prefer, you can enter a specific scaling format (de-select Auto and enter the format) to be used as the default format for numeric scale values.  Click on the Font button in this option to open the Font dialog from which you can select the default font for the scale values.


Default Scale Options - Scale >> button

Click on this button to close the current dialog (preserving all changes) and open the Default Scale Options dialog for the next axis (e.g., X, Y-left, Y-right, etc.).


Default Scale Options - Scale << button

Click on this button to close the current dialog (preserving all changes) and open the Default Scale Options dialog for the previous axis (e.g., X, Y-left, Y-right, etc.).


Default Scale Options - Tickmarks

Select the default style and size of Major or Minor tickmarks for each of the axes with this option.

Off:  Selecting Off will remove the tickmarks from the axis.

Inside, Outside, Crossed:  When you select one of these settings, the tickmarks will be displayed on the inside, outside, or both sides of the axis (respectively).

Size:  Choose the relative length (from 0 to 9) of the tickmarks here.  The default color and thickness of the tickmarks are determined by the current specifications of the respective scale line (see Scale Line, below).


Default Scale Options - Scale Line

Click on this button to open the Line Pattern dialog from which you can select the default scale line pattern, thickness, and color, or even turn off the scale line so that (by default) it will not be displayed in the graph.


Default Scale Options - Copy to Other Axes

Instead of specifying the same default Font, Line Pattern, or Tickmarks specifications for each of the axes in each of their dialogs, select these options to automatically copy your selections to the remaining axes (to be used as defaults for those axes).


General Layout Dialog Options

All of the General Layout dialogs for specific types of graphs utilize a graph icon as a "preview" to changes made in the General Layout dialog (the graph in the icon will be re-drawn to reflect the changes made in the General Layout dialog).  However, you may wish to reduce the detail of the graph icon or even disable the icon in order to speed up the processing of the dialog (note that redraws of the icon can also be stopped by a click of the mouse anywhere on the screen, or by pressing any key).  When you select General Layout Dialog from the Options pull-down menu, the General Layout Dialog Options dialog will open.

General Layout Dialog Options dialog:

Enable Graph Icon:  Deselect this option if you do not want to have the graph icon displayed in General Layout dialogs.  If you de-select this option, then the graph icon area will become gray and the icon will not be displayed.

Graph Icon Titles, Legend, Scale:  Simplify the display of the graph in the icon (and increase the speed of the icon redraw) by selecting only the graph components (Titles, Legends, or Scale Values in 3D Graphs) that you want displayed in the graph icon.


Customize Width

Specify the width of columns and row names in the Graph Data Editor.  (This is a global operation, in that the values which you specify here will be applied to every column and row in the Graph Data Editor).

Customize Width dialog:

Column Width:  Specify the global width (minimum = 1, maximum = 20) of the columns here.

Row Name Width:  Specify the row names (i.e., first column) width (minimum = 1, maximum = 20).

Decimal:  Designate here, the number of decimal places (minimum = 0, maximum = 9) for all of the values in the Graph Data Editor.

Save as Defaults:  Click on this option to save the Customized Width selections as defaults.

Note that the column width can also be adjusted interactively by dragging the border between column names or by pressing the [image] and [image] toolbar buttons.


Pie and Colum Icon Patterns

Pie and Column Icon Patterns

Click on the Areas button in the General Layout and Plot Layout - Icon Graphs dialog in order to open the Pie and Column Icon Patterns dialog.  In this dialog, you will be able to change the colors and patterns of the individual pie slices or columns in the icon graph.  Below each column or slice number in this dialog is a color box.  Click on a box to open the Area Pattern dialog and select the desired color or pattern for that pie slice or column.  (See also, Selecting Point, Lines, Area Patterns.)


Selecting Points, Lines, Area Patterns

Selecting Point, Lines, Area Patterns

When you select the color and pattern of specific graph areas (e.g., pie slices, columns), lines (e.g., borders, plot lines), or point markers in the appropriate Area, Lines, Point Markers Patterns dialog, you will be able to choose from several pattern and color combinations for those graph components.  In these dialogs, first select the desired pattern style and then the options that are available for this pattern will be displayed.

Area Patterns

Line Patterns

Point Marker Patterns


Selecting Points, Lines, Area Patterns - Area Pattern

Selecting Point, Lines, Area Patterns - Area Patterns

Solid:  This is the first pattern in the combo box Pattern.  When you choose this pattern, you may select any of the colors (including patterned colors) in the Foreground color combo box, or you may select a custom color (via the Palette button) for the graph area.  The Background and Opaque/Transparent options are not available when you select a solid pattern.

Hollow:  These patterns immediately follow the solid pattern in the combo box Pattern.  You can select a different color for the item Foreground (i.e., the lines in the selected area pattern) or Background (the area in-between the lines in the pattern) when you select Hollow patterns.  When you click on the color combo box arrow, a list of solid colors will appear from which you can select the desired color.

Pixel Patterns (P):  These patterns are identified with a P in the combo box Pattern.  You can select Foreground and Background colors (solid) from the lists, however, the Transparent option is not available.  These patterns are printer-dependent in that the thickness of lines used to draw the patterns depends on the pixel size of the output device, thus, when printed on high-resolution printers, these patterns will appear as shades of gray.

Hatched Patterns (H):  These are Windows-system fill patterns (labeled H in the combo box Pattern) which offer the Transparent option (i.e., background is not cleared or covered, but overwritten and thus partially visible).  If the Transparent option is de-selected, then you can select Foreground and Background colors (Opaque option).


Selecting Points, Lines, Area Patterns - Line Pattern

Selecting Point, Lines, Area Patterns - Line Patterns

You can select solid, hatched, or dotted (pixel) line patterns in the Pattern combo box.  Selecting a solid line pattern, will enable you to choose a line color from the Foreground color list or the color palette (via the Palette button).  If you choose one of the hatched line patterns, then you can select Foreground and Background colors (Opaque option) or have a Transparent background.  You can also select Foreground and Background colors (solid) from the respective lists for the dotted (pixel) line, however, the Transparent option is not available (see Pixel Patterns).


Selecting Points, Lines, Area Patterns - Point Marker Pattern

Selecting Point, Lines, Area Patterns - Point Marker Patterns

All point markers are treated as two-color (Foreground and Background color) objects.  Select the desired point symbol and then the solid Foreground color and for Hollow point markers the solid Background color from the respective combo box.


Graph Mapping Options

The following options allow you to specify ways in which the graph will be mapped to the screen or printed output.  The options that you select here will be applied to the current graph.  To make these selections default selections for subsequent graphs and sessions, check the Set as default option (see below) or set the options in the Graph Mapping Defaults dialog (accessible from the Global Defaults dialog).

Graph Mapping Options dialog:

Graph Area

Mapping Base

Zoom Mode

Graph Window Proportion

Restore Original

Set as default


Graph Area

This option allows you to specify how the graph will be positioned relative to the graph (window/display) viewing area by specifying the coordinates for the viewing area within a logical coordinate system of -4000 to +4000 by -4000 to +4000.  The fixed graph coordinates are Left: 0, Top: 1000, Right: 1000, and Bottom: 0.  By default, the same coordinates determine the size of the window/display viewing area (i.e., the viewing area is equal to the graph size), as shown below.

You can change the window/display coordinates in this dialog in order to relatively increase or decrease the graph viewing area, and/or shift the graph within the area.

For example, you can increase the Top and Right margins in the graph viewing area by changing the Top coordinate to 1500 and the Right coordinate to 1500.  This gives the effect of reducing the size of the graph by one third (see below).

If you enter coordinates for the Top and Right margins less than 1000 and/or Bottom and Left margins as more than 0, then the size of the viewing area will be less than the graph area, resulting in the appearance that you are "Zooming In" on a portion of the graph.

You can also increase the size of the Left or Bottom margins by entering a negative coordinate value (e.g., -750) or decrease the margin by entering a positive coordinate (e.g., 200, see below).

Alternatively, you can click on the [image] (Adjust Graph Margins, Plot Area) toolbar button and use the scrollbars to interactively position the graph in the graph viewing area or resize the graph window to change the size of the viewing area.  After making these adjustments interactively, the resulting coordinates will be displayed in this area of the Graph Mapping Options dialog.

This option is available in both the Graph Mapping Options (applicable to the current graph) and Graph Mapping Defaults (applicable to current and subsequent sessions) dialogs.


Mapping Base

Technically speaking, the Graph Mapping Base is a coefficient which controls how the logical sizes of fonts, markers, and related sizes (as set by the user in points, 1 pt = 1/72 inch) translate into physical sizes which appear on the screen or printout.  The Graph Mapping Base coefficient can be adjusted in the Graph Mapping Options or Graph Mapping Defaults dialog, or interactively via the Global Font Increase/Decrease [image] [image] toolbar buttons.

The meaning of the Graph Mapping Base value can be explained as follows.  Graph objects (e.g., fonts, point markers, widths of lines) of a specified logical size will be printed at the same physical size if the diagonal of the output (in points) is equal to the absolute value of the current Graph Mapping Base (as set in the Graph Mapping Options or Graph Mapping Defaults dialog, accessible from the Global Defaults dialog).  If the diagonal of the output is larger or smaller than the absolute value of the Graph Mapping Base, then the physical sizes of graphic objects will be proportionally larger or smaller, respectively, than their logical sizes.

If you do not change the default Graph Mapping Base, then fonts will be printed as having their specified physical sizes if letter-size paper is used, in portrait orientation with default (1 inch) margins on all sides.  If you want to print the physical sizes of the fonts using some other margin settings, paper size, or orientation, you can do so as follows.  For example, to print the physical sizes of fonts in landscape orientation with 1 inch margins, first print the graph (add a border around the graph for ease of measurement) and then measure the diagonal of the graph on the printed page (e.g., 11 inches).  Multiply this value by 72 points/inch (e.g., 11*72=792 points) and enter this value as the System Mapping Base in the Graph Mapping Defaults dialog (accessible from the Global Defaults dialog), while maintaining a Graph Mapping Base of 100%.  Now, the fonts in the printed graph will be displayed in their specified physical sizes.


Zoom Mode

This option is available in both the Graph Mapping Options (applicable only to the current graph unless you select the Set as default option) and Graph Mapping Defaults (applicable to current and subsequent sessions) dialogs.  This option allows you to specify how fonts, point markers, line widths, or anything else specified in points in the graph are treated (technically, mapped into the viewing area) when you Zoom In or Zoom Out in the graph.

Auto:  When the default Auto mode is used, the Zoom In tool offers more than just "mechanical stretching" of the picture.  Specifically, it provides a logical magnification of the selected area while maintaining the sizes of point markers, fonts, and width of all lines.  Thus, the Zoom In tool effectively increases the "functional resolution" of the display, allowing you to inspect areas of the graph which in normal (1:1) mode were not readable due to overlapping markers or point labels.  In contrast, if the zooming was "mechanical" and not logical, and the size of point markers was increased with the magnification ratio, then one would not be able to see the details (e.g., overlapping points).  When you use the Zoom Out tool while in Auto mode, the size of fonts, markers, and spacings will be proportionately reduced as you Zoom Out, to allow for true reduction of the entire graph area.

Fixed size font:  When you select this option, the font (and other aspects of the graph specified in points) will stay the same size whether you are Zooming In or Out.

Variable size font:  Select this option in order to increase or decrease the font and other aspects of the graph as you Zoom In or Out, respectively.  This is often useful when you are Zooming Out since the font will be reduced as the graph is reduced so that it will not obscure other parts of the graph (note that this can also be achieved by using the Auto setting, see above).


Graph Mapping Options - Graph Window Proportion

Select the desired graph window proportion (excluding margins) with this option.

Screen:  When you select this option, the graph window will be proportional either to the screen area used by the graph or to a custom-defined screen proportion, depending on the setting in the Graph Mapping Defaults dialog.

Printer:  When you select this option, the graph window will be proportional either to the current printer page proportions (as specified in the Print Preview, Margins, and Printer Setup dialogs) or to a custom-defined printer page proportion, depending on the setting in the Graph Mapping Defaults dialog.

Custom:  Select this option in order to custom-define the graph window proportion.  The value that you enter here is a ratio of height over width.

These options can also be adjusted using the Graph Proportions and Margins Toolbar Buttons.


Graph Mapping Options - Restore Original

Click on this button in order to restore the original settings (i.e., the settings specified when the graph was last saved) in this dialog.


Graph Mapping Options - Set as Default

Set this checkbox in order to make your selections here the default selections for subsequent graphs.  See also, Graph Mapping Defaults.

Note that when this option is de-selected, the settings from this dialog will affect only the current graph.


Graph Mapping Defaults

The following options allow you to specify the default ways in which the graph will be mapped to the screen or printed output.

Graph Mapping Defaults dialog:

Graph Area

Mapping Base

Zoom Mode

System Settings

Restore Defaults


Graph Mapping Defaults - System Settings

These options control the default settings for the graph proportion and mapping base.  Note that the options that you select here will apply to all current graphs (which are created based on settings of these defaults in the Graph Mapping Options dialog) as well as subsequent graphs when you click OK in the Global Defaults dialog.

Screen Proportion:  Specify here the default screen proportion.  Choose either Auto (the graph window will be proportional to the maximum size of the application workspace) or Custom (specify a ratio of the width/height for the screen area to be used by the graph).

Printer Proportion:  This system setting specifies the default proportion for the printer page.  You can choose either Auto (the graph window will be proportional to the current printer page proportion as specified in the Print Preview, Margins, and Printer Setup dialogs) or you can Custom-define the printer page proportion (specify a ratio of the height/width for the printer page).

System Mapping Base:  Specify here the absolute value (in points; 1 inch = 72 points) of the default diagonal which will specify the 100% mapping base.


Graph Mapping Defaults - Restore Defaults

Click on this button in order to restore the default system settings in this dialog.


  Data Management - Index

In addition to all basic data management operations (which are accessible directly from the spreadsheet in every module), the Data Management module includes the following options.

Data Management Overview

  Create (non-default) New Data File

  Sort Cases

  Merge two Data Files

  Create Subset from Data File

  Modify Variables

  Modify Cases

  Verify Variable Names/Formats

  Verify Data Values

  Standardize Variables

  Replace Missing Data by Means

  MFM:Create New Data File

  MFM:Open Data File

  MFM:Convert STATISTICA File

See also Megafile Manager Overview.


  Data Management - Modify Variables

This option will display the Modify Variables menu (from the Vars Toolbar button) for easy access to the following editing options:

Modify Variables menu

Add	Text Values

Move	Date Values

Copy	Recalculate

Delete	Shift (Lag)

Current Specs	Rank

All Specs	Recode


  Data Management - Modify Cases

This option will display the Modify Cases menu (from the Cases Toolbar button) for easy access to the following editing options:

Modify Cases menu

Add	Delete

Move	Names

Copy


  Data Management - Introductory Overview

In this overview to the Data Management module, we will introduce the basic data file organization that is common to STATISTICA and many other programs (e.g., most data base management applications), as well as some unique features supported by STATISTICA data files (see also Data Management - Index).

Spreadsheet

STATISTICA Data Files

Double Notation (Numeric/Text) of Values

Import/Export

Data transformations

Other operations

See also Megafile Manager Overview.


  Data Management Introductory Overview - Spreadsheet

The STATISTICA Spreadsheet Window offers a wide selection of data editing and restructuring options (accessible at any point in the program), including:

•	data entry and extensive formatting facilities;

•	integrated formulas for transforming values of variables, including quick recoding facilities, options to transpose data files or blocks of values, shift variables against each other, etc;

•	DDE links to external sources of data;

•	search and replace facilities;

•	quick movement to specified locations in the file;

•	Drag-and-Drop facilities [moving, copying, clearing, inserting, duplicating, and extrapolating series (AutoFill)];

•	fill/standardize values facilities;

•	Quick Basic Stats and Block Stats facilities;

•	Split-Scrolling

•	facilities to add, delete, copy, and move ranges of cases and variables;

•	facilities rank values;

and many other types of options.


  Data Management Introductory Overview - STATISTICA Data Files

The STATISTICA system data files are optimized for access time and storage efficiency.  They support Case Names, Text and numeric (double precision) data values, short and long variables labels with formulas and DDE links to other files, long value labels, and other specifications (see Edit Variable Specs).  Variables can be defined with spreadsheet formulas and recalculated with a single keystroke (see Edit Variable Specs).  There can be a practically unlimited number of cases, and up to 4092 double variables (numeric and text) in one data file (files with up to 32,000 variables can be processed in Megafile Manager).


  Data Management Introductory Overview - Double Notation (Numeric/Text) of Values

STATISTICA supports a unique double notation of variables, where each value can simultaneously have a numeric and text identity.  You can use and refer to either the numeric or text identity of these values in all STATISTICA modules.  For example, if 1 is equivalent to MALE in the data file, then in the Selection Conditions you can either enter: exclude if v1=1, or the more meaningful v1='MALE'.  A Text Values Manager is provided to manage both text values and long value labels and allows you to take full advantage of this flexible data structure with a minimum number of keystrokes.  The STATISTICA double notation of values is supported by all STATISTICA modules to facilitate specification of designs and description of results (Scrollsheets and graphs), even when the analyses are performed exclusively on numeric data.  When you view your data in the spreadsheet you can toggle between the numeric and text "identity" of variables using the ABC toolbar button.


  Data Management Introductory Overview - Import/Export

STATISTICA features a selection of comprehensive data import/export facilities (see Import Files and Export Files; see also Quick Import/Export, and importing via ODBC).  You can import/export files in a variety of industry-standard formats, including Microsoft Excel (all versions including version 5), Lotus 1-2-3 (Release 1A, 2, 3,  Lotus 1-2-3 for Windows, and release 4), all versions of Symphony, Quattro, dBASE III+, dBASE IV, Paradox, STG (STATISTICA graphics format), mainframe portable file format (import/export compatible with SPSS and import compatible with SAS), and ASCII free and fixed format data files.  In addition, you can access a variety of free format text files (sequential, matrix, incomplete matrix, etc.).  Also, you can easily import data from a wide variety of data bases (including many large system data bases (oracle, Sybase, etc.) using Microsoft Open Data Base Connectivity (ODBC ) conventions.  The ODBC import facilities in STATISTICA support multiple data base tables; specific records (rows of tables) can be selected by entering SQL query statements.

While importing formatted data, Data Management will recognize the structure of the file, value labels, text and logical variables, blank cells or fields, and convert them into STATISTICA file format equivalents.  A variety of import/export options (e.g., named ranges in spreadsheets) are available in the specific import/export dialogs to facilitate the data conversion process.


  Data Management Introductory Overview - Data Transformations

Data transformation facilities (see Edit Variable Specs) are integrated into the STATISTICA Spreadsheet and allow you to define variables using formulas.  all or selected formulas can be recalculated at once by clicking on the Recalculate toolbar button.  The spreadsheet formulas support logical operators and can be used not only for computing new values, but also for simple recoding and data verification (see Spreadsheet Formula Syntax).  In addition, the Verify, Rank, and Recode facilities are integrated within the Data Management module and, can be used to perform data transformations and recoding of unlimited complexity.

Note that you can also transform data via STATISTICA BASIC which is available in every module of STATISTICA.


  Data Management Introductory Overview - Other Operations

Facilities are provided to split files into Subsets following user-specified criteria.  A selection of file Merge operations are supported (including the relational and hierarchical relational merge).  Data files can be Sorted in a number of ways (including multiple nested sort).  File headers with labels, formulas and alphanumeric specifications can be merged or transferred to new files.  Variables can be Shifted (lagged against each other), Standardized, and Missing Values can be replaced by means.  Formatted listings of data specifications, data files, and subfiles can be printed according to user specifications (see Printing).


  Data Management - Merge Files

The Merge Files facilities are accessible from the Data Management module.

There are many circumstances when you may need to merge data files.  For example, you may need to append data from additional subjects to the end ("bottom") of an existing data file (i.e., merge it with another file that contains the same variables:  Merge Cases).  You could also perform more tests (create additional variables) on cases from an existing data file.  A file containing those new variables would be appended at the end ("right side") of the existing data file (i.e., merged with another file that contains the same cases:  Merge Variables).  You may also merge the numeric/text value assignments from two files (Merge Text Values).

When you select the Merge Two Data Files option, the Merge Files dialog will open.  You will need to specify the type of merge that you want as well as the file to be merged with the current file.

Merge Files dialog

Merge:  Select one of three merging options.

•  Merge Variables

•  Merge Cases

•  Merge Text Values

2nd File button:  Click on this button to open the Select Second File dialog from which you can select a file to merge with the current file.  Please note that you cannot merge a file to itself (i.e., you cannot enter the current file as the second STATISTICA file name).  If you wish to "double" the file, use the Save As option from the File pull-down menu to create a second copy of the file.


  Data Management - Merge Variables

The Merge Variables facilities are accessible from the Data Management module.

When you select the Merge Variables option from the Merge Files dialog, STATISTICA will add the second file's variables after the variables of the first file.  The following options (available from the Merge Variables dialog) are used to align (match) the cases of the second file with those of the first.

Merge Variables dialog:

Mode

Relational Merge Options

Unmatched Cases

Example


Data Management - Mode

  Merge Variables - Mode

If the number and order of cases in the two data files are not precisely the same (i.e., if at least one case is missing in the second data file or there is one case that has no equivalent in the first file), then all subsequent data would be merged with the wrong cases.  In order to avoid this problem, you will need to specify a mode of merging here.  When relationally merging cases from two files, you need to specify a key (case identifier) variable in each data set; then for each case the program will check the values of this key in both data files and merge the cases only if their respective keys match.

Not Relational:  Variables of the second file are simply added alongside those of the first when this mode is selected (this is the default mode).

Relational:  When you select this mode, the cases from the second file will be matched with those of the first file, based on the values of a specified key.

Relational hierarchical: This mode differs from the simple relational mode (see above) in the handling of multiple records with the same key value in either the primary or secondary file.  In the standard relational mode (see above), successive records with identical key values will be merged.  If there are uneven numbers of records with identical key values in the two files, missing data are added to "pad" the file with the lesser number of records.  In contrast, in the Relational hierarchical mode the file is padded with the values found in the last identical key record that was matched.  For example:

Standard Relational Merge, unmatched cases filled with missing data:

  File 1       File 2          Merged File

Key1  Var1  Key2  Var2    Key1  Var1  Key2  Var2

----  ----  ----  ----   ----- ----- ----- -----

 1     1     1     1       1     1     1     1

 2     4     1     2     Miss  Miss    1     2

 2     5     1     3     Miss  Miss    1     3

 3     2     2     4       2     4     2     4

 3     3     2     5       2     5     2     5

                           3     2   Miss  Miss

                           3     3   Miss  Miss

Hierarchical Relational Merge, unmatched cases filled with missing data:

                               Merged File

                          Key1  Var1  Key2  Var2

                          ----  ---- ----- -----

                           1     1     1     1

                           1     1     1     2

                           1     1     1     3

                           2     4     2     4

                           2     5     2     5

                           3     2   Miss  Miss

                           3     3   Miss  Miss

Note that the sequence of cases is not changed during merging, therefore, each file should be sorted (see Sort Data) in order of its key variable before merging.


Data Management - Relational Merge Options

  Merge Variables - Relational Merge Options

When you choose either the Relational Merge or Relational Hierarchical Merge option, you will need to specify a key variable for each file in order to merge the two files.  STATISTICA will expect the two files to be sorted (see Sort Data) by their respective key variables before a relational merge can be performed.

Key in File 1:  Enter here the number of the variable to be used as the key in the first file.

Key in File 2:  Enter here the number of the variable to be used as the key in the second file.

Key Comparison (numeric or text):  Choose to match the key variables in the two files based on their numeric or text (text) values.


Data Management - Unmatched Cases

  Merge Variables - Unmatched Cases

Select one of three ways of dealing with unmatched cases when the two files are merged.  Unmatched cases may result from unequal numbers of cases in the merged files, or because some of the cases do not meet the Relational merge criteria.

Fill with MD:  Unfilled variables in unmatched cases are padded with missing data when you select this option.

Abort merge:  The presence of unmatched cases in either file will cause an error message to be displayed and the merge procedure to be abandoned.

Delete:  Cases from either file which cannot be matched will be removed from the merged file if you select this option.


  Data Management - Merging Variables

Step 1:	Click on the Merge option from either the Start-up Panel or the Analysis pull-down menu.

Step 2:	Select the Merge Variables option and click on the 2nd File button to select the file with the variables that will be added after the current file's variables.  Click Ok to exit this dialog and open the Merge Variables dialog.

Step 3:	Select the Mode of merging the variables and the way that you want STATISTICA to handle Unmatched Cases.  Click Ok to process the Merge.


  Data Management - Merge Cases

The Merge Cases facilities are accessible from the Data Management module.

Select this option from the Merge Files dialog when you want to merge cases from the second file after the cases of the first file.  The following two notes will apply when you choose to merge cases.

•	The number of variables in the two files must be equal.

•	The lists of text values (and value labels) of the two files will be concatenated.  If a variable in the second file has numeric values with different text values or value labels than those in the first file, the text values and value labels of the first file will be used.

Example


  Data Management - Merging Cases

Step 1:	Click on the Merge option from either the Start-up Panel or the Analysis pull-down menu.

Step 2:	Select the Merge Cases option and click on the 2nd File button to select the file with the cases that will be added after the current file's cases.  Click Ok to exit the dialog and process the Merge.  Note that if the number of variables in the two files are not the same, then the Merge may not be completed.


  Data Management - Merge Text Values

The Merge Text Values facilities are accessible from the Data Management module.

Select the Merge Text Values option from the Merge Files dialog when you want to merge text values (and value labels) from the second file with those of the current data file.  Note that only the text values of variables with the same name in both files will be merged.  If two variables (from the two files) share the same name but you do not want to merge their text values, then temporarily change the name of the variable in one of the files until the merge procedure is completed.  Selecting this option will open the Merge Text Values dialog from which you can choose the mode of merging text values.

Merge Text Values dialog:

Mode:  Choose one of these options for merging text values.

Replace text values from file I with text values from file II:  Replace all text value lists in the first file with those from the second.

Concatenate - get duplicated text values from file I:  Combine the text value lists from the second file with those of the first, and if any duplicated text values are detected, then STATISTICA will use the text values from the first file.

Concatenate - get duplicated text values from file II:  Combine the text value lists from the second file with those of the first, and if any duplicated text values are detected, then STATISTICA will use the text values from the second file.

Example


  Data Management - Merging Text Values

Step 1:	Click on the Merge option from either the Start-up Panel or the Analysis pull-down menu.

Step 2:	Select the Merge Text Values option and click on the 2nd File button to select the file with the variables whose text values will be merged with the current file.  Click Ok to exit this dialog and open the Merge Text Values dialog.

Step 3:	Select the Mode of merging the text values and then click Ok to process the Merge.


  Data Management - Create New Data File

A quick facility to create new data files is included in the File menu of every module (it creates a new file with default settings and can later be modified by the user).  The facility to create new data files included in the Data Management module offers additional options (e.g., global options to automatically create variable names following user-defined criteria).

Create New File dialog:

New File Name

Number of Variables

Number of Cases

Case Name Length

Value Format

Missing Data Code

Variable Name Prefix

Variable Name Start Number

One-Line File Header

Get From

Example


  Create New Data File - New File Name

Click on this button to open the New Data:  Specify File Name dialog in which you can designate the file name for the new data file.


  Create New Data File - Number of Variables

Specify the number of variables to be included in the new data file.  Up to 4092 variables may be included in one STATISTICA data file.  (Files with up to 32,000 variables may be created and maintained in STATISTICA's Megafile Manager module.)


  Create New Data File - Number of Cases

Enter the number of cases to be included when creating the data file.  STATISTICA imposes practically no limit on the number of cases in one file (up to 2.14 billion cases may be specified).


  Create New Data File - Case Name Length

STATISTICA data files may contain (optional) case names of up to 20 characters in length.  Specify the case name length here (if the case name length varies from case to case, then specify the length of the longest case name).


  Create New Data File - Value Format

A default display width format of up to 30 characters may be defined in the form X.Y, where X is the total width, and Y is the number of digits following the decimal point (the default format, 8.3, will display a width of eight characters, with the decimal point three digits to the left, e.g., 1234.567).  The format affects only the way in which values are displayed in the spreadsheet editor and does not affect the internal storage precision of the number.


  Create New Data File - Missing Data Code

Set the initial value (default 9999) which will be used to represent "missing data" for all variables here.  This value may be changed for individual variables in the Edit Variable Specs dialog.  Note that STATISTICA displays a blank cell in the spreadsheet wherever missing data occurs.


  Create New Data File - Variable Name Prefix

Specify the variable name prefix here (all variable names in this data file will have this prefix).  The variable name prefix which is defined here will have a sequential number added to the end (i.e., VAR1, VAR2, VAR3, etc.; the last character(s) in the prefix will be replaced by the number if necessary, to maintain the overall length of 8 characters).


  Create New Data File - Variable Name Start Number

Enter the starting number for the variable name prefixes.  You may want to start with a number other than 1 if you intend to merge this file with another STATISTICA file.


  Create New Data File - One Line File Header

Enter one line (up to 77 characters) of comment about the file here.  The One-Line File Header is saved as part of the file and is printed along with the spreadsheet data file when the File Info/Notes option is selected in the Print Settings dialog, or along with the output of analyses when either a Short, Medium or Long report style is selected in the Page/Output Setup dialog.  You can edit this file header, as well as add a file comment (notes), in the Data File Header and Info dialog.


  Create New Data File - Get From

Click on this button to obtain the complete set of all variable specifications (number of variables and cases, variable names, formats, and MD codes) of an existing STATISTICA data file to be used for the newly created file.  When you click on this button, the Select File to Get Specs From dialog will open in which you can designate the file with the variable specifications.  Note that the variable specifications obtained from the designated file will override all other specifications entered in this window.


  Data Management - Creating a New Data File

Step 1:	Select the New Data option from the File pull-down menu to open the Create New File dialog.

Step 2:	Specify in this dialog the new file name and path (click on the New File button), the file dimensions (number of cases and variables), and value format, as well as other information necessary to build the data file.  Note that all specifications of the file (entered in this dialog) can be modified after the file is created.

Step 3:	Click on the Ok button to open a spreadsheet in which you can enter data into the newly created file.


  Data Management - Importing Data

The following comprehensive import/export facilities are accessible from the Data Management module by selecting the Import - More option from the File pull-down menu.  STATISTICA also features quick importing options available from this and any other module (see Quick Import) and an interface to a wide variety of data base formats via the ODBC option accessible from the Import Data submenu of the File pull-down menu.

Importing data to STATISTICA by converting foreign data files (e.g., worksheets or data bases) is one of several ways (offered in STATISTICA) of accessing data from other applications.  Other methods include establishing dynamic links (DDE, see Current Specs) between data files and using the Clipboard (which in STATISTICA recognizes special Clipboard formatting conventions used by other Windows applications such as Excel or Lotus).

Import Data From dialog:

Each of the options below represents a group of formats (e.g., Lotus can import files from Lotus version 1A, 2, 3, 4, Symphony, Lotus for Windows, etc.).  When importing files, STATISTICA will use the column/field/variable names of the source file.  If an imported name is longer than eight characters, the first eight characters will be used as the STATISTICA variable name.

•  Import STG File	•  Import dBASE File

•  Import Megafile Manager File	•  Import Paradox File

•  Import Excel File	•  Import SPSS File

•  Import Lotus File	•  Import ASCII Free

•  Import Quattro File	•  Import ASCII Fix

Options button:  Click on this button to open a dialog that will contain importing options specific to the import format that you choose.

Example


  Importing Data

Importing is a very simple operation; in the STATISTICA Data Management module, select the Import option from the File pull-down menu (or the startup panel), then follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog (change the List Files of Type setting in this dialog if necessary to show the desired file name).

Step 2:	Confirm or change the type of file to be imported in the Import Data From dialog.

Step 3:	Click the OK button in the latter dialog to import and store the data in the STATISTICA data file (spreadsheet) format.


  Data Management - Import STG File

Import data from STG file format (either from STATISTICA or CSS/3).  After you select an STG Graph File from the Select File to Import dialog, the Import Data From dialog will open (by default, STG will be selected).  Click on the OK button in this dialog to import the STG file that you select.

Each of the plots in the STG file will be imported as a pair of variables containing the X and Y values for each plot or as a triplet of variables containing the X, Y, and Z values for each plot.  If the plots were not labeled in the graph, then the default names for the imported variables will be Plot1X, Plot1Y, Plot2X, Plot2Y, etc., for 2D graphs and Plot1X, Plot1Y, Plot1Z, Plot2X, Plot2Y, Plot2Z, etc., for 3D graphs.  If legends for the plots were entered into the STG file, then they will be used to create names for the variables within the plot.  If all imported plots do not contain the same number of values, then the shorter plots will be padded with missing data.  The first line of the graph title will become the STATISTICA data file one-line header.

Example


  Importing an STG File

To import a STG file, follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that STG has been selected as the type of file to be imported in the Import Data From dialog.

Step 3:	Click the OK button in the latter dialog to import and store the data in the STATISTICA data file (spreadsheet) format.


  Data Management - Import Megafile Manager File

STATISTICA imports all types of data from Megafile Manager, including numeric, text, and logical data.  After you select a Megafile Manager (MFM) file from the Select File to Import dialog, the Import Data From dialog will open (by default, MFM will be selected).  Now, in this dialog, click on the Options button to bring up the MFM Import Options dialog.

MFM Import Options dialog:

Import Text Columns

Import Case Names

Automatic Numeric/Text Match

Range

Example


  Import Megafile Manager File - Import Text Columns

When you select this option, unpaired text columns (columns to which a numeric column has not been matched) will be imported as STATISTICA "double variables" by assigning a numeric code (consecutive integer) for each unique text value.  If the column width is greater than 8, then the remainder of the text is truncated.

If you de-select this option, then STATISTICA will not import unpaired text columns (i.e., text columns with no numeric equivalent columns).  De-selecting this option may result in fewer variables.


  Import Megafile Manager File - Import Case Names

When you select this option, case names will be imported from the first column of the Megafile Manager file.  If this variable contains numeric values instead of text, then the case names will be created as "text images" of these values.


  Import Megafile Manager File - Automatic Text/Numeric Match

This option determines whether Megafile Manager columns will be automatically combined to become STATISTICA "double variables" with numeric and text values, and optional value labels.

If you select this option, then STATISTICA will combine Megafile Manager columns to become STATISTICA "double variables" based on pairing a numeric column with one or two text columns with related names, according to the following rules.  The pairs or triplets of Megafile Manager columns which meet the following conditions are automatically generated when you export a STATISTICA data file to Megafile Manager.

•	A numeric column can be matched with one or two immediately following text columns, which will become the optional text values and value labels for the STATISTICA variable.

•	The first of the text columns may be up to 8 characters long and will become the text values for the STATISTICA variable; its column name must be the same as the numeric column name (with a $ added to the end if the numeric column name is less than 8 characters, or if the name is 8 characters long, the second character should be replaced by a $).  (Please note that if this $ column is wider than 8 characters, it will be disregarded, and no text values will be imported.)

•	The second of the text columns will become the value labels; its column name must be the same as the numeric column name with an @ added to the end (if the numeric column name is less than 8 characters - if the name is 8 characters long, the second character should be replaced by @).

A one-to-one correspondence between the numeric and text values in these columns must exist: each numeric value must be paired with only one unique text string in the text column(s).  STATISTICA will check for this correspondence during the process of creating the STATISTICA file, and if more than one text value is found to be paired with a given numeric value, then a warning will be issued.  Potentially, at least 900 Megafile Manager columns (including case names) or more (depending on your version of STATISTICA) can be imported to a single STATISTICA data file.  STATISTICA also imports the Megafile Manager long column names (as STATISTICA variable long names), as well as the one-line file header.


  Import Megafile Manager File - Range

By default, all cases and variables in the Megafile Manager file will be imported.  This option permits selection of a specific range of cases and/or variables to be imported.  Note that if you are importing case names, and the specified range of variables includes column 1 (which contains the case names), the effective range to be imported will begin with column 2.

•	Variables:  Specify the range of variables to be imported (From which variable, To which variable, inclusive).

•	Cases:  Specify the range of cases to be imported (From which case, To which case, inclusive).


  Importing a Megafile Manager File

To import a Megafile Manager file, follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that MFM has been selected as the type of file to be imported in the Import Data From dialog.  You may click on the Options button to select the range of variables and cases to import as well as other importing options.

Step 3:	Click the OK button in the latter dialog to import and store the data in the STATISTICA data file (spreadsheet) format.


  Data Management - Import SPSS File

Import SPSS Portable files, as well as all other files which follow the SPSS PFF convention (Portable File Format) with this option.  SPSS variable names will become STATISTICA variable names, and SPSS variable long names (up to 128 characters long) will become STATISTICA variable long names.

SPSS Import Options dialog:

Import Text Columns

Import Case Names

Import Value Labels

Note that missing data in SPSS variables may be defined in different ways:

•	If a single MD value has been assigned in a variable, then that MD value will be used as the MD code in the STATISTICA variable.

•	If a range of values have been defined as MD for a variable in SPSS, then STATISTICA imports the actual data values (to maximize the information extracted from the source file), and assigns the first value from the list of MD values as the MD code in the STATISTICA data file.

Example


  Import SPSS File - Import Text Columns

This option controls the importing of text (string) variables from SPSS.  When you select this option, SPSS text variables are converted into STATISTICA "double variables" by assigning each text value a consecutive numeric integer value.  Text values longer than eight characters will be truncated and only the first eight characters will be used as text values.  When you de-select this option, STATISTICA will not import the SPSS text variables.


  Import SPSS File - Import Case Names

Case names may be imported from the first variable of the SPSS file.  If this variable contains numeric values instead of text, the case names will be created as "text images" of these values.


  Import SPSS File - Import Value Labels

When you select this option, STATISTICA will import the SPSS value labels (up to 40 characters).  In the case of numeric SPSS variables, the program will create text equivalents for the numeric values out of the first 8 characters of the value label.


  Importing an SPSS File

To import an SPSS file, follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that SPSS has been selected as the type of file to be imported in the Import Data From dialog.  You may click on the Options button to bring up the SPSS Import Options dialog containing importing options specific to SPSS files.

Step 3:	Click the OK button in the latter dialog to import and store the data in the STATISTICA data file (spreadsheet) format.


  Data Management - Import Excel File

STATISTICA can import numeric and text values as well as dates from Excel.  Text entries are automatically converted to text values in STATISTICA's "double notation."  If the text string is longer than eight characters in Excel, then STATISTICA will only use the first eight characters as the text value.  Date values of variables imported from Excel are imported in Julian format (the number of days since Jan. 1, 1900; e.g., 24858 instead of 1/21/1968); if you want the dates to appear not in a numeric (Julian) format but in a standard date format, change the variable display format in the Current Specs dialog from Decimal to Date.  See Dates or Date Operations for more information on using dates in STATISTICA.

Please note that STATISTICA will automatically convert the Excel spreadsheet into a "data base" at the point of import, therefore it is not necessary to save the Excel file as a "data base" before importing it.

Excel Import Options dialog:

Import Text Columns

Import Case Names

Automatic Numeric/Text Match

Range

Variable Names

Note that in addition to the file import operation, Excel data can be accessed by STATISTICA via dynamic links (DDE, see Paste Link), as well as Clipboard (STATISTICA recognizes the Excel Clipboard format and will properly interpret "formatted" values such $100 or 2,000).

Example


  Import Excel File - Import Text Columns

When you select this option, STATISTICA converts unpaired text columns (columns to which a numeric column has not been matched) into STATISTICA "double variables" by assigning each unique text value a consecutive numeric integer value. If you de-select this option, the STATISTICA will not import unpaired text columns.


  Import Excel File - Import Case Names

Case names may be imported from the first column of the specified range in the Excel file.  If this variable contains numeric values instead of text, then the case names will be created as "text images" of these values.


  Import Excel File - Automatic Numeric/Text Match

This option determines whether Excel columns will be automatically combined to become STATISTICA "double variables" with numeric and text values, and optional value labels.  If you select this option, then STATISTICA will combine Excel columns to become STATISTICA "double variables" based on pairing a numeric column with one or two text columns with related names, according to the following rules (note that this method of naming columns occurs by default when exporting data files from Data Management to Excel).

•	A numeric column can be matched with one or two immediately following text columns, which will become the optional text values and value labels for the STATISTICA variable.

•	The first of the text columns may be up to 8 characters long and will become the text values for the STATISTICA variable; its column name must be the same as the numeric column name (with a $ added to the end if the numeric column name is less than 8 characters, or if the name is 8 characters long, the second character should be replaced by a $).  (Please note that if this $ column is wider than 8 characters, it will be disregarded, and no text values will be imported.)

•	The second of the text columns will become the value labels; its column name must be the same as the numeric column name with an @ added to the end (if the numeric column name is less than 8 characters - if the name is 8 characters long, the second character should be replaced by @).

A one-to-one correspondence between the numeric and text values in these columns must exist:  each numeric value must be paired with only one unique text string in the text column(s).  STATISTICA will check for this correspondence during the process of creating the STATISTICA file, and if more than one text value is found to be paired with a given numeric value, then a warning will be issued.


  Import Excel File - Range

By default, the entire active area of the spreadsheet is imported.  This option permits selection of a specific range of cases and/or variables to be imported.

Variables:  Specify the range of variables to be imported (From which variable, To which variable, inclusive).

Cases:  Specify the range of cases to be imported (From which case, To which case, inclusive).


  Import Excel File - Variable Name

This option specifies the source in Excel for STATISTICA variable names.

From spreadsheet:  When you select this option, STATISTICA will use the Excel column designators (A, B, C, etc.) as STATISTICA variable names.

From First Row of Selected Range:  Select this option to use the labels from the first row of the specified import range (see above).  If any label is longer than eight characters, it will be truncated and only the first eight characters will be used as the variable name.

Create (VAR1, VAR2, . . .):  This option will result in the use of a combination of the prefix VAR and a sequential number (e.g., VAR1, VAR2, etc.) as variable names in the imported file.


  Importing an Excel File

To import an Excel file, follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that Excel has been selected as the type of file to be imported in the Import Data From dialog.  You may click on the Options button to select the range of variables and cases to import as well as other importing options.

Step 3:	Click the OK button in the latter dialog to import and store the data in the STATISTICA data file (spreadsheet) format.


  Data Management - Import Lotus File

STATISTICA can import worksheets from Lotus 1-2-3 Release 1A (Lotus 1-2-3/1), Release 2.01/2.2 (Lotus 1-2-3/2), Release 3 (Lotus 1-2-3/3), and Lotus 1-2-3 for Windows (Release 1, 1.1, and 4), as well as Symphony (Symph).  Due to their 3-dimensional structure, 1-2-3/3 and Lotus 1-2-3 for Windows files are imported with each page placed in a successive set of variables in the STATISTICA file.

Date values of variables imported from Lotus are imported in Julian format (the number of days since Jan. 1, 1900; e.g., 24858 instead of 1/21/1968); if you want the dates to appear not in a numeric (Julian) format but in a standard date format, change the variable display format in the Current Specs dialog from Decimal to Date.  See Dates or Date Operations for more information on using dates in STATISTICA.

After you select a Lotus file from the Select File to Import dialog, the Import Data From dialog will open (by default, Lotus will be selected).  Now, in this dialog, click on the Options button to bring up the Lotus Import Options dialog (the same dialog is used for each version of Lotus that you are importing).

Lotus Import Options dialog:

Import Text Columns

Import Case Names

Automatic Numeric/Text Match

Range

Variable Names

Note that in addition to the file import operation, Lotus data can be accessed by STATISTICA via dynamic links (DDE, see Paste Link), as well as Clipboard (STATISTICA recognizes the Lotus Clipboard format and will properly interpret "formatted" values such $100 or 2,000).

Example


  Import Lotus File - Import Text Columns

When you select this option, STATISTICA will automatically convert unpaired text values (labels to which no numeric value has been matched) into STATISTICA "double variables" by assigning each text value a consecutive numeric integer value.  If you de-select this option, STATISTICA will not import unpaired labels.


Import Lotus File - Import Case Name

  Import Lotus File - Import Case Names

At the user's option, case names may be imported from the first column of the specified range in the Lotus file.  If this variable contains numeric values instead of text, the case names will be created as "text images" of these values.


  Import Lotus File - Automatic Numeric/Text Match

This option determines whether Lotus 1-2-3 labels will be automatically combined to become STATISTICA "double variables" with numeric and text values, and optional value labels.  When you select this option, then STATISTICA will combine Lotus columns to become STATISTICA "double variables" based on pairing a numeric column with one or two text columns with related names, according to the following rules (note that this method of naming columns occurs by default when exporting data files from Data Management to Lotus).

•	A numeric column can be matched with one or two immediately following text columns, which will become the optional text values and value labels for the STATISTICA variable.

•	The first of the text columns may be up to 8 characters long and will become the text values for the STATISTICA variable; its column name must be the same as the numeric column name (with a $ added to the end if the numeric column name is less than 8 characters, or if the name is 8 characters long, the second character should be replaced by a $).  (Please note that if this $ column is wider than 8 characters, it will be disregarded, and no text values will be imported.)

•	The second of the text columns will become the value labels; its column name must be the same as the numeric column name with an @ added to the end (if the numeric column name is less than 8 characters - if the name is 8 characters long, the second character should be replaced by @).

A one-to-one correspondence between the numeric and text values in these columns must exist:  each numeric value must be paired with only one unique text string in the text column(s).  STATISTICA will check for this correspondence during the process of creating the STATISTICA file, and if more than one text value is found to be paired with a given numeric value, then a warning will be issued.


Import Case Name - Range

  Import Lotus File - Range

By default, the entire active area of the worksheet is imported.  A portion of the worksheet can be selected by defining the range (see below).

Variables:  Specify the range of variables to be imported (From which variable, To which variable, inclusive).

Cases:  Specify the range of cases to be imported (From which case, To which case, inclusive).

Sheets:  This option is only available if a Lotus 1-2-3 Release 3 or 4 file is being imported (otherwise the option is dimmed).  By default, all sheets are imported, however you can select specific sheets to be imported using this option (From which sheet, To which sheet, inclusive).

Review Ranges button:  Click on this button to open the Review Ranges window from which you can select a named range from a listing of all of the named ranges in the selected file.


Import Case Name - Variable Names

  Import Lotus File - Variable Names

This option specifies the source for names of variables.

From Spreadsheet:  Use Lotus 1-2-3 column designators (A, B, C, etc.) as STATISTICA variable names (Lotus 1-2-3 Release 3 uses names A:A, A:B, B:A, B:B, etc.; they will appear in STATISTICA as A_A, A_B, B_A, B_B) when you select this option.  This option is especially useful in working with Release 3 files which will eventually be exported once again (using Lotus' column designators will preserve the identification of variables originating in different sheets).

From First Row of Selected Range:  STATISTICA will use labels from the first row of the specified range when you select this option.  If any label is longer than eight characters, only the first eight characters of the label will be used as the STATISTICA variable name.

Create (VAR1, VAR2, . . .):  This option will result in the use of a combination of the prefix VAR and a sequential number (e.g., VAR1, VAR2, etc.) as variable names in the imported file.


  Importing a Lotus File

To import a Lotus file, follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that Lotus has been selected as the type of file to be imported in the Import Data From dialog.  You may click on the Options button to select the range of variables and cases to import as well as other importing options .

Step 3:	Click the OK button in the latter dialog to import and store the data in the STATISTICA data file (spreadsheet) format.


  Data Management - Import Lotus - Review Ranges

In Lotus, you can define "named ranges" of data in order to define distinctive sections of the worksheet.  Clicking the Review Ranges button in the STATISTICA Lotus Import Options dialog will bring up a list of defined ranges for the Lotus worksheet that you want to import.  Now, instead of importing the whole Lotus worksheet (which might include column headings and other text), you can import only a subset of data by selecting the named worksheet range (highlight the range name and click the OK button).


  Data Management - Import Quattro File

STATISTICA can import worksheets from Quattro Pro (the DOS version; see the note about importing Quattro for Windows at the end of this section).

Quattro Import Options dialog:

Import Text Columns

Import Case Names

Automatic Numeric/Text Match

Range

Variable Names

Note that in addition to the file import operation, Quattro for Windows data can be accessed by STATISTICA via dynamic links (DDE, see Paste Link), as well as Clipboard (STATISTICA recognizes the Quattro for Windows Clipboard format and will properly interpret "formatted" values such $100 or 2,000).

Example


  Import Quattro File - Import Text Columns

When you select this option, STATISTICA will automatically convert unpaired text values (labels to which no numeric value has been matched) into STATISTICA "double variables" by assigning each text value a consecutive numeric integer value.  If you de-select this option, STATISTICA will not import unpaired labels.


  Import Quattro File - Import Case Names

At the user's option, case names may be imported from the first  column of the specified range in the Quattro file.  If this variable contains numeric values instead of text, the case names will be created as "text images" of these values.


  Import Quattro File - Automatic Numeric/Text Match

This option determines whether Quattro labels will be automatically combined to become STATISTICA "double variables" with numeric and text values, and optional value labels.  When you select this option, then STATISTICA will combine Quattro columns to become STATISTICA "double variables" based on pairing a numeric column with one or two text columns with related names, according to the following rules (note that this method of naming columns occurs by default when exporting data files from Data Management to Quattro).

•	A numeric column can be matched with one or two immediately following text columns, which will become the optional text values and value labels for the STATISTICA variable.

•	The first of the text columns may be up to 8 characters long and will become the text values for the STATISTICA variable; its column name must be the same as the numeric column name (with a $ added to the end if the numeric column name is less than 8 characters, or if the name is 8 characters long, the second character should be replaced by a $).  (Please note that if this $ column is wider than 8 characters, it will be disregarded, and no text values will be imported.)

•	The second of the text columns will become the value labels; its column name must be the same as the numeric column name with an @ added to the end (if the numeric column name is less than 8 characters - if the name is 8 characters long, the second character should be replaced by @).

A one-to-one correspondence between the numeric and text values in these columns must exist:  each numeric value must be paired with only one unique text string in the text column(s).  STATISTICA will check for this correspondence during the process of creating the STATISTICA file, and if more than one text value is found to be paired with a given numeric value, then a warning will be issued.


  Import Quattro File - Range

By default, the entire active area of the worksheet is imported.  A portion of the worksheet can be selected by defining the range (see below).

Variables:  Specify the range of variables to be imported (From which variable, To which variable, inclusive).

Cases:  Specify the range of cases to be imported (From which case, To which case, inclusive).


  Import Quattro File - Variable Name

This option specifies the source for names of variables.

From Spreadsheet:  Use Quattro column designators (A, B, C, etc.) as STATISTICA variable names.

From First Row of Selected Range:  STATISTICA will use labels from the first row of the specified range when you select this option.  If any label is longer than eight characters, only the first eight characters of the label will be used as the STATISTICA variable name.

Create (VAR1, VAR2, . . .):  This option will result in the use of a combination of the prefix VAR and a sequential number (e.g., VAR1, VAR2, etc.) as variable names in the imported file.


  Importing a Quattro File

To import a Quattro file, follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that Quattro has been selected as the type of file to be imported in the Import Data From dialog.  You may click on the Options button to select the range of variables and cases to import as well as other importing options.

Step 3:	Click the OK button in the latter dialog to import and store the data in the STATISTICA data file (spreadsheet) format.


  Data Management - Import Paradox File

STATISTICA can import data files from Paradox.

Paradox Import Options dialog:

Import Text Columns

Import Case Names

Automatic Numeric/Text Match

Range

Example


  Import Paradox File - Import Text Columns

When you select this option, STATISTICA will automatically convert unpaired text values (labels to which no numeric value has been matched) into STATISTICA "double variables" by assigning each text value a consecutive numeric integer value.  If you de-select this option, STATISTICA will not import unpaired labels.


  Import Paradox File - Import Case Names

At the user's option, case names may be imported from the first column of the specified range in the Paradox file.  If this variable contains numeric values instead of text, the case names will be created as "text images" of these values.


  Import Paradox File - Automatic Numeric/Text Match

This option determines whether Paradox labels will be automatically combined to become STATISTICA "double variables" with numeric and text values, and optional value labels.  When you select this option, then STATISTICA will combine Paradox columns to become STATISTICA "double variables" based on pairing a numeric column with one or two text columns with related names, according to the following rules (note that this method of naming columns occurs by default when exporting data files from Data Management to Paradox).

•	A numeric column can be matched with one or two immediately following text columns, which will become the optional text values and value labels for the STATISTICA variable.

•	The first of the text columns may be up to 8 characters long and will become the text values for the STATISTICA variable; its column name must be the same as the numeric column name (with a $ added to the end if the numeric column name is less than 8 characters, or if the name is 8 characters long, the second character should be replaced by a $).  (Please note that if this $ column is wider than 8 characters, it will be disregarded, and no text values will be imported.)

•	The second of the text columns will become the value labels; its column name must be the same as the numeric column name with an @ added to the end (if the numeric column name is less than 8 characters - if the name is 8 characters long, the second character should be replaced by @).

A one-to-one correspondence between the numeric and text values in these columns must exist:  each numeric value must be paired with only one unique text string in the text column(s).  STATISTICA will check for this correspondence during the process of creating the STATISTICA file, and if more than one text value is found to be paired with a given numeric value, then a warning will be issued.


  Import Paradox File - Range

By default, the entire active area of the data file is imported.  A portion of the data file can be selected by defining the range (see below).

Variables:  Specify the range of variables to be imported (From which variable, To which variable, inclusive).

Cases:  Specify the range of cases to be imported (From which case, To which case, inclusive).


  Importing a Paradox File

To import a Paradox file, follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that Paradox has been selected as the type of file to be imported in the Import Data From dialog.  You may click on the Options button to select the range of variables and cases to import as well as other importing options.

Step 3:	Click the OK button in the latter dialog to import and store the data in the STATISTICA data file (spreadsheet) format.


  Data Management - Import dBASE File

STATISTICA can import data files from dBASE versions III + and IV.  dBASE files contain a flag within each record indicating whether the record is to be read or not; STATISTICA will ignore all records marked as having been deleted.  After you select a dBASE file from the Select File to Import dialog, the Import Data From dialog will open.  Now, in this dialog, click on the Options button to bring up the dBASE Import Options dialog (the same dialog is used for either version of dBASE that you are importing).

dBASE Import Options dialog:

Import Text Columns

Import Case Names

Automatic Numeric/Text Match

Range

Example


  Import dBASE File - Import Text Columns

STATISTICA will convert unpaired text fields (fields to which a numeric field has not been matched) into STATISTICA "double variables" by assigning each alphanumeric value a consecutive numeric integer value when you select this option.  If this option is de-selected, then STATISTICA ignores (does not import) unpaired text fields.


  Import dBASE File - Import Case Names

Case names may be imported from the first field of the dBASE file when you select this option.  If this field contains numeric values instead of text, then case names will be created as "text images" of these values.


  Import dBASE File - Automatic Numeric/Text Match

This option determines whether dBASE labels will be automatically combined to become STATISTICA "double variables" with numeric and text values, and optional value labels.  When you select this option, then STATISTICA will combine dBASE fields to become STATISTICA "double variables" based on pairing a numeric field with one or two text fields with related names, according to the following rules (note that this method of naming fields occurs by default when exporting data files from Data Management to dBASE).

•	A numeric field can be matched with one or two immediately following text fields, which will become the optional text values and value labels for the STATISTICA variable.

•	The first of the text fields may be up to 8 characters long and will become the text values for the STATISTICA variable; its field name must be the same as the numeric field name (with a $ added to the end if the numeric field name is less than 8 characters, or if the name is 8 characters long, the second character should be replaced by a $).  (Please note that if this $ field is wider than 8 characters, it will be disregarded, and no text values will be imported.)

•	The second of the text fields will become the value labels; its field name must be the same as the numeric field name with an @ added to the end (if the numeric field name is less than 8 characters - if the name is 8 characters long, the second character should be replaced by @).

A one-to-one correspondence between the numeric and text values in these fields must exist:  each numeric value must be paired with only one unique text string in the text field(s).  STATISTICA will check for this correspondence during the process of creating the STATISTICA file, and if more than one text value is found to be paired with a given numeric value, then a warning will be issued.


  Import dBASE File - Ranges

By default, the entire active area of the data file is imported.  A portion of the data file can be selected by defining the range (see below).

Variables:  Specify the range of variables to be imported (From which variable, To which variable, inclusive).

Cases:  Specify the range of cases to be imported (From which case, To which case, inclusive).


  Importing a dBASE File

To import a dBASE file, follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that dBASE has been selected as the type of file to be imported in the Import Data From dialog.  You may click on the Options button to select the range of variables and cases to import as well as other importing options.

Step 3:	Click the OK button in the latter dialog to import and store the data in the STATISTICA data file (spreadsheet) format.


  Data Management - Import ASCII File

STATISTICA can import both ASCII fix (undelimited) and ASCII free (delimited) files.  Each type of ASCII file has its own dialog of options.  For more information on these options, click on the appropriate selection.

Import ASCII free file

Import ASCII fix file

Note that instead of using these import options in the Data Management module, you can import ASCII files from any module of STATISTICA using the Quick Import options.  Quick Import does not support some of the specialized options offered in these (comprehensive) import procedures, however, it is faster, and often more convenient since it automatically determines the format of the data to be imported.


  Data Management - Import ASCII Fix File

After you select an ASCII fix (fixed format) file from the Select File to Import dialog, the Import Data From dialog will open.  By default, ASCII will be selected and if the file name extension is *.fix, then Fix will automatically be checked as the ASCII version.  If STATISTICA is unable to recognize (from the file name extension) that the file is an ASCII Fix file, then the Free ASCII version will be selected and you will need to change the version to Fix.

ASCII Fix Import Options dialog:

File Size

Import Text Columns

Import Case Names

Format Statement

Example


  Import ASCII Fix File - File Size

As in ASCII Free Format Files, in order for STATISTICA to properly interpret the file, the number of variables and cases must be accurately specified.

Number of Variables:  Specify the number of variables in the ASCII file here.

Number of Cases:  Specify the number of cases in the ASCII file here.  If you are uncertain about the exact number of cases, you may overestimate (STATISTICA will detect the actual length of the file during import).  Note that each line in the ASCII source file may be up to 4000 characters in length.  This limit only applies to the individual line length and not the total length of a "case" of data:  each imported case may be represented by many lines of data in the source file.


  Import ASCII Fix File - Import Text Columns

Selecting this option converts text fields into STATISTICA "double variables" by assigning to each text value a consecutive numeric integer value.  Text values longer than eight characters will be truncated and only the first eight characters will be used as text values.  De-selecting this option will cause STATISTICA to ignore (will not import) text variables.


  Import ASCII Fix File - Import Case Names

Case names may be obtained from the first field of each record in the ASCII file.  If this field contains more than 20 characters, then only the first 20 will be used as the case name.  If this field contains numeric values instead of text, then the case names will be created as "text images" of these values.


  Import ASCII Fix File - Format Statement

This option explicitly defines for STATISTICA the exact contents of the input ASCII file.  (This is an important distinction: the format statement is a set of instructions for interpreting the structure of the input file, not a definition of the STATISTICA variables to be created.)  The format statement is entered as a list of formats in the form nXm, where n is an integer multiplier indicating the number of times the format is to be repeated (no multiplier = 1); X is the column type; m is the column width (e.g., 10A8 means 10 text value (alphanumeric) fields, each 8 characters long).

Column Type Specifiers:

A - Text (Alphanumeric)

F - Float (also R - Real)

D - Double Float (also DR - Double Real)

I - Integer (also NI - Normal Integer) - values ± 32767

S - Short Integer (also SI) - values ± 127

LI - Long Integer (also J) - values ± 2,140,000,000

L - Logical

The format specified as logical is expected to contain text designators of true and false.  The following three conventions will be recognized by STATISTICA when the data are imported:

TRUE or FALSE if the field length is 5 or more.

YES or NO if it is 3 or 4 characters long.

Y, N, or T, F respectively, if it is 1 character long.

Values of TRUE or YES will be imported as 1, FALSE or NO will be imported as 0.

The additional specifier Tx is available to instruct STATISTICA to jump to character number x in the current line in the input file (i.e., to skip to that position).  This may be used to jump over unwanted characters, or to return to an earlier character (if x specifies a character position which has already been read).

The slash character (/) may be used to indicate that the remainder of the line should be ignored (i.e., skip to the next line in the input file).  Example: 10I3 A8 T55 3I5 /  specifies the import of 14 values: ten 3-digit integers, followed by an 8-character text string, then skip to the 55th character in the record, import three 5-digit integers and ignore the rest of the record.  If the multiplier precedes a list of formats enclosed in parentheses, the list will be repeated as many times as specified in the multiplier (e.g., 10(2A3,I5)).


  Importing an ASCII Fix File

To import an ASCII file, follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that ASCII has been selected as the type of file to be imported in the Import Data From dialog and the appropriate ASCII version is checked (Fix).  Click on the Options button to open the ASCII Fix Import Options dialog.

Step 3:	In this dialog, specify the number of cases and variables in the imported file as well as the file format (in order to identify the types of values, see below).

Step 4:	Click the OK button in the latter dialog to import and store the data in the STATISTICA data file (spreadsheet) format.


  Data Management - Import ASCII Free File

After you select an ASCII Free file from the Select File to Import dialog, the Import Data From dialog will open (by default, ASCII Free will be selected).  Now, in this dialog, click on the Options button to bring up the ASCII Import Options dialog.

ASCII Free Import Options dialog:

File Size

Import Text Columns

Import Case Names

Format Statement

Separators

Example


  Import ASCII Free File - File Size

As in ASCII Fixed Format Files, the number of variables must be accurately specified.

Number of Variables:  Specify the number of variables in the ASCII file.

Number of Cases:  Specify the number of cases in the ASCII file.  If you are uncertain about the exact number of cases, you may overestimate (STATISTICA will detect the actual length of the file during import).  Note that each line in the ASCII source file may be up to 4000 characters in length.  This limit only applies to the individual line length and not the total length of a "case" of data: each imported case may be represented by many lines of data in the source file.


  Import ASCII Free File - Import Text Columns

Selecting this option converts text fields into STATISTICA "double variables" by assigning to each text value a consecutive numeric integer value.  Text values longer than eight characters will be truncated and only the first eight characters will be used as text values.  De-selecting this option will cause STATISTICA to ignore (will not import) text variables.


  Import ASCII Free File - Import Case Names

Case names may be obtained from the first field of each record in the ASCII file.  If this variable contains more than 20 characters, only the first 20 will be used as the case name.  If this field contains numeric values instead of text, the case names will be created as "text images" of these values.


  Import ASCII Free File - Format Statement

This option explicitly defines for STATISTICA the exact contents of the input ASCII file.  (This is an important distinction: the format statement is a set of instructions for interpreting the structure of the input file, not a definition of the STATISTICA variables to be created.)  The format statement is entered as a list of formats in the form nX where n is an integer multiplier indicating the number of times the format is to be repeated (no multiplier = 1) and X is the column type (e.g., 40F means 40 fields containing numeric (here float) values).

Column Type Specifiers:

A - Text (Alphanumeric)

F - Float (also R - Real)

D - Double Float (also DR - Double Real)

I - Integer (also NI - Normal Integer) - values ± 32767

S - Short Integer (also SI) - values ± 127

LI - Long Integer (also J) - values ± 2,140,000,000

L - Logical

The format specified as logical is expected to contain text designators of true and false.  The following three conventions will be recognized by STATISTICA when the data are imported:

TRUE or FALSE if the field length is 5 or more.

YES or NO if it is 3 or 4 characters long.

Y, N, or T, F respectively, if it is 1 character long.

Values of TRUE or YES will be imported as 1, FALSE or NO will be imported as 0.

Text fields (type A) must also include a length value from 1 to 255 immediately following the letter A, indicating the maximum possible length of text in this field.

The slash character (/) may be used to indicate that the remainder of the current line in the input file should be ignored (i.e., skip to the next line in the input file).  If the multiplier precedes a list of formats enclosed in parentheses, then the list of formats within the parentheses will be repeated the number of times specified by the multiplier.  Example:  2(2L a5) is equivalent to L L A5 L L A5  and specifies two Logical variables followed by a Text variable that can hold up to five characters, then two more Logical variables and a final Text variable (again up to five characters).


  Import ASCII Free File - Separators

Within this option, you will be able to define the characters used in the input file as delimiters.  (The final list of separators to be used will be the combination of the set of selected Basic and any Additional separators.)

Basic:  Select the type of delimiter used in the input file from four predefined sets of separators (CR stands for carriage return, LF stands for line feed, and FF stands for form feed).

Standard Set.  This set includes:  a comma (,), semicolon (;), <space>, <tab>, and <CR\LF>.

Undefined.  This setting means that STATISTICA will not use a predefined set (see Additional button, below).

Blank Characters.  This set includes:  <space>, <tab>, <FF>, <LF>, and <CR\LF>.

Non-Numeric.  This set includes all characters except:  0-9, period (.), minus (-), and plus (+).

Additional button:  Click on this button to bring up the ASCII Free Separators dialog from which you can select the delimiter(s).

Treat Multiple Separators as MD:  When you select this option, STATISTICA will interpret each pair of adjacent separators as an occurrence of missing data (an absent value) and will place the default missing data value (-9999) in the position between the adjacent separators.  If this option is de-selected, then multiple separator characters are treated as one separator, and missing data must be explicitly coded into the ASCII file as a unique value (for instance -9999).  This option is particularly useful if, for instance, individual values in the data file are separated by spaces, with a variable number of spaces between values.  If spaces are used as separators, then each pair of spaces would be seen as an occurrence of missing data, and the resulting file would be full of missing values.

Use Quotation Marks as Text Boundaries:  Select this option if double (") or single (') quotation marks were used as text boundaries and the specified separator characters appear within the values of text variables in the input file (e.g., "John Jones, Ph.D.", uses the comma both as part of the text and as a separator after it).  In this case, when STATISTICA imports the data, the quotation marks will be recognized only as boundaries around the text values, keeping the text values and the embedded separator character together (the quotation marks will not be included as part of the imported text values).

Note that if a text string is to contain quotation marks as part of the string itself (e.g., as in the titles of books such as "Moby Dick"), then two methods may be used to import them:

•	Select this option and enclose the entire text string within the alternate quotation mark (opposite of the embedded one); e.g., 'William Shakespeare, "King Lear", Act 2, Scene 1' will be imported as William Shakespeare, "King Lear", Act 2, Scene 1.

•	Select this option and then double the quotation mark wherever it is to be preserved; e.g., "William Shakespeare's ""King Lear"", ""Macbeth"" and ""Hamlet"" will be imported as William Shakespeare's "King Lear", "Macbeth" and "Hamlet".

If this option is de-selected, then the character will be interpreted as a separator and not as a part of the text value and the quotation marks will be imported as part of the text; e.g., .'William Shakespeare, "King Lear", Act 2, Scene 1' will be imported as 'William Shakespeare in one column, "King Lear" in another column, Act 2 in different column and Scene 1' in another column.


  Importing an ASCII Free File

To import an ASCII file, follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that ASCII has been selected as the type of file to be imported in the Import Data From dialog and the appropriate ASCII version is checked (Free).  Click on the Options button to open the ASCII Free Import Options dialog.

Step 3:	In this dialog, specify the number of cases and variables in the imported file as well as the file format (in order to identify the types of values, see below).

Step 4:	Click the OK button in the latter dialog to import and store the data in the STATISTICA data file (spreadsheet) format.


  Data Management - Exporting Data

The import/export facilities are accessible from the Data Management module.  (For information on quick exporting options available from any module, see Quick Export.)

Results of many STATISTICA statistical, data management, and graphical operations and all data transformations and recoding can be written back to STATISTICA data files.  If you intend to use them in other programs, they can easily be exported (see STATISTICA File Name Extensions).  When you choose the Export Data option in the Data Management module, the Export Data to dialog will open in which you can select the export file format.

Export Data to dialog:

The STATISTICA file will be exported in the file format that you select here.

•  Lotus, Symphony, and 3D Lotus files

•  MFM (Megafile Manager)	•  Paradox

•  Excel	•  SPSS Portable File format

•  Quattro	•  ASCII (free and fixed format)

•  dBASE III and IV	•  CSS/3 (STATISTICA's DOS version)

Other data export options are available in Megafile Manager.


  Data Management - Export File to Megafile Manager

Export data sets to STATISTICA's Megafile Manager module.  During export, STATISTICA variable long names (if they exist) will become Megafile Manager column long names, and the STATISTICA file header is exported as the Megafile Manager one-line file header.  When you select this option from the Export Data to dialog, the MFM Export Options dialog will open.

MFM Export Options dialog:

Case Names

Variables With Text Values

Example


  Export File to Megafile Manager - Case Names

Select this option to export the case names as the first column of the Megafile Manager file.


  Export File to Megafile Manager - Variables with Text Values

STATISTICA "double variables" (numeric/text) may be expanded at the user's option to become up to three Megafile Manager columns [representing the numeric values, text values, and (optional) value labels of the STATISTICA variable] with names related to the original STATISTICA variable.  The following options govern the creation of these columns, allowing the resulting pairs or triplets of columns in Megafile Manager to be converted back (i.e., "compressed") into individual STATISTICA variables (when the file is imported by STATISTICA).  If all of these options are de-selected, then only those STATISTICA variables which do not have text values will be exported.

Text Values:  If you select this option, then for "double notation" variables, STATISTICA will create text columns of alphanumeric values for that variable.  When this column is created, STATISTICA uses the variable name of the "double notation" variable and adds a $ to the name in the following manner:  if the STATISTICA variable name is shorter than eight characters, then the Megafile Manager text column name will have a $ added to the end; if the name is eight characters long, then the second character will be changed to a $ (this is done to avoid later conflicts with the requirements of Megafile Manager regarding duplicated column names).

Numeric Values:  When selected, this option creates columns of numeric values associated with the text values columns created from the above option.  When this variable is exported to Megafile Manager, STATISTICA will use the same variable name as before.  If this option is de-selected, then only numeric values from non-"double variables" (i.e., variables without text values) will be present in the exported file.

Long Value Labels:  This option controls the creation of a text columns of variable value labels.  When you select this option, STATISTICA will create a third column of text values representing the Long Value Labels for a variable.  When this column is created, STATISTICA uses the variable name of the "double notation" variable and adds an @ to the name in the following manner:  if the variable name is shorter than eight characters, then the name of the Megafile Manager text column will have an @ added to the end; if the name of the STATISTICA variable is eight characters long, then the second character will be changed to an @).

Note that if only the text values or labels are exported, then the resulting column in the MFM file will have the original STATISTICA variable name, rather than using the $ or @ conventions.


Data Management - Exporting a File to Megafile Manager

  Exporting a File to Megafile Manager

To export a STATISTICA file to Megafile Manager, follow the steps outlined below.

Step 1:	Select the Export Data - More option from the File pull-down menu to open the Export Data to dialog.

Step 2:	Select MFM as the type of file format to which the data will be exported.

Step 3:	Click the OK button to export and store (you will need to select a file name) the file in Megafile Manager format.


  Data Management - Export File to dBASE

STATISTICA exports to dBASE III+ and dBASE IV file formats.  dBASE III+ files are limited to 128 fields and dBASE IV to 255 fields.  If the current STATISTICA file is larger than this, then you can create Subsets of the file and export each of those subsets separately.  When you select the dBASE option from the Export Data to dialog, the dBASE (III+ or IV) Export Options dialog will open (the dialog is the same for each version of dBASE).

dBASE (III+ or IV) Export Options dialog:

Case Names

Variables With Text Values

Notes:

If only the text values or labels are exported, then the resulting field in the dBASE file will have the original STATISTICA variable name, rather than using the $ or @ conventions.

Although the values of variables in STATISTICA are always stored internally in extended precision, when you export to dBASE (III+ or IV), only the displayed format of those values will be exported.  For example, a value may be stored in STATISTICA as 7.3926541009725183, however, if the value is displayed as 7.39, then that displayed value of 7.39 is exported.  In order to export the value in higher precision, change the display format for that variable via the Spreadsheet Edit (Current) Specs dialog.

Example


  Export File to dBASE - Case Names

Select this option to export the case names as the first field of the dBASE file.


  Export File to dBASE - Variables with Text Values

STATISTICA "double variables" (numeric/text) may be expanded at the user's option to become up to three dBASE fields [representing the numeric values, text values, and (optional) value labels of the STATISTICA variable] with names related to the original STATISTICA variable.  The following options govern the creation of these fields allowing the resulting pairs or triplets of fields in dBASE to be converted back (i.e., "compressed") into individual STATISTICA variables (when the file is imported by STATISTICA).  If all of these options are de-selected, then only those STATISTICA variables which do not have text values will be exported.

Text Values:  If you select this option, then for "double notation" variables, STATISTICA will create text fields of alphanumeric values for that variable.  When this field is created, STATISTICA uses the variable name of the "double notation" variable and adds a $ to the name in the following manner:  if the STATISTICA variable name is shorter than eight characters, then the dBASE text field name will have a $ added to the end; if the name is eight characters long, then the second character will be changed to a $ (this is done to facilitate recombining the numeric and text data if the file is imported once again).

Numeric Values:  When selected, this option creates fields of numeric values associated with the text values fields created from the above option.  When this variable is exported to dBASE STATISTICA will use the same variable name as before.  If this option is de-selected, then only numeric values from non-"double variables" (i.e., variables without text values) will be present in the exported file.

Long Value Labels:  This option controls the creation of a text fields of variable value labels.  When you select this option, STATISTICA will create a third field of text values representing the Long Value Labels for a variable.  When this column is created, STATISTICA uses the variable name of the "double notation" variable and adds an @ to the name in the following manner:  if the variable name is shorter than eight characters, then the name of the dBASE text field will have an @ added to the end; if the name of the STATISTICA variable is eight characters long, then the second character will be changed to an @).


  Exporting a File to dBASE

To export a STATISTICA file to dBASE, follow the steps outlined below.

Step 1:	Select the Export Data option from the File pull-down menu to open the Export Data to dialog.

Step 2:	Select dBASE as the type of file into which the data will be exported and then select the dBASE version (click on either III+ or IV).  You may click on the Options button to select from several exporting options.

Step 3:	Click the OK button in the latter dialog to export and store (you will need to select a file name) the file in dBASE format.


  Data Management - Export File to SPSS

This option exports to the SPSS Portable File format (also compatible with SAS).  STATISTICA value labels are used as SPSS value labels.  SPSS variable names may be up to eight characters long, must begin either with an uppercase letter (A to Z), or the characters $ or @, and may also contain digits, and underscore (_).  Certain names are reserved as keywords and may not be used as variable names, including ALL, AND, BY, EQ, GE, GT, LE, LT, NE, NOT, OR, TO, and WITH.  (You may use the option Verify Names/Formats from the Analysis pull-down menu to check variable names for compliance with the requirements of SPSS.)  When you select the SPSS option from the Export Data to dialog, the SPSS Export Options dialog will open.

SPSS Export Options dialog:

Case Names

Variables With Text Values

Example


  Export File to SPSS - Case Names

Select this option to export the case names as text to the first variable in the SPSS file.


  Export File to SPSS - Variables with Text Values

The various components of STATISTICA's "double variables" may be exported to SPSS using the options listed below.

Text Values:  Select this option to request the export of the alphanumeric values of "double variables" as SPSS text variables.

Numeric Values:  Select this option to request the export of the numeric values of "double variables" as SPSS numeric variables.

Long Value Labels:  When you select this option, STATISTICA value labels will be exported, either as SPSS value labels or as text variables (see below).

The following combinations of the above selected options are possible:

•	Text/Numeric:  This combination creates Numeric SPSS variables with Text as value labels.

•	Text/Labels:  Choose this combination to create Text SPSS variables with Long Value Labels as value labels.

•	Numeric/Labels:  This combination creates Numeric SPSS variables with Long Value Labels as value labels.

•	If all three options are selected (Text/Numeric/Labels), then two columns will be created:  Numeric, and Text columns with Long Value Labels as labels.

•	If only one option is selected, then the appropriate type of variable (numeric or text) will be created.

•	If all options are de-selected, then only those STATISTICA variables which do not contain text values will be exported.


  Exporting a File to SPSS

To export a STATISTICA file to SPSS, follow the steps outlined below.

Step 1:	Select the Export Data option from the File pull-down menu to open the Export Data to dialog.

Step 2:	Select SPSS as the type of file into which the data will be exported.  You may click on the Options button to select from several exporting options.

Step 3:	Click the OK button in the latter dialog to export and store (you will need to select a file name) the file in SPSS format.


  Data Management - Export File to Excel

Excel files may contain up to 256 columns and 16384 rows.  If the current STATISTICA file is larger than this, then you can create Subsets of the file and export each of those subsets separately.  When you select the Excel option from the Export Data to dialog, the Excel Export Options dialog will open.

Excel Export Options dialog:

Case Names

Variable Names

Variables With Text Values

Note that if only the text values or value labels are exported, then the resulting column in the Excel file will have the original STATISTICA variable name, rather than using the $ or @ conventions.

Example


  Export File to Excel - Case Names

Select this option to export the case names to the first column of the Excel file.


  Export File to Excel - Variable Names

When this option is selected, STATISTICA will export the variable names into the first row of the Excel spreadsheet.  If this option is de-selected, then variable names will not be included in the Excel file.


  Export File to Excel - Variables with Text Values

STATISTICA "double variables" (numeric/text) may be expanded at the user's option to become up to three Excel columns [representing the numeric values, text values, and (optional) value labels of the STATISTICA variable] with names related to the original STATISTICA variable.  The following options govern the creation of these columns allowing the resulting pairs or triplets of columns in Excel to be converted back (i.e., "compressed") into individual STATISTICA variables (when the file is imported by STATISTICA).  If all of these options are de-selected, then only those STATISTICA variables which do not have text values will be exported.

Text Values:  If you select this option, then for "double notation" variables, STATISTICA will create text columns of alphanumeric values for that variable.  When this column is created, STATISTICA uses the variable name of the "double notation" variable and adds a $ to the name in the following manner:  if the STATISTICA variable name is shorter than eight characters, then the Excel text column name will have a $ added to the end; if the name is eight characters long, then the second character will be changed to a $ (this is done to facilitate recombining the numeric and text data if the file is imported once again).

Numeric Values:  When selected, this option creates columns of numeric values associated with the text values columns created from the above option.  If this option is de-selected, then only numeric values from non-"double variables" (i.e., variables without text values) will be present in the exported file.

Long Value Labels:  This option controls the creation of a text columns of variable value labels.  When you select this option, STATISTICA will create a third column of text values representing the Long Value Labels for a variable.  When this column is created, STATISTICA uses the variable name of the "double notation" variable and adds an @ to the name in the following manner:  if the variable name is shorter than eight characters, then the name of the Excel text column will have an @ added to the end; if the name of the STATISTICA variable is eight characters long, then the second character will be changed to an @).


  Exporting a File to Excel

To export a STATISTICA file to Excel, follow the steps outlined below.

Step 1:	Select the Export Data option from the File pull-down menu to open the Export Data to dialog.

Step 2:	Select Excel as the type of file into which the data will be exported.  You may click on the Options button to select from several exporting options.

Step 3:	Click the OK button in the latter dialog to export and store (you will need to select a file name) the file in Excel format.


  Data Management - Export File to Quattro

You may export STATISTICA files to Quattro.  Quattro files may contain up to 256 columns and 8192 rows.  When you select the Quattro option from the Export Data to dialog, the Quattro Export Options dialog will open.

Quattro Export Options dialog:

Case Names

Variable Names

Variables With Text Values

Note that if only the text values or value labels are exported, then the resulting column in the Quattro file will have the original STATISTICA variable name, rather than using the $ or @ conventions.

Example


  Export File to Quattro - Case Names

Select this option to export the case names to the first column of the Quattro file.


  Export File to Quattro - Variable Names

When this option is selected, STATISTICA will export the variable names into the first row of the Quattro spreadsheet.  If this option is de-selected, then variable names will not be included in the Quattro file.


  Export File to Quattro - Variables with Text Values

STATISTICA "double variables" (numeric/text) may be expanded at the user's option to become up to three Quattro columns [representing the numeric values, text values, and (optional) value labels of the STATISTICA variable] with names related to the original STATISTICA variable.  The following options govern the creation of these columns allowing the resulting pairs or triplets of columns in Quattro to be converted back (i.e., "compressed") into individual STATISTICA variables (when the file is imported by STATISTICA).  If all of these options are de-selected, then only those STATISTICA variables which do not have text values will be exported.

Text Values:  If you select this option, then for "double notation" variables, STATISTICA will create text columns of alphanumeric values for that variable.  When this column is created, STATISTICA uses the variable name of the "double notation" variable and adds a $ to the name in the following manner:  if the STATISTICA variable name is shorter than eight characters, then the Quattro text column name will have a $ added to the end; if the name is eight characters long, then the second character will be changed to a $ (this is done to facilitate recombining the numeric and text data if the file is imported once again).

Numeric Values:  When selected, this option creates columns of numeric values associated with the text values columns created from the above option.  If this option is de-selected, then only numeric values from non-"double variables" (i.e., variables without text values) will be present in the exported file.

Long Value Labels:  This option controls the creation of a text columns of variable value labels.  When you select this option, STATISTICA will create a third column of text values representing the Long Value Labels for a variable.  When this column is created, STATISTICA uses the variable name of the "double notation" variable and adds an @ to the name in the following manner:  if the variable name is shorter than eight characters, then the name of the Quattro text column will have an @ added to the end; if the name of the STATISTICA variable is eight characters long, then the second character will be changed to an @).


  Exporting a File to Quattro

To export a STATISTICA file to Quattro, follow the steps outlined below.

Step 1:	Select the Export Data option from the File pull-down menu to open the Export Data to dialog.

Step 2:	Select Quattro as the type of file into which the data will be exported.  You may click on the Options button to select from several exporting options.

Step 3:	Click the OK button in the latter dialog to export and store (you will need to select a file name) the file in Quattro format.


  Data Management - Export File to Lotus

STATISTICA can export to Lotus 1-2-3 Release 1A, 2.01/2.2, Release 3, Lotus 1-2-3 for Windows (releases 1, 1.1, and 4), and Symphony format files.  Lotus files may contain up to 256 columns and 8192 rows.  If the current STATISTICA file is larger than this, then you can create Subsets of the file and export each of those subsets separately.

Export options for Lotus 123 Release 1A and 2/2.2, Release 3, and Lotus 1-2-3 for Windows are given below.  The options are the same for each version with the exception of Lotus 1-2-3 Release 3 and Lotus 1-2-3 for Windows, which has the following new option:

New Export Option Define Sheets

When you select the Lotus option from the Export Data to dialog, the Lotus Export Options dialog will open.  The options from this dialog that are common to all Lotus versions are discussed below.

Lotus Export Options dialog:

Case Names

Variable Names

Variables With Text Values

As when exporting to Megafile Manager, if only the text values or value labels are exported, the resulting column in the Lotus file will have the original STATISTICA variable name, rather than using the $ or @ conventions.

Example


  Export File to Lotus - Define Sheets

How Many:  By default, all variables in the STATISTICA file are exported as one worksheet.  If desired, STATISTICA variables may be equally divided among a specified number of worksheets.  You can specify that number here.

By Names:  Alternately, the STATISTICA variables may be assigned to specific worksheets by names: variables named A_A through A_IV will be placed in worksheet A, variables B_A through B_IV in worksheet B, etc.  (This will be the case if the option From Spreadsheet was selected when originally importing variable names from a Release 3 or Lotus 1-2-3 for Windows worksheet.)


  Export File to Lotus - Case Names

Select this option to export the case names to the first column of the Lotus file.


  Export File to Lotus - Variable Names

When this option is selected, STATISTICA will export the variable names into the first row of the Lotus spreadsheet.  If this option is de-selected, then variable names will not be included in the Lotus file.


Export File to Lotus - Variable with Text Values

  Export File to Lotus - Variables with Text Values

STATISTICA "double variables" (numeric/text) may be expanded at the user's option to become up to three Lotus columns [representing the numeric values, text values, and (optional) value labels of the STATISTICA variable] with names related to the original STATISTICA variable.  The following options govern the creation of these columns allowing the resulting pairs or triplets of columns in Lotus to be converted back (i.e., "compressed") into individual STATISTICA variables (when the file is imported by STATISTICA).  If all of these options are de-selected, then only those STATISTICA variables which do not have text values will be exported.

Text Values:  If you select this option, then for "double notation" variables, STATISTICA will create text columns of alphanumeric values for that variable.  When this column is created, STATISTICA uses the variable name of the "double notation" variable and adds a $ to the name in the following manner:  if the STATISTICA variable name is shorter than eight characters, then the Lotus text column name will have a $ added to the end; if the name is eight characters long, then the second character will be changed to a $ (this is done to facilitate recombining the numeric and text data if the file is imported once again).

Numeric Values:  When selected, this option creates columns of numeric values associated with the text values columns created from the above option.  If this option is de-selected, then only numeric values from non-"double variables" (i.e., variables without text values) will be present in the exported file.

Long Value Labels:  This option controls the creation of a text columns of variable value labels.  When you select this option, STATISTICA will create a third column of text values representing the Long Value Labels for a variable.  When this column is created, STATISTICA uses the variable name of the "double notation" variable and adds an @ to the name in the following manner:  if the variable name is shorter than eight characters, then the name of the Lotus text column will have an @ added to the end; if the name of the STATISTICA variable is eight characters long, then the second character will be changed to an @).


  Exporting a File to Lotus

To export a STATISTICA file to Lotus, follow the steps outlined below.

Step 1:	Select the Export Data option from the File pull-down menu to open the Export Data to dialog.

Step 2:	Select Lotus as the type of file into which the data will be exported and then select the Lotus version (123/1, 123/2, 123/3, 123/w, and Symph).  You may click on the Options button to select from several exporting options.

Step 3:	Click the OK button in the latter dialog to export and store (you will need to select a file name) the file in Lotus format.


  Data Management - Export File to Paradox

STATISTICA exports to Paradox file formats.  When you select the Paradox option from the Export Data to dialog, the Paradox Export Options dialog will open.

Paradox Export Options dialog:

Case Names

Variables With Text Values

Note that if only the text values or labels are exported, then the resulting column in the Paradox file will have the original STATISTICA variable name, rather than using the $ or @ conventions.

Example


  Export File to Paradox - Case Names

Select this option to export the case names as the first field of the Paradox file.


  Export File to Paradox - Variables with Text Values

STATISTICA "double variables" (numeric/text) may be expanded at the user's option to become up to three Paradox columns [representing the numeric values, text values, and (optional) value labels of the STATISTICA variable] with names related to the original STATISTICA variable.  The following options govern the creation of these columns allowing the resulting pairs or triplets of columns in Paradox to be converted back (i.e., "compressed") into individual STATISTICA variables (when the file is imported by STATISTICA).  If all of these options are de-selected, then only those STATISTICA variables which do not have text values will be exported.

Text Values:  If you select this option, then for "double notation" variables, STATISTICA will create text columns of alphanumeric values for that variable.  When this column is created, STATISTICA uses the variable name of the "double notation" variable and adds a $ to the name in the following manner:  if the STATISTICA variable name is shorter than eight characters, then the Paradox text column name will have a $ added to the end; if the name is eight characters long, then the second character will be changed to a $ (this is done to facilitate recombining the numeric and text data if the file is imported once again).

Numeric Values:  When selected, this option creates columns of numeric values associated with the text values columns created from the above option.  When this variable is exported to Paradox STATISTICA will use the same variable name as before.  If this option is de-selected, then only numeric values from non-"double variables" (i.e., variables without text values) will be present in the exported file.

Long Value Labels:  This option controls the creation of a text column of variable value labels.  When you select this option, STATISTICA will create a third column of text values representing the Long Value Labels for a variable.  When this column is created, STATISTICA uses the variable name of the "double notation" variable and adds an @ to the name in the following manner:  if the variable name is shorter than eight characters, then the name of the Paradox text column will have an @ added to the end; if the name of the STATISTICA variable is eight characters long, then the second character will be changed to an @).


  Exporting a File to Paradox

To export a STATISTICA file to Paradox, follow the steps outlined below.

Step 1:	Select the Export Data option from the File pull-down menu to open the Export Data to dialog.

Step 2:	Select Paradox as the type of file into which the data will be exported.  You may click on the Options button to select from several exporting options.

Step 3:	Click the OK button in the latter dialog to export and store (you will need to select a file name) the file in Paradox format.


  Data Management - Export File to ASCII

STATISTICA can export to both ASCII fix (undelimited) and ASCII free (delimited) files.  Each type of ASCII file has its own dialog of options.  For more information on these options, click on the appropriate option below.

Export ASCII free file

Export ASCII fix file

Note that instead of using these export options in the Data Management module, you can export ASCII files from any module of STATISTICA using the Quick Export options.  Quick Export does not support some of the specialized options offered in these (comprehensive) ASCII export procedures, however, it is usually much faster.


  Data Management - Export File to ASCII Free Format

STATISTICA can export to ASCII free format files.  If you choose instead to export to ASCII fixed format files, then values which are shorter than the format are padded with blanks so that the absolute position of each value is "fixed" within the line in the output file.  Free format (delimited) ASCII files are created without padding values to fill out variable formats since user-specified characters are used to separate or delimit successive values.  When you select the ASCII Free option from the Export Data to dialog, the ASCII Free Export Options dialog will open.

ASCII Free Export Options dialog:

Case Names

Variable With Text Values

Line Length

Separators

Example


  Export File to ASCII Free Format - Case Names

When you select this option, case names will be exported as the first variable in the file.


  Export File to ASCII Free Format - Variable with Text Values

These options will allow you to export only the Text and/or Numeric components of STATISTICA "double variables."  If both options are selected, then a column will be created for the text values of the "double variable" and another column will be created for the numeric values of that variable.  If both options are de-selected, then only those STATISTICA variables which do not contain text values will be exported.

Text Values:  Select this option if you want to export the text values of a STATISTICA "double variable."

Numeric Values:  Select this option if you want to export the numeric values of a STATISTICA "double variable."


  Export File to ASCII Free Format - Line Length

The number of variables per line in the output file is determined by the specified line length.  Enter the length of the line in the ASCII file here (values can be from 80 to 4000).  If the specified line length is insufficient to contain all variables, then the line will be broken after the last complete variable (i.e., a variable will not be divided across lines).  If unbroken records are desired (i.e., each record occupies only one line in the output file), specify a line length no less than the sum of all variable formats.


  Export File to ASCII Free Format - Separators

Field Separator:  Click on this button to bring up the ASCII Free Separator dialog from which you can select a single character to be used to separate successive values in the output file (by default, a "," will be used as the field separator).  The numeric characters 0 through 9, period (decimal point), "+" and "-" are not permitted as delimiters.

Row Separator:  The Row Separator serves to indicate the end of each of the original rows (cases) of data (one row of data may extend across several lines of the output file).  Click on this button to bring up the ASCII Free Separator dialog from which you can select a single character to be used to indicate the completion of each row of data in the output file (by default, a "," will be used as the row separator).  The numeric characters 0 through 9, period (decimal point), "+" and "-" are not allowed as row separators.  Note that if the length of the row in the STATISTICA file is longer than the specified output Line Length (see above), then the row will extend across one or more lines in the output file.


  Exporting a File to ASCII Free Format

To export a STATISTICA file to ASCII, follow the steps outlined below.

Step 1:	Select the Export Data option from the File pull-down menu to open the Export Data to dialog.

Step 2:	Select ASCII as the type of file into which the data will be exported and Free as the ASCII version.  You may click on the Options button to select the row and field separators as well as other exporting options.

Step 3:	Click the OK button in the latter dialog to export and store (you will need to select a file name) the file in ASCII Free format.


  Data Management - Export File to ASCII Fix Format

Unlike ASCII free format files, fixed format (undelimited) ASCII files will be created using the current variable formats (values which are shorter than the format are padded with blanks so that the absolute position of each value is "fixed" within the line in the output file).  When you select the ASCII Fix option from the Export Data to dialog, the ASCII Fix Export Options dialog will open.

ASCII Fix Export Options dialog:

Case Names

Variable With Text Values

Line Length

Example


  Export File to ASCII Fix Format - Case Names

When you select this option, case names will be exported as the first variable in the file.


  Export File to ASCII Fix Format - Variable with Text Values

These options will allow you to export only the Text and/or Numeric components of STATISTICA "double variables."  If both options are selected, then a column will be created for the text values of the "double variable" and another column will be created for the numeric values of that variable.  If both options are de-selected, then only those STATISTICA variables which do not contain text values will be exported.

Text Values:  Select this option if you want to export the text values of a STATISTICA "double variable."

Numeric Values:  Select this option if you want to export the numeric values of a STATISTICA "double variable."


  Export File to ASCII Fix Format - Line Length

The number of variables per line in the output file is determined by the specified line length.  Enter the length of the line in the ASCII file here (values can be from 80 to 4000).  If the specified line length is insufficient to contain all variables, then the line will be broken after the last complete variable (i.e., a variable will not be divided across lines).  If unbroken records are desired (i.e., each record occupies only one line in the output file), specify a line length no less than the sum of all variable formats.


  Exporting a File to ASCII Fix Format

To export a STATISTICA file to ASCII, follow the steps outlined below.

Step 1:	Select the Export Data option from the File pull-down menu to open the Export Data to dialog.

Step 2:	Select ASCII as the type of file into which the data will be exported and Fix as the ASCII version.  You may click on the Options button to select from several exporting options.

Step 3:	Click the OK button in the latter dialog to export and store (you will need to select a file name) the file in ASCII Fix format.


Data Management - Export File CSS/3

  Data Management - Export File to CSS/3

You can export a file in STATISTICA for Windows to the CSS/3 (i.e., CSS:STATISTICA or STATISTICA/DOS) format.  These DOS files support most of the format specifications and conventions of STATISTICA for Windows and all of them are automatically transferred when you use this export option with the following exceptions:

•  If the current variable long names are longer than 40 characters (the limit in the DOS version format), then they are truncated to 40 characters;

•  The file notes/comments are not supported in the DOS version (only the one-line file header is exported);

•  The information about the spreadsheet color, style, and fonts is not exported.


  Data Management/Megafile Manager - Import ASCII Free - Separators

The ASCII Free Separators dialog will open whenever you want to choose an undefined character as a delimiter when importing ASCII Free Format Files.  This dialog contains a list of characters from which you can choose.  The characters or symbols listed in this dialog are as follows (CR/LF stands for carriage return/line feed):

<space>  <tab>  <CR/LF>

!  "  #  $  %  &  '  )  *  (  ,  [  \  +  -  .

0  1  2  3  4  5  6  7  8  9

]  ^  _  /  :  ;  <  =  >  ?  @  `  {  |  }  ~

Upper case alphabet (i.e., A  B  C . . . Z)

Lower case alphabet (i.e., a  b  c . . . z)

Note that if you want to import numeric values, you should not specify any of the numbers (i.e., 0 through 9) or the "+", "-", or "." as separators.


  Data Management/Megafile Manager - Export to ASCII Free - Separators

The ASCII Free Separators dialog will open whenever you want to choose field or row separators when exporting ASCII Free Format Files.  This dialog contains a list of characters from which you can choose.  The characters or symbols listed in this dialog are as follows (CR/LF stands for carriage return/line feed):

<space>  <tab>  <CR/LF>

!  "  #  $  %  &  '  )  *  (  ,  [  \  +  -  .

0  1  2  3  4  5  6  7  8  9

]  ^  _  /  :  ;  <  =  >  ?  @  `  {  |  }  ~

Upper case alphabet (i.e., A  B  C . . . Z)

Lower case alphabet (i.e., a  b  c . . . z)

Note that if you want to export numeric values, you should not specify any of the numbers (i.e., 0 through 9) or the "+", "-", or "." as separators.


  Data Management - Sort Data

The Sort Data facilities are accessible from the Data Management module.

STATISTICA performs hierarchical (nested) sorting on the basis of user-specified key variables (i.e., if two cases have identical values in a given key, the values of the next key are used to determine ranking).  When you select the Sort option from the Analysis pull-down menu (or the Sort Cases option from the Data Management Startup Panel), the Sort Options dialog will open.  You can choose up to seven key variables by which to sort in this dialog.  Each key variable has the same set of options (described below).

Sort Options dialog:

Variable

Case Name

Sorting Order

Sorting Mode

More Keys

Example


Data Management - Variable Name

  Sort Data - Variable Name

Type in the key variable name or double click on this window to open the Select Variable dialog.  The Select Variable dialog will display a list of variables from which you can select the desired key variable.


Data Management - Case Name

  Sort Data - Case Name

Select this option to sort the data by case names.  Note that you will also need to set the Sorting Mode to Text when you select this option.


Data Management - Sort Order

  Sort Data - Sort Order

Choose to use the Ascending or Descending sort order.


Data Management - Sort Mode

  Sort Data - Sort Mode

Sort either by Numeric or Text values of the key variable.  When sorting based on Text values, if some numeric codes do not have text equivalents, then STATISTICA assumes that Text is smaller than Numeric (i.e., when sorting in ascending order, all text values will be at the top, followed by the numeric values without text equivalents).


Data Management - More Keys

  Sort Data - More Keys

When this dialog first opens, only three keys are displayed.  If you need to enter more keys than this, click on the More Keys button to increase the number of displayed keys to seven (the maximum).


  Data Management - Sorting Data

In this example let's use the examples data file Adstudy.sta and sort the data file by two key variables (Gender and Advert).

Step 1:	After opening the Sort Options dialog, enter Gender as the first key variable to sort by (Key 1) and Advert as the second key variable (Key 2).

Step 2:	Specify for each of the key variables, whether you want to sort in ascending or descending order for numeric or text values.  For this example, accept the default selections of Ascending and Numeric.

Step 3:	Click Ok to proceed with the sorting operation.


  Data Management - Subset

The Subset facilities are accessible from the Data Management module.

Unlike the Case Selection Conditions which allow you to temporarily limit the data set (to be analyzed) to a subset, use this Data Management option to extract a section (subset) of the current file to be stored under a new name.  When you select this option from either the Analysis pull-down menu or the Data Management Start-up Panel, the Create a Subset dialog will open.  After you have created this subset file, you will need to save it under a different file name using the Save As option from the File pull-down menu.

Create a Subset dialog:

Variables:  Click on this button to bring up the Select Variables dialog from which you may select the variables to be included in the subset file.

Cases:  Click on this button to open the Case Selection Conditions dialog in which you may enter conditions defining the selection of cases to be included in the subset file.


Data Management - Variable Names/Format

  Data Management - Verify Names/Format

The Verification facilities are accessible from the Data Management module.

This verification facility may be used to check for (and adjust) the "fit" of column Formats (see below) to the data, to check for duplicated column names, or to check their compliance with selected standards (e.g., STATISITCA, dBASE, SPSS).  When you select this option from the Analysis pull-down menu or the Data Management Start-up Panel, the Verify Names/Format dialog will open.

Verify Names/Format dialog:

Variable Names:  This option will check the correctness of the variables names according to the requirements of STATISTICA, dBASE, or SPSS, or it will create standard names.  Select one of the options described below.  If an invalid or duplicated name is found, a Name Verification dialog will open allowing you to correct the name (either of the two names can be edited if a duplicate is found).

Do Not Verify:  Select this option if you are interested in only verifying variable formats.

STATISTICA Correctness:  This option is used to check all variable names for duplications, either for compliance with the requirements of STATISTICA BASIC, or prior to exporting the file.

dBASE Correctness:  When selected, this option checks for compliance with the requirements of dBASE.  All variables must have names which may contain the letters A-Z, a-z, the digits 0-9, and the underscore (_).  Each variable name must begin with a letter, and all variable names must be unique (which may be checked by using the STATISTICA Correctness option above).

SPSS Correctness:  When selected, this option checks for agreement with the requirements of SPSS.  All variables must have names which may contain the letters A-Z, a-z, the digits 0-9, underscore (_), period (.), @, #, and $.  Each variable name must begin with either a letter, $, or @, and cannot be one of the reserved SPSS keywords (ALL, AND, BY, EQ, GE, GT, LE, LT, NE, NOT, OR, TO, and WITH).

Create Standard Names:  When selected, this option assigns "standard" names (a prefix plus a sequential number) to all variables through the following options.

•  Prefix:  Specify a five-letter prefix for standard variable names.

•  Start Number:  Select the starting value for the numeric portion of the names (useful when you intend to merge the file with another STATISTICA file).

Formats:  When you select Yes, STATISTICA will examine all specified variables to determine whether the variable formats are an appropriate "fit" to the data values.  For example, the value 1234.5 entered in a column whose format is 4.3 would result in the variable format being expanded to 8.3 in order to accommodate the data (represented as 1234.500).  Also, if the format is longer than any of the values in the column (e.g., the value 12.34 in a variable with a 15.7 format) the format length will be adjusted to the actual length of the longest value (however, the number of decimal places remains unchanged).


  Data Management - Verify Data

The Verification facilities are accessible from the Data Management module.

Once the data (entered or imported) are already in the file, you may need to verify their integrity (logical consistency) and completeness.  Although some types of errors in the data may never be detected, there are many ways to perform data verification based on general criteria that the data are expected to meet.

For example, the verification can be as simple as checking whether values in a variable are "legal" (e.g., only 1 and 2 might be allowed for Gender) or whether they fall within allowed ranges of values (e.g., Age must be more than 0 and less than 200).  It can also be as complex as checking multiple logical conditions that some values must meet in relation to other values (a relatively simple example of conditional verification: if a person is a male or less than a certain age, then the number of pregnancies for that person cannot be more than zero).  In order to apply these conditions, you would specify (for example):

Invalid if:  (v1 = 'MALE' or AGE < 14) and PREGN <> 0

STATISTICA provides such a verification facility when you select the Verify Data option from the Analysis pull-down menu (the Verify Data dialog will open).  After you specify the verification conditions (following the conventions described below) press OK and the data set (or the selected range) will be tested sequentially (one case at a time) for its consistency with the conditions you specified.  When a case is found which does not meet the conditions, then the respective row of data in the spreadsheet will be highlighted and the Data Verification dialog will open allowing you to either ignore it (and continue or stop the verification) or edit (correct) the case.  After you edit the case, press the Cont (continue) button in the lower left corner of the screen to continue the verification.

Verify Data dialog:

A case will be considered valid if

Condition

Review Variables

Open All

Save All

Range


Verify Data - A Case will be Considered Invalid If

  Verify Data - A Case will be Considered Valid If

Select one of the two options described below to define when a case will be considered valid.

All Conditions are Met:  When you select this option, a case will be considered correct only if all of the conditions (defined below) are met.

At Least One Condition is Met:  When you select this option, a case will be considered correct if at least one of the defined conditions is met.


  Verify Data - Condition

Define a list of up to 16 different Verification Conditions as the criteria of correctness.

Verification Syntax Summary:  For more information and examples on selection (verification) conditions, see Case Selection Conditions.

•	Refer to variables either by their numbers (e.g., v1 = 1) or their names (e.g., Gender = 1); note that you can type variable names in either upper or lower case letters (i.e., 'GENDER' is equivalent to 'gender').

•	Enclose text values of a variable in single quotation marks (e.g., v1 = 'MALE'); note that you can type text values in either upper or lower case letters (i.e., 'Yes' is equivalent to 'YES').

•	Use parentheses to specify complex logical conditions (see the example above) or change the default precedence of operators.

•	Logical Operators: =	(equal)

# , <>, ><	(not equal)

<	(less than)

>	(greater than)

<=	(less than or equal to)

>=	(greater than or equal to)

NOT, ~	(logical NOT)

AND, &	(logical AND)

OR, !	(logical OR)

Valid/Invalid If:  Select whether the value will be considered Valid or Invalid If the verification condition is met.

Open/Save:  Clicking this button will open the Case Selection Conditions dialog from which you can either open a file (file name extension *.sel) containing previous case selection conditions to be used as a verification conditions or save the current verification conditions (use the Open All and Save All to open/save the entire set, see below).

Edit field:  Enter the case selection condition that will be used as verification criteria in this edit window (e.g., v1 = 1 and v2 = 'MALE' or v3 = 2 and v4 = 'YES').  For more information on valid case selection conditions, see the Case Selection Conditions dialog.


  Verify Data - Review Variables

Click on this button to open the Single Variable List in which you can review the variable names and numbers.


  Verify Data - Open All

When you click on this button, the Open Verify Conditions File dialog will open from which you can select a file with multiple case selection conditions (including all options specified in this dialog) and open them for use as verification conditions.


  Verify Data - Save All

When you click on this button, the Save Verify Conditions File dialog will open from which you can specify the file to save these verification conditions in.


  Verify Data - Range

Define the range of values to be verified (From Case number, To Case number).


  Data Management - Data Verification

During the verification process (see the Verify Data dialog), when a case is found which does not meet the specified conditions, the respective row (case) of the spreadsheet will be highlighted and the Data Verification dialog will open, displaying the following options:

Data Verification dialog:

Review/Edit the Data:  When you click on this option, you will be allowed to edit the data that did not meet the condition(s) before continuing (click on the Continue icon) the verification process.

Ignore and Continue:  Clicking this button will ignore the case that did not meet the condition(s) and continue checking the next case.

Ignore and Exit:  Clicking this button will ignore the case that did not meet the condition(s), stop the verification process, and exit to the Verify Data dialog.


  Data Management/Megafile Manager - Duplicate Names

If duplicate names are encountered while verifying the correctness of variable names in the Verify Names/Format dialog, then the Name Verification dialog will open allowing the duplicated names to be edited.

Name Verification dialog:

Variable Names:  The duplicate variable names will be listed in an edit field next to their variable number.  You can edit either or both of the names.

Accept button:  Click this button to accept the edited variable names and proceed with the verification process.

Break button:  Clicking this button will stop the verification process (all changes to names up to this point will be saved).

Undo All button:  Click this button to stop the verification procedure and undo all changes made during verification.


  Data Management/Megafile Manager - Incorrect Variable Name

If incorrect names are encountered while verifying the correctness of variable names in the Verify Names/Format dialog, then the Name Verification dialog will open allowing the incorrect names to be edited.

Name Verification dialog:

Variable Name:  The incorrect variable name will be listed in an edit field next to its variable number.  You can edit the name here.

Ignore button:  Click this button if you want to leave the variable name as it appears (uncorrected).

Accept button:  Click this button to accept the edited variable name and proceed to the next incorrect name.

Break button:  Clicking this button will stop the verification process (all changes to names up to this point will be saved).

Undo All button:  Click this button to stop the verification procedure and undo all changes made during verification.


  Data Management - Data Standardization

Options to standardize values in a selected (highlighted) block are available from the spreadsheet flying menu (accessible by pressing the right-mouse-button; see Standardize Columns).  They allow you to standardize arbitrarily selected subsets of values and to perform the standardization not only within variables (i.e., by column) but also by row.

This standardization procedure, however (available in the Data Management module), is different in that it works not on highlighted blocks of data in the spreadsheet but on all values of the selected variable(s) and while processing data from these variable(s) it takes into account the currently specified case selection conditions and case weights.

In standardization, all values of selected variables are replaced by standardized values which are computed as follows:  Std. Score = (raw score - mean) / std. deviation.  When you select this option from the Analysis pull-down menu or from the Data Management Start-up Menu, the Standardization of Values dialog will open from which you can select the variable to be standardized.

If the standardized variable has any text values, then the corresponding numeric values (assigned to the text values) will be adjusted accordingly (otherwise, after standardization, most values would "lose" their alphanumeric components).  The first six significant digits will be used as numeric equivalents of text values.

Standardization of Values dialog:

Variables

Cases

Weight


  Data Management - Variables

By default, all variables in the file will be standardized.  If desired, standardization can be performed on only selected variables.  When you click on this button, the Select Variables dialog will open from which you can select the variables to be standardized.


  Data Management - Cases

By default, all cases are used in computing means and standard deviations for each variable.  If desired, case selection conditions may be used, in which instance, the mean and standard deviation will be computed for only the selected cases, and only those cases will be standardized.  This allows you to perform a subset standardization; e.g., you can standardize values once for "Males" and then for "Females" to obtain standardized scores according to their respective (different) group means and standard deviations.  When you click on this button, the Case Selection Conditions dialog will open from which you can specify new case selection conditions or open existing conditions.


  Data Management - Weight

By default, each (selected) case contributes equally to the computation of the variable means and standard deviations.  You can select a weighting variable by clicking this button to open the Define Weight dialog.  By specifying one variable as containing weights, the influence of each case can be varied by an amount proportional to the value of the weight variable for the case.  (Although STATISTICA actually uses a faster algorithm, this system can be interpreted as reading each case a number of times that is equivalent to the current value of its weight.)


  Data Management - Missing Data Replacement

This option will permanently replace missing data values for selected variables with the means of those variables (when applicable, this option is also available in many STATISTICA modules as one of the missing data handling options and is then temporary, i.e., will apply only to the current analysis).  When you select this option, the Missing Data Replacement dialog will open.

Missing Data Replacement dialog:

Variables

Cases

Weight


  Missing Data Replacement - Variables

By default, all variables in the file will be included in missing data replacement.  If desired, replacement can be performed on only selected variables.  When you click on this button, the Select Variables dialog will open from which you can select specific variables.


  Missing Data Replacement - Cases

By default, all cases are used in computing means for each variable.  If desired, case selection conditions may be used, in which instance, the mean will be computed for only the selected cases, and only those cases will have their missing data replaced.  When you click on this button, the Case Selection Conditions dialog will open from which you can specify new case selection conditions or open existing conditions.


  Missing Data Replacement - Weight

By default, each (selected) case contributes equally to the computation of the variable means.  You can select a weighting variable by clicking this button to open the Define Weight dialog.  By specifying one variable as containing weights, the influence of each case can be varied by an amount proportional to the value of the weight variable for the case.  (Although STATISTICA actually uses a faster algorithm, this system can be interpreted as reading each case a number of times that is equivalent to the current value of its weight.)


  Data Management - Convert to a Megafile Manager File

This option will allow you to quickly open the Save Exported File As dialog in order to export (or convert) a STATISTICA data file to a Megafile Manager file.  For more information on these export options, see STATISTICA Export Options.


Elementary Concepts

Overview of Elementary Concepts in Statistics

In this introduction, we will briefly discuss those elementary statistical concepts that provide the necessary foundations for more specialized expertise in any area of statistical data analysis.  The selected topics illustrate the basic assumptions of most statistical methods and/or have been demonstrated in research to be necessary components of one's general understanding of the "quantitative nature" of reality (Nisbett, et al., 1987).

Because of space limitations, we will focus mostly on the functional aspects of the concepts discussed and the presentation will be very short.  Further information on each of those concepts can be found in the Introductory Overview and Examples sections of this manual and in statistical textbooks.  Recommended introductory textbooks are:  Kachigan (1986), and Runyon and Haber (1976); for a more advanced discussion of elementary theory and assumptions of statistics, see the classic books by Hays (1988), and Kendall and Stuart (1979).

To review the complete, continuous text see, Elementary Concepts in Statistics.

For information on a specific topic listed below, see:

What are variables?

Correlational vs. experimental research

Dependent vs. independent variables

Measurement scales

Relations between variables

Why relations between variables are important

Two basic features of every relation between variables

What is "statistical significance" (p-level)

How to determine that a result is "really" significant

Statistical significance and the number of analyses performed

Strength vs. reliability of a relation between variables

Why stronger relations between variables are more significant

Why significance of a relation between variables depends on the size of the sample

Example: "Baby boys to baby girls ratio"

Why small relations can be proven significant only in large samples

Can "no relation" be a significant result?

How to measure the magnitude (strength) of relations between variables

Common "general format" of most statistical tests

How the "level of statistical significance" is calculated

Why the "Normal distribution" is important

Illustration of how the normal distribution is used in statistical reasoning (induction)

Are all test statistics normally distributed?

How do we know the consequences of violating the normality assumption?


Elementary Concepts - What are Variables?

Variables are things that we measure, control, or manipulate in research.  They differ in many respects, most notably in the role they are given in our research and in the type of measures that can be applied to them.


Elementary Concepts - Correlational vs. Experimental Research

Most empirical research belongs clearly to one of these two general categories:  In correlational research we do not (or at least try not to) influence any variables but only measure them and look for relations (correlations) between some set of variables, such as blood pressure and cholesterol level.  In experimental research, we manipulate some variables and then measure the effects of this manipulation on other variables; for example, a researcher might artificially increase blood pressure and then record cholesterol level.  Data analysis in experimental research also comes down to calculating "correlations" between variables, specifically, those manipulated and those affected by the manipulation.  However, experimental data may potentially provide qualitatively better information:  Only experimental data can conclusively demonstrate causal relations between variables.  For example, if we found that whenever we change variable A then variable B changes, then we can conclude that "A influences B."  Data from correlational research can only be "interpreted" in causal terms based on some theories that we have, but correlational data cannot conclusively prove causality.


Elementary Concepts - Dependent vs. Independent Variables

Independent variables are those that are manipulated whereas dependent variables are only measured or registered.  This distinction appears terminologically confusing to many because, as some students say, "all variables depend on something."  However, once you get used to this distinction, it becomes indispensable.  The terms dependent and independent variable apply mostly to experimental research where some variables are manipulated, and in this sense they are "independent" from the initial reaction patterns, features, intentions, etc. of the subjects.  Some other variables are expected to be "dependent" on the manipulation or experimental conditions.  That is to say, they depend on "what the subject will do" in response.  Somewhat contrary to the nature of this distinction, these terms are also used in studies where we do not literally manipulate independent variables, but only assign subjects to "experimental groups" based on some pre-existing properties of the subjects.  For example, if in an experiment, males are compared with females regarding their white cell count (WCC), Gender could be called the independent variable and WCC the dependent variable.


Elementary Concepts - Measurement Scales

Variables differ in "how well" they can be measured, i.e., in how much measurable information their measurement scale can provide.  There is obviously some measurement error involved in every measurement, which determines the "amount of information" that we can obtain.  Another factor that determines the amount of information that can be provided by a variable is its "type of measurement scale."  Specifically variables are classified as (a) nominal, (b) ordinal, (c) interval or (d) ratio.

(a) Nominal variables allow for only qualitative classification.  That is, they can be measured only in terms of whether the individual items belong to some distinctively different categories, but we cannot quantify or even rank order those categories.  For example, all we can say is that 2 individuals are different in terms of variable A (e.g., they are of different race), but we cannot say which one "has more" of the quality represented by the variable.  Typical examples of nominal variables are gender, race, color, city, etc.

(b) Ordinal variables allow us to rank order the items we measure in terms of which has less and which has more of the quality represented by the variable, but still they do not allow us to say "how much more."  A typical example of an ordinal variable is the socioeconomic status of families.  For example, we know that upper-middle is higher than middle but we cannot say that it is, for example, 18% higher.  Also this very distinction between nominal, ordinal, and interval scales itself represents a good example of an ordinal variable.  For example, we can say that nominal measurement provides less information than ordinal measurement, but we cannot say "how much less" or how this difference compares to the difference between ordinal and interval scales.

(c) Interval variables allow us not only to rank order the items that are measured, but also to quantify and compare the sizes of differences between them.  For example, temperature, as measured in degrees Fahrenheit or Celsius, constitutes an interval scale.  We can say that a temperature of 40 degrees is higher than a temperature of 30 degrees, and that an increase from 20 to 40 degrees is twice as much as an increase from 30 to 40 degrees.

(d) Ratio variables are very similar to interval variables; in addition to all the properties of interval variables, they feature an identifiable absolute zero point, thus they allow for statements such as x is two times more than y.  Typical examples of ratio scales are measures of time or space.  For example, as the Kelvin temperature scale is a ratio scale, not only can we say that a temperature of 200 degrees is higher than one of 100 degrees, we can correctly state that it is twice as high.  Interval scales do not have the ratio property.  Most statistical data analysis procedures do not distinguish between the interval and ratio properties of the measurement scales.


Elementary Concepts - Relations between Variables

Regardless of their type, two or more variables are related if in a sample of observations, the values of those variables are distributed in a consistent manner.  In other words, variables are related if their values systematically correspond to each other for these observations.  For example, Gender and WCC would be considered to be related if most males had high WCC and most females low WCC, or vice versa; Height is related to Weight because typically tall individuals are heavier than short ones; IQ is related to the Number of Errors in a test, if people with higher IQ's make fewer errors.


Elementary Concepts - Why Relations between Variables Are Important

Generally speaking, the ultimate goal of every research or scientific analysis is finding relations between variables.  The philosophy of science teaches us that there is no other way of representing "meaning" except in terms of relations between some quantities or qualities; either way involves relations between variables.  Thus, the advancement of science must always involve finding new relations between variables.  Correlational research involves measuring such relations in the most straightforward manner.  However, experimental research is not any different in this respect.  For example, the above mentioned experiment comparing WCC in males and females can be described as looking for a correlation between two variables: Gender and WCC.  Statistics does nothing else but help us evaluate relations between variables.  Actually, all of the hundreds of procedures that are described in this manual can be interpreted in terms of evaluating various kinds of inter-variable relations.


Elementary Concepts - Two Basic Features of Every Relation between Variables

The two most elementary formal properties of every relation between variables are the relation's (a) magnitude (or "size") and (b) its reliability (or "truthfulness").

(a) Magnitude (or "size").  The magnitude is much easier to understand and measure than reliability.  For example, if every male in our sample was found to have a higher WCC than any female in the sample, we could say that the magnitude of the relation between the two variables (Gender and WCC) is very high in our sample.  In other words, we could predict one based on the other (at least among the members of our sample).

(b) Reliability (or "truthfulness").  The reliability of a relation is a much less intuitive concept, but still extremely important.  It pertains to the "representativeness" of the result found in our specific sample for the entire population.  In other words, it says how probable it is that a similar relation would be found if the experiment was replicated with other samples drawn from the same population.  Remember that we are almost never "ultimately" interested only in what is going on in our sample; we are interested in the sample only to the extent it can provide information about the population.  If our study meets some specific criteria (to be mentioned later), then the reliability of a relation between variables observed in our sample can be quantitatively estimated and represented using a standard measure (technically called p-level or statistical significance level, see What is Statistical Significance?).


Elementary Concepts - What is "Statistical Significance" (p-level)?

The statistical significance of a result is an estimated measure of the degree to which it is "true" (in the sense of "representative of the population").  More technically, the value of the p-level (the term first used by Brownlee, 1960) represents a decreasing index of the reliability of a result.  The higher the p-level, the less we can believe that the observed relation between variables in the sample is a reliable indicator of the relation between the respective variables in the population.  Specifically, the p-level represents the probability of error that is involved in accepting our observed result as valid, that is, as "representative of the population."  For example, a p-level of .05 (i.e.,1/20) indicates that there is a 5% probability that the relation between the variables found in our sample is a "fluke."  In other words, assuming that in the population there was no relation between those variables whatsoever, and we were repeating experiments like ours one after another, we could expect that approximately in every 20 replications of the experiment there would be one in which the relation between the variables in question would be equal or stronger than in ours.  In many areas of research, the p-level of .05 is customarily treated as a "border-line acceptable" error level.


Elementary Concepts - How to Determine that a Result is "Really" Significant

There is no way to avoid arbitrariness in the final decision as to what level of significance will be treated as really "significant."  That is, the selection of some level of significance, up to which the results will be rejected as invalid, is arbitrary.  In practice, the final decision usually depends on whether the outcome was predicted a priori or only found post hoc in the course of many analyses and comparisons performed on the data set, on the total amount of consistent supportive evidence in the entire data set, and on "traditions" existing in the particular area of research.  Typically, in many sciences, results that yield p ≤ .05 are considered borderline statistically significant but remember that this level of significance still involves a pretty high probability of error (5%).  Results that are significant at the p ≤ .01 level are commonly considered statistically significant, and p ≤ .005 or p ≤ .001 levels are often called "highly" significant.  But remember that those classifications represent nothing else but arbitrary conventions that are only informally based on general research experience.


Elementary Concepts - Statistical Significance and the Number of Analysis Performed

Elementary Concepts - Statistical Significance and the Number of Analyses Performed

Needless to say, the more analyses you perform on a data set, the more results will meet "by chance" the conventional significance level.  For example, if you calculate correlations between ten variables (i.e., 45 different correlation coefficients), then you should expect to find by chance that about two (i.e., one in every 20) correlation coefficients are significant at the p ≤ .05 level, even if the values of the variables were totally random and those variables do not correlate in the population.  Some statistical methods that involve many comparisons, and thus a good chance for such errors, include some "correction" or adjustment for the total number of comparisons.  However, many statistical methods (especially simple exploratory data analyses) do not offer any straightforward remedies to this problem.  Therefore, it is up to the researcher to carefully evaluate the reliability of unexpected findings.  Many examples in this manual offer specific advice on how to do this; relevant information can also be found in most research methods textbooks.


Elementary Concepts - Strength vs. Reliability of a Relation between Variables

We said before that strength and reliability are two different features of relationships between variables.  However, they are not totally independent.  In general, in a sample of a particular size, the larger the magnitude of the relation between variables, the more reliable the relation (see Why Stronger Relations between Variables Are More Significant).


Elementary Concepts - Why Stronger Relations between Variables Are More Significant

Assuming that there is no relation between the respective variables in the population, the most likely outcome would be also finding no relation between those variables in the research sample.  Thus, the stronger the relation found in the sample, the less likely it is that there is no corresponding relation in the population.  As you see, the magnitude and significance of a relation appear to be closely related, and we could calculate the significance from the magnitude and vice-versa; however, this is true only if the sample size is kept constant, because the relation of a given strength could be either highly significant or not significant at all, depending on the sample size (see Why Significance of a Relation between Variables Depends on the Size of the Sample).


Why Significance of a Relation Between Variables Depends on the Size of the Sample

Elementary Concepts - Why Significance of a Relation between Variables Depends on the Size of the Sample

If there are very few observations, then there are also respectively few possible combinations of the values of the variables, and thus the probability of obtaining by chance a combination of those values indicative of a strong relation is relatively high.  Consider the following illustration.  If we are interested in two variables (Gender: male/female and WCC: high/low) and there are only four subjects in our sample (two males and two females), then the probability that we will find, purely by chance, a 100% relation between the two variables can be as high as one-eighth.  Specifically, there is a one-in-eight chance that both males will have a high WCC and both females a low WCC, or vice versa.  Now consider the probability of obtaining such a perfect match by chance if our sample consisted of 100 subjects; the probability of obtaining such an outcome by chance would be practically zero.  Let's look at a more general example.  Imagine a theoretical population in which the average value of WCC in males and females is exactly the same.  Needless to say, if we start replicating a simple experiment by drawing pairs of samples (of males and females) of a particular size from this population and calculating the difference between the average WCC in each pair of samples, most of the experiments will yield results close to 0.  However, from time to time, a pair of samples will be drawn where the difference between males and females will be quite different from 0.  How often will it happen?  The smaller the sample size in each experiment, the more likely it is that we will obtain such erroneous results, which in this case would be results indicative of the existence of a relation between gender and WCC obtained from a population in which such a relation does not exist.


Elementary Concepts - "Baby Boys to Baby Girls Ratio"

Elementary Concepts - Example: "Baby Boys to Baby Girls Ratio"

Consider the following example from research on statistical reasoning (Nisbett, et al., 1987).  There are two hospitals: In the first one, 120 babies are born every day, in the other, only 12.  On average, the ratio of baby boys to baby girls born every day in each hospital is 50/50.  However, one day, in one of those hospitals twice as many baby girls were born as baby boys.  In which hospital was it more likely to happen?  The answer is obvious for a statistician, but as research shows, not so obvious for a lay person:  It is much more likely to happen in the small hospital.  The reason for this is that technically speaking, the probability of a random deviation of a particular size (from the population mean), decreases with the increase in the sample size.


Why Small Relations Can Be Proven Significant Only in Large Samples

Elementary Concepts - Why Small Relations Can Be Proven Significant Only in Large Samples

The previous examples (see Example: "Baby Boys to Baby Girls Ratio") indicate that if a relationship between variables in question is "objectively" (i.e., in the population) small, then there is no way to identify such a relation in a study unless the research sample is correspondingly large.  Even if our sample is in fact "perfectly representative" the effect will not be statistically significant if the sample is small.  Analogously, if a relation in question is "objectively" very large (i.e., in the population), then it can be found to be highly significant even in a study based on a very small sample.  Consider the following additional illustration.  If a coin is slightly asymmetrical, and when tossed is somewhat more likely to produce heads than tails (e.g., 60% vs. 40%), then ten tosses would not be sufficient to convince anyone that the coin is asymmetrical, even if the outcome obtained (six heads and four tails) was perfectly representative of the bias of the coin.  However, is it so that 10 tosses is not enough to prove anything?  No, if the effect in question were large enough, then ten tosses could be quite enough.  For instance, imagine now that the coin is so asymmetrical that no matter how you toss it, the outcome will be heads.  If you tossed such a coin ten times and each toss produced heads, most people would consider it sufficient evidence that something is "wrong" with the coin.  In other words, it would be considered convincing evidence that in the theoretical population of an infinite number of tosses of this coin there would be more heads than tails.  Thus, if a relation is large, then it can be found to be significant even in a small sample.


Elementary Concepts - Can "No Relation" Be a Significant Result?

The smaller the relation between variables, the larger the sample size that is necessary to prove it significant.  For example, imagine how many tosses would be necessary to prove that a coin is asymmetrical if its bias were only .000001%!  Thus, the necessary minimum sample size increases as the magnitude of the effect to be demonstrated decreases.  When the magnitude of the effect approaches 0, the necessary sample size to conclusively prove it approaches infinity.  That is to say, if there is almost no relation between two variables, then the sample size must be almost equal to the population size, which is assumed to be infinitely large.  Statistical significance represents the probability that a similar outcome would be obtained if we tested the entire population.  Thus, everything that would be found after testing the entire population would be, by definition, significant at the highest possible level, and this also includes all "no relation" results.


How To Measure the Magnitude (Strength) of Relations Between Variables

Elementary Concepts - How to Measure the Magnitude (Strength) of Relations between Variables

There are very many measures of the magnitude of relationships between variables which have been developed by statisticians; the choice of a specific measure in given circumstances depends on the number of variables involved, measurement scales used, nature of the relations, etc.  Almost all of them, however, follow one general principle: they attempt to somehow evaluate the observed relation by comparing it to the "maximum imaginable relation" between those specific variables.  Technically speaking, a common way to perform such evaluations is to look at how differentiated are the values of the variables, and then calculate what part of this "overall available differentiation" is accounted for by instances when that differentiation is "common" in the two (or more) variables in question.  Speaking less technically, we compare "what is common in those variables" to "what potentially could have been common if the variables were perfectly related."  Let us consider a simple illustration.  Let us say that in our sample, the average index of WCC is 100 in males and 102 in females.  Thus, we could say that on average, the deviation of each individual score from the grand mean (101) contains a component due to the gender of the subject; the size of this component is 1.  That value, in a sense, represents some measure of relation between Gender and WCC. However, this value is a very poor measure, because it does not tell us how relatively large this component is, given the "overall differentiation" of WCC scores.  Consider two extreme possibilities:

(a) If all WCC scores of males were equal exactly to 100, and those of females equal to 102, then all deviations from the grand mean in our sample would be entirely accounted for by gender.  We would say that in our sample, gender is perfectly correlated with WCC, that is, 100% of the observed differences between subjects regarding their WCC is accounted for by their gender.

(b) If WCC scores were in the range of 0-1000, the same difference (of 2) between the average WCC of males and females found in the study would account for such a small part of the overall differentiation of scores that most likely it would be considered negligible.  For example, one more subject taken into account could change, or even reverse the direction of the difference.  Therefore, every good measure of relations between variables must take into account the overall differentiation of individual scores in the sample and evaluate the relation in terms of (relatively) how much of this differentiation is accounted for by the relation in question.


Elementary Concepts - Common "General Format of Most Statistical Tests

Elementary Concepts - Common "General Format" of Most Statistical Tests

Because the ultimate goal of most statistical tests is to evaluate relations between variables, most statistical tests follow the general format that was explained in  How to Measure the Magnitude (Strength) of Relations Between Variables.  Technically speaking, they represent a ratio of some measure of the differentiation common in the variables in question to the overall differentiation of those variables.  For example, they represent a ratio of the part of the overall differentiation of the WCC scores that can be accounted for by gender to the overall differentiation of the WCC scores.  This ratio is usually called a ratio of explained variation to total variation.  In statistics, the term explained variation does not necessarily imply that we "conceptually understand" it.  It is used only to denote the common variation in the variables in question, that is, the part of variation in one variable that is "explained" by the specific values of the other variable, and vice versa.


Elementary Concepts - How the "Level of Statistical Significance" Is Calculated

Let us assume that we have already calculated a measure of a relation between two variables (as explained above).  The next question is "how significant is this relation?"  For example, is 40% of the explained variance between the two variables enough to consider the relation significant?  The answer is "it depends."  Specifically, the significance depends mostly on the sample size.  As explained before, in very large samples, even very small relations between variables will be significant, whereas in very small samples even very large relations cannot be considered reliable (significant).  Thus, in order to determine the level of statistical significance, we need a function that represents the relationship between "magnitude" and "significance" of relations between two variables, depending on the sample size.  The function we need would tell us exactly "how likely it is to obtain a relation of a given magnitude (or larger) from a sample of a given size, assuming that there is no such relation between those variables in the population."  In other words, that function would give us the significance (p) level, and it would tell us the probability of error involved in rejecting the idea that the relation in question does not exist in the population.  This "alternative" hypothesis (that there is no relation in the population) is usually called the null hypothesis.  It would be ideal if the probability function was linear, and for example, only had different slopes for different sample sizes.  Unfortunately, the function is more complex, and is not always exactly the same; however, in most cases we know its shape and can use it to determine the significance levels for our findings in samples of a particular size.  Most of those functions are related to a general type of function which is called normal.


Elementary Concepts - Why the "Normal Distribution" Is Important

The "Normal distribution" is important because in most cases, it well approximates the function that was introduced in How the "Level of Statistical Significance" Is Calculated.  The distribution of many test statistics is normal or follows some form that can be derived from the normal distribution.  In this sense, philosophically speaking, the Normal distribution represents one of the empirically verified elementary "truths about the general nature of reality," and its status can be compared to the one of fundamental laws of natural sciences.  The exact shape of the normal distribution (the characteristic "bell curve") is defined by a function which has only two parameters: mean and standard deviation.

A characteristic property of the Normal distribution is that 68% of all of its observations fall within a range of ±1 standard deviation from the mean, and a range of ±2 standard deviations includes 95% of the scores.  In other words, in a Normal distribution, observations that have a standardized value of less than -2 or more than +2 have a relative frequency of 5% or less.  (Standardized value means that a value is expressed in terms of its difference from the mean, divided by the standard deviation.)  You can explore the exact values of probability associated with different values in the normal distribution using the Probability calculator in Basic Statistics; for example if you enter the Z value (i.e., standardized value) of 4, the associated probability computed by STATISTICA will be less than .0001, because in the normal distribution almost all observations (i.e., more than 99.99%) fall within the range of ±4 standard deviations.


Illustration of How the Normal Distribution is Used in Statistical Reasoning (Induction)

Elementary Concepts - Illustration of How the Normal Distribution Is Used in Statistical Reasoning (Induction)

Recall the example discussed above, where pairs of samples of males and females were drawn from a population in which the average value of WCC in males and females was exactly the same.  Although the most likely outcome of such experiments (one pair of samples per experiment) was that the difference between the average WCC in males and females in each pair is close to zero, from time to time, a pair of samples will be drawn where the difference between males and females is quite different from 0.  How often does it happen?  If the sample size is large enough, the results of such replications are "normally distributed," and thus knowing the shape of the normal curve, we can precisely calculate the probability of obtaining "by chance" outcomes representing various levels of deviation from the hypothetical population mean of 0.  If such a calculated probability is so low that it meets the previously accepted criterion of statistical significance, then we have only one choice: conclude that our result gives a better approximation of what is going on in the population than the "null hypothesis."  Remember that the null hypothesis was considered only for "technical reasons" as a benchmark against which our empirical result was evaluated.


Elementary Concepts - Are All Test Statistics Normally Distributed?

Not all, but most of them are either based on the normal distribution directly or on distributions that are related to, and can be derived from normal, such as t, F, or Chi-square.  Typically, those tests require that the variables analyzed are themselves normally distributed in the population, that is, they meet the so-called "normality assumption."  Many observed variables actually are normally distributed, which is another reason why the normal distribution represents a "general feature" of empirical reality.  The problem may occur when one tries to use a normal distribution-based test to analyze data from variables that are themselves not normally distributed (see tests of normality in Nonparametrics or ANOVA/MANOVA).  In such cases we have two general choices.  First, we can use some alternative "nonparametric" test (or so-called "distribution-free test" see, Nonparametrics); but this is often inconvenient because such tests are typically less powerful and less flexible in terms of types of conclusions that they can provide.  Alternatively, in many cases we can still use the normal distribution-based test if we only make sure that the size of our samples is large enough.  The latter option is based on an extremely important principle which is largely responsible for the popularity of tests that are based on the normal function.  Namely, as the sample size increases, the shape of the sampling distribution (i.e., distribution of a statistic from the sample; this term was first used by Fisher, 1928a) approaches normal shape, even if the distribution of the variable in question is not normal.  This principle is called the central limit theorem (this term was first used by Pólya, 1920; German, "Zentraler Grenzwertsatz") .


How Do We Know the Consequences of Violating the Normality Assumption?

Elementary Concepts - How Do We Know the Consequences of Violating the Normality Assumption?

Although many of the statements made in other Elementary Concepts topics can be proven mathematically, some of them do not have theoretical proofs and can be demonstrated only empirically, via so-called Monte-Carlo experiments.  In these experiments, large numbers of samples are generated by a computer following predesigned specifications and the results from such samples are analyzed using a variety of tests.  This way we can empirically evaluate the type and magnitude of errors or biases to which we are exposed when certain theoretical assumptions of the tests we are using are not met by our data.  Specifically, Monte-Carlo studies were used extensively with normal distribution-based tests to determine how sensitive they are to violations of the assumption of normal distribution of the analyzed variables in the population.  The general conclusion from these studies is that the consequences of such violations are less severe than previously thought.  Although these conclusions should not entirely discourage anyone from being concerned about the normality assumption, they have increased the overall popularity of the distribution-dependent statistical tests in all areas of research.


Elementary Concepts in Statistics

What are variables.  Variables are things that we measure, control, or manipulate in research.  They differ in many respects, most notably in the role they are given in our research and in the type of measures that can be applied to them.

Correlational vs. experimental research.  Most empirical research belongs clearly to one of those two general categories:  In correlational research we do not (or at least try not to) influence any variables but only measure them and look for relations (correlations) between some set of variables, such as blood pressure and cholesterol level.  In experimental research, we manipulate some variables and then measure the effects of this manipulation on other variables; for example, a researcher might artificially increase blood pressure and then record cholesterol level.  Data analysis in experimental research also comes down to calculating "correlations" between variables, specifically, those manipulated and those affected by the manipulation.  However, experimental data may potentially provide qualitatively better information:  Only experimental data can conclusively demonstrate causal relations between variables.  For example, if we found that whenever we change variable A then variable B changes, then we can conclude that "A influences B."  Data from correlational research can only be "interpreted" in causal terms based on some theories that we have, but correlational data cannot conclusively prove causality.

Dependent vs. independent variables.  Independent variables are those that are manipulated whereas dependent variables are only measured or registered.  This distinction appears terminologically confusing to many because, as some students say, "all variables depend on something."  However, once you get used to this distinction, it becomes indispensable.  The terms dependent and independent variable apply mostly to experimental research where some variables are manipulated, and in this sense they are "independent" from the initial reaction patterns, features, intentions, etc. of the subjects.  Some other variables are expected to be "dependent" on the manipulation or experimental conditions.  That is to say, they depend on "what the subject will do" in response.  Somewhat contrary to the nature of this distinction, these terms are also used in studies where we do not literally manipulate independent variables, but only assign subjects to "experimental groups" based on some pre-existing properties of the subjects.  For example, if in an experiment, males are compared with females regarding their white cell count (WCC), Gender could be called the independent variable and WCC the dependent variable.

Measurement scales.  Variables differ in "how well" they can be measured, i.e., in how much measurable information their measurement scale can provide.  There is obviously some measurement error involved in every measurement, which determines the "amount of information" that we can obtain.  Another factor that determines the amount of information that can be provided by a variable is its "type of measurement scale."  Specifically variables are classified as (a) nominal, (b) ordinal, (c) interval or (d) ratio.

(a) Nominal variables allow for only qualitative classification.  That is, they can be measured only in terms of whether the individual items belong to some distinctively different categories, but we cannot quantify or even rank order those categories.  For example, all we can say is that 2 individuals are different in terms of variable A (e.g., they are of different race), but we cannot say which one "has more" of the quality represented by the variable.  Typical examples of nominal variables are gender, race, color, city, etc.

(b) Ordinal variables allow us to rank order the items we measure in terms of which has less and which has more of the quality represented by the variable, but still they do not allow us to say "how much more."  A typical example of an ordinal variable is the socioeconomic status of families.  For example, we know that upper-middle is higher than middle but we cannot say that it is, for example, 18% higher.  Also this very distinction between nominal, ordinal, and interval scales itself represents a good example of an ordinal variable.  For example, we can say that nominal measurement provides less information than ordinal measurement, but we cannot say "how much less" or how this difference compares to the difference between ordinal and interval scales.

(c) Interval variables allow us not only to rank order the items that are measured, but also to quantify and compare the sizes of differences between them.  For example, temperature, as measured in degrees Fahrenheit or Celsius, constitutes an interval scale.  We can say that a temperature of 40 degrees is higher than a temperature of 30 degrees, and that an increase from 20 to 40 degrees is twice as much as an increase from 30 to 40 degrees.

(d) Ratio variables are very similar to interval variables; in addition to all the properties of interval variables, they feature an identifiable absolute zero point, thus they allow for statements such as x is two times more than y.  Typical examples of ratio scales are measures of time or space.  For example, as the Kelvin temperature scale is a ratio scale, not only can we say that a temperature of 200 degrees is higher than one of 100 degrees, we can correctly state that it is twice as high.  Interval scales do not have the ratio property.  Most statistical data analysis procedures do not distinguish between the interval and ratio properties of the measurement scales.

Relations between variables.  Regardless of their type, two or more variables are related if in a sample of observations, the values of those variables are distributed in a consistent manner.  In other words, variables are related if their values systematically correspond to each other for these observations.  For example, Gender and WCC would be considered to be related if most males had high WCC and most females low WCC, or vice versa; Height is related to Weight because typically tall individuals are heavier than short ones; IQ is related to the Number of Errors in a test, if people with higher IQ's make fewer errors.

Why relations between variables are important.  Generally speaking, the ultimate goal of every research or scientific analysis is finding relations between variables.  The philosophy of science teaches us that there is no other way of representing "meaning" except in terms of relations between some quantities or qualities; either way involves relations between variables.  Thus, the advancement of science must always involve finding new relations between variables.  Correlational research involves measuring such relations in the most straightforward manner.  However, experimental research is not any different in this respect.  For example, the above mentioned experiment comparing WCC in males and females can be described as looking for a correlation between two variables: Gender and WCC.  Statistics does nothing else but help us evaluate relations between variables.  Actually, all of the hundreds of procedures that are described in this manual can be interpreted in terms of evaluating various kinds of inter-variable relations.

Two basic features of every relation between variables.  The two most elementary formal properties of every relation between variables are the relation's (a) magnitude (or "size") and (b) its reliability (or "truthfulness").

(a) Magnitude (or "size").  The magnitude is much easier to understand and measure than reliability.  For example, if every male in our sample was found to have a higher WCC than any female in the sample, we could say that the magnitude of the relation between the two variables (Gender and WCC) is very high in our sample.  In other words, we could predict one based on the other (at least among the members of our sample).

(b) Reliability (or "truthfulness").  The reliability of a relation is a much less intuitive concept, but still extremely important.  It pertains to the "representativeness" of the result found in our specific sample for the entire population.  In other words, it says how probable it is that a similar relation would be found if the experiment was replicated with other samples drawn from the same population.  Remember that we are almost never "ultimately" interested only in what is going on in our sample; we are interested in the sample only to the extent it can provide information about the population.  If our study meets some specific criteria (to be mentioned later), then the reliability of a relation between variables observed in our sample can be quantitatively estimated and represented using a standard measure (technically called p-level or statistical significance level, see the next paragraph).

What is "statistical significance" (p-level).  The statistical significance of a result is an estimated measure of the degree to which it is "true" (in the sense of "representative of the population").  More technically, the value of the p-level (the term first used by Brownlee, 1960) represents a decreasing index of the reliability of a result.  The higher the p-level, the less we can believe that the observed relation between variables in the sample is a reliable indicator of the relation between the respective variables in the population.  Specifically, the p-level represents the probability of error that is involved in accepting our observed result as valid, that is, as "representative of the population."  For example, a p-level of .05 (i.e.,1/20) indicates that there is a 5% probability that the relation between the variables found in our sample is a "fluke."  In other words, assuming that in the population there was no relation between those variables whatsoever, and we were repeating experiments like ours one after another, we could expect that approximately in every 20 replications of the experiment there would be one in which the relation between the variables in question would be equal or stronger than in ours.  In many areas of research, the p-level of .05 is customarily treated as a "border-line acceptable" error level.

How to determine that a result is "really" significant.  There is no way to avoid arbitrariness in the final decision as to what level of significance will be treated as really "significant."  That is, the selection of some level of significance, up to which the results will be rejected as invalid, is arbitrary.  In practice, the final decision usually depends on whether the outcome was predicted a priori or only found post hoc in the course of many analyses and comparisons performed on the data set, on the total amount of consistent supportive evidence in the entire data set, and on "traditions" existing in the particular area of research.  Typically, in many sciences, results that yield p ≤ .05 are considered borderline statistically significant but remember that this level of significance still involves a pretty high probability of error (5%).  Results that are significant at the p ≤ .01 level are commonly considered statistically significant, and p ≤ .005 or p ≤ .001 levels are often called "highly" significant.  But remember that those classifications represent nothing else but arbitrary conventions that are only informally based on general research experience.

Statistical significance and the number of analyses performed.  Needless to say, the more analyses you perform on a data set, the more results will meet "by chance" the conventional significance level.  For example, if you calculate correlations between ten variables (i.e., 45 different correlation coefficients), then you should expect to find by chance that about two (i.e., one in every 20) correlation coefficients are significant at the p ≤ .05 level, even if the values of the variables were totally random and those variables do not correlate in the population.  Some statistical methods that involve many comparisons, and thus a good chance for such errors, include some "correction" or adjustment for the total number of comparisons.  However, many statistical methods (especially simple exploratory data analyses) do not offer any straightforward remedies to this problem.  Therefore, it is up to the researcher to carefully evaluate the reliability of unexpected findings.  Many examples in this manual offer specific advice on how to do this; relevant information can also be found in most research methods textbooks.

Strength vs. reliability of a relation between variables.  We said before that strength and reliability are two different features of relationships between variables.  However, they are not totally independent.  In general, in a sample of a particular size, the larger the magnitude of the relation between variables, the more reliable the relation (see the next paragraph).

Why stronger relations between variables are more significant.  Assuming that there is no relation between the respective variables in the population, the most likely outcome would be also finding no relation between those variables in the research sample.  Thus, the stronger the relation found in the sample, the less likely it is that there is no corresponding relation in the population.  As you see, the magnitude and significance of a relation appear to be closely related, and we could calculate the significance from the magnitude and vice-versa; however, this is true only if the sample size is kept constant, because the relation of a given strength could be either highly significant or not significant at all, depending on the sample size (see the next paragraph).

Why significance of a relation between variables depends on the size of the sample.  If there are very few observations, then there are also respectively few possible combinations of the values of the variables, and thus the probability of obtaining by chance a combination of those values indicative of a strong relation is relatively high.  Consider the following illustration.  If we are interested in two variables (Gender: male/female and WCC: high/low) and there are only four subjects in our sample (two males and two females), then the probability that we will find, purely by chance, a 100% relation between the two variables can be as high as one-eighth.  Specifically, there is a one-in-eight chance that both males will have a high WCC and both females a low WCC, or vice versa.  Now consider the probability of obtaining such a perfect match by chance if our sample consisted of 100 subjects; the probability of obtaining such an outcome by chance would be practically zero.  Let's look at a more general example.  Imagine a theoretical population in which the average value of WCC in males and females is exactly the same.  Needless to say, if we start replicating a simple experiment by drawing pairs of samples (of males and females) of a particular size from this population and calculating the difference between the average WCC in each pair of samples, most of the experiments will yield results close to 0.  However, from time to time, a pair of samples will be drawn where the difference between males and females will be quite different from 0.  How often will it happen?  The smaller the sample size in each experiment, the more likely it is that we will obtain such erroneous results, which in this case would be results indicative of the existence of a relation between gender and WCC obtained from a population in which such a relation does not exist.

Example: "Baby boys to baby girls ratio."  Consider the following example from research on statistical reasoning (Nisbett, et al., 1987).  There are two hospitals: In the first one, 120 babies are born every day, in the other, only 12.  On average, the ratio of baby boys to baby girls born every day in each hospital is 50/50.  However, one day, in one of those hospitals twice as many baby girls were born as baby boys.  In which hospital was it more likely to happen?  The answer is obvious for a statistician, but as research shows, not so obvious for a lay person:  It is much more likely to happen in the small hospital.  The reason for this is that technically speaking, the probability of a random deviation of a particular size (from the population mean), decreases with the increase in the sample size.

Why small relations can be proven significant only in large samples.  The examples in the previous paragraphs indicate that if a relationship between variables in question is "objectively" (i.e., in the population) small, then there is no way to identify such a relation in a study unless the research sample is correspondingly large.  Even if our sample is in fact "perfectly representative" the effect will not be statistically significant if the sample is small.  Analogously, if a relation in question is "objectively" very large (i.e., in the population), then it can be found to be highly significant even in a study based on a very small sample.  Consider the following additional illustration.  If a coin is slightly asymmetrical, and when tossed is somewhat more likely to produce heads than tails (e.g., 60% vs. 40%), then ten tosses would not be sufficient to convince anyone that the coin is asymmetrical, even if the outcome obtained (six heads and four tails) was perfectly representative of the bias of the coin.  However, is it so that 10 tosses is not enough to prove anything?  No, if the effect in question were large enough, then ten tosses could be quite enough.  For instance, imagine now that the coin is so asymmetrical that no matter how you toss it, the outcome will be heads.  If you tossed such a coin ten times and each toss produced heads, most people would consider it sufficient evidence that something is "wrong" with the coin.  In other words, it would be considered convincing evidence that in the theoretical population of an infinite number of tosses of this coin there would be more heads than tails.  Thus, if a relation is large, then it can be found to be significant even in a small sample.

Can "no relation" be a significant result?  The smaller the relation between variables, the larger the sample size that is necessary to prove it significant.  For example, imagine how many tosses would be necessary to prove that a coin is asymmetrical if its bias were only .000001%!  Thus, the necessary minimum sample size increases as the magnitude of the effect to be demonstrated decreases.  When the magnitude of the effect approaches 0, the necessary sample size to conclusively prove it approaches infinity.  That is to say, if there is almost no relation between two variables, then the sample size must be almost equal to the population size, which is assumed to be infinitely large.  Statistical significance represents the probability that a similar outcome would be obtained if we tested the entire population.  Thus, everything that would be found after testing the entire population would be, by definition, significant at the highest possible level, and this also includes all "no relation" results.

How to measure the magnitude (strength) of relations between variables.  There are very many measures of the magnitude of relationships between variables which have been developed by statisticians; the choice of a specific measure in given circumstances depends on the number of variables involved, measurement scales used, nature of the relations, etc.  Almost all of them, however, follow one general principle: they attempt to somehow evaluate the observed relation by comparing it to the "maximum imaginable relation" between those specific variables.  Technically speaking, a common way to perform such evaluations is to look at how differentiated are the values of the variables, and then calculate what part of this "overall available differentiation" is accounted for by instances when that differentiation is "common" in the two (or more) variables in question.  Speaking less technically, we compare "what is common in those variables" to "what potentially could have been common if the variables were perfectly related."  Let us consider a simple illustration.  Let us say that in our sample, the average index of WCC is 100 in males and 102 in females.  Thus, we could say that on average, the deviation of each individual score from the grand mean (101) contains a component due to the gender of the subject; the size of this component is 1.  That value, in a sense, represents some measure of relation between Gender and WCC. However, this value is a very poor measure, because it does not tell us how relatively large this component is, given the "overall differentiation" of WCC scores.  Consider two extreme possibilities:

(a) If all WCC scores of males were equal exactly to 100, and those of females equal to 102, then all deviations from the grand mean in our sample would be entirely accounted for by gender.  We would say that in our sample, gender is perfectly correlated with WCC, that is, 100% of the observed differences between subjects regarding their WCC is accounted for by their gender.

(b) If WCC scores were in the range of 0-1000, the same difference (of 2) between the average WCC of males and females found in the study would account for such a small part of the overall differentiation of scores that most likely it would be considered negligible.  For example, one more subject taken into account could change, or even reverse the direction of the difference.  Therefore, every good measure of relations between variables must take into account the overall differentiation of individual scores in the sample and evaluate the relation in terms of (relatively) how much of this differentiation is accounted for by the relation in question.

Common "general format" of most statistical tests.  Because the ultimate goal of most statistical tests is to evaluate relations between variables, most statistical tests follow the general format that was explained in the previous paragraph.  Technically speaking, they represent a ratio of some measure of the differentiation common in the variables in question to the overall differentiation of those variables.  For example, they represent a ratio of the part of the overall differentiation of the WCC scores that can be accounted for by gender to the overall differentiation of the WCC scores.  This ratio is usually called a ratio of explained variation to total variation.  In statistics, the term explained variation does not necessarily imply that we "conceptually understand" it.  It is used only to denote the common variation in the variables in question, that is, the part of variation in one variable that is "explained" by the specific values of the other variable, and vice versa.

How the "level of statistical significance" is calculated.  Let us assume that we have already calculated a measure of a relation between two variables (as explained above).  The next question is "how significant is this relation?"  For example, is 40% of the explained variance between the two variables enough to consider the relation significant?  The answer is "it depends."  Specifically, the significance depends mostly on the sample size.  As explained before, in very large samples, even very small relations between variables will be significant, whereas in very small samples even very large relations cannot be considered reliable (significant).  Thus, in order to determine the level of statistical significance, we need a function that represents the relationship between "magnitude" and "significance" of relations between two variables, depending on the sample size.  The function we need would tell us exactly "how likely it is to obtain a relation of a given magnitude (or larger) from a sample of a given size, assuming that there is no such relation between those variables in the population."  In other words, that function would give us the significance (p) level, and it would tell us the probability of error involved in rejecting the idea that the relation in question does not exist in the population.  This "alternative" hypothesis (that there is no relation in the population) is usually called the null hypothesis.  It would be ideal if the probability function was linear, and for example, only had different slopes for different sample sizes.  Unfortunately, the function is more complex, and is not always exactly the same; however, in most cases we know its shape and can use it to determine the significance levels for our findings in samples of a particular size.  Most of those functions are related to a general type of function which is called normal.

Why the "Normal distribution" is important.  The "Normal distribution" is important because in most cases, it well approximates the function that was introduced in the previous paragraph.  The distribution of many test statistics is normal or follows some form that can be derived from the normal distribution.  In this sense, philosophically speaking, the Normal distribution represents one of the empirically verified elementary "truths about the general nature of reality," and its status can be compared to the one of fundamental laws of natural sciences.  The exact shape of the normal distribution (the characteristic "bell curve") is defined by a function which has only two parameters: mean and standard deviation.

A characteristic property of the Normal distribution is that 68% of all of its observations fall within a range of ±1 standard deviation from the mean, and a range of ±2 standard deviations includes 95% of the scores.  In other words, in a Normal distribution, observations that have a standardized value of less than -2 or more than +2 have a relative frequency of 5% or less.  (Standardized value means that a value is expressed in terms of its difference from the mean, divided by the standard deviation.)  You can explore the exact values of probability associated with different values in the normal distribution using the Probability calculator in Basic Statistics; for example if you enter the Z value (i.e., standardized value) of 4, the associated probability computed by STATISTICA will be less than .0001, because in the normal distribution almost all observations (i.e., more than 99.99%) fall within the range of ±4 standard deviations.

Illustration of how the normal distribution is used in statistical reasoning (induction).  Recall the example discussed above, where pairs of samples of males and females were drawn from a population in which the average value of WCC in males and females was exactly the same.  Although the most likely outcome of such experiments (one pair of samples per experiment) was that the difference between the average WCC in males and females in each pair is close to zero, from time to time, a pair of samples will be drawn where the difference between males and females is quite different from 0.  How often does it happen?  If the sample size is large enough, the results of such replications are "normally distributed," and thus knowing the shape of the normal curve, we can precisely calculate the probability of obtaining "by chance" outcomes representing various levels of deviation from the hypothetical population mean of 0.  If such a calculated probability is so low that it meets the previously accepted criterion of statistical significance, then we have only one choice: conclude that our result gives a better approximation of what is going on in the population than the "null hypothesis."  Remember that the null hypothesis was considered only for "technical reasons" as a benchmark against which our empirical result was evaluated.

Are all test statistics normally distributed?  Not all, but most of them are either based on the normal distribution directly or on distributions that are related to, and can be derived from normal, such as t, F, or Chi-square.  Typically, those tests require that the variables analyzed are themselves normally distributed in the population, that is, they meet the so-called "normality assumption."  Many observed variables actually are normally distributed, which is another reason why the normal distribution represents a "general feature" of empirical reality.  The problem may occur when one tries to use a normal distribution-based test to analyze data from variables that are themselves not normally distributed (see tests of normality in Nonparametrics or ANOVA/MANOVA).  In such cases we have two general choices.  First, we can use some alternative "nonparametric" test (or so-called "distribution-free test" see, Nonparametrics); but this is often inconvenient because such tests are typically less powerful and less flexible in terms of types of conclusions that they can provide.  Alternatively, in many cases we can still use the normal distribution-based test if we only make sure that the size of our samples is large enough.  The latter option is based on an extremely important principle which is largely responsible for the popularity of tests that are based on the normal function.  Namely, as the sample size increases, the shape of the sampling distribution (i.e., distribution of a statistic from the sample; this term was first used by Fisher, 1928a) approaches normal shape, even if the distribution of the variable in question is not normal.  This principle is called the central limit theorem (this term was first used by Pólya, 1920; German, "Zentraler Grenzwertsatz") .

How do we know the consequences of violating the normality assumption?  Although many of the statements made in the preceding paragraphs can be proven mathematically, some of them do not have theoretical proofs and can be demonstrated only empirically, via so-called Monte-Carlo experiments.  In these experiments, large numbers of samples are generated by a computer following predesigned specifications and the results from such samples are analyzed using a variety of tests.  This way we can empirically evaluate the type and magnitude of errors or biases to which we are exposed when certain theoretical assumptions of the tests we are using are not met by our data.  Specifically, Monte-Carlo studies were used extensively with normal distribution-based tests to determine how sensitive they are to violations of the assumption of normal distribution of the analyzed variables in the population.  The general conclusion from these studies is that the consequences of such violations are less severe than previously thought.  Although these conclusions should not entirely discourage anyone from being concerned about the normality assumption, they have increased the overall popularity of the distribution-dependent statistical tests in all areas of research.


  Basic Statistics - Index

Introductory Overview

  Descriptive statistics

  Correlations

  t-test for independent samples

  t-test for dependent samples

  Breakdown: Descriptive statistics by groups

  Frequency tables

  Crosstabulation & stub-and-banner tables

Statistics in crosstabulation tables

Multiple responses/dichotomies

  Probability Distribution Calculator

  Other Significance Tests

Startup Panel

  Descriptive statistics

  Correlation matrices

  t-test for independent samples

  t-test for dependent samples

  Breakdown: Descriptive statistics by groups

  Frequency tables

  Crosstabulation & stub-and-banner tables

Multiple responses/dichotomies

  Probability Distribution Calculator

  Other Significance Tests

Notes and Technical Information


  Basic Statistics - Introductory Overview

The statistics included in this module are conventionally called basic statistics and are often discussed as a group because they are usually used as a group in the initial, exploratory phase of data analysis.  In fact, they include tests that serve different purposes.  In this introduction, we will briefly review each of the basic statistics available in this module.  Further information can be found in the Examples section of the manual and in statistical textbooks.  Recommended introductory textbooks are: Kachigan (1986), and Runyon and Haber (1976); for a more advanced discussion of elementary theory of basic statistics, see the classic books by Hays (1988), and Kendall and Stuart (1979).

Specific types of basic statistics and tables available in this module, and their utility, are described in some detail in the subsequent help screens.

  Descriptive Statistics Introductory Overview

Choose this option to compute summary statistics such as means, medians, standard deviations, etc. Note that additional ordinal descriptive statistics (including user-specified percentages) can also be computed in the Nonparametric Statistics module.

  Correlations Introductory Overview

Choose this option to compute Pearson product-moment correlations (the term correlation was first used by Galton, 1888; the correlation coefficient was first introduced by Pearson, 1896).  The basic statistics module allows you to compute square and rectangular correlation matrices, as well as expanded format correlation matrices with pairwise n and significance levels.  Note that nonparametric correlation statistics (e.g.,  Spearman R, Kendall tau, Gamma, etc.) can also be computed in the Nonparametric Statistics module and various distance measures can be computed in the Cluster Analysis module.

  t-test for Independent Samples Introductory Overview

This option allows you to compare means for two groups (within a variable).  Note that various nonparametric tests for comparing groups are also available in the Nonparametric Statistics module; methods for comparing groups of (partially) censored observations are also available in the Survival Analysis module.

  t-test for Dependent Samples Introductory Overview

This option allows you to compare means among variables, measured in the same sample of cases (subjects, individuals; so-called dependent samples).  Note that various nonparametric tests for comparing variables are also available in the Nonparametric Statistics module.

  Breakdown: Descriptive Statistics by Groups Introductory Overview

This option will compute various descriptive statistics (e.g., means, standard deviations, correlations, etc.) broken down by one or more categorical variables (e.g., by Gender and Region).  It will also perform a one-way ANOVA on selected variables, and is particularly suited for analyzing single-factor designs with very many groups (e.g., with more than 200 groups; such as some designs used in agricultural research).

  Frequency Tables Introductory Overview

This option allows you to compute frequency tables (and histograms).  STATISTICA provides various options for determining the categories for the frequency table (e.g., integer intervals, specific codes, etc.).  The user can also tabulate the data according to logical categorization conditions that can be directly typed in.

  Crosstabulation & Stub-and-Banner Tables Introductory Overview

This options allows you to crosstabulate data and produce various types of crosstabulation tables.  A wide variety of statistics for two-way tables are also available.  Note that the Log-Linear module and the Correspondence Analysis module will also tabulate multi-way crosstabulation tables, and perform analyses on such tables.

  Multiple Responses/Dichotomies Introductory Overview

The Basic Statistics and Tables module allows you to compute summary tables for so-called multiple response variables as well as multiple dichotomies.  Usually, categorical variables or factors divide the sample into exclusive groups, for example, into males and females.  Obviously, only a single categorical variable is necessary to code the gender of the subjects in the data file.  However, in some areas of research, the categories of interest are not mutually exclusive.  For example, in a marketing research survey, respondents may be asked to list their top three preferences for soft drinks.  A total of, for example, 60 different soft drinks may be mention in the survey, which can be coded accordingly in three categorical variables (first three preferences).  In this case, the categories are not mutually exclusive: A person may mentioned three different soft drinks as his or her favorite.  Such categorical variables are called multiple response variables (multiple dichotomies are similar in nature), and can be easily analyzed with the Basic Statistics and Tables module.

  Probability Calculator Introductory Overview

Use this option to compute the significance levels for various statistics as well as critical values (e.g., critical value of Chi-square significant at the p=.05 level; the term Chi-square was first used by Pearson, 1900); various hypothesis testing facilities are also included (e.g., comparing means, correlations, percentages, etc.).  For example, the user can type in the desired significance level and sample size, and compute the magnitude of the correlation coefficient that would be significant at the p=.05 level.


  Descriptive Statistics - Introductory Overview

Purpose (and the Arrangement of Data)

"True" mean and confidence interval

Shape of the distribution; normality

Other descriptive statistics

See also, Quick Basic Stats


  Descriptive Statistics Introductory Overview - "True" Mean and Confidence Interval

Descriptive statistics are calculated separately for each variable, and they provide such basic information as the mean, minimum and maximum values, different measures of variation, as well as data about the shape of the distribution of the variable.  Those statistics are reviewed in this overview (see also the Basic Statistics Options dialog for a complete listing).  For the descriptive statistics procedure, you can select all variables in the current data set and a sequential table of "descriptives" for the consecutive variables will be generated (one row per variable).  The measures of variation include the standard deviation, and the standard error (the standard error is the standard deviation of the sampling distribution of a mean).  Numerous tests of whether the distribution of variables follows the normal distribution are also provided (refer to the Descriptive Statistics dialog for a complete description of all options).


  Descriptive Statistics Introductory Overview - "True" Mean and Confidence Interval

Probably the most often used descriptive statistic is the mean.  The mean is a particularly informative measure of the "central tendency" of the variable if it is reported along with its confidence intervals.  As mentioned earlier, usually we are interested in statistics (such as the mean) from our sample only to the extent to which they can infer information about the population.  The confidence intervals for the mean give us a range of values around the mean where we expect the "true" (population) mean is located (with a given level of certainty, see also Elementary Concepts).  In the Basic Statistics and Tables module you can request confidence intervals for any p-level; for example, if the mean in your sample is 23, and the lower and upper limits of the p=.05 confidence interval are 19 and 27 respectively, then you can conclude that there is a 95% probability that the population mean is greater than 19 and lower than 27.  If you set the p-level to a smaller value, then the interval would become wider thereby increasing the "certainty" of the estimate, and vice versa; as we all know from the weather forecast, the more "vague" the prediction (i.e., wider the confidence interval), the more likely it will materialize.  Note that the width of the confidence interval depends on the sample size and on the variation of data values.  The larger the sample size, the more reliable its mean.  The larger the variation, the less reliable the mean (see also Elementary Concepts).  The calculation of confidence intervals is based on the assumption that the variable is normally distributed in the population.  The estimate may not be valid if this assumption is not met, unless the sample size is large, say n=100 or more.


  Descriptive Statistics Introductory Overview - Shape of the Distribution, Normality

An important aspect of the "description" of a variable is the shape of its distribution, which tells you the frequency of values rom different ranges of the variable.  Typically, a researcher is interested in how well the distribution can be approximated by the normal distribution (see also Elementary Concepts).  Simple descriptive statistics can provide some information relevant to this issue.  For example, if the skewness (which measures the deviation of the distribution from symmetry) is clearly different from 0, then that distribution is asymmetrical, while normal distributions are perfectly symmetrical.  If the kurtosis (which measures "peakedness" of the distribution) is clearly different from 0, then the distribution is either flatter or more peaked than normal; the kurtosis of the normal distribution is 0.  More precise information can be obtained by performing one of the tests of normality to determine the probability that the sample came from a normally distributed population of observations (e.g., the so-called Kolmogorov-Smirnov test, or the Shapiro-Wilks' W test).  However, none of these tests can entirely substitute for a visual examination of the data using a histogram (i.e., a graph that shows the frequency distribution of a variable).  As in practically all modules of STATISTICA, histograms can be generated directly from a Scrollsheet containing descriptive statistics by pointing to the desired variable (with cursor keys or the mouse, see Spreadsheet and Scrollsheet Stats Graphs).

The graph allows you to evaluate the normality of the empirical distribution because it also shows the normal curve superimposed over the histogram.  It also allows you to examine various aspects of the distribution qualitatively.  For example, the distribution could be bimodal (have 2 peaks).  This might suggest that the sample is not homogeneous but possibly its elements came from two different populations, each more or less normally distributed.  In such cases, in order to understand the nature of the variable in question, you should look for a way to quantitatively identify the two sub-samples.


  Descriptive Statistics Introductory Overview - Other Descriptive Statistics

The Basic Statistics and Tables module includes a selection of the most often-used descriptive statistics.  An additional set of ordinal descriptive statistics and some less frequently-used ones (e.g., user-specified percentiles, harmonic means, etc.) are also included in the Nonparametrics and Distributions module; in that module a variety of non-normal distributions can also be fit to the data.  More specialized descriptive statistics are included in other modules of STATISTICA.


  Correlations - Introductory Overview

Purpose (What is correlation?)

Arrangement of data

Simple linear correlation (Pearson r)

How to interpret the value of correlations

Significance of correlations

Outliers

Quantitative approach to outliers

Correlations in non-homogeneous groups

Nonlinear relations between variables

Measuring nonlinear relations

Exploratory examination of correlation matrices

Casewise vs. pairwise deletion of missing data

How to identify biases caused by the bias due to pairwise deletion of missing data

Pairwise deletion of missing data vs. mean substitution

Spurious correlations

Are correlation coefficients "additive?"

How to determine whether two correlation coefficients are significantly different

Other correlation coefficients


  Correlations Introductory Overview - Purpose (What is Correlation?)

Correlation is a measure of the relation between two or more variables.  The measurement scales used should be at least interval scales, but other correlation coefficients are available to handle other types of data.  Correlation coefficients can range from −1.00 to +1.00.  The value of −1.00 represents a perfect negative correlation while a value of +1.00 represents a perfect positive correlation.  A value of 0.00 represents a lack of correlation.

The most widely-used type of correlation coefficient is Pearson r, also called linear or product-moment correlation.  It is the basic type of correlation that is offered in the Basic Statistics and Tables module.  More specialized correlations are included in other modules, as explained later.


  Correlations Introductory Overview - Arrangement of Data

You can correlate any variables in your data set, but if the selected variables contain nominal data (see Elementary Concepts), you need to use a special type of correlation, such as those included in the Crosstabulation tables procedures of Basic Statistics and Tables).


Correlations Introductory Overview - Simple Linear Correlation

  Correlations Introductory Overview - Simple Linear Correlation (Pearson r)

Pearson correlation (hereafter called correlation), assumes that the two variables are measured on at least interval scales (see Elementary Concepts), and it determines the extent to which values of the two variables are "proportional" to each other.  The value of correlation (i.e., correlation coefficient) does not depend on the specific measurement units used; for example, the correlation between height and weight will be identical regardless of whether inches and pounds, or centimeters and kilograms are used as measurement units.  Proportional means linearly related; that is, the correlation is high if it can be "summarized" by a straight line (sloped upwards or downwards).

This line is called the regression line or least squares line, because it is determined such that the sum of the squared distances of all the data points from the line is the lowest possible.  Note that the concept of squared distances will have important functional consequences on how the value of the correlation coefficient reacts to various specific arrangements of data (as we will later see).


  Correlations Introductory Overview - How to Interpret the Values of Correlations

As mentioned before, the correlation coefficient (r) represents the linear relationship between two variables.  If the correlation coefficient is squared, then the resulting value (r², the coefficient of determination) will represent the proportion of common variation in the two variables (i.e., the "strength" or "magnitude" of the relationship).  In order to evaluate the correlation between variables, it is important to know this "magnitude" or "strength" as well as the significance of the correlation.


  Correlations Introductory Overview - Significance of Correlations

The significance level calculated for each correlation is a primary source of information about the reliability of the correlation.  In order to facilitate identifying those coefficients that are significant at some desired level, the Correlation Matrices dialog in Basic Statistics and Tables provides an option to have STATISTICA highlight or mark significant correlations with a different color.  As explained before (see Elementary Concepts), the significance of a correlation coefficient of a particular magnitude will change depending on the size of the sample from which it was computed.  The test of significance is based on the assumption that the distribution of the residual values (i.e., the deviations from the regression line) for the dependent variable y follows the normal distribution, and that the variability of the residual values is the same for all values of the independent variable x.  However, Monte Carlo studies suggest that meeting those assumptions closely is not absolutely crucial if your sample size is not very large.  It is impossible to formulate precise recommendations based on those Monte-Carlo results, but many researchers follow a rule of thumb that if your sample size is 50 or more then serious biases are unlikely, and if your sample size is over 100 then you should not be concerned at all with the normality assumptions.  There are, however, much more common and serious threats to the validity of information that a correlation coefficient can provide; they are briefly discussed in the following paragraphs.


  Correlations Introductory Overview - Outliers

Outliers are atypical (by definition), infrequent observations.  Because of the way in which the regression line is determined (especially the fact that it is based on minimizing not the sum of simple distances but the sum of squares of distances of data points from the line), outliers have a profound influence on the slope of the regression line and consequently on the value of the correlation coefficient.  A single outlier is capable of considerably changing the slope of the regression line and, consequently, the value of the correlation.  Typically, we believe that outliers represent a random error that we would like to be able to control.  Unfortunately, there is no widely accepted method to remove outliers automatically (however, see the next paragraph), thus what we are left with is to identify any outliers by examining a scatterplot of each important correlation.  Note that the graphics options on the Correlation Matrices dialog and graphics editing facilities offer numerous ways to experiment with the interactive removal of outliers ("brushing"), to allow you to instantly see their influence on the regression line.  Needless to say, outliers may not only artificially increase the value of a correlation coefficient, but they can also decrease the value of a "legitimate" correlation.


  Correlations Introductory Overview - Quantitative Approach to Outliers

Some researchers use quantitative methods to exclude outliers.  For example, they exclude observations that are outside the range of ±2 standard deviations (or even ±1.5 sd's) around the group or design cell mean.  In some areas of research, such "cleaning" of the data is absolutely necessary.  For example, in cognitive psychology research on reaction times, even if almost all scores in an experiment are in the range of 300-700 milliseconds, just a few "distracted reactions" of 10-15 seconds will completely change the overall picture.  Unfortunately, defining an outlier is subjective (as it should be), and the decisions concerning how to identify them must be made on an individual basis (taking into account specific experimental paradigms and/or "accepted practice" and general research experience in the respective area).  It should also be noted that in some rare cases, the relative frequency of outliers across a number of groups or cells of a design can be subjected to analysis and provide interpretable results.  For example, outliers could be indicative of the occurrence of a phenomenon that is qualitatively different than the typical pattern observed or expected in the sample, thus the relative frequency of outliers could provide evidence of a relative frequency of departure from the process or phenomenon that is typical for the majority of cases in a group.


  Correlations Introductory Overview - Correlations in Non-homogeneous Groups

A lack of homogeneity in the sample from which a correlation was calculated can be another factor that biases the value of the correlation.  Imagine a case where a correlation coefficient is calculated from data points which came from two different experimental groups but this fact is ignored when the correlation is calculated.  Let us assume that the experimental manipulation in one of the groups increased the values of both correlated variables and thus the data from each group form a distinctive "cloud" in the scatterplot.

In such cases, a high correlation may result that is entirely due to the arrangement of the two groups, but which does not represent the "true" relation between the two variables, which may practically be equal to 0 (as could be seen if we looked at each group separately).  If you suspect the influence of such a phenomenon on your correlations and know how to identify such "subsets" of data, try to run the correlations separately in each subset of observations.  For example, you could use the Breakdowns option or the Categorized Scatterplots option.  If you do not know how to identify the hypothetical subsets, try to examine the data with some of the exploratory multivariate techniques offered in STATISTICA (e.g., Cluster Analysis).


  Correlations Introductory Overview - Nonlinear Relations between Variables

Another potential source of problems with the linear (Pearson r) correlation is the shape of the relation.  As mentioned before, Pearson r measures a relation between two variables only to the extent to which it is linear; deviations from linearity will increase the total sum of squared distances from the regression line even if they represent a "true" and very close relationship between two variables.  The possibility of such non-linear relationships is another reason why examining scatterplots is a necessary step in evaluating every correlation.


  Correlations Introductory Overview - Measuring Nonlinear Relations

What do you do if a correlation is strong but clearly nonlinear (as concluded from examining scatterplots)?  Unfortunately, there is no simple answer to this question, because there is no easy-to-use equivalent of Pearson r that is capable of handling nonlinear relations.  If the curve is monotonous (continuously decreasing or increasing) you could try to transform one or both of the variables to remove the curvilinearity and then recalculate the correlation.  For example, a typical transformation used in such cases is the logarithmic function which will "squeeze" together the values at one end of the range (to explore this possibility you could first try to switch the scale from linear to logarithmic in the scatterplot, see General Layout:  2D Graphs).  Another option available if the relation is monotonous is to try a nonparametric correlation (e.g., Spearman R, see Nonparametrics and Distributions) which is sensitive only to the ordinal arrangement of values, thus, by definition, it ignores monotonous curvilinearity.  However, nonparametric correlations are generally less sensitive and sometimes this method will not produce any gains.  Unfortunately, the two most precise methods are not easy to use and require a good deal of "experimentation" with the data.  Therefore you could:

(a)	Try to identify the specific function that best describes the curve.  A convenient facility to explore various fits is provided by the interactive Overlay Function Plotter option in the all graphs (for example, see Plot Layout:  2D Graphs).  After a function has been found, you can test its "goodness-of-fit" to your data using options available in the Nonlinear Estimation module.

(b)	Alternatively, you could experiment with dividing one of the variables into a number of segments (e.g., 4 or 5) of an equal width, treat this new variable as a grouping variable and run an analysis of variance on the data (i.e., Recode the variable).


  Correlations Introductory Overview - Exploratory Examination of Correlation Matrices

A common first step of many data analyses that involve more than a very few variables is to run a correlation matrix of all variables and then examine it for expected (and unexpected) significant relations.  When this is done, you need to be aware of the general nature of statistical significance (see Elementary Concepts); specifically, if you run many tests (in this case, many correlations), then significant results will be found "surprisingly often" due to pure chance.  For example, by definition, a coefficient significant at the .05 level will occur by chance once in every 20 coefficients.  There is no "automatic" way to weed out the "true" correlations.  Thus, you should treat all results that were not predicted or planned with particular caution and look for their consistency with other results; ultimately, though, the most conclusive (although costly) control for such a randomness factor is to replicate the study.  This issue is general and it pertains to all analyses that involve "multiple comparisons and statistical significance."  This problem is also briefly discussed in the context of post-hoc comparisons of means and the Breakdowns option.


  Correlations Introductory Overview - Casewise vs. Pairwise Deletion of Missing Data

The default way of deleting missing data while calculating a correlation matrix is to exclude all cases that have missing data in at least one of the selected variables; that is, by casewise deletion of missing data.  Only this way will you get a "true" correlation matrix, where all correlations are obtained from the same set of observations.  However, if missing data are randomly distributed across cases, you could easily end up with no "valid" cases in the data set, because each of them will have at least one missing data in some variable.  The most common solution used in such instances is to use so-called pairwise deletion of missing data in correlation matrices, where a correlation between each pair of variables is calculated from all cases that have valid data on those two variables.  In many instances there is nothing wrong with that method, especially when the total percentage of missing data is low, say 10%, and they are relatively randomly distributed between cases and variables.  However, it may sometimes lead to serious problems.

For example, a systematic bias may result from a "hidden" systematic distribution of missing data, causing different correlation coefficients in the same correlation matrix to be based on different subsets of subjects.  In addition to the possibly biased conclusions that you could derive from such "pairwise calculated" correlation matrices, real problems may occur when you subject such matrices to another analysis (e.g., multiple regression, factor analysis, or cluster analysis) that expects a "true correlation matrix," with a certain level of consistency and "transitivity" between different coefficients.  Such a correlation matrix may turn out to be not a "true" correlation matrix, and the other program will either be unable to process it, or will give erroneous results.  (Note that in STATISTICA you can either save a matrix in Basic Statistics and Tables and access it with another program or calculate a matrix casewise or pairwise in the respective program.)  Thus, if you are using the pairwise method of deleting the missing data, be sure to examine the distribution of missing data across the cells of the matrix for possible systematic "patterns."


  Correlations Introductory Overview - How to Identify Biases Caused by the Bias due to Pairwise Deletion of Missing Data

The Correlation Matrices option will produce Scrollsheets with n's, means and standard deviationscalculated separately for "each variable with each variable," that is, based on subsets of values included in the calculation of individual correlation coefficients.  If the pairwise deletion of missing data does not introduce any systematic bias to the correlation matrix, then all those pairwise descriptive statistics for one variable should be very similar.  However, if they differ, then there are good reasons to suspect a bias.  For example, if the mean (or standard deviation) of the values of variable A that were taken into account in calculating its correlation with variable B is much lower than the mean (or standard deviation) of those values of variable A that were used in calculating its correlation with variable C, then we would have good reason to suspect that those two correlations (A-B and A-C) are based on different subsets of data, and thus, that there is a bias in the correlation matrix caused by a non-random distribution of missing data.


  Correlations Introductory Overview - Pairwise Deletion of Missing Data vs. Mean Substitution

Another common method to avoid loosing data due to casewise deletion is the so-called mean substitution of missing data (replacing all missing data in a variable by the mean of that variable).  This way of handling missing data can be requested in many modules; you can also use this method to permanently "remove" the missing data from your data set (via the Data Management module).  Mean substitution offers some advantages and some disadvantages as compared to pairwise deletion.  Its main advantage is that it produces "internally consistent" sets of results ("true" correlation matrices).  The main disadvantages are:

(a)	Mean substitution artificially decreases the variation of scores, and this decrease in individual variables is proportional to the number of missing data (i.e., the more missing data, the more "perfectly average scores" will be artificially added to the data set).

(b)	Because it substitutes missing data with artificially created "average" data points, mean substitution may considerably change the values of correlations.


  Correlations Introductory Overview - Spurious Correlations

Although you cannot prove causal relations based on correlation coefficients (see Elementary Concepts), you can still identify so-called spurious correlations; that is, correlations that are due mostly to the influences of "other" variables.  For example, there is a correlation between the total amount of losses in a fire and the number of firemen that were putting out the fire; however, what this correlation does not indicate is that if you call fewer firemen then you would lower the losses.  There is a third variable (the initial size of the fire) that influences both the amount of losses and the number of firemen.  If you "control" for this variable (e.g., consider only fires of a fixed size), then the correlation will either disappear or perhaps even change its sign.  The main problem with spurious correlations is that we typically do not know what the "hidden" agent is.  However, in cases when we know where to look, we can use partial correlations that control for (partial out) the influence of specified variables.  In STATISTICA, partial correlation procedures are included as part of the Multiple Regression module.


  Correlations Introductory Overview - Are correlation coefficients "additive?"

No, they are not.  For example, an average of correlation coefficients in a number of samples does not represent an "average correlation" in all those samples.  Because the value of the correlation coefficient is not a linear function of the magnitude of the relation between the variables, correlation coefficients cannot simply be averaged.  In cases when you need to average correlations, they first have to be converted into additive measures.  For example, before averaging, you can square them to obtain coefficients of determination which are additive (as explained before in this section), or convert them into so-called Fisher z values, which are also additive (an r-to-Z transformation procedure is available in the Probability calculator).


  Correlations Introductory Overview - How to Determine Whether Two Correlation Coefficients are Significant

A test is available that will evaluate the significance of differences between two correlation coefficients in two samples (see the Probability calculator).  The outcome of this test depends not only on the size of the raw difference between the two coefficients but also on the size of the samples and on the size of the coefficients themselves.  Consistent with the previously discussed principle, the larger the sample size, the smaller the effect that can be proven significant in that sample.  In general, due to the fact that the reliability of the correlation coefficient increases with its absolute value, relatively small differences between large correlation coefficients can be significant.  For example, a difference of .10 between two correlations may not be significant if the two coefficients are .15 and .25, although in the same sample, the same difference of .10 can be highly significant if the two coefficients are .80 and .90.


  Correlations Introductory Overview - Other Correlation Coefficients

There are many other types of correlation coefficients, and they are included in other modules of STATISTICA.  A variety of nonparametric correlations are included in the Nonparametrics and Distributions module; such correlation coefficients are also computed by the Crosstabulation Tables option, partial correlations are included in the Multiple Regression module, various autocorrelations (i.e., correlations between a variable and itself lagged by a specified lag) are included in the Time Series module (other, more specialized measures of relations between variables or groups of variables are included in many other modules).

See also, Quick Basic Stats


  t-test for Independent Samples - Introductory Overview

Purpose, assumptions

Arrangement of data

Alternative arrangement of data

t-test graphs

More complex group comparisons


  t-test for Independent Samples Introductory Overview - Purpose, Assumptions

The t-test is the most commonly used method to evaluate the differences in means between two groups.  For example, the t-test can be used to test for a difference in test scores between a group of patients who were given a drug and a control group who received a placebo.  Theoretically, the t-test can be used even if the sample sizes are very small (e.g., as small as 10; some researchers claim that even smaller n's are possible), as long as the variables are normally distributed within each group and the variation of scores in the two groups is not reliably different (see also Elementary Concepts).  As mentioned before, the normality assumption can be evaluated by looking at the distribution of the data (via histograms) or by performing a normality test (via the Descriptive Statistics option).  The equality of variances assumption can be verified with the F test (which is included in the t-test output), or you can use the more robust Levene's test option.  If these conditions are not met, then you can evaluate the differences in means between two groups using one of the nonparametric alternatives to the t-test (see Nonparametrics and Distributions).

The p-level reported with a t-test represents the probability of error involved in accepting our research hypothesis about the existence of a difference.  Technically speaking, this is the probability of error associated with rejecting the hypothesis of no difference between the two categories of observations (corresponding to the groups) in the population when, in fact, the hypothesis is true.  Some researchers suggest that if the difference is in the predicted direction, you can consider only one half (one "tail") of the probability distribution and thus divide the standard p-level reported with a t-test (a "two-tailed" probability) by two.  Others, however, suggest that you should always report the standard, two-tailed t-test probability.  For more details, see the recommended references in the manual.


  t-test for Independent Samples Introductory Overview - Arrangement of Data

In order to perform the t-test for independent samples, one independent (grouping) variable (e.g., Gender: male/female) and at least one dependent variable (e.g., a test score) are required.  The means of the dependent variable will be compared between selected groups based on the specified values (grouping codes, e.g., male and female) of the independent variable.  The following data set can be analyzed with a t-test comparing the average WCC score in males and females.

        GENDER  WCC

        ------  ---

case 1    male  111

case 2    male  110

case 3    male  109

case 4  female  102

case 5  female  104

      mean WCC in males   = 110

      mean WCC in females = 103

If you specified not one, but a list of dependent variables, then a series of t-tests will be performed (one for each dependent variable).


  t-test for Independent Samples Introductory Overview - Alternative Arrangement of Data

Sometimes, the data are already arranged (e.g., as in a spreadsheet) such that each column or variable in the file represents one group:

        Male  Female

        ----  ------

case 1  111    102

case 2  110    104

case 3  109

Note that the Independent t-test option of the Basic Statistics and Tables module can also compute t-tests for data arranged in this manner.  However, we should stress that this arrangement is atypical and generally not recommended when creating large data files.  Practically all data analysis software, including STATISTICA, usually assumes data to be arranged as shown earlier.  The earlier arrangement allows us to identify each individual respondent or subject in the data file; thus, when there are multiple dependent variables of interest, various multivariate methods can be applied which rely on the (within-group) correlation matrices of variables.


  t-test for Independent Samples Introductory Overview - t-test Graphs

In the t-test analysis, comparisons of means and measures of variation in the two groups can be visualized in box and whisker plots that can be called directly from the results Scrollsheet by simply pointing to a selected t-test (using cursor keys or the mouse); various graphs of the distribution of scores by group can also be requested directly from the t-test for independent samples dialog.  These graphs help us to quickly evaluate and "intuitively visualize" the strength of the relation between the grouping and dependent variable.


  t-test for Independent Samples Introductory Overview - More Complex Group Comparisons

It often happens in research practice that you need to compare more than two groups (e.g., drug 1, drug 2, and placebo), or compare groups created by more than one independent variable while controlling for the separate influence of each of them (e.g., Gender, type of Drug, and size of Dose).  In these cases, you need to analyze the data using Analysis of Variance, which can be considered to be a generalization of the t-test.  In fact, for two group comparisons, ANOVA will give results identical to a t-test (t**2 [df] = F[1,df]).  However, when the design is more complex, ANOVA offers numerous advantages that t-tests cannot provide (even if you run a series of t-tests comparing various cells of the design).


  t-test for Dependent Samples - Introductory Overview

Within-group variation

Purpose

Assumptions

Arrangement of data

Matrices of t-tests

More complex group comparisons


  t-test for Dependent Samples Introductory Overview - Within-group Variation

As explained in Elementary Concepts, the size of a relation between two variables, such as the one measured by a difference in means between two groups, depends to a large extent on the differentiation of values within the group.  Depending on how differentiated the values are in each group, a given "raw difference" in group means will indicate either a stronger or weaker relationship between the independent (grouping) and dependent variable.  For example, if the mean WCC (White Cell Count) was 102 in males and 104 in females, then this difference of "only" 2 points would be extremely important if all values for males fell within a range of 101 to 103, and all scores for females fell within a range of 103 to 105; for example, we would be able to predict WCC pretty well based on gender.  However, if the same difference of 2 was obtained from very differentiated scores (e.g., if their range was 0-200), then we would consider the difference entirely negligible.  That is to say, reduction of the within-group variation increases the sensitivity of our test.


  t-test for Dependent Samples Introductory Overview - Purpose

The t-test for dependent samples helps us to take advantage of one specific type of design in which an important source of within-group variation (or so-called, error) can be easily identified and excluded from the analysis.  Specifically, if two groups of observations (that are to be compared) are based on the same sample of subjects who were tested twice (e.g., before and after a treatment), then a considerable part of the within-group variation in both groups of scores can be attributed to the initial individual differences between subjects.  Note that, in a sense, this fact is not much different than in cases when the two groups are entirely independent (see t-test for independent samples), where individual differences also contribute to the error variance; but in the case of independent samples, we cannot do anything about it because we cannot identify (or "subtract") the variation due to individual differences in subjects.  However, if the same sample was tested twice, then we can easily identify (or "subtract") this variation.  Specifically, instead of treating each group separately, and analyzing raw scores, we can look only at the differences between the two measures (e.g., "pre-test" and "post test") in each subject.  By subtracting the first score from the second for each subject and then analyzing only those "pure (paired) differences," we will exclude the entire part of the variation in our data set that results from unequal base levels of individual subjects.  This is precisely what is being done in the t-test for dependent samples, and, as compared to the t-test for independent samples, it always produces "better" results (i.e., it is always more sensitive).


  t-test for Dependent Samples Introductory Overview - Assumptions

The theoretical assumptions of the t-test for independent samples also apply to the dependent samples test; that is, the paired differences should be normally distributed.  If these assumptions are clearly not met, then one of the nonparametric alternative tests should be used (see the Nonparametrics and Distributions module).


  t-test for Dependent Samples Introductory Overview - Arrangement of Data

Technically, we can apply the t-test for dependent samples to any two variables in our data set and the selection of variables is identical to that used for correlations (see Correlation Matrices).  However, applying this test will make very little sense if the values of the two variables in the data set are not logically and methodologically comparable.  For example, if you compare the average WCC in a sample of patients before and after a treatment, but using a different counting method or different units in the second measurement, then a highly significant t-test value could be obtained due to an artifact; that is, to the change of units of measurement.  Following, is an example of a data set (spreadsheet) that can be analyzed using the t-test for dependent samples.

           WCC    WCC

        before  after

        ------  -----

case 1   111.9    113

case 2     109    110

case 3     143    144

case 4     101    102

case 5      80     80.9

...        ...    ...

   average change between WCC

   "before" and "after" = 1

The average difference between the two conditions is relatively small (d=1) as compared to the differentiation (range) of the raw scores (from 80 to 143, in the first sample).  However, the t-test for dependent samples analysis is performed only on the paired differences , "ignoring" the raw scores and their potential differentiation.  Thus, the size of this particular difference of 1 will be compared not to the differentiation of raw scores but to the differentiation of the individual difference scores, which is relatively small: 0.2 (from 0.9 to 1.1).  Compared to that variability, the difference of 1 is extremely large and can yield a highly significant t value.


  t-test for Dependent Samples Introductory Overview - Matrices of t-tests

t-tests for dependent samples can be calculated for long lists of variables, and reviewed in the form of matrices produced with casewise or pairwise deletion of missing data, much like the correlation matrices option.  Thus, the precautions discussed in the context of correlations also apply to t-test matrices; see:

(a) the issue of artifacts caused by the pairwise deletion of missing data in t-tests and

(b) the issue of "randomly" significant test values.


  t-test for Dependent Samples Introductory Overview - More Complex Group Comparisons

If there are more than two "correlated samples" (e.g., before treatment, after treatment 1, and after treatment 2), then analysis of variance with repeated measures should be used.  The repeated measures ANOVA can be considered a generalization of the t-test for dependent samples and it offers various features that increase the overall sensitivity of the analysis.  For example, it can simultaneously control not only for the base level of the dependent variable, but it can control for other factors and/or include in the design more than one interrelated dependent variable (MANOVA; for additional details refer to ANOVA/MANOVA).


  Descriptive Statistics by Groups (Breakdown) - Introductory Overview

Purpose

Arrangement of data

Statistical tests in breakdowns

Other related data analysis techniques

Post-hoc comparison of means

The ANOVA/MANOVA module

Breakdowns vs. discriminant function analysis

Breakdowns vs. frequency tables

Graphical breakdowns


  Descriptive Statistics by Groups (Breakdown) Introductory Overview - Purpose

The breakdowns program calculates descriptive statistics and correlations for dependent variables in each of a number of groups defined by one or more grouping (independent) variables.  The concept of grouping or coding variables is also explained in the General Conventions chapter of the manual (in the section on Selecting group codes).


  Descriptive Statistics by Groups (Breakdown) Introductory Overview - Arrangement of Data

In the following example data set (spreadsheet), the dependent variable WCC (White Cell Count) can be broken down by 2 independent variables: Gender (values: males and females), and Height (values: tall and short).

        GENDER  HEIGHT  WCC

        ------  ------  ---

case 1    male   short  101

case 2    male    tall  110

case 3    male    tall   92

case 4  female    tall  112

case 5  female   short   95

     .       .       .    .

     .       .       .    .

The resulting breakdowns might look as follows (we are assuming that Gender was specified as the first independent variable, and Height as the second).

                    Entire sample

                    Mean=100

                    SD=13

                    N=120

         ---------------------------------

         Males                    Females

         Mean=99                  Mean=101

         SD=13                    SD=13

         N=60                     N=60

----------------------  ------------------------

Tall/males Short/males  Tall/femal. Short/femal.

Mean=98    Mean=100     Mean=101    Mean=101

SD=13      SD=13        SD=13       SD=13

N=30       N=30         N=30        N=30

The composition of the "intermediate" level cells of the "breakdown tree" depends on the order in which independent variables are arranged.  For example, in the above example, you see the means for "all males" and "all females" but you do not see the means for "all tall subjects" and "all short subjects" which would have been produced had you specified independent variable Height as the first grouping variable rather than the second.  Thus, ideally, in a breakdown program you should have an option to easily "reorder" independent variables and thus see different "cross-sections" of the data.  The Basic Statistics and Tables module gives you not only the option to reorder the variables in the table, but it also allows you to compute any marginal table in which you may be interested.  For example, you could easily compute the means for Tall and Short individuals.


  Descriptive Statistics by Groups (Breakdown) Introductory Overview - Statistical Tests in Breakdowns

Breakdowns are typically used as an exploratory data analysis technique; the typical question that this technique can help answer is very simple: Are the groups created by the independent variables different regarding the dependent variable?  If you are interested in differences concerning the means, then the appropriate test is the breakdowns one-way ANOVA (F test).  If you are interested in variation differences, then you should test for homogeneity of variances.  The STATISTICA breakdowns procedure offers the Levene's test of homogeneity of variance (this test has practically replaced the older and less robust Bartlett's test and Chi-square test; note that a comprehensive selection of univariate and multivariate tests is also offered in the ANOVA/MANOVA module).


  Descriptive Statistics by Groups (Breakdown) Introductory Overview - Other Related Data Analysis Techniques

Although for exploratory data analysis, breakdowns can use more than one independent variable, the statistical procedures in breakdowns assume the existence of a single grouping factor (even if, in fact, the breakdown results from a combination of a number of grouping variables).  Thus, those statistics do not reveal or even take into account any possible interactions between grouping variables in the design.  For example, there could be differences between the influence of one independent variable on the dependent variable at different levels of another independent variable (e.g., tall people could have lower WCC than short ones, but only if they are males; see the "tree" data above).  You can explore such effects by examining breakdowns "visually," using different orders of independent variables, but the magnitude or significance of such effects cannot be estimated by the breakdown statistics.


Descriptive Statistics by Groups (Breakdown) Introductory Overview - Post-Hoc Comparison of Means

  Descriptive Statistics by Groups (Breakdown) Introductory Overview - Post-Hoc Comparisons of Means

The breakdowns facility in the Descriptive Statistics module also offers all common post-hoc tests for means comparisons.  Usually, after obtaining a statistically significant F test from the ANOVA, one wants to know which of the means contributed to the effect (i.e., which groups are particularly different from each other).  One could of course perform a series of simple t-tests to compare all possible pairs of means.  However, such a procedure would capitalize on chance.  This means that the reported probability levels would actually overestimate the statistical significance of mean differences.  Without going into too much detail, suppose you took 20 samples of 10 random numbers each, and computed 20 means.  Then, take the group (sample) with the highest mean and compare it with that of the lowest mean.  The t-test for independent samples will test whether or not those two means are significantly different from each other, provided they were the only two samples taken.  Post-hoc comparison techniques on the other hand specifically take into account the fact that more than two samples were taken.


  Descriptive Statistics by Groups (Breakdown) Introductory Overview - The ANOVA/MANOVA Module

The ANOVA/MANOVA module offers other, more sophisticated tests to evaluate the differences between groups created by a number of independent (grouping) variables, such as descriptive statistics for more than one dependent variable, correlations between several dependent variables in each group, etc.


  Descriptive Statistics by Groups (Breakdown) Introductory Overview - Breakdowns vs. Discriminant Function Analysis

Breakdowns can be considered as a first step toward another type of analysis that explores differences between groups: Discriminant function analysis.  Similar to breakdowns, discriminant function analysis explores the differences between groups created by values (group codes) of an independent (grouping) variable.  However, unlike breakdowns, discriminant function analysis simultaneously analyzes more than one dependent variable and it identifies "patterns" of values of those dependent variables.  Technically, it determines a linear combination of the dependent variables that best predicts the group membership.  For example, discriminant function analysis can be used to analyze differences between three groups of persons who have chosen different professions (e.g., lawyers, physicians, and engineers) in terms of various aspects of their scholastic performance in high school.  One could claim that such analysis could "explain" the choice of a profession in terms of specific talents shown in high school; thus discriminant function analysis can be considered to be an "exploratory extension" of simple breakdowns.  For more details concerning this procedure refer to the Discriminant Analysis module (the Help text and the respective chapter in the manual).


  Descriptive Statistics by Groups (Breakdown) Introductory Overview - Breakdowns vs. Frequency Tables

Another related type of analysis that cannot be directly performed with breakdowns is comparisons of frequencies of cases (n's) between groups.  Specifically, often the n's in individual cells are not equal because the assignment of subjects to those groups typically results not from an experimenter's manipulation, but from subjects' pre-existing dispositions.  If, in spite of the random selection of the entire sample, the n's are unequal, then it may suggest that the independent variables are related.  For example, crosstabulating levels of independent variables Age and Education most likely would not create groups of equal n, because education is distributed differently in different age groups.  If you are interested in such comparisons, you can explore specific frequencies in the breakdowns tables, trying different orders of independent variables.  However, in order to subject such differences to statistical tests, you should use the Crosstabulation Tables option which offers a variety of ways for examining crosstabulations and frequency tables, or the Log-Linear or Correspondence Analysis modules (for more advanced analyses on multi-way frequency tables).


  Descriptive Statistics by Groups (Breakdown) Introductory Overview - Graphical Breakdowns

Graphs can often identify effects (both expected and unexpected) in our data more quickly and sometimes "better" than any other data analysis method.  The Results dialog of the Breakdown procedure offers numerous graphics options to plot the means, distributions, correlations, etc. across the groups of the respective table (so-called categorized plots).


  Frequency Tables - Introductory Overview

Purpose

Arrangement of data

Applications

See also, Quick Basic Stats


  Frequency Tables Introductory Overview - Purpose

Frequency or one-way tables represent the simplest method for analyzing categorical (nominal) data (refer to Elementary Concepts).  They are often used as one of the exploratory procedures to review how different categories of values are distributed in the sample.  For example, in a survey of spectator interest in different sports, we could summarize the respondents' interest in watching football in a frequency table as follows:

+--------------------------------+-----------------------------------------+

| STATISTICA                     |FOOTBALL: "Watching football"            |

| BASIC                          |                                         |

| STATS                          |                                         |

+--------------------------------+--------+----------+----------+----------+

|                                |        | Cumulatv |          | Cumulatv |

| Category                       | Count  |   Count  |  Percent |  Percent |

+--------------------------------+--------+----------+----------+----------+

| ALWAYS  : Always interested    |     39 |       39 | 39.00000 |  39.0000 |

| USUALLY : Usually interested   |     16 |       55 | 16.00000 |  55.0000 |

| SOMETIMS: Sometimes interested |     26 |       81 | 26.00000 |  81.0000 |

| NEVER   : Never interested     |     19 |      100 | 19.00000 | 100.0000 |

| Missing                        |      0 |      100 |  0.00000 | 100.0000 |

+--------------------------------+--------+----------+----------+----------+

The table above shows the number, proportion, and cumulative proportion of respondents who characterized their interest in watching football as either (1) Always interested, (2) Usually interested, (3) Sometimes interested, or (4) Never interested.  Of course, STATISTICA provides numerous graphics options in order to visualize the distribution of the data (see the Frequency tables dialog).


  Frequency Tables Introductory Overview - Arrangement of Data

Any variable in a data set can be analyzed and presented in frequency tables.  In addition to tabulation by integer codes, the user can also enter specific codes for the table, specify intervals for the frequency table, and even specify a set of (arbitrary) logical conditions which will assign specific cases to categories.


  Frequency Tables Introductory Overview - Applications

In practically every research project, a first "look" at the data usually includes frequency tables.  For example, in survey research, frequency tables can show the number of males and females who participated in the survey, the number of respondents from particular ethnic and racial backgrounds, and so on.  Responses on some labeled attitude measurement scales (e.g., interest in watching football) can also be nicely summarized via the frequency table.  In medical research, one may tabulate the number of patients displaying specific symptoms; in industrial research one may tabulate the frequency of different causes leading to catastrophic failure of products during stress tests (e.g., which parts are actually responsible for the complete malfunction of television sets under extreme temperatures?).  Customarily, if a data set includes any categorical data, then one of the first steps in the data analysis is to compute a frequency table for those categorical variables.


  Crosstabulation & Stub-and-Banner Tables - Introductory Overview

Description of Joint Frequency Distributions via Crosstabulations

Purpose and arrangement of data

2 by 2 table

Marginal frequencies

Column, row, and total percentages

Graphical representations of crosstabulation

Stub-and-Banner Tables

See also,

Multiple Responses/Dichotomies

Interpreting the Banner Table

Multi-way tables with control variables

Graphical representations of multi-way tables


  Description of Joint Frequency Distributions via Crosstabulations - Stub-and-Banner Tables

Stub-and-Banner tables, or Banners for short, are a way to display several two-way tables in a compressed form.  This type of table is most easily explained with an example.  Let us return to the survey of sports spectators example.  (Note that, in order simplify matters, only the response categories Always and Usually were tabulated in the table below.)

+--------------------+--------------------------------+

| STATISTICA         |   Stub-and-Banner Table:       |

| BASIC              |        Row Percent             |

| STATS              |                                |

+--------------------+----------+----------+----------+

|                    | FOOTBALL | FOOTBALL |     Row  |

| Factor             |  ALWAYS  |  USUALLY |   Total  |

+--------------------+----------+----------+----------+

| BASEBALL: ALWAYS   |    92.31 |     7.69 |    66.67 |

| BASEBALL: USUALLY  |    61.54 |    38.46 |    33.33 |

+--------------------+----------+----------+----------+

| BASEBALL: Total    |    82.05 |    17.95 |   100.00 |

+--------------------+----------+----------+----------+

| TENNIS  : ALWAYS   |    87.50 |    12.50 |    66.67 |

| TENNIS  : USUALLY  |    87.50 |    12.50 |    33.33 |

+--------------------+----------+----------+----------+

| TENNIS  : Total    |    87.50 |    12.50 |   100.00 |

+--------------------+----------+----------+----------+

| BOXING  : ALWAYS   |    77.78 |    22.22 |    52.94 |

| BOXING  : USUALLY  |   100.00 |     0.00 |    47.06 |

+--------------------+----------+----------+----------+

| BOXING  : Total    |    88.24 |    11.76 |   100.00 |

+--------------------+----------+----------+----------+


Description of Joint Frequency Distributions via Crosstabulations - Purpose and Arrangement of Tables

  Description of Joint Frequency Distributions via Crosstabulations - Purpose and Arrangement of Table

Crosstabulation is a combination of two (or more) frequency tables arranged such that each cell in the resulting table represents a unique combination of specific values of crosstabulated variables.  Thus, crosstabulation allows us to examine frequencies of observations that belong to specific categories on more than one variable.  By examining these frequencies, we can identify relations between crosstabulated variables.  Only categorical (nominal) variables or variables with a relatively small number of different meaningful values should be crosstabulated.  Note that in the cases where we do want to include a continuous variable in a crosstabulation (e.g., income), we can first recode it into a particular number of distinct ranges (e.g., low, medium, high).


  Description of Joint Frequency Distributions via Crosstabulations - 2x2 Table

The simplest form of crosstabulation is the 2 by 2 table where two variables are "crossed," and each variable has only two distinct values.  For example, suppose we conduct a simple study in which males and females are asked to choose one of two different brands of soda pop (brand A and brand B); the data file can be arranged like this:

         GENDER  SODA

case 1     MALE     A

case 2   FEMALE     B

case 3   FEMALE     B

case 4   FEMALE     A

case 4     MALE     B

     .        .     .

     .        .     .

The resulting crosstabulation could look as follows.

               | SODA: A  | SODA: B  |

---------------+----------+----------+----------

GENDER: MALE   | 20 (40%) | 30 (60%) | 50 (50%)

---------------+----------+----------+----------

GENDER: FEMALE | 30 (60%) | 20 (40%) | 50 (50%)

---------------+----------+----------+----------

               | 50 (50%) | 50 (50%) |100 (100%)

Each cell represents a unique combination of values of the two crosstabulated variables (row variable Gender and column variable Soda), and the numbers in each cell tell us how many observations fall into each combination of values.  In general, this table shows us that more females than males chose the soda pop brand A, and that more males than females chose soda B.  Thus, gender and preference for a particular brand of soda may be related (later we will see how this relationship can be measured).


  Description of Joint Frequency Distributions via Crosstabulations - Marginal Frequencies

The values in the margins of the table are simply one-way (frequency) tables for all values in the table.  They are important in that they help us to evaluate the arrangement of frequencies in individual columns or rows.  For example, the frequencies of 40% and 60% of males and females (respectively) who chose soda A (see the first column of the above table), would not indicate any relationship between Gender and Soda if the marginal frequencies for Gender were also 40% and 60%; in that case they would simply reflect the different proportions of males and females in the study.  Thus, the differences between the distributions of frequencies in individual rows (or columns) and in the respective margins informs us about the relationship between the crosstabulated variables.


  Description of Joint Frequency Distributions via Crosstabulations - Column, Row, and Total Percentages

The example in the previous paragraph demonstrates that in order to evaluate relationships between crosstabulated variables, we need to compare the proportions of marginal and individual column or row frequencies.  Such comparisons are easiest to perform when the frequencies are presented as percentages.  The Crosstabulation option allows you to display the crosstabulated frequencies in Scrollsheets along with counts, column percentages, row percentages, and total percentages; a combined summary table where each cell in the table contains all of those numbers can also be produced.


  Description of Joint Frequency Distributions via Crosstabulations - Graphical Representations of Crosstabulations

For analytic purposes, the individual rows or columns of a table can be represented as column graphs.  However, often it is useful to visualize the entire table in a single graph.  There are several ways to do this via the Crosstabulation Tables option.  A two-way table can be visualized in a 3-dimensional histogram; alternatively, a categorized histogram can be produced, where one variable is represented by individual histograms which are drawn at each level (category) of the other variable in the crosstabulation.  The advantage of the 3D histogram is that it produces an integrated picture of the entire table; the advantage of the categorized graph is that it allows us to precisely evaluate specific frequencies in each cell of the table.  Refer to the Crosstabulation Results dialog for a complete overview of available graphics options.


Description of Joint Frequency Distributions via Crosstabulations - Interpreting the Banner Table

  Stub-and-Banner Tables - Interpreting the Banner Table

In the table above, we see the two-way tables of expressed interest in Football by expressed interest in Baseball, Tennis, and Boxing.  The table entries represent percentages of rows, so that the percentages across columns will add up to 100 percent.  For example, the number in the upper left hand corner of the Scrollsheet (92.31) shows that 92.31 percent of all respondents who said they are always interested in watching football also said that they were always interested in watching baseball.  Further down we can see that the percent of those always interested in watching football who were also always interested in watching tennis was 87.50 percent; for boxing this number is 77.78 percent.  The percentages in the last column (Row Total) are always relative to the total number of cases.  There are many options in the Crosstabulation Results dialog that will allow you to produce different formats of banner tables; for example, you can simultaneously display the cell counts, row, column, and total percentages in the same table.


Description of Joint Frequency Distributions via Crosstabulations - Multi-way Tables with Control Variables

  Stub-and-Banner Tables - Multi-way Tables with Control Variables

When only two variables are crosstabulated, we call the resulting table a two-way table.  However, the general idea of crosstabulating values of variables can be generalized to more than just two variables.  For example, to return to the "soda" example presented earlier (see above), a third variable could be added to the data set.  This variable might contain information about the state in which the study was conducted (either Nebraska or New York).

         GENDER  SODA     STATE

------   ------  ----  --------

case 1     MALE     A  NEBRASKA

case 2   FEMALE     B  NEW YORK

case 3   FEMALE     B  NEBRASKA

case 4   FEMALE     A  NEBRASKA

case 5     MALE     B  NEW YORK

     .        .     .         .

     .        .     .         .

The crosstabulation of these variables would result in a 3-way table:

         STATE: NEW YORK      STATE: NEBRASKA

         -------------------  -------------------

          SODA:A  SODA:B       SODA:A  SODA:B

-------- ------- ------- ---  ------- ------- ---

G:MALE      20      30    50      5      45    50

-------- ------- ------- ---  ------- ------- ---

G:FEMALE    30      20    50     45       5    50

-------- ------- ------- ---  ------- ------- ---

            50      50   100     50      50   100

Theoretically, an unlimited number of variables can be crosstabulated in a single multi-way table.  However, research practice shows that it is usually difficult to examine and "understand" tables that involve more than 4 variables.  (Even though the Crosstabulation option will produce tables of much greater complexity, it is recommended to analyze relationships between the factors in such tables using modeling techniques such as Log-Linear Analysis or Correspondence Analysis).


Description of Joint Frequency Distributions via Crosstabulations - Graphical Representations of Multi-way Tables

  Stub-and-Banner Tables - Graphical Representations of Multi-way Tables

As with all analyses in STATISTICA, there are numerous graphics options available to aid in the interpretation of tables.  You can produce "double categorized" histograms, 3D histograms, or line-plots that will summarize the frequencies for up to 3 factors in a single graph (batches of graphs are produced to summarize higher-way tables).  Refer to the Crosstabulation Results dialog for further descriptions of these graphics options.


  Statistics in Crosstabulations - Introductory Overview

General Introduction

Pearson Chi-square

Maximum-Likelihood (M-L) Chi-square

Yates' correction

Fisher exact test

McNemar Chi-square

Coefficient Phi

Tetrachoric correlation

Coefficient of contingency (C)

Interpretation of contingency measures

Statistics Based on Ranks

See also,

Spearman R

Kendall tau

Sommer's d: d(X|Y), d(Y|X)

Gamma

Uncertainty Coefficients: S(X,Y), S(X|Y), S(Y|X)


  Statistics in Crosstabulations Introductory Overview - Statistics Based on Ranks

In many cases the categories used in the crosstabulation contain meaningful rank-ordering information; that is, they measure some characteristic on an ordinal scale (see Elementary Concepts).  Suppose we asked a sample of respondents to indicate their interest in watching different sports on a 4-point scale with the explicit labels (1) always, (2) usually, (3) sometimes, and (4) never interested.  Obviously, we can assume that the response sometimes interested is indicative of less interest than always interested, and so on.  Thus, we could rank the respondents with regard to their expressed interest in, for example, watching football.  When categorical variables can be interpreted in this manner, there are several additional indices that can be computed to express the relationship between variables.


  Statistics in Crosstabulations Introductory Overview - General Introduction

Crosstabulations generally allow us to identify relationships between the crosstabulated variables.  The following table illustrates an example of a very strong relationship between two variables: variable Age (Adult vs. Child) and variable Cookie preference (A vs. B).

           |COOKIE: A | COOKIE: B|

-----------+----------+----------+----

AGE: ADULT |    50    |      0   | 50

-----------+----------+----------+----

AGE: CHILD |     0    |     50   | 50

-----------+----------+----------+----

           |    50    |     50   |100

All adults chose cookie A, while all children chose cookie B.  In this case there is little doubt about the reliability of the finding, because it is hardly conceivable that one would obtain such a pattern of frequencies by chance alone; that is, without the existence of a "true" difference between the cookie preferences of adults and children.  However, in real-life, relations between variables are typically much weaker, and thus the question arises as to how to measure those relationships, and how to evaluate their reliability (statistical significance).  The following review includes the most common measures of relationships between two categorical variables; that is, measures for two-way tables.  The techniques used to analyze simultaneous relations between more than two variables in higher order crosstabulations are discussed in the context of the Log-Linear Analysis module and the Correspondence Analysis module.

Crosstabulation tables with up to 6 variables (6-way tables) can be generated automatically.  Higher-way tables of practically unlimited order can be produced using the case selection conditions option.  All measures of relations between crosstabulated variables are reported for two-way tables, even if they represent only "slices" of a larger multi-way table (see the description of the Crosstabulation Results dialog).


  Statistics in Crosstabulations Introductory Overview - Pearson Chi-square

The Pearson Chi-square is the most common test for significance of the relationship between categorical variables.  This measure is based on the fact that we can compute the expected frequencies in a two-way table (i.e., frequencies that we would expect if there was no relationship between the variables).  For example, suppose we ask 20 males and 20 females to choose between two brands of soda pop (brands A and B).  If there is no relationship between preference and gender, then we would expect about an equal number of choices of brand A and brand B for each sex.  The Chi-square test becomes increasingly significant as the numbers deviate further from this expected pattern; that is, the more this pattern of choices for males and females differs.

The value of the Chi-square and its significance level depends on the overall number of observations and the number of cells in the table.  Consistent with the principles discussed in Elementary Concepts, relatively small deviations of the relative frequencies across cells from the expected pattern will prove significant if the number of observations is large.

The only assumption underlying the use of the Chi-square (other than random selection of the sample) is that the expected frequencies are not very small.  The reason for this is that, actually, the Chi-square inherently tests the underlying probabilities in each cell; and when the expected cell frequencies fall, for example, below 5, those probabilities cannot be estimated with sufficient precision.  For further discussion of this issue refer to Everitt (1977), Hays (1988), or Kendall and Stuart (1979).


  Statistics in Crosstabulations Introductory Overview - Maximum-Likelihood Chi-square

The Maximum-Likelihood Chi-square tests the same hypothesis as the Pearson Chi-square statistic; however, its computation is based on Maximum-Likelihood theory.  In practice, the M-L Chi-square is usually very close in magnitude to the Pearson Chi-square statistic.  For more details about this statistic refer to Bishop, Fienberg, and Holland (1975), or Fienberg, S. E. (1977); the Log-Linear Analysis chapter of the manual also discusses this statistic in greater detail.


  Statistics in Crosstabulations Introductory Overview - Yates Correction

The approximation of the Chi-square statistic in small 2 x 2 tables can be improved by reducing the absolute value of differences between expected and observed frequencies by 0.5 before squaring (Yates' correction).  This correction, which makes the estimation more conservative, is usually applied when the table contains only small observed frequencies, so that some expected frequencies become less than 10 (for further discussion of this correction, see Conover, 1974; Everitt, 1977; Hays, 1988; Kendall & Stuart, 1979; and Mantel, 1974).


  Statistics in Crosstabulations Introductory Overview - Fisher Exact Test

This test is only available for 2x2 tables; it is based on the following rationale:  Given the marginal frequencies in the table, and assuming that in the population the two factors in the table are not related, how likely is it to obtain cell frequencies as uneven or worse than the ones that were observed?  For small n, this probability can be computed exactly by counting all possible tables that can be constructed based on the marginal frequencies.  Thus, the Fisher exact test computes the exact probability under the null hypothesis of obtaining the current distribution of frequencies across cells, or one that is more uneven.  Both one-sided and two-sided probabilities are reported.


  Statistics in Crosstabulations Introductory Overview - McNemar Chi-square

This test is applicable in situations where the frequencies in the 2 x 2 table represent dependent samples.  For example, in a before-after design study, we may count the number of students who fail a test of minimal math skills at the beginning of the semester and at the end of the semester.  Two Chi-square values are reported: A/D and B/C.  The Chi-square A/D tests the hypothesis that the frequencies in cells A and D (upper left, lower right) are identical.  The Chi-square B/C tests the hypothesis that the frequencies in cells B and C (upper right, lower left) are identical.


  Statistics in Crosstabulations Introductory Overview - Coefficient Phi

The Phi-square is a measure of correlation between two categorical variables in a 2 x 2 table.  Its value can range from 0 (no relation between factors; Chi-square=0.0) to 1 (perfect relation between the two factors in the table).  For more details concerning this statistic see Castellan and Siegel (1988, p. 232).


  Statistics in Crosstabulations Introductory Overview - Tetrachoric Correlation

This statistic is also only computed for (applicable to) 2 x 2 tables.  If the 2 x 2 table can be thought of as the result of two continuous variables that were (artificially) forced into two categories each, then the tetrachoric correlation coefficient will estimate the correlation between the two.


Statistics in Crosstabulations Introductory Overview - Coefficient of Cotingency

  Statistics in Crosstabulations Introductory Overview - Coefficient of Contingency

The coefficient of contingency is a Chi-square based measure of the relation between two categorical variables (proposed by Pearson, the originator of the Chi-square test).  Its advantage over the ordinary Chi-square is that it is more easily interpreted, since its range is always limited to 0 through 1 (where 0 means complete independence).  The disadvantage of this statistic is that its specific upper limit is "limited" by the size of the table; C can reach the limit of 1 only if the number of categories is unlimited (see Siegel, 1956, p. 201).


Statistics in Crosstabulations Introductory Overview - Interpretation of Cotingency Measures

  Statistics in Crosstabulations Introductory Overview - Interpretation of Contingency Measures

An important disadvantage of measures of contingency (reviewed above) is that they do not lend themselves to clear interpretations in terms of probability or "proportion of variance," as is the case, for example, of the Pearson r (see Correlations).  There is no commonly accepted measure of relation between categories that has such a clear interpretation.


  Statistics in Crosstabulations Introductory Overview - Spearman R

Spearman R can be thought of as the regular Pearson product-moment correlation coefficient (Pearson r); that is, in terms of the proportion of variability accounted for, except that Spearman R is computed from ranks.  As mentioned above, Spearman R assumes that the variables under consideration were measured on at least an ordinal (rank order) scale; that is, the individual observations (cases) can be ranked into two ordered series.  Detailed discussions of the Spearman R statistic, its power and efficiency can be found in Gibbons (1985), Hays (1981), McNemar (1969), Siegel (1956), Siegel and Castellan (1988), Kendall (1948), Olds (1949), or Hotelling and Pabst (1936).


  Statistics in Crosstabulations Introductory Overview - Kendall tau

Kendall tau is equivalent to the Spearman R statistic with regard to the underlying assumptions.  It is also comparable in terms of its statistical power.  However, Spearman R and Kendall tau are usually not identical in magnitude because their underlying logic, as well as their computational formulas are very different.  Siegel and Castellan (1988) express the relationship of the two measures in terms of the inequality:

-1 ≤ 3 * Kendall tau - 2 * Spearman R ≤ 1

More importantly, Kendall tau and Spearman R imply different interpretations:  While Spearman R can be thought of as the regular Pearson product-moment correlation coefficient as computed from ranks, Kendall tau rather represents a probability.  Specifically, it is the difference between the probability that the observed data are in the same order for the two variables versus the probability that the observed data are in different orders for the two variables.  Kendall (1948, 1975), Everitt (1977), and Siegel and Castellan (1988) discuss Kendall tau in greater detail.  Two different variants of tau are computed, usually called taub and tauc.  These measures differ only with regard as to how tied ranks are handled.  In most cases these values will be fairly similar, and when discrepancies occur, it is probably always safest to interpret the lowest value.


  Statistics in Crosstabulations Introductory Overview - Sommer's d:  d(X|Y), d(Y|X)

Sommer's d is an asymmetric measure of association related to tb (see Siegel & Castellan, 1988, p. 303-310).


  Statistics in Crosstabulations Introductory Overview - Gamma

The Gamma statistic is preferable to Spearman R or Kendall tau when the data contain many tied observations.  In terms of the underlying assumptions, Gamma is equivalent to Spearman R or Kendall tau; in terms of its interpretation and computation, it is more similar to Kendall tau than Spearman R.  In short, Gamma is also a probability; specifically, it is computed as the difference between the probability that the rank ordering of the two variables agree minus the probability that they disagree, divided by 1 minus the probability of ties.  Thus, Gamma is basically equivalent to Kendall tau, except that ties are explicitly taken into account.  Detailed discussions of the Gamma statistic can be found in Goodman and Kruskal (1954, 1959, 1963, 1972), Siegel (1956), and Siegel and Castellan (1988).


  Statistics in Crosstabulations Introductory Overview - Uncertainty Coefficients

These are indices of stochastic dependence; the concept of stochastic dependence is derived from the information theory approach to the analysis of frequency tables and the user should refer to the appropriate references (see Kullback, 1959; Ku & Kullback, 1968; Ku, Varner, & Kullback, 1971; see also Bishop, Fienberg, & Holland, 1975, p. 344-348).  S(Y,X) refers to symmetrical dependence, S(X|Y) and S(Y|X) refer to asymmetrical dependence.


  Multiple Responses/Dichotomies - Introductory Overview

Multiple response variables or multiple dichotomies often arise when summarizing survey data.  The nature of such variables or factors in a table is best illustrated with examples.  The many specific options for tabulating such variables are discussed in the context of the Multiple responses/dichotomies dialog.

Multiple Response Variables

Multiple Dichotomies

Crosstabulation of Multiple Responses/Dichotomies

Paired Crosstabulation of Multiple Response Variables

A Final Comment


  Multiple Responses/Dichotomies Introductory Overview - Multiple Response Variables

As part of a larger market survey, suppose you asked a sample of consumers to name their three favorite soft drinks.  The specific item on the questionnaire may look like this:

Write down your three favorite soft drinks:

1:________    2:________    3:________

Thus, the questionnaires returned to you will contain somewhere between 0 and 3 answers to this item.  Also, a wide variety of soft drinks will most likely be named.  Your goal is to summarize the responses to this item; that is, to produce a table that summarizes the percent of respondents who mentioned a respective soft drink.

The next question is how to enter the responses into a data file.  Suppose 50 different soft drinks were mentioned among all of the questionnaires.  You could of course set up 50 variables - one for each soft drink - and then enter a 1 for the respective respondent and variable (soft drink), if he or she mentioned the respective soft drink (and a 0 if not); for example:

          COKE  PEPSI  SPRITE  ....

          ----  -----  ------

case 1      0     1       0

case 2      1     1       0

case 3      0     0       1

     .      .     .       .

     .      .     .       .

This method of coding the responses would be very tedious and "wasteful."  Note that each respondent can only give a maximum of three responses; yet we use 50 variables to code those responses.  (However, if we are only interested in these three soft drinks, then this method of coding just those three variables would be satisfactory; to tabulate soft drink preferences, we could then treat the three variables as a multiple dichotomy; see below.)

Coding multiple response variables.  Alternatively, we could set up three variables, and a coding scheme for the 50 soft drinks.  Then we could enter the respective codes (or alpha labels) into the three variables, in the same way that respondents wrote them down in the questionnaire.

        Resp.1    Resp.2    Resp.3

        --------  --------  ------------

case 1  COKE      PEPSI     JOLT

case 2  SPRITE    SNAPPLE   DR PEPPER

case 3  PERRIER   GATORADE  MOUNTAIN DEW

 ...     ...       ...       ...

To produce a table of the number of respondents by soft drink we would now treat Resp.1 to Resp3 as a multiple response variable.  That table could look like this:

+-------------------------+---------+-----------+----------+

| N=500                   |         | Prcnt.of  | Prcnt.of |

| Category                |  Count  | Responses |  Cases   |

+-------------------------+---------+-----------+----------+

| COKE    : Coca Cola     |      44 |      5.23 |    8.80  |

| PEPSI   : Pepsi Cola    |      43 |      5.11 |    8.60  |

| MOUNTAIN: Mountain Dew  |      81 |      9.62 |   16.20  |

| PEPPER  : Doctor Pepper |      74 |      8.79 |   14.80  |

|  ...    :    ....       |      .. |      ...  |    ...   |

+-------------------------+---------+-----------+----------+

| Total Responses         |     842 |    100.00 |  168.40  |

+-------------------------+---------+-----------+----------+

Interpreting the multiple response frequency table.  The total number of respondents was n=500.  Note that the counts in the first column of the table do not add up to 500, but rather to 842.  That is the total number of responses; since each respondent could make up to 3 responses (write down three names of soft drinks), the total number of responses is naturally greater than the number of respondents.  For example, referring back to the sample listing of the data file shown above, the first case (Coke, Pepsi, Jolt) "contributes" three times to the frequency table, once to the category Coke, once to the category Pepsi, and once to the category Jolt.  The second and third columns in the table above report the percentages relative to the number of responses (second column) as well as respondents (third column).  Thus, the entry 8.80 in the first row and last column in the table above means that 8.8% of all respondents mentioned Coke either as their first, second, or third soft drink preference.

Repeated identical responses.  Unlike some other popular programs for computing tables for multiple response variables, the Crosstabulation option in the Basic Statistics and Tables module by default will ignore multiple identical responses.  For example, suppose a respondent lists as his three preferences Jolt, Jolt, Jolt.  STATISTICA will count that case only once, and consequently that person will only contribute once to the Jolt category in the frequency table (as well as crosstabulation tables; see below).


  Multiple Responses/Dichotomies Introductory Overview - Multiple Dichotomies

Suppose in the above example we were only interested in Coke, Pepsi, and Sprite.  As pointed out earlier, one way to code the data in that case would be as follows:

          COKE  PEPSI  SPRITE  ....

          ----  -----  ------

case 1            1

case 2      1     1

case 3                    1

 ...       ...   ...     ...

In other words, one variable was created for each soft drink, then a value of 1 was entered into the respective variable whenever the respective drink was mentioned by the respective respondent.  Note that each variable represents a dichotomy; that is, only 1''s and "not 1"s are allowed (we could have entered 1's and 0's, but to save typing we can also simply leave the 0's blank or missing).  When tabulating these variables, we would like to obtain a summary table very similar to the one shown earlier for multiple response variables; that is, we would like to compute the number and percent of respondents (and responses) for each soft drink.  In a sense, we "compact" the three variables Coke, Pepsi, and Sprite into a single variable (Soft Drink) consisting of multiple dichotomies.


Multiple Responses/Dichotomies Introductory Overview - Crosstabulation of Multiple Response/Dichotomies

  Multiple Responses/Dichotomies Introductory Overview - Crosstabulation of Multiple Responses/Dichotomies

The Crosstabulation option of the Basic Statistics and Tables module allows you to specify simple categorical variables (e.g., Gender: male or female), multiple response variables, as well as multiple dichotomies.  All of these types of variables can then be used in crosstabulation tables.  For example, we could crosstabulate a multiple dichotomy for Soft Drink (coded as described in the previous paragraph) with a multiple response variable Favorite Fast Foods (with many categories such as Hamburgers, Pizza, etc.), by the simple categorical variable Gender.  As in the frequency table, the percentages and marginal totals in that table can be computed from the total number of respondents as well as the total number of responses.  For example, consider the following hypothetical respondent:

Gender Coke Pepsi Sprite Food1 Food2

------ ---- ----- ------ ----- -----

FEMALE   1     1         FISH  PIZZA

This female respondent mentioned Coke and Pepsi as her favorite drinks, and Fish and Pizza as her favorite fast foods.  In the complete crosstabulation table she will be counted in the following cells of the table:

                       Food

                ---------------------      TOTAL No.

Gender  Drink   HAMBURG.  FISH  PIZZA  ... of RESP.

-------------------------------------  ... ---------

FEMALE  COKE                X     X            2

        PEPSI               X     X            2

        SPRITE

MALE    COKE

        PEPSI

        SPRITE

This female respondent will "contribute" to (i.e., be counted in) the crosstabulation table a total of 4 times.  In addition, she will be counted twice in the Female--Coke marginal frequency column if that column is requested to represent the total number of responses; if the user requests the marginal totals to be computed as the total number of respondents, then this respondent will only be counted once.


  Multiple Responses/Dichotomies Introductory Overview - Paired Crosstabulation of Multiple Response Variables

A unique option for tabulating multiple response variables is to treat the variables in two or more multiple response variables as matched pairs.  Again, this method is best illustrated with a simple example.  Suppose we conducted a survey of past and present home ownership.  We asked the respondents to describe their last three (including the present) homes that they purchased.  Naturally, for some respondents the present home is the first and only home; others have owned more than one home in the past.  For each home we asked our respondents to write down the number of rooms in the respective house, and the number of occupants.  Here is how the data for one respondent (say case number 112) may be entered into a data file:

Case no.  Rooms 1  2  3  No.Occ. 1  2  3

-------   -------------- ---------------

 112            3  3  4          2  3  5

This respondent owned three homes; the first had 3 rooms, the second also had 3 rooms, and the third had 4 rooms.  The family apparently also grew; there were 2 occupants in the first home, 3 in the second, and 5 in the third.

Now suppose we wanted to crosstabulate the number of rooms by the number of occupants for all respondents.  One way to do so is to prepare three different two-way tables; one for each home.  We can also treat the two factors in this study (Number of Rooms, Number of Occupants) as multiple response variables.  However, it would obviously not make any sense to count the example respondent 112 shown above in cell 3 Rooms - 5 Occupants of the crosstabulation table (which we would, if we simply treated the two factors as ordinary multiple response variables).  In other words, we want to ignore the combination of occupants in the third home with the number of rooms in the first home.  Rather, we would like to count these variables in pairs; we would like to consider the number of rooms in the first home together with the number of occupants in the first home, the number of rooms in the second home with the number of occupants in the second home, and so on.  This is exactly what will be accomplished if we asked for a paired crosstabulation of these multiple response variables.


  Multiple Responses/Dichotomies Introductory Overview - A Final Comment

When preparing complex crosstabulation tables with multiple responses/dichotomies, it is sometimes difficult (in our experience) to "keep track" of exactly how the cases in the file are counted.  The best way to verify that one understands the way in which the respective tables are constructed is to crosstabulate some simple example data, and then to trace how each case is counted.  The example section of the Crosstabulation chapter in the manual employs this method to illustrate how data are counted for tables involving multiple response variables and multiple dichotomies.


  Probability Distribution Calculator - Introductory Overview

The Probability Distribution Calculator facility allows you to compute, for various theoretical distributions and parameters (e.g., F, df 1, df 2), either (1) the upper or lower tail areas, given a user-specified variate value (two sided probability values can be computed for symmetrical distributions; e.g., the normal distribution), or (2) the critical values, given a user-specified probability value.

One of the useful functions of the Probability Distribution Calculator facility is to compute critical values for statistical significance testing, or to compute p-levels (significance levels), given the variate values of a particular distribution (usually F, t, or z).  The Elementary Concepts chapter of the manual describes the logic behind statistical significance testing.  To summarize, suppose we have two groups - 50 males and 50 females - and we measure the height of each person in our sample.  Our goal is to test whether or not males are taller than females in the population from which we obtained our sample (e.g., among college students).  The appropriate statistical test here would be the t-test for independent samples.  Without going into computational details, the t statistic is basically the mean difference between the two groups, standardized by the variability in the data.

Now suppose we have replicated our study over and over and have repeatedly taken samples of 50 males and 50 females from the population, measured their heights, and computed a t statistic for each sample.  After replicating the study 1000 times or so, we could plot a distribution of the t statistic over the 1000 "experiments;" this distribution is called a sampling distribution.  Luckily, given some assumptions about the nature and distribution of the variables of interest (Height in this case), we can infer what that sampling distribution will be without having to replicate the study 1000 times.  In this case, if Height is normally distributed in the population and if there is no difference in the means or in the variability of males and females, then we can look up the percentage points of the t distribution in a table.  The Probability Calculator option in STATISTICA provides exactly this function; that is, it allows you to "look up" the "tabulated" percentage values for the sampling distributions of the most common statistics such as the t statistic.

To continue with the simple example above, if after just one sample from our population, we obtain a t value that is highly "unusual" or improbable (e.g., p < .01) given the tabulated values of t, then we conclude (after making sure that the variability in the two groups is about the same) that the assumption of equal means must not be true.  Thus we reject the hypothesis that females are as tall as males.

The Probability Distribution Calculator option will compute the percentage points (integral) for various distributions.  It will also compute the inverse of the integral; that is, you can enter a desired significance level and STATISTICA will compute the critical value of the respective statistic.  For details of available tests, refer to Probability Distribution Calculator.


  Other Significance Tests - Introductory Overview

This option brings up a dialog in which you can perform various statistical tests for comparing means, correlations, percentages, etc.  Refer to the Other Significance Tests dialog for more information.


Basic Statistics - Opening Menu

  Basic Statistics - Startup Panel

The Basic Statistics and Tables module of STATISTICA contains the following analytic procedures (see also Basic Statistics and Tables - Index).

  Descriptive Statistics Introductory Overview

Use this option to produce descriptive summary statistics, simple frequency tables, and summary graphs.  The available statistics are further described in the context of the Descriptive Statistics dialog and the Descriptive Statistics Options dialog.

  Correlation Matrices Introductory Overview

Use this option to compute Pearson product-moment correlations (Pearson r).  STATISTICA can compute square and rectangular matrices, using pairwise or casewise deletion of missing data.  Numerous accompanying statistics (including significance levels, means, standard deviations, etc.) can also be computed.  Various 2D and 3D graphs can be created in order to visualize the relationships among variables.  For further details concerning available options refer to the Correlation matrices dialog.  Additional nonparametric alternatives to the Pearson product-moment are available for crosstabulation tables (see the description of the Crosstabulation Results dialog; or the brief description of statistics), as well as via the Nonparametrics and Distributions module.

  t-test for Independent Samples Introductory Overview

Use this option to compute the t-test for independent samples or groups (for example, to compare the responses of male and female respondents to a question on a survey).  It is recommended that the data file be arranged so that each case represents one individual, identified by a grouping variable.  Alternatively, STATISTICA can also compute t-tests if the data were entered such that each column (variable) in the data file represents the data for one group.  Various graphs are available to aid in the interpretation of results (see the description of the t-test for independent samples dialog).  Significance of difference between a group mean and population or expected means can be tested using the Probability Calculator.  The Probability Calculator can also be used to test differences between proportions.  Nonparametric alternatives to the t-test for independent samples are also available in the Nonparametrics and Distributions module.

  t-test for Dependent Samples Introductory Overview

Use this option to compute t-tests for dependent or correlated samples (for example, to compare the responses from the same persons to a question on a survey before and after an election).  Both individual t-tests as well as matrices of t-tests can be computed.  Various graphs are available to aid in the interpretation of results (see the description of the t-test for dependent samples dialog).  Nonparametric alternatives to the t-test for dependent samples are also available in the Nonparametrics and Distributions module.

  Breakdown:  Descriptive Statistics by Groups Introductory Overview

Use this option to compute various descriptive statistics broken down by groups (e.g., by gender and age group).  Specifically, the user can compute -- broken down by groups -- various descriptive statistics (e.g., means, standard deviations, etc.), correlation matrices, summary graphs, etc.  This option also allows the user to perform complete one-way ANOVA's, and provides tests of the homogeneity of variances and post-hoc tests of mean differences.  Refer to the Breakdown Results and the Post-hoc Comparison dialog for a more detailed description of the available statistics.

  Frequency Tables Introductory Overview

Use this option to compute and review the distribution of variables.  Frequency tables can be computed for categorical variables, variables containing integer values, or for continuous variables.  The user can also define categories for frequency counts by specifying logical selection (categorization) conditions for assigning cases to categories.  A number of tests for the normal distribution are also available. For a description of available options refer to the Frequency tables dialog.  Additional distribution fitting methods (for non-normal distributions) are available in the Nonparametrics and Distributions module and the Survival Analysis module.

  Tables and Banners Introductory Overview

Use this option to compute crosstabulation tables.  STATISTICA will compute various statistics for two-way tables as well as a wide variety of 2D and 3D graphical summaries (see the description of the Crosstabulation Results dialog).  Note that the user can crosstabulate categorical variables, as well as multiple response and multiple dichotomy variables.

  Probability Distribution Calculator Introductory Overview

This option will pop up a probability calculator for computing:

(1)  The significance levels for the common statistical distributions (e.g., t, Chi-square, F, z);

(2)  The "critical values" for selected distributions given user-specified probabilities;

Refer to the Probability Distribution Calculator dialog  for detailed descriptions of the available options.

  Other Significance Tests Introductory Overview

This option will allow you to perform various statistical tests for comparing means, correlations, percentages, etc.  Refer to the Other Significance Tests dialog for more information.


  Basic Statistics - Descriptive Statistics

A general discussion of descriptive statistics is provided in the overview section.  When you click on the Descriptive Statistics option in the Startup Panel, the Descriptive Statistics dialog will open.

Descriptive Statistics dialog:

Variables

Detailed Descriptive Statistics

Options

Statistics

Distribution

Categorization

Box & Whisker Plot for All Variables

Probability Plots

2D Scatterplot (/with names)

Matrix

3D Scatterplot (/with names)

Surface

Categorized Box & Whisker Plots

Categorized Means (interaction) plots

Categorized Histograms

Categorized Scatterplots

3D Bivariate Distribution Histogram

Other descriptive statistics.  The Basic Statistics and Tables module includes a selection of the most often-used descriptive statistics.  An additional set of ordinal descriptive statistics and some less frequently-used ones (e.g., user-specified percentiles, harmonic means, etc.) are also included in the Nonparametrics and Distributions module; in that module a variety of non-normal distributions can also be fit to the data.  More specialized descriptive statistics are included in other modules of STATISTICA.

See also, Quick Basic Stats


  Descriptive Statistics - Variables

This option will bring up the standard variable selection dialog in which you can select the variables for the analysis.


  Descriptive Statistics - Detailed Descriptive Statistics

This option will open a Scrollsheet with the descriptive statistics for all of the previously selected variables.  You can request specific descriptive statistics in the Statistics dialog via the More Statistics button.


  Descriptive Statistics - Options

Casewise (listwise) deletion of MD:  If casewise deletion of missing data is selected, then STATISTICA will ignore all cases that have missing data for any of the variables selected in the list.  If this check box is not selected, then all valid data points will be included in the analyses for the respective variables (pairwise deletion of missing data, resulting possibly in unequal valid n per variable).

Display long variable names:  If this check box is set, then long variable names (if any, see Spreadsheet Edit Specs) will be displayed along with the short names in the first column of the Scrollsheet.  If no long variable names have been specified for any of the selected variables, then the setting of this check box will have no effect.

Extended precision calculations:  STATISTICA employs proprietary extended precision algorithms in order to minimize round-off error in the computations.  This option should be selected if the variables in the analysis show extremely small relative variances (variance divided by the mean), for example, if all values for a variable range between 10000.000001 and 10000.000002 (note that there is a difference between small variance and small relative variance; e.g., the relative variance of values in the range of .0000000000000001 to .0000000000000002 is not small).  For extremely large data files with many thousands of cases, the computations may be somewhat slower when this check box is set.


  Descriptive Statistics - Statistics

Note that additional descriptive statistics (mode, average deviation, etc.) are available in the Nonparametrics and Distributions module.

Median & quartiles:  If checked, the Detailed descriptive statistics Scrollsheet will contain the median (50th percentile) and quartiles (25th and 75th percentiles) for all variables.  The median is defined as the value that divides the distribution of all values in half; that is, 50% of all values for the respective variable will fall below the median and 50% will be greater than the median.  The 25th and 75th percentiles (quartiles) are defined accordingly.

Confidence limits for the means:  The idea of confidence limits for the mean is introduced in the Overview section.  This option will compute the respective (Alpha) confidence limits around the means.

More statistics:  This button will bring up a dialog window for selecting additional descriptive statistics that are to be reported in the Detailed descriptive statistics Scrollsheet. Available statistics are: valid n, mean, sum, median, standard deviation, variance, standard error of the mean, 95% confidence limits of the mean, minimum, maximum, lower and upper quartiles, range, quartile range, skewness, kurtosis, and the standard errors of the skewness and kurtosis (additional statistics are available in the Nonparametrics and Distributions module).


  Descriptive Statistics - Distribution

Frequency tables:  This option will bring up a cascade of Scrollsheets with the frequency distributions for the selected variables (one Scrollsheet per variable).  The manner in which the selected variables will be categorized depends on the selections made in the Categorization box (to the right):  The full range of values in the selected variables can be divided into a specific Number of intervals (use this method if the selected variables have continuous non-integer values).  Alternatively, STATISTICA can use Integer intervals (categories); if this option is chosen then:

(1)  All non-integer values will be ignored;

(2)  Tests of normality (see below) will not be available.

Note that an extensive selection of categorization methods and frequency table statistics are available if you choose the Frequency Tables option from the Basic Statistics and Tables startup panel.

Histograms:  This option will produce a cascade of histograms, analogous to the Frequency tables.  If Normal expected frequencies (see below) is selected then the histograms will also display the normal curve, superimposed over the observed frequencies.

Normal expected frequencies:  This check box is only available (active) if the Number of intervals button is set in the Categorization box (to the right).  If selected, subsequent Scrollsheets will contain the expected normal frequencies (cumulative frequencies and relative frequencies) for each category.  The Histograms option will display the normal curve superimposed over the observed frequencies.  A wide variety of non-normal distributions can be fit to observed data in the Nonparametrics and Distributions module; specialized distributions for survival and reliability studies are available in the Survival Analysis module.

Kolmogorov-Smirnov test for normality:  This check box is only available (active) if the Number of intervals button is set in the Categorization box (to the right).  If selected, subsequent frequency Scrollsheets will include the results of the Kolmogorov-Smirnov one-sample test of normality.  If the D statistic is significant, then the hypothesis that the respective distribution is normal should be rejected.  Two probability (significance) values will be reported for each Kolmogorov-Smirnov D:  The first is based on the probability values as tabulated by Massey (1951); those probability values pertain to cases when the mean and standard deviation of the normal distribution are known a-priori and not estimated from the data.  However, these parameters are typically computed from the actual data.  In this case, the test for normality involves a complex conditional hypothesis ("how likely is it to obtain a D statistic of this magnitude or greater, contingent upon the mean and standard deviation computed from the data"), and the Lilliefors probabilities should be interpreted (Lilliefors, 1967).  Note that, in recent years, the Shapiro-Wilks'' W test (see below) has become the preferred test of normality because of its good power properties as compared to a wide range of alternative tests (see Shapiro, Wilk, & Chen, 1968).

Shapiro-Wilks' W test:  This check box is only available (active) if the Number of intervals button is set in the Categorization box (to the right).  If selected, subsequent frequency Scrollsheets will include the results of the Shapiro-Wilks' W test of normality.  If the W statistic is significant, then the hypothesis that the respective distribution is normal should be rejected.  The Shapiro-Wilks' W test is the preferred test of normality because of its good power properties as compared to a wide range of alternative tests (see Shapiro, Wilk, & Chen, 1968).  The algorithm implemented in STATISTICA employs an extension to the test described by Royston (1982), which allows it to be applied to samples with up to 2000 observations; if there are more than 2000 observations, then this test cannot be performed.


  Descriptive Statistics - Categorization

The options selected in this box will only affect the frequency tables and histograms produced via the options in the Distribution box (to the left).  The Descriptive Statistics option has only two modes of categorizing the values of selected variables for the frequency table; a number of additional options, graphs, and statistics are available via the Frequency tables option (on the Basic Statistics and Tables startup panel).

Number of intervals:  If this radio button is set, then the range of values will for the selected variables will be divided into approximately the requested number of intervals for subsequent Frequency tables Scrollsheets or Histograms.  This option is appropriate when the variables to be tabulated are continuous in nature.  The tests of normality (Normal expected frequencies and KS and Lilliefors test) are only available if this option is chosen.  Note that the actual number of categories that will be produced may sometimes differ from the number of intervals requested.  STATISTICA will produce "neat" intervals; that is, interval boundaries and widths with the last digit being 1, 2, or 5 (e.g., 10.5, 11.0, 11.5, etc.).  Such "simple" or "neat" intervals are more easily interpreted than interval boundaries defined by many significant digits (e.g., 10.12423, 10.13533, etc.).  Full control over the method of categorization of variables is available via the Basic Statistics and Tables Frequency tables option.

Integer intervals:  Chose this method of categorization if the variables to be tabulated can be interpreted as integer categories, or contain only integer values.  If this method is chosen, all non-integer values will be ignored when producing Frequency tables or Histograms via the Distribution options; the choice of Categorization in this box will not affect other computations (e.g., of Detailed descriptive statistics).


  Descriptive Statistics - Box & Whisker Plot for All Variables

This option will produce a box and whisker plot for the selected variables.  The box and whisker plot will summarize each variable by three components:

(1)	A central line to indicate central tendency or location;

(2)	A box to indicate variability around this central tendency;

(3)	Whiskers around the box to indicate the range of the variable.

After clicking on this button you can choose to plot for each variable:

(1)	Medians (central line), quartiles (box), and ranges (whiskers);

(2)	Means, standard errors of the means, and standard deviations;

(3)	Means, standard deviations, and 1.96 times the standard deviations (95% normal confidence interval for individual observations around the mean);

(4)	Means, standard errors of the means, and 1.96 times the standard errors of the means (95% normal confidence interval for means).


  Descriptive Statistics - Probability Plots

Normal probability plots button:  This option will produce a cascade of normal probability plots for the selected variables, one plot per selected variable.  For more information on how the standard normal probability plot is constructed, see Normal Probability Plots.

Half-normal probability plots button:  This option will produce a cascade of half-normal probability plots for the selected variables, one plot per selected variable.  For more information on how the half-normal probability plot is constructed, see Half-Normal Probability Plots.

Detrended normal probability plots button:  This option will produce a cascade of detrended normal probability plots for the selected variables, one plot per selected variable.  For more information on how the detrended normal probability plot is constructed, see Detrended Normal Probability Plots.


  Descriptive Statistics - 2D Scatterplots (/with names)

This option will produce a cascade of scatterplots for selected pairs of variables, one plot per variable pair.  If the 2D scatterplot option is chosen, then the plot will show the regression line and the standard error of the predicted values (as error lines) in the scatterplot.  If the /w names button is used, then the scatterplot will not contain those lines, but will identify the points in the scatterplot with the case numbers or names (if case names are specified in the respective data file).


  Descriptive Statistics - Matrix

This option will produce a scatterplot matrix for selected variables.


  Descriptive Statistics - 3D Scatterplots (/with names)

This option will produce a 3D scatterplot for a selected triplet of variables.  If the /w names button is used, then the points in the scatterplot will be identified by the case numbers or names (if case names are specified in the respective data file).


  Descriptive Statistics - Surface

This option will produce a 3D scatterplot for a selected triplet of variables, and fit a quadratic surface to the data.


  Descriptive Statistics - Categorized Box & Whisker Plots

This option will produce a cascade of categorized box and whisker plots (see above) for the selected variables, one plot per selected variable.  After clicking on this button, the user is first prompted to select up to three categorical variables (e.g., Gender, Ethnic Origin).  For each selected variable (via the Variables button), STATISTICA will produce a box and whisker plot broken down (categorized) by the categorical variables (e.g., separately for males and females for each ethnic group).  Note that more complex Breakdown analyses are available via the Breakdown: Descriptive statistics by groups option on the startup panel.


  Descriptive Statistics - Categorized Means (Interaction) Plots

This option will produce a standard interaction plot of means by one, two, or three categorical variables (e.g., by Gender and Ethnic Origin).  After selecting this option, the user is prompted to select the categorization variables.  Overall, the interaction plot can show the means broken down by three categories (cascades of interaction plots to show higher-way interactions can be produced via the Breakdown: Descriptive statistics by groups option on the startup panel).  If one ("dependent") variable was selected via the Variable option, then the user can specify up to three categorization variables.  If more than one variable was selected via the Variable option, then up to two categorization variables can be selected; the different (dependent) variables will be represented by different line patterns (colors) in the graph.


  Descriptive Statistics - Categorized Histograms

This option will produce a cascade of categorized histograms for the selected variables, one plot per selected variable.  After clicking on this button, the user is first prompted to select up to two categorical variables (e.g., Gender, Ethnic Origin).  For each selected (via the Variables button) variable STATISTICA will then produce a histogram, broken down (categorized) by the categorical variables (e.g., separately for males and females for each ethnic group).  Note that more complex Breakdown analyses and graphs are available via the Breakdown: Descriptive statistics by groups option on the startup panel.


  Descriptive Statistics - Categorized Scatterplots

This option will produce a cascade of categorized scatterplots for selected pairs of variables, one plot per pair.  After clicking on this button, the user is first prompted to select two lists of variables (from among those originally selected via the Variables button).  Scatterplots will be produced for each variable in the first list with each variable in the second list.  Next the user will be prompted to select up to two categorical variables (e.g., Gender, Ethnic Origin).  STATISTICA will then produce a cascade of scatterplots broken down (categorized) by the categorical variables (e.g., separately for males and females for each ethnic group).  Note that more complex Breakdown analyses and graphs are available via the Breakdown: Descriptive statistics by groups option on the startup panel.


Descriptive Statistics - 3D Bivariate Distribution

  Descriptive Statistics - 3D Bivariate Distribution Histogram

This option will produce a cascade of 3D histograms for selected pairs of variables, one plot per pair.  After clicking on this button, the user will first be prompted to select two lists of variables (from among those originally selected via the Variables button).  3D histograms will be produced for each variable in the first list with each variable in the second list.


  Statistics Dialog

The options selected in this dialog will determine which statistics will be computed when the user selects Detailed descriptive statistics from the Descriptive Statistics dialog.  Refer to the introductory overview section for a discussion of the most common descriptive statistics and their interpretation.

Computation of median and quartiles (25th, 50th, and 75th percentiles).  When the distribution of values cannot be exactly divided into halves and quartiles, then there are different ways to compute the respective median and quartile values (and percentiles).  The specific method of computation for those values can be configured "system-wide" via the STATISTICA Defaults:  General dialog (see General Conventions chapter in Volume I of the manual; this dialog is accessible via the Options pull-down menu option General).

Statistics dialog:

Default button:  This option will reset the selection of descriptive statistics to the default selection; the default statistics are: Valid n, Mean, Standard Deviation, and Minimum & Maximum.

All button:  This option will automatically select all available statistics.

Valid n:  Set this check box to compute the number of valid cases for each selected variable.

Mean:  Set this check box to compute the means.

Sum:  Set this check box to compute the sums.

Median:  Set this check box to compute the medians.  The median (or 50th percentile) is defined as the value that divides the distribution of all values in half; that is, 50% of all values for a respective variable will fall below the median, 50% will be greater than the median.  Note the specific computational procedure that is used to determine the median can be configured "system-wide" via the STATISTICA Defaults:  General dialog (see General Conventions chapter in Volume I of the manual; this dialog is accessible via the Options pull-down menu option General).

Standard deviation:  Set this check box to compute the standard deviations.  The standard deviation is computed as the square root of the sum of squared deviations (from the mean) divided by n-1.

Variance:  Set this check box to compute the variances.  The variance of a variable is computed as the sum of squared deviations (from the mean) divided by n-1.

Standard error of the mean:  The standard error of the mean is computed as the standard deviation divided by the square root of n.

95% confidence limits of the mean:  The confidence limits of the mean are computed based on the respective critical t values.  Refer to the Introductory Overview section for a basic discussion of confidence limits.

Minimum & Maximum:  Set this check box to compute the minima and maxima.

Lower & upper quartiles:  Set this check box to compute the 25th and 75th percentile (lower and upper quartile, respectively; user-specified percentiles can be computed via the Nonparametrics and Distributions module).  Note the specific computational procedure that is used to determine the quartile values can be configured "system-wide" via the STATISTICA Defaults:  General dialog (see General Conventions chapter in Volume I of the manual; this dialog is accessible via the Options pull-down menu option General).

Range:  Set this check box to compute ranges (maximum minus minimum).

Quartile range:  The quartile range is computed as the upper quartile value (75th percentile) minus the lower quartile value (25th percentile).

Skewness:  The skewness is a measure of the symmetry of the distribution of values.  If the distribution is symmetrical, then the skewness is equal to zero.

Kurtosis:  The kurtosis is a measure of "peakedness" of the distribution of values.  If the distribution follows the standard normal distribution, then the value of the kurtosis is zero.

Standard error of skewness:  Set this check box to compute the standard error of the skewness.

Standard error of kurtosis:  Set this check box to compute the standard error of the kurtosis.


  t-test for Independent Samples

A general overview covering the t-test for independent samples is provided in the overview section.

t-test for Independent Samples (Groups) dialog:

Input File

Variables

Code for Group 1; Code for Group 2

t-tests

Options

Box & Whisker Plots

Categorized Graphs


  t-test for Independent Samples - Input File

This combo box has two settings: One record per case (use grouping variable) and Each variable contains the data for one group.  The appropriate setting of this box depends on the way in which the user has set up the data file for the t-test for independent samples.  The default and recommended way to set up a data file is to enter data case by case; that is, to let each row in the data file represent one case (e.g., individual, respondent) and to let each column in the data file represent one variable or measurement (e.g., response to a questionnaire item).  In this set-up, a grouping variable (e.g., Gender) should be included to denote to which group each case belongs.  The default setting of this combo box (One record per case) expects the data to be arranged precisely in this manner.  However, for simple data analyses, it is sometimes easier to enter the data so that each column in the data file (variable) represents the responses of one group (e.g., the data for all male respondents were entered into the first column of the file and the data for all female respondents were entered into the second column).  If your data are arranged in this manner, set this combo switch to Each variable contains the data for one group.


  t-test for Independent Samples - Variables

This option will bring up the standard two variable selection dialog.  Specify one grouping variable (e.g., Gender) and a list of dependent variables for the comparison.  STATISTICA will compute the t-test for all variables in the dependent variable list, comparing the two groups that are identified by the two selected group codes (see below) in the grouping variable.


  t-test for Independent Samples - Code for Group 1; Code for Group 2

Specify the two codes that identify the two groups in the grouping variable that are to be compared.  If you are not sure about the codes that were used in the grouping variables to identify the groups, double-click on the edit field, and a pop-up window (see Variable Values Window) will appear containing all integer codes and their alphanumeric equivalents found in the grouping variable in the current data file.  You can select a grouping code in this pop-up window (i.e., transfer it to the edit field) by double-clicking on it.


  t-test for Independent Samples - t-tests

After clicking on this button, the t- tests for independent samples will be computed and displayed in a results Scrollsheet.  The detail and formatting of the results depends on your selections in the Options box below this button.


  t-test for Independent Samples - Options

The selections from this group of check boxes will determine the detail and formatting of the t-test for independent samples results Scrollsheet.

Casewise deletion of missing data:  By default, missing data will be excluded on a variable-by-variable basis (i.e., pairwise missing data deletion).  If this check box is set, then STATISTICA will exclude all cases from the analysis that have missing data for any of the variables in the dependent variable list (i.e., casewise missing data deletion).

Display long variable names:  If this check box is set, then the first column of the Scrollsheet will show not only the names of the respective dependent variables, but also their long variable names (if one was specified, see Spreadsheet Edit Specs).

t-test with separate variance estimate:  In order to compute the t-test for independent samples, STATISTICA has to estimate the variance of the difference for the respective dependent variable.  By default, this variance is estimated from the pooled (averaged) within-group variances.  If the variances in the two groups are widely different, and the number of observations in each group also differs, then the t-test computed in this manner may not accurately reflect the statistical significance of the difference.  In that case one should use this option to compute the t-test with separate variance estimates and approximate degrees of freedom (see Blalock, 1972).

Multivariate test (Hotelling T**2):  Hotelling T**2 test is a multivariate test for differences in means between two groups.  This test will only be computed if more than one dependent variable was selected.  Because this test is based on the within-group variance/covariance matrices for the dependent variables, it will automatically exclude missing data casewise from the computations.  That is, this test will be computed only for cases that have complete data for all dependent variables in the selected list.

Levene's test (homogeneity of variances):  The standard t-test for independent samples is based on the assumption that the variances in the two groups are the same (homogeneous).  A powerful statistical test of this assumption is Levene's test.  For each dependent variable, an analysis of variance is performed on the absolute deviations of values from the respective group means.  If the Levene test is statistically significant, then the hypothesis of homogeneous variances should be rejected.  However, note that the t-test for independent samples is a robust test as long as the n per group is greater than 30; thus, a significant Levene test does not necessarily call into question the validity of the t-test (refer to the manual for details; see also the general overview to the t-test for independent samples).


  t-test for Independent Samples - Box & Whisker Plots

This option will produce a cascade of box and whisker plots for the dependent variables; one box plot for each variable will be produced.  Box and whisker plots summarize the distribution of the dependent variable for each group.  Specifically each group will be represented by one box and whisker "component"  which is made up of three "parts":

(1)	A central line to indicate central tendency or location;

(2)	A box to indicate variability around this central tendency;

(3)	Whiskers around the box to indicate the range of the variable.

After clicking on this button you can choose to plot for each group:

(1)	Medians (central line), quartiles (box), and ranges (whiskers);

(2)	Means, standard errors of the means, and standard deviations;

(3)	Means, standard deviations, and 1.96 times the standard deviations (95% normal confidence interval for individual observations around the mean);

(4)	Means, standard errors of the means, and 1.96 times the standard errors of the means (95% normal confidence interval for means).


  t-test for Independent Samples - Categorized Graphs

Categorized histograms button:  This option will produce a cascade of categorized histograms (one for each dependent variable), summarizing the distribution of the respective variable in the two groups.

Categorized normal probability plots button:  This option will produce a cascade of normal probability plots for the dependent variables, categorized by the two groups.

Categorized detrended probability plots button:  This option will produce a cascade of detrended normal probability plots for the dependent variables, categorized by the two groups.

Categorized scatterplots button:  This option will produce a cascade of categorized scatterplots for selected pairs of variables, one plot per pair.  After clicking on this button, the user will be prompted to select two lists of variables (from the list of dependent variables).  Scatterplots will be produced for each variable in the first list with each variable in the second list, categorized by the two groups for the t-test.


  t-test for Independent Samples - Compare Columns (Variables)

A general discussion of the t-test for independent samples is provided in the overview section.  This dialog becomes available when you select the Each variable contains the data for one group option as the Input File (see below).

t-test for Independent Samples (Groups) dialog:

Input File

Variables (Groups)

t-tests

Options

Box & Whisker Plots


  t-test for Independent Samples - Input File

This combo box has two settings: One record per case (use grouping variable) and Each variable contains the data for one group.  The appropriate setting of the this box depends on the way in which the user has set up the data file for the t-test for independent samples.  The default and recommended way to set up a data file is to enter data case by case; that is, to let each row in the data file represent one case (individual, respondent) and to let each column in the data file represent one variable or measurement (e.g., response to a questionnaire item).  In this set-up, a grouping variable (e.g., Gender) should be included to denote to which group each case belongs.  The default first setting of this combo box expects the data to be arranged in this manner.  However, for simple data analyses, it is sometimes easier to enter the data so that each column in the data file (variable) represents the responses of one group (e.g., the data for all male respondents was entered into the first column of the file and the data for all female respondents was entered into the second column).  If your data are arranged in this manner, set this combo switch to Each variable contains the data for one group.


  t-test for Independent Samples - Variables (Groups)

This option will bring up the standard two variable selection dialog.  Specify two lists of variables.  Since this setting of the Input file combo box assumes that each variable represents the data for one group, each variable (group) in the first list will be compared with each variable (group) in the second list.


  t-test for Independent Samples - t-tests

After clicking on this button, the t-tests for independent samples will be computed and displayed in a results Scrollsheet.  The detail and formatting of the results depends on the selections that you made in the Options box below this button.


  t-test for Independent Samples - Options

The selections from this group of check boxes will determine the detail and formatting of the t-test for independent samples results Scrollsheet.

Display long variable names:  If this check box is set, then the first column of the Scrollsheet will show not only the names of the respective variables (groups), but also their long (variable) names (if one was specified, see Spreadsheet Edit Specs).

t-test with separate variance estimate:  In order to compute the t-test for independent samples, STATISTICA has to estimate the variance of the difference for the respective pair of variables (groups).  By default, this variance is estimated from the pooled (averaged) within-group variances.  If the variances in the two groups are widely different, and the number of observations in each group also differs, then the t-test computed in this manner may not accurately reflect the statistical significance of the difference.  In that case one should compute the t-test with separate variance estimates and approximated degrees of freedom (see Blalock, 1972).

Levene's test (homogeneity of variances):  The standard t-test for independent samples is based on the assumption that the variances in the two groups are the same (homogeneous).  A powerful statistical test of this assumption is Levene's test.  For each dependent variable, an analysis of variance is performed on the absolute deviations of values from the respective group means.  If the Levene test is statistically significant, then the hypothesis of homogeneous variances should be rejected.  However, note that the t-test for independent samples is a robust test as long as the n per group is greater than 30; thus, a significant Levene's test does not necessarily call into question the validity of the t-test (refer to the manual for details; see also the general overview to the t-test for independent samples).


  t-test for Independent Samples - Box & Whisker Plots

This option will produce a cascade of box and whisker plots for the selected variables (groups).  Specifically, a graph will be produced for each pair of variables (groups) from the first list with the second list (i.e., one graph for each t-test).  Box and whisker plots summarize the distributions within each group; specifically each group will be represented by one box and whisker "component" which is made up of three "parts:"

(1)	A central line to indicate central tendency or location;

(2)	A box to indicate variability around this central tendency;

(3)	Whiskers around the box to indicate the range of the variable.

After clicking on this button you can choose to plot for each group:

(1)	Medians (central line), quartiles (box), and ranges (whiskers);

(2)	Means, standard errors of the means, and standard deviations;

(3)	Means, standard deviations, and 1.96 times the standard deviations (95% normal confidence interval for individual observations around the mean);

(4)	Means, standard errors of the means, and 1.96 times the standard errors of the means (95% normal confidence interval for means).


  Highlighting Significant Results

In the current Scrollsheet, statistically significant results (p < alpha) are highlighted.  Enter the desired new alpha level, and a new Scrollsheet will be prepared with highlights reflecting the new significance criterion.  You can later request a different threshold p-level by pressing on the Options Toolbar button on the Scrollsheet Toolbar.

The general logic of significance testing is described in the Elementary Concepts chapter of the manual.


  t-test for Dependent Samples

A general discussion of the t-test for dependent samples is provided in the overview section.

t test for Dependent (Correlated) Samples dialog:

Variables

t-tests

Box & whisker plots

Display

Options


  t-test for Dependent Samples - Variables

This option will bring up the standard two-variable-lists selection dialog in which you can specify two lists of variables to be analyzed.  Each variable in the first list will be compared with each variable in the second list.


  t-test for Dependent Samples - t-tests

After clicking on this button, the t-tests for dependent samples will be computed and displayed in a results Scrollsheet.  The detail and formatting of the results depends on the selections that you made in the Display box below this button.


  t-test for Dependent Samples - Box & Whisker Plot

This option will produce a cascade of box and whisker plots for the selected variables.  Specifically, a graph will be produced for each pair of variables from the first list with the second list (i.e., one graph for each t-test).  Box and whisker plots summarize the distribution of each variable in the comparison.  Specifically, each variable will be represented by one box and whisker "component"  which is made up of three "parts:"

(1)	A central line to indicate central tendency or location;

(2)	A box to indicate variability around this central tendency;

(3)	Whiskers around the box to indicate the range of the variable.

After clicking on this button you can choose to plot for each variable:

(1)	Medians (central line), quartiles (box), and ranges (whiskers);

(2)	Means, standard errors of the means, and standard deviations;

(3)	Means, standard deviations, and 1.96 times the standard deviations (95% normal confidence interval for individual observations around the mean);

(4)	Means, standard errors of the means, and 1.96 times the standard errors of the means (95% normal confidence interval for means).


  t-test for Dependent Samples - Display

Matrix of t-tests:  If this button is set, then clicking on the t-tests button will produce a cascade of Scrollsheets reporting for each pair of variables (from the two lists) the mean difference, the t-value for the respective difference, and the significance level (p-level) for the respective t-value.

Detailed table of results:  If this radio button is set then clicking on the t-tests button will produce a summary results Scrollsheet reporting for each t-test the means, standard deviations, valid n, etc.


  t-test for Dependent Samples - Options

Casewise deletion of missing data:  By default, STATISTICA will include in the computations all cases with valid data for the respective two variables in the comparison (i.e., pairwise deletion of missing data).  If this check box is set, then STATISTICA will exclude all cases that have missing data for any of the variables in the two lists (i.e., casewise deletion of missing data).

Display long variable names:  If this check box is set, then the results Scrollsheet will report in the first column the long variable names of the respective variables.  If no long names were specified for any of the variables selected for the analyses, then the setting of this check box will not effect the format of the results Scrollsheet.


  Correlation Matrices

A general discussion of correlation matrices is provided in the overview section.

Pearson Product-Moment Correlations dialog:

One Variable List (Square Matrix)

Two Lists (Rectangular Matrix)

Correlations

Save Matrix

Display Options

Options

2D Scatterplot (/with names)

Matrix

Categorized Scatterplots

3D Scatterplot (/with names)

Surface

3D Bivariate Distribution Histogram


  Correlation Matrices - One Variable List (Square Matrix)

This option will bring up the standard single variable list selection dialog.  Use this option to compute a square matrix of correlations.  Note that such matrices can be saved (via the Save matrix button) for further analysis with other modules (e.g., Multiple Regression, Factor Analysis).  Matrices up to 300 x 300 can be produced in this module.  Larger correlation matrices can be computed in every module of STATISTICA via the Quick Basic Stats options, and correlation matrices of virtually unlimited size (up to 32,000 x 32,000) can be computed in Megafile Manager.


  Correlation Matrices - Two Variable List (Rectangular Matrix)

This option will bring up the standard two-variable list selection dialog.  Use this option to compute a rectangular matrix of correlations for two lists.  Note that rectangular correlation matrices cannot be saved for further analysis with other modules.


  Correlation Matrices - Correlations

This button will bring up the results Scrollsheet for the currently selected variables.  The computation of correlations and the display format of results depends on the current settings in the Display and Options boxes (see below).


  Correlation Matrices - Save Matrix

Use this option to save Square Matrices of correlations in a file.  When you click on this button, the Save Matrix As dialog will open in which you can specify a name under which the matrix will be stored.


  Correlation Matrices - Display Options

Correlation matrix:  If this button is set, then clicking on the Correlations button will produce a matrix of correlation coefficients.  The significant correlations will be highlighted in the Scrollsheet; use the Options Toolbar button on the Scrollsheet Toolbar to change the default p (alpha) level (default p = .05).

Correlation matrix with p & n:  If this radio button is set, then clicking on the Correlations button (see above) will produce an augmented summary correlation matrix; that is, each cell in the matrix will not only contain the respective correlation coefficient but also the p-level and valid n (if the Casewise deletion of missing data check box is not set).  Again, significant correlations (cells in the matrix) will be highlighted in the Scrollsheet and you can use the Options Toolbar button on the Scrollsheet Toolbar to change the default p (alpha) level.

Detailed table of results:  If this radio button is set, then clicking on the Correlations button (see above) will produce a detailed table of results (not in matrix format).  This table will report not only the correlation coefficients but also the pairwise means, pairwise standard deviations, regression weights, intercepts, and other regression statistics.


  Correlation Matrices - Options

Extended precision calculations:  STATISTICA can employ proprietary extended precision calculations when extreme precision is necessary for "difficult" data.  Set this option when one or more of the variables that are to be correlated have extremely small relative variances (e.g., the ratio of the standard deviation divided by the mean is less than .0000000000001).

Casewise deletion of missing data:  If this check box is set, then only the cases that have complete (valid) data for all variables that are currently selected for the analysis (i.e., casewise deletion of missing data) will be included in the computation of the correlations.  If this check box is not set (i.e., pairwise deletion of missing data), then each correlation will be computed from all cases that have complete (valid) data for the respective pair of variables, possibly resulting in unequal n for different correlations.

Display long variable names:  If this check box is set then the results Scrollsheet will report in the first column the long variable labels along with the variable names.  If none of the selected variables have any long variable names, this check box will have no effect.


  Correlation Matrices - 2D Scatterplots (/with names)

This option will produce a cascade of scatterplots for selected pairs of variables, one plot per variable pair (i.e., correlation).  If the 2D scatterplot option is chosen, then the plot will show the regression line and the standard error of the predicted values (as error lines) in the scatterplot.  If the /w names button is used, then the scatterplot will not contain those lines, but will identify the points in the scatterplot with the case numbers or names (if case names are specified in the respective data file).


  Correlation Matrices - Matrix

This option will produce a scatterplot matrix for selected variables.


  Correlation Matrices - Categorized Scatterplots

This option will produce a cascade of categorized scatterplots for selected pairs of variables, one plot per pair (i.e., per correlation).  If a single list of variables was previously selected (One variable list (square matrix)), then you will be asked to select two lists of variables from among the previously selected variables and scatterplots will be produced for each variable in the first list with each variable in the second list.  Next, you will be prompted to select up to two categorical variables (e.g., Gender, Ethnic Origin).  STATISTICA will then produce a cascade of scatterplots broken down (categorized) by the categorical variables (e.g., separately for males and females for each ethnic group).  Note that more complex Breakdown analyses and graphs are available via the Breakdown: Descriptive statistics by groups option in the startup panel.


  Correlation Matrices - 3D Scatterplots (/with names)

This option will produce a 3D scatterplot for a selected triplet of variables.  If the /w names button is used, then the points in the scatterplot will be identified by the case numbers or names (if case names are specified in the respective data file).


  Correlation Matrices - Surface

This option will produce a 3D scatterplot for a selected triplet of variables, and fit a quadratic surface to the data.


  Correlation Matrices - 3D Bivariate Distribution Histogram

This option will produce a cascade of 3D histograms for selected pairs of variables, one plot per pair.  If a single list of variables was previously selected (One variable list (square matrix)), then you will be asked to select two lists of variables from among the previously selected variables and 3D histograms will be produced for each variable in the first list with each variable in the second list.


  Descriptive Statistics and Correlations by Groups (Breakdown)

A general discussion of the Breakdown procedure is provided in the overview section.

Descriptive Statistics and Correlations by Groups (Breakdown) dialog:

Analysis:  This combo box has two settings, discussed below.

Detailed analysis of single tables:  In this setting, the user can specify one set of categorical (breakdown) variables and a list of dependent variables.  The Breakdown Results dialog then provides numerous options to examine and graph various descriptive statistics broken down by groups.

Batch process (and print) lists of tables:  This setting of the combo box allows the user to specify up to six lists of grouping variables and a list of dependent variables.  STATISTICA will then compute breakdown tables for all possible combinations of variables from the lists of grouping variables.  This option allows the user to compute a large number of breakdown tables in batch; that is, without requiring any further user input.

Variables button:  This option will bring up the standard two-variable list selection dialog in which you can select a set of up to 6 grouping (categorization) variables and a list of dependent variables.

Codes for grouping variables button:  This option will bring up a standard codes selection dialog in which you can specify the codes that were used in the grouping variables (in order to denote the group membership of each case).  If you click OK without selecting any codes, STATISTICA will automatically determine all integer codes for the grouping variables in the data file, and compute the breakdown tables accordingly.

Casewise (listwise) deletion of MD:  If this check box is set, then all cases that have missing data in any of the dependent variables will be excluded from the analysis (i.e., casewise deletion of missing data).  If this check box is not set, then cases will only be excluded from the computations for those variables where they have missing data (i.e., pairwise deletion of missing data), possibly resulting in different numbers of valid cases for different dependent variables.


  Reordering Grouping Variables

This option allows you to change the order of grouping variables for the current analysis.  Note that, when reporting the within-group statistics, STATISTICA will cycle through the groups in the current breakdown analysis so that the factor that was selected last is the one with the fastest changing subscript, the factor that was selected next to last is the one with the second fastest changing subscript, and so on.  This option allows you to change the order of selected grouping variables, and thus the order in which within-group statistics are reported.

To change the order of grouping variables, move them in the desired (new order) from the left side (Default order) to the right (Selected order) and then click OK.  You can return to the default order at any time by clicking on the Sort Sel. button.


  Descriptive Statistics by Groups - Marginal Means

This option allows you to compute summary statistics for the selected marginal table; that is, only for the combination of selected grouping variables, ignoring those that are not selected.  For example, suppose there are three grouping variables Gender, Age Group, and Ethnic Origin.  If you selected (highlighted) only Gender and Ethnic Origin, then summary statistics will be computed for the two-way table of Gender by Ethnic Origin, ignoring (averaging over) Age Group.

Note that the marginal means (sums, standard deviations, etc.) are not necessarily identical to the averages across the non-selected factors.  Rather, they represent weighted averages taking into account unequal n''s across groups.


  Post-Hoc Comparison of Means

This dialog provides a choice of various post-hoc procedures.  You may refer to the Overview section for a discussion of the basic logic behind these tests.  Discussions of post-hoc procedures are also provided in Winer (1962), Hays (1988), or Milliken and Johnson (1984).  In short, usually, after obtaining a statistically significant F test from the ANOVA, one wants to know which means contributed to the effect; that is, which groups are particularly different from each other.  One could of course perform a series of simple t-tests to compare all possible pairs of means.  However, such a procedure would capitalize on chance.  This means that the reported probability levels would actually overestimate the statistical significance of mean differences.  Without going into much detail, suppose you took 20 samples of 10 random numbers each, and computed 20 means.  Then, take the group (sample) with the highest mean and compare it with that of the lowest mean.  The t-test for independent samples will test whether or not those two means are significantly different from each other, provided that they were the only two samples taken.  Post-hoc comparison techniques on the other hand, specifically take into account the fact that more than two samples were taken.

Post-hoc Comparison of Means dialog:

LSD test:  This test is equivalent to the t-test for independent samples, based on the n in the groups involved in the comparison.  It offers the least amount of protection against the increased alpha error rate due to multiple post-hoc comparisons.  After choosing this option, a matrix of p-values will be displayed in a Scrollsheet.  These p-values indicate the post-hoc significance levels for the respective pairs of means.

Scheffé test:  This option will bring up a Scrollsheet with the post-hoc p-levels for the Scheffé test.  The Scheffé test is usually more conservative than the Newman-Keuls or Duncan test (see Winer, 1962).

Newman-Keuls test & critical ranges:  This test is based on the studentized range statistic.  Computationally, STATISTICA first sorts the means into ascending order.  For each pair of means STATISTICA then assesses the probability under the null hypothesis (no differences between means in the population) of obtaining differences between means of this (or greater) magnitude, given the respective number of samples.  Thus, it actually tests the significance of ranges, given the respective number of samples.  Note that STATISTICA does not merely report cut-off values for p, but will compute the actual probabilities based on the distribution of the studentized range statistics.

A second Scrollsheet will display the critical ranges between ordered means, given the respective alpha level (by default p < .05).

Duncan's multiple range test & critical ranges:  This test is based on the same logic as the Newman-Keuls procedure; however, it uses a less conservative test criterion (see, for example, Milliken & Johnson, 1984).

Tukey HSD (honest significant difference) test:  The Tukey HSD test falls between the Newman-Keuls and Scheffé procedures with regard to conservatism.

Tukey HSD for unequal sample sizes (Spjotvoll & Stoline test):  This test is a generalization of Tukey's test to the case of unequal sample sizes (see Spjotvoll & Stoline, 1973, p. 975).

Alpha level for highlighting:  In all results Scrollsheets, significant differences are highlighted.  Enter the desired critical p (alpha) level for highlighting into the edit field.


  Within-Group Correlations

Your choice of options in the Breakdown for Within-Group Correlations dialog (resulting from the Options button in the Breakdown Means and One-Way ANOVA Results dialog) will determine the detail of results reported after selecting the Within-group correlations option.

Within-Group Correlations dialog:

Compute & show significance (p) levels:  If this check box is set, then for each correlation matrix, a matrix of p (significance) levels will be computed.

Compute & show covariance:  If this check box is set, then for each correlation matrix, a matrix of covariances will be computed.

Display options for pairwise MD deletion:  The options in this box are only meaningful and available if pairwise deletion of missing data was selected prior to processing the data.

Show pairwise n:  If this check box is set, then for each correlation matrix, a matrix of valid n for each correlation will be displayed.

Show pairwise means:  If this check box is set, then for each correlation matrix, a matrix of pairwise means will be displayed.  For each correlation, those means will be computed from all cases that were included in the computation of the respective correlation coefficient.

Show pairwise standard deviations:  If this check box is set, then for each correlation matrix, a matrix of pairwise standard deviations will be displayed.  For each correlation, those standard deviations will be computed from all cases that were included in the computation of the respective correlation coefficient.


  Selecting Groups

Select a specific group by highlighting (clicking on) it.  Select All groups to produce a cascade of results Scrollsheets for all groups.


  Assigning Factors to Aspects (Axes) of the Interaction Plot

This dialog allows you to control the assignment of grouping variables (factors) to the line patterns, upper X axis, and lower X axis.  If more than three factors need to be plotted, the plot is produced in "chunks" within the levels of the other (not-selected) factors.


  Type of Normal Probability Plot

Select the desired type of probability plot (see also Spreadsheet and Scrollsheet Stats Graphs - Probability Plot of . . .).

Normal probability plot:  The standard normal probability plot is constructed as follows.  First, the deviations from the respective means (residuals) are rank ordered.  From these ranks we can compute z values (i.e., standardized values of the normal distribution) based on the assumption that the data come from a normal distribution.  These z values are plotted on the Y-axis in the plot.  If the observed residuals (plotted on the X-axis) are normally distributed, then all values should fall onto a straight line (marked Normal Expected in the plot).  If the residuals are not normally distributed, then they will deviate from the line.  Outliers may also become evident in this plot.  If there is a general lack of fit, and the data seem to form a clear pattern (e.g., an S shape) around the line, then the dependent variable may have to be transformed in some way (e.g., a log transformation to "pull in" the tail of the distribution, etc., see Edit Variable Specs or STATISTICA BASIC).

Half-normal probability plot:  The half-normal probability plot is constructed in the same way as the standard normal probability plot, except that only the positive half of the normal curve is considered.  Consequently, only positive normal values will be plotted on the Y-axis.  This plot is used when one wants to ignore the sign of the residual; that is, when one is mostly interested in the distribution of absolute residuals, regardless of sign.

Detrended normal probability plot:  The detrended normal probability plot is constructed in the same way as the standard normal probability plot, except that before the plot is generated, the linear trend is removed.  This often "spreads out" the plot, thereby allowing the user to detect patterns of deviations more easily.


  Descriptive Statistics and Correlations by Groups (Breakdown) - Lists

A general discussion of the Breakdown procedure is provided in the overview section.

Descriptive Statistics and Correlations by Groups (Breakdown) - Lists dialog:

Analysis

Grouping variables

Dependent variables

Casewise (listwise) deletion of MD

Output Tables

Statistics


  Descriptive Statistics and Correlations by Groups (Breakdown) Lists - Analysis

This combo box has two settings, discussed below.

Detailed analysis of single tables:  In this setting, the user can specify one set of categorical (breakdown) variables and a list of dependent variables.  The Breakdown Results dialog then provides numerous options to examine and graph various descriptive statistics broken down by groups.

Batch process (and print) lists of tables:  This setting of the combo box allows the user to specify up to six lists of grouping variables and a list of dependent variables.  STATISTICA will then compute breakdown tables for all possible combinations of variables from the lists of grouping variables.  This option allows the user to compute a large number of breakdown tables in batch; that is, without requiring any further user input.


  Descriptive Statistics and Correlations by Groups (Breakdown) Lists - Grouping Variables

This option will bring up a standard six-variable lists selection window in which you will need to select at least one list of grouping variables; breakdown tables will be computed for all possible combinations of grouping variables from the six lists.  Note that STATISTICA will automatically take all valid integer codes in the respective grouping variables to construct the tables.


  Descriptive Statistics and Correlations by Groups (Breakdown) Lists - Dependent Variables

This option will bring up a standard single variable list selection window in which you can select the list of dependent variables for the breakdown tables.


  Descriptive Statistics and Correlations by Groups (Breakdown) Lists - Casewise (Listwise) Deletion of Missing Data

If this check box is set then all cases that have missing data in any of the dependent variables will be excluded from the analyses (i.e., casewise deletion of missing data).  If this check box is not set, then cases will only be excluded from the computations for those dependent variables, where they have missing data (possibly resulting in different numbers of valid cases for different dependent variables).


  Descriptive Statistics and Correlations by Groups (Breakdown) Lists - Output Tables

Note that in this setting of the Analysis combo box (i.e., Batch process (and print) lists of tables), a cascade of results Scrollsheets will be computed for each table (combination of grouping variables).  The settings in this group of check boxes will determine the types of Scrollsheets that will be computed for each table, and the detail of results for each dependent variable (Statistics).

Summary table of means:  Set this check box to display (and print if printer or disk output is selected, see Printing) summary breakdown tables.  The statistics reported in the Scrollsheets depend on the selection of Statistics.

Detailed two-way tables:  Set this check box to compute Scrollsheets with two-way tables.  If more than two lists of grouping variables were selected, then the tables will be produced for the last two grouping variables in the current table, within the respective levels of preceding grouping variables.  The statistics that are reported in the Scrollsheets depend on your selection of Statistics.

Within-group correlations:  Set this check box to compute Scrollsheets of within-group correlation matrices for the dependent variables.

Analysis of variance:  Set this check box to compute Scrollsheets of summary ANOVA tables for the dependent variables.

Levene's test:  The significance tests reported by the Analysis of variance option (see above) is based on the assumption that the variances in the different groups are the same (homogeneous).  A powerful statistical test of this assumption is Levene's test.  For each dependent variable, an analysis of variance is performed on the absolute deviations of values from the respective group means.  If the Levene's test is statistically significant, then the hypothesis of homogeneous variances should be rejected.  However, note that the F statistic (in ANOVA) provides a robust test for mean differences as long as (1) the n per group is greater than 10, and (2) the means across groups are not correlated with the standard deviations across groups.  Thus, a significant Levene's test does not necessarily call into question the validity of the ANOVA results (refer to the manual for details).


  Descriptive Statistics and Correlations by Groups (Breakdown) Lists - Statistics

The selections in this box will determine the statistics that are reported in the Summary tables of means and the Detailed two-way tables.

Number of observations:  Set this check box to compute the number of observations in each group.

Sums:  Set this check box to compute the sums for the dependent variables for each group.

Standard deviations:  Set this check box to compute the standard deviations for the dependent variables for each group.  Note that standard deviations are computed as the square roots of the sums of squared deviation (from the mean) divided by n-1; the resulting standard deviations are estimates of the population standard deviations.

Variances:  Set this check box to compute the variances for the dependent variables for each group.  The variance is computed as the sum of squared deviations (from the mean) divided by n-1; the resulting variances are estimates of the population variances.


  Descriptive Statistics and Correlations by Groups - Results

The Breakdown of Means and One-Way ANOVA Results dialog will allow you to calculate various statistics as well as graphs of the data.  A general overview of the Breakdown procedure is provided in the overview section.

Breakdown of Means and One-Way ANOVA Results dialog:

Summary box

Summary Table of Means

Statistics

Detailed Two-way Tables

Marginal Means

Analysis of Variance

Post-hoc Comparisons of Means

Levene's test (homogeneity of variances)

Within-group correlations

Reorder Factors in Table

Categorized Plots

Interaction Plot

Plot of means vs. standard deviations


  Descriptive Statistics and Correlations by Groups Results - Summary Box

The summary box lists your choices for the dependent variable and grouping (independent) variables as well as the codes for the grouping variables.


  Descriptive Statistics and Correlations by Groups Results - Summary Table of Means

This button will bring up a summary table of descriptive statistics broken down by the grouping variables.  The statistics reported in the table depend on the selections in the Statistics box to the right of the button.


  Descriptive Statistics and Correlations by Groups Results - Statistics

The selections in this box will determine the statistics that are reported in the results Scrollsheets when the user chooses either the Summary table of means, Detailed two-way tables, or Marginal means (see below).

Number of Observations:  Set this check box to compute the number of observations in each group.

Sums:  Set this check box to compute the sums for the dependent variables for each group.

Standard Deviations:  Set this check box to compute the standard deviations for the dependent variables for each group.  Note that standard deviations are computed as the square roots of the sums of squared deviation (from the mean) divided by n-1; the resulting standard deviations are therefore (biased) estimates of the population standard deviations.

Variances:  Set this check box to compute the variances for the dependent variables for each group.  The variance is computed as the sum of squared deviations (from the mean) divided by n-1; the resulting variances are therefore (unbiased) estimates of the population variances.


  Descriptive Statistics and Correlations by Groups Results - Detailed Two-way Tables

This button will bring up a cascade of Scrollsheets with two-way tables.  If two or less grouping variables were selected, then only a single Scrollsheet will be produced.  If more than two grouping variables were selected, then the tables will be produced for the last two grouping variables, within the respective levels of the remaining (preceding) grouping variables.  Use the Reorder factors in table option (see below) to change the order of grouping variables and therefore the order in which the two-way tables are produced.  The statistics reported in the Scrollsheets depend on your selections in the Statistics box (see above).  Additional formatting options are available via the check boxes below this button (see below).  The two-way tables will not only report summary statistics within each group, but also marginal summary statistics; that is, statistics for each factor ignoring the other.  User-specified marginal tables are available via the Marginal means option (see below).

Display long variables names:  Set this check box to display the long variable labels for the grouping variables in the header of the first Scrollsheet column.  If no long variable labels are specified for the grouping variables in the table, then the setting of this check box is ignored.

Display long value labels:  Set this check box to report long value labels for the levels of the grouping variables in the first column of the Scrollsheet.  If no long value labels exist for the grouping variables in the two-way table, then the setting of this check box is ignored.


  Descriptive Statistics and Correlations by Groups Results - Marginal Means

This option allows you to compute summary statistics (selected in the Statistics box, see above) for any marginal table; that is, for tables consisting of a subset of the current grouping variables, ignoring those not in the subset.  After clicking on this button, the user will be prompted to select the grouping variables for the marginal table.  To change the order of factors in the table, use the Reorder factors in table option before specifying the marginal table.


  Descriptive Statistics and Correlations by Groups Results - Analysis of Variance

This option will bring up a Scrollsheet with the results of univariate analyses of variance for each dependent variable.  If statistically significant, it can be concluded that the means across the groups are different in magnitude; you can use the Post-hoc comparisons of means option (see below) to identify significant differences between individual groups (means).  Use the ANOVA/MANOVA module to compute complete univariate and multivariate analysis of variance tables.  However, note that the one-way ANOVA available from this dialog is particularly suited for quickly analyzing one-way univariate designs with very many groups.


  Descriptive Statistics and Correlations by Groups Results - Post-hoc Comparisons of Means

This option allows the user to compute the common post-hoc tests for multiple comparisons of means (LSD, Scheffé, Newman-Keuls, Duncan, Tukey, Spjotvoll & Stoline).  After clicking on this button, select a dependent variable for the tests; a pop-up window with available tests will then be displayed (see Post-hoc comparison of means).


  Descriptive Statistics and Correlations by Groups Results - Levene's Test

The significance tests reported by the Analysis of variance option (see above) are based on the assumption that the variances in the different groups are the same (homogeneous).  A powerful statistical test of this assumption is Levene's test.  For each dependent variable, an analysis of variance is performed on the absolute deviations of values from the respective group means.  If the Levene's test is statistically significant,  then the hypothesis of homogeneous variances should be rejected.  However, note that the F statistic (in ANOVA) provides a robust test for mean differences as long as (1) the n per group is greater than 10, and (2) the means across groups are not correlated with the standard deviations across groups.  Thus, a significant Levene's test does not necessarily call into question the validity of the ANOVA results (refer to the manual for details).  The assumption of uncorrelated means and standard deviations can easily be checked by producing the Plot of means vs. standard deviations from this dialog.


  Descriptive Statistics and Correlations by Groups Results - Within-group Correlations

If more than one dependent variable was selected for the current analysis, then this option will allow you to compute the within-group correlation matrices for those variables.  After clicking this option, you will be prompted to select the group for which to display the correlation matrix or you can select to display a cascade of Scrollsheets (displaying the correlation matrices for all groups).  Note that the default Scrollsheet graph for this option is the scatterplot; thus, from within the Scrollsheet containing a within-group correlation matrix, you can produce a scatterplot of selected within-group correlations.

Options button:  This button will pop-up a dialog of display options for the within-group correlation matrices (see above).  Specifically, you can determine an alpha (p) level for highlighting significant correlations, request to compute within-group covariance matrices, or report various additional statistics (e.g., pairwise n, means, standard deviations; see Within group correlations for details).


  Descriptive Statistics and Correlations by Groups Results - Reorder Factors in the Table

When reporting the within-group statistics, STATISTICA will cycle through the groups in the current breakdown analysis so that the factor that was selected last is the one with the fastest changing subscript, the factor that was selected next to last is the one with the second fastest changing subscript, and so on.  This option will allow you to change the order of selected grouping variables, and thus the order in which the within-group statistics are reported.


  Descriptive Statistics and Correlations by Groups Results - Categorized Plots

Categorized Box & Whisker plots.  This option will produce a cascade of categorized box and whisker plots for the dependent variables, one plot per dependent variable.  For each variable STATISTICA will produce a box and whisker plot, broken down (categorized) by the grouping variables (e.g., separately for males and females for each ethnic group).

Categorized histograms.  This option will produce a cascade of categorized histograms.  After clicking on this button you can select variables for the plot from among the list of dependent variables in the current analysis.  For each selected variable, a categorized histogram will be produced, summarizing the within-group distribution of the respective variable.

Categorized normal probability plots.  This option will produce a cascade of normal probability plots for the selected dependent variables, categorized by the grouping variables.  After clicking on this button, you can select standard normal probability plots, half-normal plots, or detrended normal plots.

Categorized scatterplots.  This option will produce a cascade of categorized scatterplots.  After clicking on this button you can select variables for the plot from among the list of dependent variables in the current analysis.  A categorized scatterplot will be produced for each selected variable.


  Descriptive Statistics and Correlations by Groups Results - Interaction Plots

This option will produce an interaction plot of means by groups.  Interaction plots will be produced according to the following specifications, within the levels of any additional grouping factors.

•	More than one dependent variable was selected for the current analysis:  In this case, when you click on the Interaction plot button, the resulting Select the variables for interaction plot dialog will display each of the previously selected dependent variables.  You can select only those variables that you want plotted, or click OK to accept the default selection (all variables in the list); each variable in the resulting interaction plots will be represented by a different line color or pattern.  Clicking OK in this dialog will open the Arrangement of factors dialog (see below).

•	One dependent variable was selected for the current analysis:  Since you have already selected the dependent variable to plot, when you click on the Interaction plot button, the Arrangement of factors dialog will open (see below).  In this interaction plot, the grouping variables will be represented by different line colors and patterns.

•	Arrangement of factors dialog:  Once you selected the variables (see above) to be plotted, the Arrangement of factors dialog will open, allowing you to assign two (if two or more dependent variables were selected) or three (if one dependent variable was selected) grouping variables to different aspects of the interaction plot (line pattern, lower X axis, upper X axis).


  Descriptive Statistics and Correlations by Groups Results - Plot of Means vs. Standard Deviations

This option allows you to plot the means for selected variables across groups against the respective standard deviations.  This plot is useful in order to spot potential outliers among the means that may contribute to an erroneous conclusion of statistically significant differences between means.  One of the most common and most serious violations of assumptions for ANOVA is when the means are correlated with the standard deviations across groups.  For example, suppose there are 5 groups of 10 observations each.  If in one group, two observations are extreme outliers, then the variance in that group will be much larger and the mean will be very different (larger or smaller) from the grand mean.  However, for the overall F test (ANOVA) the pooled (averaged) within-group variance is taken as an estimate of the error variance.  Thus, the reliability of the outlier mean will be overestimated, and the ANOVA may erroneously yield a significant F statistic.


  Frequency Tables - Results

A general discussion of the Frequency tables option is provided in the overview section.

Frequency Tables dialog:

Variables

Frequency Tables

Histograms

Descriptive Statistics

Categorization Method for Tables & Graphs

Casewise (listwise) Deletion of MD

Display options

Missing data

Tests of normality

Box & Whisker Plot for all Variables

Probability Plots

3D Bivariate Distribution Histogram


  Frequency Tables Results - Variables

This option will bring up a standard single variable list selection window in which you can select the variables for the analyses.


  Frequency Tables Results - Frequency Tables

This option will produce a cascade of frequency tables for the selected variables, one Scrollsheet per variable.  The manner in which the variables are categorized for the frequency tables is determined by the selection of options in the Categorization method for tables & graphs box (see below).  The options in the Display option box (see below) determine the different summary statistics that will be reported in the frequency tables.  If any Tests for normality are selected (i.e., if any of the check boxes in that box are set, see below), then for each variable, an additional Scrollsheet with the results for the respective selected tests will be displayed (test for other non-normal distributions are available in the Nonparametrics and Distributions and the Survival analysis modules).


  Frequency Tables Results - Histograms

This option will produce a cascade of histograms for the selected variables, one histogram per variable.  The manner in which the variables are categorized for the histograms is determined by the same settings of options as in Frequency tables.


  Frequency Tables Results - Descriptive Statistics

This option will produce a Scrollsheet of descriptive statistics for the selected variables.  Note that the manner in which data are processed in the computation of descriptive statistics depends on the Categorization method for tables & graphs (see below).  Specifically:

(1)	If the Step size radio button is selected and a user-specified minimum is specified, then all cases with values less than the minimum will be ignored;

(2)	If the Integer categories button is selected, then all non-integer values will be ignored;

(3)	If the Specific grouping codes (labels) button is selected then all values that do not match any of the selected integer codes will be ignored;

(4)	If the User-specified intervals button is selected, then the Descriptive statistics button will be dimmed (because complex compound conditions can be specified to assign cases to categories which could result in a case being eligible for more than one category).  A case will be assigned to the first User-specified interval to which it "fits" and Descriptive statistics will not be calculated for these intervals (see Categorization Methods for Tables and Graphs; see also Specifying intervals (categories)).

In all cases, missing data will either by deleted casewise or pairwise, depending on whether or not the Casewise (listwise) deletion of MD check box is set (see Casewise (listwise) Deletion of MD).


  Frequency Tables Results - Categorization Methods for Tables and Graphs

The settings in this box will determine (1) how the currently selected variables will be categorized or tabulated for the Frequency tables and Histograms, and (2) how cases are processed for Descriptive statistics.

All distinct values:  Select this option if you want the frequencies to be based on all of the distinct values for each of the selected variables.

With Text Values:  Select this option if you want the frequencies to be based on the distinct text values for each of the selected variables.

No of exact intervals:  If this radio button is set, then the entire range of values for each variable will be divided into the respective number of intervals.

"Neat" intervals; app. no.:  If this radio button is set, then the category or interval boundaries and step-sizes (interval ranges) for the frequency tables will be "neat;" that is, those values will be rounded to simple values with the last digit being either a 1, 2, or 5 (e.g., 10.5, 11.0, 11.5, etc.).  In this manner, clean and easy to read tables can be produced; however, the tables may not always have the exact number of intervals requested in the No. of intervals option.

Step size:  If this radio button is set, then the frequency tables (and histograms) will be based on the user-specified step sizes (interval widths).

Starting at minimum:  If this check box is set, then the first inclusive interval boundary for the frequency tables will be set as equal to the minimum value for the respective variable.  If this check box is not set, then the first inclusive interval boundary for the frequency tables will be set as equal to the user-specified value entered into the respective edit box.

Integer categories:  If this radio button is set, then the frequency tables (and histograms) will be based on integer category (interval) boundaries and step sizes, starting with the smallest integer value found in the respective variable.  All non-integer values will be ignored (in the Frequency tables, Histograms, and Descriptive statistics options).

With text labels:  If this check box is set, then the categories in the Frequency tables and  Histograms will be labeled with text values (e.g., males, females) rather than integer values (e.g., 1, 2), provided that text values are available for the respective variables in the current data file.

Specific grouping codes (labels):  If this radio button is set, then the frequency tables (and histograms) will be based on integer categories (codes) specified by the user (via the button next to this option).  All non-integer values and codes that are not selected will be ignored.  If no codes are specified, all integer codes found in the data file for the respective variables will be used.

User-specified intervals:  This option allows the user to specify a set of up to 16 logical case selection conditions, defining how cases are to be assigned to (up to 16) categories for the Frequency table.  These logical case selection conditions can be complex, and reference more than one variable in the data file, as well as case numbers.  For each case in the data file, the case selection conditions are processed in sequence, and a respective case is assigned to the first category where it "fits" (where the respective logical case selection condition is true).  Click on the button next to this option to specify the case selection conditions; for a brief overview of the syntax for those case selection conditions refer to the description of the Specifying intervals (categories) dialog.


  Frequency Tables Results - Casewise (listwise) Deletion of MD

If this check box is set then cases are excluded from computations if they have missing data for any of the variables currently selected for the analysis (i.e., casewise deletion of missing data).  If this check box is not set, then cases are excluded from the computations for only those variables for which they have missing data (possibly resulting in different numbers of valid cases for different variables).


  Frequency Tables Results - Display Options

The selection of options in this box determines the statistics that are computed for each category in the Frequency tables (see above).  Note that all percentages are computed with respect to the total number of cases reported in the table; that is, including or excluding missing data and/or out-of-range values, depending on the settings in the Missing data box.

Cumulative frequencies:  If this check box is set then the cumulative frequencies are reported.

Percentages (relative frequencies):  If this check box is set then the relative frequencies (percentages) are reported.

Cumulative percentages:  If this check box is set then the relative cumulative frequencies (cumulative percentages) are reported.

100% minus cumulative percentages:  If this check box is set then 100-minus-cumulative-percent-values are reported for each category.

Logit transformed proportions:  If this check box is set then for each category in the frequency table, the logit-transformed cumulative proportions will be reported.  Specifically, the logits for a category i are computed from the respective cumulative proportion pi as: Logiti=natural log(pi/(1-pi)).

Probit transformed proportions:  If this check box is set then for each category in the frequency table, the probit-transformed cumulative proportions will be reported.  Specifically, probits are computed as the normal values (z-values) associated with the probability (cumulative proportion of observations) in the respective cell.

Normal expected frequencies:  If this check box is set then for each category in the frequency table, the expected frequencies are computed based on the normal distribution.


  Frequency Tables Results - Missing Data

Count missing data (MD):  If this check box is set then an extra category for missing data will be displayed in the frequency table Scrollsheets.  Also, percentages and cumulative percentages will be computed relative to the total number of cases plus the number of missing data.

Count MD & non-selected cases:  If this check box is set then an extra category for non-selected (and non-missing) cases will be displayed in the frequency table Scrollsheets.  Also, percentages and cumulative percentages will be computed relative to the total number of cases plus the number of non-selected, non-missing cases.  Note that this option is not available (active) if the current Categorization method for tables & graphs is No. of intervals or Step size.., starting at minimum.  In those instances, the regular categories of the frequency table will always include all non-missing data.


  Frequency Tables Results - Tests of Normality

If any of the following check boxes are set, then after the frequency tables for the selected variable have been displayed, additional Scrollsheets will be displayed with the requested tests of normality (one Scrollsheet per test).  To display these tests only, use the Tests for normality button.

Tests for normality:  This option will bring up the results Scrollsheets with the requested tests of normality for the selected variables.

Kolmogorov-Smirnov test, mean/std.dv known:  If this check box is set, then the Kolmogorov-Smirnov one-sample test of normality will be computed.  Specifically, if the Kolmogorov-Smirnov D statistic is significant, then the hypothesis that the respective distribution is normal should be rejected.  The probability values that will be reported are based on those tabulated by Massey (1951); those probability values are valid when the mean and standard deviation of the normal distribution are known a-priori and not estimated from the data.  However, usually those parameters are computed from the actual data.  In that case, the test for normality involves a complex conditional hypothesis ("how likely is it to obtain a D statistic of this magnitude or greater, contingent upon the mean and standard deviation computed from the data"), and the Lilliefors probabilities should be interpreted (Lilliefors, 1967).  Note that, in recent years, the Shapiro-Wilks'' W test (see below) has become the preferred test of normality because of its good power properties as compared to a wide range of alternative tests (Shapiro, Wilk, & Chen, 1968).

Lilliefors test, mean/std.dv unknown:  If this check box is set, then the Kolmogorov-Smirnov one-sample D statistic will be computed, and Lilliefors probabilities will be reported (see previous paragraph; see also Lilliefors, 1967).

Shapiro-Wilks' W test:  If this check box is set, then the Shapiro-Wilks' W test of normality will be computed for each selected variable.  If the W statistic is significant, then the hypothesis that the respective distribution is normal should be rejected.  The Shapiro-Wilks'' W test is the preferred test of normality because of its good power properties as compared to a wide range of alternative tests (Shapiro, Wilk, & Chen, 1968).  The algorithm implemented in STATISTICA employs an extension to the test described by Royston (1982), which allows it to be applied to large samples (with up to 2000 observations).


  Frequency Tables Results - Box & Whisker Plot for all Variables

This option will produce a box and whisker plot for the selected variables.  The box and whisker plot will summarize each variable by three components:

(1)	A central line to indicate central tendency or location;

(2)	A box to indicate variability around this central tendency;

(3)	Whiskers around the box to indicate the range of the variable.

After clicking on this button you can choose to plot for each variable:

(1)	Medians (central line), quartiles (box), and ranges (whiskers);

(2)	Means, standard errors of the means, and standard deviations;

(3)	Means, standard deviations, and 1.96 times the standard deviations (95% normal confidence interval for individual observations around the mean);

(4)	Means, standard errors of the means, and 1.96 times the standard errors of the means (95% normal confidence interval for means).


  Frequency Tables Results - Probability Plots

Normal probability plots:  This option will produce a cascade of normal probability plots for the selected variables, one plot per selected variable.  For more information on how the standard normal probability plot is constructed, see Normal Probability Plots.

Half-normal probability plots:  This option will produce a cascade of half-normal probability plots for the selected variables, one plot per selected variable.  For more information on how the half-normal probability plot is constructed, see Half-Normal Probability Plots.

Detrended normal probability plots:  This option will produce a cascade of detrended normal probability plots for the selected variables, one plot per selected variable.  For more information on how the detrended normal probability plot is constructed, see Detrended Normal Probability Plots.


  Frequency Tables Results - 3D Bivariate Distribution Histogram

This option will produce a cascade of 3D histograms for selected pairs of variables, one plot per pair.  After clicking on this button, the user is first prompted to select two lists of variables (from among those originally selected via the Variables option).  3D histograms will be produced for each variable in the first list with each variable in the second list.


  Crosstabulation & Stub-and-Banner Tables

When you select Tables and Banners from the Startup Panel, the Specify Table dialog will open.  The options below are available when you select Crosstabulation Tables in the Analysis option (see below).

Specify Table dialog:

Analysis

Multi-way Crosstabulation Tables

Stub-and-Banners Table

Use all Integer Codes in the Selected Variables

Use Selected Codes Only


  Crosstabulation & Stub-and-Banner Tables - Analysis

This combo box has two settings:

Crosstabulation tables: In this setting, STATISTICA expects to crosstabulate standard categorical (grouping) variables (e.g., Gender, Ethnic Origin; see also Crosstabulation & stub-and-banner tables).

Tables for multiple response items:  If this setting is chosen, then the user can specify so-called multiple response variables and multiple dichotomies (see Multiple responses/dichotomies), and compute (1) frequency tables for such variables or (2) compute crosstabulation tables involving such variables (e.g., ordinary categorical variables can be crosstabulated with multiple response variables/dichotomies).


  Crosstabulation & Stub-and-Banner Tables - Multi-way Crosstabulation Tables

Specify tables button:  Use this option to select variables for a multiway crosstabulation table.  After clicking on this button, a standard six-variable list selection window will open.  Crosstabulation tables will be computed for all possible combinations of variables from up to six selected lists.  You can repeatedly use this option to add tables or lists of tables to the total list of tables that will be computed.  To review or edit the current list of selected tables use the Review or delete tables option.

Review or delete tables:  This option allows you to review and edit the current list of selected tables.


Crosstabulation & Stub-and-Banner Tables - Stub-and-Banner Tables

  Crosstabulation & Stub-and-Banner Tables - Stub-and-Banners Tables

Stub-and-banner tables are essentially two-way tables, except that two lists of categorical variables are crosstabulated.  In the stub-and-banner results table, one list will be tabulated in the columns (horizontally) and the second list will be tabulated in the rows (vertically) of the Scrollsheet.  After clicking on the Specify tables button, a standard two-variable list selection window will be displayed.  Note that, after selecting this option, the list of crosstabulation tables will be cleared (if one has previously been selected via the Multi-way crosstabulation tables options).


Crosstabulation & Stub-and-Banner Tables - Use all Integer Code in the Selected Variable

  Crosstabulation & Stub-and-Banner Tables - Use all Integer Codes in the Selected Variable

If this radio button is set, then all integer code values in the selected variables will be used for the crosstabulation.


  Crosstabulation & Stub-and-Banner Tables - Use Selected Code Only

If this radio button is set then the user can specify the codes that are to be used for the crosstabulation tables.


  Deleting Tables from List

To delete tables from the currently selected list of tables, first highlight the respective tables and then click Delete.


  Crosstabulation Results

A general discussion of the Crosstabulation & stub-and-banner tables option is provided in the overview section.

Crosstabulation Tables Results dialog:

Review Summary Tables

Detailed Two-way Tables

Stub-and-Banner Table

Display Long Value Labels

Include Missing Data

Display Selected %'s in Sep. Tables

Statistics for Two-way Tables

Tables

Categorized Histograms

Interaction Plots of Frequencies

3D Histograms


  Crosstabulation Results - Review Summary Tables

This option will bring up summary tables for multi-way crosstabulation tables.  If more than one table was specified, then a dialog will open allowing the user to select the table(s) to be displayed.  The summary crosstabulation table will report the frequencies for the entire respective table; the last variable (factor) that makes up the table will be tabulated in the columns of the Scrollsheet and all remaining variables (factors) will be tabulated in the rows.  If there are more than two variables (factors) in a table, then the structure of the table will be as if several two-way tables (for the last two factors) were "glued" together one-after-another for the different levels of the remaining factors.  In this manner even 6-way tables can be reviewed in a single Scrollsheet.  The detail of results that are reported depends on the selections of options in the Tables box.  Note that, if Expected frequencies or Residual frequencies are requested, then they will be computed simultaneously for the entire multi-way table, via iterative proportional fitting (e.g., see Haberman, 1972, 1974; see also the Log-Linear Analysis module).  Specifically, expected frequencies are computed contingent upon the single-factor marginal tables; that is, it is assumed that there are no interactions between factors in the table.  For three- or higher-way tables these values will be different from those that are displayed when Detailed two-way tables are requested, where the expected frequencies are computed based on the respective two-way tables alone.


  Crosstabulation Results - Detailed Two-way Tables

This option will bring up Scrollsheets with two-way tables.  If more than one table was specified, then a dialog will open allowing the user to select the table(s) to be displayed.  For tables with more than two variables (factors), a cascade of Scrollsheets will be produced for the last two factors in the table, within the levels of the other factors.  The detail of reported results depends on the choices of options in the Statistics for two-way tables box as well as the Tables box (see below).  If any Statistics for two-way tables are selected, then a Scrollsheet with requested statistics will be computed for each two-way table.


  Crosstabulation Results - Stub-and-Banner Tables

This option is only available (active) if the Stub-and-banner tables option was selected on the previous dialog (see Crosstabulation & stub-and-banner tables).  In general, stub-and-banner tables are two-way tables where one list is tabulated in the columns (horizontally) and the second list is tabulated in the rows (vertically) of the Scrollsheet.  The detail of reported results depends on the choices of options in the Tables box.


  Crosstabulation Results - Display Long Value Labels

If this check box is set then long value labels will be displayed in the first column of the two-way table results Scrollsheets.  If the respective variable (factor) tabulated in the rows of a Scrollsheet does not have any long value labels (none were specified in the data file), then the setting of this check box will be ignored.


  Crosstabulation Results - Include Missing Data

If this check box is set, then an extra category (level) for missing data is added to each variable (factor) in the table.  Thus the table will show the number of missing cases crosstabulated with the other variables (factors), and all marginal frequencies and percentages will be adjusted accordingly.


  Crosstabulation Results - Display Selected %'s in Sep. Tables

This check box is only available (active) if one of the Percentages... options is selected in the Tables box.  By default, if percentages are requested they will be displayed in the same table together with the frequencies; thus each cell in such results Scrollsheets will consist of more than one line.  If this check box is set, then the percentage tables will be displayed in separate Scrollsheets (this is desirable when you want to produce graphs of percentages from the Scrollsheets).


  Crosstabulation Results - Statistics for Two-way Tables

The options selected in this box will determine the statistics that will be computed when Detailed two-way tables are requested.  If any of these statistics are selected, a separate Scrollsheet will be displayed after each two-way table, reporting the respective statistics for that table.


  Crosstabulation Results - Tables

The selection of options in this box will determine the detail of results reported in Summary tables and Detailed two-way tables, and some apply to Stub-and-banner tables.

Highlight counts > . . . :  If this check box is set, then all counts (raw frequencies) in the table that are greater than the value in the edit box will be highlighted.

Expected frequencies:  If this check box is set, then for all two-way tables and summary tables, the expected cell frequencies are computed contingent upon complete independence of all factors in the table.  Thus, for Detailed two-way tables, those expected frequencies are computed based on the marginal frequencies for the two factors in the current table; for Summary tables with more than two variables (factors), the expected frequencies are based on the marginal frequencies of all factors in the table (i.e., no interactions between factors are assumed).  Expected frequencies for tables with more than two factors are computed via Iterative proportional fitting (e.g., see Haberman, 1972, 1974; see also the Log-Linear Analysis module).

Residual frequencies:  If this check box is set, then for all two-way tables and summary tables, the residual frequencies (observed minus expected frequencies; see above) will be displayed.

Percentages of total count:  If this check box is set, then for each cell in the Summary tables, Detailed two-way tables, and Stub-and-banner tables, percentages are computed relative to the total number of cases in the current table.  If the Display selected %'s in sep. tables option is not set, then the percentages will be shown in the same table together with the raw frequencies.

Percentages of row counts:  If this check box is set, then for each cell in the Summary tables, Detailed two-way tables, and Stub-and-banner tables, percentages are computed relative to the total number of cases in the respective row of the current table.  If the Display selected %'s in sep. tables option is not set, then the percentages will be shown in the same table together with the raw frequencies.

Percentages of column counts:  If this check box is set, then for each cell in the Summary tables, Detailed two-way tables, and Stub-and-banner tables, percentages are computed relative to the total number of cases in the respective column of the current table.  If the Display selected %'s in sep. tables option is not set, then the percentages will be shown in the same table together with the raw frequencies.


  Crosstabulation Results - Categorized Histograms

After choosing this option, if more than one table was computed, the user can select the table(s) for the plot.  STATISTICA will then compute the categorized histograms for the selected tables.  Note that each plot can summarize up to three variables (factors); that is, one categorized histogram can summarize a three-way table:  The last (fastest changing) factor will be represented by the columns in the graph; the next-to-last factor will be represented by the different histograms "tabulated" horizontally; the third factor will be represented by the different histograms "tabulated" vertically.  Cascades of categorized histograms are produced for tables with more than three factors.


  Crosstabulation Results - Interaction Plot of Frequencies

Another way of summarizing the distribution of frequencies across up to three variables (factors) is by a line graph (interaction plot).  (If there are more than three factors in the respective table, then a cascade of interaction plots will be produced for each combination of levels of the remaining factors.)  After clicking on this button, if more than one table was computed, then the user can select the table(s) for the plot(s).  STATISTICA will then compute the interaction plot(s) for the selected table(s).  In each graph, the last (fastest changing) factor will be represented by different line patterns and colors; the next-to-last factor will be represented by "upper-x" labels; the last factor will be represented by "lower x" labels.


  Crosstabulation Results - 3D Histogram

This option will produce 3D histograms for selected tables.  After clicking on this button, if more than one table was originally computed, the user can select the table(s) for the plot(s).  Each 3D histogram will summarize the joint frequency distribution for two variables (factors); it is in a sense the graphical equivalent to the Detailed two-way tables option.


  Selecting Tables for Review

Select the tables to be reviewed by highlighting them, then click OK.  If you select All tables, a cascade of results tables (Scrollsheets) or graphs will be produced for all tables.


Specifying Multiple Response/Dichotomies

  Specifying Multiple Responses/Dichotomies

When you select Tables and Banners from the Startup Panel you select Tables for Multiple Response Items in the Analysis option (see below), the Multiple Response Tables dialog will open.

Multiple Response Tables dialog:

Analysis

Specify Table

Paired Crosstabulation

Name of Factor (Multiple Response Set)

Type of Multiple Response Factor

Long Factor Labels

Exclude Missing Data Listwise Within Each Multiple Dichotomy Set

Exclude Missing Data Listwise Within Each Multiple Response Set

Include Missing Data as an Additional Category for Each Factor


Specifying Multiple Response/Dichotomies - Analysis

  Specifying Multiple Responses/Dichotomies - Analysis

This combo box has two settings:

Crosstabulation tables: In this setting, STATISTICA expects to crosstabulate standard categorical (grouping) variables (e.g., Gender, Ethnic Origin; see also Crosstabulation & stub-and-banner tables).

Tables for multiple response items:  If this setting is chosen, then the user can specify so-called multiple response variables and multiple dichotomies (see Multiple responses/dichotomies), and compute (1) frequency tables for such variables or (2) compute crosstabulation tables involving such variables (e.g., ordinary categorical variables can be crosstabulated with multiple response variables/dichotomies.)


Specifying Multiple Response/Dichotomies - Specify Table

  Specifying Multiple Responses/Dichotomies - Specify Table

This option will bring up a standard six-variable lists selection window.  Each list will be interpreted as a single multiple response/dichotomy variable or factor.  If only a single variable is chosen in a list, then the respective variable will be treated as a standard categorical (grouping) variable in the crosstabulation.  By default, (1) short and long names as well as (2) short and long alphanumeric value labels for the factors will be taken from the first variable in each list.  Factor names can later be changed (see 1, 2, ... and Long factor labels).


Specifying Multiple Response/Dichotomies - Paired Crosstabulation

  Specifying Multiple Responses/Dichotomies - Paired Crosstabulation

The logic of paired crosstabulation of multiple response variables is explained in the overview section (under the header Paired Crosstabulation of Multiple Response Variables).  This option is only applicable if there are two or more multiple response variables specified for the current table and if at least two of them consist of identical numbers of actual variables.  If so, STATISTICA will proceed as follows:

•	The number of actual variables in each multiple response factor is counted;

•	Paired crosstabulation is performed on the first two or more multiple response variables with identical numbers of actual variables.

Thus, for example, if there are three multiple response factors, the first two with 2 actual variables and the third with 3, then only the first two factors will be processed as paired factors.


Specifying Multiple Response/Dichotomies - Name of Factor (Multiple Response Set)

  Specifying Multiple Responses/Dichotomies - Name of Factor (Multiple Response Set)

By default, the names for factors are taken from the first variable in each respective list.  To change the names, simply enter the new name into the edit field next to the respective factor.


Specifying Multiple Response/Dichotomies - Type of Multiple Response Factor

  Specifying Multiple Responses/Dichotomies - Type of Multiple Response Factor

The general logic of multiple response variables and multiple dichotomies is explained in the overview section.

Multiple dichotomy:  Set this radio button to treat the respective factor (list of actual variables) as a multiple dichotomy.  Be sure that the desired Count value is set (by default 1, see below).  All values that do not match the count value will be ignored in the analysis.

Count value:  This is the actual value that will be counted in the multiple response table; that is, STATISTICA will count how frequent this value is present in the different actual variables (levels) that comprise the respective multiple dichotomy.

Multiple response:  Set this radio button to treat the respective factor (list of actual variables) as a multiple response variable.  If no Codes are selected, then STATISTICA will automatically tabulate all integer values found in the first variable of the respective list.  If there is only one variable in the list, then the respective variable will be treated (tabulated) as an ordinary categorical (grouping) variable.

Count unique responses only (ignore multiple identical responses):  If this check box is set (default), then multiple identical responses in the different actual variables comprising a respective multiple response factor will be ignored.  For example, if a multiple response factor Preferred Sport consists of two actual variables (first preference, second preference) and a respondent listed the same sport for both preferences, then STATISTICA will only count this as one response.  (In other popular programs that compute multiple response tables, this respondent would be counted twice; do not set this check box if this is what is desired for the current crosstabulation or frequency table.)


Specifying Multiple Response/Dichotomies - Long Factor Labels

  Specifying Multiple Responses/Dichotomies - Long Factor Labels

Use this option to enter long labels for the factors.  By default, STATISTICA will take as the long label for a factor, the long variable name from the first actual variable in the respective list (if one is specified in the data file).


Specifying Multiple Response/Dichotomies - Exclude Missing Data Listwise Within Each Multiple Dichotomy Set

  Specifying Multiple Responses/Dichotomies - Exclude Missing Data Listwise Within Each Multiple Dichotomy Set

If this check box is set, then a case will be "declared" as missing ("no response") if it has missing data for any of the actual variables comprising the respective multiple dichotomy factor.


Specifying Multiple Response/Dichotomies - Exclude Missing Data Listwise Within Each Multiple Response Set

  Specifying Multiple Responses/Dichotomies - Exclude Missing Data Listwise Within Each Multiple Response Set

If this check box is set, then a case will be "declared" as missing ("no response") if it has missing data for any of the actual variables comprising the respective multiple response factor.


Specifying Multiple Response/Dichotomies - Include Missing Data as an Additional Category for Each Factor

  Specifying Multiple Responses/Dichotomies - Include Missing Data as an Additional Category for Each Factor

By default, missing data are ignored in the analysis.  If this check box is set, STATISTICA will count (tabulate) missing data as an additional category (level) for each factor.


  Specifying Factor Labels

By default, STATISTICA will take as the short and long label for a factor the short and long variable name from the first actual variable in the respective list (if one is specified in the data file).  You can change those labels by typing in the desired names into the respective edit fields.  To return to the default, click on the Set default button.


  Reviewing Multiple Response/Dichotomies Tables

A general discussion of the Crosstabulation & stub-and-banner tables option is provided in the overview section.

Multiple Response Table Results dialog:

Review Summary Table

Frequency Tables

Detailed Two-way Tables

Display Long Value Labels

Display Selected %'s in Sep. Tables

Interaction Plots of Frequencies

Crosstabulation Tables

Percentages of Row Counts

Percentages of Column Counts

Base Totals/Percentages on

Summary of Table Specifications


  Reviewing Multiple Response/Dichotomies Tables - Review Summary Tables

This option will bring up a summary table for multi-way crosstabulation tables.  The summary crosstabulation table will report the frequencies for the entire respective table; the last factor that makes up the table will be tabulated in the columns of the Scrollsheet, all remaining factors will be tabulated in the rows.  If there are more than two factors in a table, then the structure of the table will be as if several two-way tables (for the last two factors) were "glued" together one-after-another for the different levels of the remaining factors.  In this manner even 6-way tables can be reviewed in a single Scrollsheet.  The detail of results that are reported depends on the selections of options in the Crosstabulation Tables box.


  Reviewing Multiple Response/Dichotomies Tables - Frequency Tables

This option will bring up a cascade of frequency tables, one for each factor in the table.  For each category or level of a factor, the Scrollsheet will report:

(1)	The number of responses;

(2)	The percentage of responses relative to the total number of responses;

(3)	The percentage of responses relative to the total number of respondents (cases); that is, the percentage of respondents who gave the respective response (provided that multiple identical responses were ignored; see the option Count unique responses only, Specifying multiple responses/dichotomies).  For multiple response variables and multiple dichotomies, each respondent can give multiple responses; thus, the last column of the table will not add to 100%.


  Reviewing Multiple Response/Dichotomies Tables - Detailed Two-way Tables

This option will bring up Scrollsheets with two-way tables.  For tables with more than two variables (factors), a cascade of Scrollsheets will be produced for the last two factors in the table, within the levels of the other factors.  The detail of reported results depends on the choices of options in the Crosstabulation Tables box (and other options in this dialog).


  Reviewing Multiple Response/Dichotomies Tables - Display Long Value Labels

If this check box is set then long value labels will be displayed in the first column of the two-way table results Scrollsheets.


  Reviewing Multiple Response/Dichotomies Tables - Display Selected %'s in Sep. Tables

This check box is only available (active) if one of the Percentages... options is selected in the Crosstabulation Tables box.  By default, if percentages are requested they will be displayed in the same table together with the frequencies; thus each cell in such results Scrollsheets will consist of more than one line.  If this check box is set, then the percentage tables will be displayed in separate Scrollsheets (this is desirable when you want to produce graphs of percentages from the Scrollsheets).


  Reviewing Multiple Response/Dichotomies Tables - Interaction Plots of Frequencies

One way to summarize the distribution of frequencies across up to three variables (factors) in a single graph is via a line graph (interaction plot).  In each graph, the last (fastest changing) factor will be represented by different line patterns and colors; the next-to-last factor will be represented by "upper-x" labels; the last factor will be represented by "lower x" labels.  If there are more than three factors in the respective table, a cascade of interaction plots will be produced for each combination of levels of the remaining factors.


  Reviewing Multiple Response/Dichotomies Tables - Crosstabulation Tables

The selection of options in this box will determine the detail of results reported in the Summary tables and Detailed two-way tables (see above).

Highlight counts > . . . :  If this check box is set, then all counts (raw frequencies) in the table that are greater than the value in the edit box will be highlighted.

Percentages of total count:  If this check box is set, then for each cell in the Summary tables and Detailed two-way tables, percentages are computed relative to the total number of responses or respondents in the current table.  If the Display selected %'s in sep. tables is not set, then the percentages will be shown in the same table together with the raw frequencies.


  Reviewing Multiple Response/Dichotomies Tables - Percentages of Row Counts

If this check box is set, then for each cell in the Summary tables and Detailed two-way tables percentages are computed relative to the total number of responses or respondents in the row of the current table.  If the Display selected %'s in sep. tables is not set, then the percentages will be shown in the same table together with the raw frequencies.


  Reviewing Multiple Response/Dichotomies Tables - Percentages of Column Counts

If this check box is set, then for each cell in the summary tables and detailed two-way tables percentages are computed relative to the total number of responses or respondents in the column of the current table.  If the Display selected %'s in sep. tables is not set, then the percentages will be shown in the same table together with the raw frequencies.


  Reviewing Multiple Response/Dichotomies Tables - Base Totals/Percentages on

For multiple response variables and multiple dichotomies, a single respondent (case) may contribute more than one answer, and be counted more than once.  The setting of these radio buttons will determine whether the totals and percentages reported in the tables will be based on the total number of responses, or the total number of respondents (cases) that contributed to the respective marginal frequency (provided that multiple identical responses were ignored; see the option Count unique responses only, Specifying multiple responses/dichotomies).

Number of responses:  If this radio button is set, then the frequencies reported in the margins of the tables will be based on the number of responses.  Thus, they will be the sum of the respective reported (i.e., in that row or column) cell frequencies.  If percentages were requested, they will be computed with reference to those marginal frequencies.

Number of respondents:  If this radio button is set, then the frequencies reported in the margins of the tables will be based on the number of respondents (cases) that "contributed" to or were counted in the respective column or row (or two-way table, for total frequencies).  For multiple response variables and multiple dichotomies, those marginal frequencies will usually not be identical to the sum of the respective reported (i.e., in that row, column, or two-way table) cell frequencies.  If percentages were requested, then they will be computed with reference to these marginal frequencies of number of respondents.  This option is not available, if Paired crosstabulation was requested for multiple response variables (see Specifying multiple responses/dichotomies, see also the overview section under the header Paired Crosstabulation of Multiple Response Variables).


  Reviewing Multiple Response/Dichotomies Tables - Summary of Table Specifications

This option will bring up a Scrollsheet with the summary specifications for the factors in the current table.  For each factor, the Scrollsheet will report:

(1)	The name of the factor and the number of levels;

(2)	The type of factor (ordinary categorical variable, multiple response, multiple dichotomy);

(3)	The names of all actual variables comprising the multiple responses and dichotomies.


  Probability Distribution Calculator

The Probability Distribution Calculator facility allows you to compute, for various theoretical distributions and parameters (e.g., F, df 1, df 2), either (1) the upper or lower tail areas, given a user-specified variate value (two sided probability values can be computed for symmetrical distributions; e.g., the normal distribution), or (2) the critical values, given a user specified probability value.

Overview

Probability Distribution Calculator dialog:

Fixed Scaling

Inverse

Two-tailed

(1-Cumulative p)

Print

Create Graph

Compute

Distributions and Parameters

Beta	F	Pareto

Cauchy	Gamma	Rayleigh

Chi-square	Laplace	t (Student)

Exponential	Log-Normal	Weibull

Extreme Value	Logistic	Z (Normal)


  Probability Distribution Calculator - Overview

The Probability Distribution Calculator is a facility which allows you to compute critical values for a specified distribution based on user-specified parameters or degrees of freedom, or significance levels for the distribution.  One of the unique features of this calculator is the interactive graph icons which display the density function and cumulative distribution function for the specified distribution based on the respective parameters.  You can display those graphs in the standard (customizable) graph window and print them via the Create Graph option (see below).  This calculator is accessible via the Basic Statistics startup panel or in every module via the Quick Basic Stats - Probability Calculator option from the pull-down menu Analysis (also accessible by pressing the Quick Basic Stats toolbar button [image]).

Note that you can change the values of the parameters by either manually editing them in the respecitve edit field (you will need to click on the Compute button to complete the calculations) or by using the micro scrolls to incrementally change the values in the edit fields.  When you use the micro scrolls to change a value, STATISTICA will automatically recompute the other values.


Beta Distribution for the Probability Distribution Calculator

Probability Density Function:  The beta distribution has the probability density function:

                             ν-1        ω-1

f(x) = Γ(ν+ω)/[Γ(ν)Γ(ω)] * x    * (1-x)

0 ≤ x ≤ 1, ν > 0, ω > 0

where

Γ	(gamma) is the Gamma function

ν, ω	are the shape parameters (Shape1 and Shape2, respectively)

Distribution function:  The beta distribution function (the term distribution function was first introduced by von Mises, 1919) is related to the incomplete Beta function.  For more information, see Pearson, 1968.

Beta:  This edit field displays the current variate value for the Beta distribution.  When you edit this value (either manually or with the micro scrolls), STATISTICA will compute the associated p-value for the distribution with the specified degrees of freedom.

p:  This edit field displays the p-value computed from the specified variate value and degrees of freedom or you can enter a desired p-value (either manually or edit the existing value with the micro scrolls) and compute the critical value for the specified degrees of freedom.

Shape1, Shape2:  Specify here the shape parameters of the distribution, ν and ω, respectively.  If one or both of these parameters are changed, then the p-value will be recomputed based on the respective variate value.


Cauchy Distribution for the Probability Distribution Calculator

Probability Density Function:  The Cauchy distribution has the probability density function:

f(x) = 1/( θ*π*{1+[(x- η)/ θ]^2})

0 < θ

where

η	is the location parameter (median)

θ	is the scale parameter

π 	is the constant Pi (3.1415...)

Cumulative Distribution Function:  The cumulative distribution function (the term was first introduced by Wilks, 1943) for the Cauchy distribution is:

F(x) = 1/2 + 1/π*arctan[(x-η)/ θ]

C:  This edit field displays the current variate value for the Cauchy distribution.  When you edit this value (either manually or with the micro scrolls), STATISTICA will compute the associated p-value for the specified parameters.

p:  This edit field displays the p-value computed from the specified variate value and parameters or you can enter a desired p-value (either manually or edit the existing value with the micro scrolls) and compute the critical value for the specified parameters.

Location, Scale:  Specify here the location and scale parameters of the distribution, η and θ, respectively.  If one or both of these parameters are changed, then the p-value will be recomputed based on the respective variate value.


Chi-square Distribution for the Probability Distribution Calculator

Probability Density Function:  The Chi-square distribution is defined by:

f(x) = {1/[2^ν/2 * Γ(ν/2)]} * {x^[(ν/2)-1] * e^-x/2}

ν = 1, 2, ..., 0 < x

where

ν	is the degrees of freedom

e	is Euler's constant (2.71...)

Γ	(gamma) is the Gamma function (of argument alpha)

Chi**2:  This edit field displays the current variate value for the Chi-square distribution.  When you edit this value (either manually or with the micro scrolls), STATISTICA will compute the associated p-value for the specified shape parameter.

p:  This edit field displays the p-value computed from the specified variate value and shape parameter (df) or you can enter a desired p-value (either manually or edit the existing value with the micro scrolls) and compute the critical value of the distribution for the specified df.

df:  Specify here the shape parameter of the distribution, ν.  If this parameter is changed, then the p-value will be recomputed based on the respective variate value.


Exponential Distribution for the Probability Distribution Calculator

Probability Density Function:  The exponential distribution has the probability density function:

f(x) = λe^(-λx)

0 ≤ x < ∞, λ > 0

where

λ	is the scale parameter (an alternative parameterization is b=1/λ)

e	is Euler's constant (2.718...)

Cumulative Distribution Function:  The cumulative distribution function (the term was first introduced by Wilks, 1943) for the Exponential distribution is:

F(x) = 0             x≤0

     = 1 - e^(-λx)   x>0

Exp:  This edit field displays the current variate value for the Exponential distribution.  When you edit this value (either manually or with the micro scrolls), STATISTICA will compute the associated p-value for the specified scale parameter.

p:  This edit field displays the p-value computed from the specified variate value and scale parameter or you can enter a desired p-value (either manually or edit the existing value with the micro scrolls) and compute the critical value of the distribution for the specified parameter.

Lambda:  Specify here the scale parameter of the distribution, λ.  If this parameter is changed, then the p-value will be recomputed based on the respective variate value.


Extreme Value Distribution for the Probability Distribution Calculator

Probability Density Function:  The extreme value (Type I) distribution has the probability density function:

f(x) = 1/b * e^[-(x-a/b] * e^{-e^[-(x-a)/b]}

-∞ < x < ∞, b > 0

where

a	is the location parameter

b	is the scale parameter

e	is Euler's constant (2.71...)

Cumulative Distribution Function:  The cumulative distribution function (the term was first introduced by Wilks, 1943) for the Extreme Value distribution is:

F(x) = e^{-e^[-(x-a)/b]}

V:  This edit field displays the current variate value for the Extreme Value distribution.  When you edit this value (either manually or with the micro scrolls), STATISTICA will compute the associated p-value for the specified parameters.

p:  This edit field displays the p-value computed from the specified variate value and parameters or you can enter a desired p-value (either manually or edit the existing value with the micro scrolls) and compute the critical value of the distribution for the specified parameters.

Location, Scale:  Specify here the threshold and scale parameters of the distribution, a and b, respectively.  If this parameter is changed, then the p-value will be recomputed based on the respective variate value.


F Distribution for the Probability Distribution Calculator

Probability Density Function:  The F distribution (for x > 0) has the probability density function (for ν = 1, 2, ...; ω = 1, 2, ...):

f(x) = [Γ{(ν+ω)/2}]/[Γ(ν/2)Γ(ω/2)] * (ν/ω)^(ν/2) *

       x^[(ν/2)-1] * {1+[(ν/ω)*x]}^[-(ν+ω)/2]

0 ≤ x < ∞

ν=1,2,..., ω=1,2,...

where

ν, ω 	are the shape parameters, degrees of freedom

Γ	(gamma) is the Gamma function

F:  This edit field displays the current variate value for the F distribution.  When you edit this value (either manually or with the micro scrolls), STATISTICA will compute the associated p-value for the specified degrees of freedom.

p:  This edit field displays the p-value computed from the specified variate value and degrees of freedom or you can enter a desired p-value (either manually or edit the existing value with the micro scrolls) and compute the critical value of the distribution for the specified degrees of freedom.

df1, df2:  Specify here the shape parameters of the distribution, ν and ω, respectively.  If one or both of these parameters are changed, then the p-value will be recomputed based on the respective variate value.


Gamma Distribution for the Probability Distribution Calculator

Probability Density Function:  The gamma distribution has the probability density function:

f(x) = [1/Γ(c)] * x^(c−1) * e^-x

0≤x

c>0

where

Γ	(gamma) is the Gamma function (of argument alpha)

c	is the shape parameter

e	is Euler's constant (2.718...)

G:  This edit field displays the current variate value for the Gamma distribution.  When you edit this value (either manually or with the micro scrolls), STATISTICA will compute the associated p-value for the specified shape parameter.

p:  This edit field displays the p-value computed from the specified variate value and shape parameter or you can enter a desired p-value (either manually or edit the existing value with the micro scrolls) and compute the critical value of the distribution for the specified shape parameter.

Shape:  Specify here the shape parameter of the distribution, c.  If this parameter is changed, then the p-value will be recomputed based on the respective variate value.


Laplace Distribution for the Probability Distribution Calculator

Probability Density Function:  The Laplace (or Double Exponential) distribution has the probability density function:

f(x) = 1/(2b) * e^[-(|x-a|/b)]    -∞<x<∞

where

a	is the location parameter (mean)

b	is the scale parameter

e 	is Euler's constant (2.71...)

Cumulative Distribution Function:  The cumulative distribution function (the term was first introduced by Wilks, 1943) for the Laplace distribution is:

F(x) = 1/2 * e^[-(a-x)/b]          x < a

     = 1 - {1/2 * e^[-(x-a)/b]}    x ≥ a

L:  This edit field displays the current variate value for the Laplace distribution.  When you edit this value (either manually or with the micro scrolls), STATISTICA will compute the associated p-value for the specified parameters.

p:  This edit field displays the p-value computed from the specified variate value and parameters or you can enter a desired p-value (either manually or edit the existing value with the micro scrolls) and compute the critical value of the distribution for the specified parameters.

Location, Scale:  Specify here the location and scale parameters of the distribution, θ and b, respectively.  If one or both of these parameters are changed, then the p-value will be recomputed based on the respective variate value.


Lognormal Distribution for the Probability Distribution Calculator

Probability Density Function:  The log-normal distribution has the probability density function:

                                    2   2

                1/2     -{log(x)-μ]} /2σ

f(x) = 1/[xσ(2π)   ] * e

0 < x < ∞

μ > 0

σ > 0

where

μ	is the scale parameter

σ	is the shape parameter

e	is Euler's constant (2.71...)

π	is the constant Pi (3.1415...)

L:  This edit field displays the current variate value for the Lognormal distribution.  When you edit this value (either manually or with the micro scrolls), STATISTICA will compute the associated p-value for the specified parameters.

p:  This edit field displays the p-value computed from the specified variate value and parameters or you can enter a desired p-value (either manually or edit the existing value with the micro scrolls) and compute the critical value of the distribution for the specified parameters.

Mu, Sigma:  Specify here the scale and shape parameters of the distribution, μ and σ, respectively.  If one or both of these parameters are changed, then the p-value will be recomputed based on the respective variate value.


Logistic Distribution for the Probability Distribution Calculator

Probability Density Function:  The Logistic distribution has the probability density function:

f(x) = (1/b) * e^[-(x-a)/b] * {1+e^[-(x-a)/b]}^-2

-∞ < x < ∞, 0<b

where

a	is the location parameter (mean)

b	is the scale parameter

e 	is Euler's constant (2.71...)

Cumulative Distribution Function:  The cumulative distribution function (the term was first introduced by Wilks, 1943) for the Logistic distribution is:

F(x) = {1 + e^[-(x-a)/b]}^-1

Logistic:  This edit field displays the current variate value for the Logistic distribution.  When you edit this value (either manually or with the micro scrolls), STATISTICA will compute the associated p-value for the specified parameters.

p:  This edit field displays the p-value computed from the specified variate value and parameters or you can enter a desired p-value (either manually or edit the existing value with the micro scrolls) and compute the critical value of the distribution for the specified parameters.

Location, Scale:  Specify here the location and scale parameters of the distribution, a and b, respectively.  If one or both of these parameters are changed, then the p-value will be recomputed based on the respective variate value.


Normal Distribution for the Probability Distribution Calculator

Z (Normal) Distribution for the Probability Distribution Calculator

Probability Density Function:  The normal distribution function is determined by the following formula:

f(x) = 1/[σ(2*π)^1/2] * e^{-1/2*[(x-μ)/σ]^2}

-∞ < x < ∞

where

μ	is the mean

σ	is the standard deviation

e	is Euler's constant (2.71...)

π	is the constant Pi (3.1415...)

Z:  This edit field displays the current variate value for the Z (Normal) distribution.  When you edit this value (either manually or with the micro scrolls), STATISTICA will compute the associated p-value for the specified parameters.

p:  This edit field displays the p-value computed from the specified variate value and parameters or you can enter a desired p-value (either manually or edit the existing value with the micro scrolls) and compute the critical value of the distribution for the specified parameters.

mean, st. dev.:  Specify here the location and scale parameters of the distribution, mean and st. dev., respectively.  If one or both of these parameters are changed, then the p-value will be recomputed based on the respective variate value.


Pareto Distribution for the Probability Distribution Calculator

Probability Density Function:  The standard Pareto distribution has the probability density function:

          c+1

f(x) = c/x         1 ≤ x, c < 0

where

c	is the shape parameter

Cumulative Distribution Function:  The cumulative distribution function (the term was first introduced by Wilks, 1943) for the Pareto distribution is:

            -c

F(x) = 1 - x

Pareto:  This edit field displays the current variate value for the Pareto distribution.  When you edit this value (either manually or with the micro scrolls), STATISTICA will compute the associated p-value for the specified shape parameter.

p:  This edit field displays the p-value computed from the specified variate value and shape parameter or you can enter a desired p-value (either manually or edit the existing value with the micro scrolls) and compute the critical value of the distribution for the specified parameters.

Shape:  Specify here the shape parameter of the distribution, c.  If this parameter is changed, then the p-value will be recomputed based on the respective variate value.


Rayleigh Distribution for the Probability Distribution Calculator

Probability Density Function:  The Rayleigh distribution has the probability density function:

f(x) = x/b^2 * e^[-(x^2/2b^2)]

0 ≤ x < ∞, b > 0

where

b	is the scale parameter

e	is Euler's constant (2.71...)

Cumulative Distribution Function:  The cumulative distribution function (the term was first introduced by Wilks, 1943) for the Rayleigh distribution is:

F(x) = 1 - e^[-(x^2/2b^2)]

R:  This edit field displays the current variate value for the Rayleigh distribution.  When you edit this value (either manually or with the micro scrolls), STATISTICA will compute the associated p-value for the specified scale parameter.

p:  This edit field displays the p-value computed from the specified variate value and scale parameter or you can enter a desired p-value (either manually or edit the existing value with the micro scrolls) and compute the critical value of the distribution for the specified parameter.

Scale:  Specify here the scale parameter of the distribution, b.  If this parameter is changed, then the p-value will be recomputed based on the respective variate value.


t (Student) Distribution for the Probability Distribution Calculator

Probability Density Function:  The Student's t distribution has the probability density function (for ν = 1, 2, . . .):

       Γ{(ν+1)/2}      -1/2      2   -{(ν+1)/2}

f(x) =   Γ(ν/2)   *(ν*π)   *{1+(x /ν)}

where

ν	is the shape parameter, degrees of freedom

Γ 	(gamma) is the Gamma function

π 	is the constant Pi (3.1415 . . .)

Cumulative Distribution Function:  The cumulative distribution function (the term was first introduced by Wilks, 1943) for the Student's t distribution depends on whether v is odd or even and is completely described in Evans, Hastings, and Peacock, 1993.

t:  This edit field displays the current variate value for the Student's t distribution.  When you edit this value (either manually or with the micro scrolls), STATISTICA will compute the associated p-value for the specified degrees of freedom.

p:  This edit field displays the p-value computed from the specified variate value and degrees of freedom or you can enter a desired p-value (either manually or edit the existing value with the micro scrolls) and compute the critical value of the distribution for the specified degrees of freedom.

df:  Specify here the shape parameter of the distribution, ν.  If this parameter is changed, then the p-value will be recomputed based on the respective variate value.


Weibull Distribution for the Probability Distribution Calculator

Probability Density Function:  The Weibull distribution has the probability density function:

f(x) = c/b*(x/b)^(c-1) * e^[-(x/b)^c]

0 ≤ x < ∞, b > 0, c > 0

where

b	is the scale parameter

c	is the shape parameter

e	is Euler's constant (2.718...)

Cumulative Distribution Function:  The cumulative distribution function (the term was first introduced by Wilks, 1943) for the Weibull distribution is:

F(x) = 1 - e^[-(x/b)^c]

W:  This edit field displays the current variate value for the Weibull distribution.  When you edit this value (either manually or with the micro scrolls), STATISTICA will compute the associated p-value for the specified parameters.

p:  This edit field displays the p-value computed from the specified variate value and parameters or you can enter a desired p-value (either manually or edit the existing value with the micro scrolls) and compute the critical value of the distribution for the specified parameters.

Scale, Shape:  Specify here the scale and shape parameters of the distribution, b and c, respectively.  If one or both of these parameters are changed, then the p-value will be recomputed based on the respective variate value.


  Probability Distribution Calculator - Fixed Scaling

This option affects the scaling of the (continuously updated) graph depicted in the icons at the bottom of the dialog, and the graphs that are produced if you select the option Create Graph.  When this option (check box) is selected, the program will use a fixed scale for the graphs, and as you change the parameters of the respective distribution, you can observe the changes in the graph relative to the same fixed scales.  Note that for extreme parameter settings, this may result in the graphs "running-off the screen."  To avoid this, deselect the Fixed Scale option, which causes the program to recompute the optimum scaling for the graphs for each parameter setting, resulting in optimum resolution.  However, for some distributions, this will give the appearance that the shapes of the functions are not changing in response to different parameter settings; this happens, for example, when you change the st.dev. (standard deviation) parameter for the normal (z) distribution, while the Fixed Scale option is deselected.


  Probability Distribution Calculator - Inverse

When set, this option allows you to compute the inverse of the integral; that is, you can enter a desired significance level and STATISTICA will compute the critical value of the respective statistic.  Note that if you change the value of p in the respective edit field, then this option will automatically be selected.


Probability Distribution Calculator - Two-Tailed Test

  Probability Distribution Calculator - Two-Tailed

This option allows you to specify a two-tailed (set the check box) or one-tailed test.  This option is only available for symmetric distributions.


  Probability Distribution Calculator - (1-Cumulative p)

Set this check box in order to compute the critical value for the specified distribution based on a (1-cumulative p) value or the (1-cumulative p) value based on a specified critical value.


  Probability Distribution Calculator - Print

Set this check box if you want to print (send to the printer, file, and/or Text/output Window whichever output destination you selected in the Page/Output Setup dialog) the p-value and critical value for the specified distribution and parameters.  These values will be printed when you click on the Compute button, and not when you change the parameters with the micro scrolls.  Therefore, you can edit the parameters using the micro scrolls and review the results in the edit fields in the dialog, then when you are ready, click on the Compute button to print the resulting values.

In order to print the graphs created when you select the Create Graph option, you can use the Print Graph option or the graphics window Print Graph [image] toolbar button to print the selected graphs or if the Automatically Print All Graphs option was previously selected (in the Page/Output Setup dialog), then the graphs will automatically be printed when they are created.


  Probability Distribution Calculator - Create Graph

Set this option if you would like the Probability Density Function and Cumulative Distribution Function graphs for the specified distribution and parameters to be placed in a compound graph.  The graph will be created when you click on the Compute button, and not when you change the parameters with the micro scrolls.  Therefore, you can edit the parameters using the micro scrolls and review the results in the graph icons in the dialog, then when you are ready, click on the Compute button to create the desired graph.

In order to print the graphs created when you select the Create Graph option, you can use the Print Graph option or the graphics window Print Graph [image] toolbar button to print the selected graphs or if the Automatically Print All Graphs option was previously selected (in the Page/Output Setup dialog), then the graphs will automatically be printed when they are created.


  Probability Distribution Calculator - Compute

Clicking on this button will enter the value currently edited in an edit box (if micro scrolls are not used) and will compute the p-value or critical value for the specified distribution based on the distribution's parameters and (when the respective options are checked):

Print the resulting critical value and p-value to the printer, file, and/or Text/output Window (whichever output destination you selected in the Page/Output Setup dialog);

Create a compound graph containing the Probability Density Function and Cumulative Distribution Function for the specified distribution and parameters.


  Other Significance Tests

Print Results for each Compute

Difference Between Two Correlation Coefficients

Difference Between Two Means (Normal Distribution)

Difference Between Two Percentages


  Other Significance Tests - Print Results for each Compute

Set this check box if you want to automatically print (send to printer file, or the Text/output Window whichever output destination you selected in the Page/Output Setup dialog) the results of the selected probability computations.  (For more information on printing results, see Printing.)


  Other Significance Tests - Difference Between Two Correlation Coefficients

The options in this box allow you to compare the statistical significance of differences between two Pearson r's.  Both One-sided and Two-sided tests can be performed.

See also Correlations.


  Other Significance Tests - Difference Between Two Means (Normal Distribution)

These options allow you to compute:

(1)  The significance level for the difference between two means computed from two samples;

(2)  The significance level for the difference between one mean computed from a sample and a population mean (if the Single mean 1 vs. population mean 2 check box is set).

The p-level is computed based on the t-value for the respective comparison; both One-sided and Two-sided tests can be performed.

See also t-test for independent samples.


  Other Significance Tests - Difference Between Two Percentages

These options allow you to compute the significance level for the difference between two percentages; both One-sided and Two-sided tests can be performed.  The p-level is computed based on the t-value for the respective comparison:

|t|=Sqrt[(N1*N2)/(N1+N2)]*|p1-p2|/Sqrt(p*q)

where

p=(p1*N1+p2* N2)/(N1+N2)

q=1-p.

See also t-test for independent samples.


  Specifying Intervals (Categories)

This option allows you to specify up to 16 case selection conditions that will be used in the computation of the frequency table to assign cases to categories.  The selection conditions will be checked sequentially; that is, a case will be assigned to the first category where it "fits."

Note that you could also create a new (grouping) variable in the data file and compute it accordingly.  For example, this is useful when you need to recode data in a way that requires that the values of the target variable are not fixed but calculated following some specific formulas (e.g., as an average of values of some other variables), use the spreadsheet Formulas or the user-defined recoding functions in the STATISTICA BASIC programming language.

Example

Define Categories dialog:

Category

Review Vars

Open All

Save All

Other

Print


  Specifying Intervals (Categories) - Category

You can define up to 16 categories by entering up to 16 case selection conditions.  The selection conditions will be checked sequentially; that is, a case will be assigned to the first category where it "fits."

•	Include/Exclude if:  When you choose Include if and the selection condition evaluates to true, cases (observations) that meet the condition will be assigned to the respective category (unless the same case was placed into a previous category where it also fit).  Exclude if will assign cases to the respective category if they do not meet the specified selection condition.

•	Case selection condition:  Specify the case selection condition in the blank Category line following the standard STATISTICA Case Selection Conditions.

•	Operators:  =, <>, <, >, <=, >=, NOT, AND, OR

•	Variable Names:  Specify either variable numbers (e.g., v1, v2, v3, . . . ) or variable names (e.g., GENDER, Date, time, . . .).

•	Case Number:  v0

•	Examples:  v1=0 OR v2>=0;

(v1<1 OR v9='YES' ) AND v4<>0

•	Note:  Be sure to use single quotation marks to reference the text values of variables, e.g., 'Yes'.

•	Open/Save button:  Use this option to open (and use for categorizing) an existing standard STATISTICA Case Selection Condition file (those which can be used to select/filter cases for all analyses in STATISTICA) as well as save the current condition in each Category.  Clicking on the Open/Save button will open the Case Selection Condition dialog where you can edit, save or open case selection conditions (these are the same conditions which are used for processing subsets of cases throughout STATISTICA).  Case selection conditions saved in this dialog are saved under the file name extension *.sel.  These case selection conditions are then used as categorization conditions when you click <OK> in the Case Selection Condition dialog.


  Specifying Intervals (Categories) - Review Vars

Clicking this button will open the Variables dialog from which you can view the variables in the spreadsheet.


  Specifying Intervals (Categories) - Open All

This button opens the Open Case Selection Conditions File dialog from which you can select a file (containing all of the case selection conditions) to open into the Define Categories dialog.  Files opened from this dialog are text files with the file name extension *.txt.


  Specifying Intervals (Categories) - Save All

This button opens the Save Case Selection Conditions File dialog from which you can designate a file to save the case selection conditions into.  This file will be saved in text file format (*.txt extension).


  Specifying Intervals (Categories) - Other

All cases that do not fit any of the case selection conditions will be excluded from the analyses.


  Specifying Intervals (Categories) - Print

Click on this button to print the category selection conditions.


  Specifying Intervals (Categories)

This set of (two) case selection conditions will result in ("translate" to ) two categories in the frequency table.  The first will include all cases with values for variable 1 greater than or equal to zero; the second category will include all cases with values for variable 1 less than zero.

Category 1:	Include if:  v1>=0

Category 2:	Include if:  v1<0


  Normal, Half-Normal, and Detrended Normal Probability Plots

Normal probability plot:  The standard normal probability plot is constructed as follows.  First, the deviations from the respective means (residuals) are rank ordered.  From these ranks we can compute Z values (i.e., standardized values of the normal distribution) based on the assumption that the data come from a normal distribution.  These Z values are plotted on the Y axis in the plot.  If the observed residuals (plotted on the X axis) are normally distributed, then all values should fall onto a straight line (marked Normal Expected in the plot).  If the residuals are not normally distributed, then they will deviate from the line.  Outliers may also become evident in this plot.  If there is a general lack of fit, and the data seem to form a clear pattern (e.g., an S shape) around the line, then the dependent variable may have to be transformed in some way (e.g., a log transformation to "pull in" the tail of the distribution, etc., see Edit Variable Specs or STATISTICA BASIC).

Half-normal probability plot:  The half-normal probability plot is constructed in the same way as the standard normal probability plot, except that only the positive half of the normal curve is considered.  Consequently, only positive normal values will be plotted on the Y axis.  This plot is used when one wants to ignore the sign of the residual; that is, when one is mostly interested in the distribution of absolute residuals, regardless of sign.

Detrended normal probability plot:  The detrended normal probability plot is constructed in the same way as the standard normal probability plot, except that before the plot is generated, the linear trend is removed.  This often "spreads out" the plot, thereby allowing the user to detect patterns of deviations more easily.


  Box and Whisker Plots

The box and whisker plot typically will summarize the distribution of a variable by three components:

(1)  A central line to indicate central tendency or location;

(2)  A box to indicate variability around this central tendency;

(3)  Whiskers around the box to indicate the range of the variable.

In Quick Stats Graphs, you can choose to plot for each variable:

(1)  Medians (central line), quartiles (box), and ranges (whiskers);

(2)  Means, standard errors of the means, and standard deviations;

(3)  Means, standard deviations, and 1.96 times the standard deviations (95% normal confidence interval for individual observations around the mean);

(4)  Means, standard errors of the means, and 1.96 times the standard errors of the means (95% normal confidence interval for means).


  Basic Statistics - Notes and Technical Information

Precision:  All raw data processing "engines" in Basic Statistics and Tables always operate in double precision, internally preserving at least 16 significant digits (for example, 0.8272615207152749).  The selection of single vs. double precision offered in some of the procedures mostly affects the way in which the results of calculations are stored.  In cases where single precision is the default, changing to double precision may slow down the program somewhat, but in most cases the speed difference is negligible.  Also, the accuracy gains are negligible in most cases since all internal data processing engines in STATISTICA always operate in double precision anyway:  in extended precision 80 bit (10-byte) or 64 bit (8-byte) real numbers.

Precision benchmarks:  In order to assess the performance of accuracy optimization routines in STATISTICA, be sure that the raw data file (used in you accuracy benchmark) is stored in extended precision format.


Statistical Advisor

Based on your answers to the successive questions about the nature of your research, the Statistical Advisor will suggest to you which statistical methods should be used and where to find them in STATISTICA.  For each question, click on the appropriate answer to go to the next question or suggestion.  If you are unsure of the answer to the question, click on the Get More Info option to read more about that particular topic.

Do you want to:

(1)  Describe/summarize/tabulate data,

(2)  Test hypotheses (predictions) about your data,

(3)  Explore data and search for structure/patterns/factors/clusters, or

(4)  Compute statistics for industrial quality control/improvement?

Get More Info


Do you want to:

(1)  Summarize/plot the shape of the distribution of continuous variables/measurements,

(2)  Tabulate/plot categorical data (such as gender, occupation) and compute frequencies, percentages, etc., or

(3)  Explore/summarize a time series?

Get More Info


You can compute:

(1)  Simple descriptive statistics and frequency distributions,

(2)  Detailed descriptive statistics,

(3)  Descriptive statistics by groups, samples, or variables, or

(4)  Specialized industrial descriptive stats and stats for survival/failure times?


You can compute descriptive statistics for:

(1)  Censored data (failure times, survival times),

(2)  Process capability (of an industrial/manufacturing process), or

(3)  Gage repeatability & reproducibility.

Get more Info


You can compute:

(1)  Simple frequency tables and plot histograms or stem-and-leaf diagrams, or

(2)  Crosstabulate two or more variables to describe their joint distribution (crosstabulation tables, banner tables).


You can test hypotheses regarding:

(1)  The shape of (or fitting) distributions,

(2)  Differences between groups/samples,

(3)  Differences between variables,

(4)  Relationships between variables, or

(5)  Differences in relationships between variables in different groups.

Get More Info


You can perform:

(1)  Comparison of means/variances in two groups/samples,

(2)  Comparison of means/variances in multiple groups,

(3)  General (nonparametric) comparisons of distributions in two or more groups, or

(4)  Comparison of survival/failure times in two or more groups.

Get More Info


You can perform:

(1)  Comparisons of means for two variables or measurements,

(2)  Comparisons of means for several variables or repeated measurements,

(3)  General (nonparametric) comparison of two variables, or

(4)  General (nonparametric) comparison of several variables.

Get More Info


You can test for:

(1)  Simple linear relationships between two continuous variables,

(2)  Simple relationships between two categorical variables,

(3)  Multiple linear relationships between continuous variables,

(4)  Multiple relationships between categorical variables,

(5)  Nonlinear relationships, or

(6)  Time-dependent (lagged) relationships.


You can perform:

(1)  Polynomial regression analysis,

(2)  Probit/logit regression for categorical dependent and continuous independent variables,

(3)  General nonlinear regression, or

(4)  Nonlinear regression analysis for censored survival times.


You may perform:

(1)  Analysis of covariance (ANCOVA), or

(2)  Stratified linear or nonlinear regression.


You may search for:

(1)  Factors or dimensions in multiple continuous variables,

(2)  Clusters or 'natural' groups of variables or cases,

(3)  Patterns or trends in observations over time,

(4)  Relationships in multi-way crosstabulation tables.


You can:

(1)  Compute Quality control charts,

(2)  Develop/analyze sampling plans,

(3)  Perform process capability analysis,

(4)  Perform gage repeatability/reproducibility analysis,

(5)  Designing/analyzing experiments (including Taguchi), or

(6)  Analyze failure times.


You can:

(1)  Compute quality control charts for on-line quality control (Shewhart control charts),

(2)  Regression control charts, or

(3)  Perform Pareto chart analyses.


More Info

If you have just collected the data, it is always a good idea to look first at the appropriate summary statistics for each variable in the file.  For example, you may want to compute frequency distributions for all variables to identify outliers.

Usually, data are collected to test specific hypotheses or models concerning some variables.  For example, we may want to find out whether men are more likely to agree with an item on a questionnaire than women.  More complicated hypotheses may pertain to the nature of relationships between variables, for example, whether it is linear or non-linear.

If you have no specific hypotheses, and the nature of the study is exploratory, you may want to use some techniques that are designed to help 'make sense' of the data, that is, to detect patterns, clusters, etc.

The fourth option (quality control/improvement) will guide you through the various techniques for industrial quality control, experimentation, and reliability analysis.


More Info

In general, variables (and data) either represent measurements on some continuous scale, or they represent information about some categorical or discrete characteristics.

For example, the weight, height, and age of respondents in a survey would represent continuous variables; in industrial or medical applications, survival/failure times are also continuous variables.  However, a person's gender, occupation, or marital status are categorical or discrete variables: either a person is male or female, never married, married, or divorced, etc.

Some variables could be considered in either way.  For example, a person's rating of someone else's attractiveness on a 4 point scale may be considered a continuous variable, or we may consider it a discrete variable with 4 categories.

Time series data are usually collected for continuous variables, over time. For example, stock quotes for a particular stock over successive trading days represent a time series of data.


Simple Descriptive Statistics/Distributions

Use one of the following:

BASIC STATISTICS will compute the mean, standard deviation, variance, skewness, and kurtosis of variables. The mean is a measure of the average or central tendency of a continuous distribution. The standard deviation and variance are measures of dispersion, that is, the variability of data. The skewness is a measure of the 'sidedness' of the distribution, that is, the extent to which the distribution of data points is skewed towards the left or right side of the mean. The kurtosis is a measure of 'pointedness' or 'peakedness' of the distribution, that is, the extent to which the distribution is spread or centered closely around the mean.  Basic Statistics allows you to compute frequency distribution tables, and to visualize distributions in histograms .  After the descriptive statistics have been computed, you can plot the distribution of variables by clicking on them in the Scrollsheet.

STATS GRAPHS contains a wide range of descriptive graphs such as histograms, pie-charts, or 3D histograms, as well as numerous specialized graphs for describing data (e.g., Chernoff faces, star, sun ray plots, etc.).


Detailed Descriptive Statistics

Use NONPARAMETRICS AND DISTRIBUTION FITTING.  This module will compute detailed descriptive statistics for your data.

In addition to the standard mean (average), this module will compute the harmonic and geometric means, mode (most frequent value), median (50'th percentile), quartiles (25'th and 75'th percentiles) and other percentiles. In addition to the standard deviation and variance, this module will compute the average absolute deviation, range, quartile range, etc.

Additional descriptive statistics include the skewness, kurtosis, minimum, maximum, and sum.

After the descriptive statistics have been computed, you can plot the distribution of variables by clicking on them in the Scrollsheet.


Statistics by Groups, Samples, Variables

Use one of the following:

BASIC STATISTICS:  This module contains a breakdown facility that allows you to 'break down' means (and standard deviations) by one or more grouping variables (see, Breakdown: Descriptive statistics by groups).  For example, you could compute a breakdown table of means of a variable Income by gender (male, female), within gender by occupation, and within gender and occupation by ethnic background.  This module will compute box plots, and report various statistics broken down by another variable.

STATS GRAPHS:  Stats Graphs contain a wide range of descriptive graphics (e.g., histograms, line graphs) that can be computed by groups (categorized plots).


More Info

CENSORED DATA:  A data set is said to be 'censored' if some observations are incomplete, but not missing.  For example, in a medical research study of recovery from serious illness, we may lose contact with a subject because he or she moved.  In that case, we know that the respective patient survived at least as long as we were able to maintain contact; however, we do not know what happened thereafter, and this observation is therefore censored.  In industrial reliability testing, censored data sets are also common.  For example, a part or product may not fail (break) within the time span covered by a study.  However, we do not know how long it will function properly thereafter.

PROCESS CAPABILITY:  There are various summary statistics and specialized graphs that describe the capability/quality of manufacturing processes or suppliers. For example, one can compute the ratio of the range of sizes of parts manufactured relative to engineering specifications.  One can also estimate the proportion of parts that fall within specified limits.

GAGE REPEATABILITY & REPRODUCIBILITY:  In order to precisely monitor the quality of a production process, it is necessary to employ reliable measurement gages.  Several specialized statistics and graphs are available to assess the reliability of gages.


Process Capability

Use PROCESS ANALYSIS.  This module will compute various indices of process capability, tolerance limits, and produce the standard process capability histogram.

The process capability indices are ratios that summarize the extent to which a manufacturing process or supplier turns out products or parts within specified engineering limits.  For example, the so-called Cp index is the ratio of the specification range over the effective range manufactured by the process (typically defined by 6 times sigma, the standard deviation of the process).

The module will allow you to summarize the process capability in the standard histogram form, showing the observed distribution of parts, the normal curve, and the specification limits.  You can also compute tolerance limits, and estimate with a specified degree of certainty the percentage of manufactured parts that fall within the specification limits.


Gage Repeatability & Reproducibility

Use PROCESS ANALYSIS.  This module includes facilities to design and analyze gage repeatability & reproducibility studies.

Gage repeatability refers to the extent to which repeated measurements of the same part by the same operator (of the gage) produce identical results. Gage reproducibility refers to the extent to which different operators measuring the same parts with the same gage produce identical measurement.

Gage repeatability and reproducibility can be expressed in terms of variability (across measurements or operators, respectively).  The size of that variability relative to the variability between parts, and the required precision necessary to detect quality problems, determines the reliability, and thus usefulness of the measurement procedures used in the quality control effort.


Descriptive Statistics for Survival/Failure Times

Use SURVIVAL ANALYSIS.  This module will compute standard life tables as well as Kaplan-Meier product-limit estimates.  Facilities are also included to fit specialized distributions (Weibull, Gompertz, linear hazard) to observed survival/failure times.

In the standard life table analysis, the survival or failure times are divided into a user-specified number of intervals.  The program will then compute various statistics for each interval, for example, the proportion surviving up to the respective interval, the proportion failing in the interval, the hazard rate for the interval (probability of death/failure per unit of time), etc.  In addition, the percentiles of the cumulative survival function can be computed.  As in all modules of STATISTICA, extensive graphics are available to visualize the results.

The Kaplan-Meier product-limit method will compute statistics similar to those in the life table, however, they are computed 'continuously,' that is, for each distinct failure time in the data set.  Therefore, results using this method are not affected by the (arbitrary) choice of the number of time intervals to be used for the analysis.


Simple Frequency Tables/Histograms

Use one of the following modules:

BASIC STATISTICS:  This module will compute frequency distribution tables and report percentages, cumulative percentages, etc.

STATS GRAPHS:  Stats Graphs contains a wide range of descriptive graphs for categorical and discrete data, such as histograms, pie-charts, or 3D histograms, as well as numerous specialized graphs for describing data (e.g., Chernoff faces, star, sun ray plots, etc.).


Crosstabulation/Banner Tables

Use one of the following:

BASIC STATISTICS:  This module includes extensive facilities to produce two-and higher-way crosstabulation tables.  Lists of two-way tables can be represented in so-called banner tables.  Those are summary tables where one or more categorical variable, represented by the rows of the Scrollsheet, are crosstabulated against one or more categorical variables, represented by the columns of the Scrollsheet.  For example, those tables may allow you to summarize consumer choices (e.g., which brand of toothpaste was purchased) by various demographic characteristics such as gender, ethnic background, occupation, etc.  You can choose to express the frequencies in the table in terms of overall percentages, row percentages, column percentages, or raw frequencies.  The program will also compute a variety of statistics describing the strength of the relationship between the categorical variables in the two-way tables.

LOG LINEAR:  This module provides general facilities for computing, displaying, and analyzing multi-way frequency tables.  This module is particularly useful for analyzing complex crosstabulation tables (e.g., gender by occupation by age group by ethnic background).

STATS GRAPHS:  Stats Graphs contains a wide range of descriptive graphs for categorical and discrete data, such as 2D and 3D histograms, etc.


Explore/Summarize a Time Series

Use TIME SERIES.  This module contains various facilities for displaying as well as transforming/smoothing time series data.

Time series data typically arise when one studies one or more variables over time; for example, one may track the price of stock over successive trading days. TIME SERIES contains a modeling/transformation 'workbench' which allows you to display or plot the series of stock quotes.  You can then choose from among many different transformations to smooth the data, so as to remove random 'noise' fluctuations in the stock price.  When reviewing plots of such smoothed data, trends or recurring patterns over time often become more clearly visible.

Additional advanced time series techniques provided in this module include autocorrelation analysis, Fourier decomposition, and seasonal and non-seasonal ARIMA.  The purpose of all of these methods is to detect patterns or structure in the movement of the respective variable(s) over time.


More Info

Hypotheses are predictions that one has prior to collecting the data concerning the pattern of results.  For example, one may predict that males are more likely to endorse a questionnaire item than females, that age is related to respondents' agreement with a questionnaire item, etc.

We may have hypotheses about the specific shape of distributions; for example, many variables can be expected to follow the normal distribution. We may have hypotheses about differences between groups or samples, for example, gender differences.  We may have hypotheses about differences between variables; for example, we may predict that students like art courses more than math courses (where the liking for arts courses would be recorded in one variable, and liking for math courses in the other; note that in this example each student would rate both courses).  We may have hypotheses about relationships between variables; for example, we may predict that age is related to (correlated with) a respondents' expressed liking of a product.  Finally, we may have hypotheses about differences in the relationships between variables in different groups.  For example, we may predict that, while age is related to liking of a product in males, it is unrelated in females.


Shape of (or Fitting) Distributions

Use one of the following:

NONPARAMETRICS & DISTRIBUTIONS:  This module provides facilities for plotting and comparing the observed distribution of variables against several theoretical distributions such as the normal distribution, the exponential distribution, the gamma distribution, the log-normal distribution, the Chi-square distribution, the binomial distribution, geometric distribution, etc.  Statistical significance tests are provided for evaluating the discrepancy of the observed data from the respective theoretical distributions (Chi-square test, Kolmogorov-Smirnov test). In addition, this module also allows you fit any set of predicted (hypothesized or expected) frequencies to observed frequencies.

SURVIVAL ANALYSIS:  This module provides facilities for fitting special distributions to censored survival/failure times (Weibull, Gompertz, linear and exponential hazard).  A data set is said to be 'censored' if some observations are incomplete, but not missing.  For example, in industrial reliability testing, a part or product may not fail (break) within the time span covered by a study.  However, we do not know how long it will function properly thereafter, and thus, that observation is 'censored.'

STATS GRAPHS:  Stats Graphs also contains various curve fitting routines.


Comparison of Means/Variances in Two Groups

Use one of the following:

BASIC STATISTICS:  This module will compute the so-called t-test for independent samples, comparing the means in two groups.  The test assumes that the data in the two groups are normally distributed.  If the resultant t value is statistically significant, then one can conclude that the means in the two groups are different (that is, in the two populations from which the observations where sampled).  The results Scrollsheet for the t-test will also include the F-test for the comparison of the variances in the two groups; if statistically significant, one can conclude that the variances (variability) in the two groups are different.  Basic Statistics also includes a probability calculator that allows you to compare a single mean against any hypothesized value.

NONPARAMETRICS & DISTRIBUTIONS:  This module includes numerous so-called nonparametric tests for comparing groups.  These tests should be used if one is not sure of the distribution of the variables used in the comparison.  For example, the data may actually consist of rankings rather than precise measurements.

STATS GRAPHS:  Stats Graphs contains numerous facilities for producing histograms, line graphs, scatterplots, etc. by groups.  These graphs offer a wide variety of methods to visualize differences between groups.


Comparison of Means/Variances in Multiple Groups

Use one of the following:

ANOVA/MANOVA:  This module will perform so-called analysis of variance (ANOVA).  ANOVA is used, among other applications, for simultaneously comparing means in several groups.  ANOVA assumes that the variables in the comparison are normally distributed within the groups, and that the variances are about the same in each group.  ANOVA/MANOVA also contains several statistical tests for comparing the variances across groups.

DISCRIMINANT FUNCTION ANALYSIS:  This module will perform analyses similar to ANOVA; specifically, it will allow you to identify the specific variables that show different means in different groups.

NONPARAMETRICS AND DISTRIBUTIONS:  This module includes numerous so-called nonparametric tests for comparing groups.  These test should be used if one is not sure of the distribution of the variables used in the comparison.  For example, the data may actually consist of rankings rather than precise measurements.

STATISTICAL GRAPHS:  This module contains numerous facilities for producing histograms, line graphs, scatterplots, etc. by groups.  Thus, this module will provide the most complete visual comparison between groups.


General (Nonparametric) Comparisons of Groups

Use NONPARAMETRICS AND DISTRIBUTIONS or STATS GRAPHS.

NONPARAMETRICS AND DISTRIBUTIONS:  This module contains numerous so-called nonparametric tests for comparing groups.  Compared to parametric tests (t-test, ANOVA), nonparametric tests are based on less restrictive assumptions about the nature and distribution of the variables in the comparisons.  For example, there are several tests for variables containing only rank order information.  Such data may arise, if one asks respondents in a consumer survey to rank order their preferences for several competing brands of soap.

Other tests, such as the Kolmogorov-Smirnov two sample test, do not make any assumptions about underlying distributions, and will compare not only the central tendency (e.g., mean, median) of a variable in two groups, but also the general shapes of distributions.

Refer to the STATISTICA manual for a discussion of the different nonparametric tests available, their applications, and interpretation.

STATS GRAPHS:  Stats Graphs contains numerous facilities for producing histograms, line graphs, scatterplots, etc. by groups.  These graphs offer a wide variety of methods to visualize differences between groups.


Comparison of Survival/Failure Times

Use SURVIVAL ANALYSIS.  This module contains several tests for comparing survival/failure times in two or more groups.  These tests are applicable to censored or uncensored data sets.

SURVIVAL ANALYSIS contains five different (mostly nonparametric) tests for censored data: Gehan's generalized Wilcoxon test, the Cox-Mantel test, the Cox F-test, the log-rank test, and Peto and Peto's generalized Wilcoxon test.  A nonparametric test for the comparison of multiple groups is also available.

A data set is said to be 'censored' if some observations are incomplete, but not missing.  For example, in industrial reliability testing, a part or product may not fail (break) within the time span covered by a study. However, we do not know how long it will function properly thereafter, and thus, that observation is 'censored.'  If your data set contains no censored data points, you can also use the tests for comparing groups or samples available in NONPARAMETRICS AND DISTRIBUTIONS.


More Info

The distinction between options 1/2 and 3/4 (general nonparametric comparison between groups) should be based on the following considerations:

1.  Is the variable (or variables) on which the comparison is to be based measured on at least an interval scale level?  Interval scale measurement means that, for example, a difference between the values 1 and 2 in that variable is comparable to the difference between 3 and 4.  Often, the values of variables contain only rank order information, and do not allow us to compare intervals.  Refer to the manual (Elementary Concepts) for more details concerning this issue.

2.  Does the distribution of data points follow (approximately) the normal distribution? You can easily check this condition by running descriptive statistics in the BASIC STATISTICS module.  Then select the histogram from within the results Scrollsheet.

3.  Is the data set reasonably large?  For example, are there at least 20 observations in the comparison?

If any of these three conditions are not met, it is advisable to verify any results via the appropriate nonparametric tests in NONPARAMETRICS & DISTRIBUTIONS.


Comparisons of Two Variables

Use one of the following:

BASIC STATISTICS:  That module will compute the so-called t-test for dependent samples, which compares the means of two variables or measurements. The test assumes that the data in the two variables are normally distributed.  If the resultant t-value is statistically significant, then one can conclude that the means in the two variables are different.

NONPARAMETRICS & DISTRIBUTIONS:  That module includes several so-called nonparametric tests for comparing variables.  These test should be used if one is not sure of the distribution of the variables used in the comparison.  For example, the data may actually consist of rankings rather than precise measurements.

STATS GRAPHS:  Stats Graphs contains numerous facilities for producing histograms, line graphs, scatterplots, etc., simultaneously for more than one variable.  These graphs offer a wide variety of methods to visualize differences between variables.


Comparisons of Several Variables or Repeated Measures

Use one of the following:

GENERAL ANOVA/MANOVA:  This module will perform so-called analysis of variance (ANOVA).  ANOVA is used, among other applications, for simultaneously comparing means in several groups or for several variables. The latter application is referred to as repeated measures ANOVA, because one simultaneously compares repeated measurements on the same subjects (or observations).  ANOVA assumes that the variables in the comparison are normally distributed.

NONPARAMETRICS & DISTRIBUTIONS:  This module includes so-called nonparametric tests for comparing variables or repeated measurements.  The most commonly used test is the Friedman analysis of variance.  This test should be used if one is not sure of the distribution of the variables used in the comparison.  For example, the data may actually consist of rankings rather than precise measurements.

STATS GRAPHS:  Stats Graphs contains numerous facilities for producing histograms, line graphs, scatterplots, etc., simultaneously for more than one variable.  These graphs offer a wide variety of methods to visualize differences between variables.


General Comparison of Two Variables

Use NONPARAMETRICS & DISTRIBUTIONS or STATS GRAPHS:

NONPARAMETRICS & DISTRIBUTIONS:  This module contains several so-called nonparametric tests for comparing variables.  Compared to parametric tests (t-test, ANOVA), nonparametric tests are based on less restrictive assumptions about the nature and distribution of the variables in the comparisons.  For example, there are several tests for variables containing only rank order information.  Such data may arise, if one asks respondents in a consumer survey to rank order their preferences for several competing brands of soap.

The NONPARAMETRICS & DISTRIBUTIONS module will also compute the McNemar test for changes in proportions.  Such data may, for example, arise if one wants to compare how many students in a class fail a particular test at the beginning of the semester, and at the end of the semester.

Refer to the STATISTICA manual for a discussion of the different available nonparametric tests, their applications, and interpretation.

STATS GRAPHS:  Stats Graphs contain numerous facilities for producing histograms, line graphs, scatterplots, etc., simultaneously for more than one variable.  These graphs offer a wide variety of methods to visualize differences between variables.


General Comparison, Several Variables or Repeated Measures

Use NONPARAMETRICS & DISTRIBUTIONS or STATS GRAPHS:

NONPARAMETRICS & DISTRIBUTIONS:  This module contains two so-called nonparametric tests for comparing variables.  Compared to parametric tests (t-test, ANOVA), nonparametric tests are based on less restrictive assumptions about the nature and distribution of the variables in the comparisons.  For example, there are several tests for variables containing only rank order information.  Such data may arise, if one asks respondents in a consumer survey to rank order their preferences for several competing brands of soap.

If your data consist of rank orderings, use the Friedman analysis of variance test.  If your data are categorical in nature, for example, contains codes identifying one of two possible choices that each respondent made (repeatedly), use the Cochran Q test.  For more details concerning these tests, refer to the STATISTICA manual.

STATS GRAPHS:  Stats Graphs contains numerous facilities for producing histograms, line graphs, scatterplots, etc., simultaneously for more than one variable.  These graphs offer a wide variety of methods to visualize differences between variables.


Simple Linear Relationships, Two Continuous Variables

Use one of the following:

BASIC STATISTICS:  This module allows you to compute matrices of the standard Pearson r.  The r statistic is appropriate when the data are normally distributed and continuous.

MULTIPLE REGRESSION:  This module will also compute the standard Pearson r; it contains extensive facilities for residual analyses.

NONPARAMETRICS & DISTRIBUTIONS:  This module contains several nonparametric alternatives to the Pearson r (Spearman R, Kendall tau, Gamma coefficient).  These statistics are appropriate when one is not certain whether the data are normally distributed, for example, if the respective variables only contain rank order information.

SURVIVAL ANALYSIS:  This module allows you to compute simple linear (as well as multiple and nonlinear) correlations between a continuous predictor variable, and censored or uncensored survival times. A popular nonparametric alternative to linear correlation, the so-called proportional hazard regression model, can also be computed in this module.

STATS GRAPHS:  Stats Graphs contains numerous facilities for producing 2D scatterplots, line graphs, etc.


Simple Relationships, Two Categorical Variables

Use one of the following:

BASIC STATISTICS:  This module contains extensive facilities for generating and analyzing two-way (or higher-way) crosstabulation tables.  For each crosstabulation table, the module will compute a wide range of statistics that describe and test the relationship between the two categorical variables that make up the table.

NONPARAMETRICS & DISTRIBUTIONS:  That module contains a specialized 2 x 2 tables option.  In addition to the standard statistics (e.g. Chi-square test) for crosstabulation tables, that module will also compute the Fisher exact test (for small n) and McNemar's test for the significance of changes.

STATS GRAPHS:  Stats Graphs contains numerous facilities for producing 3D histograms that allow you to visually explore the relationship between the two categorical variables.


Multiple Linear Relationships, Continuous Variables

Use MULTIPLE REGRESSION or SURVIVAL ANALYSIS:

MULTIPLE REGRESSION:  This module allows you to compute a standard multiple regression analysis, in which one dependent (criterion, endogenous) variable is related to multiple independent (predictor, exogenous) variables.  A wide range of options is available for various specialized analyses (e.g., stepwise selection of independent variables by the program, extensive analyses/plotting of residuals, etc.).

SURVIVAL ANALYSIS:  This module also allows you to compute multiple linear (as well as nonlinear) correlations between continuous predictor variables, and censored or uncensored survival times.  A popular nonparametric alternative to multiple linear correlation with survival/failure times, the so-called proportional hazard regression model, can also be computed in this module.


Multiple Relationships, Categorical Variables

LOG LINEAR:  This module contains a full implementation of the so-called log-linear model for analyzing multiway frequency tables.  Using the log-linear model, you can assess the additive as well as multiplicative effects of one or more categorical independent (predictor) variables with a categorical dependent (criterion) variable.  A typical application would be to predict staff turnover (a categorical yes/no variable) from various categorical independent variables such as gender, ethnic origin, occupation, etc.

CORRESPONDENCE ANALYSIS:  Correspondence analysis is a descriptive/exploratory technique designed to analyze two-way and multi-way tables containing some measure of correspondence (typically frequencies) between the rows and columns.  The results provide information which is similar in nature to those produced by factor analysis techniques, and they allow one to explore the structure of categorical variables included in the table (see also multiple correspondence analysis and predictive mapping).


Time-Dependent (Lagged) Relationships

Use TIME SERIES:  This module contains various facilities for describing and analyzing time-lagged relationships.  For example, advertising expenditures may correlate with sales over time, however, with some lag (because it may take a while before the effect of a new advertisement is felt).  A variable may also correlate with itself, with some lag.  For example, retail sales may go through a regular 12 month cycle, with most sales in the month of December.  Thus, if monthly sales were recorded in a file, every observation could correlate fairly highly with the 13th observation preceding it.  Such correlations are referred to as autocorrelations.

Distributed Lags (available in this module) is a specialized option for analyzing the lagged effects of one independent (predictor, exogenous) variable with one dependent (criterion, endogenous) variable.  Unlike the autocorrelation feature in Time Series, Distributed Lags can simultaneously evaluate multiple lags.


Polynomial Multiple Regression

Use MULTIPLE REGRESSION.  This module contains various facilities for polynomial regression analysis.  Other transformations of independent variables are also supported.

Polynomial (or 'fixed nonlinear') regression computes the relationship between a dependent variable with one or more independent (predictor) variables, and those independent variables squared, cubed, etc.  For example, for one independent variable one could estimate the regression equation:

                  2

y = a + b1*x +b2*x

Here, the dependent variable y is a linear function of x and x**2. Polynomial regression is common in cases when one wants to detect some curvilinearity in a relationship.  For example, stress (the independent variable) may have a curvilinear relationship to performance on a complex task (dependent variable).  For low to moderate stress, performance may increase, but as stress increases beyond moderate stress, performance may deteriorate.  If so, the nonlinear (quadratic) component or regression coefficient in the regression equation would be significant.


Probit/Logit Regression for Categorical Dependent Variable

Use NONLINEAR ESTIMATION.  This module includes facilities to perform logit and probit regression, using a maximum likelihood criterion.

Logit and probit regression are used for analyzing the relationship between one or more independent (predictor) variables with a categorical dependent (criterion) variable at two levels.  For example, one may want to predict success or failure in a test from various continuous variables, such as length preparation time for the test.  Here, success vs. failure represents a categorical dependent variable at two levels while preparation time would be a continuous independent variable.

There are numerous advantages of logit/probit regression over linear multiple regression (see the manual).  In most general terms, these regression methods imply that the dependent variable is actually the result of a transformation of an underlying variable, which is not restricted in range.  For example, the probit model assumes that the actual underlying dependent variable is measured in terms of z-values for the normal curve; if one transforms those values to probabilities (under the normal curve) then the predictions for the dependent variable will always fall between 0 and 1.  Thus, we are actually predicting probabilities from the independent variables.


General Nonlinear Regression

Use NONLINEAR ESTIMATION or STATS GRAPHS:

NONLINEAR ESTIMATION.  This module contains facilities for estimating any type of regression equation.  In most general terms, all multiple regression equations, that is, relationships between variables, can be expressed as y = F(x).  In other words, the dependent variable y is a function of one or more variables x.  The nature of the function may be linear, exponential, logarithmic, or even discontinuous.

For example, we could explicitly specify a so-called breakpoint regression model.  That is, we may hypothesize that the relationship between x and y is generally linear, but that the slope is different in different regions of the x variable.  Thus, the number of bedrooms in a house may be related to the price of the house; however, the relationship may not be as strong for large houses that have more than 5 bedrooms.

NONLINEAR ESTIMATION allows you to type in any kind of regression equation, and to specify how it is to be estimated (least squares, weighted least squares, etc.)

STATS GRAPHS:  Stats Graphs contains various facilities for 2D and 3D fitting of lines or surfaces to observed data.  These graphs offer a wide variety of methods to visualize relationships between variables.


Regression for Censored Survival Times

Use SURVIVAL ANALYSIS.  This module contains several multiple regression models commonly used with censored or uncensored data sets with survival/failure times.

A data set is said to be 'censored' if some observations are incomplete, but not missing.  For example, in industrial reliability testing, a part or product may not fail (break) within the time span covered by a study. However, we do not know how long it will function properly thereafter, and thus, that observation is 'censored.'  If we had several predictor variables of a part's resilience (e.g., some characteristics of the manufacturing process of that part), the SURVIVAL ANALYSIS module would be appropriate for testing the predictive power of those independent variables.

Typical multiple regression models that are used to predict survival or failure times are the Cox proportional hazard model, the normal and log-normal regression model, and the exponential regression model.  The SURVIVAL ANALYSIS module will compute maximum likelihood estimates for all of these models.


Analysis of Covariance

Analysis of Covariance (ANCOVA)

Use GENERAL ANOVA/MANOVA.  This module contains facilities to perform analyses with one or more covariates, and to test for parallelism of regression lines/planes in different groups.

Usually, the purpose of analysis of variance (ANOVA) is to compare means between different groups/samples or variables/measurements.  In analysis of covariance (ANCOVA), one can simultaneously perform a regression analysis, that is, evaluate the relationship between one or more independent or predictor variables (also called covariates) with the dependent variable(s).  For example, we may have two different methods for teaching math that were used in two different classes (groups/samples).  In addition to final math ability, we may have collected data on general intelligence. It would be of interest to see, whether the relationship between general intelligence and math ability is stronger or weaker, depending on the teaching method.

In ANCOVA terminology, this hypothesis refers to the parallelism of the regression lines in the two classes.  If those lines are parallel, then the relationship in the two classes is the same, and thus the relationship between intelligence and math ability is not moderated by the teaching method.  If they are not parallel, we conclude that the teaching method does, in fact, moderate that relationship.


Stratified Regression

Use one of the following:

NONLINEAR ESTIMATION:  This module contains facilities to estimate any kind of regression equation (relationship) between variables.  Such equations may contain logical variables, and thus, stratified (by groups) analyses can easily be performed.  For example, one may hypothesize that compensation and performance are related in one occupational group, but not another.  Refer to the manual for details.

SURVIVAL ANALYSIS:  This module contains facilities to perform linear regression as well as various nonlinear regression analyses.  In addition, one can perform stratified (by group) analyses, that is, test whether or not the respective regression equation (and thus relationship between variables) is the same in all groups.  SURVIVAL ANALYSIS will also handle censored survival/failure times.  A data set is said to be 'censored' if some observations are incomplete, but not missing.  For example, in industrial reliability testing, a part or product may not fail (break) within the time span covered by a study.  However, we do not know how long it will function properly thereafter, and thus, that observation is 'censored.'

STATS GRAPHS:  Stats Graphs allows you to produce scatterplots, surface plots, etc., stratified (categorized) by groups.


Searching for Factors or Dimensions

Use FACTOR ANALYSIS, CORRESPONDENCE ANALYSIS, or MULTIDIMENSIONAL SCALING:

FACTOR ANALYSIS:  This module contains facilities to perform factor and principal components analysis.  In general, the goal of these analyses is to detect underlying dimensions that explain relations between multiple variables.  For example, if one would factor analyze four different measures of size (e.g., height, weight, shoe-size, arm length) taken in a sample of 100 people, then factor analysis would most likely return one dimension.  One might appropriately label that dimension as 'size.'  Computationally, factor analysis is based on the correlation matrix; the program will attempt to find the minimum number of factors necessary to reproduce the observed correlations.

CORRESPONDENCE ANALYSIS:  Correspondence analysis is a descriptive/exploratory technique designed to analyze two-way and multi-way tables containing some measure of correspondence between the rows and columns.  The results provide information which is similar in nature to those produced by factor analysis techniques, and they allow one to explore the structure of categorical variables included in the table.  The most common kind of table of this type is the two-way frequency crosstabulation table (see for example the Basic Statistics or Log-Linear module).

MULTIDIMENSIONAL SCALING:  This module will perform non-metric multidimensional scaling, based on similarities or dissimilarities.  Like factor analysis, the goal of multidimensional scaling is to detect underlying dimensions for a set of multiple input variables.  However, unlike factor analysis which is based on the correlation matrix of variables, multidimensional scaling begins with a similarity or dissimilarity matrix. These dis/similarities can be actual ratings, or derived in other ways (e.g., geographic distances).  It is not necessary for these dis/similarities to be precise measurements; it is only required that the dis/similarity values contain rank order information (for example, that greater similarity values indeed indicate greater similarity).


Searching for Clusters or Natural Groups

Use CLUSTER ANALYSIS.  This module contains facilities to perform tree clustering (joining) based on various distance measures and amalgamation (linkage) rules, k-means clustering, and two-way joining.

In tree clustering or joining, 'objects' are linked together in successive steps, yielding a tree that ultimately joins all objects.  The term 'objects' here refers to cases or variables; both can be analyzed with CLUSTER analysis.  The final tree diagram may reveal clear branches or groupings of objects that are more similar amongst themselves, than to objects not in the branch or grouping.  Thus, some natural structure of objects may emerge from the joining analysis.

In k-means clustering, one specifies a priori how many clusters to expect. The program will then try to find the best division of objects into the requested number of clusters.  Various statistics are provided to aid in the decision, whether an adequate clustering of objects was achieved, that is, whether the objects within each cluster are indeed more similar to each other than objects in different clusters.

In two-way joining, both cases and variables are clustered simultaneously. Specifically, the program will attempt to form clusters of similar data points (values).


Searching for Patterns or Trends Over Time

Use TIME SERIES AND DISTRIBUTED LAGS:  This module contains full implementations of autocorrelation analysis, ARIMA, and Fourier analysis.  In addition, a modeling 'work bench' is provided which allows you to apply various transformations and smoothing techniques to the data.  Such transformations often reveal trends or recurring patterns more clearly.  The goal of ARIMA is to detect such seasonal patterns.  Autocorrelation analysis allows you to examine the lagged effect (correlation) of a variable with itself or with another variable.  Such effects may, for example, occur when correlating advertising expenditures over time with resultant sales; most likely, sales will be affected by increased advertising with some lag.  The goal of Fourier analysis is to decompose a time series into simple underlying waves forms.  All techniques make extensive use of graphics, allowing you to visualize any patterns.

DISTRIBUTED LAGS is a specialized option for analyzing the lagged effects of one independent (predictor, exogenous) variable with one dependent (criterion, endogenous) variable.  Unlike the autocorrelation feature, this option can simultaneously evaluate multiple lags.


Searching for Relationships/Patterns in Tables

Use LOG LINEAR.  This module contains various facilities for the analysis of multi-way frequency (crosstabulation) tables.  It includes an automatic model selection feature that will automatically select a best model for the data, that is, it will determine which factors in the table are related to each other.

Multi-way frequency tables arise when one crosstabulates multiple categorical variables.  For example, one might study staff turnover (a yes/no categorical variable) as a function of occupational level, gender, ethnic background, etc.  Based on those categorical variables, the program will compute a multi-way crosstabulation table.

The automatic model selection feature in LOG LINEAR will then suggest which variables (or factors) are related to turnover.  Interactions between factors will also be revealed.  For example, it is conceivable that only white Caucasian males in a particular occupational level are more likely to leave the organization (i.e., fall into the category turnover=yes).  This example illustrates an interaction between the factors gender, ethnic background, occupational level, and turnover.  In complex tables (e.g., 9-way crosstabulation tables), a very large number of such interactions may exist, and the program will automatically search for them.


Quality Control Charts

Use QUALITY CONTROL.  This module contains a wide selection of control charting methods.

In general, the purpose of quality control charts is to monitor the quality of an ongoing process.  For example, in the manufacture of piston rings, one could take samples of piston rings and measure their diameters.  One can continuously plot the means for successive samples that are taken. With the aid of statistical techniques (proper control limits), this will allow the quality control engineer to detect if and when the process mean (piston ring diameter) shifts outside acceptable limits.

There are several variations on this basic idea.  Quality control charts can be produced for mean measurements (as in the example above), process variability (e.g., ranges, standard deviations), simultaneously for means and variability, or for attributes (e.g., number of defective items). Rather than plotting means, one can plot some moving average across samples or the cumulative sum of deviations from engineering specifications (CUSUM).  One can also simultaneously monitor several measurements (T**2 chart).


Sampling Plans

Use PROCESS ANALYSIS.  This module contains facilities to generate and analyze fixed and sequential sampling plans for normal means, binomial frequencies, and Poisson frequencies.

In general, sampling plans are devised in order to detect quality problems in a production process or supplier with a particular degree of certainty. After specifying the extent of acceptable deviation from specifications, the amount of random (acceptable) variability, and the probability or certainty with which one desires to detect shifts in the product quality, one can compute the necessary size of the sample that one needs to take from the production process.

Fixed sampling plans are those where single samples of a fixed size are taken from the production process or from product lots shipped by the supplier.  Sequential sampling plans are those where individual items (parts, products) are inspected, one by one.  The cumulative deviation of those items from specification is then plotted.  The program will establish critical limits (lines) in that plot that will allow the engineer to decide whether or not the process or supplier complies with specifications. Sequential sampling plans are usually more efficient than fixed sampling plans.


Process Capability Analysis

Use PROCESS ANALYSIS.  This module allows you to plot the standard process capability histogram, to compute various capability indices, and to compute normal and distribution-free tolerance limits.

The general purpose of process capability analysis is to estimate the percentage of items (products, parts) that fall outside the specification limits.  For example, one may compute the proportion of vegetables supplied to a restaurant that fall outside specification limits, that is, that are of such poor quality that they cannot be used in the kitchen.

A common summary of process capability is the histogram, with the normal curve and the specification limits superimposed.  This histogram can serve as a quick check regarding the proportion of items that fall within specification limits.  This information can also be expressed in various process capability ratios.

The facilities for computing tolerance limits allow you to, for example, estimate the proportion of items that will fall within certain limits with a particular degree of certainty.  Put another way, how sure are we that a certain proportion of items falls within a particular set of limits.


Designing & Analyzing Experiments

Use EXPERIMENTAL DESIGN.  That module contains various facilities to design and analyze factorial experiments with two-level factors, Latin square designs, response surfaces or first and second order central composite designs, and Taguchi robust design experiments.

In general, experiments can be used in order to identify the factors that impact the quality or quantity of the production process.  By systematically varying the different settings and factors, one may identify crucial factors, and their optimum setting (e.g., temperature, chemical composition, etc.).

In addition to factorial designs, this module will design and analyze experiments for studying response surfaces (first and second order central composite designs), and for optimizing signal-to-noise (S/N) ratios (Taguchi robust design experiments).


Analyzing Failure Times

Use SURVIVAL ANALYSIS.  This module contain various analytic routines commonly used with censored or uncensored survival/failure time data.

A data set is said to be 'censored' if some observations are incomplete, but not missing.  For example, in industrial reliability testing, a part or product may not fail (break) within the time span covered by a study. However, we do not know how long it will function properly thereafter, and thus, that observation is 'censored.'

SURVIVAL ANALYSIS allows you to describe the distribution of failure times via life tables analysis or the Kaplan-Meier product limit method.  Various theoretical distributions can be fit to the data (Weibull, Gompertz, exponential, linear hazard).  That module also contains several tests for comparing failure times in two or more groups or samples. It also allows you to evaluate the relationship of one or more continuous predictor variables to the observed failure times. Various linear and nonlinear regression models are supported (normal and lognormal regression, exponential regression, proportional hazard regression).


Regression Control Charts

Use QUALITY CONTROL.  This module allows you to construct a regression control chart.

The general idea of the regression control chart is as follows:  Suppose one is monitoring the relationship between the number of parts produced and the number of work hours expended.  Within reasonable limits, on may expect that the greater the number of work hours, the more parts are produced.  One could randomly draw 5 sample work days from each month, and monitor that relationship.  The control limits established in the regression control chart will allow one to detect, when the relationship changes, for example, when productivity drops and more work hours are necessary to produce the same number of parts.


Pareto Chart Analyses

Use QUALITY CONTROL.  This module contains facilities for performing Pareto chart analyses.

The Pareto chart analysis is a simple but powerful way of identifying the causes of quality problems or loss.  It amounts to constructing a histogram of the number of quality problems or loss by some meaningful units, for example, by type of problem or division within the company.  According to the so-called Pareto principle, the majority of the quality loss is caused by a small number of factors.  Put another way, in many cases, few types of problems often cause the majority of quality loss, or a few divisions within the company may produce the majority of loss.  Such 'maldistribution' (uneven distribution) of quality loss is very common, and can easily be detected via the Pareto chart.


  Reliability and Item Analysis - Index

Introductory Overview

Startup Panel

Review Descriptive Stats

Results Dialog

Attenuation Correction

What if ... - More Items

How Many Items to Add

Split-Half Reliability

Notes and Technical Information


  Reliability and Item Analysis - Introductory Overview

General Introduction

Basic Ideas

Classical Testing Model

Reliability

Sum Scales

Cronbach's Alpha

Split-Half Reliability

Correction for Attenuation

Designing a Reliable Scale

Final Remarks


Reliability and Item Analysis - General Introduction

  Reliability and Item Analysis Introductory Overview - General Introduction

In many areas of research, the precise measurement of hypothesized processes or variables (theoretical constructs) poses a challenge by itself.  For example, in psychology, the precise measurement of personality variables or attitudes is usually a necessary first step before any theories of personality or attitudes can be considered.  In general, in all social sciences, unreliable measurements of people's beliefs or intentions will obviously hamper efforts to predict their behavior.  The issue of precision of measurement will also come up in applied research, whenever variables are difficult to observe.  For example, reliable measurement of employee performance is usually a difficult task; yet, it is obviously a necessary precursor to any performance-based compensation system.

In all of these cases, Reliability & Item Analysis may be used to construct reliable measurement scales, to improve existing scales, and to evaluate the reliability of scales already in use.  Specifically, Reliability & Item Analysis will aid in the design and evaluation of sum scales, that is, scales that are made up of multiple individual measurements (e.g., different items, repeated measurements, different measurement devices, etc.).  The program will compute numerous statistics that allow the user to build and evaluate scales following the so-called classical testing theory model.

The assessment of scale reliability is based on the correlations between the individual items or measurements that make up the scale, relative to the variances of the items.  If you are not familiar with the correlation coefficient or the variance statistic, we recommend that you review the respective discussions provided in the Introductory Overview section of Basic Statistics.

The classical testing theory model of scale construction has a long history, and there are many textbooks available on the subject.  For additional detailed discussions, you may refer to, for example, Carmines and Zeller (1980), De Gruitjer and Van Der Kamp (1976), Kline (1979, 1986), or Thorndyke and Hagen (1977).  A widely acclaimed "classic" in this area, with an emphasis on psychological and educational testing, is Nunally (1970).

Testing hypotheses about relationships between items and tests.  Note that STATISTICA includes the general linear structural equation modeling procedure SEPATH.  In that module, you can test specific hypotheses about the relationship between sets of items or different tests (e.g., test whether two sets of items measure the same construct, analyze multi-trait, multi-method matrices, etc.).  For additional details and illustrations, refer to the Examples section of SEPATH.


Reliability and Item Analysis - Basic Ideas

  Reliability and Item Analysis Introductory Overview - Basic Ideas

Suppose we want to construct a questionnaire to measure people's prejudices against foreign-made cars.  We could start out by generating a number of items such as: "Foreign cars lack personality," "Foreign cars all look the same," etc.  We could then submit those questionnaire items to a group of subjects (for example, people who have never owned a foreign-made car).  We could ask subjects to indicate their agreement with these statements on 9-point scales, anchored at 1=disagree and 9=agree.

True scores and error.  Let us now consider more closely what we mean by precise measurement in this case.  We hypothesize that there is such a thing (theoretical construct) as "prejudice against foreign cars," and that each item "taps" into this concept to some extent.  Therefore, we may say that a subject's response to a particular item reflects two aspects: first, the response reflects the prejudice against foreign cars, and second, it will reflect some esoteric aspect of the respective question.  For example, consider the item "Foreign cars all look the same."  A subject's agreement or disagreement with that statement will partially depend on his or her general prejudices, and partially on some other aspects of the question or person.  For example, the subject may have a friend who just bought a very different looking foreign car.

Testing hypotheses about relationships between items and tests.  To test specific hypotheses about the relationship between sets of items or different tests (e.g., whether two sets of items measure the same construct, analyze multi-trait, multi-method matrices, etc.) use the Structural Equation Modeling (SEPATH) procedure.


Reliability and Item Analysis - Classical Testing Model

  Reliability and Item Analysis Introductory Overview - Classical Testing Model

To summarize, each measurement (response to an item) reflects to some extent the true score for the intended concept (prejudice against foreign cars), and to some extent esoteric, random error.  We can express this in an equation as:

X = tau + error

In this equation, X refers to the respective actual measurement, that is, subject's response to a particular item; tau is commonly used to refer to the true score, and error refers to the random error component in the measurement.


Reliability and Item Analysis - Reliability

  Reliability and Item Analysis Introductory Overview - Reliability

In this context the definition of reliability is straightforward: a measurement is reliable if it reflects mostly true score, relative to the error.  For example, an item such as "Red foreign cars are particularly ugly" would likely provide an unreliable measurement of prejudices against foreign-made cars.  This is because there probably are ample individual differences concerning the likes and dislikes of colors.  Thus, this item would "capture" not only a person's prejudice but also his or her color preference.  Therefore, the proportion of true score (for prejudice) in subjects' response to that item would be relatively small.

Measures of reliability.  From the above discussion, one can easily infer a measure or statistic to describe the reliability of an item or scale.  Specifically, we may define an index of reliability in terms of the proportion of true score variability that is captured across subjects or respondents, relative to the total observed variability.  In equation form, we can say:

               2             2

Reliability = σ            /σ

               (true score)  (total observed)


Reliability and Item Analysis - Sum Scales

  Reliability and Item Analysis Introductory Overview - Sum Scales

What will happen when we sum up several more or less reliable items designed to measure prejudice against foreign-made cars?  Suppose the items were written so as to cover a wide range of possible prejudices against foreign-made cars.  If the error component in subjects' responses to each question is truly random, then we may expect that the different components will cancel each other out across items.  In slightly more technical terms, the expected value or mean of the error component across items will be zero.  The true score component remains the same when summing across items.  Therefore, the more items are added, the more true score (relative to the error score) will be reflected in the sum scale.

Number of items and reliability.  This conclusion describes a basic principle of test design.  Namely, the more items there are in a scale designed to measure a particular concept, the more reliable will the measurement (sum scale) be.  Perhaps a somewhat more practical example will further clarify this point.  Suppose you want to measure the height of 10 persons, using only a crude stick as the measurement device.  Note that we are not interested in this example in the absolute correctness of measurement (i.e., in inches or centimeters), but rather in the ability to distinguish reliably between the 10 individuals in terms of their height.  If you measure each person only once in terms of multiples of lengths of your crude measurement stick, the resultant measurement may not be very reliable.  However, if you measure each person 100 times, and then take the average of those 100 measurements as the summary of the respective person's height, then you will be able to make very precise and reliable distinctions between people (based solely on the crude measurement stick).

Let us now look at some of the common statistics that are used to estimate the reliability of a sum scale.


Reliability and Item Analysis - Cronbach's Alpha

  Reliability and Item Analysis Introductory Overview - Cronbach's Alpha

To return to the prejudice example, if there are several subjects who respond to our items, then we can compute the variance for each item, and the variance for the sum scale.  The variance of the sum scale will be smaller than the sum of item variances if the items measure the same variability between subjects, that is, if they measure some true score.  Technically, the variance of the sum of two items is equal to the sum of the two variances minus (two times) the covariance, that is, the amount of true score variance common to the two items.

We can estimate the proportion of true score variance that is captured by the items by comparing the sum of item variances with the variance of the sum scale.  Specifically, we can compute:

                      2    2

α = (k/(k-1)) * [1-Σ(s  )/s    ]

                      i    sum

This is the formula for the most common index of reliability, namely, Cronbach's coefficient alpha (α).  In this formula, the si**2's denote the variances for the k individual items; ssum**2 denotes the variance for the sum of all items.  If there is no true score but only error in the items (which is esoteric and unique, and, therefore, uncorrelated across subjects), then the variance of the sum will be the same as the sum of variances of the individual items.  Therefore, coefficient alpha will be equal to zero.  If all items are perfectly reliable and measure the same thing (true score), then coefficient alpha is equal to 1.  (Specifically, 1-Σ(si**2)/ssum**2 will become equal to (k-1)/k; if we multiply this by k/(k-1) we obtain 1.)

Alternative terminology.  Cronbach's alpha, when computed for binary (e.g., true/false) items, is identical to the so-called Kuder-Richardson-20 formula of reliability for sum scales.  In either case, because the reliability is actually estimated from the consistency of all items in the sum scales, the reliability coefficient computed in this manner is also referred to as the internal-consistency reliability.


Reliability and Item Analysis - Split-Half Reliability

  Reliability and Item Analysis Introductory Overview - Split-Half Reliability

An alternative way of computing the reliability of a sum scale is to divide it in some random manner into two halves.  If the sum scale is perfectly reliable, we would expect that the two halves are perfectly correlated (i.e., r = 1.0).  Less than perfect reliability will lead to less than perfect correlations.  We can estimate the reliability of the sum scale via the Spearman-Brown split half coefficient:

r   = 2r  /(1+r  )

 sb     xy     xy

In this formula, rsb is the split-half reliability coefficient, and rxy represents the correlation between the two halves of the scale.


Reliability and Item Analysis - Correction for Attenuation

  Reliability and Item Analysis Introductory Overview - Correction for Attenuation

Let us now consider some of the consequences of less than perfect reliability.  Suppose we use our scale of prejudice against foreign-made cars to predict some other criterion, such as subsequent actual purchase of a car.  If our scale correlates with such a criterion, it would raise our confidence in the validity of the scale, that is, that it really measures prejudices against foreign-made cars, and not something completely different.  In actual test design, the validation of a scale is a lengthy process that requires the researcher to correlate the scale with various external criteria that, in theory, should be related to the concept that is supposedly being measured by the scale.

How will validity be affected by less than perfect scale reliability?  The random error portion of the scale is unlikely to correlate with some external criterion.  Therefore, if the proportion of true score in a scale is only 60% (that is, the reliability is only .60), then the correlation between the scale and the criterion variable will be attenuated, that is, it will be smaller than the actual correlation of true scores.  In fact, the validity of a scale is always limited by its reliability.

Given the reliability of the two measures in a correlation (i.e., the scale and the criterion variable), we can estimate the actual correlation of true scores in both measures.  Put another way, we can correct the correlation for attenuation:

r             = r  /√(r  *r  )

 xy,corrected    xy    xx  yy

In this formula, rxy,corrected stands for the corrected correlation coefficient, that is, it is the estimate of the correlation between the true scores in the two measures x and y.  The term rxy denotes the uncorrected correlation, and rxx and ryy denote the reliability of measures (scales) x and y.  The Reliability module provides an option to compute the attenuation correction based on user-specified values, or based on actual raw data (in which case the reliabilities of the two measures are estimated from the data).


Reliability and Item Analysis - Designing a Reliable Scale

  Reliability and Item Analysis Introductory Overview - Designing a Reliable Scale

After the discussion so far, it should be clear that, the more reliable a scale, the better (e.g., more valid) the scale.  As mentioned earlier, one way to make a sum scale more valid is by adding items.  The Reliability module includes options that allow the user to compute how many items would have to be added in order to achieve a particular reliability, or how reliable the scale would be if a certain number of items were added.  However, in practice, the number of items on a questionnaire is usually limited by various other factors (e.g., respondents get tired, overall space is limited, etc.).  Let us return to our prejudice example, and outline the steps that one would generally follow in order to design the scale so that it will be reliable:

Step 1: Generating items.  The first step is to write the items.  This is essentially a creative process where the researcher makes up as many items as possible that seem to relate to prejudices against foreign-made cars.  In theory, one should "sample items" from the domain defined by the concept.  In practice, for example in marketing research, focus groups are often utilized to illuminate as many aspects of the concept as possible.  For example, we could ask a small group of highly committed American car buyers to express their general thoughts and feelings about foreign-made cars.  In educational and psychological testing, one commonly looks at other similar questionnaires at this stage of the scale design, again, in order to gain as wide a perspective on the concept as possible.

Step 2: Choosing items of optimum difficulty.  In the first draft of our prejudice questionnaire, we will include as many items as possible (note that the Reliability module will handle up to 300 items in a single scale).  We then administer this questionnaire to an initial sample of typical respondents, and examine the results for each item.  First, we would look at various characteristics of the items, for example, in order to identify floor or ceiling effects.  If all respondents agree or disagree with an item, then it obviously does not help us discriminate between respondents, and thus, it is useless for the design of a reliable scale.  In test construction, the proportion of respondents who agree or disagree with an item, or who answer a test item correctly, is often referred to as the item difficulty.  In essence, we would look at the item means and standard deviations and eliminate those items that show extreme means, and zero or nearly zero variances.

Step 3: Choosing internally consistent items.  Remember that a reliable scale is made up of items that proportionately measure mostly true score; in our example, we would like to select items that measure mostly prejudice against foreign-made cars, and few esoteric aspects we consider random error.  To do so, we would look at the following Scrollsheet:

+----------+-----------------------------------------------------------------+

| STAT.    |   Summary for scale: Mean=46.1100 Std.Dv.=8.26444 Valid n:100   |

| RELIABL. |      Cronbach alpha: .794313   Standardized alpha: .800491      |

| ANALYSIS |                Average inter-item corr.: .297818                |

+----------+----------+----------+----------+----------+----------+----------+

|          |  Mean if |  Var. if | StDv. if | Itm-Totl |  Squared | Alpha if |

| variable |  deleted |  deleted |  deleted |  Correl. | Multp. R |  deleted |

+----------+----------+----------+----------+----------+----------+----------+

|    ITEM1 | 41.61000 | 51.93790 | 7.206795 |  .656298 |  .507160 |  .752243 |

|    ITEM2 | 41.37000 | 53.79310 | 7.334378 |  .666111 |  .533015 |  .754692 |

|    ITEM3 | 41.41000 | 54.86190 | 7.406882 |  .549226 |  .363895 |  .766778 |

|    ITEM4 | 41.63000 | 56.57310 | 7.521509 |  .470852 |  .305573 |  .776015 |

|    ITEM5 | 41.52000 | 64.16961 | 8.010593 |  .054609 |  .057399 |  .824907 |

|    ITEM6 | 41.56000 | 62.68640 | 7.917474 |  .118561 |  .045653 |  .817907 |

|    ITEM7 | 41.46000 | 54.02840 | 7.350401 |  .587637 |  .443563 |  .762033 |

|    ITEM8 | 41.33000 | 53.32110 | 7.302130 |  .609204 |  .446298 |  .758992 |

|    ITEM9 | 41.44000 | 55.06640 | 7.420674 |  .502529 |  .328149 |  .772013 |

|   ITEM10 | 41.66000 | 53.78440 | 7.333785 |  .572875 |  .410561 |  .763314 |

+----------+----------+----------+----------+----------+----------+----------+

Shown above are the results for 10 items, that are discussed in greater detail in the Example section of the manual.  Of most interest to us are the three right-most columns in this Scrollsheet.  They show us the correlation between the respective item and the total sum score (without the respective item), the squared multiple correlation between the respective item and all others, and the internal consistency of the scale (coefficient alpha) if the respective item would be deleted.  Clearly, items 5 and 6 "stick out," in that they are not consistent with the rest of the scale.  Their correlations with the sum scale are .05 and .12, respectively, while all other items correlate at .45 or better.  In the right-most column, we can see that the reliability of the scale would be about .82 if either of the two items were to be deleted.  Thus, we would probably delete the two items from this scale.

Step 4: Returning to Step 1.  After deleting all items that are not consistent with the scale, we may not be left with enough items to make up an overall reliable scale (remember that, the fewer items, the less reliable the scale).  In practice, one often goes through several rounds of generating items and eliminating items, until one arrives at a final set that makes up a reliable scale.


Reliability and Item Analysis - Final Remarks

  Reliability and Item Analysis Introductory Overview - Final Remarks

The Reliability module was designed to make the construction of sum scales as efficient as possible.  STATISTICA will handle a large number of items (e.g., 300 items in a single scale), allows the user to identify and delete "bad" items efficiently, provides various options for estimating the number of items that should be added to the scale, and allows the user to examine the correlation of the scale with other measures after correcting for attenuation (validity).  The Example section in the manual will provide additional details concerning the utility of the various options and statistics provided in the program.

Tetrachoric correlations.  In educational and psychological testing, it is common to use yes/no type items, that is, to prompt the respondent to answer either yes or no to a question.  An alternative to the regular correlation coefficient in that case is the so-called tetrachoric correlation coefficient.  Usually, the tetrachoric correlation coefficient is larger than the standard correlation coefficient, therefore, Nunally (1970, p. 102) discourages the use of this coefficient for estimating reliabilities.  However, it is a widely used statistic (e.g., in mathematical modeling), and the Reliability module offers different ways to compute this coefficient.


  Reliability and Item Analysis - Startup Panel

The following options are available on the Reliability and Item Analysis Startup Panel (see also, Reliability and Item Analysis - Index).  Once you have made your selections, click OK to continue the analysis.

Reliability and Item Analysis dialog:

Variables

Split-half reliability

Input File

Missing Data Deletion

Correlation Matrix

Codes for Dichotomized Vars

Compute Multiple Regression Items/Scale

Batch Processing/Printing


  Reliability and Item Analysis Startup Panel - Variables

In order to perform an item analysis and to compute the reliability of a scale, first select the variables (items) via the Variables button.


  Reliability and Item Analysis Startup Panel - Split-Half Reliability

This button remains dimmed until after the variables (items) have been selected, above.  Once the variables have been selected for the analysis, you can divide the items into two variable (item) lists (the two lists do not have to contain all the items that were originally selected, see also Split-Half Reliability).  For each item list, the program will calculate the reliability, the correlation between the two lists (i.e., their sums), the correlation corrected for attenuation, as well as the split-half reliability.


  Reliability and Item Analysis Startup Panel - Input File

Raw data files or correlation matrices may be read as input into the Reliability module.


  Reliability and Item Analysis Startup Panel - Missing Data Deletion

Missing data can be deleted casewise, or substituted by means.


  Reliability and Item Analysis Startup Panel - Correlation Matrices

The following types of correlations are available in this option:

No correlations:  In order to speed up calculations, the calculation of the correlation matrix can be suppressed by selecting No.  Note that if more than 100 variables (items) are selected, the correlation matrix will not be computed and this option will automatically default to No.  However, as in all modules of STATISTICA, you can compute an overall correlation matrix for more variables (e.g., 500 or more, depending on the amount of memeory available in your computer) via the Quick Basic Stats - Correlation matrices option from the Analysis pull-down menu.

Pearson r:  If you select this option, STATISTICA will compute the standard Pearson product-moment correlation coefficients, and the reliability analysis will be based on those correlations.

Tetrachoric r (quick cos p approx):  In this setting, the analysis will be based on tetrachoric correlations, computed via the cosine pi formula (applicable to dichotomous data) that yields up to 4 digits of precision, as long as the proportions (i.e., the number of 0's and 1's) are not extreme (e.g., 95% 0's and 5% 1's).

Tetrachoric r (iterative approx):  In this setting, the analysis will be based on tetrachoric correlations, computed using a more time consuming but also more precise procedure based on Gaussian quadrature and Newton-Raphson iterations (see Kirk, 1973).  This iterative procedure is considerably slower than the above tetrachoric correlation procedure.

Tetrachoric correlations are not recommended for most standard analyses (consult the manual or the Introductory Overview section for details).


  Reliability and Item Analysis Startup Panel - Codes for Dichotomized Variables

This option is only available if tetrachoric correlations are selected, above.  The tetrachoric correlation coefficient assumes that the data in the selected variables (items) consist of codes that indicate which one of two responses the respective respondent gave for the respective item.  You may enter two integer values in the range from -999 to +999 to indicate the (integer) values used in the selected items to indicate the two responses.  Note that the program always assumes that the first code that is entered represents the lower value, and the second code the higher value of the dichotomized variable, and the directions of the tetrachoric correlations are determined accordingly.


Reliability and Item Analysis Startup Panel - Compute Multiple Regression Items/Scales

  Reliability and Item Analysis Startup Panel - Compute Multiple Regression Items/Scale

The multiple correlation (between each item and the sum of all others in the scale) may be calculated by selecting this check box; this may increase processing time if the scale contains many items (i.e., if many items were selected for the analysis).


  Reliability and Item Analysis Startup Panel - Batch Processing/Printing

This option is only available if printer, disk file, and/or Text/output Window is currently selected in the Page/Output Setup dialog (click on the Output field on the status bar to open this dialog).  The selection of the Batch Processing/Printing option affects the way in which the reliability output is printed.  The default setting of the option is interactive processing (i.e., Batch Processing/Printing is de-selected).  In this mode you can determine (interactively) which Scrollsheets to print.  In the Batch Processing/Printing mode, the resulting Scrollsheets will automatically be printed, saved to the printer file, and/or sent to the Text/output Window (whichever you have selected in the Page/Output Setup dialog).


  Reliability and Item Analysis - Review Descriptive Statistics

This intermediate dialog (available if you selected one of the three types of correlations in the Reliability and Item Analysis - Startup Panel) in reliability analysis will allow you to review specific descriptive statistics on the previously selected variables (items).

Review Descriptive Statistics dialog:

Means and standard deviations

Correlations

Covariances

Save correlation matrix

Box and whisker plot

Matrix plot of Correlations

The SD check box


Review Descriptive Statistics - Means and Standard Deviations

  Reliability and Item Analysis Review Descriptive Statistics - Means and Standard Deviations

This option will bring up a Scrollsheet with means and standard deviations for all items in the scale.  By default the standard deviation is computed as the square root of the sum of squared deviations about the mean (SS) divided by n - 1.  The resulting statistic is an estimate of the population sigma (this statistic can then be used to draw inferences about the population from which the sample was drawn).  You can use the SD = Sums of Squares/n option to compute the standard deviation as the SS divided by n.

The default graph for this Scrollsheet is a histogram (frequency distribution) of the chosen variable, with the normal distribution superimposed.  This plot can be very useful as a quick check of whether the assumption of normality has been violated (on which the computation of the correlation coefficients is based, see Basic Statistics).


Review Descriptive Statistics - Correlations

  Reliability and Item Analysis Review Descriptive Statistics - Correlations

This option will bring up a Scrollsheet with correlations (either tetrachoric correlations or Pearson-product moment correlations, whichever was selected in the Reliability and Item Analysis - Startup Panel).  The default graph for this Scrollsheet is a scatterplot of the respective correlation coefficients.  The plot will indicate the regression line as well as the 95% confidence limits for the regression line.


Review Descriptive Statistics - Covariances

  Reliability and Item Analysis Review Descriptive Statistics - Covariances

This option will bring up a Scrollsheet with the covariance matrix for all items in the scale.  The default graph for this Scrollsheet is a scatterplot of the selected variables.  The plot will indicate the regression line as well as the 95% confidence limits for the regression line.


Review Descriptive Statistics - Save Correlation Matrix

  Reliability and Item Analysis Review Descriptive Statistics - Save Correlation Matrix

When you click on this button, the Save Matrix As dialog will open in which you can save the correlation matrix as a standard STATISTICA matrix file.


Review Descriptive Statistics - Box and Whisker Plot

  Reliability and Item Analysis Review Descriptive Statistics - Box and Whisker Plot

This option allows you to produce a box and whisker plot (showing medians and quartiles, means and standard deviations, etc.) for the selected variables (items).

Medians and quartiles:  After selecting this option and after selecting a variable for the plot, the Box-whisker Type dialog will open.  If you select to compute for the box-whisker plot, the medians and quartiles, then those values will be computed according to the setting of the Percentiles option on the STATISTICA Defaults: General dialog.


Review Descriptive Statistics - Matrix Plot of Correlation

  Reliability and Item Analysis Review Descriptive Statistics - Matrix Plot of Correlations

This option will bring up a matrix scatterplot for the selected variables.


Review Descriptive Statistics - The SD Checkbox

  Reliability and Item Analysis Review Descriptive Statistics - The SD Checkbox

There are two ways in which standard deviations can be computed: as the sums of (deviation) squares divided by n (the valid number of cases) or n-1.  If divided by n-1, the resulting standard deviations are estimates of the standard deviations in the population (sigma); if divided by n, the resulting standard deviations are descriptions of the sample only.  The setting of this switch will not affect the subsequent computations of the reliability coefficients.


  Reliability and Item Analysis - Results

This dialog allows the user to review the key results of the analysis; the interpretation of the available statistics are discussed in the Introductory Overview section.

Reliability Results dialog:

Item total statistics	Means and standard deviations

Split-half reliability	Box and whisker plot

Analysis of variance	Attenuation correction

Correlation matrix	What if more items

Graph (Matrix plot)	How many more items


  Reliability and Item Analysis Results - Item Total Statistics

After clicking on this button, a Scrollsheet with various statistics regarding the relationship between each item and the scale (without the respective item) will be displayed:  the mean of the scale without the respective item, the variance of the scale without the respective item, the standard deviation of the scale without the respective item, the correlation between the respective item and the scale (without the item), and Cronbach's alpha for the scale without the respective item.  In addition, if multiple regression statistics were requested from the Startup Panel, the multiple R-square of each item with the scale without the respective item will be displayed.  Summary statistics for the analysis (e.g., Cronbach's alpha, scale mean, etc.) are shown in the header of the Scrollsheet.


  Reliability and Item Analysis Results - Split-Half Reliability

This option is only available if split-half reliability was requested from the Startup Panel (i.e., two variable lists were specified).  After clicking on this button, the program will display Cronbach's alpha for each half, the correlation between the two halves, the correlation corrected for attenuation, the split-half reliability, and the Guttman split-half reliability.


  Reliability and Item Analysis Results - Analysis of Variance

Clicking on this button will bring up a Scrollsheet with a complete analysis of variance table for the items in the scale.  This analysis is equivalent to a one-way repeated measures ANOVA, where each item represents one level of the repeated measures factor (refer to the Introductory Overview section of ANOVA/MANOVA for more details concerning repeated measures ANOVA).


  Reliability and Item Analysis Results - Correlation Matrix

This option is only available if a correlation matrix was requested from the Reliability Startup Panel (default).  After clicking on this button, a Scrollsheet with the correlation matrix will be displayed.  The default plot for this Scrollsheet is the scatterplot of the respective two variables that are highlighted in the Scrollsheet.


  Reliability and Item Analysis Results - Graph (Matrix Plot)

This option allows you to produce a scatterplot matrix for the selected variables.


  Reliability and Item Analysis Results - Means and Standard Deviations

After clicking on the Means & SD button, a Scrollsheet with the means and standard deviations for all items will be displayed.  The standard deviations will be computed in the manner indicated by the SD=sums of squares/n check box on the Review Descriptive Statistics dialog.  Namely, they will either be computed as the square roots of the sums of deviation squares divided by n-1 or n.  If divided by n-1, the resulting standard deviations are estimates of the standard deviations in the population (sigma); if divided by n, the resulting standard deviations are descriptions of the sample only.

The default graph for this Scrollsheet is a histogram (frequency distribution) of the chosen variable, with the normal distribution superimposed.  This plot can be very useful as a quick check of whether the assumption of normality has been violated (on which the computation of the correlation coefficients is based, see Basic Statistics).


  Reliability and Item Analysis Results - Box and Whisker Plot

This option allows you to produce a box and whisker plot (showing medians and quartiles, means and standard deviations, etc.) for the selected variables (items).  For computational details concerning the median and the quartiles, refer to the description of percentiles in the STATISTICA Defaults: General dialog.


  Reliability and Item Analysis Results - Attenuation Correction

With this option, the user may estimate the correlation, corrected for attenuation (due to less than perfect reliability of measures), between the current test (given its current reliability) with a criterion (given its user-specified reliability).  After clicking on this button, the user can enter the value of a correlation between the current test and another measure, and the reliability of the other measure in the Correction for Attenuation dialog.  STATISTICA will then compute the corrected correlation.


  Reliability and Item Analysis Results - What if More Items?

This option estimates the reliability of the scale if a particular number of items are added.  It is assumed that the intercorrelations among the new items are equivalent to that of the old items.  After clicking on this button, the user can enter the number of items to be added to the scale in the What if more items? dialog; STATISTICA will then compute the reliability of the scale that may be expected if that many items were added.


  Reliability and Item Analysis Results - How Many More Items?

This option will estimate the number of items which would have to be added to the scale in order to attain a user-specified reliability.  The computations will assume that the items that will be added are of approximately equal "quality" as the other items in the scale, that is, that they will be of comparable reliability.  After clicking on this button, the user can enter the desired scale reliability in the How many more items? dialog, and STATISTICA will compute the number of items that would have to be added to attain that reliability.


  Reliability and Item Analysis - Attenuation Correction

With this option, the user may estimate the correlation, corrected for attenuation (due to less than perfect reliability of measures), between the current test (given its current reliability) with a criterion (given its user-specified reliability).  Enter the value of a correlation between the current test and another measure, and the reliability of the other measure.  The program will then compute the corrected correlation.  For more information on the correction for attenuation, see the Introductory Overview section.


Reliability and Item Analysis - What if ... - More Items

  Reliability and Item Analysis - What if More Items in Scale?

This option estimates the reliability of the scale if a particular number of items are added.  It is assumed that the intercorrelations among the new items are equivalent to that of the old items.  Enter the number of items to be added to the scale; the program will then compute the reliability of the scale that may be expected if that many items were added.  For more information on the number of items and reliability, see the Overview section.


  Reliability and Item Analysis - How Many Items to Add...

This option will estimate the number of items which would have to be added to the scale in order to attain a user-specified reliability.  The computations will assume that the items that will be added are of approximately equal "quality" as the other items in the scale, that is, that they will be of comparable reliability.  Enter the desired scale reliability and the program will compute the number of items that would have to be added to attain that reliability.  For more information on the number of items and reliability, see the Introductory Overview section.


  Reliability and Item Analysis - Split-Half Reliability

This window displays a summary of the descriptive statistics and reliabilities for the two halves of the scale, as specified on the Startup Panel.

You can display the descriptive statistics for each of the items in each half of the scale by clicking on the respective Means & standard deviations buttons (for the first or second half of the items).  You can also create box and whisker plot (showing medians and quartiles, means and standard deviations, etc.) for the selected items in each half of the scale by clicking on the appropriate Box and Whisker button.

Summary.  This option will bring up a Scrollsheet with summary statistics for the split-half analysis, as well as statistics for each half of the scale.


  Reliability and Item Analysis - Notes and Technical Information

Computations

All computation in Reliability and Item Analysis are performed in double precision.  The standard formulas from classical testing theory are used to compute Cronbach's alpha, and for the attenuation correction (see Nunally, 1970).

Standardized alpha:  The standardized alpha may be interpreted as the reliability that would result if all values for each item were standardized (z transformed) before computing Cronbach's alpha.  The computational formula is:

α = k*r    /(1+(k-1)*r    )

       avrg           avrg

In this formula, k stands for the number of items in the scale; ravrg stands for the average inter-item correlation.

Guttman split-half reliability:  The Guttman split-half coefficient is similar to the Spearman-Brown split-half coefficient, but does not assume equal reliabilities or equal variances of the two halves.  It is computed as:

          2    2     2    2

r  = 2*(s  - s   - s  )/s

 G       t    t1    t2   t

where

rG	is the Guttman split-half coefficient

st**2	is the variance of the total scale (both halves)

st1**2	is the variance of the first half

st2**2	is the variance of the second half

Items With Zero Variances

If an item has zero variance a correlation matrix cannot be computed (a warning will be issued by the program).  In that case, either eliminate the item(s) with zero variances, or choose not to compute the correlation matrix.  If the latter option is chosen, the item(s) with zero variances will be included in all subsequent computations.  Note that if no correlation matrix is requested the following formula is used to compute Cronbach's alpha:

                    2   2

α = [k/(k-1)]*(1-∑s  /s  )

                   i   t

where k is the number of items in the scale, ∑si**2 denotes the sum of item variances, and st**2 is the variance of the scale.  If items with zero variances are included, they will not affect the variances but only the factor [k/(k-1)].


Canonical Analysis - Index
  Canoncal Analysis - Index

Introductory Overview

Startup Panel

Review Descriptive Statistics

Define Model

Review Results

Notes and Technical Information


  Canonical Analysis - Introductory Overview

Several STATISTICA modules will compute measures of correlation to express the relationship between two or more variables.  For example, the standard Pearson product moment correlation coefficient (r) measures the extent to which two variables are related; Nonparametrics and Distributions offers various measures of relationships that are based on the similarity of ranks in two variables; Multiple Regression allows one to assess the relationship between a dependent variable and a set of independent variables; Multiple Correspondence Analysis is useful for exploring the relationships between a set of categorical variables.

Canonical Correlation is an additional procedure for assessing the relationship between variables.  Specifically, this module allows us to investigate the relationship between two sets of variables.  For example, an educational researcher may want to compute the (simultaneous) relationship between three measures of scholastic ability with five measures of success in school.  A sociologist may want to investigate the relationship between two predictors of social mobility based on interviews, with actual subsequent social mobility as measured by four different indicators.  A medical researcher may want to study the relationship of various risk factors to the development of a group of symptoms.  In all of these cases, the researcher is interested in the relationship between two sets of variables, and Canonical Correlation would be the appropriate method of analysis.

In the following topics we will briefly introduce the major concepts and statistics in canonical correlation analysis.  We will assume that you are familiar with the correlation coefficient as described in Basic Statistics, and the basic ideas of multiple regression as described in the Introductory Overview section of Multiple Regression.

General Ideas

Sum Scores

Canonical Roots/Variates

Number of Roots

Extraction of Roots

Computational Methods and Results

Assumptions


  Canonical Analysis - Computational Methods and Results

Some of the computational issues involved in canonical correlation and the major results that are commonly reported will now be reviewed.

Eigenvalues.  When extracting the canonical roots, STATISTICA will compute the eigenvalues.  These can be interpreted as the proportion of variance accounted for by the correlation between the respective canonical variates.  Note that the proportion here is computed relative to the variance of the canonical variates, that is, of the weighted sum scores of the two sets of variables; the eigenvalues do not tell how much variability is explained in either set of variables.  The program will compute as many eigenvalues as there are canonical roots, that is, as many as the minimum number of variables in either of the two sets.

Successive eigenvalues will be of smaller and smaller size.  The program will first compute the weights that maximize the correlation of the two sum scores.  After this first root has been extracted, the program will find the weights that produce the second largest correlation between sum scores, subject to the constraint that the next set of sum scores does not correlate with the previous one, and so on.

Canonical correlations.  If the square root of the eigenvalues is taken, then the resulting numbers can be interpreted as correlation coefficients (see also Basic Statistics and Tables).  Because the correlations pertain to the canonical variates, they are called canonical correlations.  Like the eigenvalues, the correlations between successively extracted canonical variates are smaller and smaller.  Therefore, as an overall index of the canonical correlation between two sets of variables, it is customary to report the largest correlation, that is, the one for the first root.  However, the other canonical variates can also be correlated in a meaningful and interpretable manner (see below).

Significance of Roots.  The significance test of the canonical correlations is straightforward in principle.  Simply stated, the different canonical correlations are tested, one by one, beginning with the largest one.  Only those roots that are statistically significant are then retained for subsequent interpretation.  Actually, the nature of the significance test is somewhat different.  The program will first evaluate the significance of all roots combined, then of the roots remaining after removing the first root, the second root, etc.

Some authors have criticized this sequential testing procedure for the significance of canonical roots (e.g., Harris, 1976).  However, this procedure was "rehabilitated" in a subsequent Monte Carlo study by Mendoza, Markos, and Gonter (1978).

In short, the results of that study showed that this testing procedure will detect strong canonical correlations most of the time, even with samples of relatively small size (e.g., n = 50).  Weaker canonical correlations (e.g., R = .3) require larger sample sizes (n > 200) to be detected at least 50% of the time.  Note that canonical correlations of small magnitude are often of little practical value, as they account for very little actual variability in the data.  This issue, as well as the sample size issue, will be discussed shortly.

Canonical weights.  After determining the number of significant canonical roots, the question arises as to how to interpret each (significant) root.  Remember that each root actually represents two weighted sums, one for each set of variables.  One way to interpret the "meaning" of each canonical root would be to look at the weights for each set.  These weights are called the canonical weights.

In general, the larger the weight (i.e., the absolute value of the weight), the greater is the respective variable's unique positive or negative contribution to the sum.  To facilitate comparisons between weights, the canonical weights are usually reported for the standardized variables, that is, for the z transformed variables with a mean of 0 and a standard deviation of 1.

If you are familiar with multiple regression, you may interpret the canonical weights in the same manner as you would interpret the beta weights in a multiple regression equation.  In a sense, they represent the partial correlations of the variables with the respective canonical root.  If you are familiar with factor analysis, you may interpret the canonical weights in the same manner as you would interpret the factor score coefficients.  To summarize, the canonical weights allow the user to understand the "make-up" of each canonical root, that is, it lets the user see how each variable in each set uniquely contributes to the respective weighted sum (canonical variate).

Canonical Scores.  Canonical weights can also be used to compute actual values of the canonical variates; that is, you can simply use the weights to compute the respective sums.  Again, remember that the canonical weights are customarily reported for the standardized (z transformed) variables.  The Canonical Correlation module will automatically compute the canonical scores for you, which then can be saved for further analyses with other modules.

Factor structure.  Another way of interpreting the canonical roots is to look at the simple correlations between the canonical variates (or factors) and the variables in each set.  These correlations are also called canonical factor loadings.  The logic here is that variables that are highly correlated with a canonical variate have more in common with it.  Therefore, you should weigh them more heavily when deriving a meaningful interpretation of the respective canonical variate.  This method of interpreting canonical variates is identical to the manner in which factors are interpreted in factor analysis.

Factor structure versus canonical weights.  Sometimes, the canonical weights for a variable are nearly zero, but the respective loading for the variable is very high.  The opposite pattern of results may also occur.  At first, such a finding may seem contradictory; however, remember that the canonical weights pertain to the unique contribution of each variable, while the canonical factor loadings represent simple overall correlations.  For example, suppose you included in your satisfaction survey two items which measured basically the same thing, namely:  (1) "Are you satisfied with your supervisors?" and (2) "Are you satisfied with your bosses?"  Obviously, these items are very redundant.  When the program computes the weights for the weighted sums (canonical variates) in each set so that they correlate maximally, it only "needs" to include one of the items to capture the essence of what they measure.  Once a large weight is assigned to the first item, the contribution of the second item is redundant; consequently, it will receive a zero or negligibly small canonical weight.  Nevertheless, if you then look at the simple correlations between the respective sum score with the two items (i.e., the factor loadings), those may be substantial for both.  To reiterate, the canonical weights pertain to the unique contributions of the respective variables with a particular weighted sum or canonical variate; the canonical factor loadings pertain to the overall correlation of the respective variables with the canonical variate.

Variance extracted.  As discussed earlier, the canonical correlation coefficient refers to the correlation between the weighted sums of the two sets of variables.  It tells nothing about how much variability (variance) each canonical root explains in the variables.  However, you can infer the proportion of variance extracted from each set of variables by a particular root by looking at the canonical factor loadings.  Remember that those loadings represent correlations between the canonical variates and the variables in the respective set.  If you square those correlations, the resulting numbers reflect the proportion of variance accounted for in each variable.  For each root, you can take the average of those proportions across variables to get an indication of how much variability is explained, on the average, by the respective canonical variate in that set of variables.  Put another way, you can compute in this manner the average proportion of variance extracted by each root.

Redundancy.  The canonical correlations can be squared to compute the proportion of variance shared by the sum scores (canonical variates) in each set.  If you multiply this proportion by the proportion of variance extracted, you arrive at a measure of redundancy, that is, of how redundant one set of variables is, given the other set of variables.  In equation form, you may express the redundancy as:

                                2       2

Redundancy     = [Σ(loadings     )/p]*R

          left              left       c

                                  2       2

Redundancy      = [Σ(loadings      )/q]*R

          right              right       c

In these equations, p denotes the number of variables in the first (left) set of variables, and q denotes the number of variables in the second (right) set of variables; Rc**2 is the respective squared canonical correlation.

Note that you can compute the redundancy of the first (left) set of variables given the second (right) set, and the redundancy of the second (right) set of variables, given the first (left) set.  Because successively extracted canonical roots are uncorrelated, you could sum up the redundancies across all (or only the first significant) roots to arrive at a single index of redundancy (as proposed by Stewart and Love, 1968).

Practical significance.  The measure of redundancy is also useful for assessing the practical significance of canonical roots.  With large sample sizes (see below), canonical correlations of magnitude R = .30 may become statistically significant (see above).  If you square this coefficient (R-square = .09) and use it in the redundancy formula shown above, it becomes clear that such canonical roots account for only very little variability in the variables.  Of course, the final assessment of what does and does not constitute a finding of practical significance is subjective by nature.  However, to maintain a realistic appraisal of how much actual variance (in the variables) is accounted for by a canonical root, it is important to always keep in mind the redundancy measure, that is, how much of the actual variability in one set of variables is explained by the other.


  Canonical Analysis - Assumptions

The following discussion provides only a list of the most important assumptions of canonical correlation analysis, and the major threats to the reliability and validity of results.

Distributions.  The tests of significance of the canonical correlations is based on the assumption that the distributions of the variables in the population (from which the sample was drawn) are multivariate normal.  As in most programs in STATISTICA, the Canonical Correlation module allows the user to graph the variables in the analysis, that is, to produce frequency histograms with the normal curve superimposed, and scatterplots.  Little is known about the effects of violations of the multivariate normality assumption.  However, with a sufficiently large sample size (see below) the results from canonical correlation analysis are usually quite robust.

Sample sizes.  Stevens (1986) provides a very thorough discussion of the sample sizes that should be used in order to obtain reliable results.  As mentioned earlier, if there are strong canonical correlations in the data (e.g., R > .7), then even relatively small samples (e.g., n = 50) will detect them most of the time.  However, in order to arrive at reliable estimates of the canonical factor loadings (for interpretation), Stevens recommends that there should be at least 20 times as many cases as variables in the analysis, if one wants to interpret the most significant canonical root only.  To arrive at reliable estimates for two canonical roots, Barcikowski and Stevens (1975) recommend, based on a Monte Carlo study, to include 40 to 60 times as many cases as variables.

Outliers.  Outliers can greatly affect the magnitudes of correlation coefficients (see Basic Statistics and Tables).  Since canonical correlation analysis is based on (computed from) correlation coefficients, they can also seriously affect the canonical correlations.  Of course, the larger the sample size, the smaller is the impact of one or two outliers.  However, it is a good idea to examine the various scatterplots available in the Canonical Correlation module to detect possible outliers.  Note that scatterplots can be produced not only for variables, but also for canonical variates.

Matrix Ill-Conditioning.  One assumption is that the variables in the two sets should not be completely redundant.  For example, if you included the same variable twice in one of the sets, then it is not clear how to assign different weights to each of them.  Computationally, such complete redundancies will "upset" the canonical correlation analysis.  When there are perfect correlations in the correlation matrix, or if any of the multiple correlations between one variable and the others is perfect (R = 1.0), then the correlation matrix cannot be inverted, and the computations for the canonical analysis cannot be performed.  Such correlation matrices are said to be ill-conditioned.

Once again, this assumption appears trivial on the surface; however, it often is "almost" violated when the analysis includes very many highly redundant measures, as is often the case when analyzing questionnaire responses.  In extreme cases, the program will "refuse" to perform the analysis, and issue a respective error message ("matrix ill-conditioned...").


Canonical Analysis - General Ideas

  Canonical Analysis Introductory Overview - General Ideas

Suppose you conduct a study in which you measure satisfaction at work with three questionnaire items, and satisfaction in various other domains with an additional seven items.  The general question that you may want to answer is how satisfaction at work relates to the satisfaction in those other domains.


Canonical Analysis - Sum Scores

  Canonical Analysis Introductory Overview - Sum Scores

A first approach that you might take is simply to add up the responses to the work satisfaction items, and to correlate that sum with the responses to all other satisfaction items.  If the correlation between the two sums is statistically significant, we could conclude that work satisfaction is related to satisfaction in other domains.

In a way this is a rather "crude" conclusion.  We still know nothing about the particular domains of satisfaction that are related to work satisfaction.  In fact, we could potentially have lost important information by simply adding up items.  For example, suppose there were two items, one measuring satisfaction with one's relationship with the spouse, the other measuring satisfaction with one's financial situation.  Adding the two together is, obviously, like adding "apples to oranges."  Doing so implies that a person who is dissatisfied with her finances but happy with her spouse is comparable overall to a person who is satisfied financially but not happy in the relationship with her spouse.  Most likely, people's psychological make-up is not that simple...

The problem then with simply correlating two sums is that one might lose important information in the process, and, in the worst case, actually "destroy" important relationships between variables by adding "apples to oranges."

Using a weighted sum.  It seems reasonable to correlate some kind of a weighted sum instead, so that the "structure" of the variables in the two sets is reflected in the weights.  For example, if satisfaction with one's spouse is only marginally related to work satisfaction, but financial satisfaction is strongly related to work satisfaction, then we could assign a smaller weight to the first item and a greater weight to the second item.  We can express this general idea in the following equation:

a *y +a *y +...+a y  = b *x +b *x +...+b x

 1  1  2  2      p p    1  1  2  2      q q

If we have two sets of variables, the first one containing p variables and the second one containing q variables, then we would like to correlate the weighted sums on each side of the equation with each other.

Determining the weights.  We have now formulated the general "model equation" for canonical correlation.  The only problem that remains is how to determine the weights for the two sets of variables.  It seems to make little sense to assign weights so that the two weighted sums do not correlate with each other.  A reasonable approach to take is to impose the condition that the two weighted sums shall correlate maximally with each other.  This is exactly what Canonical Correlation will do when performing a canonical analysis based on the overall correlation matrix of all variables.


Canonical Analysis - Canonical Roots/Variates

  Canonical Analysis Introductory Overview - Canonical Roots/Variates

In the terminology of canonical correlation analysis, the weighted sums define a canonical root or variate.  You can think of those canonical variates (weighted sums) as describing some underlying "latent" variables.  For example, if for a set of diverse satisfaction items we were to obtain a weighted sum marked by large weights for all items having to do with work, we could conclude that the respective canonical variate measures satisfaction with work.


Canonical Analysis - Number of Roots

  Canonical Analysis Introductory Overview - Number of Roots

So far we have pretended as if there is only one set of weights (weighted sum) that can be extracted from the two sets of variables.  However, suppose that we had among our work satisfaction items particular questions regarding satisfaction with pay, and questions pertaining to satisfaction with one's social relationships with other employees.  It is possible that the pay satisfaction items correlate with satisfaction with one's finances, and that the social relationship satisfaction items correlate with the reported satisfaction with one's spouse.  If so, we should really derive two weighted sums to reflect this "complexity" in the structure of satisfaction.

In fact, the computations involved in canonical correlation analysis will lead to more than one set of weighted sums.  To be precise, the number of roots extracted by the program will be equal to the minimum number of variables in either set.  For example, if we have three work satisfaction items and seven general satisfaction items, then the program will extract exactly three canonical roots.


Canonical Analysis - Extraction of Roots

  Canonical Analysis Introductory Overview - Extraction of Roots

As mentioned before, the program will generally extract roots so that the resulting correlation between the canonical variates is maximal.  When extracting more than one root, each successive root will explain a unique additional proportion of variability in the two sets of variables.  Therefore, successively extracted canonical roots will be uncorrelated with each other, and account for less and less variability.


  Canonical Analysis - Startup Panel

In this dialog, you can select all variables that are to be included in the analysis (see also Canonical Analysis - Index).

Canonical Analysis Startup Panel:

Select Variables

Input File

MD Deletion

Review Desc. Stats, Corr. Matrix


Canonical Analysis Opening Menu - Select Variables

  Canonical Analysis Startup Panel - Select Variables

Clicking on this button will bring up the standard variable selection window in which you can select the variables that will later be used in the canonical analysis.  Only variables that are selected at this point will be available later for the specification of the canonical correlation.  A correlation matrix will be calculated for all variables that are selected in this dialog.


Canonical Analysis Opening Menu - Input File

  Canonical Analysis Startup Panel - Input File

This combo box has two settings: raw data and correlation matrix.

Raw Data File:  If you set the combo box to raw data, then the program expects as input, a standard raw data file.

Matrix File:  If you set the combo box to matrix, then you will need to select a correlation matrix file as the input file.  Correlation matrix files can be created from within various other modules (e.g., Basic Statistics, Factor Analysis, Multiple Regression, etc.), or they can be created directly via Data Management (see also, Matrix File Format).


Canonical Analysis Opening Menu - Missing Data Deletion

  Canonical Analysis Startup Panel - Missing Data Deletion

This combo box is only active if a raw data file has been specified.  Missing data can be deleted casewise or substituted by means (mean substitution).


Canonical Analysis Opening Menu - Review Descriptive Statistics, Correlation Matrix

  Canonical Analysis Startup Panel - Review Descriptive Statistics, Correlation Matrix

Select this check box in order to open the Review Descriptive Statistics dialog after you leave the Startup Panel.  In the Review Descriptive Statistics dialog, you can review detailed descriptive statistics for the variables selected above.  Click OK in the Review Descriptive Statistics dialog in order to continue the analysis and open the Model Definition dialog.


  Canonical Analysis - Review Descriptive Statistics

This dialog allows you to compute detailed descriptive statistics for the variables in the current analysis.

Review Descriptive Statistics dialog:

Means & SD

Correlations

Covariances

Save correlations

Box & whisker plots

Matrix plot of Correlations

The SD Check Box


  Review Descriptive Statistics - Means and Standard Deviations

This option will bring up a Scrollsheet with the descriptive statistics for the variables in the analysis.  If a raw data file is analyzed, then the default statistical graph for that Scrollsheet is the histogram with fitted normal distribution.


  Review Descriptive Statistics - Correlations

This option will bring up a Scrollsheet with the current correlation matrix.  If a raw data file is analyzed, then the default statistical graph for that Scrollsheet is the scatterplot with the fitted regression line.


  Review Descriptive Statistics - Covariances

This option will bring up a Scrollsheet with the current covariance matrix.  If a raw data file is analyzed, then the default statistical graph for that Scrollsheet is the scatterplot with the fitted regression line.


  Review Descriptive Statistics - Save Correlations

This option allows you to save the current correlation matrix in STATISTICA Matrix File Format.  The correlation matrix can then be directly read in subsequent canonical analyses (or analyses via Multiple Regression, Factor Analysis, Reliability and Item Analysis, Cluster Analysis, Multidimensional Scaling, etc.).


Review Descriptive Statistics - Box & Whisker Plots

bmc m_can.bmp}  Review Descriptive Statistics - Box & Whisker Plots

This option allows you to produce box and whisker plots for the variables in the current analysis.  The box and whisker plot will summarize each variable by three components:

(1)	A central line to indicate central tendency or location;

(2)	A box to indicate variability around this central tendency;

(3)	Whiskers around the box to indicate the range of the variable.

After clicking on this button you can choose to plot for each variable:

(1)	Medians (central line), quartiles (box), and ranges (whiskers); note that the specific method that is used to compute these values can be configured in the STATISTICA Defaults: General dialog.

(2)	Means, standard errors of the means, and standard deviations;

(3)	Means, standard deviations, and 1.96 times the standard deviations (95% normal confidence interval for individual observations around the mean);

(4)  Means standard errors of the means, and 1.96 times the standard errors of the means (95% normal confidence interval for means).


  Review Descriptive Statistics - Matrix Plot of Correlations

This option will bring up a matrix scatterplot for the variables selected for the analysis.


  Review Descriptive Statistics - The SD Checkbox

There are two ways in which standard deviations can be computed: as the sums of (deviation) squares divided by n (the valid number of cases) or n-1.  If divided by n-1, the resulting standard deviations are estimates of the standard deviations in the population (sigma); if divided by n, then the resulting standard deviations are descriptions of the sample only.  The setting of this switch will not affect the subsequent computations for the canonical analysis.


  Canonical Analysis - Define Model

This dialog will allow you to specify the variables for the canonical analysis as well as other options described below.

Model Definition dialog:

Variables for Canonical Analysis

Batch processing/printing

Means and Standard Deviations

Box and Whisker Plot

Correlation Matrix

Matrix plot


  Canonical Analysis Define Model - Variables for Canonical Analysis

Clicking on this option will bring up the standard two variable list selection window in which you can select the two sets of variables for the canonical correlation analysis.


  Canonical Analysis Define Model - Batch Processing/Printing

This check box is only available if printer, disk file, and/or Text/output Window was selected in the Page/Output Setup dialog.  When this box is checked (and printer output was selected), then the entire output from the analysis will be printed without requiring any user input.


  Canonical Analysis Define Model - Means and Standard Deviations

Clicking on this button will bring up a Scrollsheet with the means and standard deviations for all variables (selected from the Startup Panel).  The default graph for this Scrollsheet is the histogram of the frequency distribution for the respective variable.  That plot will also indicate the normal distribution, so it may serve as a quick visual check for any violations of the normality assumption.


  Canonical Analysis Define Model - Box & Whisker Plots

This option allows you to produce a box and whisker plot (showing medians and quartiles, means and standard deviations, etc.) for selected variables.


  Canonical Analysis Define Model - Correlation Matrix

This option will bring up a Scrollsheet with the correlation matrix for all variables (selected from the Startup Panel).  The default plot for this Scrollsheet is the scatterplot of the respective two variables that are highlighted.


  Canonical Analysis Define Model - Matrix Plot

This option allows you to produce a scatterplot matrix for selected variables.


  Canonical Analysis - Results

The canonical correlation reported at the top of this window denotes the correlation between the first and most significant canonical variates in each set (the first canonical root that is extracted).  The interpretation of the values reported in the columns labeled variance extracted and total redundancy are explained under option Factor structures and redundancies below.

Canonical Analysis Results dialog:

Correlations within and between sets

Eigenvalues

Canonical weights for left and right set

Factor structures and redundancies

Chi-square tests of successive roots

Save canonical scores

Summary

Plot of eigenvalues

Plot of canonical correlations

Scatterplot of canonical correlations


  Canonical Analysis Results - Correlations within and between Sets

This button will bring up Scrollsheets with the correlations within each set of variables, and between sets.


  Canonical Analysis Results - Eigenvalues

This button will bring up a Scrollsheet with the eigenvalues for the canonical roots.  Note that the square roots of the eigenvalues are the canonical correlation coefficients.


  Canonical Analysis Results - Canonical Weights for Left and Right Set

This button will bring up a Scrollsheet with the canonical weights for each set.  These weights can be used to compute the canonical scores for each canonical root, for each set of variables.  Note, that the weights pertain to the standardized (i.e., z transformed) variables in each set.  The canonical weights may also be used in the interpretation of the canonical roots.


  Canonical Analysis Results - Factor Structures and Redundancies

This button will bring up Scrollsheets with the canonical factor loadings and redundancies (variance extracted) for both sets of variables.

The canonical factor loadings can be interpreted as in factor analysis (see Factor Analysis), that is, they represent the correlations between the variables with the respective canonical variates.

The variance extracted is computed by summing up the squared canonical factor loadings across variables in a set for a particular canonical root, and then dividing that sum by the number of variables in the set.  The resulting proportion can be interpreted as the average proportion of variance accounted for in the respective variables by the respective root.  The total proportion of variance extracted that is reported at the top of the results dialog can be interpreted as the average proportion of variance accounted for by all canonical roots.

Redundancies are computed by multiplying the proportion of variance extracted by the squared canonical correlation.  The redundancies for a particular root can be interpreted as the average proportion of variance accounted for in the respective set of variables by that root, given the variables in the other set.  The total redundancy reported at the top of the results dialog is the sum of the redundancies across all roots.


  Canonical Analysis Results - Chi-square Test of Successive Roots

This button will bring up a Scrollsheet reporting, for each canonical root, the canonical R, R-square, Chi-square, degrees of freedom, p-level, and lambda value.  The results displayed in this Scrollsheet can be used to decide how many canonical roots are statistically significant, and should be examined further (that is, interpreted).  The so-called sequential significance test works as follows (see also, Introductory Overview).  First we look at all canonical roots together, that is, without any roots removed.  That test (Chi-square and p-level) is reported in the first row of the Scrollsheet.  If that test is significant, then we conclude that at least one canonical root is statistically significant.  Next we "remove" the first (and most significant) root and test the statistical significance of the remaining roots.  That test is reported in the second row of the Scrollsheet.  If significant, we conclude that at least two canonical roots are statistically significant.  If not, we stop and only retain the first root for interpretation.  If the second root is also significant, then we "remove" that root and test the statistical significance of the remaining roots, and so on.


  Canonical Analysis Results - Save Canonical Scores

This option is only available if a raw data file was specified in the Canonical Analysis Startup Panel.  After clicking on this button, the user will be prompted for an output file name.  A variable selection window will then be displayed allowing the user to select the variables from the input file that are to be saved together with the canonical scores.


  Canonical Analysis Results - Summary

This option will bring up a Scrollsheet with the summary statistics for the current analysis.


  Canonical Analysis Results - Plot of Eigenvalues

After choosing this option, a line graph of eigenvalues will be displayed.


  Canonical Analysis Results - Plot of Canonical Correlations

After clicking on this button, a line graph of canonical correlations (square roots of eigenvalues) will be displayed.


  Canonical Analysis Results - Scatterplot of Canonical Correlations

This option is only available if raw data are analyzed (i.e., raw data file was specified in the Canonical Correlation Startup Panel).  After clicking on this button, the user can specify pairs of canonical variables for which to plot the scatterplot of canonical scores.


  Canonical Analysis - Scatterplot of Canonical Correlations

Select the canonical variables for the plot.


  Canonical Analysis - Notes and Technical Information

Confirmatory models.  If you have specific hypotheses about the relationships between the different variables in your data, you can test those hypotheses via the Structural Equation Modeling (SEPATH) module.  With SEPATH, you can fit (confirmatory) factor models, path models, models with intercepts, etc.  Also, models can be fit to multiple samples, and parameter estimates can be constrained (to be equal) across samples.


  Log-Linear Analysis of Frequency Tables - Index

Introductory Overview

Startup Panel

Specifying tables directly (frequency table input)

Model specification

Reviewing tables (slicing tables)

Specifying and testing specific models

Automatic (stepwise) selection of best model

Specifying structural zeros

Results

Notes and Technical Information


  Log-Linear Analysis of Frequency Tables - Introductory Overview

General Purpose

Two-way Frequency Tables

Multi-Way Frequency Tables

The Log-Linear Model

Goodness-of-fit

Automatic Model Fitting


Log-Linear Analysis of Frequency Tables - General Purpose

  Log-Linear Analysis of Frequency Tables Introductory Overview - General Purpose

One basic and straightforward method for analyzing data is via crosstabulation.  For example, a medical researcher may tabulate the frequency of different symptoms by patients' age and gender; an educational researcher may tabulate the number of high school drop-outs by age, gender, and ethnic background; an economist may tabulate the number of business failures by industry, region, and initial capitalization; a market researcher may tabulate consumer preferences by product, age, and gender; etc.  In all of these cases, the major results of interest can be summarized in a multi-way frequency table, that is, in a crosstabulation table with two or more factors.

STATISTICA contains a designated module, Basic Statistics, for generating, analyzing, and reviewing different types of tables.  Log-Linear provides a more "sophisticated" way of looking at crosstabulation tables.  Specifically, this module allows the user to test the different factors that are used in the crosstabulation (e.g., gender, region, etc.) and their interactions for statistical significance (see Elementary Concepts for a discussion of statistical significance testing).  The following text will present a brief introduction to these methods, their logic, and interpretation.

Note that STATISTICA also includes a designated module for performing correspondence analysis for two-way and multi-way frequency tables (i.e., to perform multiple correspondence analysis).  Correspondence analysis is a descriptive/exploratory technique designed to analyze two-way and multi-way tables containing some measure of correspondence between the rows and columns.  The results provide information which is similar in nature to those produced by Factor Analysis techniques, and they allow one to explore the structure of the categorical variables included in the table.


Log-Linear Analysis of Frequency Tables - Two-way Frequency Tables

  Log-Linear Analysis of Frequency Tables Introductory Overview - Two-way Frequency Tables

Let us begin with the simplest possible crosstabulation, the 2 by 2 table.  Suppose we were interested in the relationship between age and the graying of people's hair.  We took a sample of 100 subjects, and determined who does and does not have gray hair.  We also recorded the approximate age of the subjects.  The results of this study may be summarized as follows:

                  Age

Gray     -----------------------

Hair     Below 40    40 or older   Total

--------------------------------   -----

No         40            5            45

Yes        20           35            55

--------------------------------   -----

Total      60           40           100

While interpreting the results of our little study, let us introduce the terminology that will allow us to generalize to complex tables more easily.

Design variables and response variables.  In multiple regression see (Multiple Regression) or analysis of variance (ANOVA/MANOVA) one customarily distinguishes between independent and dependent variables.  Dependent variables are those that we are trying to explain, that is, that we hypothesize to depend on the independent variables.  We could classify the factors in the 2 by 2 table accordingly: we may think of hair color (gray, not gray) as the dependent variable, and age as the independent variable.  Alternative terms that are often used in the context of frequency tables are response variables and design variables, respectively.  Response variables are those that vary in response to the design variables.  Thus, in the example table above, hair color can be considered to be the response variable, and age the design variable.

Fitting marginal frequencies.  Let us now turn to the analysis of our example table.  We could ask ourselves what the frequencies would look like if there were no relationship between variables (the null hypothesis).  Without going into details, intuitively one could expect that the frequencies in each cell would proportionately reflect the marginal frequencies (Totals).  For example, consider the following table:

                  Age

Gray     -----------------------

Hair     Below 40    40 or older   Total

--------------------------------   -----

No         27           18            45

Yes        33           22            55

--------------------------------   -----

Total      60           40           100

In this table, the proportions of the marginal frequencies are reflected in the individual cells.  Thus, 27/33=18/22=45/55 and 27/18=33/22=60/40.  Given the marginal frequencies, these are the cell frequencies that we would expect if there were no relationship between age and graying.  If you compare this table with the previous one you will see that the previous table does reflect a relationship between the two variables: There are more than expected (under the null hypothesis) cases below age 40 without gray hair, and more cases above age 40 with gray hair.

This example illustrates the general principle on which the log-linear analysis is based:  Given the marginal totals for two (or more) factors, we can compute the cell frequencies that would be expected if the two (or more) factors are unrelated.  Significant deviations of the observed frequencies from those expected frequencies reflect a relationship between the two (or more) variables.

Model fitting approach.  Let us now rephrase our discussion of the 2 by 2 table so far.  We can say that fitting the model of two variables that are not related (age and hair color) amounts to computing the cell frequencies in the table based on the respective marginal frequencies (totals).  Significant deviations of the observed table from those fitted frequencies reflect the lack of fit of the independence (between two variables) model.  In that case we would reject that model for our data, and instead accept the model that allows for a relationship or association between age and hair color.


Log-Linear Analysis of Frequency Tables - Multi-way Frequency Tables

  Log-Linear Analysis of Frequency Tables Introductory Overview - Multi-way Frequency Tables

The reasoning presented for the analysis of the 2 by 2 table can be generalized to more complex tables.  For example, suppose we had a third variable in our study, namely whether or not the individuals in our sample experience stress at work.  Because we are interested in the effect of stress on graying, we will consider Stress as another design variable.  (Note that, if our study were concerned with the effect of gray hair on subsequent stress, variable stress would be the response variable, and hair color would be the design variable.).  The resultant table is a three-way frequency table.

Fitting models.  We can apply our previous reasoning to analyze this table.  Specifically, we could fit different models that reflect different hypotheses about the data.  For example, we could begin with a model that hypothesizes independence between all factors.  As before, the expected frequencies in that case would reflect the respective marginal frequencies.  If any significant deviations occur, we would reject this model.

Interaction effects.  Another conceivable model would be that age is related to hair color, and stress is related to hair color, but the two (age and stress) factors do not interact in their effect.  In that case, we would need to simultaneously fit the marginal totals for the two-way table of age by hair color collapsed across levels of stress, and the two-way table of stress by hair color collapsed across the levels of age.  If this model does not fit the data, we would have to conclude that age, stress, and hair color all are interrelated.  Put another way, we would conclude that age and stress interact in their effect on graying.

The concept of interaction here is analogous to that used in analysis of variance (ANOVA/MANOVA).  For example, the age by stress interaction could be interpreted such that the relationship of age to hair color is modified by stress.  While age brings about only little graying in the absence of stress, age is highly related when stress is present.  Put another way, the effects of age and stress on graying are not additive, but interactive.

If you are not familiar with the concept of interaction, we recommend that you read the Introductory Overview to ANOVA/MANOVA.  Many aspects of the interpretation of results from a log-linear analysis of a multi-way frequency table are very similar to ANOVA.

Iterative proportional fitting.  The computation of expected frequencies becomes increasingly complex when there are more than two factors in the table.  However, they can be computed, and, therefore, we can easily apply the reasoning developed for the 2 by 2 table to complex tables.  The commonly used method for computing the expected frequencies is the so-called iterative proportional fitting procedure.


Log-Linear Analysis of Frequency Tables - The Log-Linear Model

  Log-Linear Analysis of Frequency Tables Introductory Overview - The Log-Linear Model

The term log-linear derives from the fact that one can, through logarithmic transformations, restate the problem of analyzing multi-way frequency tables in terms that are very similar to ANOVA.  Specifically, one may think of the multi-way frequency table to reflect various main effects and interaction effects that add together in a linear fashion to bring about the observed table of frequencies.  Bishop, Fienberg, and Holland (1974) provide details on how to derive log-linear equations to express the relationship between factors in a multi-way frequency table.


Log-Linear Analysis of Frequency Tables - Goodness-of-Fit

  Log-Linear Analysis of Frequency Tables Introductory Overview - Goodness-of-Fit

In the previous discussion we have repeatedly made reference to the "significance" of deviations of the observed frequencies from the expected frequencies.  One can evaluate the statistical significance of the goodness-of-fit of a particular model via a Chi-square test.  Log-Linear will compute two types of Chi-squares, the traditional Pearson Chi-square statistic and the maximum likelihood ratio Chi-square statistic (the term likelihood ratio was first introduced by Neyman and Pearson, 1931; the term maximum likelihood was first used by Fisher, 1922a).  In practice, the interpretation and magnitude of those two Chi-square statistics are essentially identical.  Both tests evaluate whether the expected cell frequencies under the respective model are significantly different from the observed cell frequencies.  If so, the respective model for the table is rejected.

Reviewing and plotting residual frequencies.  After one has chosen a model for the observed table, it is always a good idea to inspect the residual frequencies, that is, the observed minus the expected frequencies.  If the model is appropriate for the table, then all residual frequencies should be "random noise," that is, consist of positive and negative values of approximately equal magnitudes that are distributed evenly across the cells of the table.  Log-Linear also allows the user to produce various plots of residual frequencies and related statistics.

Statistical significance of effects.  The Chi-squares of models that are hierarchically related to each other can be directly compared.  For example, if we first fit a model with the age by hair color interaction and the stress by hair color interaction, and then fit a model with the age by stress by hair color (three-way) interaction, then the second model is a superset of the previous model.  We could evaluate the difference in the Chi-square statistics, based on the difference in the degrees of freedom; if the differential Chi-square statistic is significant, then we would conclude that the three-way interaction model provides a significantly better fit to the observed table than the model without this interaction.  Therefore, the three-way interaction is statistically significant.

In general, two models are hierarchically related to each other if one can be produced from the other by either adding terms (variables or interactions) or deleting terms (but not both at the same time).


Log-Linear Analysis of Frequency Tables - Automatic Model Fitting

  Log-Linear Analysis of Frequency Tables Introductory Overview - Automatic Model Fitting

When analyzing four- or higher-way tables, finding the best fitting model can become increasingly difficult.  Log-Linear contains automatic model fitting options to facilitate the search for a "good model" that fits the data.  The general logic of this algorithm is as follows.  First the program will fit a model with no relationships between factors; if that model does not fit (i.e., the respective Chi-square statistic is significant), then it will fit a model with all two-way interactions.  If that model does not fit either, then the program will fit all three-way interactions, and so on.  Let us assume that this process found the model with all two-way interactions to fit the data.  The program will then proceed to eliminate all two-way interactions that are not statistically significant.  The resulting model will be the one that includes the least number of interactions necessary to fit the observed table.


  Log-Linear Analysis - Startup Panel

The options available on this dialog will differ slightly, depending on the setting of the Input File combo box (see below) in the Log-Linear Startup Panel (see also, Log-Linear - Index).

Log-Linear Startup Panel:

Input File

Variables

Select Codes

Specify Table


  Log-Linear Analysis Startup Panel - Input File

Log-Linear can process three different types of data files:  Raw Data with coding variables, Frequencies with Coding Variables, and Frequencies without Coding Variables.

Raw data:  If the raw data option is selected, then STATISTICA will compute the frequency table from the data.  The program expects that the data file contains coding variables with integer values or text values that uniquely identify to which cell in the table each case belongs.  This way of specifying the design of a table is very much like specifying the design of an ANOVA in ANOVA/MANOVA.

Frequencies with coding variables:  If the file contains frequencies, then STATISTICA can read those directly.  If frequencies with coding variables is specified, then STATISTICA expects coding variables with integer codes or text values that uniquely specify the cell in the table to which each frequency belongs, and a variable containing the frequency.  The example data file Center2.sta provided with STATISTICA and discussed in the manual is organized in this manner.

Frequencies without coding variables:  If frequencies without coding variables is specified, the program will read the data variable by variable, and case by case, and interpret consecutive data points as frequencies of the table as specified by the Specify Table option (see below).  Thus, the user can type tables directly into Data Management (without having to add any codes) and process them with Log-Linear.


  Log-Linear Analysis Startup Panel - Variables

Clicking on this button will bring up a standard variable selection window.  If the Input File combo box is set to raw data or frequencies with coding variables, then use this option to select the variables denoting the factors; those variables should contain the codes or text values that identify the cells of the table.  If the Input File combo box is set to frequencies with coding variables, then clicking on the Variables button will bring up the two-variable list selection dialog.  Select the variable containing the frequencies and the variables (factors) with the codes that specify the table.  The different ways in which tables can be specified in data files, and read by Log-Linear, are also demonstrated in the Example section of the respective chapter in the manual.


  Log-Linear Analysis Startup Panel - Select Codes

This option is only available if the Input File combo box is set to either raw data or frequencies with coding variables (see above), and after variables (i.e., factors or "independent" variables) have been selected via the Variables option (see above).  Clicking on this button will bring up the standard code selection windows, one for each selected variable (factor).  Note that you can use the asterisk (*) option in each edit box to automatically select all codes or text values in the respective variable or factor, or you can click on the Select All button in the code selection windows.


  Log-Linear Analysis Startup Panel - Specify Table

This option is only available if the input data file was specified to contain frequencies without coding variables.  In that case, the program will interpret all consecutive data points that are read (variable by variable, case by case) as frequencies of the table.  In order to instruct the program as to which cell of the table each frequency belongs, the user must specify the design (or "shape") of the table.  The logic of specifying the design is as follows: the first factor that is specified should be the fastest changing factor, the second factor the second-fastest changing factor, etc.


  Specifying Tables Directly (Frequency Table Input)

It is assumed that you typed the frequencies for the table directly into the data file.  Internally, STATISTICA will simply read the frequencies in the selected variables as one long string of numbers, reading row by row, starting from the left-most variable.  The information supplied here allows the program to "understand" the structure of the table.

For each factor in the table, specify the number of levels and a name.  When reading the data (frequencies) the program will interpret the first factor to be the one with the "fastest changing subscript," the second factor as the one with the second-fastest changing subscript, and so on.  Refer to this topic in the manual for detailed examples of how to specify tables in this manner.

Example


  Log-Linear Analysis - Specifying Tables Directly (Frequency Table Input)

In this example, we will specify a 4x2x3x3 frequency table that is read directly, i.e., without any coding variables.  This file is saved under the filename Center.sta in the STATISTICA Examples directory.

Step 1.  Startup Panel:  If you have not already done so, open the file containing the frequencies by clicking on the Open Data button in the Startup Panel and then selecting the file Center.sta.  Once the file is opened, select Frequencies w/out coding variables as the Input file and select all variables in the file.  Click on the Specify Table button in this dialog to open the Specify Dimensions of the Table dialog.

Step 2.  Specifying the Dimensions of the Table:  Now, in this dialog, you will need to specify exactly how the frequencies are represented in the table.  In the spreadsheet, the levels of four factors (Appearance, Survival, Age, and Location) are used as the case names and variable names (or column headings).  The first factor that we will list in the Specifying the Dimensions of the Table dialog, needs to be the one with the "fastest changing subscript," the second factor as the one with the second-fastest changing subscript, and so on.  Since STATISTICA reads the frequencies across rows, the factor with the fastest changing subscript in this example, is the factor whose levels are listed in the column headings of the spreadsheet -- Appearance.  In the Specify Dimensions of the Table, type in 4 for the number of levels for this factor and Appearnc as the factor name.  The next fastest changing factor is Survival since the 2 levels of this factor (Yes or No) change from line to line (listed in the Case Names column).  Type in this factor name and the number of levels in the second line of this dialog.  Specify the remaining two factors in lines 3 and 4, respectively, as follows:  3 levels (under 50, 50-69, and over 69) for factor Age, and 3 levels (Tokyo, Boston, and Glmrgn) for factor Location.  Now, click OK to return to the Startup Panel where the table to be analyzed will be displayed in the lower half of the Startup Panel.


  Log-Linear Analysis - Model Specification

The Log-Linear Model Specification dialog will allow you to review the observed tables, specify specific models, and other options.

Log-Linear Model Specification dialog:

Review Complete Observed Table

Display Slices of Table

Specify Model to be Tested

Test all Marginal & Partial Models

Automatic Selection of Best Model

Define Structural Zeros

Delta

Maximum Number of Iterations

Convergence Criterion

Save the Table


  Log-Linear Analysis Model Specification - Review Complete Observed Table

Via this option you can review the multi-way frequency table in the most flexible manner, slice by slice, as specified by the user.  If there are more than two factors in the frequency table, the program allows the user to view any two-way table within each of the levels of the remaining factors.  After clicking on this button (if the table contains more than 2 factors) the user is prompted to select the two factors by which to view the table.  Scrollsheets will then be displayed showing the frequencies in two-way tables, within the levels of all remaining factors.

The default custom graph for all tables is the 3D histogram.  This graph is very helpful in order to visualize the pattern of frequencies in the table.


  Log-Linear Analysis Model Specification - Display Slices of Table

This setting of the radio buttons in this group will determine how tables are displayed in this module, and it will affect the display of tables selected from this as well as the Results dialog window.

As many as fit at a time:  By default, the program will automatically display as many slices of the table (Scrollsheets) as can be simultaneously viewed.  Note that you can easily increase the default (3 Scrollsheets at a time) via the Scrollsheet Manager option on the Window pull-down menu.

One by one:  Alternatively, the user may set the One by one radio button.  In this case, only one slice at time will be displayed, and the user will be prompted to Continue after each slice.

NOTE:  If printer (or disk) output is selected in the Page/Output Setup dialog, then before the first table is displayed, the user has the option to automatically print (to a disk or the printer) the entire table (without interruption).


  Log-Linear Analysis Model Specification - Specify Model to be Tested

Clicking on this button will bring up a window for specifying the model to be tested.  The logic of specifying models in STATISTICA is as follows:

•	Refer to factors in the table by their respective numbers.

•	Use those numbers in order to specify main effects and interactions.  For example, in order to specify a model with no interactions but only main effects for each of three factors, enter 1 2 3 (separated by spaces or commas).

•	In order to specify a model with a 2-way interaction between factors 1 and 3, and the main effect for factor 2, enter 13 2 (or 2 31; the order does not matter).

•	Higher-order interactions are specified analogously (e.g., 124 134 15).  After exiting the dialog via OK the program will begin to estimate the model.


  Log-Linear Analysis Model Specification - Test all Marginal and Partial Models

The utility and interpretation of these tests is described in the Introductory Overview section and the Example section of the Log-Linear chapter.

The partial association between, for example, two factors 1 and 2 (denoted by 12) is computed by comparing the fit (i.e., evaluating the Chi-square difference) of the model that includes all two-way interactions with the model that excludes the interaction between factors 1 and 2.  The marginal association between, for example, two factors 1 and 2 is computed by comparing the fit of the model including all main effects (i.e., all effects of lower order than the one of interest) with the model including the interaction between factors 1 and 2.

Note that these tests are actually computed only the first time after this option is chosen.  Thereafter (unless the user returns to the Startup Panel), these tests are stored in memory and are available instantaneously.


  Log-Linear Analysis Model Specification - Automatic Selection of Best Model

This option will bring up the Automatic Selection of Best Model dialog.  The logic of the automatic selection algorithm is described in the Overview section.


  Log-Linear Analysis Model Specification - Define Structural Zeros

With Log-Linear one can analyze incomplete tables, that is, tables containing structural zeros.  Structural (as opposed to sampling) zeros are empty cells in the table that are empty by design.  For example, suppose you tabulated the number of patients in a hospital by gender and diagnosis.  If the hospital has a maternity ward, then the table will contain empty cells by design, namely, there will not be any males who are in the hospital to give birth.

After pressing this button, the program will first "find" all zero frequencies in the table, you can then select the structural zeros from that list.  Note that the correct computation of the degrees of freedom for models fit to tables with structural zeros can be extremely complex.  Log-Linear will correctly compute the degrees of freedom for models involving structural zeros as long as those zero frequencies do not result in zeros in the marginal tables of the respective model.


  Log-Linear Analysis Model Specification - Delta

The constant delta (0.5 by default) is added to all frequencies in the observed table before it is submitted to the actual analysis.  This is a recommended procedure when the table contains several cells with low frequencies (e.g., less than 10); it is a correction analogous to the Yate's correction for two-way tables, and this correction does not affect the results unless the table contains low frequencies.

NOTE:  Be sure to set delta to zero if you want to use this module as a tabulation program.  Otherwise, you will not obtain accurate cell (raw) frequencies and marginal counts when requesting those tables later from the Results dialog.


  Log-Linear Analysis Model Specification - Maximum Number of Iterations

Fitting a model (i.e., marginal tables) to a multi-way frequency table is accomplished via an iterative procedure: the so-called iterative proportional fitting. The default setting of 50 iterations will practically always ensure that this iterative procedure will converge, that is, that the respective model will be fitted to the table with sufficient accuracy.


  Log-Linear Analysis Model Specification - Convergence Criterion

Fitting a model (i.e., marginal tables) to a multi-way frequency table is an iterative procedure (iterative proportional fitting).  At each iteration, the fitted marginal tables (i.e., the fitted model) will approximate more closely the observed marginal tables.  The iterative procedure will terminate when there is no difference between fitted and observed margins that is greater than the convergence criterion.  The default value (0.01) ensures an accuracy that is usually more than sufficient.


  Log-Linear Analysis Model Specification - Save the Table

This option allows the user to save the observed table in a STATISTICA data file.  The file will be saved with coding variables (indicating the levels for each factor) and a variable named Frequncy that contains the frequencies for each cell in the table.


  Reviewing Tables (Slicing Tables)

Tables can be reviewed slice by slice, as specified in the Log-Linear Model Specification dialog.  In the Specify How Table is to be Reviewed dialog, you can select the two factors (row and column variables) by which to view the table.  Scrollsheets will be displayed showing the two-way tables within the levels of all remaining factors.

Reviewing all slices at once:  By default, the program will automatically display as many slices of the table (Scrollsheets) as can be simultaneously viewed.  Note that you can easily increase the default (3 Scrollsheets at a time) via the Scrollsheet Manager option on the Window pull-down menu.  If you want to review the slices of the table one by one, set the One by one radio button on the Model Specification dialog.  The program will then prompt the user to Continue after each slice is displayed.

The default custom graph for all tables is the 3D histogram.  That graph is very helpful in order to visualize the pattern of frequencies in the table.


  Specifying and Testing Specific Models

The logic of specifying models in STATISTICA is as follows:

•	Refer to factors in the table by their respective numbers.

•	Use those numbers in order to specify main effects and interactions.  For example, in order to specify a model with no interactions but only main effects for each of three factors, enter 1 2 3 (separated by spaces or commas).

•	In order to specify a model with a 2-way interaction between factors 1 and 3, and the main effect for factor 2, enter 13 2 (or 2 31; the order does not matter).

•	Higher-order interactions are specified analogously (e.g., 124 134 15).  After exiting the dialog via OK the program will begin to estimate the model.


  Automatic (Stepwise) Selection of Best Model

Automatic Selection of Best Model dialog:

1 - p(1), 2 - p(2):  The logic of the automatic selection algorithm is described in the Log-Linear Overview section.  In short, the program will first fit a model with no interactions, then with all two-way interactions, three-way interactions, etc. until a model that fits at the p-level greater than p(1) has been found.  You can change this p-level via option 1-p(1).  Note that this first part is skipped if an initial user defined "starting model" is selected (see below).

Next, the program will eliminate from this initial model in a stepwise manner all effects that do not contribute significantly to the overall fit at the p(2) level of significance.

Starting model:  This option allows you to skip the first step of the automatic selection procedure (see above).  If you set this combo box to user defined, then after clicking OK, the regular model specification dialog will appear.  The model that you then specify will serve as the initial model from which non-significant effects (as specified by p(2)) will be eliminated.  This option is also useful if you want to perform statistical significance tests for all effects in a previously determined model.  As described above, during the backwards elimination stage of the automatic model selection procedure, the program will drop out each effect, one by one, and test its statistical significance.  You can print the results at each step by requesting Long output.


  Specifying Structural Zeros

With Log-Linear, one can analyze incomplete tables, that is, tables containing structural zeros.  Structural (as opposed to sampling) zeros are empty cells in the table that are empty by design.  For example, suppose you tabulated the number of patients in a hospital by gender and diagnosis.  If the hospital has a maternity ward, then the table will contain empty cells by design, namely, there will not be any males who are in the hospital to give birth.

Shown in this window are all cells in the table with zero frequencies.  Select the structural zeros from that list.  Note that the correct computation of the degrees of freedom for models fit to tables with structural zeros can be extremely complex.  Log-Linear will correctly compute the degrees of freedom for models involving structural zeros as long as those zero frequencies do not result in zeros in the marginal tables of the respective model.


  Log-Linear Analysis - Results

Note that the observed and marginal frequency tables that can be displayed from this dialog will include the delta constant, as specified on the Model Specification dialog.  Therefore, when using Log-Linear as a crosstabulation program make sure that delta is set to 0 (zero); otherwise you will not obtain accurate frequency counts.

The default custom graph for all results tables is the 3D histogram.  That graph is very helpful in order to visualize the pattern of frequencies, residuals, etc. in the table.

Log-Linear Results dialog:

Observed Table

Fitted Table

Residuals (observed - fitted)

Residuals Standardized

Components of Max-Likelihood Ratio Chi-square

Freeman-Tukey Deviates

Marginal Tables

Plot Options


  Log-Linear Analysis Results - Observed Table

Via this option the user can review the multi-way frequency table in the most flexible manner, slice by slice, as specified by the user.  If there are more than two factors in the frequency table, the program allows the user to view any two-way table within each of the levels of the remaining factors.  After clicking on this button (if the table contains more than 2 factors) the user is prompted to select the two factors by which to view the table.  Scrollsheets will then be displayed showing the frequencies in two-way tables, within the levels of all remaining factors.

Reviewing all Slices at Once:  By default, STATISTICA will automatically display as many slices of the table (Scrollsheets) as can be simultaneously viewed.  Note that you can easily increase the default (3 Scrollsheets at a time) via the Scrollsheet Manager option on the Window pull-down menu.  If you want to review the slices of the table one by one, set the One by one radio button on the Model Specification dialog.  The program will then prompt the user to Continue after each slice is displayed.

Printing the Entire Observed Table:  If printer, disk output, and/or Text/output Window is selected in the Page/Output Setup dialog, then before the first table is displayed, the user has the option to automatically print (to a disk, the printer, or Text/output Window) the entire table (without interruption).


  Log-Linear Analysis Results - Fitted Table

This option allows the user to review the fitted table, in the same manner (slice by slice) as described in Observed table.


  Log-Linear Analysis Results - Residuals (Observed-Fitted)

This option allows the user to review the residualized table (i.e., the table of observed minus fitted frequencies), in the same manner (slice by slice) as described above.


  Log-Linear Analysis Results - Residuals Standardized

This option allows the user to review the table of standardized residuals, in the same manner (slice by slice) as described in Observed table.  Standardized residuals (sijk..) are computed as:

                                1/2

s     = (f     -F     )/(F     )

 ijk..    ijk..  ijk..    ijk..

Fijk.. denotes the fitted or expected cell frequency for cell i,j,k,...; fijk.. denotes the observed frequency.


  Log-Linear Analysis Results - Components of Max-Likelihood Ratio Chi-Square

This option allows the user to review the table of components of the maximum likelihood ratio Chi-square, in the same manner (slice by slice) as described in Observed table.  These are the contributions of each cell to the overall maximum likelihood ratio Chi-square goodness-of-fit statistic:

c     = 2*f     *ln(f     /F     )

 ijk..     ijk..     ijk..  ijk..

In this equation, ln denotes the natural logarithm;  Fijk.. denotes the fitted or expected cell frequency for cell i,j,k,...; fijk.. denotes the observed frequency.


Log-Linear Analysis Results - Components of Max-Likelihood Ratio Chi-Square

  Log-Linear Analysis Results - Freeman-Tukey Deviates

This option allows the user to review the table of Freeman-Tukey deviates, in the same manner (slice by slice) as described in Observed table.  Freeman-Tukey deviates (frijk..) represent a normalizing transformation that is appropriate when the frequencies in the table come from a Poisson distribution:

               1/2           1/2             1/2

fr     = f        +(f     +1)   -(4*F     +1)

  ijk..   ijk..      ijk..           ijk..


  Log-Linear Analysis Results - Marginal Tables

This option allows the user to review the marginal tables, as specified by the current model, that were fit to the observed table.  These tables will be displayed one by one, and slice by slice if marginal tables involving more than two factors are displayed.  The number of tables (Scrollsheets) that will be simultaneously displayed depends on the respective setting of the maximum number of Scrollsheets parameter in the Scrollsheet Manager dialog window on the Window pull-down menu. (Default is 3).

Note that the marginal tables will include the delta constant, as specified on the Model Specification dialog.  Therefore, when using Log-Linear as a crosstabulation program make sure that delta is set to 0; otherwise you will not obtain accurate marginal counts.


  Log-Linear Analysis Results - Plot Options

After choosing any of the plot options, a scatterplot of the respective values will be displayed:

(1)	A plot of the observed versus fitted (expected) frequencies;

(2)	A plot of the fitted frequencies versus residual frequencies (observed minus fitted);

(3)	A plot of fitted frequencies versus standardized residuals;

(4)	A plot of fitted frequencies versus components of the maximum likelihood ratio Chi-square;

(5)	A plot of the fitted frequencies versus Freeman-Tukey deviates.

These graphs are very useful for evaluating the overall fit of the model for different magnitudes of frequencies, and for detecting outliers.


  Log-Linear Analysis - Notes and Technical Information

Algorithms

The fitting of models (marginal tables) to observed frequency tables is accomplished via iterative proportional fitting (see Deming & Stephan, 1940; Brown, 1959; Ireland & Kullback, 1968; Haberman, 1972, 1974).  The computations of the Pearson Chi-square and maximum likelihood ratio Chi-square statistics are described in detail by Bishop, Fienberg, and Holland (1975) and Fienberg (1978).  The logic of the automatic selection algorithm is described in Goodman (1971).

Residual Statistics

The following residual statistics are available from the Results dialog (note:  Fijk.. denotes the fitted or expected cell frequency for cell i,j,k,...; fijk.. denotes the observed frequency):

Raw residuals:  Raw residuals (rijk..) are computed as:

r      = f     - F

 ijk..    ijk..   ijk..

Standardized residuals:  Standardized residuals (sijk..) are computed as:

                                  1/2

s      = (f     - F     )/(F     )

 ijk..     ijk..   ijk..    ijk..

Components of maximum likelihood:  These are the contributions of each cell to the overall maximum likelihood ratio Chi-square goodness of fit statistic:

c      = 2*f     * ln(f     /F     )

 ijk..      ijk..      ijk..  ijk..

In this equation, ln denotes the natural logarithm.

Freeman-Tukey deviates:  Freeman-Tukey deviates (frijk..) represent a normalizing transformation that is appropriate when the frequencies in the table come from a Poisson distribution:

              1/2            1/2              1/2

fr      = f      + (f     +1)   - (4*F     +1)

  ijk..    ijk..     ijk..            ijk..


  Survival Analysis - Index

  Introductory Overview

Survival Analysis - Regression Models

Startup Panel

  Life Table Analysis - Raw Data

  Life Table Analysis - Analyzing Tables

Results & Distribution Fitting

  Kaplan-Meier (Product-Limit) Method

Results

  Comparing Survival in 2 Samples

Results

  Comparing Survival in k Samples

Results

  Regression Models for Censored Data

Setting Parameters for Estimation

Results

Notes and Technical Information


  Survival & Failure Time Analysis - Introductory Overview

General Information

Censored Observations

Analytic Techniques

See also:

Life Table Analysis

Distribution Fitting

Kaplan-Meier Product-Limit Estimator

Comparing Samples


Survival & Failure Time Analysis - General Information

  Survival & Failure Time Analysis Introductory Overview - General Information

The techniques available in this module were primarily developed in the medical and biological sciences, but they are also widely used in the social and economic sciences, as well as in engineering (reliability and failure time analysis).

Imagine that you are a researcher in a hospital who is studying the effectiveness of a new treatment for a generally terminal disease.  The major variable of interest is the number of days that the respective patients survive.  In principle, one could use the standard parametric and nonparametric statistics for describing the average survival, and for comparing the new treatment with traditional methods (see Basic Statistics and Nonparametrics and Distributions).  However, at the end of the study there will be patients who survived over the entire study period, in particular among those patients who entered the hospital (and the research project) late in the study; there will be other patients with whom we will have lost contact.  Surely, one would not want to exclude all of those patients from the study by declaring them to be missing data (since most of them are "survivors" and, therefore, they reflect on the success of the new treatment method).  Those observations, which contain only partial information are called censored observations (e.g., "patient A survived at least 4 months before he moved away and we lost contact;" the term censoring was first used by Hald, 1949) ).


Survival & Failure Time Analysis - Censored Observations

  Survival & Failure Time Analysis Introductory Overview - Censored Observations

In general, censored observations arise whenever the dependent variable of interest represents the time to a terminal event, and the duration of the study is limited in time.  Censored observations may occur in a number of different areas of research.  For example, in the social sciences we may study the "survival" of marriages, high school drop-out rates (time to drop-out), turnover in organizations, etc.  In each case, by the end of the study period, some subjects will still be married, will not have dropped out, or are still working at the same company; thus, those subjects represent censored observations.

In economics we may study the "survival" of new businesses or the "survival" times of products such as automobiles.  In quality control research, it is common practice to study the "survival" of parts under stress (failure time analysis).


Survival & Failure Time Analysis - Analytic Techniques

  Survival & Failure Time Analysis Introductory Overview - Analytic Techniques

Essentially, the methods offered in this module address the same research questions as many of the other STATISTICA procedures; however, all methods in Survival Analysis will handle censored data.  The life table, survival distribution, and Kaplan-Meier survival function estimation are all descriptive methods for estimating the distribution of survival times from a sample.  Several techniques are included for comparing the survival in two or more groups.  Finally, Survival Analysis includes several regression models for estimating the relationship of (multiple) continuous variables to survival times.


Survival & Failure Time Analysis - Life Table Analysis

  Survival & Failure Time Analysis Introductory Overview - Life Table Analysis

The most straightforward way to describe the survival in a sample is to compute the Life Table.  The life table technique is one of the oldest methods for analyzing survival (failure time) data (e.g., see Berkson & Gage, 1950; Cutler & Ederer, 1958; Gehan, 1969).  This table can be thought of as an "enhanced" frequency distribution table.  The distribution of survival times is divided into a certain number of intervals.  For each interval we can then compute the number and proportion of cases or objects that entered the respective interval "alive," the number and proportion of cases that failed in the respective interval (i.e., number of terminal events, or number of cases that "died"), and the number of cases that were lost or censored in the respective interval.

Based on those numbers and proportions, several additional statistics can be computed:

Number of Cases at Risk

Proportion Failing

Proportion surviving

Cumulative Proportion Surviving (Survival Function)

Probability Density

Hazard rate

Median survival time

Required sample sizes


Life Table Analysis Introductory Overview - General Introduction

  Survival & Failure Time Analysis Life Table Analysis Introductory Overview - General Introduction

The most straightforward way to describe the survival in a sample is to compute the Life Table.  The life table technique is one of the oldest methods for analyzing survival (failure time) data (e.g., see Berkson & Gage, 1950; Cutler & Ederer, 1958; Gehan, 1969).  This table can be thought of as an "enhanced" frequency distribution table.  The distribution of survival times is divided into a certain number of intervals.  For each interval we can then compute the number and proportion of cases or objects that entered the respective interval "alive," the number and proportion of cases that failed in the respective interval (i.e., number of terminal events, or number of cases that "died"), and the number of cases that were lost or censored in the respective interval.

Based on those numbers and proportions, several additional statistics can be computed:

Number of Cases at Risk

Proportion Failing

Proportion surviving

Cumulative Proportion Surviving (Survival Function)

Probability Density

Hazard rate

Median survival time

Required sample sizes


Life Table Analysis Introductory Overview - Number of Cases at Risk

  Survival & Failure Time Analysis Life Table Analysis Introductory Overview - Number of Cases at Risk

This is the number of cases that entered the respective interval alive, minus half of the number of cases lost or censored in the respective interval.


Life Table Analysis Introductory Overview - Proportion Failing

  Survival & Failure Time Analysis Life Table Analysis Introductory Overview - Proportion Failing

This proportion is computed as the ratio of the number of cases failing in the respective interval, divided by the number of cases at risk in the interval.


Life Table Analysis Introductory Overview - Proportion Surviving

  Survival & Failure Time Analysis Life Table Analysis Introductory Overview - Proportion Surviving

This proportion is computed as 1 minus the proportion failing.


Life Table Analysis Introductory Overview - Cumulative proportion surviving (survival function)

  Survival & Failure Time Analysis Life Table Analysis Introductory Overview - Cumulative Proportion Surviving (Survival Function)

This is the cumulative proportion of cases surviving up to the respective interval.  Since the probabilities of survival are assumed to be independent across the intervals, this probability is computed by multiplying out the probabilities of survival across all previous intervals.  The resulting function is also called the survivorship or survival function.


Life Table Analysis Introductory Overview - Probability Density

  Survival & Failure Time Analysis Life Table Analysis Introductory Overview - Probability Density

This is the estimated probability of failure in the respective interval, computed per unit of time, that is:

F =(S -q )/h

 i   i  i   i

In this formula, Fi is the respective probability density in the i'th interval, Si is the estimated cumulative proportion surviving at the end of the it interval, qi is the proportion failing in the respective interval, and hi is the width of the respective interval.


Life Table Analysis Introductory Overview - Hazard Rate

  Survival & Failure Time Analysis Life Table Analysis Introductory Overview - Hazard Rate

The hazard rate (the term was first used by Barlow, 1963) is defined as the probability per time unit that a case that has survived to the beginning of the respective interval will fail in that interval.  Specifically, it is computed as the number of failures per time units in the respective interval, divided by the average number of surviving cases at the mid-point of the interval.


Life Table Analysis Introductory Overview - Median Survival Time

  Survival & Failure Time Analysis Life Table Analysis Introductory Overview - Median Survival Time

This is the survival time at which the cumulative survival function is equal to 0.5.  Other percentiles (25th and 75th percentile) of the cumulative survival function can be computed accordingly.  Note that the 50th percentile (median) for the cumulative survival function is usually not the same as the point in time up to which 50% of the sample survived.  (This would only be the case if there were no censored observations prior to this time).


Life Table Analysis Introductory Overview - Required Sample Sizes

  Survival & Failure Time Analysis Life Table Analysis Introductory Overview - Required Sample Sizes

In order to arrive at reliable estimates of the three major functions (survival, probability density, and hazard) and their standard errors at each time interval the minimum recommended sample size is 30.


Survival & Failure Time Analysis - Distribution Fitting

  Survival & Failure Time Analysis Introductory Overview - Distribution Fitting

General Introduction

Estimation

Goodness-of-fit

Plots


Distribution Fitting Introductory Overview - General Introduction

  Survival & Failure Time Analysis Distribution Fitting Introductory Overview - General Introduction

In summary, the life table gives us a good indication of the distribution of failures over time.  However, for predictive purposes it is often desirable to understand the shape of the underlying survival function in the population.  The major distributions that have been proposed for modeling survival or failure times are the exponential (and linear exponential) distribution, the Weibull distribution of extreme events, and the Gompertz distribution.  Survival Analysis will fit all of these theoretical distributions to the observed life table.


Distribution Fitting Introductory Overview - Estimation

  Survival & Failure Time Analysis Distribution Fitting Introductory Overview - Estimation

The parameter estimation procedure (for estimating the parameters of the theoretical survival functions) is essentially a least squares linear regression algorithm (see Gehan & Siddiqui, 1973).  A linear regression algorithm can be used because all four theoretical distributions can be "made linear" by appropriate transformations (see the Notes and Technical Information section in the respective chapter in the manual).  Such transformations sometimes produce different variances for the residuals at different times, leading to biased estimates.  Therefore, the fitting algorithm in Survival Analysis also computes two types of weighted least squares estimates.


Distribution Fitting Introductory Overview - Goodness-of-Fit

  Survival & Failure Time Analysis Distribution Fitting Introductory Overview - Goodness-of-Fit

Given the parameters for the different distribution functions and the respective model, we can compute the likelihood of the data.  One can also compute the likelihood of the data under the null model, that is, a model that allows for different hazard rates in each interval.  Without going into details, these two likelihoods can be compared via an incremental Chi-square test statistic.  If this Chi-square is statistically significant, then we conclude that the respective theoretical distribution fits the data significantly worse than the null model; that is, we reject the respective distribution as a model for our data.


Distribution Fitting Introductory Overview - Plots

  Survival & Failure Time Analysis Distribution Fitting Introductory Overview - Plots

Survival Analysis will produce plots of the survival function, hazard, and probability density for the observed data and the respective theoretical distributions.  These plots provide a quick visual check of the goodness-of-fit of the theoretical distribution.


Survival & Failure Time Analysis - Kaplan-Meier Product-Limit Estimator

  Survival & Failure Time Analysis Introductory Overview - Kaplan-Meier Product-Limit Estimator

Rather than classifying the observed survival times into a life table, we can estimate the survival function directly from the continuous survival or failure times.  Intuitively, imagine that we create a life table so that each time interval contains exactly one case.  Multiplying out the survival probabilities across the "intervals" (i.e., for each single observation) we would get for the survival function:

       t                δ(j)

S(t)=∏   [(n-j)/(n-j+1)]

      j=1

In this equation, S(t) is the estimated survival function, n is the total number of cases, and ∏ denotes the multiplication (geometric sum) across all cases less than or equal to t; δ(j) is a constant that is either 1 if the j'th case is uncensored (complete), and 0 if it is censored.  This estimate of the survival function is also called the product-limit estimator, and was first proposed by Kaplan and Meier (1958).  The advantage of the Kaplan-Meier Product-Limit method over the life table method for analyzing survival and failure time data is that the resulting estimates do not depend on the grouping of the data (into a certain number of time intervals).  Actually, the Product-Limit method and the life table method are identical if the intervals of the life table contain at most one observation.


Survival & Failure Time Analysis - Comparing Samples

  Survival & Failure Time Analysis Introductory Overview - Comparing Samples

General Introduction

Available tests

Choosing a two-sample test

Multiple sample test

Unequal proportions of censored data


Comparing Samples Introductory Overview - General Introduction

  Survival & Failure Time Analysis Comparing Samples Introductory Overview - General Introduction

One can compare the survival or failure times in two or more samples.  In principle, because survival times are not normally distributed, nonparametric tests that are based on the rank ordering of survival times should be applied.  Nonparametrics and Distributions offers a wide range of nonparametric tests that can be used in order to compare survival times; however, the tests in that module cannot "handle" censored observations.


Comparing Samples Introductory Overview - Available Tests

  Survival & Failure Time Analysis Comparing Samples Introductory Overview - Available Tests

Survival Analysis contains five different (mostly nonparametric) tests for censored data: Gehan's generalized Wilcoxon test, the Cox-Mantel test, the Cox's F test , the log-rank test, and Peto and Peto's generalized Wilcoxon test.  A nonparametric test for the comparison of multiple groups is also available.  Most of these tests are accompanied by appropriate z-values (values of the standard normal distribution); these z-values can be used to test for the statistical significance of any differences between groups.  However, note that most of these tests will only yield reliable results with fairly large samples sizes; the small sample "behavior" is less well understood.


Comparing Samples Introductory Overview - Choosing a Two Sample Test

  Survival & Failure Time Analysis Comparing Samples Introductory Overview - Choosing a Two Sample Test

There are no widely accepted guidelines concerning which test to use in a particular situation.  Cox's F test tends to be more powerful than Gehan's generalized Wilcoxon test when:

(1)  Sample sizes are small (i.e., n per group less than 50);

(2)  If samples are from an exponential or Weibull distribution;

(3)  If there are no censored observations (see Gehan & Thomas, 1969).

Lee, Desu, and Gehan (1975) compared Gehan's test to several alternatives and showed that the Cox-Mantel test and the log-rank test are more powerful (regardless of censoring) when the samples are drawn from a population that follows an exponential or Weibull distribution; under those conditions there is little difference between the Cox-Mantel test and the log-rank test.  Lee (1980) discusses the power of different tests in greater detail.


Comparing Samples Introductory Overview - Multiple Sample Test

  Survival & Failure Time Analysis Comparing Samples Introductory Overview - Multiple Sample Test

The multiple-sample test implemented in Survival Analysis is an extension (or generalization) of Gehan's generalized Wilcoxon test, Peto and Peto's generalized Wilcoxon test, and the log-rank test.  First, a score is assigned to each survival time using Mantel's procedure (Mantel, 1967); next a Chi-square value is computed based on the sums (for each group) of this score.  If only two groups are specified, then this test is equivalent to Gehan's generalized Wilcoxon test, and the computations will default to that test in this case.


Comparing Samples Introductory Overview - Unequal Proportions of Censored Data

  Survival & Failure Time Analysis Comparing Samples Introductory Overview - Unequal Proportions of Censored Data

When comparing two or more groups it is very important to examine the number of censored observations in each group.  Particularly in medical research, censoring can be the result of, for example, the application of different treatments: patients who get better faster or get worse as the result of a treatment may be more likely to drop out of the study, resulting in different numbers of censored observations in each group.  Such systematic censoring may greatly bias the results of comparisons.


  Survival Analysis - Regression Models

General Introduction

Methods

Cox's Proportional Hazard Model

Cox's Proportional Hazard Model with Time-Dependent Covariates

Exponential Regression

Normal and Log-Normal Regression

Stratified Analyses


Regression Models - General Introduction

  Survival Analysis Regression Models - General Introduction

A common research question in medical, biological, or engineering (failure time) research is to determine whether or not certain continuous (independent) variables are correlated with the survival or failure times.  There are two major reasons why this research issue cannot be addressed via straightforward multiple regression techniques (as available in Multiple Regression):  First, the dependent variable of interest (survival/failure time) is most likely not normally distributed -- a serious violation of an assumption for ordinary least squares multiple regression.  Survival times usually follow an exponential or Weibull distribution.  Second, there is the problem of censoring, that is, some observations will be incomplete (as described the Introductory Overview section).


Regression Models - Methods

  Survival Analysis Regression Models - Methods

Survival Analysis includes the five common regression models for censored survival/failure time data:

(1)	Cox's proportional hazard model;

(2)	Cox's proportional hazard model with time-dependent covariates;

(3)	Exponential regression model;

(4)	Log-normal linear regression model (which is a modification of [3]);

(5)	Normal linear regression model;

For each model, the program will compute the maximum likelihood parameter estimates and evaluate the overall goodness-of-fit.


Regression Models - Cox's Proportional Hazard Model

  Survival Analysis Regression Models - Cox's Proportional Hazard Model

The proportional hazard model is the most general of the regression models because it is not based on any assumptions concerning the nature or shape of the underlying survival distribution.  The model assumes that the underlying hazard rate (rather than survival time) is a function of the independent variables (covariates); no assumptions are made about the nature or shape of the hazard function.  Thus, in a sense, Cox's regression model may be considered to be a nonparametric method.  The model may be written as:

h{(t),(z , z ,..,z )} = h (t)*exp(b *z +...+b *z )

        1   2     m      0         1  1      m  m

where h(t,...) denotes the resultant hazard, given the values of the m covariates for the respective case (z1, z2, ..., zm) and the respective survival time (t).  The term h0(t) is called the baseline hazard; it is the hazard for the respective individual when all independent variable values are equal to zero.  We can linearize this model by dividing both sides of the equation by h0(t) and then taking the natural logarithm of both sides:

log[h{(t),(z...)}/h (t)] = b *z +...+b *z

                   0        1  1      m  m

We now have a fairly "simple" linear model that can be readily estimated.

Assumptions.  While no assumptions are made about the shape of the underlying hazard function, the model equations shown above do imply two assumptions.  First, they specify a multiplicative relationship between the underlying hazard function and the log-linear function of the covariates.  This assumption is also called the proportionality assumption.  In practical terms, it is assumed that, given two observations with different values for the independent variables, the ratio of the hazard functions for those two observations does not depend on time.  The second assumption of course, is that there is a log-linear relationship between the independent variables and the underlying hazard function.


Regression Models - Cox's Proportional Hazard Model with Time-Dependent Covariates

  Survival Analysis Regression Models - Cox's Proportional Hazard Model with Time-Dependent Covariates

An assumption of the proportional hazard model is that the hazard function for an individual (i.e., observation in the analysis) depends on the values of the covariates and the value of the baseline hazard.  Given two individuals with particular values for the covariates, the ratio of the estimated hazards over time will be constant -- hence the name of the method: the proportional hazard model.  The validity of this assumption may often be questionable.  For example, age is often included in studies of physical health.  Suppose you studied survival after surgery.  It is likely, that age is a more important predictor of risk immediately after surgery, than some time after the surgery (after initial recovery).  In accelerated life testing one sometimes uses a stress covariate (e.g., amount of voltage) that is slowly increased over time until failure occurs (e.g., until the electrical insulation fails; see Lawless, 1982, page 393).  In this case, the impact of the covariate is clearly dependent on time.  The user can specify arithmetic expressions to define covariates as functions of several variables and survival time.

Stratification.  In the case of categorical covariates, such as whether or not a patient has had surgery, Kalbfleish and Prentice (1980) recommend to perform a stratified analysis.  The Survival Analysis module allows you to fit the proportional hazard model to the data, separately for each group in a stratified analysis.  In that manner, one can explicitly allow the hazard function to be different in each group.

Testing the Proportionality Assumption.  As indicated by the previous examples, there are many applications where it is likely that the proportionality assumption does not hold.  In that case, one can explicitly define covariates as functions of time.  For example, the analysis of a data set presented by Pike (1966) consists of survival times for two groups of rats that had been exposed to a carcinogen (see also Lawless, 1982, page 393, for a similar example).  Following the notation used in Chapter 10, Volume III, Survival Analysis (page 3473), suppose that z is a grouping variable with codes 1 and 0 to denote whether or not the respective rat was exposed.  One could then fit the proportional hazard model:

h(t,z) = h (t)*exp{b *z+b *[z*log(t)-5.4]}

          0         1    2

Thus, in this model the conditional hazard at time t is a function of (1) the baseline hazard h0, (2) the covariate z, and (3) of z times the logarithm of time.  Note that the constant 5.4 is used here for scaling purposes only: the mean of the logarithm of the survival times in this data set is equal to 5.4.  In other words, the conditional hazard at each point in time is a function of the covariate and time; thus, the effect of the covariate on survival is dependent on time; hence the name time-dependent covariate.  This model allows one to specifically test the proportionality assumption.  If parameter b2  is statistically significant (e.g., if it is at least twice as large as its standard error), then one can conclude that, indeed, the effect of the covariate z on survival is dependent on time, and, therefore, that the proportionality assumption does not hold.

Specifying Time-Dependent Covariates.  The Survival Analysis module allows the user to type in arithmetic expressions to define the time-dependent covariates.  These expressions may contain all standard arithmetic and logical operators and functions, and thus a wide variety of models can be specified.  See Cox Proportional Hazard Model with Time-Dependent Covariates for additional details.

Estimating Parameters for Time-Dependent Covariates.  The Technical Notes section (see Estimating the Parameters for Time-Dependent Covariates) contains a description of the parameter estimation procedure for Cox proportional hazard regression models with time-dependent covariates.  In general, the partial likelihood (see Breslow, 1974) for these types of models is slightly modified, to reflect the respective transformation of the covariates.  As usual, the partial likelihood for a given set of parameters is the geometric sum of the likelihood across cases.  For time-dependent covariates, to compute the partial likelihood for a particular case, the program must process all cases with survival times as long or longer.  Thus, when the data set is large, these computations may require noticeably more time than those necessary to estimate models with fixed covariates only.

Categorical Variables and Coding.  The arithmetic expressions that define the covariates do not have to include references to survival time.  Instead, you may specify some functions of two or more other covariates.  This may be, for example, a convenient method for evaluating models for data collected in multi-factor experiments.  For each factor, one can create a variable in the data file to define the desired contrasts.  The logic and selection of a priori contrast coefficients is explained in detail in Chapter 7, Volume I, General ANOVA/MANOVA.  When specifying the covariates for the proportional hazard regression model, one can then type in the respective multiplications to define the interaction terms.  For example, suppose Factor A has two levels.  All individuals assigned to the first level of the factor were assigned a value of -1 in the respective variable in the data file (variable A), all individuals assigned to the second level of that factor were assigned a value of +1.  A second Factor B, also with two levels, was coded in the same manner (variable B).  One could now specify as the covariates variables A and B, and the expression A * B as a third covariate to test for the interaction between the two factors in the experiment.  However, remember that the estimation of parameters for time-dependent covariates (i.e., using expressions) can be much slower (for large files) than using simple fixed covariates; thus, it is usually easier to define the appropriately coded covariates using the STATISTICA BASIC language, and then to treat them as fixed covariates.

Segmented Time-Dependent Covariates.  When specifying the arithmetic expressions for the time-dependent covariates, you may follow the same syntax as that used for entering spreadsheet formulas for transforming individual variables in the file.  In some cases one may hypothesize that the effect of one or more covariates on the hazard is a non-continuous function of time.  For example, the hazard for a patient after surgery may depend on age during the first two days after the operation, and thereafter on some other factors.  In that case, you can use the same logical operators that are also supported in spreadsheet formulas.  For example, you could specify a time dependent covariate as:

Age * (T_ <= 2)

Note that the logical expression T_ <= 2 will evaluate to 0 (false) if the survival time for an individual is greater than 2, and to 1 (true) otherwise.  Thus, the parameter estimated for this time-dependent covariate pertains to the effect of age during the first two days only.

For more information, see Cox Proportional Hazard Model with Time-Dependent Covariates.  See also, the Estimating the Parameters for Time-Dependent Covariates.


Regression Models - Exponential Regression

  Survival Analysis Regression Models - Exponential Regression

Basically, this model assumes that the survival time distribution is exponential, and contingent on the values of a set of independent variables (zi).  The rate parameter of the exponential distribution can then be expressed as:

S(z) = exp(a + b *z +b *z +...+b *z )

                1  1  2  2      m  m

S(z) denotes the survival times, a is a constant, and the bi's are the regression parameters.

Goodness-of-fit.  The Chi-square goodness-of-fit value is computed as a function of the log-likelihood for the model with all parameter estimates (L1), and the log-likelihood of the model in which all covariates are forced to 0 (zero; L0).  If this Chi-square value is significant, we reject the null hypothesis and assume that the independent variables are significantly related to survival times.

Standard exponential order statistic.  One way to check the exponentiality assumption of this model is to plot the residual survival times against the standard exponential order statistic theta.  If the exponentiality assumption is met, then all points in this plot will be arranged roughly in a straight line.


Regression Models - Normal and Log-Normal Regression

  Survival Analysis Regression Models - Normal and Log-Normal Regression

In this model, it is assumed that the survival times (or log survival times) come from a normal distribution; the resulting model is basically identical to the ordinary multiple regression model, and may be stated as:

t = a + b *z  + b *z  + ... + b *z

         1  1    2  2          m  m

where t denotes the survival times.  If log-normal regression is requested, t is replaced by its natural logarithm.  The normal regression model is particularly useful because many data sets can be transformed to yield approximations of the normal distribution.  Thus, in a sense this is the most general fully parametric model (as opposed to Cox's proportional hazard model which is non-parametric), and estimates can be obtained for a variety of different underlying survival distributions.

Goodness-of-fit.  The Chi-square value is computed as a function of the log-likelihood for the model with all independent variables (L1), and the log-likelihood of the model in which all independent variables are forced to 0 (zero, L0).


Regression Models - Stratified Analysis

  Survival Analysis Regression Models - Stratified Analyses

The purpose of a stratified analysis is to test the hypothesis whether identical regression models are appropriate for different groups, that is, whether the relationships between the independent variables and survival are identical in different groups.  If a stratified analysis is requested, Survival Analysis will first fit the respective regression model separately within each group.  The sum of the log-likelihoods from these analyses represents the log-likelihood of the model with different regression coefficients (and intercepts where appropriate) in different groups.  The program will then fit the requested regression model to all data in the usual manner (i.e., ignoring group membership), and compute the log-likelihood for the overall fit.  The difference between the log-likelihoods is then tested for statistical significance (via the Chi-square statistic).


  Survival Analysis - Startup Panel

Essentially, the methods offered in this module address the same research questions as many of the other STATISTICA procedures; however, all methods in Survival Analysis will handle censored data (see also, Survival Analysis - Index).  The startup panel will allow you to select the desired type of analysis.

Survival and Failure Time Analysis dialog:

Life Tables and Distributions

Kaplan-Meier Product-Limit Method

Comparing Two Samples

Comparing Multiple Samples

Regression Models


  Survival Analysis Startup Panel - Life Tables and Distributions

This method is the most straightforward way to describe the survival in a sample.  This table can be thought of as an "enhanced" frequency distribution table.  The distribution of survival times is divided into a certain number of intervals.  For each interval we can then compute the number and proportion of cases or objects that entered the respective interval "alive," the number and proportion of cases that failed in the respective interval (i.e., number of terminal events, or number of cases that "died"), and the number of cases that were lost or censored in the respective interval.


Survival Analysis Startup Panel - Kaplan-Meier Product Limit Method

  Survival Analysis Startup Panel - Kaplan-Meier Product-Limit Method

This method estimates the survival function directly from the continuous survival or failure times.  The advantage of the Kaplan-Meier Product-Limit method over the Life Table method (see above) for analyzing survival and failure time data is that the resulting estimates do not depend on the grouping of the data (into a certain number of time intervals).  Actually, the Product-Limit method and the life table method are identical if the intervals of the life table contain at most one observation.


  Survival Analysis Startup Panel - Comparing Two Samples

You can compare the survival or failure times in two or more samples when you select this method.


  Survival Analysis Startup Panel - Comparing Multiple Samples

The multiple-sample test implemented in Survival Analysis is an extension (or generalization) of Gehan's generalized Wilcoxon test, Peto and Peto's generalized Wilcoxon test, and the log-rank test.  When you select this method, a score is first assigned to each survival time using Mantel's procedure (Mantel, 1967); next a Chi-square value is computed based on the sums (for each group) of this score.  If only two groups are specified, then this test is equivalent to Gehan's generalized Wilcoxon test, and the computations will default to that test in this case.


  Survival Analysis Startup Panel - Regression Models

Selecting this method will allow you to choose between four different regression models:  Cox's proportional hazard regression, exponential regression, log-normal linear regression, and normal linear regression.  See Survival Analysis - Regression Models for more information on each method.


  Survival Analysis - Life Table Analysis (Raw Data)

When you select Life Tables and Distributions from the startup panel, the Life Table and Distribution of Survival Times dialog will open.  You can choose between Raw Data as the input data or a Table of Survival Times.  If you select Raw Data, then the following options will be available to you (when you select Table of Survival Times, a separate dialog will display those options, see Survival analysis - Life Table Analysis (Analyzing Tables)).

In this dialog you will be able to select one variable with survival times, or two or six variables with dates (see below); select the censoring indicator variable and the codes (or text values) used in this variable to denote whether a respective case is complete or censored (defaults are 0 and 1, respectively).

Life Table and Distribution of Survival Times dialog:

Input Data

Variables

Specifying Survival Times

Codes for complete and censored responses

Compute Table Based On

Correct Intervals Containing no Terminations/Deaths


Life Table Analysis (Raw Data) - Input Data

  Survival Analysis Life Table Analysis (Raw Data) - Input Data

The Life Tables and Distributions routine in Survival Analysis will accept as input both Raw Data as well as Tables of Survival Times.


Life Table Analysis (Raw Data) - Variables

  Survival Analysis Life Table Analysis (Raw Data) - Variables

This button will bring up a standard variable selection window for specifying (1) the variable(s) with the survival times and (2) the censoring indicator variable.


Life Table Analysis (Raw Data) - Specifying Survival Times

  Survival Analysis Life Table Analysis (Raw Data) - Specifying Survival Times

There are two ways for specifying survival times.  Either select one variable with survival times (e.g., the number of weeks, days, years, etc. surviving) or select variables containing dates (either 2 variables or 6 variables, see Dates).  Specifically, these variables should contain the month (1 to 12), day (1 to 31), and year when the particular observation began (e.g., when the patient was admitted to the hospital), and the month, day, and year when the observation was terminated (due to death/failure or censoring, for example, when a patient was dismissed from the hospital).  The six variables containing these dates must be specified in exactly this order (month, day, year at entry; month, day, year at termination).  While processing the data, Survival Analysis will compute the number of days that elapsed between dates, and perform the analysis on this measure.  Note that if the value of the year is less than 100, the program will automatically assume that the year refers to the 20th century; for example, the year 88 would be converted into 1988.

The censoring indicator is the variable containing integer codes or text values that uniquely identify complete and censored observations.


Life Table Analysis (Raw Data) - Codes for Complete and Censored Responses

  Survival Analysis Life Table Analysis (Raw Data) - Codes for Complete and Censored Responses

Specify the codes or text values that were used in the censoring indicator variable to uniquely identify complete (uncensored) and incomplete (censored) observations.  To review all codes in the respective variable, double-click on the respective edit box.  The default codes for uncensored and censored data are 0 and 1, respectively.


Life Table Analysis (Raw Data) - Compute Table Based On

  Survival Analysis Life Table Analysis (Raw Data) - Compute Table Based On

Number of intervals:  This option allows you to determine the number of intervals for the life table.  Instead of selecting a particular number of intervals, you can also use option:

Step size (Interval width):  Via this option you can specify the step size that is to be used for tabulating the survival times.


Life Table Analysis (Raw Data) - Correct Intervals Containing No Terminations/Deaths

  Survival Analysis Life Table Analysis (Raw Data) - Correct Intervals Containing No Terminations/Deaths

This check box determines whether intervals in which there are no deaths/terminations will be adjusted so that survival distributions can be fitted.  Parameters cannot be computed for intervals where no deaths/terminations occur; by default (box is checked) the proportion surviving in those intervals is therefore adjusted by the program (the proportion surviving is set to .5/number exposed).  Do not check this box (do not adjust) when generating a life table for descriptive purposes only.


Survival Analysis - Life Table Analysis (Analyzing Tables)

  Survival Analysis - Life Tables and Distributions (Analyzing Tables)

When you select Life Tables and Distributions from the startup panel, the Life Table and Distribution of Survival Times dialog will open.  You can choose between Raw Data as the input data or a Table of Survival Times.  If you select Table of Survival Times, then the following options will be available to you (when you select Raw Data, a separate dialog will display those options, see Survival analysis - Life Table Analysis (Raw Data)).

In this dialog you can specify the respective variables (see below) and the number of individuals (observations) entering the first interval.

Life Table and Distribution of Survival Times dialog:

Input Data

Variables

Correct Intervals Containing no Terminations/Deaths


Life Table Analysis (Analyzing Tables) - Input Data

  Survival Analysis Life Tables and Distributions (Analyzing Tables) - Input Data

The Life Tables and Distributions routine in Survival Analysis will accept as input both Raw Data as well as Tables of Survival Times.


Life Table Analysis (Analyzing Tables) - Variables

  Survival Analysis Life Tables and Distributions (Analyzing Tables) - Variables

This button will bring up a standard variable selection window for specifying the variables of the survival table.  Specifically, select 3 variables with the following information:

(1)	The lower limits for each time interval;

(2)	The number of individuals withdrawn alive from each interval;

(3)	The number of individuals dying in each interval.

The variables that you select here will be appropriately displayed in the statements below the Variables button.


Life Table Analysis (Analyzing Tables) - Correct Intervals Containing no Terminations/Deaths

  Survival Analysis Life Tables and Distributions (Analyzing Tables) - Correct Intervals Containing no Terminations/Deaths

This check box determines whether intervals in which there are no deaths/terminations will be adjusted so that survival distributions can be fitted.  Parameters cannot be computed for intervals where no deaths/terminations occur; by default (box is checked) the proportion surviving in those intervals is therefore adjusted by the program (the proportion surviving is set to .5/number exposed).  Do not check this box (do not adjust) when generating a life table for descriptive purposes only.


Survival Analysis - Life Tables & Distribution Fitting Results

  Survival Analysis - Life Tables and Distribution Fitting Results

The Life Table and Survival Time Results dialog offers many options (described below) to analyze the survival data and visually display the results.

Life Table and Survival Time Results dialog:

Life Table

Model

Parameter Estimates

Estimates of Hazard, Survival Function, and Probability Density Function

Graph of Hazard, Survival Function, and Probability Density Function


Life Tables & Distribution Fitting Results - Life Table

  Survival Analysis Life Tables and Distributions & Distribution Fitting Results - Life Table

Clicking on this button will bring up a Scrollsheet with the complete life table.  In addition to the standard descriptive statistics, this Scrollsheet will contain estimates of the cumulative survival, the hazard rate, survival probability density, and the median life expectancy at each interval (see the Introductory Overview section for a definition of these estimates).  The standard errors of these estimates are also computed.


Life Tables & Distribution Fitting Results - Model

  Survival Analysis Life Tables and Distributions & Distribution Fitting Results - Model

The Life Tables and Distributions routine in Survival Analysis will automatically fit to the data the four common theoretical distributions of survival times:  Exponential, Weibull, Gompertz, and Linear Hazard (see the Introductory Overview section).  This combo box allows the user to choose between these distributions, that is, the setting of this box will determine the output (parameters, graphs) displayed after selecting other options in this dialog.


Life Tables & Distribution Fitting Results - Parameter Estimates

  Survival Analysis Life Tables and Distributions & Distribution Fitting Results - Parameter Estimates

This option will bring up a Scrollsheet with the parameter estimates for the respective theoretical survival distribution.  The particular model (theoretical distribution) to which the parameter estimates pertain can be chosen via the Model combo box.  Survival Analysis will fit the theoretical distributions via ordinary unweighted least squares (i.e., all weights equal to 1), and two methods of weighted least squares.


Life Tables & Distribution Fitting Results - Estimates of Hazard, Survival Function, and Probability Density Function

  Life Tables and Distributions & Distribution Fitting Results - Estimates of Hazard, Survival, and Probability Density Functions

Choosing any of these output options will bring up a Scrollsheet with the respective estimates for each time interval, based on the respective theoretical distribution.  The particular model (theoretical distribution) to which the parameter estimates pertain can be chosen via the option Model combo box.  Estimates based on the unweighted and two weighted least squares methods will be reported in the Scrollsheet.


Life Tables & Distribution Fitting Results - Graph of Hazard, Survival Function, and Probability Density Function

  Life Tables and Distributions & Distribution Fitting Results - Graph of Hazard, Survival, and Probability Density Functions

Choosing any of the graphics output options will bring up a graph of the respective estimated function, and the actual observed data.  The particular model (theoretical distribution) to which the estimated functions pertain can be chosen via the option Model combo box.


  Kaplan-Meier Product-Limit Analysis

When you select Kaplan & Meier Product-Limit Method from the startup panel, the Product-Limit (Kaplan & Meier) Analysis dialog will open in which you can specify the respective variables (see below) for the analysis.

Product-Limit (Kaplan & Meier) Analysis dialog:

Variables

Codes for Complete and Censored Responses


  Kaplan-Meier Product-Limit Analysis - Variables

Clicking the Variables button will bring up a standard variable selection window for specifying (1) the variable(s) with the survival times and (2) the censoring indicator variable.

Specifying survival times:  There are two ways of specifying survival times.  Either select one variable with survival times (e.g., number of weeks surviving) or select six variables containing dates.  Specifically, these variables should contain the month (1 to 12), day (1 to 31), and year when the particular observation began (e.g., when the patient was admitted to the hospital), and the month, day, and year when the observation was terminated (due to death/failure or censoring, e.g., when a patient was dismissed from the hospital).  While processing the data, Survival Analysis will compute the number of days that elapsed between dates, and perform the analysis on this measure.  Note that if the value of the year is less than 100, the program will automatically assume that the year refers to the 20th century; for example, the year 88 would be converted into 1988.

Censoring indicator variable:  This variable should contain the integer codes or text values that uniquely identify complete and censored observations.


  Kaplan-Meier Product-Limit Analysis - Codes for Complete and Censored Responses

Specify the codes or text values that were used in the censoring indicator variable to uniquely identify complete (uncensored) and incomplete (censored) observations.  To review all codes in the respective variable, double-click on the respective edit box.  The default codes for uncensored and censored observations are 0 and 1, respectively.


  Kaplan-Meier Product-Limit Analysis - Results

The Product-Limit (Kaplan-Meier) Analysis Results dialog offers many options (described below) to analyze the survival data and visually display the results.

Product-Limit (Kaplan-Meier) Analysis Results dialog:

Product-Limit Survival Analysis

Percentiles of the Survival Function

Graphs of Survival Functions


  Kaplan-Meier Product-Limit Analysis Results - Product-Limit Survival Analysis

Clicking on this button will bring up a Scrollsheet with the Product-Limit (Kaplan-Meier) estimates of the cumulative survival curve.  Note that censored observations are marked by a + (plus) sign next to the survival times displayed in the left-most column of the Scrollsheet.


  Kaplan-Meier Product-Limit Analysis Results - Percentiles of the Survival Function

This option will bring up a Scrollsheet with estimates of the 25th, 50th, and 75th percentile of the survival function.  Note that the program will interpolate values if the respective quartile boundary is not exactly defined by an uncensored case.


  Kaplan-Meier Product-Limit Analysis Results - Graphs of Survival Functions

Choosing any of the graphics output options will bring up a graph of the survival function, that is, a plot of cumulative survival across time, a plot of cumulative survival versus the natural logarithm (log) of the survival times, or a plot of the log cumulative survival versus the log of the survival times.  In these plots, the observed survival times are indicated by circles, and the censored observations are marked as crosses.  This graph can also be produced for two and multiple sample comparison tests.


  Survival Analysis - Comparing Two Groups

When you select Comparing Two Samples from the startup panel, the Comparing Survival in Two Groups dialog will open in which you can specify the respective variables (see below) for the analysis.

Comparing Survival in Two Groups dialog:

Variables

Variable with Group Codes

Codes for Complete and Censored Responses

Codes for First and Second Group


  Survival Analysis Comparing Two Groups - Variables

This option will bring up a standard variable selection window for specifying (1) the variable(s) with the survival times, (2) the censoring indicator variable, and (3) the grouping variable.

Specifying survival times:  There are two ways of specifying survival times.  Either select one variable with survival times (e.g., number of weeks surviving) or select six variables containing dates.  Specifically, these variables should contain the month (1 to 12), day (1 to 31), and year when the particular observation began (e.g., when the patient was admitted to the hospital), and the month, day, and year when the observation was terminated (due to death/failure or censoring, e.g., when a patient was dismissed from the hospital).  While processing the data, Survival Analysis will compute the number of days that elapsed between dates, and perform the analysis on this measure.  Note that if the value of the year is less than 100, the program will automatically assume that the year refers to the 20th century; for example, the year 88 would be converted into 1988.

Variable with censoring indicator:  This variable should contain the integer codes or text values that uniquely identify complete and censored observations.


  Survival Analysis Comparing Two Groups - Variable with Group Code

This variable should contain the integer codes or text values that uniquely identify to which group (sample) each observation belongs.


Survival Analysis Comparing Two Groups - Code for Complete and Censored Response

  Survival Analysis Comparing Two Groups - Codes for Complete and Censored Response

Specify the codes or text values that were used in the censoring indicator variable to uniquely identify complete (uncensored) and incomplete (censored) observations.  To review all codes in the respective variable, double-click on the respective edit box.  The default codes for uncensored and censored observations are 0 and 1, respectively.


Survival Analysis Comparing Two Groups - Code for First and Second Group

  Survival Analysis Comparing Two Groups - Codes for First and Second Group

Specify the codes or text variables that were used in the grouping variable to uniquely identify to which one of the two groups each observation belongs.  To review all codes in the respective variable, double-click on the respective edit box.


  Comparing Survival in Two Groups - Results

Survival Analysis will compute five different nonparametric tests for comparing the survival function in two groups.  Brief descriptions of these methods are provided in the Introductory Overview section.

Two-Sample Tests dialog:

Gehan's Wilcoxon Test

Cox's F test

Cox-Mantel Test

Log-rank Test

Peto & Peto's Wilcoxon Test

Display Proportion Surviving for Each Group

Graph of Proportion Surviving for Each Group

Graph of Cumulative Proportion Surviving for Each Group


  Comparing Survival in Two Groups Results - Gehan's Wilcoxon Test

This option will bring up a Scrollsheet with the results of Gehan's Wilcoxon test.  In addition to the Gehan-Wilcoxon test statistic, the Scrollsheet will list all observations (survival times; note that censored observations are marked by a + sign), the group to which each belongs, the number of observations that are smaller than the respective observation (under the column header R1), and the number of observations that are larger than the respective observation (under the column header R2).


  Comparing Survival in Two Groups Results - Cox's F Test

This option will bring up a Scrollsheet with the results of the Cox's F test.  In addition to the F test, the Scrollsheet will list all distinct failure times, the number of observations at risk at the respective failure time (under the column header R[I]), the multiplicity of each distinct failure time (under the header M[I]), the ratio of the two, and the Kaplan-Meier product-limit estimate of the survival function (in the right-most column of the Scrollsheet).


  Comparing Survival in Two Groups Results - Cox-Mantel Test

This option will bring up a Scrollsheet with the results of the Cox-Mantel test.  In addition to the Cox-Mantel test statistic, the Scrollsheet will list the risk set at each failure time (the number of observations whose failure time are at least this long or longer), and the proportion of observations in group 2 that belong to the respective risk set.


  Comparing Survival in Two Groups Results - Log-rank Test

This option will bring up a Scrollsheet with the results of the log-rank test.  In addition to the log-rank test statistic, the Scrollsheet will list all observations (survival times; note that censored observations are marked by a + sign), the group to which each case belongs, and the scores that are used in the computation of this test.


  Comparing Survival in Two Groups Results - Peto & Peto's Wilcoxon Test

This option will bring up a Scrollsheet with the results of Peto & Peto's Wilcoxon test (Peto & Peto, 1972; see also Lee, 1980).  In addition to the test statistic, the Scrollsheet will list all observations (survival times; note that censored observations are marked by a + sign), the group to which each belongs,  and the scores that are used in the computation of this test.


  Comparing Survival in Two Groups Results - Display Proportion Surviving for each Group

This option will bring up a Scrollsheet with the comparative life tables for the two groups.


  Comparing Survival in Two Groups Results - Graph of Proportion Surviving for each Group

This option will bring up a graph of the survival function for each group.


  Comparing Survival in Two Groups Results - Graph of Cumulative Proportion Surviving for each Group

This option will bring up a graph of the cumulative survival function for each group.


  Survival Analysis - Comparing k Groups

When you select Comparing Multiple Samples from the startup panel, the Comparing Survival in Multiple Groups dialog will open in which you can specify the respective variables (see below) for the analysis.

Comparing Survival in k Groups dialog:

Variables

Variable with Group Codes

Codes for Complete and Censored Responses

Codes (for groups)


  Survival Analysis Comparing k Groups - Variables

This option will bring up a standard variable selection window for specifying (1) the variable(s) with the survival times, (2) the censoring indicator variable, and (3) the grouping variable.

Specifying survival times:  There are two ways of specifying survival times.  Either select one variable with survival times (e.g., number of weeks surviving) or select six variables containing dates.  Specifically, these variables should contain the month (1 to 12), day (1 to 31), and year when the particular observation began (e.g., when the patient was admitted to the hospital), and the month, day, and year when the observation was terminated (due to death/failure or censoring, e.g., when a patient was dismissed from the hospital).  While processing the data, Survival Analysis will compute the number of days that elapsed between dates, and perform the analysis on this measure.  Note that if the value of the year is less than 100, the program will automatically assume that the year refers to the 20th century; for example, the year 88 would be converted into 1988.

Variable with censoring indicator:  This variable should contain the integer codes or text values that uniquely identify complete and censored observations.


  Survival Analysis Comparing k Groups - Variable with Group Code

This variable should contain the integer codes or text values that uniquely identify to which group (sample) each observation belongs.


  Survival Analysis Comparing k Groups - Codes for Complete and Censored Response

Specify the codes or text values that were used in the censoring indicator variable to uniquely identify complete (uncensored) and incomplete (censored) observations.  To review all codes in the respective variable, double-click on the respective edit box.  The default codes for uncensored and censored observations are 0 and 1, respectively.


  Survival Analysis Comparing k Groups - Codes for Groups

Specify the codes or text variables that were used in the grouping variable to uniquely identify to which one of the two groups each observation belongs.  To review all codes in the respective variable, double-click on the respective edit box.


  Survival Analysis - Comparing k Groups, Results

Several options (described below) are available in the Comparing Survival in Multiple Groups Results dialog.

Comparing Survival in Multiple Groups Results dialog:

Survival Times and Scores

Scores for Each Group

Percent Surviving in each Group

Descriptive Statistics

Plot Histogram of the Sum of Scores for Each Group

Plot Percent Surviving in each Group

Plot Cumulative Percent Surviving in each Group


Comparing k Groups, Results - Survival Times and Scores

  Survival Analysis Comparing k Groups, Results - Survival Times and Scores

This option will bring up a Scrollsheet with all survival times (note that censored observations are marked by a + sign) and the scores (computed according to Mantel's procedure; see Mantel, 1967) used for the computation of the test statistic.


Comparing k Groups, Results - Scores for Each Group

  Survival Analysis Comparing k Groups, Results - Scores for each Group

This option will bring up a Scrollsheet with the sum of scores for each group (computed according to Mantel's procedure; see Mantel, 1967) used for the computation of the test statistic; in addition, the number and percent of complete and censored cases in each group are displayed.


Comparing k Groups, Results - Percent Surviving in Each Group

  Survival Analysis Comparing k Groups, Results - Percent Surviving in each Group

This option will bring up the life tables for each group.  Note that you can use the Scrollsheet Manager option from the Window pull-down menu to adjust the number of Scrollsheets that can simultaneously be displayed on the screen.


Comparing k Groups, Results - Descriptive Statistics

  Survival Analysis Comparing k Groups, Results - Descriptive Statistics

This option will bring up a Scrollsheet with descriptive statistics for each group, and for all groups combined.  These statistics are computed according to the standard formulas (disregarding censoring), and include the mean and median survival times in each group.


Comparing k Groups, Results - Plot Histogram of the Sum of Scores for each Group

  Survival Analysis Comparing k Groups, Results - Plot Histogram of the Sum of Scores for each Group

This option will bring up a histogram of the sum of scores for each group (computed according to Mantel's procedure, Mantel, 1967) used for the computation of the test statistic.


Comparing k Groups, Results - Plot Porportion Surviving in each Group

  Survival Analysis Comparing k Groups, Results - Plot Proportion Surviving in each Group

This option will bring up a graph of the survival function for each group.


Comparing k Groups, Results - Plot Cumulative Proportion Surviving in each Group

  Survival Analysis Comparing k Groups, Results - Plot Cumulative Proportion Surviving in each Group

This option will bring up a graph of the cumulative survival function for each group.


  Survival Analysis - Regression Models

When you select Regression Models from the startup panel, the Regression Models for Censored Data dialog will open in which you can specify the respective variables (see below) for the analysis.

Regression Models for Censored Data dialog:

Model

Variables

Codes for complete and censored responses

Codes (for groups)

Equal Coefficients, different baseline h0


Regression Models - Equal Coefficients, Different Baseline h0

  Survival Analysis Regression Models - Equal Coefficients, Different Baseline h0

This option is only available if (1) the current Model is Proportional hazard (Cox) regression and (2) after you selected a stratification (grouping) variable.  If this checkbox is set, then the program will fit a stratified model with constant coefficient vector for each group, but allowing for different baseline hazard (h0) in each group.  In effect, observations in the same group (stratum) are assumed to have proportional hazard functions, but this is not necessarily the case for observations in different groups.  If this checkbox is de-selected, then the program will allow for different baseline hazards as well as coefficient vectors in each group.  For more information about stratification of proportional hazard models, see Lawlass (1982, page 365).


Regression Models - Model

  Survival Analysis Regression Models - Model

This combo box allows you to choose between the five different regression models available in Survival Analysis: Cox's proportional hazard regression, Cox's proportional hazard regression with time-dependent covariates, exponential regression, log-normal linear regression, and normal linear regression (see Regression Models).  If you select the Prop. hazard (Cox) /w time-dep. covariates option, then the Cox Proportional Hazard Model with Time-Dependent Covariates dialog will open.


Regression Models - Variables

  Survival Analysis Regression Models - Variables

Clicking on this button will bring up a standard variable selection window for specifying (1) the variable(s) with the survival times, (2) a list of independent variables (covariates), (3) the censoring indicator variable, and (4) an optional grouping variable (for a stratified, by-group analysis).

Specifying survival times:  There are two ways of specifying survival times.  Either select one variable with survival times (e.g., number of weeks surviving) or select six variables containing dates.  Specifically, these variables should contain the month (1 to 12), day (1 to 31), and year when the particular observation began (e.g., when the patient was admitted to the hospital), and the month, day, and year when the observation was terminated (due to death/failure or censoring, e.g., when a patient was dismissed from the hospital).  While processing the data, Survival Analysis will compute the number of days that elapsed between dates, and perform the analysis on this measure.  Note that if the value of the year is less than 100, the program will automatically assume that the year refers to the 20th century; for example, the year 88 would be converted into 1988.

Variable with censoring indicator:  This variable should contain the integer codes or text values that uniquely identify complete and censored observations.

Variable with group codes:  This optional variable should contain the integer codes or text values that uniquely identify to which group (sample) each observation belongs.  If no grouping variable is specified, a regular analysis will be performed on all data.  If a variable is specified here, then a stratified analysis will be performed.  In a stratified analysis, separate regression models are first fit to each group and the log-likelihoods for those models are summed up.  This log-likelihood is then compared to that of the overall model (collapsed across groups).


Regression Models - Codes for Complete and Censored Responses

  Survival Analysis Regression Models - Codes for Complete and Censored Responses

Specify the codes or text values that were used in the censoring indicator variable to uniquely identify complete (uncensored) and incomplete (censored) observations.  To review all codes in the respective variable, double-click on the respective edit box.  The default codes for uncensored and censored observations are 0 and 1, respectively.


Regression Models - Codes for Groups

  Survival Analysis Regression Models - Codes for Groups

These codes can only be specified if a stratified (by-group) analysis was requested, that is, when a grouping variable was selected.  Specify the codes or text variables that were used in the grouping variable to uniquely identify to which one of the groups each observation belongs.  To review all codes in the respective variable, double-click on the respective edit box.


  Survival Analysis - Setting Parameters for Estimation

You can set the parameters for the regression model estimation in the Regression Model Estimation dialog.

Regression Model Estimation dialog:

Maximum Number of Iterations

Convergence Criterion

Start Values

Missing Data Deletion

Review Expressions for Time-Dependent Covariates


Setting Parameters for Estimation - Maximum Number of Iterations

  Survival Analysis Setting Parameters for Estimation - Maximum Number of Iterations

The estimation of the maximum likelihood parameters is an iterative procedure; this option allows the user to specify the maximum number of iterations (default is 50).


Setting Parameters for Estimation - Convergence Criteria

  Survival Analysis Setting Parameters for Estimation - Convergence Criteria

The iterative estimation procedure will terminate when either the maximum number of iterations has been exceeded, or when the change in the parameter estimates from iteration to iteration does not exceed the convergence criterion.  The smaller the value of the convergence criterion, the more iterations will be performed by the program (within the limits of the maximum number of iterations).


Setting Parameters for Estimation - Start Values

  Survival Analysis Setting Parameters for Estimation - Start Values

This option is only available if the Cox's proportional hazard regression model was requested on the previous dialog.  Click on this button to specify parameter values to be used in the first iteration of the parameter estimation procedure.


Setting Parameters for Estimation - Missing Data Deletion

  Survival Analysis Setting Parameters for Estimation - Missing Data Deletion

There are two ways to handle missing data:  Missing data may either be casewise deleted, or substituted by means.


Setting Parameters for Estimation - Review Expressions for Time-Dependent Covariates

  Survival Analysis Setting Parameters for Estimation - Review Expressions for Time-Dependent Covariates

Click on this button in order to bring up a Scrollsheet containing the expressions for time-dependent covariates which were specified in the Cox Proportional Hazard Modes with Time-Dependent Covariates dialog.


  Survival Analysis - Cox Proportional Hazard Regression Model with Time-Dependent Covariates

This dialog will come up when you select Regression Models from the Survival Analysis startup panel, and then set the Model combo box to Prop. hazard (Cox) /w time-dep. covariates in the Regression Models for Censored Data dialog.  On this dialog you can specify the dependent variable for the analysis, the censoring indicator, an optional stratification (grouping) variable, and the time-dependent covariates.  The syntax rules for the arithmetic expressions defining the time-dependent covariates are similar to those for the spreadsheet formulas.

Cox Proportional Hazard Regression Model with Time-Dependent Covariates dialog:

Model

Variables (Survival Times, Censoring, [Optional] Grouping)

Codes for Complete and Censored Responses

Independent Variables (Covariates)

Delete highl. expression

Select variables

Open expressions

Save expressions

Codes (for Groups)


  Cox Proportional Hazard Regression Model with Time-Dependent Covariates - Model

This combo box allows you to choose between the five different regression models available in Survival Analysis.  When this combo box is set to Prop. hazard (Cox) /w time-dep. covariates, then this dialog will be displayed.


  Cox Proportional Hazard Regression Model with Time-Dependent Covariates - Variables

Clicking on this button will bring up a standard variable selection window for specifying:

(1) 	The variable(s) with the survival times,

(2) 	The censoring indicator variable, and

(3) 	An optional grouping variable (for a stratified by-group analysis).

Use the edit fields in the Independent variables (covariates) box to specify the independent variables for the analysis.


Cox Proportional Hazard Regression Model with Time-Dependent Covariates - Code for Complete and Censored Response

  Cox Proportional Hazard Regression Model with Time-Dependent Covariates - Codes for Complete and Censored Response

Specify the codes or text values that were used in the censoring indicator variable to uniquely identify complete (uncensored) and incomplete (censored) observations.  To review all codes in the respective variable, double-click on the respective edit box.  The default codes for uncensored and censored observations are 0 and 1, respectively.


  Cox Proportional Hazard Regression Model with Time-Dependent Covariates - Independent Variables (Covariates)

Use the two edit lists to specify the covariates in the model.  In the left edit field, under the header Covariate, enter a label for the covariate; that label will be used in the results Scrollsheets.  Use the Expression edit field to define the respective covariate by entering an arithmetic expression.

Syntax.  The syntax rules for the expressions are identical to those for spreadsheet formulas.  In addition to the available arithmetic operators and functions, the expression interpreter will also recognize the symbol t_ or T_ (i.e., letter t and the underscore) to denote the survival times.  By using this symbol, you can define time-dependent covariates.  Shown below are a few examples:

Covariate = Expression

---------   --------------------------------

timdep      v2*(log(t_)-5.4); time-dependent

Covar2      Age*(Group=1) - Age*(Group=2)

FactorA     FactorA

FactorB     FactorB

AXB         FactorA*FactorB

As illustrated in the first example (timdep = ... ), you may include comments in the expressions by placing them after the expressions, separated by a semicolon.  Variables may be referenced by name, or via the standard Vxxx convention where xxx is the respective variable number in the data file.  The second expression illustrates the use of logical operators:  If a case belongs to Group 1 (where Group is a variable name), then Covar2 is defined as +Age; if a case belongs to Group 2, then Covar2 is defined as -Age.  The third and fourth expressions define the fixed covariates FactorA and FactorB; the fifth expression defines their interaction.  Note that in the examples above, only the first expression actually defines a time-dependent covariate; while the others make no reference to the survival times (i.e., they do not include the symbol t_ or T_).

Editing expressions.  To edit expressions, you can highlight them, and then either double-click on them or press F2 to place the cursor in the respective field.  The standard Windows conventions for copying (CTRL+C) and pasting (CTRL+V) are also supported.  You can use the arrow keys to move up and down through the list of expressions.  To add an expression, use the INS (Insert) key on your keyboard; to delete an expression, highlight it and then click on the Delete highl. expression button, or use the DEL key on the keyboard.  Note that you can also save the expressions, and later use them in future analyses.


  Cox Proportional Hazard Regression Model with Time-Dependent Covariates - Delete Highl. Expression

Use this button to delete the highlighted expression.


  Cox Proportional Hazard Regression Model with Time-Dependent Covariates - Select Variables

When you click on this button, a standard variable selection dialog will come up.  The variables (i.e., their names) that you select in this dialog will be moved to both the left edit box (as the Covariate labels) and the right edit box (as the Expression).  Thus, by default the selected variables will be defined as fixed covariates.


  Cox Proportional Hazard Regression Model with Time-Dependent Covariates - Open Expressions

When you click on this button, a file selection dialog will come up where you can select a previously saved file with the expressions.  Those files are by default saved with the file name extension *.ini.  Note that the program will automatically append the expressions in the file to the ones that were previously entered.

Workbook options.   Note that if you do not remember the name (of the file) under which you saved the previous expressions for the current data set, then you can retrieve the name from the Workbook list available in every Open/Save dialog.


  Cox Proportional Hazard Regression Model with Time-Dependent Covariates - Save Expressions

Use this option to save the current expressions in a file; by default the program will suggest the file name extension *.ini.


  Cox Proportional Hazard Regression Model with Time-Dependent Covariates - Codes for Groups

These codes can only be specified if a stratified (by-group) analysis was requested, that is, if a grouping variable was selected.  Specify the codes or text values that were used in the grouping variable to uniquely identify to which of the groups each observation belongs.


  Regression Models for Survival Data - Results

After you have set the parameters for the regression model estimation in the Regression Model Estimation dialog and the iterative procedure is complete, the Regression Results dialog will open.

Regression Results dialog:

Parameter Estimates

Parameter Variance/Covariance Matrix

Stratified Analysis

Means & Standard Deviations

Graphs


  Regression Models for Survival Data Results - Parameter Estimates

This option will bring up a Scrollsheet with parameter estimates, their standard errors, the ratio of the parameter estimates divided by their standard errors (under the heading t-value), and the Wald statistic (which for large samples has a Chi-square distribution under the null hypothesis that the coefficient is equal to 0).  Note that the standard errors (and t-values) are computed from the second order partial derivatives of the log-likelihood function, resulting in asymptotic standard errors (and t-values) for the parameters.


  Regression Models for Survival Data Results - Parameter Variance/Covariance Matrix

This option will bring up two Scrollsheets, one with the variance/covariance matrix of the parameter estimates and one with the correlation matrix.


  Regression Models for Survival Data Results - Stratified Analysis

This option is only available if a stratified analysis (analysis by groups) was requested.  Clicking on this button will bring up a Scrollsheet with the results of the stratified analysis; specifically, the Scrollsheet will show the sum of the log-likelihoods of the model, fitted within each group, and the log-likelihood of the model fitted to all observations combined.

In order to examine the parameter estimates for a particular group, specify the appropriate case selection conditions (i.e., select only cases belonging to the group of interest), and then fit the respective model in the usual manner.


  Regression Models for Survival Data Results - Means and Standard Deviations

This option will bring up a Scrollsheet with the means and standard deviations for the survival times and the independent variables (covariates).


  Regression Models for Survival Data Results - Graphs

The graphs that are available from the Regression Results dialog depend on the currently selected regression model.  The following paragraphs describe the graphs for each of the models.

Cox's Proportional Hazard Model:

Graph of survival function for mean values of covariates:  This option will bring up a graph of the survival function when the values for the independent variables (covariates) are at their respective means.

Graph survival for user-defined values of the independent variables:  This option allows the user to specify values for the independent variables (covariates); the survival function will then be drawn based on those values.

Exponential Regression Model:

Graph of residuals vs. exponential order statistic (alpha):  This option will bring up a scatterplot of the residual survival times and the standard exponential order statistic.  If all points are arranged roughly on a straight line, then the data are consistent with the assumption of exponentiality.

Graph of residual vs. predicted survival times:  This option will bring up a scatterplot of the residual versus predicted survival times.

Graph of residuals vs. log-survival times:  This option will bring up a scatterplot of the residual survival times versus the observed log-survival times.

Normal and Log-Normal Regression Models:

Graph of observed vs. predicted survival times:  This option will bring up a scatterplot of the observed survival times and the estimated survival times.

Graph of predicted vs. residual survival times:  Pressing this button will bring up a scatterplot of the predicted versus residual survival times.

Normal probability plot of residuals:  This option will bring up a normal probability plot of the residual survival times.  If the residual survival times (or log-survival times) are normally distributed, all plotted points in this graph should be arranged roughly in a straight line.


Proportional Hazard (Cox) Regression - Start Values

  Proportional Hazard (Cox's) Regression - Start Values

An iterative procedure is used to estimate the parameters for the proportional hazard regression model.  In this dialog window you can specify the parameter values that are to be used in the first iteration of the computations.


  Proportional Hazard Regression - Graph of Survival

Specify the desired values for the independent variables.  The program will then compute and draw the respective survival function based on those values.


  Survival Analysis - Notes and Technical Information

Life Table

The life table technique is one of the oldest methods for analyzing survival (failure time) data (e.g., see Berkson & Gage, 1950; Cutler & Ederer, 1958; Gehan, 1969).  In order to arrive at reliable estimates of the three major functions (survival, probability density, and hazard), the minimum recommended sample size is 30 (see Lee, 1980).  The life table estimates are computed according to standard formulas as described in Lawless (1982), Lee (1980), Nelson (1982), and others (refer also to the Introductory Overview).

Specifying tabulated survival data as input:  The life table routine in Survival Analysis will accept already tabulated data as input.  For example, suppose we had 750 observations in a study, and have already tabulated the survival times in the following manner:

Var_1:      Var_2:        Var_3:

--------    ----------    ----------

Interval    No. of Obs.   No. of Obs.

 Start       Censored       Failed

------------------------------------

   0            10           185

   1            10            88

   2            10            55

   3            10            43

   4            14            32

   5            52            31

   6            38            20

   7            24             7

   8            25             6

   9            24             6

In the Life Table & Distribution of Survival Time, we would first set the Input data option to Table of survival times.  Then we would specify the three variables in exactly this order (1-3) in the variable selection window (click on the Variables button).  Finally, we would enter the number of observations at the beginning of the study (that entered the first interval) via the edit box in this dialog.

Fitting Theoretical Survival Distribution

The regression procedure for fitting the four theoretical distributions to the life table is based on algorithms proposed by Kennedy and Gehan (1971), and discussed in detail in Lee (1980).  Basically, the hazard functions (specifically, the logarithmic transforms of the hazard functions) of all four theoretical distributions are linear functions of the survival times (or log-survival times).  Thus, the hazard functions [h(t)] may be expressed in terms of linear regression functions as:

1. h(t) = L           Exponential

              g-1

2. h(t) = Lg*t        Weibull

3. h(t) = exp(L+g*t)  Gompertz

4. h(t) = L+g*t       Linear exponential

If we set y=h(t) or y=log h(t), then all four models can be stated in the general form:

y = a + b*x

Weighted least squares:  Gehan and Siddiqui (1973) suggest weighted least squares methods to fit the parameters of the respective models to the data.  Specifically, the program will minimize the quantity:

                     2

WSS = Σ(w (y -a-b*x ) )

         i  i      i

Three different weights are used in the estimation:

(1)	wi = 1 (unweighted least squares)

(2)	wi = 1/vi

(3)	wi = ni*hi

where vi is the variance of the hazard estimate, and hi and ni are the interval width and number of observations exposed to risk in the i'th interval, respectively.

Correcting intervals without terminations (deaths):  The Correct intervals containing no terminations/deaths check-box on the Life Tables and Distributions dialog determines whether intervals in which there are no deaths/terminations will be adjusted so that survival distributions can be fitted.  Parameters cannot be computed for intervals where no deaths/terminations occur; by default (box is checked) the proportion surviving in those intervals is therefore adjusted by the program (the proportion surviving is set to .5/number exposed).  De-select this option when generating a life table for descriptive purposes only.

Two Sample Tests

There are five two-sample tests that can be computed with this module, namely, Gehan's generalized Wilcoxon test (Gehan, 1965a,b, computed via Mantel's procedure; Mantel, 1967), Cox's F-test (Cox, 1964), Cox-Mantel's test (Cox 1959, 1972; Mantel, 1966), the log-rank statistic (Peto & Peto, 1972), and Peto & Peto's generalized Wilcoxon test (Peto & Peto, 1972).  All of these procedures test the statistical significance of survival in two groups.

Analyzing large samples:  Because of the nature of the algorithms used in the two-sample comparison routines, this program imposes stricter limitations on the maximum group size than other routines available in Survival Analysis.  Use the multiple sample comparison option to analyze large data sets; if only two groups are specified for the multiple sample procedure, the computations and resulting statistics will be identical to those of Gehan's generalized Wilcoxon test.

Cox's Proportional Hazard Model

The proportional hazard model (Cox, 1972) is the most general of the regression models because it does not make any assumptions about the nature or shape of the underlying survival distribution.  The model assumes that the underlying hazard rate (rather than survival time) is a function of the independent variables (covariates); thus, in a sense, Cox's regression model may be considered to be a nonparametric method.  The model may be expressed as:

h(t,z) = h (t)*exp(b'z)

          0

In the above expression h(t,z) is the hazard rate, contingent on a particular covariate vector z; h0(t) is referred to as the baseline hazard, that is, it is the hazard rate when the values for all independent variables (i.e., in z) are equal to zero; b is the vector of regression coefficients.

The program uses the Newton-Raphson method to maximize the simplified partial likelihood (proposed by Breslow, 1974):

                            d(i)

L = Π exp(b's )/[Σexp(b'z )]

             i           j

In this formula, d(i) stands for the number of cases observed to fail at time ti, si stands for the sum (over the d(i) cases observed to fail at time ti) of the covariates, zj stands for the covariate vector for a case j in the risk set at time ti.  (The geometric sum Π is over all k distinct failure times, the regular sum Σ is over all cases j∈Ri in the respective risk set Ri, that is, cases that are observed to fail at or after the respective failure time ti.)

To estimate the survival function S contingent on a particular covariate vector z, the algorithm uses the relationship:

              exp(b'z)

S(t,z) = S (t)

          0

In this formula, S0 is the baseline survival function which is independent of the covariates.  Breslow (1974) proposed the following estimator of the baseline survival function:

S (t ) = Π[1-(d/∑exp(b'z))]

 0  i

The Chi-square value is computed as a function of the log-likelihood for the model with all covariates (l1), and the log-likelihood of the model in which all covariates are forced to 0 (L0); specifically:

Chi-square = 2*(L  - L )

                 0    1

Estimating the Parameters for Time-Dependent Covariates

The method of parameter estimation for proportional hazard regression models is briefly discussed in the Technical Notes section of Chapter 10, Volume III, Survival Analysis.  To accommodate time-dependent covariates, the following modification to the simplified partial likelihood (Breslow, 1974) is introduced (see Lawless, 1982, page 393):

                                   d(i)

L = Π exp(b's(t ))/Σ[exp(b'z (t ))]

             i i            j  i

In this formula, si(ti) stands for the sum of the transformed (time-dependent) covariates observed to fail at a particular time ti, and zi(ti) stands for the transformed (time-dependent) covariate vector for a case j in the risk set at time ti, and d(i) stands for the number of cases observed to fail at time ti. (The geometric sum Π is over all cases, the regular sum Σ is over all cases in the respective risk set, that is, cases that are observed to fail at or after the respective failure time ti.)

This partial likelihood function is minimized using the Newton-Raphson method.  Note that in order to compute the likelihood for a given set of parameters, for each case i, all cases with survival times greater than or equal to that of case i have to be processed.  Thus, fitting models with time-dependent covariates may require extensive computations, particularly when there are many cases in the data file.

Wald Statistic:

The results Scrollsheet with the parameter estimates for the Cox proportional hazard regression model includes the so-called Wald statistic, and the p level for that statistic.  This statistic is based on the asymptotic normality property of maximum likelihood estimates, and is computed as:

W = β * 1/Var(β) * β

In this formula , β stands for the parameter estimates, and Var(β) stands for the asymptotic variance of the parameter estimates.  The Wald statistic is tested against the Chi-square distribution.

Exponential Regression

The regression model for censored exponential survival data has been described by Feigl and Zelen (1965), Glasser (1967), Prentice (1973), and Zippin and Armitage (1966).  The algorithm for obtaining the maximum Likelihood estimates uses the Newton-Raphson method and is based on Lagakos and Kuhns (1978).  The model assumes that the survival time distribution, contingent on the values of a covariate vector z, is exponential, and that the rate parameter can be expressed as:

L(z) = exp(a + b*z)

The Chi-square value is computed as usual, that is, as a function of the log-likelihood for the model with all covariates (L1), and the log-likelihood of the model in which all covariates are forced to 0 (zero; L0).

Computation of the standard exponential order statistic:  One way to check the exponentially assumption of this model is to plot the residual survival times against the standard exponential order statistic α (see Lawless, 1982).  Specifically, α is computed as:

α  = S(N-j+1) - 1

 i

If the exponentiality assumption is met, all points in this plot should be arranged roughly in a straight line.

Normal and log-Normal Regression

In this model, it is assumed that the survival time (or log survival times) come from a normal distribution, and that the model may be stated as:

t  = a + z *b

 i        i

where zi is the covariate vector for subject i, and a is a constant.  If log-normal regression is requested, ti is replaced by its natural logarithm.

Estimation:  The program uses a very efficient method - the so-called expectation maximization (EM) algorithm - for obtaining the maximum likelihood estimates for this model.  This algorithm was first proposed by Dempster, Laird, and Rubin (1977) and is discussed in Cox and Oakes (1984).  Specifically, Survival analysis uses routines that follow the logic developed by Wolynetz ((1979a, b).

Goodness-of-fit:  The Chi-square value is computed as usual, that is, as a function of the log-likelihood for the model with all covariates (L1), and the log-likelihood of the model in which all covariates are forced to 0 (zero; L0).  Note that the null model contains two parameters, namely maximum likelihood estimates of the variance and the mean (also estimated via the EM algorithm), and the full model contains parameters for all covariates, a constant (the intercept), and the variance.

The normal regression model is particularly useful because many data sets can be transformed to yield approximations of the normal distribution.  Thus, in a sense this is the most general fully parametric model (as opposed to Cox's proportional hazard model which is non-parametric), and estimates can be obtained for a variety of different underlying survival distributions (see Schneider, 1986, for a discussion of the normal distribution and its transforms).


Multiple Regression Analysis - Index
  Multiple Regression - Index

Introductory Overview

Startup Panel

Fixed nonlinear (and polynomial) regression

Reviewing descriptive statistics

Specifying the multiple regression analysis

Multiple regression results

Computing predicted values

Residual analysis

Stepwise multiple regression

Notes and Technical Information


Multiple Regression Analysis - Overview

  Multiple Regression Analysis - Introductory Overview

General Purpose

Computational Approach

Assumptions, Limitations, and Practical Considerations


Multiple Regression Analysis - General Purpose

  Multiple Regression Analysis Introductory Overview - General Purpose

The general purpose of multiple regression (the term was first used by Pearson, 1908) is to learn more about the relationship between several independent or predictor variables and a dependent or criterion variable.  For example, a real estate agent might record for each listing the size of the house (in square feet), the number of bedrooms, the average income in the respective neighborhood according to census data, and a subjective rating of appeal of the house.  Once this information has been compiled for various houses it would be interesting to see whether and how these measures relate to the price for which a house is sold.  For example, one might learn that the number of bedrooms is a better predictor of the price for which a house sells in a particular neighborhood than how "pretty" the house is (subjective rating).  One may also detect "outliers," that is, houses that should really sell for more, given their location and characteristics.

Personnel professionals customarily use multiple regression procedures to determine equitable compensation.  One can determine a number of factors or dimensions such as "amount of responsibility" (Resp) or "number of people to supervise" (No_Super) that one believes to contribute to the value of a job.  The personnel analyst then usually conducts a salary survey among comparable companies in the market, recording the salaries and respective characteristics (i.e., values on dimensions) for different positions.  This information can be used in a multiple regression analysis to build a regression equation of the form:

Salary = .5 * Resp + .8 * No_Super

Once this so-called regression line has been determined, the analyst can now easily construct a graph of the expected (predicted) salaries and the actual salaries of job incumbents in his or her company.  Thus, the analyst is able to determine which position is underpaid (below the regression line) or overpaid (above the regression line), or paid equitably.

In the social and natural sciences multiple regression procedures are very widely used in research.  In general, multiple regression allows the researcher to ask (and hopefully answer) the general question "what is the best predictor of ...".  For example, educational researchers might want to learn what are the best predictors of success in high-school.  Psychologists may want to determine which personality variable best predicts social adjustment.  Sociologists may want to find out which of the multiple social indicators best predict whether or not a new immigrant group will adapt and be absorbed into society.


Multiple Regression Analysis - Computational Approach

  Multiple Regression Analysis Introductory Overview - Computational Approach

The general computational problem that needs to be solved in multiple regression analysis is to fit a straight line to a number of points.  In the simplest case -- one dependent and one independent variable -- one can visualize this in a scatterplot (scatterplots can automatically be created from the Scrollsheet of correlations).

Least Squares

The Regression Equation

Unique Prediction and Partial Correlation

Predicted and Residual Scores

Residual Variance and R-square

Interpreting the Correlation Coefficient R


Multiple Regression Analysis Computational Approach - Linear Least Squares

  Multiple Regression Analysis Introductory Overview Computational Approach - Least Squares

In the scatterplot, we have an independent or X variable, and a dependent or Y variable.  These variables may, for example, represent IQ (intelligence as measured by a test) and school achievement (grade point average; GPA), respectively.  Each point in the plot represents one student, that is, the respective student's IQ and GPA.  The goal of linear regression procedures is to fit a line through the points.  Specifically, the program will compute a line so that the squared deviations of the observed points from that line are minimized.  Thus, this general procedure is sometimes also referred to as least squares estimation.


Multiple Regression Analysis Computational Approach - The Regression Equation

  Multiple Regression Analysis Introductory Overview Computational Approach - The Regression Equation

A line in a two dimensional or two-variable space is defined by the equation Y=a+b*X; in full text:  the Y variable can be expressed in terms of a constant (a) and a slope (b) times the X variable.  The constant is also referred to as the intercept, and the slope as the regression coefficient or B coefficient.  For example, GPA may best be predicted as 1+.02*IQ.  Thus, knowing that a student has an IQ of 130 would lead us to predict that her GPA would be 3.6 (since, 1+.02*130=3.6).  In the multivariate case, when there is more than one independent variable, the regression line cannot be visualized in the two dimensional space, but can be computed just as easily (via Multiple Regression; the computations are actually quite complex).  For example, if in addition to IQ we had additional predictors of achievement (e.g., Motivation, Self-discipline) we could construct a linear equation containing all those variables.  In general then, multiple regression procedures will estimate a linear equation of the form:

Y=a+b *X +b *X +...+b *X

     1  1  2  2      p  p


Multiple Regression Analysis Computational Approach - Unique Prediction and Partial Correlation

  Multiple Regression Analysis Introductory Overview Computational Approach - Unique Prediction and Partial Correlation

Note that in this equation, the regression coefficients (or B coefficients) represent the independent contributions of each independent variable to the prediction of the dependent variable.  Another way to express this fact is to say that, for example, variable X1 is correlated with the Y variable, after controlling for all other independent variables.  This type of correlation is also referred to as a partial correlation (this term was first used by Yule, 1907).  Perhaps the following example will clarify this issue.  One would probably find a significant negative correlation between hair length and height in the population (i.e., short people have longer hair).  At first this may seem odd; however, if we were to add the variable Gender into the multiple regression equation, this correlation would probably disappear.  This is because women, on the average, have longer hair than men; they also are shorter on the average than men.  Thus, after we remove this gender difference by entering Gender into the equation, the relationship between hair length and height disappears because hair length does not make any unique contribution to the prediction of height, above and beyond what it shares in the prediction with variable Gender.  Put another way, after controlling for the variable Gender, the partial correlation between hair length and height is zero.


Multiple RegressionComputational Approach - Predicted and Residual Scores

  Multiple Regression Analysis Introductory Overview Computational Approach - Predicted and Residual Scores

The regression line expresses the best prediction of the dependent variable (Y), given the independent variables (X).  However, nature is rarely (if ever) perfectly predictable, and usually there is substantial variation of the observed points around the fitted regression line (as in the scatterplot shown earlier).  The deviation of a particular point from the regression line (its predicted value) is called the residual value.


Multiple Regression Computational Approach - Residual Variance and R-square

  Multiple Regression Analysis Introductory Overview Computational Approach - Residual Variance and R-square

The smaller the variability of the residual values around the regression line relative to the overall variability, the better is our prediction.  For example, if there is no relationship between the X and Y variables, then the ratio of the residual variability of the Y variable to the original variance is equal to 1.0.  If X and Y are perfectly related then there is no residual variance and the ratio of variance would be 0.0.  In most cases, the ratio would fall somewhere between these extremes, that is, between 0.0 and 1.0.  1.0 minus this ratio is referred to as R-square or the coefficient of determination.  This value is immediately interpretable in the following manner.  If we have an R-square of 0.4 then we know that the variability of the Y values around the regression line is 1-0.4 times the original variance; in other words we have explained 40% of the original variability, and are left with 60% residual variability.  Ideally, we would like to explain most if not all of the original variability.  The R-square value is an indicator of how well the model fits the data (e.g., an R-square close to 1.0 indicates that we have accounted for almost all of the variability with the variables specified in the model).


Multiple Regression Computational Approach - Interpreting the Correlation Coefficient R

  Multiple Regression Analysis Introductory Overview Computational Approach - Interpreting the Correlation Coefficient R

Customarily, the degree to which two or more predictors (independent or X variables) are related to the dependent (Y) variable is expressed in the correlation coefficient R, which is the square root of R-square.  In multiple regression, R can assume values between 0 and 1.  To interpret the direction of the relationship between variables, one looks at the signs (plus or minus) of the regression or B coefficients.  If a B coefficient is positive, then the relationship of this variable with the dependent variable is positive (e.g., the greater the IQ the better the grade point average); if the B coefficient is negative then the relationship is negative (e.g., the lower the class size the better the average test scores).  Of course, if the B coefficient is equal to 0 then there is no relationship between the variables.


Multiple Regression Analysis - Assumptions, Limitations, Practical Considerations

  Multiple Regression Analysis Introductory Overview - Assumptions, Limitations, Practical Considerations

Assumption of Linearity

Normality Assumption

Limitations

Choice of the number of variables

Multicollinearity and matrix ill-conditioning

The importance of residual analysis


Multiple Regression-Assumptions, Limitations, Practical Considerations - Assumption of Linearity

  Multiple Regression Analysis-Assumptions, Limitations, Practical Considerations - Assumption of Linearity

First of all, as is evident in the name multiple linear regression, it is assumed that the relationship between variables is linear.  In practice this assumption can virtually never be confirmed; fortunately, multiple regression procedures are not greatly affected by minor deviations from this assumption.  However, as a rule it is prudent to always look at bivariate scatterplot of the variables of interest.  In Multiple Regression these plots are readily available from anywhere within the program by simply requesting the Scrollsheet with the correlation matrix, and then displaying the customized graph (scatterplot) for the respective highlighted cell.  If curvature in the relationships is evident, one may consider either transforming the variables (via STATISTCA BASIC or Spreadsheet Formulas), or explicitly allowing for nonlinear components.  Multiple Regression 's Fixed Nonlinear option allows you to fit various nonlinear components, that is, to test explicitly for the significance of a nonlinear component in the relationship between two or more variables (other nonlinear regression options are available in the Nonlinear Regression module).


Multiple Regression-Assumptions, Limitations, Practical Considerations - Normality Assumption

  Multiple Regression Analysis-Assumptions, Limitations, Practical Considerations - Normality Assumption

It is assumed in multiple regression that the residuals (prediced minus observed values) are distributed normally (i.e., follow the normal distribution).  Again, even though most tests (specifically the F-test) are quite robust with regard to violations of this assumption, it is always a good idea, before drawing final conclusions, to review the distributions of the major variables of interest.  In Multiple Regression one can produce a histogram (with the normal curve superimposed) from within the descriptive statistics Scrollsheet that is available at all times in the program.  Also, the user can produce histograms for the residuals as well as normal probability plots, in order to inspect the distribution of the residual values.


Multiple Regression-Assumptions, Limitations, Practical Considerations - Limitations

  Multiple Regression Analysis-Assumptions, Limitations, Practical Considerations - Limitations

The major conceptual limitation of all regression techniques is that one can only ascertain relationships, but never be sure about underlying causal mechanism.  For example, one would find a strong positive relationship (correlation) between the damage that a fire does and the number of firemen involved in fighting the blaze.  Do we conclude that the firemen cause the damage?  Of course, the most likely explanation of this correlation is that the size of the fire (an external variable that we forgot to include in our study) caused the damage as well as the involvement of a certain number of firemen (i.e., the bigger the fire, the more firemen are called to fight the blaze).  Even though this example is fairly obvious, in real correlation research, alternative causal explanations are often not considered.


Multiple Regression -Assumptions, Limitations, Practical Considerations - Choice of the Number of Variables

  Multiple Regression Analysis-Assumptions, Limitations, Practical Considerations - Choice of the Number of Variables

Multiple regression is a seductive technique: "plug in" as many predictor variables as you can think of and usually at least a few of them will come out significant.  This is because one is capitalizing on chance when simply including as many variables as one can think of as predictors of some other variable of interest.  This problem is compounded when, in addition, the number of observations is relatively low.  Intuitively, it is clear that one can hardly draw conclusions from an analysis of 100 questionnaire items based on 10 respondents.  Most authors recommend that one should have at least 10 to 20 times as many observations (cases, respondents) as one has variables, otherwise the estimates of the regression line are probably very unstable and unlikely to replicate if one were to do the study over.


Multiple Regression -Assumptions, Limitations, Practical Considerations - Multicolinearity and Matrix Ill-Conditioning

  Multiple Regression Analysis-Assumptions, Limitations, Practical Considerations - Multicollinearity and Matrix Ill-Conditioning

This is a common problem in many correlation analyses.  Imagine that you have two predictors (X variables) of a person's height: (1) weight in pounds and (2) weight in ounces.  Obviously, our two predictors are completely redundant; weight is one and the same variable, regardless of whether it is measured in pounds or ounces.  Trying to decide which one of the two measures is a better predictor of height would be rather silly; however, this is exactly what one would try to do if one were to perform a multiple regression analysis with height as the dependent (Y) variable and the two measures of weight as the independent (X) variables.  STATISTICA would issue a matrix ill-conditioned message to let the user know that he or she is trying to do the impossible.  When there are very many variables involved, it is often not immediately apparent that this problem exists, and it may only manifest itself after several variables have already been entered into the regression equation.  Nevertheless, when this problem occurs it means that at least one of the predictor variables is (practically) completely redundant with other predictors.  Multiple Regression contains many statistical indicators of this type of redundancy (tolerances, semi-partial R, etc., see Specifying the Multiple Regression Analysis) as well as some remedies (e.g., Ridge regression).


  Multiple Regression Analysis-Assumptions, Limitations, Practical Considerations - The Importance of Residual Analysis

Even though most assumptions of multiple regression cannot be tested explicitly, gross violations can be detected and should be dealt with appropriately.  In particular outliers (i.e., extreme cases) can seriously bias the results by "pulling" or "pushing" the regression line in a particular direction, thereby leading to biased regression coefficients.  Often, excluding just a single extreme case can yield a completely different set of results.  Therefore, one of the design goals for Multiple Regression was to make residual analyses as readily available as possible to the user so that violations of assumptions that threaten the validity of results can easily be identified.


  Multiple Regression - Startup Panel

When you first open the Multiple Regression module, the Multiple Regression Startup Panel will open from which you can designate the variables for the analysis, type of data file, and other options (see below; see also, Multiple Regression - Index).

Multiple Regression Startup Panel:

Variables

Input

Missing data deletion

Mode

Perform Default Analysis

Review Desc. Stats, Corr. Matrix

Extended Precision Computations

Batch processing and printing

Print residual analysis


  Multiple Regression Startup Panel - Variables

Clicking on this button will bring up the standard variable selection dialog in which you can select the variables that will be used in the regression analysis (a correlation matrix will be calculated for all variables that are selected).


  Multiple Regression Startup Panel - Input

Select either raw data input or a correlation matrix previously created via Multiple Regression, another STATISTICA module (e.g., Basic Statistics and Tables, Factor Analysis, Canonical Analysis, or Reliability), or by entering matrix data into the spreadsheet (see STATISTICA Matrix File Format).


  Multiple Regression Startup Panel - Missing Data Deletion

This switch is only active if a raw data file has been specified as the input data (see above).  Missing data can be deleted casewise; substituted by means, or deleted pairwise by selecting the appropriate option from the combo box.

Casewise deletion of missing data:  If this option is selected, then only cases that do not contain any missing data for any of the variables selected for the analysis will be included in the analysis.

Mean substitution:  If this option is selected, then missing data will be replaced by the means for the respective variables (for this analysis only, not in the data file).

Pairwise deletion of missing data:  If this option is requested, then cases will be excluded from the calculation of correlations involving variables for which they have missing data.  In subsequent analyses, all tests of statistical significance in that instance will be based on the smallest number of valid cases found in any of the selected variables.


  Multiple Regression Startup Panel - Mode

In this combo box, the user can select either a standard or fixed nonlinear regression.

Standard Regression Mode:  In the default standard setting, the standard correlation matrix of all selected variables will be computed.

Fixed Nonlinear Regression:  This mode allows the user to select various transformations of the independent variables (see Fixed Nonlinear Regression); thus, new variables will be created (in memory) as transformations of the raw data and included in the overall correlation matrix.  A common application of this technique is to estimate the linear, squared, cubic, etc. components of the relationship of an independent variable with the dependent variable.  Note that STATISTICA also includes the module Nonlinear Estimation for estimating true nonlinear regression models (e.g., probit, logit, discontinuous regression models, etc.).


  Multiple Regression Startup Panel - Perform Default Analysis

When you select this option and then click OK in the Startup Panel, the program will accept the default selections (i.e., a Standard regression model which includes the intercept) in the Model Definition dialog and proceed to the Regression Results dialog.  If this option is de-selected, then when you click OK in the Startup Panel, the Model Definition dialog will open in which you can select the type of regression analysis (i.e., stepwise, ridge, etc.) as well as other options.


  Multiple Regression Startup Panel - Review Desc. Stats, Corr. Matrix

Select this check box in order to open the Review Descriptive Statistics dialog after you leave the Startup Panel.  In the Review Descriptive Statistics dialog, you can review detailed descriptive statistics (and pairwise n, if Pairwise deletion of missing data was requested, above) for the variables selected above.  Click OK in the Review Descriptive Statistics dialog in order to continue the analysis and open the Model Definition dialog.


Multiple Regression Startup Panel - Batch Processing and Printing

  Multiple Regression Startup Panel - Extended Precision Computation

Check this set box in order to use the extended precision algorithm in generating the input correlation matrix that is used for multiple regression calculations.  This option is useful if the data follow a very rare pattern of so-called small relative variance.  The default double precision calculations performed in Multiple Regression feature precision optimizations and offer superior accuracy and for almost all data sets obtained from measurements (i.e., not artificially created), will produce results identical to those which can be obtained by using the extended precision option.


Multiple Regression Startup Panel - Extended Precision Computation

  Multiple Regression Startup Panel - Batch Processing and Printing

This option is only available if Perform Default Analysis is checked (see above) and either the printer, disk file, and/or Text/output Window is currently selected in the Page/Output Setup dialog (click on the Output field on the status bar to open this dialog).  The selection of the Batch Processing/Printing option affects the way in which the regression output is printed.  The default setting of the option is interactive processing (i.e., Batch Processing/Printing is de-selected).  In this mode you can determine (interactively) which Scrollsheets to print.  In the Batch Processing/Printing mode, the resulting Scrollsheets will automatically be printed, filed in the printer file, and/or sent to the Text/output Window (whichever you have selected in the Page/Output Setup dialog).

If this option is checked the program will perform the specified regression analysis (or set of analyses if more than one dependent variable was specified), "print" the results, and return to the dialog entitled Defining Multiple Regression.  This option is particularly useful when one wants to print the results of a stepwise regression after each step for several dependent variables.


  Multiple Regression Startup Panel - Print Residual Analysis

This option is only available if Perform Default Analysis is checked (see above) and either the printer, disk file, and/or Text/output Window is currently selected in the Page/Output Setup dialog and Batch processing/printing was selected (see above).  If this option is checked, the default printed output will include the Scrollsheet with various residual statistics for each case.


  Multiple Regression - Fixed Nonlinear Regression

The Non-linear Components Regression dialog is only available after the mode switch in the Startup Panel was set to Fixed Nonlinear.  This dialog allows you to specify nonlinear transformations of the previously selected variables.  Selected transformations are marked by a "check" in the check box next to the respective function.

For each selected variable, new temporary variables (in memory, the actual data file will not be changed) will be created, containing the results of the respective transformations (a new variable will be created for each selected transformation for each selected variable).  The new variable names will be a combination of the respective original variable number and the chosen transformation, e.g., V4**2, 10**V7, etc.

The available transformations and their valid ranges are listed below.  You can select more than one transformation.

•  X**2  (X-squared)	-5.0E+08 to 5.0E+08

•  X**3  (X-cubed)	-5.0E+05 to 5.0E+05

•  X**4  (X to the fourth power)	-5.0E+04 to 5.0E+04

•  X**5  (X to the fifth power)	-5.0E+03 to 5.0E+03

•  Sqrt(X)  (Square root of X)	X≥0

•  LN(X)  (Natural log of X)	X>0

•  LOG(X)  (Log base 10 of X)	X>0

•  e**X  (Euler [e] = 2.71...)	-40 to +40

•  10**X  (10 to the power X)	-18 to +18

•  1/X  (Inverse of X)	X _≠ 0

The default missing value code (-9999) will be assigned to the new (transformed) variables for a case if:

(a)  The original (un-transformed) variable contains a missing value for the same case;

(b)  The value for the case does not fall within the valid range.


  Multiple Regression - Review Descriptive Statistics

This intermediate dialog in the regression analysis will allow you to review specific descriptive statistics on the previously selected variables (and any transformed variables).

Review Descriptive Statistics dialog:

Means and standard deviations

Box and whisker plot

Correlations

Matrix plot

Covariances

Save correlation matrix

Pairwise n

SD=Sums of Squares/n


Review Descriptive Statistics - Means and Standard Deviations

  Multiple Regression Review Descriptive Statistics - Means and Standard Deviation

This option will bring up a Scrollsheet with means and standard deviations.  The mean of the sample is an unbiased estimate of the population mean.  By default the standard deviation is computed as the square root of the sum of squared deviations about the mean (SS) divided by n - 1 (an unbiased estimate of sigma**2).  The resulting statistic is an estimate of the population sigma (this statistic can then be used to draw inferences about the population from which the sample was drawn).  You can use the SD = Sums of Squares/n option (see below) to compute the standard deviation as the SS divided by n.  This resultant statistic is a description of the standard deviation in this sample (no inferences should be drawn from this statistic, about the population that the sample came from).

The default graph for this Scrollsheet is a histogram (frequency distribution) of the chosen variable, with the normal distribution superimposed (this option is not available for Fixed Non-linear Regression).  This plot can be very useful as a quick check of whether the assumption of normality has been violated by the respective variable.


Review Descriptive Statistics - Box and Whisker Plot

  Multiple Regression Review Descriptive Statistics - Box and Whisker Plot

This option allows you to produce a box and whisker plot (showing medians and quartiles, means and standard deviations, etc.) for the selected variables.


Review Descriptive Statistics - Correlations

  Multiple Regression Review Descriptive Statistics - Correlations

This option will bring up a Scrollsheet with correlations.  The default graph for this Scrollsheet is a scatterplot of the respective two variables.  The plot will indicate the regression line as well as the 95% confidence limits for the regression line.


Review Descriptive Statistics - Matrix Plot

  Multiple Regression Review Descriptive Statistics - Matrix Plot

This option will bring up a matrix scatterplot for the variables selected for the analysis.


Review Descriptive Statistics - Covariances

  Multiple Regression Review Descriptive Statistics - Covariances

This option will bring up a Scrollsheet with covariances.  The default graph for this Scrollsheet is a scatterplot of the respective two variables.  The plot will indicate the regression line as well as the 95% confidence limits for the regression line.


Review Descriptive Statistics - Save Correlation Matrix

  Multiple Regression Review Descriptive Statistics - Save Correlation Matrix

When you click on this button, the Save Matrix As dialog will open in which you can save the correlation matrix as a standard STATISTICA matrix file


Review Descriptive Statistics - Pairwise n

  Multiple Regression Review Descriptive Statistics - Pairwise n

This option is only available if raw data input and pairwise deletion of missing data was selected in the Startup Panel.  This option will bring up a Scrollsheet with the number of valid cases for each pair of variables in the correlation matrix.


Review Descriptive Statistics - SD = Sums of Squares/n

  Multiple Regression Review Descriptive Statistics - SD = Sums of Squares/n

This check box affects the way in which the standard deviations (Means and standard deviations) and variances/covariances (option Covariances) are computed.  If this box is checked, the resultant statistics are descriptions of the standard deviation, variance, and covariance in this sample (see Means and Standard Deviations, above).  The setting of this switch only affects the respective values in the Scrollsheets; it does not affect any subsequent computations.


  Multiple Regression - Defining the Regression Analysis

Select the independent and dependent variables for the multiple regression analysis in the Model Definition dialog.  If multiple dependent variables are selected, then the program will cycle through the dependent variables list one by one.

Model Definition dialog:

Variables

Method

Stepwise regression in blocks (hierarchical regression)

Intercept

Tolerance

F to enter, F to remove

Number of steps

Displaying results

Ridge regression

Batch processing and printing

Print residual analysis

Review Correlation matrix/means/SD


Defining the Regression Analysis - Variables

  Multiple Regression Defining the Regression Analysis - Variables

Choosing this option will bring up the standard two-variable selection dialog in which you can select the dependent and independent variables.  If more than one dependent variable is selected, then regression analyses will be performed consecutively for each variable in the dependent variable list.


Defining the Regression Analysis - Method

  Multiple Regression Defining the Regression Analysis - Method

This option allows you to choose the type of regression analysis.

Standard Regression:  When you select this option, all variables will be entered into the regression equation in one single block or step.

Forward Stepwise Regression:  When you select this option, the independent variables will be individually added or deleted from the model at each step of the regression (depending on your choice of F to Enter or F to Remove) until the "best" regression model is obtained.

Backward Stepwise Regression:  When you select this option, the independent variables will be removed from the regression equation one at a time (depending on your choice of F to Enter or F to Remove) until the "best" regression model is obtained.


Defining the Regression Analysis - Stepwise regression in blocks (hierarchical regression)

  Multiple Regression Defining the Regression Analysis - Stepwise Regression in Blocks (Hierarchical Regression)

The Multiple Regression module automatically keeps track of successive analyses.  When the standard method is selected, the program will automatically calculate and evaluate the R-square increase or decrease in consecutive analyses of the same dependent variable.  For example, if in the first analysis, variables 1, 2, and 3 are selected as independent variables, and in the next analysis variables 1, 2, 3, 4, and 5 (without changing the dependent variable), then Multiple Regression will automatically calculate and evaluate the increment in R-square due to variables 4 and 5 (these statistics are available via the Stepwise options) on the Multiple Regression Results dialog.


Defining the Regression Analysis - Intercept

  Multiple Regression Defining the Regression Analysis - Intercept

This option allows you to specify a regression equation with an intercept (select Include in model) or without an intercept (intercept forced to zero, regression through the origin, select Set to zero).  Regression without  the intercept is often used in analyses of economic data in cases when, by definition, the regression line describing the relationship between some variables would be predicted to have a zero intercept.  For example, if one were to correlate tax revenues with gross national product (GNP) then it is obvious that, if there is zero GNP, there is zero tax revenue.  However, in the majority of applications (in particular in the social and natural sciences) variables of interest are measured on more or less arbitrary scales where the zero points have no special meaning.  Therefore, the default setting of the intercept combo box is Include in model.


Defining the Regression Analysis - Tolerance

  Multiple Regression Defining the Regression Analysis - Tolerance

The tolerance of a variable is defined as 1 minus the squared multiple correlation of this variable with all other independent variables in the regression equation.  Therefore, the smaller the tolerance of a variable, the more redundant is its contribution to the regression (i.e., it is redundant with the contribution of other independent variables).  If the tolerance of any of the variables in the regression equation is equal to zero (or very close to zero) then the regression equation cannot be evaluated (the matrix is said to be ill-conditioned, and it cannot be inverted).

This option allows you to specify the minimum tolerance that is considered acceptable by STATISTICA.  The minimum value that can be specified here is 1.00E-25 (i.e., a number with 24 zeros past the decimal point).  However, it is not recommended to reset this switch to such an extremely low value.  If the tolerance of a variable about to be entered into the regression equation is less than the default tolerance value (.01) it means that this variable is 99 percent redundant with (identical to) the variables already in the equation.  Forcing very redundant variables into the regression equation is not only questionable in terms of relevance of results, but the resultant estimates (regression coefficients) will become increasingly unreliable.


Defining the Regression Analysis - F to enter, F to remove

  Multiple Regression Defining the Regression Analysis - F to Enter, F to Remove

These options are only available if Forward or Backward Stepwise regression was selected.  The F to enter value that you specify here determines how significant the contribution of a variable to the regression has to be in order for it to be added to the equation.  The F to remove value that you specify here determines how "insignificant" the contribution of a variable in the regression equation has to be in order for it to be removed from the regression equation.

If it is desirable in Forward Stepwise regression to force all (or almost all) variables into the equation (one at a time), then the F to enter value should be set to its minimum (0.0001), and the F to remove value should be set to its minimum (0.0; the F to remove must always be less than the F to enter).

If it is desired in Backward Stepwise regression, to remove all variables from the equation (one at a time), then the F to enter value should be set to a very large value (e.g., 999) and the F to remove value should be set to a value of similar magnitude (e.g., 998; remember that the F to remove value must always be less than the F to enter value).


Defining the Regression Analysis - Displaying Results

  Multiple Regression Defining the Regression Analysis - Number of Steps

This option is only available if Forward Stepwise or Backward Stepwise regression was selected.  This option allows the user to select the maximum number of steps that STATISTICA will perform before displaying the final results of the stepwise regression analysis.


Defining the Regression Analysis - Number of Steps

  Multiple Regression Defining the Regression Analysis - Displaying Results

This option affects the display of results from stepwise (Forward or Backward) multiple regression analyses.  You can elect to review only the final (summary) results of the stepwise regression analysis (select Summary Only) or you may review the results after each step of the analysis (select At Each Step).


Defining the Regression Analysis - Ridge Regression

  Multiple Regression Defining the Regression Analysis - Ridge Regression

Ridge regression analysis is used when the independent variables are highly intercorrelated, and stable estimates for the regression coefficients cannot be obtained via ordinary least squares methods (see Hoerl, 1962; Schmidt & Muller, 1978; Rozeboom, 1979).  Specifically, a constant (lambda) will be added to the diagonal of the correlation matrix, which is then re-standardized so that all diagonal elements are equal to 1.0 (and the off-diagonal elements are divided by the constant).  In other words, ridge regression artificially decreases the correlation coefficients so that more stable (yet biased) estimates (beta coefficients) can be computed.  Note that the standard errors for B and beta are calculated using the formulas for standard regression.  After selecting this option, you will need to enter a value for lambda.


Defining the Regression Analysis - Batch Processing and Printing

  Multiple Regression Defining the Regression Analysis - Batch Processing and Printing

This option is only available if printer, disk file, and/or Text/output Window is currently selected in the Page/Output Setup dialog (click on the Output field on the status bar to open this dialog).  The selection of the Batch Processing/Printing option affects the way in which the regression output is printed.  The default setting of this option is interactive processing (i.e., Batch Processing/Printing is de-selected).  In this mode you can determine (interactively) which Scrollsheets to print.  In the Batch Processing/Printing mode, the resulting Scrollsheets will automatically be printed, filed in the printer file, and/or sent to the Text/output Window (whichever you have selected in the Page/Output Setup dialog).

If this option is checked the program will perform the specified regression analysis (or set of analyses if more than one dependent variable was specified), "print" the results, and return to the dialog entitled Defining Multiple Regression.  This option is particularly useful when one wants to print the results of a stepwise regression after each step for several dependent variables.


Defining the Regression Analysis - Print Residual analysis

  Multiple Regression Defining the Regression Analysis - Print Residual Analysis

This option is only available if printer, disk file, and/or Text/output Window is currently selected in the Page/Output Setup dialog and Batch processing/printing was selected (see above).  If this option is checked, the default printed output will include the Scrollsheet with various residual statistics for each case.


Defining the Regression Analysis - Review Correlation matrix/means/SD

  Multiple Regression Defining the Regression Analysis - Review Correlation matrix/means/SD

Click on this button to return to the Review Descriptive Statistics dialog from which you can choose to review the means and standard deviations, the correlation matrix and the covariance matrix, or choose to save the correlation matrix in a standard STATISTICA matrix file.


  Multiple Regression - Results

The Multiple Regression Results dialog shows the summary of results for the current regression analysis and offers several options to review specific results.

Multiple Regression Results dialog:

Summary box

Model box

Regression summary

Analysis of variance

ANOVA, adjusted for mean

Covariances of weights

Current sweep matrix

Partial correlations

Stepwise summary

Predict dependent variable

Redundancy

Correlations and descriptive statistics

Alpha (display)


Multiple Regression Results - ANOVA Adjusted for Means

  Multiple Regression Results - ANOVA, Adjusted for Mean

This option is only available if the current regression model does not include an intercept.  In that case, you can compute the multiple R-square value either based on the variability around the origin (zero), or based on the variability around the mean.  The default R-square value reported in the Summary Box pertains to the former, that is, it is the proportion of variability of the dependent variable around 0 (zero) that is accounted for by the predictor variables.  If you click on this button, then the program will compute the ANOVA table, including the sums of squares and R-square value, based on the proportion of variability around the mean for the dependent variable, explained by the predictor variables.  For various alternative ways for computing the R-square value, refer to Kvalseth (1985).


  Multiple Regression Results - Summary Box

The following information is summarized in this area of the dialog:

Dep. Var.:  The name of the dependent variable is given here.

No. of Cases:  The minimum valid sample size (n) is displayed here (depending on the Missing Data Deletion option that you selected).

Multiple R:  The is the coefficient of multiple correlation is the positive square root of R-square (the coefficient of multiple determination, see Residual Variance and R-Square).  This statistic is useful in multivariate regression (i.e., multiple independent variables) when you want to describe the relationship between the variables.

R-square:  This coefficient of multiple determination measures the reduction in the total variation of the dependent variable due to the (multiple) independent variables.

R-square = 1 - [Residual SS/Total SS]

Adjusted R-square:  The R-square is adjusted by dividing the error sum of squares and total sums of square by their respective degrees of freedom.

R-square (adjusted) = 1 - [(Residual SS/df)/(Total SS/df)]

Std. Error of estimate:  This statistic measures the dispersion of the observed values about the regression line.

Intercept:  If you selected a regression analysis which includes the intercept (see Defining the Regression Analysis, then the value for the intercept will be displayed here.

Std. Error:  This is the standard error of the intercept.

t(df) and p-value:  The t-value and resulting p-value is used to test the hypothesis that the intercept is equal to 0.

F, df, and p-value:  The F-value and resulting p-value is used as an overall F test of the relationship between the dependent variable and the set in independent variables.  Here:

F = Regression Mean Square/Residual Mean Square.


  Multiple Regression Results - Model Box

Statistically significant regression coefficients (beta coefficients) for the variables in the analysis are highlighted in this box.  The criterion for determining statistical significance (alpha level) can be changed from the .05 default.


  Multiple Regression Results - Regression Summary

This option will bring up a Scrollsheet with the standardized (beta) and non-standardized (B) regression coefficients (weights), their standard error, and statistical significance.  The summary statistics for the regression analysis (e.g., R, R-square, etc.) will be displayed in the headers of the Scrollsheet.


  Multiple Regression Results - Analysis of Variance

Clicking on this button will bring up a Scrollsheet with a complete Analysis of Variance table for the current regression equation (for more information see, Analysis of Variance).


  Multiple Regression Results - Covariances of Weights

This option will bring up (1) a Scrollsheet with the correlations of the regression coefficients and (2) a Scrollsheet with the variances and covariances of the regression coefficients.


  Multiple Regression Results - Current Sweep Matrix

This option will bring up a Scrollsheet with the current sweep matrix.  Matrix inversion in Multiple Regression is accomplished via sweeping (refer to the user manual for details).  The sweep matrix of all independent variables that are currently in the regression equation is also -1 times the inverse of the correlation matrix of those variables (that is, the sign of each element in the matrix is reversed).  The diagonal elements for those variables that are not in the equation can be interpreted as the (1 - R-square) values, treating the respective variable as the dependent variable, and using all current independent variables.

Variance inflation factor:  Note that the diagonal elements of the inverse correlation matrix (i.e., -1 times the diagonal elements of the sweep matrix displayed via this option) for variables that are in the equation are also sometimes called variance inflation factors (VIF; e.g., see Kneter, Wasserman, Kutner, 1985). This terminology denotes the fact that the variances of the standardized regression coefficients can be computed as the product of the residual variance (for the correlation transformed model) times the respective diagonal elements of the inverse correlation matrix.  If the predictor variables are uncorrelated, then the diagonal elements of the inverse correlation matrix are equal to 1.0; thus, for correlated predictors, these elements represent an "inflation factor" for the variance of the regression coefficients, due to the redundancy of the predictors.


  Multiple Regression Results - Partial Correlations

Clicking on this button will bring up Scrollsheets with:

(1)	The beta in (standard regression coefficient for the respective variable if it were to enter into the regression equation as an independent variable);

(2)	The partial correlation (between the respective variable and the dependent variable, after controlling for all other independent variables in the equation);

(3)	The semi-partial (part) correlation (the correlation between the unadjusted dependent variable with the respective variable after controlling for all independent variables in the equation);

(4)	The tolerance for the respective variable (defined as 1 minus the squared multiple correlation between the respective variable and all independent variables in the regression equation);

(5)	The minimum tolerance (the smallest tolerance among all independent variables in the equation if the respective variable were to be entered as an additional independent variable);

(6)	The t-value associated with these statistics for the respective variable, and;

(7)	The statistical significance of the t-value.

These statistics will first be displayed separately for variables not currently in the regression equation, and for the variables in the regression equation (if any).


  Multiple Regression Results - Stepwise Summary

This option will only appear on the Multiple Regression Results dialog if (1) the user has selected forward or backward stepwise regression, or (2) if in the previous standard regression analysis the same dependent variable was analyzed and the independent variable list in the previous analysis was a subset of the current independent variable list or vice versa.  Thus, in the later case, the user may evaluate the change in R-square caused by removing or entering several variables in a single step (hierarchical analysis).

For example, if in the first analysis, variables 1 through 5 were selected as independent variables, and in the subsequent analysis with the same dependent variable the user specified variables 1 through 3 as the independent variables, then choosing this option will bring up a Scrollsheet with R-square, the R-square decrease, F to remove, and the number of variables removed in the single step (two in this example).

If forward or backward stepwise regression was specified, the Scrollsheet will contain the R-square increment (or decrease) at each step.


  Multiple Regression Results - Predict Dependent Variable

This option will bring up a data entry window that allows you to enter values for each independent variable in the regression equation and to calculate the predicted value for the dependent variable based on the current regression equation.

The confidence limits (labeled CL in the Scrollsheet) or prediction limits (labeled PL) for the predicted value will also be computed, depending on whether the Compute confidence limits or Compute prediction limits radio button is set. You can enter the respective alpha value for the confidence or prediction limits in the edit field labeled Alpha.  The program will compute the 1-alpha confidence limits for the expected value (mean) of the dependent variable, or the 1-alpha prediction limits for individual predictions of the dependent variable (see also Neter, Wasserman, & Kutner, 1985, for details).


  Multiple Regression Results - Redundancy

This option will bring up a Scrollsheet with various indicators of the redundancy of independent variables (currently included or not included in the equation).  Specifically, for each variable, the Scrollsheet will show (1) the tolerance (defined as 1 - R-square for the respective variable with all other variables currently in the equation), (2) the R-square (between the current variable and all other variables in the regression equation, (3) the partial correlation (between the respective variable and the dependent variable, after controlling for all other independent variables in the equation), and (4) the semi-partial (part) correlation (the correlation between the unadjusted dependent variable with the respective variable after controlling for all independent variables in the equation).


Multiple Regression Results - Correlation and Descriptive Statistics

  Multiple Regression Results - Correlations and Descriptive Statistics

This button will bring up the Correlation Review dialog.  From this dialog you can choose to review the means and standard deviations, the correlation matrix and the covariance matrix, or choose to save the correlation matrix in a standard STATISTICA matrix file.


  Multiple Regression Results - Alpha (Display)

The default value for alpha is .05.  This value is used as a "cut-off" for statistical significance (i.e., if the p-value is less than alpha, then the effect is highlighted in the Scrollsheet to indicate significance).  In this dialog, you can edit this "cut-off" value (.0001 < α < .5) and then click on the Apply button to immediately apply this change to the next copy of the current Scrollsheet.


  Multiple Regression - Predicting Dependent Variable Values

You can enter specific values for the independent variables in this dialog, in order to predict the value of the dependent variable.  Enter the values individually for each variable in the current regression equation or enter one common value (click on the Apply button to transfer this value to each variable).  STATISTICA will then compute the value for the dependent variable, given the current regression equation.


  Multiple Regression - Residual Analysis

This dialog is only available if you choose Raw Data File as the type of data input.  Here, you can choose from several summary statistics and graphics options.

Residual Analysis dialog:

Statistics:

Correlations and descriptive statistics

Regression summary	Durbin-Watson statistic

Display residuals	Save residuals

Casewise Plots:

Plots of residuals

Plots of outliers

Plots of predicted

Scatterplots:

Predicted & residuals	Predicted & observed values

Predicted & squared residuals	Residuals & deleted residuals

Observed & residual values and Observed & squared residual values

Histograms:

Plot of observed

Plots of predicted

Plots of residuals

Probability Plots:

Normal plot of residuals

Half-normal plot of residuals

Detrended normal plot of residuals

Bivariate Scatterplots:

Bivariate correlation	Predicted & independent variable

Residual & independent variable	Partial residual plot


  Multiple Regression Residual Analysis - Correlations and Descriptive Statistics

This option will bring up the Review Descriptive Statistics dialog from which you can choose to review the means and standard deviations, the correlation matrix and the covariance matrix, or choose to save the correlation matrix in a standard STATISTICA matrix file.


  Multiple Regression Residual Analysis - Regression Summary

Click on this button to bring up a Scrollsheet with the standardized (beta) and non-standardized (B) regression coefficients, their standard errors, and statistical significance's.  The summary statistics for the regression analysis (e.g., R, R-square, etc.) will be displayed in the headers of the Scrollsheet.


  Multiple Regression Residual Analysis - Display Residuals

This option will bring up a Scrollsheet with various statistics (types of residuals) for each observation.

Observed value:  This is the observed value for the dependent variable.

Predicted value:  This is the predicted value given the current regression equation.

Residual value:  This is the observed value minus the predicted value.

Standard predicted value:  This is the standardized predicted value of the dependent variable.

Standard residual value:  This is the standardized residual value (observed minus predicted divided by the square root of the residual mean square).

Standard error of predicted value:  This is the standard error of the unstandardized predicted value.

Mahalanobis distance:  One can think of the independent variables (in the equation) as defining a multidimensional space in which each observation can be plotted.  Also, one can plot a point representing the means for all independent variables.  This "mean point" in the multidimensional space is also called the centroid.  The Mahalanobis distance is the distance of a case from the centroid in the multidimensional space, defined by the correlated independent variables (if the independent variables are uncorrelated, it is the same as the simple Euclidean distance).  Thus, this measure provides an indication of whether or not an observation is an outlier with respect to the independent variable values.

Deleted residual:  The deleted residual is the residual value for the respective case, had it not been included in the regression analysis, that is, if one would exclude this case from all computations.  If the deleted residual differs greatly from the respective standardized residual value, then this case is possibly an outlier because its exclusion changed the regression equation.

Cook's distance:  This is another measure of the impact of the respective case on the regression equation.  It indicates the difference between the computed B values and the values one would have obtained, had the respective case been excluded.  All distances should be of about equal magnitude; if not, then there is reason to believe that the respective case(s) biased the estimation of the regression coefficients.

Remedies for outliers:  The purpose of all of these statistics is to identify outliers.  Remember that particularly with small n (less than 100), multiple regression estimates (the B coefficients) are not very stable.  In other words, single extreme observations can greatly influence the final estimates.  Therefore, it is advisable always to review these statistics (using these or the following options), and to repeat crucial analyses after discarding any outliers.  Another alternative is to repeat crucial analysis using absolute deviations rather than least squares regression, thereby "dampening" the effect of outliers.  Nonlinear Estimation allows you to estimate such models.


  Multiple Regression Residual Analysis - Durbin-Watson Statistic

The Durbin-Watson statistic is useful for evaluating the presence or absence of a serial correlation of residuals (i.e., whether or not residuals for adjacent cases are correlated, indicating that the observations or cases in the data file are not independent).  Note that all statistical significance tests in multiple regression assume that the data consist of a random sample of independent observations.  If this is not the case, then the estimates (B coefficients) may be more unstable than the significance levels would lead one to believe.  Intuitively, it should be clear that, for example, giving the same questionnaire to the same person 100 times will yield less information about the general population than administering that questionnaire to a random sample of 100 different individuals, who complete the questionnaire only once.  In the former case, observations are not independent of each other (the same respondent will give similar responses in repeated questionnaires), while in the latter case, the observations are independent (different people).

After clicking on this button, a Scrollsheet will be displayed with the Durbin-Watson D statistic and the serial correlation (correlation of adjacent residuals).  For more information about the Durbin-Watson statistic refer to the user manual.


  Multiple Regression Residual Analysis - Save Residual

This option is useful if one wants to save predicted and/or residual scores for further analyses with other STATISTICA modules.  Click on this button to open the Save Pred/Resid As dialog in which you can select the file name under which the file will be saved.  Next, a variable selection window will appear, allowing you to select additional variables to be saved together with the predicted and residual values.  Note that all values shown in the Scrollsheet will be saved along with the residuals.


  Multiple Regression Residual Analysis - Plot of Residuals

After clicking on this button, a dialog will appear from which you can choose the specific residual for the plot.

Available residual values are raw residuals, standard residuals, Mahalanobis distances, deleted residuals, and Cook's distances.  These statistics are explained above ( see the option Display residuals).  After selecting the desired residual for the plot, a Scrollsheet will come up in which the selected values are plotted in the left-most column.  At the same time, all residual statistics are computed and can be reviewed (in the subsequent columns of the Scrollsheet).


  Multiple Regression Residual Analysis - Plot of Outliers

After clicking on this button, a dialog will open that will allow you to choose to:  (1) plot only cases for which the absolute standard residual value is greater than +2, or (2) plot the 100 most extreme cases, sorted in descending order of magnitude, of either the standard predicted values, standard residuals, Mahalanobis distances, deleted residuals, or Cook's distances (for explanations of these statistics see above under option Display residuals).  Thus, this option allows you to identify outliers in even very large data files, since only the most extreme cases are plotted.  In the Scrollsheet the selected values are plotted in the left-most column; at the same time, all residual statistics are computed and can be reviewed (in the subsequent columns of the Scrollsheet).


  Multiple Regression Residual Analysis - Plot of Predicted

After clicking on this button you can choose to plot the raw predicted values or the standard predicted values.  In the Scrollsheet the selected values are plotted in the left-most column; at the same time, all residual statistics are computed and can be reviewed (in the subsequent columns of the Scrollsheet).


  Multiple Regression Residual Analysis - Predicted and Residual

This option will bring up a scatterplot of the raw predicted values (on the X axis) versus the raw residuals (on the Y axis).  This plot is very useful for testing the assumption of linearity regarding the relationship between the independent variables and dependent variable.  Specifically, if the relationship is linear, then the residual scores can be expected to form a homogeneous "cloud" around the center line.  However, if non-linearity is present, then peculiar patterns may emerge.  For example, if the true relationship between variables is curvilinear rather than linear, the residuals may form an inverted U around the center line, indicating that predictions are consistently too high on the extreme ends of the scale, but too low in the central region of the scale.  In that case, one may try to include second or third order polynomial transformations of the original independent variables in the regression (that is, X**2, X**3, etc.).  This can easily be accomplished via the fixed nonlinear regression option available in Multiple Regression.


  Multiple Regression Residual Analysis - Predicted and Squared Residual

This option will bring up a scatterplot of the raw predicted values (on the X-axis) versus the squared raw residuals (on the Y-axis).


  Multiple Regression Residual Analysis - Predicted and Observed Values

This option allows you to plot a scatterplot of the predicted versus the observed values.  This plot is particularly useful for identifying potential clusters of cases that are not well predicted.  For example, if one were to analyze job performance data (using some employment test as the predictor variable), it could happen that the test predicts success well for the majority of employees, but that there is a distinct group of employees for whom the prediction based on the employment test is consistently too low (a common problem in tests that rely heavily on verbal skills), and who would be unfairly discriminated against if the test were to be used as the sole criterion for selection.


  Multiple Regression Residual Analysis - Observed & Residual Values and Observed & Squared Residual Values

These plots are also very useful for detecting outliers or groups of observations that are consistently over- or under-predicted.


  Multiple Regression Residual Analysis - Residuals and Deleted Residuals

Deleted residuals are the residuals that one would obtain if the respective case would be excluded from the estimation of the multiple regression (i.e., the computation of the regression coefficients).  Thus, if there are large discrepancies between the deleted residuals and the regular standardized residuals, then we can conclude that the regression coefficients are not very stable, that is, they are greatly affected by the exclusion of single cases (see also the discussion of the Display residuals option).


  Multiple Regression Residual Analysis - Plot of Observed

This option will bring up a histogram (frequency distribution) of the observed values for the dependent variable, and superimpose the expected normal distribution values over this plot.


  Multiple Regression Residual Analysis - Plot of Predicted

After clicking on this button you can choose to plot a histogram of the raw (unstandardized) predicted values or the standardized predicted values.


Multiple Regression Residual Analysis - Plot of Residual

  Multiple Regression Residual Analysis - Plot of Residuals

After clicking on this button, a submenu will appear from which you can choose the specific residual for the histogram.  Available residual values are raw residuals, standard residuals, Mahalanobis distances, deleted residuals, and Cook's distances.  These statistics are briefly explained in the option, Display residuals).


Multiple Regression Residual Analysis - Normal Plot of Residual

  Multiple Regression Residual Analysis - Normal Plot of Residuals

Multiple regression assumes that the residual values (observed minus predicted values) are normally distributed, and that the regression function (the relationship between the independent and dependent variables) is linear in nature.  If any of these assumptions is grossly violated, then the regression coefficients (B coefficients) may be affected (inflated or deflated), and the statistical significance tests inflated or deflated.  If "all is well," one can expect the residual values to be normally distributed.  Normal probability plots provide a quick way to visually inspect to what extent the pattern of residuals follows a normal distribution.  If the residuals are not normally distributed, they will deviate from the line.  Outliers may also become evident in this plot.  If there is a general lack of fit, and the data seem to form a clear pattern (e.g., an S shape) around the line, then the dependent variable may have to be transformed in some way (e.g., a log transformation to "pull in" the tail of the distribution, etc.; refer to the manual for additional details).  For more information on how the standard normal probability plot is constructed, see Normal Probability Plots.


Multiple Regression Residual Analysis - Half-Normal Plot of Residual

  Multiple Regression Residual Analysis - Half-Normal Plot of Residuals

The half-normal probability plot is constructed in the same way as the standard normal probability plot, except that only the positive half of the normal curve is considered.  Consequently, only positive normal values will be plotted on the Y-axis.  This plot is basically used when one wants to ignore the sign of the residual, that is, when one is mostly interested in the distribution of absolute residuals, regardless of sign.


Multiple Regression Residual Analysis - Detrended Normal Plot of Residual

  Multiple Regression Residual Analysis - Detrended Normal Plot of Residuals

The detrended normal probability plot is constructed in the same way as the standard normal probability plot, except that, before the plot is produced, the linear trend is removed.  This often "spreads out" the plot, thereby allowing the user to detect patterns of deviations more easily.


Multiple Regression Residual Analysis - Bivariate Correlation

  Multiple Regression Residual Analysis - Bivariate Correlations

This option allows you to produce a scatterplot of any two variables in the data file, regardless of whether or not they are included in the regression analysis.


  Multiple Regression Residual Analysis - Residual and Independent Variable

This option allows you to produce a scatterplot of various residual values (for the dependent variable) with any variable in the data file, regardless of whether or not it was included in the regression analysis.  After clicking on this button, a dialog will appear that allows you to choose the specific residual for the scatterplot.  Available residual values are raw residuals, standard residuals, Mahalanobis distances, deleted residuals, and Cook's distances.  These statistics are briefly explained above in the Display residuals option.  Next you will be prompted to enter the other variable for the plot.  This option allows you to explore the relationship between the residualized dependent variable with other variables in your data file.


  Multiple Regression Residual Analysis - Predicted and Independent Variable

This option allows you to produce a scatterplot of various residual values with any variable in the data file, regardless of whether or not the respective variable was included in the regression analysis.  After clicking on this button, a dialog will come up from which you can elect to plot either raw predicted or standardized predicted values.  Next you will be prompted to select the other variable for the plot.


  Multiple Regression Residual Analysis - Partial Residual Plot

This option allows you to produce a partial residual plot for any variable currently in the regression equation.  In a partial residual plot, the residual plus the contribution of the respective independent variable to the regression (i.e., residual+bi*xii) is plotted against the values for that independent variable.  This plot is discussed in detail by Larsen and McCleary (1972).  After clicking on this button you are prompted to select one independent variable from among those currently in the regression equation.


  Multiple Regression - Stepwise Analysis

This dialog gives a summary of the stepwise analysis.  Click OK in this dialog to review the results of the analysis; click Cancel to specify another regression analysis.


  Multiple Regression - Selecting Variables

Select the independent and dependent variable lists here.  To select a variable, click on it.  To select a range of variables, hold down the left-mouse-button and move the mouse over the respective list.  To add or delete variables from a list, hold down the CTRL key and then click on the respective variable.  Click OK to finalize your choice.


  Multiple Regression - Notes and Technical Information

General

The Multiple Regression routine consists of two major parts.  The first part calculates a correlation matrix (or extracts a correlation matrix if matrix input is selected) according to the user's specifications (i.e., missing data, selection conditions, etc.).  The second part performs the actual multiple regression analyses.

Calculating Multiple Regression, Matrix Inversion

All calculations involved in the actual multiple regression analysis are performed in double precision.  Matrix inversion is accomplished via sweeping (see Dempster, 1969, p. 62).  The regression weights, residual Sums of Squares, tolerances, and partial correlations are also calculated as part of the sweeping operation (see also Jennrich, 1977).

Statistical Significance Tests

The standard formulas are used for calculating the F-value associated with the multiple R, and for the t-values associated with the regression coefficients (e.g., see Cooley & Lohnes, 1971; Darlington, 1990; Lindeman, Merenda, and Gold, 1980; Morrison, 1967; Neter, Wasserman, & Kutner, 1985; Pedhazur, 1973; Stevens, 1986; Younger, 1985).

Residuals

The standard error of a residual score is computed as the square root of:

                           -1

[1 - 1/n - (X    - X    )*C  *(X    - X    )']*RMS

             raw    mean        raw    mean

where

Xraw	is the vector of raw data for the independent variables

Xmean	is the vector of means for the independent variables

C**-1	is the inverse of the matrix of crossproducts of deviations for the independent variables

n	is the number of valid cases

RMS	is the residual mean square

The terms 1/n and Xmean are dropped if there is no intercept (regression forced through the origin).

The standardized residuals are obtained by dividing each residual by its standard error.

The Mahalanobis distance is the distance of a case from the centroid of all cases in the space defined by the independent variables.  It is computed as:

                      -1

(n-1)*(X    - X    )*C  *(X    - X    )'

        raw    mean        raw    mean

where

Xraw	is the vector of raw data for the independent variables

Xmean	is the vector of means for the independent variables

C**-1	is the inverse of the matrix of crossproducts of deviations for the independent variables

n	is the number of valid cases

The terms 1/n and Xmean are dropped if there is no intercept (regression forced through the origin).  Refer to the Example section of the manual for an example of how Mahalanobis distances can aid in the detection of outliers.

The deleted residual is the residual which would have been obtained had the case not been included in the estimation of the regression equation.  It is calculated by dividing the ordinary residual by:

                            -1

1 - (1/n) - (X    - X    )*C  *(X    - X    )'

              raw    mean        raw    mean

where

Xraw	is the vector of raw data for the independent variables

Xmean	is the vector of means for the independent variables

C**-1	is the inverse of the matrix of crossproducts of deviations for the independent variables

n	is the number of valid cases

The terms 1/n and Xmean are dropped if there is no intercept (regression forced through the origin).  Refer to the Example section of the manual for an example of how deleted residuals can aid in the detection of outliers.

Cook's distance (Cook, 1977) is useful for assessing the changes that would result in all residuals if the respective case were to be omitted from the regression analysis.  It is defined as:

             2

{Deleted res. *[1/n + MD/(n-1)]}/[(No. of vars + 1)*RMS]

where:

MD	is the Mahalanobis distance

RMS	is the residual mean square

If there is no intercept, n-1 is replaced by n, the term 1/n is dropped, and the term +1 (adding 1 to the number of independent variables) is dropped.

Power Transformations for Dependent and Independent Variables

Statistical significance testing in multiple regression is based on the assumption of homogenous residual variance over the range of the dependent variable.  When this assumption is violated, in some cases an appropriate transformation of the dependent or independent variables may correct the problem.  A class of power transformations that can be applied to the dependent variable or the independent variables is:

y' = y**λ            for λ≠0

   = natural log(y)  for λ=0

This formulation encompasses the reciprocal transformation (λ=-1), the square root transformation (λ=½), the square transformation (λ=2), and the logarithmic transformation (=0).  However, note that it is required that all values of y be greater than 0 (zero).  For additional details about these transformations, refer to Box and Cox (1964), Box and Tidwell (1962), Gunst, Mason, and Hess (1989), or Snee (1986).

STATISTICA contains two example STATISTICA BASIC programs for finding the best value of the parameter λ for transforming the dependent variables (using the so-called Box-Cox procedure; see the STATISTICA BASIC program Boxcox.stb, in the STBASIC subdirectory) and the independent variable values (using the so-called Box-Tidwell procedure; see the STATISTICA BASIC program Boxtid.stb, in the STBASIC subdirectory).

Transforming the Dependent Variable (Box-Cox Procedure):  The STATISTICA BASIC program Boxcox.stb (in the STBASIC subdirectory) will find the best value of λ for transforming the dependent variable values, following the procedures described in Gunst, Mason, and Hess (1989, page 557) or Maddala (1977, page 315).  The program will minimize the residual sums of squares for the regression model, after transforming the dependent variable via:

y' = (y**λ - 1)/(λ*h**(λ-1))    for λ≠0

   = natural log(y)*h           for λ=0

where h stands for the geometric mean for the dependent variable values.  The final value of λ can then be used to re-express the dependent variable values using the formula shown at the beginning of this topic.  Note that it is often convenient to round the value of λ to the nearest value that facilitates the interpretation of the transformed values (e.g., to ½ so that the resultant transformation is the square root transformation).

Transforming the Independent Variable (Box-Tidwell Procedure):  The STATISTICA BASIC program Boxtid.stb (in the STBASIC subdirectory) will find the best values of λ for transforming the independent (predictor) variable values, following the procedures described in Gunst, Mason, and Hess (1989, page 560).  The estimation of the λ parameters for this procedure is not iterative in nature, but is accomplished by expanding the terms of the regression model for the transformed predictor variables in a first-order Taylor series.  Additional details concerning this procedure can also be found in the comments at the beginning of the program Boxtid.stb.

Other Useful STATISTICA BASIC Programs

The following STATISTICA BASIC example programs are useful for solving certain regression problems.

Weighted Least Squares Estimation:  The STATISTICA BASIC program Wls.stb (in the STBASIC subdirectory) will perform weighted least squares analyses and compute various alternative R-square statistics (see Kvålseth, 1985).  Instead of the iterative derivative-free estimation method used in the Nonlinear Estimation module (see Volume III), program Wls.stb uses matrix algebra expressions (e.g., see Neter, Wassermann, and Kutner, 1985) to estimate the weighted least squares parameters.  Thus, for large data files, the program Wls.stb is more efficient, and often much faster.

Two-Stage Least Squares Estimation:  The STATISTICA BASIC program 2stls.stb (in the STBASIC subdirectory) provides an example for 2-stage least squares regression.  That program can easily be expanded or tailored to, for example, perform iteratively reweighted least squares analysis.


  Discriminant Function Analysis - Index

Introductory Overview

Startup Panel

Defining the Discriminant Analysis

Descriptive Statistics and Graphs

Reviewing Results and Classifying Cases

Canonical Analysis

Notes and Technical Information


  Discriminant Function Analysis - Introductory Overview

General Purpose

Computational Approach

Stepwise Discriminant Analysis

Interpreting a Two-Group Discriminant Function

Discriminant Functions for Multiple Groups

Assumptions

Classification


Discriminant Function Analysis - General Purpose

  Discriminant Function Analysis Introductory Overview - General Purpose

Discriminant function analysis is used to determine which variables discriminate between two or more naturally occurring groups.  For example, an educational researcher may want to investigate which variables discriminate between high school graduates who decide (1) to go to college, (2) to attend a trade or professional school, or (3) to seek no further training or education.  For that purpose the researcher could collect data on numerous variables prior to students' graduation.  After graduation, most students will naturally fall into one of the three categories.  Discriminant Analysis could then be used to determine which variable(s) are the best predictors of students' subsequent educational choice.

A medical researcher may record different variables relating to patients' backgrounds in order to learn which variables best predict whether a patient is likely to recover completely (group 1), partially (group 2), or not at all (group 3).  A biologist could record different characteristics of similar types (groups) of flowers, and then perform a discriminant function analysis to determine the set of characteristics that allows for the best discrimination between the types.


Discriminant Function Analysis - Computational Approach

  Discriminant Function Analysis Introductory Overview - Computational Approach

Computationally, discriminant function analysis is very similar to analysis of variance (ANOVA).  Let us consider a simple example.  Suppose we measure height in a random sample of 50 males and 50 females.  Females are, on the average, not as tall as males, and this difference will be reflected in the difference in means (for the variable Height).  Therefore, variable height allows us to discriminate between males and females with a better than chance probability: if a person is tall, then he is likely to be a male, if a person is short, then she is likely to be a female.

We can generalize this reasoning to groups and variables that are less "trivial."  For example, suppose we have two groups of high school graduates:  Those who choose to attend college after graduation and those who do not.  We could have measured students' stated intention to continue on to college one year prior to graduation.  If the means for the two groups (those who actually went to college and those who did not) are different, then we can say that intention to attend college as stated one year prior to graduation allows us to discriminate between those who are and are not college bound (and this information may be used by career counselors to provide the appropriate guidance to the respective students).

To summarize the discussion so far, the basic idea underlying discriminant function analysis is to determine whether groups differ with regard to the mean of a variable, and then to use that variable to predict group membership (e.g., of new cases).

Analysis of Variance.  Stated in this manner, the discriminant function problem can be rephrased as a one-way analysis of variance (ANOVA) problem.  Specifically, one can ask whether or not two or more groups are significantly different from each other with respect to the mean of a particular variable.  To learn more about how one can test for the statistical significance of differences between means in different groups you may want to read the Introductory Overview section to ANOVA/MANOVA,.  However, it should be clear that, if the means for a variable are significantly different in different groups, then we can say that this variable discriminates between the groups.

In the case of a single variable, the final significance test of whether or not a variable discriminates between groups is the F test.  As described in Elementary Concepts and ANOVA/MANOVA, F is essentially computed as the ratio of the between-groups variance in the data over the pooled (average) within-group variance.  If the between-group variance is significantly larger then there must be significant differences between means.

Multiple Variables.  Usually, one includes several variables in a study in order to see which one(s) contribute to the discrimination between groups.  In that case, we have a matrix of total variances and covariances; likewise, we have a matrix of pooled within-group variances and covariances.  We can compare those two matrices via multivariate F tests in order to determined whether or not there are any significant differences (with regard to all variables) between groups.  This procedure is identical to multivariate analysis of variance or MANOVA.  As in MANOVA, one could first perform the multivariate test, and, if statistically significant, proceed to see which of the variables have significantly different means across the groups.  Thus, even though the computations with multiple variables are more complex, the principal reasoning still applies, namely, that we are looking for variables that discriminate between groups, as evident in observed mean differences.  In fact, you may perform discriminant function analysis with the ANOVA/MANOVA module; however, different types of statistics are customarily computed and interpreted in discriminant analysis (as described later).


Discriminant Function Analysis - Stepwise Discriminant Analysis

  Discriminant Function Analysis Introductory Overview - Stepwise Discriminant Analysis

Probably the most common application of discriminant function analysis is to include many measures in the study, in order to determine the ones that discriminate between groups.  For example, an educational researcher interested in predicting high school graduates' choices for further education would probably include as many measures of personality, achievement motivation, academic performance, etc. as possible in order to learn which one(s) offer the best prediction.

Model.  Put another way, we want to build a "model" of how we can best predict to which group a case belongs.  In the following discussion we will use the term "in the model" in order to refer to variables that are included in the prediction of group membership, and we will refer to variables as being "not in the model" if they are not included.

Forward stepwise analysis.  In stepwise discriminant function analysis, STATISTICA will "build" a model of discrimination step-by-step.  Specifically, at each step STATISTICA will review all variables and evaluate which one will contribute most to the discrimination between groups.  That variable will then be included in the model, and STATISTICA will proceed to the next step.

Backward stepwise analysis.  One can also step backwards; in that case STATISTICA will first include all variables in the model and then, at each step, eliminate the variable that contributes least to the prediction of group membership.  Thus, as the result of a successful discriminant function analysis, one would only keep the "important" variables in the model, that is, those variables that contribute the most to the discrimination between groups.

F to enter, F to remove.  The stepwise procedure is "guided" by the respective F to enter and F to remove values.  The F value for a variable indicates its statistical significance in the discrimination between groups, that is, it is a measure of the extent to which a variable makes a unique contribution to the prediction of group membership.  If you are familiar with stepwise multiple regression procedures (see Multiple Regression), then you may interpret the F to enter/remove values in the same way as in stepwise regression.

In general, STATISTICA will continue to choose variables to be included in the model, as long as the respective F values for those variables are larger than the user-specified F to enter; STATISTICA will exclude (remove) variables from the model if their significance is less that the user-specified F to remove.

Capitalizing on chance.  A common misinterpretation of the results of stepwise discriminant analysis is to take statistical significance levels at face value.  When STATISTICA decides which variable to include or exclude in the next step of the analysis, it will actually compute the significance of the contribution of each variable under consideration.  Therefore, by nature, the stepwise procedures will capitalize on chance because they "pick and choose" the variables to be included in the model so as to yield maximum discrimination.  Thus, when using the stepwise approach the researcher should be aware that the significance levels do not reflect the true alpha error rate, that is, the probability of erroneously rejecting H0 (the null hypothesis that there is no discrimination between groups).


Discriminant Function Analysis - Interpreting a Two-Group Discriminant Function

  Discriminant Function Analysis Introductory Overview - Interpreting a Two-Group Discriminant Function

In the two-group case, discriminant function analysis can also be thought of as (and is analogous to) multiple regression (see Multiple Regression; the two-group discriminant analysis is also called Fisher linear discriminant analysis after Fisher, 1936; computationally all of these approaches are analogous).  If we code the two groups in the analysis as 1 and 2, and use that variable as the dependent variable in a multiple regression analysis, then we would get results that are analogous to those we would obtain via Discriminant Analysis.  In general, in the two-group case we fit a linear equation of the type:

Group = a + b *x  + b *x + ... + b *x

             1  1    2  2         m  m

where a is a constant and b1 through bm are regression coefficients.  The interpretation of the results of a two-group problem is straightforward and closely follows the logic of multiple regression:  Those variables with the largest (standardized) regression coefficients are the ones that contribute most to the prediction of group membership.


Discriminant Function Analysis - Discriminant Functions for Multiple Groups

  Discriminant Function Analysis Introductory Overview - Discriminant Functions for Multiple Groups

When there are more than two groups, then we can estimate more than one discriminant function like the one presented above.  For example, when there are three groups, we could estimate (1) a function for discriminating between group 1 and groups 2 and 3 combined, and (2) another function for discriminating between group 2 and group 3.  For example, we could have one function that discriminates between those high school graduates that go to college and those who do not (but rather get a job or go to a professional or trade school), and a second function to discriminate between those graduates that go to a professional or trade school versus those who get a job.  The b coefficients in those discriminant functions could then be interpreted as before.

Canonical analysis.  When actually performing a multiple group discriminant analysis, we do not have to specify how to combine groups so as to form different discriminant functions.  Rather, STATISTICA will automatically determine some optimal combination of variables so that the first function provides the most overall discrimination between groups, the second provides second most, and so on.  Moreover, the functions will be independent or orthogonal, that is, their contributions to the discrimination between groups will not overlap.  Computationally, STATISTICA will perform a canonical correlation analysis (see also Canonical Correlation) that will determine the successive functions and canonical roots (the term root refers to the eigenvalues that are associated with the respective canonical function).  The maximum number of functions that STATISTICA will compute will be equal to the number of groups minus one, or the number of variables in the analysis, whichever is smaller.

Interpreting the discriminant functions.  As before, we will get b (and standardized beta) coefficients for each variable in each discriminant (now also called canonical) function, and they can be interpreted as usual:  the larger the standardized coefficient, the greater is the contribution of the respective variable to the discrimination between groups.  (Note that we could also interpret the structure coefficients; see below.)  However, these coefficients do not tell us between which of the groups the respective functions discriminate.  We can identify the nature of the discrimination for each discriminant (canonical) function by looking at the means for the functions across groups.  We can also visualize how these two functions discriminate between groups by plotting the individual scores for the two discriminant functions.

Factor structure matrix.  Another way to determine which variables "mark" or define a particular discriminant function is to look at the factor structure.  The factor structure coefficients are the correlations between the variables in the model and the discriminant functions; if you are familiar with factor analysis (see Factor Analysis) you may think of these correlations as factor loadings of the variables on each discriminant function.

Some authors have argued that these structure coefficients should be used when interpreting the substantive "meaning" of discriminant functions.  The reasons given by those authors are that (1) supposedly the structure coefficients are more stable, and (2) they allow for the interpretation of factors (discriminant functions) in the manner that is analogous to factor analysis.  However, subsequent Monte Carlo research (Barcikowski & Stevens, 1975; Huberty, 1975) has shown that the discriminant function coefficients and the structure coefficients are about equally unstable, unless the n is fairly large (e.g., if there are 20 times more cases than there are variables).  The most important thing to remember is that the discriminant function coefficients denote the unique (partial) contribution of each variable to the discriminant function(s), while the structure coefficients denote the simple correlations between the variables and the function(s).  If one wants to assign substantive "meaningful" labels to the discriminant functions (akin to the interpretation of factors in factor analysis), then the structure coefficients should be used (interpreted); if one wants to learn what is each variable's unique contribution to the discriminant function, use the discriminant function coefficients (weights).

Significance of discriminant functions.  One can test the number of roots that add significantly to the discrimination between group.  Only those found to be statistically significant should be used for interpretation; non-significant functions (roots) should be ignored.

Summary.  To summarize, when interpreting multiple discriminant functions, which arise from analyses with more than two groups and more than one variable, one would first test the different functions for statistical significance, and only consider the significant functions for further examination.  Next, we would look at the standardized b coefficients for each variable for each significant function.  The larger the standardized b coefficient, the larger is the respective variable's unique contribution to the discrimination specified by the respective discriminant function.  In order to derive substantive "meaningful" labels for the discriminant functions, one can also examine the factor structure matrix with the correlations between the variables and the discriminant functions.  Finally, we would look at the means for the significant discriminant functions in order to determine between which groups the respective functions seem to discriminate.


Discriminant Function Analysis - Assumptions

  Discriminant Function Analysis Introductory Overview - Assumptions

As mentioned earlier, discriminant function analysis is computationally very similar to MANOVA, and all assumptions for MANOVA mentioned in ANOVA/MANOVA apply.  In fact, you may use the wide range of diagnostics and statistical tests of assumption that are available in ANOVA/MANOVA to examine your data for the discriminant analysis (to avoid unnecessary duplications, the extensive set of facilities provided in ANOVA/MANOVA is not repeated in Discriminant Analysis).

Normal distribution.  It is assumed that the data (for the variables) represent a sample from a multivariate normal distribution.  Note that Discriminant Analysis makes it very simple to produce histograms of frequency distributions from within Scrollsheets (with a single keystroke).  Thus, the user can examine whether or not variables are normally distributed.  However, note that violations of the normality assumption are usually not "fatal," meaning, that the resultant significance tests etc. are still "trustworthy."  ANOVA/MANOVA provides specific tests for normality.

Homogeneity of variances/covariances.  It is assumed that the variance/covariance matrices of variables are homogeneous across groups.  Again, minor deviations are not that important; however, before accepting final conclusions for an important study it is probably a good idea to review the within-groups variances and correlation matrices.  In particular the scatterplot matrix that can be produced from the Descriptive Statistics dialog can be very useful for this purpose.  When in doubt, try re-running the analyses excluding one or two groups that are of less interest.  If the overall results (interpretations) hold up, you probably do not have a problem.  You may also use the numerous tests and facilities in ANOVA/MANOVA to examine whether or not this assumption is violated in your data.  However, as mentioned in ANOVA/MANOVA, the multivariate Box M test for homogeneity of variances/covariances is particularly sensitive to deviations from multivariate normality, and should not be taken too "seriously."

Correlations between means and variances.  The major "real" threat to the validity of significance tests occurs when the means for variables across groups are correlated with the variances (or standard deviations).  Intuitively, if there is large variability in a group with particularly high means on some variables, then those high means are not reliable.  However, the overall significance tests are based on pooled variances, that is, the average variance across all groups.  Thus, the significance tests of the relatively larger means (with the large variances) would be based on the relatively smaller pooled variances, resulting erroneously in statistical significance.  In practice, this pattern may occur if one group in the study contains a few extreme outliers, who have a large impact on the means, and also increase the variability.  To guard against this problem, inspect the descriptive statistics, that is, the means and standard deviations or variances for such a correlation.  ANOVA/MANOVA also allows you to plot the means and variances (or standard deviations) in a scatterplot.

The matrix ill-conditioning problem.  Another assumption of discriminant function analysis is that the variables that are used to discriminate between groups are not completely redundant.  As part of the computations involved in discriminant analysis, STATISTICA will invert the variance/covariance matrix of the variables in the model.  If any one of the variables is completely redundant with the other variables then the matrix is said to be ill-conditioned, and it cannot be inverted.  For example, if a variable is the sum of three other variables that are also in the model, then the matrix is ill-conditioned.

Tolerance values.  In order to guard against matrix ill-conditioning, STATISTICA will constantly check the so-called tolerance value for each variable.  This value is also routinely displayed when you ask to review the summary statistics for variables that are in the model, and those that are not in the model.  This tolerance value is computed as 1 minus R-square of the respective variable with all other variables included in the current model.  Thus, it is the proportion of variance that is unique to the respective variable.  You may also refer to Multiple Regression to learn more about multiple regression and the interpretation of the tolerance value.  In general, when a variable is almost completely redundant (and, therefore, the matrix ill-conditioning problem is likely to occur), the tolerance value for that variable will approach 0.  The default value in Discriminant Analysis for the minimum acceptable tolerance is 0.01.  STATISTICA will issue a matrix ill-conditioning message when the tolerance for any variable falls below that value, that is if any variable is more than 99% redundant (the user may change this default value).


Discriminant Function Analysis - Classification

  Discriminant Function Analysis Introductory Overview - Classification

Another major purpose to which discriminant analysis is applied is the issue of predictive classification of cases.  Once a model has been finalized and the discriminant functions have been derived, how well can we predict to which group a particular case belongs?

A priori and post hoc predictions.  Before going into the details of different estimation procedures, we would like to make sure that this difference is clear.  Obviously, if we estimate, based on some data set, the discriminant functions that best discriminate between groups, and then use the same data to evaluate how accurate our prediction is, then we are very much capitalizing on chance.  In general, one will always get a worse classification when predicting cases that were not used for the estimation of the discriminant function.  Put another way, post hoc predictions are always better than a priori predictions.  (The trouble with predicting the future a priori is that one does not know what will happen; it is much easier to find ways to predict what we already know has happened.)  Therefore, one should never base one's confidence regarding the correct classification of future observations on the same data set from which the discriminant functions were derived; rather, if one wants to classify cases predictively, it is necessary to collect new data to "try out" (validate) the utility of the discriminant functions.

Classification functions.  Discriminant Analysis will automatically compute the classification functions.  These are not to be confused with the discriminant functions.  The classification functions can be used to determine to which group each case most likely belongs.  There are as many classification functions as there are groups.  Each function allows us to compute classification scores for each case for each group, by applying the formula:

S  = c  + w  *x  + w  *x  + ... + w  *x

 i    i    i1  1    i2  2          im  m

In this formula, the subscript i denotes the respective group; the subscripts 1, 2, ..., m denote the m variables; ci is a constant for the i'th group, wij is the weight for the j'th variable in the computation of the classification score for the i'th group; xj is the observed value for the respective case for the j'th variable.  Si is the resultant classification score.

We can use the classification functions to directly compute classification scores for some new observations (for example, these function can be specified in the spreadsheet formulas as the formulas for computing new variables; as new cases are added to the file, the classification scores are then automatically computed).

Classification of cases.  Once we have computed the classification scores for a case, it is easy to decide how to classify the case: in general we classify the case as belonging to the group for which it has the highest classification score (unless the a priori classification probabilities are widely disparate; see below).  Thus, if we were to study high school students' post-graduation career/educational choices (e.g., attending college, attending a professional or trade school, or getting a job) based on several variables assessed one year prior to graduation, we could use the classification functions to predict what each student is most likely to do after graduation.  However, we would also like to know the probability that the student will make the predicted choice.  Those probabilities are called posterior probabilities, and can also be computed.  However, to understand how those probabilities are derived, let us first consider the so-called Mahalanobis distances.

Mahalanobis distances.  You may have read about these distances in other parts of STATISTICA user manual (e.g., in Multiple Regression).  In general, the Mahalanobis distance is a measure of distance between two points in the space defined by two or more correlated variables.  For example, if there are two variables that are uncorrelated, then we could plot points (cases) in a standard two-dimensional scatterplot; the Mahalanobis distances between the points would then be identical to the Euclidean distance; that is, the distance as, for example, measured by a ruler.  If there are three uncorrelated variables, we could also simply use a ruler (in a 3-D plot) to determine the distances between points.  If there are more than 3 variables, we cannot represent the distances in a plot any more.  Also, when the variables are correlated, then the axes in the plots can be thought of as being non-orthogonal that is, they would not be positioned in right angles to each other.  In those cases, the simple Euclidean distance is not an appropriate measure, while the Mahalanobis distance will adequately account for the correlations.

Mahalanobis distances and classification.  For each group in our sample, we can determine the location of the point that represents the means for all variables in the multivariate space defined by the variables in the model.  These points are called group centroids.  For each case we can then compute the Mahalanobis distances (of the respective case) from each of the group centroids.  Again, we would classify the case as belonging to the group to which it is closest, that is, where the Mahalanobis distance is smallest.

Posterior classification probabilities.  Using the Mahalanobis distances to do the classification, we can now derive probabilities.  The probability that a case belongs to a particular group is basically proportional to the Mahalanobis distance from that group centroid (it is not exactly proportional because we assume a multivariate normal distribution around each centroid).  Because we compute the location of each case from our prior knowledge of the values for that case on the variables in the model, these probabilities are called posterior probabilities.  In summary, the posterior probability is the probability, based on our knowledge of the values of other variables, that the respective case belongs to a particular group.  Of course, Discriminant Analysis will automatically compute those probabilities for all cases (or for selected cases only for validation studies).

A priori classification probabilities.  There is one additional factor that needs to be considered when classifying cases.  Sometimes, we know ahead of time that there are more observations in one group than in any other; thus, the a priori probability that a case belongs to that group is higher.  For example, if we know ahead of time that 60% of the graduates from our high school usually go to college (20% go to a professional school, and another 20% get a job), then we should adjust our prediction accordingly: a priori, and all other things being equal, it is more likely that a student will attend college that choose either of the other two options.  Discriminant Analysis will allow you to specify different a priori probabilities, which will then be used to adjust the classification of cases (and the computation of posterior probabilities) accordingly.

In practice, the researcher needs to ask him or herself whether the unequal number of cases in different groups in the sample is a reflection of the true distribution in the population, or whether it is only the (random) result of the sampling procedure.  In the former case, we would set the a priori probabilities to be proportional to the sizes of the groups in our sample, in the latter case we would specify the a priori probabilities as being equal in each group.  The specification of different a priori probabilities can greatly affect the accuracy of the prediction.

Summary of the prediction.  A common result that one looks at in order to determine how well the current classification functions predict group membership of cases is the classification matrix.  The classification matrix shows the number of cases that were correctly classified (on the diagonal of the matrix) and those that were misclassified.

Another word of caution.  To reiterate, post hoc predicting of what has happened in the past is not that difficult.  It is not uncommon to obtain very good classification if one uses the same cases from which the classification functions were computed.  In order to get an idea of how well the current classification functions "perform," one must classify (a priori) different cases, that is, cases that were not used to estimate the classification functions.  In Discriminant Analysis you can flexibly use the selection conditions to include or exclude cases from the computations; thus, the classification matrix can be computed for "old" cases as well as "new" cases.  Only the classification of new cases allows us to assess the predictive validity of the classification functions; the classification of old cases only provides a useful diagnostic tool to identify outliers or areas where the classification function seems to be less adequate.

Summary

In general Discriminant Analysis is a very useful tool (1) for detecting the variables that allow the researcher to discriminate between different (naturally occurring) groups, and (2) for classifying cases into different groups with a better than chance accuracy.


  Discriminant Function Analysis - Startup Panel

When you first open the Discriminant Analysis module, the Stepwise Discriminant Function Analysis dialog will open (see also, Discriminant Function Analysis - Index).  Here, you will be able to specify the variables for the analysis and the type of missing data deletion (see below).

Stepwise Discriminant Function Analysis dialog:

Variables button:  Choosing this option will bring up a standard variable selection window.  STATISTICA expects (1) that you specify a grouping variable containing codes (text values) that uniquely identify to which group each case belongs, and (2) that you specify an independent variable list of continuous variables that will later be used in the discriminant function analysis.  Note that you can later "deselect" independent variables.  Therefore, specify at this point that all variables that you might want to use later.

Codes for Grouping Variable button:  This option will bring up a standard codes selection window in which you can specify the codes that are used in the data file to identify to which group each case belongs.

Missing Data:  Discriminant Analysis allows the user to ignore cases with missing data on any variable (missing data are casewise deleted), or to substitute missing data by the overall means for the respective variables (missing data are substituted by means).  This combo box allows the user to choose between these two methods of dealing with missing data.


  Discriminant Function Analysis - Specifying the Analysis

The Model Definition dialog allows you to specify the type of analysis and other options.

Model Definition dialog:

Variables

Method

Tolerance Value

Stepwise Discriminant Function Analysis

Review Correlation Matrix/Means/SD


Specifying the Analysis - Variables

  Specifying the Discriminant Function Analysis - Variables

With this option the user can select or de-select variables for the analysis from among those selected on the startup panel.  After clicking on this button the standard variable selection dialog window will appear.


Specifying the Analysis - Method

  Specifying the Discriminant Function Analysis - Method

This combo box has three settings: standard, forward stepwise, and backward stepwise.

Standard:  If the standard method is selected, then all selected variables will be simultaneously entered into the model.

Forward Stepwise:  If forward stepwise is selected, then STATISTICA will move variables into the model in successive steps; at each step the variable with the largest F to enter value will be chosen for inclusion in the model.  The stepping will terminate when no other variable has an F to enter value that is greater than that specified under option F to enter.

Backward Stepwise:  If backward stepwise is selected, STATISTICA will first move all selected variables into the equation, and then remove variables one by one; at each step, the variable with the smallest F to remove value will be removed from the model.  The stepping will terminate when no other variable in the model has an F to remove value smaller than that specified under option F to remove.


Specifying the Analysis - Tolerance Value

  Specifying the Discriminant Function Analysis - Tolerance Value

The tolerance value is discussed in the Introductory Overview section as well as the user manual.  In short, the tolerance value of a variable is computed as the 1-R square of that variable with all other variables in the model.  Thus, if a variable has a tolerance value that is smaller than the default value of 0.01, then that variable is more than 99% redundant with the other variables already in the model.  If STATISTICA detects a variable with a tolerance value smaller than that specified in this option, it will issue an error message.  It is not recommended to set this value much smaller than the default value.  The inclusion of highly redundant variables in the analysis may later lead to potentially serious round-off errors in the matrix inversion or canonical analysis, due to matrix ill-conditioning.


Specifying the Analysis - Stepwise Discriminant Function Analysis

  Specifying the Discriminant Function Analysis - Stepwise Discriminant Function Analysis

This set of options is only available if you select one of the two stepwise methods above.

F to enter/remove:  In general, in stepwise discriminant function analysis, variables will be entered into the model if their respective F to enter value is larger than that specified in this option; variables will be removed from the model if their respective F to remove value is smaller than that specified in this option.  Note that the F to enter value must always be larger than the F to remove value.  If, in a forward stepwise analysis, you want to enter all variables, set the F to enter value to a very small number (e.g., 0.0001) and the F to remove value to 0.0.  If, in a backward stepwise analysis, you want to remove all variables from a model, set the F to enter value to a very large number (e.g., 9999.), and the F to remove value to a marginally smaller value of equal magnitude (e.g., 9998.).

Number of steps:  The number specified in this option will determine the maximum number of steps that will be performed.  Note that this option takes precedence over the F to enter/remove values, that is, stepping will terminate after the maximum number of steps has been reached, regardless of whether or not additional variables would qualify for inclusion in or exclusion from the model based on their F to enter or F to remove values.

Display of results:  If this combo box is set to summary only, then STATISTICA will perform all steps of the stepwise analysis, and only display the full results dialog after the last step.  However, that dialog will include an option to review the major summary statistics for the stepwise procedure.  Specifically, the Summary of stepwise analysis option on the results dialog will display for each step in the analysis the respective F to enter or remove and associated p-level, the number of variables in the model, and the overall Wilks' lambda with the associated F value and significance level.  If this combo box is set to at each step, then STATISTICA will display at each step (starting with step 0) the full results dialog at each step (starting with step 0).


Specifying the Analysis - Review Correlation Matrix/Mean/SD

  Specifying the Discriminant Function Analysis - Review Correlation Matrix/Mean/SD

This option will bring up the Descriptive Statistics and Graphs dialog that allows the user to review the means, standard deviations, and the variances/covariances or correlations for all variables.  Means and standard deviations can be reviewed for all groups combined or by groups; the correlations can be computed by collapsing across groups, or by pooling the within-groups correlations.  Histograms of the frequency distributions of the variables can also be produced for all groups combined or by groups; scatterplots can be produced for the overall correlations (collapsed across groups) as well as for the pooled within-groups correlations.


Discriminant Function Analysis - Descriptive Stats & Graphs

  Discriminant Analysis - Descriptive Stats & Graphs

When you click on the Review Correlation Matrix/Means/SD button in the Model Definition dialog, the Descriptive Statistics dialog will open.

Descriptive Statistics dialog:

Pooled Within-Groups Covariances & Correlations

Total Covariances & Correlations

Graph (Scatterplot Matrix)

Means & Number of Cases

Box and Whisker Plot

Standard Deviations

Other Plot Options


  Descriptive Stats & Graphs - Pooled Within-Groups Covariances & Correlations

This option will first bring up a Scrollsheet with the pooled within-groups covariances for all variables, and another Scrollsheet with the pooled within-groups correlations.  The default graph for these Scrollsheets is the scatterplot, which will be computed to reflect the pooled within-groups correlations.  Specifically, the scatterplot will show the individual values in terms of their deviations from the respective group mean.  In this plot, the variable on the horizontal axis actually represents deviations of the respective cases from the means of the variable in the respective groups to which the cases belong; in short, the two axes in the plot represent within-groups deviation scores (from the respective means).


  Descriptive Stats & Graphs - Total Covariances & Correlations

This option will first bring up a Scrollsheet with the overall covariances, and another Scrollsheet with the overall correlations.  These covariances and correlations are computed in the usual manner, that is, collapsed across all groups.  The default graph in these Scrollsheets is again the scatterplot which is constructed in the usual manner.


  Descriptive Stats & Graphs - Graph (Scatterplot Matrix)

This option will bring up a scatterplot matrix for the independent variables selected for the analysis.


  Descriptive Stats & Graphs - Means and Number of Cases

This option will bring up a Scrollsheet with the means for each variable for each group; the last column of the Scrollsheet will contain the number of cases in each group and the last row of the Scrollsheet will contain the overall means (collapsed across all groups, i.e., the weighted means).  The default graph for this Scrollsheet is the histogram, which can be produced for all cases or for selected groups only.  In all histograms, the normal distribution will be superimposed over the observed distribution.

Histogram for Selected Groups:  To produce a histogram for a selected group, first move the highlight (click with the mouse) in the Scrollsheet over the desired variable (column) and the desired group (row).  Then click with the right-mouse-button on that cell and select Quick Stats Graphs from the flying menu.  In the Quick Stats Graph menu, select the Histogram/Normal option to produce this graph.

Histogram for all groups combined:  To produce a histogram for all groups combined, move the highlight (click with the mouse) in the Scrollsheet over the desired variable (column) and into the last row (labeled All Groups).  Then click with the right-mouse-button on that cell and select Quick Stats Graphs from the flying menu.  In the Quick Stats Graph menu, select the Histogram/Normal option to produce this graph.


  Descriptive Stats & Graphs - Box & Whisker Plot

With this option the user can produce a box and whisker plot for the selected variables.  Note that this is a graph of each selected variable, collapsed across all groups.  In order to graphically compare groups, choose the Box and whisker plot (by group) plot or the Categorized histogram option.

Median and quartiles.  After selecting this option and after selecting a variable for the plot, the Box-Whisker Type dialog will open.  If you select to compute for the box-whisker plot, the median and quartiles, then those values will be computed according to the setting of the Percentiles option on the STATISTICA Defaults:  General dialog (choose option General on the Options pull-down menu).  For computational details, see Percentiles.


  Descriptive Stats & Graphs - Standard Deviations

This option will bring up a Scrollsheet of the standard deviations.  As in the Scrollsheet of means, the total number of cases in each group will be displayed in the last column of the Scrollsheet, and the total standard deviations for each variable will be displayed in the last row of the Scrollsheet.  The default graph for this Scrollsheet is also the histogram which works in the same way as described under option Means & number of cases.


  Descriptive Stats & Graphs - Other Plot Options

Categorized Histogram (by group) button:  This option allows the user to produce a categorized histogram for a selected variable.  This graph shows the distribution of the variable in the different groups.

Box and Whisker Plot (by group) button:  This option allows the user to produce a box and whisker plot for a selected variable.  This graph shows the mean or median, and different measures of dispersion for the variable (e.g., standard deviation, quartile range) in the different groups.  The specific type of box and whisker plot is selected in an intermediate dialog.  For computational details concerning the median and quartiles, see the description of percentiles in the STATISTICA Defaults:  General dialog.

Categorized Scatterplot (by group) button:  This option allows the user to produce a categorized scatterplot for two selected variables, by group.

Categorized Probability Plot (by group) button:  This option allows the user to produce a categorized probability plot for a selected variable, by group.  The normal probability plot provides a quick check of whether or not the respective variable is normally distributed in the groups.  If so, the points in the plot will approximate a straight line.


  Discriminant Function Analysis - Results & Classification

The Discriminant Function Analysis Results dialog offers the following options:

Discriminant Function Analysis Results dialog:

Variables in the Model

Variables Not in the Model

Distances Between Groups

Summary of Stepwise Analysis

Canonical Analysis

Classification Functions

Classification Matrix

Classification of Cases

Squared Mahalanobis Distances

Posterior Probabilities

Save classif/distances/probs

A priori Classification Probabilities

Next


Results & Classification - Variables in the Model

  Discriminant Function Analysis Results & Classification - Variables in the Model

This option will first bring up a Scrollsheet with summary statistics for all variables currently in the model:

Wilks' Lambda:  This is the Wilks' lambda for the overall model that will result after removing the respective variable.  Remember that Wilks' lambda can assume values in the range of 0 (perfect discrimination) to 1 (no discrimination).

Partial Lambda:  This is the Wilks' lambda associated with the unique contribution of the respective variable to the discriminatory power of the model.

F to remove:  This is the F value associated with the respective partial Wilks' lambda.

p-level:  This is the p-level associated with the respective F to remove.  Note that in stepwise analyses, these p-levels should be interpreted with caution; refer to the Overview section.

Tolerance:  The tolerance value of a variable is computed as 1-R square of the respective variable with all other variables in the model (in this Scrollsheet).  Thus, the tolerance is a measure of the respective variable's redundancy.  For example, a tolerance value of .10 means that the variable is 90% redundant with the other variables in the model.

1-Tolerance (R-square):  This is the R square value of the respective variable with all other variables in the model (in this Scrollsheet).


Results & Classification - Variables Not in the Model

  Discriminant Function Analysis Results & Classification - Variables Not in the Model

This option will bring up a Scrollsheet with the summary statistics for all variables that are currently not in the model.  The statistics displayed in this Scrollsheet are essentially identical to those described in Variables in the model.


Results & Classification - Distances Between Groups

  Discriminant Function Analysis Results & Classification - Distances Between Groups

This option will bring up a Scrollsheet with the squared Mahalanobis distances between the group centroids.  The Mahalanobis distance is similar to the standard Euclidean distance measure, except that it takes into account the correlations between variables.  The larger the differences in this Scrollsheet, the farther are the respective groups apart from each other, and the more discriminatory power does our current model possess for discriminating between the respective two groups.

Together with the Scrollsheet of Mahalanobis distances, two other Scrollsheets will be displayed: one with the F values associated with the respective distances and another with the respective p-levels.  Again, those p-levels should be interpreted with caution, unless one brings to the analysis strong a priori hypotheses concerning which pairs of groups should show particularly large (and significant) distances.


Results & Classification - Summary of Stepwise Analysis

  Discriminant Function Analysis Results & Classification - Summary of Stepwise Analysis

This option is only available if a stepwise discriminant function analysis was performed.  After clicking on this button, a Scrollsheet will come up which summarizes for each step:

(1)	which variable was entered or removed (indicated by the letters E or R in parentheses after the respective variable name in the first column of the Scrollsheet);

(2)	the step number;

(3)	the F to enter or remove;

(4)	the respective degrees of freedom for that F value;

(5)	the p-level for that F value;

(6)	the number of variables in the model after the respective step;

(7)	the overall value of Wilks' lambda after the respective step;

(8)	the F value associated with the lambda;

(9)	the degrees of freedom for that F value;

(10)	the p-level for that F value.


Results & Classification - Canonical Analysis

  Discriminant Function Analysis Results & Classification - Canonical Analysis

A canonical analysis can only be performed if at least three groups were specified for the analysis, and if there are at least two variables in the model.  In that case, STATISTICA will perform a complete canonical analysis, and compute the discriminant functions.  These and related values can be reviewed from a separate results dialog (Canonical Analysis).


Results & Classification - Classification Functions

  Discriminant Function Analysis Results & Classification - Classification Functions

This option will bring up the classification functions.  Classification functions are computed for each group and can be used directly to classify cases.  We would classify a case into the group for which it has the highest classification score.  We could use these functions in Data Management to define the transformations for three new variables (one for each group).  As we would then enter new cases, STATISTICA would automatically compute the classification scores for each group.


Results & Classification - Classification Matrix

  Discriminant Function Analysis Results & Classification - Classification Matrix

The classification matrix contains information about the number and percent of correctly classified cases in each group.  Note that you can use the standard case selection conditions (click on the Sel field on the status bar) to classify only cases that were not used to compute the current classification functions.  Also, the computations for the classification of cases will be based on a priori classification probabilities that are either (1) the same for all groups, (2) proportional to the respective group sizes, or (3) user defined (see a priori Classification Probabilities, below).  If User defined a priori probabilities are selected, then, before the computations begin, you will be prompted to specify the a priori classification probabilities for each group.


Results & Classification - Classification of Cases

  Discriminant Function Analysis Results & Classification - Classification of Cases

After clicking on this button a Scrollsheet will be displayed with the classification for each selected case.  The classifications are ordered into a first, second, and third choice.  The column under the header 1 contains the first classification choice, that is, the group for which the respective case had the highest posterior probability (see option Posterior Probabilities).  The rows marked by the asterisk are cases that are misclassified.


Results & Classification - Squared Mahalanobis Distances

  Discriminant Function Analysis Results & Classification - Squared Mahalanobis Distances

After clicking on this option a Scrollsheet with the squared Mahalanobis distances of each case from each group centroid will be displayed.  These distances are similar to the squared Euclidean distances of the respective case from the centroids for each group (the point defined by the means for all variables in the respective group).  However, unlike the Euclidean distance, the Mahalanobis distance takes into account the intercorrelations between the variables in the model (which define the multivariate space).

A case will generally be classified into the group that it is closest to, unless widely disparate a priori probabilities lead to very different posterior classification probabilities.  Asterisks in the first column of the Scrollsheet will mark misclassified cases.

The default custom graph for this Scrollsheet is the iconplot which allows you to quickly compare the Mahalanobis distances of each case from the different groups.


Results & Classification - Posterior Probabilities

  Discriminant Function Analysis Results & Classification - Posterior Probabilities

Given the Mahalanobis distances of a case from the different group centroids, we can compute the respective posterior classification probabilities for each group.  In general, the further away a case is from a group centroid, the less likely it is that the case belongs to that group.  The posterior probabilities are determined by the Mahalanobis distances and the a priori probabilities (see below).  A case will be classified into the group for which it has the highest posterior classification probability.  Misclassified cases will be marked in the Scrollsheet by asterisks.

The default custom graph for this Scrollsheet is the iconplot which allows you to quickly compare the posterior probabilities for each case, for each group.


Results & Classification - Save Classifications, Distances, Probabilities

  Discriminant Function Analysis Results & Classification - Save Classifications, Distances, Probabilities

After clicking on this button, a pop-up menu will be displayed that allows you to save the actual classifications for each case, the squared Mahalanobis distances, or the posterior probabilities.


Results & Classification - A Priori Classification Probabilities

  Discriminant Function Analysis Results & Classification - A Priori Classification Probabilities

There are three choices available here: proportional to group sizes, same for all groups, and user defined.  The a priori probabilities specify how likely it is, without using any prior knowledge of the values for the variables in the model, that a case will fall into one of the groups.  For example, in an educational study of high school drop-outs, it may happen that overall, there are fewer drop-outs than students who stay (i.e., there are different base rates); thus, the a priori probability that a student drops out is lower than that a student remains in school.  The a priori probabilities can greatly affect the accuracy of the classification.  If differential base rates are not of interest for the study, or if one knows that there are about an equal number of cases in each group, then one could set the a priori probabilities to be the same for all groups.  If the differential base rates are reflected in the sample sizes (as they would be, if the sample is a probability sample) then set the a priori probabilities to be proportional to group sizes.

Finally, if you have specific knowledge about the base rates (for example, based on previous research), then set the a priori probabilities to user defined.  In that case, after you subsequently request classification of cases, a dialog window will appear allowing you to specify the a priori probabilities for each group. If those probabilities do not add up to 1, STATISTICA will automatically adjust them proportionately.


Results & Classification - Next Button

  Discriminant Function Analysis Results & Classification - Next Button

This button will only appear if you are in the process of performing a stepwise discriminant analysis, and requested to display results At each step.  Clicking the Next button will bring up the results for the next step in the stepwise analysis.


  Discriminant Function Analysis - Canonical Analysis

When you click on the Canonical Analysis button in the Discriminant Function Analysis Results dialog, the Canonical Analysis dialog will open.

Canonical Analysis dialog:

Chi-square Tests of Successive Roots

Coefficients for Canonical Variables

Factor Structure

Means for Canonical Variables

Canonical Scores for Each Case

Save Canonical Scores

Histogram of Canonical Scores for Selected Group

Combined Histogram for all Groups

Scatterplot of Canonical Scores


Canonical Analysis - Chi-square Tests of Successive Roots

  Discriminant Function Analysis (Canonical Analysis) - Chi-square Tests of Successive Roots

This option will first bring up a Scrollsheet with a step-down test for canonical roots (and discriminant functions).  The first row in that Scrollsheet contains the test of significance for all roots combined.  The second row contains the significance of the remaining roots, after removing the first root, and so on.  Thus, this Scrollsheet allows us to evaluate how many significant roots to interpret.


Canonical Analysis - Coefficients for Canonical Variables

  Discriminant Function Analysis (Canonical Analysis) - Coefficients for Canonical Variables

This option will first bring up a Scrollsheet with the raw discriminant (canonical) function coefficients.  These are the coefficients that can be used to compute the raw canonical scores for each case for each discriminant function.  Also included in this Scrollsheet will be the eigenvalues for each discriminant function and the cumulative proportion of (common) variance extracted by each discriminant function.

Standardized Discriminant Function Weights.  A second Scrollsheet that will be displayed reports the standardized discriminant function coefficients.  These are the coefficients that are based on standardized variables, and thus, these coefficients pertain to equal scales of measurement.  Therefore, these coefficients may be compared in order to determine the magnitudes and directions of the (unique) contributions of the variables to each canonical function.


Canonical Analysis - Factor Structure

  Discriminant Function Analysis (Canonical Analysis) - Factor Structure

This option will bring up a Scrollsheet with the pooled within-groups correlations of variables with the respective discriminant (canonical) functions.  If you are familiar with factor analysis (see Factor Analysis), you may think of these correlations as the factor loadings of the respective variables on the discriminant functions.

Some authors have argued that to interpret the "meaning" of the discriminant functions, one should use these structure coefficients rather than the standardized discriminant function coefficients.  Refer to the Introductory Overview section of the Discriminant Analysis for a discussion of this argument.  The most important thing to remember is that the discriminant function weights denote the unique (partial) contribution of each variable to the discriminant functions, while the structure coefficients denote the simple correlations between the variables and the functions; therefore, the structure coefficients are usually more appropriate for substantive interpretations of functions.


Canonical Analysis - Means for Canonical Variables

  Discriminant Function Analysis (Canonical Analysis) - Means for Canonical Variables

This option will bring up the means for the discriminant functions.  These means allow one to determine the groups that are best identified (discriminated) by each discriminant function.


Canonical Analysis- Canonical Scores for each Case

  Discriminant Function Analysis (Canonical Analysis) - Canonical Scores for each Case

This option will allow the user to review the discriminant function scores for each case.


Canonical Analysis - Save Canonical Scores

  Discriminant Function Analysis (Canonical Analysis) - Save Canonical Scores

This option allows the user to save the canonical scores in a STATISTICA data file.


Canonical Analysis - Histogram of Canonical Scores for Selected Group

  Discriminant Function Analysis (Canonical Analysis) - Histogram of Canonical Scores for Selected Group

This option allows the user to produce a histogram of the frequency distribution of the canonical scores for selected groups.


Canonical Analysis- Combined Histogram for all Groups

  Discriminant Function Analysis (Canonical Analysis) - Combined Histogram for all Groups

This option allows the user to produce a histogram of the frequency distribution of the canonical scores for all groups combined.


Canonical Analysis- Scatterplot of Canonical Scores

  Discriminant Function Analysis (Canonical Analysis) - Scatterplot of Canonical Scores

This option allows the user to produce a scatterplot of the canonical scores for pairs of discriminant functions (canonical roots).  This option is not available if only one canonical (discriminant) function was extracted.  This plot is very useful for determining how each discriminant function contributes to the discrimination between groups.


  Discriminant Function Analysis - A Priori Probabilities

Specify the a priori classification probabilities for each group.  You can enter a common value for the probabilities that will be used in each group (e.g., .333) and then click on the Apply button to apply that value to the individual groups or you can specify individual probabilities for each group by typing in the values in the appropriate edit fields.  The probabilities should add up to 1.0; if they don't, then STATISTICA will proportionately adjust them accordingly.

The a priori probabilities specify how likely it is, without using any prior knowledge of the values for the variables in the model, that a case will fall into one of the groups.  For example, in an educational study of high school drop-outs, it may happen that there are overall fewer drop-outs than students who stay (i.e., there are different base rates); thus, the a priori probability that a student drops out is lower than that a student remains in school.  The a priori probabilities can greatly affect the accuracy of the classification.  If differential base rates are not of interest for the study, or if one knows that there are about an equal number of cases in each group, then one could set the a priori probabilities to be the same for all groups.  If the differential base rates are reflected in the sample sizes (as they would be, if the sample is a probability sample) then set the a priori probabilities to be proportional to group sizes.  Finally, if you have specific knowledge about the base rates (for example, based on previous research), then set the a priori probabilities to user defined.


  Discriminant Function Analysis - Selecting a Group

Click on the group for which to produce the graph.


  Discriminant Function Analysis - Selecting a Canonical Root

Select the canonical root for which to produce the graph.


  Discriminant Function Analysis - Selecting two Canonical Roots

Select the two canonical roots for which to produce the scatterplot.


  Discriminant Function Analysis - Notes and Technical Information

General

The Discriminant Function Analysis module uses the standard formulas for computing the discriminant functions, performing the canonical analysis, and for computing the classification statistics.  A step-by-step discussion of the computations can be found in Jennrich (1977), who also describes the computation of the group classification function coefficients and the posterior classification probabilities.

Formulas

The formulas for computing the Mahalanobis distances and classification of cases, given a-priori probabilities, are described in Lindeman, Merenda, and Gold (1980, Chapter 6).  Detailed descriptions of computational formulas and examples are also presented in, for example, Cooley and Lohnes (1971, Chapters 9 and 10) and Pedhazur (1973, Chapters 17 and 18).

Wilks' lambda:  The Wilks' lambda statistic for the overall discrimination is computed as the ratio of the determinant (det) of the within-groups variance/covariance matrix over the determinant of the total variance covariance matrix:

Wilks' lambda = det(W)/det(T)

The F approximation to Wilks' lambda is computed following Rao (1951).

Partial lambda:  The partial lambda is computed as the multiplicative increment in lambda that results from adding the respective variable:

partial lambda = lambda(after)/lambda(before)

Put another way, the partial lambda is the ratio of Wilks' lambda after adding the respective variable over the Wilks' lambda before adding the variable.

The corresponding F statistic (see Rao, 1965, 0. 470) is computed as:

F = [(n-q-p)/(q-1)]*[(1-partial lambda)/partial lambda]

Where:

n	is the number of cases

q	is the number of groups

p	is the number of variables

Testing complex hypotheses using SEPATH

In order to test complex hypotheses about relationships between variables in different groups, you can use the Structural Equation Modeling (SEPATH) module of STATISTICA.  In that module, you can fit hypothesized models about the relationships between variables to correlation (covariance) matrices in one or more groups.  The SEPATH module allows you to constrain parameters (to equality) across groups, and to analyze moment matrices so that you can test hypotheses about the differences in means.


  Nonparametric Statistics & Distribution Fitting - Index

Introductory Overview

Startup Panel

  Two-by-two frequency tables

  Observed vs. expected frequencies

Nonparametric correlation

  Spearman R, Kendall Tau, Gamma

Comparing two groups

  Wald-Wolfowitz, Mann-Whitney, Kolmogorov-Smirnov

Comparing multiple groups

  Kruskal-Wallis ANOVA

  Median test

Comparing two variables

  Sign test, Wilcoxon matched pairs test

Comparing multiple variables

  Friedman test & Kendall concordance

  Cochran test

  Descriptive statistics

Distribution fitting

Notes and Technical Information


  Nonparametric Statistics & Distribution Fitting - Introductory Overview

General Purpose

Brief Overview of Nonparametric Procedures

When to Use Which Method

Distribution Fitting


Nonparametric Statistics & Distribution Fitting - General Purpose

  Nonparametric Statistics & Distribution Fitting Introductory Overview - General Purpose

Brief review of the idea of significance testing.  To understand the idea of nonparametric statistics (the term nonparametric was first used by Wolfowitz, 1942) first requires a basic understanding of parametric statistics.  The Elementary Concepts chapter of the manual introduces the concept of statistical significance testing based on the sampling distribution of a particular statistic (you may want to review that chapter before reading on).  In short, if we have a basic knowledge of the underlying distribution of a variable, then we can make predictions about how, in repeated samples of equal size, this particular statistic will "behave," that is, how it is distributed.  For example, if we draw 100 random samples of 100 adults each from the general population, and compute the mean height in each sample, then the distribution of the standardized means across samples will likely approximate the normal distribution (to be precise, Student's t distribution with 99 degrees of freedom; see below).  Now imagine that we take an additional sample in a particular city ("Tallburg") where we suspect that people are taller than the average population.  If the mean height in that sample falls outside the upper 95% tail area of the t distribution then we conclude that, indeed, the people of Tallburg are taller than the average population.

Are most variables normally distributed?  In the above example we relied on our knowledge that, in repeated samples of equal size, the standardized means (for height) will be distributed following the t distribution (with a particular mean and variance).  However, this will only be true if in the population the variable of interest (height in our example) is normally distributed, that is, if the distribution of people of particular heights follows the normal distribution (the bell-shape distribution).  For many variables of interest, we simply do not know for sure that this is the case.  For example, is income distributed normally in the population?  -- probably not.  The incidence rates of rare diseases are not normally distributed in the population, the number of car accidents is also not normally distributed, and neither are very many other variables in which a researcher might be interested.

Sample size.  Another factor that often limits the applicability of tests based on the assumption that the sampling distribution is normal is the size of the sample of data available for the analysis (sample size; n).  We can assume that the sampling distribution is normal even if we are not sure that the distribution of the variable in the population is normal, as long as our sample is large enough (e.g., 100 or more observations).  However, if our sample is very small, then those tests can be used only if we are sure that the variable is normally distributed, and there is no way to test this assumption if the sample is small.

Problems in measurement.  Applications of tests that are based on the normality assumptions are further limited by a lack of precise measurement.  For example, let us consider a study where grade point average (GPA) is measured as the major variable of interest.  Is an A average twice as good as a C average?  Is the difference between a B and an A average comparable to the difference between a D and a C average?  Somehow, the GPA is a crude measure of scholastic accomplishments that only allows us to establish a rank ordering of students from "good" students to "poor" students.  This general measurement issue is usually discussed in statistics textbooks in terms of types of measurement or scale of measurement.  Without going into too much detail, most common statistical techniques such as analysis of variance (and t-tests), regression, etc. assume that the underlying measurements are at least of interval quality, meaning that equally spaced intervals on the scale can be compared in a meaningful manner (e.g, B minus A is equal to D minus C).  However, as in our example, this assumption is very often not tenable, and the data rather represent a rank ordering of observations (ordinal scale) rather than precise measurements.

Parametric and nonparametric methods.  Hopefully, after this somewhat lengthy introduction, the need is evident for statistical procedures that allow us to process data of "low quality," from small samples, on variables about which nothing is known (concerning their distribution).  Specifically, nonparametric methods were developed to be used in cases when the researcher knows nothing about the parameters of the variable of interest in the population (hence the name nonparametric).  In more technical terms, nonparametric methods do not rely on the estimation of parameters (such as the mean or the standard deviation) describing the distribution of the variable of interest in the population.  Therefore, these methods are also sometimes (and more appropriately) called parameter-free methods or distribution-free methods.


Nonparametric Statistics & Distribution Fitting - Brief Overview of Nonparametric Methods

  Nonparametric Statistics & Distribution Fitting Introductory Overview - Brief Overview of Nonparametric Methods

Basically, there is at least one nonparametric equivalent for each parametric general type of test.  In general, these tests fall into the following categories:

•	Tests of differences between groups (independent samples);

•	Tests of differences between variables (dependent samples);

•	Tests of relationships between variables.

Differences between independent groups.  Usually, when we have two samples that we want to compare concerning their mean value for some variable of interest, we would use the t-test for independent samples (in Basic Statistics); nonparametric alternatives for this test are the Wald-Wolfowitz runs test, the Mann-Whitney U test, and the Kolmogorov-Smirnov two-sample test.  If we have multiple groups, we would use analysis of variance (see ANOVA/MANOVA; the nonparametric equivalents to this method are the Kruskal-Wallis analysis of ranks and the Median test.

Differences between dependent groups.  If we want to compare two variables measured in the same sample we would customarily use the t-test for dependent samples (in Basic Statistics; for example, if we wanted to compare students' math skills at the beginning of the semester with their skills at the end of the semester).  Nonparametric alternatives to this test are the Sign test and Wilcoxon's matched pairs test.  If the variables of interest are dichotomous in nature (i.e., "pass" vs. "no pass") then McNemar's Chi-square test is appropriate.  If there are more than two variables that were measured in the same sample, then we would customarily use repeated measures ANOVA.  Nonparametric alternatives to this method are Friedman's two-way analysis of variance and Cochran Q test (if the variable was measured in terms of categories, e.g., "passed" vs. "failed").  Cochran Q is particularly useful for measuring changes in frequencies (proportions) across time.

Relationships between variables.  To express a relationship between two variables one usually computes the correlation coefficient.  Nonparametric equivalents to the standard correlation coefficient are Spearman R, Kendall Tau, and coefficient Gamma (see Nonparametric correlation.  If the two variables of interest are categorical in nature (e.g., "passed" vs. "failed" by "male" vs. "female") appropriate nonparametric statistics for testing the relationship between the two variables are the Chi-square test, the Phi coefficient, and the Fisher exact test (see Nonparametrics Startup Panel).  In addition, a simultaneous test for relationships between multiple cases is available:  Kendall coefficient of concordance.  This test is often used for expressing inter-rater agreement among independent judges who are rating (ranking) the same stimuli.

Descriptive statistics.  When one's data are not normally distributed, and the measurements at best contain rank order information, then computing the standard descriptive statistics (e.g., mean, standard deviation) is sometimes not the most informative way to summarize the data.  For example, in the area of psychometrics it is well known that the rated intensity of a stimulus (e.g., perceived brightness of a light) is often a logarithmic function of the actual intensity of the stimulus (brightness as measured in objective units of Lux).  In this example, the simple mean rating (sum of ratings divided by the number of stimuli) is not an adequate summary of the average actual intensity of the stimuli.  (In this example, one would probably rather compute the geometric mean.)  Nonparametrics and Distributions will compute a wide variety of measures of location (mean, median, mode, etc.) and dispersion (variance, average deviation, quartile range, etc.) to provide the "complete picture" of one's data (see Descriptive Statistics).


Nonparametric Statistics & Distribution Fitting - When to Use Which Method

  Nonparametric Statistics & Distribution Fitting Introductory Overview - When to Use Which Method

It is not easy to give simple advice concerning the use of nonparametric procedures.  Each nonparametric procedure has its peculiar sensitivities and blind spots.  For example, the Kolmogorov-Smirnov two-sample test is not only sensitive to differences in the location of distributions (for example, differences in means) but is also greatly affected by differences in their shapes.  The Wilcoxon matched pairs test assumes that one can rank order the magnitude of differences in matched observations in a meaningful manner.  If this is not the case, one should rather use the Sign test.  In general, if the result of a study is important (e.g., does a very expensive and painful drug therapy help people get better?), then it is always advisable to run different nonparametric tests; should discrepancies in the results occur contingent upon which test is used, one should try to understand why some tests give different results.  On the other hand, nonparametric statistics are less statistically powerful (sensitive) than their parametric counterparts, and if it is important to detect even small effects (e.g., is this food additive harmful to people?) one should be very careful in the choice of a test statistic.

Large data sets and nonparametric methods.  Nonparametric methods are most appropriate when the sample sizes are small.  When the data set is large (e.g., n > 100) it often makes little sense to use nonparametric statistics at all.  The Elementary Concepts chapter of the manual briefly discusses the idea of the central limit theorem.  In a nutshell, when the samples become very large, then the sample means will follow the normal distribution even if the respective variable is not normally distributed in the population, or is not measured very well.  Thus, parametric methods, which are usually much more sensitive (i.e., have more statistical power) are in most cases appropriate for large samples.  However, the tests of significance of many of the nonparametric statistics described here are based on asymptotic (large sample) theory; therefore, meaningful tests can often not be performed if the sample sizes become too small.  Please refer to the descriptions of the specific tests to learn more about their power and efficiency.


Nonparametric Statistics & Distribution Fitting - Distribution Fitting

  Nonparametric Statistics & Distribution Fitting Introductory Overview - Distribution Fitting

In some research applications one can formulate hypotheses about the specific distribution of the variable of interest.  For example, variables whose values are determined by an infinite number of independent random events will be distributed following the normal distribution: one can think of a person's height as being the result of very many independent factors such as numerous specific genetic predispositions, early childhood diseases, nutrition, etc.  As a result, height tends to be normally distributed in the U.S. population.  On the other hand, if the values of a variable are the result of very rare events, then the variable will be distributed according to the Poisson distribution (sometimes called the distribution of rare events).  For example, industrial accidents can be thought of as the result of the intersection of a series of unfortunate (and unlikely) events, and their frequency tends to be distributed according to the Poisson distribution.  These and other available distributions are described in greater detail in the respective help sections (see Distribution Fitting Startup Panel).  The Nonparametrics and Distributions module allows you to test the goodness-of-fit of your data to the respective hypothesized distribution.  You can also enter any set of arbitrary expected values (i.e., "make up" a hypothesized distribution) and test the fit of an observed set of values (observed vs. expected frequencies).

Normality assumption.  Another common application where distribution fitting procedures are useful is when one wants to verify the assumption of normality before using some parametric test (see above).


  Nonparametrics & Distributions - Startup Panel

This dialog gives access to all nonparametric statistics and distributions included in this module (see also, Nonparametrics & Distributions - Index).  Each dialog option is described in detail in the following topics (click on a topic name for more information about that topic):

Nonparametric Statistics

Descriptive Statistics

Distribution Fitting

Note that alternative fitting options are available in Process Analysis, Stats 2D Graphs (P-P plots, Q-Q plots, Histograms) and Survival Analysis.


  Nonparametric Statistics - Startup Panel

The following nonparametric tests are available from the Nonparametrics & Distributions - Startup Panel.

  2x2 Tables, Chi/V/Phi square, McNemar, Fisher exact

  Observed vs. expected Chi-square

  Correlation

  Wald-Wolfowitz runs test

  Mann-Whitney U test

  Kolmogorov-Smirnov two-sample test

  Kruskal-Wallis ANOVA by ranks and Median test

  Sign test

  Wilcoxon matched pairs test

  Friedman ANOVA & Kendall concordance

  Cochran Q test


  Nonparametric Statistics Startup Panel - 2x2 Tables, Chi/V/Phi square, McNemar, Fisher exact

This option will bring up a dialog (see 2x2 Tables, Chi/V/Phi square, McNemar, Fisher exact) that allows the user to enter frequencies into a 2 x 2 table, and to calculate various statistics to evaluate the relationship between two dichotomous variables.  Thus, the 2 x 2 option can be used as an alternative to correlation when the two variables of interest are dichotomous.  STATISTICA will also compute the McNemar Chi-square Test for the significance of changes.  In that case, one can think of the 2 x 2 option as an alternative to the t-test for dependent samples when the variable of interest is dichotomous.

For more detailed information, see 2x2 Tables, Chi/V/Phi square, McNemar, Fisher exact.


  Nonparametric Statistics Startup Panel - Observed vs. Expected Chi-square

This option allows the user to evaluate the fit of data (frequencies) to any arbitrary set of expected frequencies.  The procedure will prompt the user to enter 2 variables, one containing the expected and another containing the observed frequencies.  The standard Chi-square value is then computed.

For more information, see Nonparametric Statistics Introductory Overview.


  Nonparametric Statistics Startup Panel - Correlation

This option allows the user to compute three different alternatives to the parametric Pearson product-moment correlation coefficient: Spearman R, Kendall tau, and Gamma.  After selecting this option, a dialog will be displayed from which the user can select variables, and the specific type of correlation to be computed (see Correlation).  The user can choose to compute single nonparametric correlations, or matrices of nonparametric correlations.  The results Scrollsheet features the scatterplot as the default graph, so the user can easily graph the correlations.  A scatterplot matrix for all variables can also be produced.  Note that alternative nonparametric measures of contingency between two variables are also available in Basic Statistics (tables).

Spearman R.  Spearman R assumes that the variables under consideration were measured on at least an ordinal (rank order) scale, that is, that the individual observations can be ranked into two ordered series.

Kendall tau.  Kendall tau is equivalent to Spearman R with regard to the underlying assumptions.  It is also comparable in terms of its statistical power.  However, Spearman R and Kendall tau are usually not identical in magnitude because their underlying logic as well as their computational formulas are very different.  Siegel and Castellan (1988) express the relationship of the two measures in terms of the inequality:

-1 ≤ 3 * Kendall tau - 2 * Spearman R ≤ 1

More importantly, Kendall tau and Spearman R imply different interpretations: Spearman R can be thought of as the regular Pearson product moment correlation coefficient; that is, in terms of proportion of variability accounted for, except that Spearman R is computed from ranks.  Kendall tau, on the other hand, represents a probability; that is, it is the difference between the probability that the two variables are in the same order in the observed data versus the probability that the two variables are in different orders.

Gamma.  The Gamma statistic is preferable to Spearman R or Kendall tau when the data contain many tied observations.  In terms of the underlying assumptions, Gamma is equivalent to Spearman R or Kendall tau; in terms of its interpretation and computation, it is more similar to Kendall tau than Spearman R.  In short, Gamma is also a probability; specifically, it is computed as the difference between the probability that the rank ordering of the two variables agree minus the probability that they disagree, divided by 1 minus the probability of ties.  Thus, Gamma is basically equivalent to Kendall tau, except that ties are explicitly taken into account.

For more information, see Correlation.


  Nonparametric Statistics Startup Panel - Wald-Wolfowitz Runs Test

The Wald-Wolfowitz runs test is a nonparametric alternative to the t-test for independent samples.  The procedure expects the data to be arranged in the same way as for the t-test for independent samples (Basic Statistics).  Specifically, the data file should contain a coding variable (independent variable) with at least two distinct codes that uniquely identify the group membership of each case in the data file.  Choosing this option will bring up a dialog window for selecting the coding variable and a dependent variable list (variables in which the two groups are to be compared), and the codes used in the coding variable for identifying the two groups (option Codes).

Assumptions and interpretation.  The Wald-Wolfowitz runs test works as follows:  Imagine that you want to compare male and female subjects on some variable.  You can sort the data by that variable and look for cases when, in the sorted data, same-gender subjects are adjacent to each other.  If there are no differences between male and female subjects, then the number and "lengths" of such adjacent "runs" of subjects of the same gender will be more or less random.  If not, the two groups (genders in our example) are somehow different from each other.  This test assumes that the variable under consideration is continuous, and that it was measured on at least an ordinal scale (i.e., rank order).  The Wald-Wolfowitz runs test assesses the hypothesis that two independent samples were drawn from two populations that differ in some respect, i.e., not just with respect to the mean, but also with respect to the general shape of the distribution.  The null hypothesis is that the two samples were drawn from the same population.  In this respect, this test is different from the parametric t-test which strictly tests for differences in locations (means) of two samples.

See also, Wald-Wolfowitz Runs test.


  Nonparametric Statistics Startup Panel - Mann-Whitney U Test

The Mann-Whitney U test is a nonparametric alternative to the t-test for independent samples.  The procedure expects the data to be arranged in the same way as for the t-test for independent samples.  Specifically, the data file should contain a coding variable (independent variable) with at least two distinct codes that uniquely identify the group membership of each case in the data file.  Pressing this button will bring up a dialog window for selecting the coding variable and a dependent variable list (variables for which the two groups are to be compared), and the codes used in the coding variable for identifying the two groups (option Codes).

Assumptions and interpretation.  The Mann-Whitney U test assumes that the variable under consideration was measured on at least an ordinal (rank order) scale.  The interpretation of the test is essentially identical to the interpretation of the result of a t-test for independent samples, except that the U test is computed based on rank sums rather than means.  The U test is the most powerful (or sensitive) nonparametric alternative to the t-test for independent samples; in fact, in some instances it may offer even greater power to reject the null hypothesis than the t-test.

With samples larger than 20, the sampling distribution of the U statistic rapidly approaches the normal distribution (see Siegel, 1956).  Hence, the U statistic (adjusted for ties) will be accompanied by a z value (normal distribution variate value), and the respective p value.

Exact probabilities for small samples.  For small to moderate sized samples, STATISTICA will compute an exact probability associated with the respective U statistic.  This probability is based on the enumeration of all possible values of U (unadjusted for ties), given the number of observations in the two samples (see Dinneen & Blakesley, 1973).  Specifically, for small to moderate sized samples, the program will report (in the last column of the Scrollsheet) the value 2 * p, where p is 1 minus the cumulative (one-sided) probability of the respective U statistic.  To reiterate, the computations for this probability value are based on the assumption of no ties in the data (ranks).  Note that this limitation usually leads to only a small underestimation of the statistical significance of the respective effects (see Siegel, 1956).

See also, Mann-Whitney U Test.


  Nonparametric Statistics Startup Panel - Kolmogorov-Smirnov Test

The Kolmogorov-Smirnov test is another nonparametric alternative to the t-test for independent samples.  The procedure expects the data to be arranged in the same way as for the t-test for independent samples.  Specifically, the data file should contain a coding variable (independent variable) with at least two distinct codes that uniquely identify the group membership of each case in the data file.  Choosing this option will bring up a dialog window for selecting the coding variable and a dependent variable list (variables on which the two groups are to be compared), and the codes used in the coding variable for identifying the two groups (option Codes).

Assumptions and interpretation.  The Kolmogorov-Smirnov test assesses the hypothesis that two samples were drawn from different populations.  Unlike the parametric t-test for independent samples or the Mann-Whitney U test (see above), which test for differences in the location of two samples (differences in means, differences in average ranks, respectively), the Kolmogorov-Smirnov test is also sensitive to differences in the general shapes of the distributions in the two samples (i.e., to differences in dispersion, skewness, etc.).  Thus, its interpretation is similar to that of the Wald-Wolfowitz runs test.

See also, Kolmogorov-Smirnov Test.


  Nonparametric Statistics Startup Panel - Kruskal-Wallis ANOVA by Ranks and Median Test

These two tests are nonparametric alternatives to between-groups one-way analysis of variance.  STATISTICA expects the data to be arranged in the same way as one would arrange a data file for an analysis with ANOVA/MANOVA.  Specifically, the data file should contain a coding variable with codes to uniquely identify the group membership of each case.  Up to 10 groups can be compared.

Choosing this option will bring up a dialog window for specifying the coding variable (Variables) and a dependent variables list (variables on which the groups are to be compared), and the codes (Codes) used in the coding variable for identifying the different groups that are to be compared.

Assumptions and interpretation.  The Kruskal-Wallis ANOVA by Ranks test assumes that the variable under consideration is continuous and that it was measured on at least an ordinal (rank order) scale.  The test assesses the hypothesis that the different samples in the comparison were drawn from the same distribution or from distributions with the same median.  Thus, the interpretation of the Kruskal-Wallis test is basically identical to that of the parametric one-way ANOVA, except that it is based on ranks rather than means.

The Median test is a "crude" version of the Kruskal-Wallis ANOVA in that it frames the computation in terms of a contingency table.  Specifically, STATISTICA will simply count the number of cases in each sample that fall above or below the common median, and compute the Chi-square value for the resulting 2 x k samples contingency table.  Under the null hypothesis (all samples come from populations with identical medians), we expect approximately 50% of all cases in each sample to fall above (or below) the common median.  The Median test is particularly useful when the scale contains artificial limits, and many cases fall at either extreme of the scale ("off the scale").  In this case, the Median test is in fact the only appropriate method for comparing samples.

See also, Kruskal-Wallis ANOVA and Median Test.


  Nonparametric Statistics Startup Panel - Sign Test

The sign test is a nonparametric alternative to the t-test for dependent samples.  The test is applicable to situations when the researcher has two measures (e.g., under two conditions) for each subject and wants to establish that the two measurements (or conditions) are different.  After choosing this option, a dialog will be displayed from which the user can choose variables from two lists.  Each variable in the first list will be compared to each variable in the second list.

Assumptions and interpretation.  The only assumption required by this test is that the underlying distribution of the variable of interest is continuous; no assumptions about the nature or shape of the underlying distribution are required.  The test simply computes the number of times (across subjects) that the value of the first variable (A) is larger than that of the second variable (B).  Under the null hypothesis (stating that the two variables are not different from each other) we expect this to be the case about 50% of the time.  Based on the binomial distribution we can compute a z value for the observed number of cases where A > B, and compute the associated tail probability for that z value.  For small n's (less than 20) you may prefer to use the tabulated values found in Siegel and Castellan (1988) to evaluate statistical significance.

See also, Sign Test.


Nonparametric Statistics Startup Panel - Wilcoxon Matched Pairs

  Nonparametric Statistics Startup Panel - Wilcoxon Matched Pairs Test

This test is a nonparametric alternative to the t-test for dependent (correlated) samples.  Choosing this option will bring up a dialog for specifying variables from two lists.  Each variable from the first list will be compared with each variable from the second list.  This is the same arrangement of data that is expected for the t-test (dependent samples) in the Basic Statistics module.

Assumptions and interpretation.  The procedure assumes that the variables under consideration were measured on a scale that allows the rank ordering of observations based on each variable (i.e., ordinal scale) and that allows rank ordering of the differences between variables (this type of scale is sometimes referred to as an ordered metric scale, see Coombs, 1950).  Thus, the required assumptions for this test are more stringent than those for the Sign test (see above).  However, if they are met, that is, if the magnitudes of differences (e.g., different ratings by the same individual) contain meaningful information, then this test is more powerful than the sign test.  In fact, if the assumptions for the parametric t-test for dependent samples (interval scale) are met, then this test is almost as powerful as the t-test.

See also, Wilcoxon Matched Pairs Test.


  Nonparametric Statistics Startup Panel - Friedman ANOVA and Kendall's Concordance

These two tests are somewhat different in nature, however, they require similar user input.  Friedman ANOVA is a nonparametric alternative to one-way repeated measures analysis of variance.  The Kendall concordance statistic is similar to Spearman R (nonparametric correlation between two variables, see above) except that it expresses the relationship between multiple cases.  For Friedman ANOVA, the procedure expects the data to be arranged in the same way as one would arrange a data file for a within-subjects (repeated measures) analysis of variance with ANOVA/MANOVA.  Specifically, the values for each level of the repeated measures factor should be contained in a different variable.  Choosing this option will bring up a dialog window for specifying a list of variables.

Assumptions and interpretation:  Friedman ANOVA.  The Friedman ANOVA by ranks test assumes that the variables (levels) under consideration were measured on at least an ordinal (rank order) scale.  The null hypothesis for the procedure is that the different columns of data (i.e., STATISTICA variables) contain samples drawn from the same population, or specifically, populations with identical medians.  Thus, the interpretation of results from this procedure is similar to that of a repeated measures ANOVA.

Assumptions and interpretation:  Kendall concordance.  The Kendall concordance coefficient expresses the simultaneous association (relatedness) between k sets of rankings (i.e., cases; correlated samples).  For example, this statistic is commonly used to assess inter-judge reliability.  Basically, the concordance coefficient is the average of all Spearman R's between cases; specifically:

average Spearman R = (k * concordance -1)/(k-1)

Thus the general assumptions of this test are identical to that of the Spearman rank order correlation.

The range of Kendall concordance is from 0 to +1.  Values close to zero represent lack of agreement in the rankings of the variables (e.g., objects) among cases (e.g., judges), while values close to 1 represent perfect agreement in the rankings of the variables (objects) among cases (judges).

See also, Friedman ANOVA & Kendall's Concordance dialog.


  Nonparametric Statistics Startup Panel - Cochran Q Test

The Cochran Q test is an extension of McNemar's Chi-square test for changes (see option 2 x 2 Tables ..., see above) in frequencies or proportions to k (more than two) dependent samples.  Specifically, it tests whether several matched frequencies or proportions differ significantly among themselves.  After selecting this option, you will be prompted to specify a variable list and codes that identify the two categories or levels of the dichotomous measure.  The test assumes that the variables are coded as 1's and 0's, and the codes specified by the user will cause the variables to be transformed accordingly (only for this analysis, the data file itself will not be changed).

Assumptions and interpretation.  The Cochran Q test only requires a nominal scale, or that the data have been artificially dichotomized.  A typical example where the Q test is useful is when one wants to compare the difficulty of dichotomous questionnaire items that can either be answered right or wrong.  Here, each variable in the data file would represent one item, and contain 0's (wrong) and 1's (right).  If the Q test is significant, then we conclude that the items are of different difficulty since different items were answered correctly by more or fewer respondents.

See also, Cochran Q Test.


  Ordinal Descriptive Statistics - Startup Panel

Choosing this option will allow the user to calculate various ordinal descriptive statistics (median, percentiles, quartiles, range, quartile range) and other descriptive statistics (mean, harmonic mean, geometric mean, standard deviation, skewness, kurtosis, variance, average deviation, sum) for selected variables.

The user can also specify specific percentiles values to be computed and displayed in the Scrollsheet; by default the program will compute the quartile values, that is, the 25'th and 75'th percentiles.

In addition to the standard descriptive statistics (minimum value, maximum value, mean, valid n) the statistics discussed below are computed for each variable.

Median	Average deviation

Mode	Range

Geometric mean	Quartile range

Harmonic mean	Skewness

Variance and standard deviation	Kurtosis


  Ordinal Descriptive Statistics Startup Panel - Median

The median value is the value that "splits the sample in half," given the respective variable.  Fifty percent of the cases will fall below the median, and fifty percent will fall above the median.  If the median value is very different from the mean, then the distribution of data is skewed.


  Ordinal Descriptive Statistics Startup Panel - Mode

The mode is the value that occurs with the greatest frequency.  The frequency with which the mode occurs is also displayed; if there is a tie (i.e., more than one value occurs with equal frequency) then the respective frequency column will contain the label multiple to indicate that more than one mode was found.


  Ordinal Descriptive Statistics Startup Panel - Geometric Mean

The geometric mean is the product of all scores to the power of 1/n (one over the valid number of cases).  The geometric mean is useful in instances when we know that the measurement scale is not linear.  For example, in the area of psychometrics it is well known that the rated intensity of a stimulus (e.g., brightness of a light) is often a logarithmic function of the actual intensity of the stimulus (brightness measured in units of Lux).  In this instance, the geometric mean is a better "summary" of ratings than the simple mean.  STATISTICA calculates the geometric mean via the logarithm (log):

                         n

log(geometric mean) = [Σ   (log(x ))]/n

                        i=1      i

where:

xi	is the i'th score

n	is the number of valid cases

Note that if a variable contains negative values or a zero (0), then the geometric mean cannot be calculated.


  Ordinal Descriptive Statistics Startup Panel - Harmonic Mean

The harmonic mean is sometimes used to average frequencies (sample sizes).  The harmonic mean is calculated as:

           n

HM = n / Σ   (1/x )

          i=1    i

where:

HM	is the harmonic mean

n	is the number of valid cases

xi	is the score for the i'th valid case

If a variable contains a zero (0) as a valid score, then the harmonic mean cannot be calculated (since it implies division by zero).


  Ordinal Descriptive Statistics Startup Panel - Variance and Standard Deviation

The variance and standard deviation are standard measures of variability (see Basic Statistics).  STATISTICA will calculate the variance as the sum of squared deviations about the mean divided by n-1 (not n).  The standard deviation is calculated as the square root of this value.  The n-1 vs. n issue is usually of little practical importance.  Technically, we most often want to estimate the variability of the population from which the current sample was drawn (for example, we would like to generalize our results to all males, given our random sample of males).  In this case we should always use n-1 as the divisor in the computations; using n as the divisor results in purely descriptive statistics for the current sample.


  Ordinal Descriptive Statistics Startup Panel - Average Deviation

The average deviation is another measure of variability.  It is calculated as the sum of absolute deviations (mean for respective variable minus raw score) divided by n (number of valid cases).


  Ordinal Descriptive Statistics Startup Panel - Range

The range of a variable is also an indicator of variability.  It is calculated as the largest valid score minus the smallest valid score.


  Ordinal Descriptive Statistics Startup Panel - Quartile Range

The quartile range of a variable is calculated as the value of the 75th percentile minus the value of the 25th percentile.  Thus it is the width of the range about the median that includes 50% of the cases.


  Ordinal Descriptive Statistics Startup Panel - Skewness

As implied by the term, the skewness is a measure of the extent to which the distribution of the respective variable is skewed to the left (negative value) or right (positive value), relative to the standard normal distribution (for which the skewness is 0).  The measure skewness is related to the third moment of the distribution.  The skewness is defined as:

                              3

Skewness = n*M /[(n-1)*(n-2)*σ  ]

              3

where:

M3	is equal to:  Σ(xi-Meanx)**3

n	is the valid number of cases

σ**3	is the standard deviation (sigma) raised to the third power


  Ordinal Descriptive Statistics Startup Panel - Kurtosis

The kurtosis is a measure of how "wide" or "skinny" ("flat" or "peaked") the distribution is for the respective variable, relative to the standard normal distribution (for which the kurtosis is equal to 0).  It is also sometimes referred to as the fourth moment of the distribution.  The kurtosis is defined as:

                                                            4

Kurtosis = [n*(n+1)*M  - 3*M *M *(n-1)]/[(n-1)*(n-2)*(n-3)*σ  ]

                     4      2  2

where:

Mj	is equal to:  Σ(xi-Meanx)**j

n	is the valid number of cases

σ**4	is the standard deviation (sigma) raised to the fourth power


  Distribution Fitting - Startup Panel

General

After choosing any of the following distributions, you are prompted to specify the variable to which the chosen distribution will be fitted.  Regardless of the distribution selected from this dialog, you can toggle through all other distributions of the same type (continuous or discrete) on the subsequent dialog.  After a variable has been specified, the parameters yielding the best fit for each of the respective types of distributions are computed.  These parameters are displayed as default values, but user-specified values may be entered.

  Normal Distribution	  Chi-square distribution

  Rectangular distribution	  Binomial distribution

  Exponential distribution	  Poisson distribution

  Gamma distribution	  Geometric distribution

  Lognormal distribution	  Bernoulli distribution


  Distribution Fitting Startup Panel - Normal Distribution

The normal distribution (the "bell-shaped curve" which is symmetrical about the mean) is a theoretical function commonly used in inferential statistics as an approximation to sampling distributions (see also Elementary Concepts).  In general, the normal distribution provides a good model for a random variable, when:

(1)  There is a strong tendency for the variable to take a central value;

(2)  Positive and negative deviations from this central value are equally likely;

(3)  The frequency of deviations falls off rapidly as the deviations become larger.

As an underlying mechanism that produces the normal distribution, one may think of an infinite number of independent random (binomial) events that bring about the values of a particular variable.  For example, there are probably a nearly infinite number of factors that determine a person's height (thousands of genes, nutrition, diseases, etc.).  Thus, height can be expected to be normally distributed in the population.

The normal distribution function is determined by the following formula:

                1/2                        2

f(x) = 1/[(2*π)   * σ] * e**{-1/2*[(x-μ)/σ] }

-∞ < x < ∞

where

μ	is the mean

σ	is the standard deviation

e	is Euler's constant (2.71...)

π	is the constant Pi (3.14...)


  Distribution Fitting Startup Panel - Rectangular Distribution

The rectangular distribution is useful for describing random variables with a constant probability density over the defined range a<b:

f(x) = 1/(b-a)     a<x<b

     = 0           elswhere

where

a<b	are constants


  Distribution Fitting Startup Panel - Exponential Distribution

If T is the time between occurrences of rare events that happen on the average with a rate λ per unit of time, then T is distributed exponentially with parameter λ (lambda).  Thus, the exponential distribution is frequently used to model the time interval between successive random events.  Examples of variables distributed in this manner would be the gap length between cars crossing an intersection, life-times of electronic devices, or arrivals of customers at the check-out counter in a grocery store.

The exponential distribution function is defined as:

          -λx

f(x) = λ*e

0 ≤ x < ∞

λ > 0

where:

λ	(lambda) is an exponential function parameter (an alternative parameterization is scale parameter b=1/λ)

e	is Euler's constant (2.71...)


  Distribution Fitting Startup Panel - Gamma Distribution

The probability density function of the exponential distribution has a mode of zero.  In many instances, it is known a priori that the mode of the distribution of a particular random variable of interest is not equal to zero (e.g., when modeling the distribution of the life-times of a product such as an electric light bulb, or the serving time taken at a ticket booth at a baseball game).  In those cases, the Gamma distribution is more appropriate for describing the  underlying distribution.  The Gamma distribution is defined as:

                         c−1  -x/b

f(x) = {1/[bΓ(c)]}*[x/b]    *e

0 ≤ x, c > 0

where

Γ	(gamma) is the Gamma function

c	is the Shape parameter

b	is the Scale parameter

e	is Euler's constant (2.71...)


Distribution Fitting Startup Panel - Log-normal Distribution

  Distribution Fitting Startup Panel - Lognormal Distribution

The log-normal distribution is often used in simulations of variables such as personal incomes, age at first marriage, or tolerance to poison in animals.  In general, if x is a sample from a normal distribution, then y = e**x is a sample from a log-normal distribution.  Thus, the log-normal distribution is defined as:

                                   2   2

                1/2     -[log(x)-μ] /2σ

f(x) = 1/[xσ(2)   ] * e

0 < x < ∞

μ > 0

σ > 0

where

μ	is the scale parameter

σ	is the shape parameter

e	is Euler's constant (2.71...)


  Distribution Fitting Startup Panel - Chi-square Distribution

The sum of v independent squared random variables, each distributed following the standard normal distribution, is distributed as Chi-square with v degrees of freedom.  This distribution is most frequently used in the modeling of random variables (e.g., representing frequencies) in statistical applications.  The Chi-square distribution is defined by:

            ν/2                (ν/2)-1    -x/2

f(x) = {1/[2    * Γ(ν/2)]} * [x        * e    ]

ν = 1, 2, ..., 0 < x

where

ν	is the degrees of freedom

e	is Euler's constant (2.71...)

Γ	(gamma) is the Gamma function


  Distribution Fitting Startup Panel - Binomial Distribution

The binomial distribution is useful for describing distributions of binomial events, such as the number of males and females in a random sample of companies, or the number of defective components in samples of 20 units taken from a production process.  The binomial distribution is defined as:

                         x    n-x

f(x) = [n!/(x!*(n-x)!)]*p  * q

for x = 0,1,2,...,n

where:

p	is the probability that the respective event will occur

q	is equal to 1-p

n	is the maximum number of independent trials


  Distribution Fitting Startup Panel - Poisson Distribution

The Poisson distribution is also sometimes referred to as the distribution of rare events.  Examples of Poisson distributed variables are number of accidents per person, number of sweepstakes won per person, or the number of catastrophic defects found in a production process.  It is defined as:

         x    -λ

f(x) = (λ  * e   )/x!

for x = 0,1,2,..., 0 < λ

where:

λ	(lambda) is the expected value of x (the mean)

e	is Euler's constant (2.71...)


  Distribution Fitting Startup Panel - Geometric Distribution

If independent Bernoulli trials are made until a "success" occurs, then the total number of trials required is a geometric random variable.  The geometric distribution is defined as:

              x-1

f(x) = p*(1-p)

for x = 1,2,...

where:

p	is the probability that a particular event (e.g., success) will occur


  Distribution Fitting Startup Panel - Bernoulli Distribution

This distribution best describes all situations where a "trial" is made resulting in either "success" or "failure," such as when tossing a coin, or when modeling the success or failure of a surgical procedure.  The Bernoulli distribution is defined as:

        x      1-x

f(x) = p *(1-p)

for x ∈ {0,1}

where:

p	is the probability that a particular event (e.g., success) will occur


  Nonparametrics - Two by Two Frequency Tables

Specify the frequencies for the 2x2 Table in this dialog.  In addition to the standard Pearson Chi-square statistic, and the corrected Chi-square statistic (V-square), the following statistics will be computed:

Yates' correction

Phi-square

Fisher exact test

McNemar Chi-square

Note that STATISTICA also includes two designated modules (the Tables option in Basic Statistics and Log-Linear) for the analysis of frequencies and contingencies in multi-dimensional tables of practically unlimited size and complexity.  The Tables option of Basic Statistics produces a comprehensive set of descriptive and inferential statistics; Log-Linear performs complete log-linear analyses of multi-way frequency tables.


Nonparametrics Two by Two Frequency Tables - Yate's Correction

  Nonparametrics Two by Two Frequency Tables - Yates Correction

The approximation of the Chi-square statistic in small 2x2 tables can be improved by reducing the absolute value of differences between expected and observed frequencies by 0.5 before squaring (Yates' correction).  This correction, which makes the estimation more conservative, is usually applied when the table contains only small observed frequencies, so that some expected frequencies become less than 10 (for further discussion of this correction, see Conover, 1974; Everitt, 1977; Hays, 1988; Kendall & Stuart, 1979; and Mantel, 1974).


  Nonparametrics Two by Two Frequency Tables - Phi-square

The Phi-square is a measure of correlation between the two categorical variables in the table.


  Nonparametrics Two by Two Frequency Tables - Fisher Exact Test

Given the marginal frequencies in the table, and assuming that in the population the two factors in the table are not related, how likely is it to obtain cell frequencies as uneven or worse than the ones that were observed?  For small n, this probability can be computed exactly by counting all possible tables that can be constructed based on the marginal frequencies.  This is the underlying rationale for the Fisher exact test.  It computes the exact probability under the null hypothesis of obtaining the current distribution of frequencies across cells, or one that is more uneven.


  Nonparametrics Two by Two Frequency Tables - McNemar Chi-square

This test is applicable in situations where the frequencies in the 2 x 2 table represent dependent samples.  For example, in a before-after design study, we may count the number of students who fail a test of minimal math skills at the beginning of the semester and at the end of the semester.  Two Chi-square values are reported: A/D and B/C.  The Chi-square A/D tests the hypothesis that the frequencies in cells A and D (upper left, lower right) are identical.  The Chi-square B/C tests the hypothesis that the frequencies in cells B and C (upper right, lower left) are identical.


  Nonparametrics - Observed vs. Expected Frequencies

This option allows the user to evaluate the fit of data (frequencies) to any arbitrary set of expected frequencies.  The procedure will prompt the user to enter 2 variables, one containing the expected and another containing the observed frequencies.  The standard Chi-square value is then computed.


  Nonparametrics - Correlation Coefficients

When you select the Correlations (Spearman, Kendall tau, Gamma) option from the Nonparametrics start-up panel, the Nonparametrics Correlations dialog will open.

Nonparametrics Correlations dialog:

Variables

Correlation

Compute

Matrix Plot


  Nonparametrics Correlation Coefficients - Variables

Select at least two variables for which correlations will be computed (each variable in the first list will be correlated with each variable in the second list).


  Nonparametrics Correlation Coefficients - Correlations

This combo box allows you to choose between the Spearman R, Kendall Tau, and Gamma coefficients (discussed below).

Spearman R:  Spearman R assumes that the variables under consideration were measured on at least an ordinal (rank order) scale, that is, that the individual observations can be ranked into two ordered series.

Kendall tau:  Kendall tau is equivalent to Spearman R with regard to the underlying assumptions.  It is also comparable in terms of its statistical power.  However, Spearman R and Kendall tau are usually not identical in magnitude because their underlying logic as well as their computational formulas are very different.  Siegel and Castellan (1988) express the relationship of the two measures in terms of the inequality:

-1 ≤ 3 * Kendall tau - 2 * Spearman R ≤ 1

More importantly, Kendall tau and Spearman R imply different interpretations: Spearman R can be thought of as the regular Pearson product moment correlation coefficient, that is, in terms of proportion of variability accounted for, except that Spearman R is computed from ranks.  Kendall tau, on the other hand, represents a probability, that is, it is the difference between the probability that in the observed data the two variables are in the same order versus the probability that the two variables are in different orders.

Gamma:  The Gamma statistic is preferable to Spearman R or Kendall tau when the data contain many tied observations.  In terms of the underlying assumptions, Gamma is equivalent to Spearman R or Kendall tau; in terms of its interpretation and computation it is more similar to Kendall tau than Spearman R.  In short, Gamma is also a probability; specifically, it is computed as the difference between the probability that the rank ordering of the two variables agree minus the probability that they disagree, divided by 1 minus the probability of ties.  Thus, Gamma is basically equivalent to Kendall tau, except that ties are explicitly taken into account.


  Nonparametrics Correlation Coefficients - Compute

You can choose to compute single nonparametric correlations or matrices of nonparametric correlations with the options in this combo box (described below).  The results Scrollsheet features the scatterplot as the default graph, so you can easily graph the correlations.

Detailed report:  Selecting this option will result not only in the correlations between the specified variables (see above), but also in the Valid n, t-value, and p-level for each correlation.

Matrix of two lists:  This option will compute only the correlations between the variables specified in the first list against the variables specified in the second list.

Square Matrix:  This option will compute correlations from a single list of variables (resulting in a square matrix of correlations).  Note that if you have already specified two lists of variables and then select this option, the two lists will be "stacked" to make one list of variables.


  Nonparametrics Correlation Coefficients - Matrix Plot

Click on this button to produce a scatterplot matrix for all selected variables.


  Nonparametrics - Comparing Two Groups

The following nonparametric tests are available for comparing two groups (the dialog options for each of the three tests are discussed below).

Wald-Wolfowitz runs test

Mann-Whitney U test

Kolmogorov-Smirnov two-sample test

Comparing two groups dialog:

Variables

Box and whisker plot

Categorized histogram


  Nonparametrics Comparing Two Groups - Wald-Wolfowitz Runs Test

The Wald-Wolfowitz runs test works as follows: Imagine that you want to compare male and female subjects on some variable.  You can sort the data by that variable and look for instances when, in the sorted data, same-gender subjects are adjacent to each other.  If there are no differences between male and female subjects, then the number and "lengths" of such adjacent "runs" of subjects of the same gender will be more or less random.  If not, the two groups (genders in our example) are somehow different from each other.  This test assumes that the variable under consideration is continuous, and that it was measured on at least an ordinal scale (i.e., rank order).  The Wald-Wolfowitz runs test assesses the hypothesis that two independent samples were drawn from two populations that differ in some respect, i.e., not just with respect to the mean, but also with respect to the general shape of the distribution.  The null hypothesis is that the two samples were drawn from the same population.  In this respect, this test is different from the parametric t-test which strictly tests for differences in locations (means) of two samples.

Siegel (1956) recommends a continuity correction when the combined sample sizes is not very large.  This adjusted z-score, along with its adjusted p-value, is given on the Wald-Wolfowitz Runs Test Results Scrollsheet.


  Nonparametrics Comparing Two Groups - Mann-Whitney U Test

The Mann-Whitney U test assumes that the variable under consideration was measured on at least an ordinal (rank order) scale.  The interpretation of the test is essentially identical to the interpretation of the result of a t-test for independent samples, except that the U test is computed based on rank sums rather than means.  The U test is the most powerful (or sensitive) nonparametric alternative to the t-test for independent samples; in fact, in some instances it may offer even greater power to reject the null hypothesis than the t-test.

With samples larger than 20, the sampling distribution of the U statistic rapidly approaches the normal distribution (see Siegel, 1956).  Hence, the U statistic (adjusted for ties) will be accompanied by a z value (normal distribution variate value), and the respective p value.

Exact probabilities for small samples.  For small to moderate sized samples, STATISTICA will compute an exact probability associated with the respective U statistic.  This probability is based on the enumeration of all possible values of U (unadjusted for ties), given the number of observations in the two samples (see Dinneen & Blakesley, 1973).  Specifically, for small to moderate sized samples, the program will report (in the last column of the Scrollsheet) the value 2 * (1-p), where p is the cumulative (one-sided) probability of the respective U statistic.  To reiterate, the computations for this probability value are based on the assumption of no ties in the data (ranks).  Note that this limitation usually leads to only a small underestimation of the statistical significance of the respective effects (see Siegel, 1956).


  Nonparametrics Comparing Two Groups - Kolmogorov-Smirnov Test

The Kolmogorov-Smirnov test assesses the hypothesis that two samples were drawn from different populations.  Unlike the parametric t-test for independent samples or the Mann-Whitney U test, which test for differences in the location of two samples (differences in means, differences in average ranks, respectively), the Kolmogorov-Smirnov test is also sensitive to differences in the general shapes of the distributions in the two samples, i.e., to differences in dispersion, skewness, etc.  Thus, its interpretation is similar to that of the Wald-Wolfowitz runs test.


  Nonparametrics Comparing Two Groups - Variables

Choosing this option will bring up the regular two-variable lists selection dialog.  In general, the procedure expects the data to be arranged in the same way as in the t-test for independent sample.  Specifically, the data file should contain a coding variable (independent or grouping variable) with at least two distinct codes that uniquely identify the group membership of each case in the data file.  Thus, in the first list, select the variable containing the grouping codes; then in the second list, select a list of variables for the respective comparison.

Next, specify the codes that were used in the grouping variable to uniquely identify the group membership of each case.  You can also double-click on the code edit field to bring up the Variable Values Window in order to select the appropriate grouping code.


  Nonparametrics Comparing Two Groups - Box and Whisker Plot

The box and whisker plot is a useful graphical method to compare the distribution of a variable in two groups.  Both medians and quartiles, or means and related measures of dispersion can be plotted.


  Nonparametrics Comparing Two Groups - Categorized Histogram

This option will produce a categorized histogram of the distribution of a selected variable, separately (categorized) for each group.


  Nonparametrics - Kruskal-Wallis ANOVA & Median Test

The Kruskal-Wallis ANOVA by ranks test assumes that the variable under consideration is continuous and that it was measured on at least an ordinal (rank order) scale.  This test assesses the hypothesis that the different samples in the comparison were drawn from the same distribution or from distributions with the same median.  Thus, the interpretation of the Kruskal-Wallis test is basically identical to that of the parametric one-way ANOVA, except that it is based on ranks rather than means.

The Median test is a "crude" version of the Kruskal-Wallis ANOVA in that it frames the computation in terms of a contingency table.  Specifically, the program will simply count the number of cases in each sample that fall above or below the common median, and compute the Chi-square value for the resulting 2 x k samples contingency table.  Under the null hypothesis (all samples come from populations with identical medians), we expect approximately 50% of all cases in each sample to fall above (or below) the common median.  The Median test is particularly useful when the scale contains artificial limits, and many cases fall at either extreme of the scale ("off the scale").  In this case, the Median test is in fact the most appropriate method for comparing samples.

Kruskal-Wallis ANOVA & Median Test dialog:

Variables

Codes

Batch Processing/Printing

Box and whisker plot

Categorized histogram


Kruskal-Wallis ANOVA & Median Test - Variables

  Nonparametrics Kruskal-Wallis ANOVA & Median Test - Variables

Clicking on this button will bring up the regular two-variable lists selection dialog.  In general, the procedure expects the data to be arranged in the same way as in the t-test for independent samples or between-groups ANOVA.  Specifically, the data file should contain a coding variable (independent or grouping variable) with at least two distinct codes that uniquely identify the group membership of each case in the data file.  Thus, in the first list, select the variable containing the grouping codes; then in the second list, select a list of variables for the respective comparison.


Kruskal-Wallis ANOVA & Median Test - Codes

  Nonparametrics Kruskal-Wallis ANOVA & Median Test - Codes

When you click on this button, the Selecting Codes dialog will open in which you can specify the codes that were used in the grouping variable (in order to uniquely identify the group membership of each case).


Kruskal-Wallis ANOVA & Median Test - Batch Processing and Printing

  Nonparametrics Kruskal-Wallis ANOVA & Median Test - Batch Processing and Printing

This option is applicable if you have selected either the Printer, Disk File, and/or Text/output Window as the output destination in the Page/Output Setup dialog.  If you set the Batch Processing/Printing option here, then all variables in the dependent variable list will be processed and the results printed without requiring any other user input.


Kruskal-Wallis ANOVA & Median Test - Box and Whisker Plot

  Nonparametrics Kruskal-Wallis ANOVA & Median Test - Box and Whisker Plot

The box and whisker plot is a useful graphical method to compare the distribution of a variable in the different groups.  Both medians and quartiles, or means and related measures of dispersion can be plotted.


Kruskal-Wallis ANOVA & Median Test - Categorized Histogram

  Nonparametrics Kruskal-Wallis ANOVA & Median Test - Categorized Histogram

This option will produce a categorized histogram of the distribution of a selected variable, separately (categorized) for each group.


  Nonparametrics - Comparing Two Variables

The following two nonparametric tests are available for comparing two variables (the dialog options for both tests are discussed below).

Sign test

Wilcoxon matched pairs test

Comparing Two Variables dialog:

Variables

Box and whisker plot


  Nonparametrics Comparing Two Variables - Sign Test

The only assumption required by this test is that the underlying distribution of the variable of interest is continuous; no assumptions about the nature or shape of the underlying distribution are required.  The test simply computes the number of times (across subjects) that the value of the first variable (A) is larger than that of the second variable (B).  Under the null hypothesis (stating that the two variables are not different from each other) we expect this to be the case about 50% of the time.  Based on the binomial distribution we can compute a z value for the observed number of cases where A > B, and compute the associated tail probability for that z value.  For small n's (less than 20) you may prefer to use the tabulated values found in Siegel and Castellan (1988) to evaluate statistical significance.


  Nonparametrics Comparing Two Variables - Wilcoxon Matched Pairs Test

This procedure assumes that the variables under consideration were measured on a scale that allows the rank ordering of observations based on each variable (i.e., ordinal scale) and that allows rank ordering of the differences between variables (this type of scale is sometimes referred to as an ordered metric scale, see Coombs, 1950).  Thus, the required assumptions for this test are more stringent than those for the Sign test.  However, if they are met, that is, if the magnitudes of differences (e.g., different ratings by the same individual) contain meaningful information, then this test is more powerful than the Sign test.  In fact, if the assumptions for the parametric t-test for dependent samples (interval scale) are met, then this test is almost as powerful as the t-test.


  Nonparametrics Comparing Two Variables - Variables

Choosing this option will bring up the standard two-variable lists selection dialog.  After you select the variables in the two lists, click on the OK button to compare each variable in the first list against each variable in the second list.


  Nonparametrics Comparing Two Variables - Box and Whisker Plot

The box and whisker plot is a useful graphical method to compare the distribution of two variables.  After clicking on this button, select the two variables for the plot.  Both medians and quartiles, or means and related measures of dispersion can be plotted.


Nonparametrics - Friedman ANOVA and Kendall Concordance

  Nonparametrics - Friedman ANOVA & Kendall Concordance

When you compute the Friedman ANOVA, the Kendall Concordance coefficient is also computed (the dialog options for both tests are discussed below).

Friedman ANOVA

Kendall concordance

Friedman ANOVA by Ranks dialog:

Variables

Box and whisker plot

The box and whisker plot is a useful graphical method to compare the distribution of two or more variables.  Both medians and quartiles, or means and related measures of dispersion can be plotted.


Friedman ANOVA and Kendall Concordance - Friedman ANOVA

  Nonparametrics Friedman ANOVA & Kendall Concordance - Friedman ANOVA

The Friedman ANOVA by ranks test assumes that the variables (levels) under consideration were measured on at least an ordinal (rank order) scale.  The null hypothesis for the procedure is that the different columns of data (i.e., STATISTICA variables) contain samples drawn from the same population, or specifically, populations with identical medians.  Thus, the interpretation of results from this procedure is similar to that of a repeated measures ANOVA.


Friedman ANOVA and Kendall Concordance - Kendall Concordance

  Nonparametrics Friedman ANOVA & Kendall Concordance - Kendall Concordance

Kendall concordance coefficient expresses the simultaneous association (relatedness) between k cases (correlated samples).  For example, this statistic is commonly used to assess inter-judge reliability.  Basically, the concordance coefficient is the average of all Spearman R's between variables; specifically:

average Spearman R = (k * concordance -1)/(k-1)

Thus the general assumptions of this test are identical to that of the Spearman rank order correlation.


Friedman ANOVA and Kendall Concordance - Variables

  Nonparametrics Friedman ANOVA & Kendall Concordance - Variables

Choosing this option will bring up the standard single variable list selection dialog from which you may select the variables to be analyzed.


Friedman ANOVA and Kendall Concordance - Box and Whisker Plot

  Nonparametrics Friedman ANOVA & Kendall Concordance - Box and Whisker Plot

The box and whisker plot is a useful graphical method to compare the distribution of two or more variables.  Both medians and quartiles, or means and related measures of dispersion can be plotted.


  Nonparametrics - Cochran Q Test

The Cochran Q test is an extension of McNemar's Chi-square test for changes (see option 2 x 2 Tables ...) in frequencies or proportions to k (more than two) dependent samples.  Specifically, it tests whether several matched frequencies or proportions differ significantly among themselves.  The Cochran Q test requires only a nominal scale, or that the data have been artificially dichotomized.  A typical example where the Q test is useful is when one wants to compare the difficulty of dichotomous questionnaire items that can either be answered right or wrong.  Here, each variable in the data file would represent one item, and contain 0's (wrong) and 1's (right).  If the Q test is significant, then we conclude that the items are of different difficulty since different items were answered correctly by more or fewer respondents.

Cochran's Q Test dialog:

Variables:  Choosing this option will bring up the standard single variable list selection dialog.  Note that this test requires that the selected variables contain two integer values or codes.

Codes:  The Cochran Q test assumes that the selected variables only contain 0's and 1's.  If you used different codes, you may specify them in the edit boxes; the program will then (internally) recode those values to 0's and 1's (only temporarily; the data file will not be changed).


  Nonparametrics - Descriptive Statistics

This option will allow you to compute several descriptive statistics (each of the statistics computed are explained in detail in Startup Panel - Descriptive Statistics).  When you click on the Ordinal Descriptive Statistics option from the Nonparametrics and Distributions start-up panel, the Descriptive Statistics dialog will open.

Descriptive Statistics dialog:

Variables button:  After clicking on this button a standard single variable list selection dialog window will appear in which you can select the variables for which the statistics will be computed.

Compute Percentile Boundaries:  Specify here specific percentile values to be computed and displayed in the Scrollsheet; by default the program will compute the quartile values, that is, the 25'th and 75'th percentiles.

Descriptive Statistics Computed:  In addition to the standard descriptive statistics, STATISTICA computes several other ordinal descriptive statistics when you click OK in this dialog.  For a complete list and descriptions of each of the descriptive statistics computed, see Startup Panel - Descriptive Statistics.


  Nonparametrics - Distribution Fitting

When you click on the distribution of interest in the Nonparametrics start-up panel, the appropriate distribution fitting dialog (continuous or discrete) will open.  Each of the available distributions are discussed in Startup Panel - Distribution Fitting.  Please note that additional specialized distributions can also be estimated (fit to data) using the Survival Analysis module.  That module is particularly useful for fitting the Weibull and Gompertz distributions which are widely used for modeling survival or failure times.  That module are also specifically "equipped" to handle censored data, that is, data that are incomplete.

Distribution (Continuous or Discrete) Fitting dialog:

Variable

Distribution

Controlling the number of categories

Chi-square test of goodness-of-fit

Kolmogorov-Smirnov one-sample test

Graph

NOTE: The tabulation (assignment of values into categories) is based on the first 6 significant digits of the data values.  Use the Basic Statistics module for computing standard frequency tables.  You can also use the Process Analysis module to fit various distributions to the data, including Weibull, Beta, Rayleigh, etc., using the method of matching moments, or maximum likelihood.


  Nonparametrics Distribution Fitting - Variables

To fit a distribution to a variable, first specify the variable to which the chosen distribution will be fitted, by clicking on the Variable button.


  Nonparametrics Distribution Fitting - Distribution

Once you have specified the variable of interest, you can then switch between fitting the different distributions (of the same type, i.e., continuous or discrete) via the Distribution combo box.  After a variable has been specified, the parameters yielding the best fit for each of the respective types of distributions are computed.  These parameters are displayed as default values, but user-specified values may be entered.


  Nonparametrics Distribution Fitting - Controlling the Number of Categories

The way in which the frequency distribution is computed (and the histogram of observed data is drawn) can be controlled by the user.  Use the option No. of Categories to specify the number of categories in the frequency table or histogram, use the Lower limit or Upper limit fields to control the lower and upper limits, respectively.  Note that, where appropriate, the program will re-define the most extreme categories into open-ended classes.


  Nonparametrics Distribution Fitting - Chi-square Test of Goodness of Fit

By default, the program will compute the Chi-square test based on the observed and expected frequencies.  Categories where the expected frequency is less than 5 are collapsed to form larger categories.  If this test is significant, we reject the hypothesis that the observed data follow the hypothesized distribution.

Degrees of freedom.  The degrees of freedom for the Chi-square test are computed as:

df = number of categories - number of parameters - 1

where the number of categories refers to the number of categories in the frequency table where the expected frequencies are greater than 5 and number of parameters refers to the number of parameters defining the respective theoretical distribution.

df adjusted.  If the Chi-square test resutls shown in the distribution Scrollsheet or histogram are accompanied by the qualifier df adjusted, then the program, in order to compute the Chi-square test, will combine categories where the expected frequencies are less than 5.  Specifically, those categories are combined with adjacent categories until the expected frequency for the combined category exceeds 5.0.


  Nonparametrics Distribution Fitting - Kolmogorov-Smirnov One Sample Test

This test can be computed either from the tabulated values (which is faster; set the Kolmogorov-Smirnov categorized radio button) or based on the raw data (which is slower; set the Continuous distribution button).

Kolmogorov-Smirnov categorized:  In this case (categorized), the program will compute the D-max statistic from the tabulated data in the Scrollsheet.  If the Kolmogorov-Smirnov test is statistically significant, we reject the hypothesis that the observed data follow the hypothesized distribution.

Continuous distribution:  In this case, the program will "step" through the sorted observed data and compute the cumulative expected frequency at each point; the Kolmogorov D-max statistic is the largest absolute difference between the cumulative observed and expected distribution.


  Nonparametrics Distribution Fitting - Graph

If no variables have been selected, click on the Graph button to select the variables.  After the variables have been selected, clicking on the graph button will produce a graph specified by the following options:

Plot Distribution:  Choose to plot the Frequency Distributions or the Cumulative Distribution by selecting the appropriate radio button.

Plot Raw Freq or %:  You will be able to select between plotting the Raw Frequencies or Relative Frequencies (%) with this option.


Nonparametrics & Distributions - Notes and Technical Information

Tied Ranks

In all methods that are based on ranks, the program will adjust for tied ranks using procedures discussed in Siegel (1956) and Siegel and Castellan (1988).

Significance Tests for Samples of Small Size

If the sample size is very small (e.g., n = 10 or less) significance levels for those tests that use z approximations should be treated as rough estimates only.  Refer to Hays (1981), Siegel (1956), and Siegel and Castellan (1988) for detailed discussions of these z approximations.

z-adjusted for the Wald-Wolfowitz Runs Test

When n1+n2 is not very large, then a correction for continuity should be used in the computation of z, resulting in:

                                                                         2            ½

z-adjusted = {|r-[(2n n /n +n )+1|]-.5} / {[2n n *(2n n -n -n )]/[(n +n ) *(n +n -1)]}

                     1 2  1  2                1 2    1 2  1  2      1  2     1  2

where

n1 and n2	are the respective sample sizes

r	is the number of runs

For more information, see Siegel, 1956, page 140.

Weibull and Gompertz Distribution

These distributions are commonly used in biomedical as well as engineering research as theoretical distributions for failure times (time to failure) or survival times (time to death).  An additional special problem in those areas of research is the issue of incomplete or censored observations, for example, patients who survived until after the study was terminated, or parts that did not fail at all.  Those observations obviously contain valuable information (patient X survived over 3 years) but they are not complete (how long did patient X survive?).  Because of these special issues involved in fitting the Weibull and Gompertz distribution to survival or failure times, fitting procedures for incomplete or censored data sets are available in the Survival Analysis module of STATISTICA.


  Cluster Analysis - Index

Introductory Overview

Startup Panel

  Joining (Tree Clustering)

Startup Panel

Results Dialog

  Two-way Joining

Startup Panel

Results Dialog

  K-means Clustering

Startup Panel

Results Dialog


  Cluster Analysis - Introductory Overview

General Purpose

  Joining (Tree Clustering)

  Two-way Joining

  K-means Clustering

Statistical Significance Testing

Areas of Application


Cluster Analysis - General Purpose

  Cluster Analysis Introductory Overview - General Purpose

The term cluster analysis (first used by Tryon, 1939) actually encompasses a number of different classification algorithms.  A general question facing researchers in many areas of inquiry is how to organize observed data into meaningful structures, that is, to develop taxonomies.  For example, biologists have to organize the different species of animals before a meaningful description of the differences between animals is possible.  According to the modern system employed in biology, man belongs to the primates, the mammals, the amniotes, the vertebrates, and the animals.  Note how in this classification, the higher the level of aggregation the less similar are the members in the respective class.  Man has more in common with all other primates (e.g., apes) than it does with the more "distant" members of the mammals (e.g., dogs), etc.  In the following three sections (see below) we will review the general categories of cluster analysis methods: joining (tree clustering), two-way joining (block clustering), and k-means clustering.


Cluster Analysis - Statistical Significance Testing

  Cluster Analysis Introductory Overview - Statistical Significance Testing

Note that the above discussions refer to clustering algorithms and do not mention anything about statistical significance testing.  In fact, cluster analysis is not as much a typical statistical test as it is a "collection" of different algorithms that "put objects into clusters."  The point here is that, unlike many other statistical procedures, cluster analysis methods are mostly used when we do not have any a priori hypotheses, but are still in the exploratory phase of our research.  In a sense, cluster analysis finds the "most significant solution possible."  Therefore, statistical significance testing is really not appropriate here, even in cases when p-levels are reported (as in k-means clustering).


Cluster Analysis - Area of Application

  Cluster Analysis Introductory Overview - Area of Application

Clustering techniques have been applied to a wide variety of research problems.  Hartigan (1975) provides an excellent summary of the many published studies reporting the results of cluster analyses.  For example, in the field of medicine, clustering diseases, cures for diseases, or symptoms of diseases can lead to very useful taxonomies.  In the field of psychiatry, the correct diagnosis of clusters of symptoms such as paranoia, schizophrenia, etc. is essential for successful therapy.  In archeology, researchers have attempted to establish taxonomies of stone tools, funeral objects, etc. by applying cluster analytic techniques.  In general, whenever one needs to classify a "mountain" of information into manageable meaningful piles, cluster analysis is of great utility.


  Joining (Tree Clustering) - Introductory Overview

General Logic

The examples given in the Introductory Overview section illustrates the goal of the joining or tree clustering algorithm.  The purpose of this algorithm is to join together objects (e.g., animals) into successively larger clusters, using some measure of similarity or distance.  A typical result of this type of clustering is the hierarchical tree.

Hierarchical Tree

Distance Measures

Amalgamation or Linkage Rules


Joining (Tree Clustering) - Hierarchical Tree

  Joining (Tree Clustering) Introductory Overview - Hierarchical Tree

Consider a Horizontal Hierarchical Tree Plot, on the left of the plot, we begin with each object in a class by itself.  Now imagine that, in very small steps, we "relax" our criterion as to what is and is not unique.  Put another way, we lower our threshold regarding the decision when to declare two or more objects to be members of the same cluster.  As a result we link more and more objects together and aggregate (amalgamate) larger and larger clusters of increasingly dissimilar elements.  Finally, in the last step, all objects are joined together.  In these plots, the horizontal axis denotes the linkage distance (in Vertical Icicle Plots, the vertical axis denotes the linkage distance).  Thus, for each node in the graph (where a new cluster is formed) we can read off the criterion distance at which the respective elements were linked together into a new single cluster.  When the data contain a clear "structure" in terms of clusters of objects that are similar to each other, then this structure will often be reflected in the hierarchical tree as distinct branches.  As the result of a successful analysis with the joining method, one is able to detect clusters (branches) and interpret those branches.


Joining (Tree Clustering) - Distance Measures

  Joining (Tree Clustering) Introductory Overview - Distance Measures

The joining or tree clustering method uses the dissimilarities or distances between objects when forming the clusters.  These distances can be based on a single dimension or multiple dimensions.  For example, if we were to cluster fast foods, we could take into account the number of calories they contain, their price, subjective ratings of taste, etc.  The most straightforward way of computing distances between objects in a multi-dimensional space is to compute Euclidean distances.  If we had a two- or three-dimensional space this measure is the actual geometric distance between objects in the space (i.e., as if measured with a ruler).  However, the joining algorithm does not "care" whether the distances that are "fed" to it are actual real distances, or some other derived measure of distance that is more meaningful to the researcher; and it is up to the researcher to select the right method for his/her specific application.  The Cluster Analysis module will compute various types of distance measures, or the user can compute a matrix of distances him or herself and directly use it in the procedure.

Euclidean distance.  This is probably the most commonly chosen type of distance.  It simply is the geometric distance in the multidimensional space.  It is computed as:

                         2  1/2

distance(x,y)={Σ (x - y )  }

                i  i   i

Squared Euclidean distance.  One may want to square the standard Euclidean distance in order to place progressively greater weight on objects that are further apart.  This distance is computed as:

                        2

distance(x,y)=Σ (x - y )

               i  i   i

City-block (Manhattan) distance.  This distance is simply the average difference across dimensions.  In most cases, this distance measure yields results similar to the simple Euclidean distance.  However, note that in this measure, the effect of single large differences (outliers) is dampened (since they are not squared).  The city-block distance is computed as:

distance(x,y)=Σ |x - y |

               i  i   i

Chebychev distance.  This distance measure may be appropriate in cases when one wants to define two objects as "different" if they are different on any one of the dimensions.  The Chebychev distance is computed as:

distance(x,y)=Maximum|x - y |

                      i   i

Power distance.  Sometimes one may want to increase or decrease the progressive weight that is placed on dimensions on which the respective objects are very different.  This can be accomplished via the power distance.  The power distance is computed as:

                         p 1/r

distance(x,y)=(Σ |x - y | )

                i  i   i

where r and p are user-defined parameters.  A few example calculations may demonstrate how this measure "behaves."  Parameter p controls the progressive weight that is placed on differences on individual dimensions, parameter r controls the progressive weight that is placed on larger differences between objects.  If r and p are equal to 2, then this distance is equal to the Euclidean distance.

Percent disagreement.  This measure is particularly useful if the data for the dimensions included in the analysis are categorical in nature.  This distance is computed as:

distance(x,y)=(Number of x ≠ y )/i

                          i    i


Joining (Tree Clustering) - Amalgamation or Linkage Rules

  Joining (Tree Clustering) Introductory Overview - Amalgamation or Linkage Rules

At the first step, when each object represents its own cluster, the distances between those objects are defined by the chosen distance measure.  However, once several objects have been linked together, how do we determine the distances between those new clusters?  In other words, we need a linkage or amalgamation rule to determine when two clusters are sufficiently similar to be linked together.  There are various possibilities:  for example, we could link two clusters together when any two objects in the two clusters are closer together than the respective linkage distance.  Put another way, we use the "nearest neighbors" across clusters to determine the distances between clusters; this method is called single linkage.  This rule produces "stringy" types of clusters, that is, clusters "chained together" by only single objects that happen to be close together.  Alternatively, we may use the neighbors across clusters that are furthest away from each other; this method is called complete linkage.  There are numerous other linkage rules such as these that have been proposed, and the Cluster Analysis module offers a wide choice of them.

Single linkage (nearest neighbor).  As described above, in this method the distance between two clusters is determined by the distance of the two closest objects (nearest neighbors) in the different clusters.  This rule will, in a sense, string objects together to form clusters, and the resulting clusters tend to represent long "chains."

Complete linkage (furthest neighbor).  In this method, the distances between clusters are determined by the greatest distance between any two objects in the different clusters (i.e., by the "furthest neighbors").  This method usually performs quite well in cases when the objects actually form naturally distinct "clumps."  If the clusters tend to be somehow elongated or of a "chain" type nature, then this method is inappropriate.

Unweighted pair-group average.  In this method, the distance between two clusters is calculated as the average distance between all pairs of objects in the two different clusters.  This method is also very efficient when the objects form natural distinct "clumps," however, it performs equally well with elongated, "chain" type clusters.  Note that in their book, Sneath and Sokal (1973) introduced the abbreviation UPGMA to refer to this method as unweighted pair-group method using arithmetic averages.

Weighted pair-group average.  This method is identical to the unweighted pair-group average method, except that in the computations, the size of the respective clusters (i.e., the number of objects contained in them) is used as a weight.  Thus, this method (rather than the previous method) should be used when the cluster sizes are suspected to be greatly uneven.  Note that in their book, Sneath and Sokal (1973) introduced the abbreviation WPGMA to refer to this method as weighted pair-group method using arithmetic averages.

Unweighted pair-group centroid.  The centroid of a cluster is the average point in the multidimensional space defined by the dimensions.  In a sense, it is the center of gravity for the respective cluster.  In this method, the distance between two clusters is determined as the difference between centroids.  Sneath and Sokal (1973) use the abbreviation UPGMC to refer to this method as unweighted pair-group method using the centroid average.

Weighted pair-group centroid (median).  This method is identical to the previous one, except that weighting is introduced into the computations to take into consideration differences in cluster sizes (i.e., the number of objects contained in them).  Thus, when there are (or one suspects there to be) considerable differences in cluster sizes, this method is preferable to the previous one.  Sneath and Sokal (1973) use the abbreviation WPGMC to refer to this method as weighted pair-group method using the centroid average.

Ward's method.  This method is distinct from all other methods because it uses an analysis of variance approach to evaluate the distances between clusters.  In short, this method attempts to minimize the Sum of Squares (SS) of any two (hypothetical) clusters that can be formed at each step.  Refer to Ward (1963) for details concerning this method.  In general, this method is regarded as very efficient, however, it tends to create clusters of small size.

For an overview of the other two methods of clustering, see Two-way Joining and K-means Clustering.


  Two-way Joining - Introductory Overview

Previously, we have discussed this method in terms of "objects" that are to be clustered (see Joining (Tree Clustering)).  In all other types of analyses in STATISTICA the research question of interest is usually expressed in terms of cases (observations) or variables.  It turns out that the clustering of both may yield useful results.  For example, imagine a study where a medical researcher has gathered data on different measures of physical fitness (variables) for a sample of heart patients (cases).  The researcher may want to cluster cases (patients) to detect clusters of patients with similar syndromes.  At the same time, the researcher may want to cluster variables (fitness measures) to detect clusters of measures that appear to tap similar physical abilities.  In the Cluster Analysis module, you can choose to cluster cases as well as variables.

Two-way Joining

Given the discussion in the paragraph above concerning whether to cluster cases or variables, one may wonder why not to cluster both simultaneously?  The Cluster Analysis module contains a two-way joining procedure to do exactly that.  Two-way joining is useful in (the relatively rare) circumstances when one expects that both cases and variables will simultaneously contribute to the uncovering of meaningful patterns of clusters.  For example, returning to the example above, the medical researcher may want to identify clusters of patients that are similar with regard to particular clusters of similar measures of physical fitness.  The difficulty with interpreting these results may arise from the fact that the similarities between different clusters may pertain to (or be caused by) somewhat different subsets of variables.  Thus, the resulting structure (clusters) is by nature not homogeneous. This may seem a bit confusing at first, and, indeed, compared to the other clustering methods described (see Joining (Tree Clustering) and K-means Clustering), two-way joining is probably the one least commonly used.  However, some researchers believe that this method offers a powerful exploratory data analysis tool (for more information you may want to refer to the detailed description of this method in Hartigan, 1975).


  K-means Clustering - Introductory Overview

General logic

This method of clustering is very different from the Joining (Tree Clustering) and Two-way Joining methods.  Suppose that you already have hypotheses concerning the number of clusters in your cases or variables.  You may want to "tell" the computer to form exactly 3 clusters that are to be as distinct as possible.  This is the type of research question that can be addressed by the k-means clustering algorithm.  In general, the k-means method will produce exactly k different clusters of greatest possible distinction.

Example.  In the physical fitness example (see Two-way Joining), the medical researcher may have a "hunch" from clinical experience that her heart patients fall basically into three different categories with regard to physical fitness.  She might wonder whether this intuition can be quantified, that is, whether a k-means cluster analysis of the physical fitness measures would indeed produce the three clusters of patients as expected.  If so, the means on the different measures of physical fitness for each cluster would represent a quantitative way of expressing the researcher's hypothesis or intuition (i.e., patients in cluster 1 are high on measure 1, low on measure 2, etc.).

Computations.  Computationally, you may think of this method as analysis of variance (ANOVA) "in reverse."  The program will start with k random clusters, and then move objects between those clusters with the goal to (1) minimize variability within clusters and (2) maximize variability between clusters.  This is analogous to "ANOVA in reverse" in the sense that the significance test in ANOVA evaluates the between group variability against the within-group variability when computing the significance test for the hypothesis that the means in the groups are different from each other.  In k-means clustering, the program tries to move objects (e.g., cases) in and out of groups (clusters) to get the most significant ANOVA results.  (Because, among other results, the ANOVA results are part of the standard output from a k-means clustering analysis, you may want to refer to ANOVA/MANOVA to learn more about that method.)

Interpretation of results.  Usually, as the result of a k-means clustering analysis, we would examine the means for each cluster on each dimension to assess how distinct our k clusters are.  Ideally, we would obtain very different means for most, if not all dimensions, used in the analysis.  The magnitude of the F values from the analysis of variance performed on each dimension is another indication of how well the respective dimension discriminates between clusters.


  Cluster Analysis - Startup Panel

Select the desired clustering method in the Clustering Method dialog (see also Cluster Analysis - Index).  Refer to the Overview section for brief descriptions of the different clustering techniques.

In short, the Joining technique will create tree diagrams of clusters.

The 2-way joining method will simultaneously cluster cases and variables.

The k-means clustering method will move objects around a user-specified number of clusters with the goal of minimizing within-cluster variability while maximizing between-cluster variability.


  Joining (Tree Clustering) - Startup Panel

When you click on the Joining (Tree Clustering) option in the Startup Panel, the Cluster Analysis: Joining (Tree Clustering) dialog will open.  Here, you can select the type of linkage and distance measure as well as other options (described below).

Cluster Analysis: Joining (Tree Clustering) dialog:

Variables

Input Data

Cluster Cases or Variables

Amalgamation (linkage) Rules

Distance Measures

Missing Data Deletion

Batch Processing and Printing


  Joining (Tree Clustering) Startup Panel - Variables

Choosing this option will bring up a standard variable selection window.  Note that the variables that are selected here will be interpreted by the program as dimensions if the Cluster combo box is set to cases; they will be interpreted as objects if that combo box is set to variables.


  Joining (Tree Clustering) Startup Panel - Input Data

This combo box allows you to select either Raw Data or a matrix (select Distance Matrix) for input into the cluster analysis.  The input matrix may either be a correlation matrix, or a distance (dissimilarity) matrix with numbers indicating the distances or dissimilarities between objects.  STATISTICA will automatically determine the contents of the matrix (i.e., whether it contains correlations or dissimilarities, see Matrix File Format).  If the input matrix is a correlation matrix (which indicates the similarity and closeness between objects), it is converted to distances before the analysis begins; specifically, all correlations are transformed as 1-Pearson r.


  Joining (Tree Clustering) Startup Panel - Cluster Cases or Variables

This combo box allows the user to select clustering of Variables (columns) or clustering of Cases (rows).


  Joining (Tree Clustering) Startup Panel - Amalgamation (linkage) Rules

One of the main parameters that guides the joining (tree-clustering) process is the linkage rule, that is, the rule that determines when two clusters are to be joined (linked or amalgamated).  There are 7 different amalgamation rules available:  Single Linkage, Complete Linkage, Unweighted Pair-group Average, Weighted Pair-group Average, Unweighted Pair-group Centroid, Weighted Pair-group Centroid (median), and Ward's Method.  The default rule is single linkage (also called the "method of the nearest neighbors;" for a further discussion of amalgamation rules, also see the Overview section).


  Joining (Tree Clustering) Startup Panel - Distance Measures

The joining algorithm starts by first computing a matrix of distances between the objects that are to be clustered.  There are 6 different distance measures that can be computed from Raw Data:  Squared Euclidean Distances, Euclidean Distances, City-block (Manhattan) Distances, Chebychev Distances, Power Distances, Percent Disagreement, and 1-Pearson r.  For definitions of each of these distances refer to the Cluster Analysis Overview.

If Power Distances are selected, then you can specify the two parameters p and r for the power distance in the edit boxes below this combo box.

If Distance Matrix was selected as the source of input, then the combo box will automatically be set to Dissimilarities from matrix.  If the input matrix is a correlation matrix, then the correlations (which denote the degree of similarity) will be transformed to dissimilarities (1 - r).


  Joining (Tree Clustering) Startup Panel - Missing Data Deletion

This combo box allows you to select one of two ways of treating missing data.

Casewise deletion of missing data:  When this option is selected, a case will be deleted from the analysis if it has missing data for any variable selected for the analysis.

Substitution by Means:  When this option is selected, missing data are substituted by the means for the respective dimensions.  Note that the substitution by means is performed after the program has determined what are the (logical) variables (i.e., dimensions) and what are the (logical) cases (i.e., objects) for the respective analysis.  For example, when joining (tree clustering) cases, logically, the variables become cases and the cases become variables.  In that instance, a distance matrix would be computed for cases, treating the variables as dimensions.  When the program computes the means for the substitution of missing data, it will compute the means for each case, across variables.


  Joining (Tree Clustering) Startup Panel - Batch Processing and Printing

This option is only available if printer, disk file, and/or Text/output Window was selected as the output destination in the Page/Output Setup dialog.  If checked, STATISTICA will automatically perform the entire analysis, print the results (either to the printer, disk file, and/or Text/output Window, whichever was selected in the Page/Output Setup dialog), and then return to this dialog.


  K-Means Clustering - Startup Panel

When you click on the K-means Clustering option in the Startup Panel, the Cluster Analysis: K-Means Clustering dialog will open.

Cluster Analysis: K-Means Clustering dialog:

Variables

Cluster Cases or Variables

Number of Clusters

Maximum number of iterations

Missing Data Deletion

Batch Processing and Printing

Initial Cluster Centers


  K-Means Clustering Startup Panel - Initial Cluster Centers

These options control the way in which the initial cluster centers are computed.  Note that the results from the K-means clustering method depend to some extent on the initial configuration (i.e., cluster means or centers).  This is particularly the case when there are many small clusters (with few objects) that are clearly distinct.

Maximize between-cluster distances.  This option will take observations or objects as the initial cluster centers; the choice of the object follows rules to maximize the initial cluster distances.  Specifically, (1) the program will select the first N (number of clusters) cases to be the respective cluster centers; (2) subsequent cases will replace previous cluster centers if their smallest distance to any of the cluster centers is larger than the smallest distance between clusters; if this is not the case, then (3) subsequent cases will replace initial cluster centers if their smallest distance from a cluster center is larger the distance of that cluster center from any other cluster center.  The effect of this selection procedure is to maximize the initial distances between clusters.  Note that this procedure may yield clusters with single observations if there are clear outliers in the data.

Sort distances and take observations at constant intervals.  If this option is chosen, the distances between all objects will first be sorted, and then objects at constant intervals will be chosen as initial cluster centers.

Choose the first N (number of clusters) clusters observations.  This option will take the first N (number of clusters) observations to be the initial cluster centers.  Thus, this option provides the user full control over the choice of the initial configuration.  This is often useful if one brings a priori expectations regarding the nature of the clusters to the analysis.  In that case, move the cases that you want to choose as the initial cluster centers to the beginning of the file.


  K-Means Clustering Startup Panel - Variables

Choosing this option will bring up a standard variable selection window.  Note that the variables that are selected here will be interpreted by the program as dimensions if the Cluster combo box is set to cases; they will be interpreted as objects if that switch is set to variables.


  K-Means Clustering Startup Panel - Cluster Cases or Variables

This combo box allows the user to select clustering of Variables (columns) or clustering of Cases (rows).


  K-Means Clustering Startup Panel - Number of Clusters

The purpose of the k-means clustering procedure is to classify objects into a user-specified number of clusters.  The algorithm will move objects into different clusters with the goal of minimizing the within-cluster variability while maximizing the between-cluster variability.  For a further discussion of this method, refer also to the Cluster Analysis Overview.  This edit box allows the user to enter the desired number of clusters, which must be greater than 1 and less than the number of objects (i.e., cases or variables depending on the setting of the Cluster combo box, see above).


  K-Means Clustering Startup Panel - Maximum Number of Iterations

K-means clustering is an iterative procedure; in each iteration objects are moved into different clusters.  This edit box allows the user to specify the maximum number of iterations that are to be performed.  The algorithm implemented in the Cluster Analysis module is very efficient, and the default setting (10 iterations) usually does not have to be changed.


  K-Means Clustering Startup Panel - Missing Data Deletion

This combo box allows you to select one of two ways of treating missing data.

Casewise deletion of missing data:  When this option is selected, a case will be deleted from the analysis if it has missing data for any variable selected for the analysis.

Substitution by Means:  When this option is selected, missing data are substituted by the means for the respective dimensions.  Note that the substitution by means is performed after the program has determined what are the (logical) variables (i.e., dimensions) and what are the (logical) cases (i.e., objects) for the respective analysis.


  K-Means Clustering Startup Panel - Batch Processing and Printing

This option is only available if printer, disk file, and/or Text/output Window was selected as the output destination in the Page/Output Setup dialog.  If checked, STATISTICA will automatically perform the entire analysis, print the results (either to the printer, disk file, and/or Text/output Window, whichever was selected in the Page/Output Setup dialog), and then return to this dialog.


  Two-way Joining (Block Clustering) - Startup Panel

When you click on the Two-way Joining option in the Startup Panel, the Cluster Analysis: Two-way Joining dialog will open.

Cluster Analysis: Two-way Joining dialog:

Variables

Threshold Value

Missing Data Deletion

Batch Processing and Printing


  Two-way Joining (Block Clustering) Startup Panel - Variables

Choosing this option will bring up a standard variable selection window from which you can select the variables for the analysis.


  Two-way Joining (Block Clustering) Startup Panel - Threshold Value

The 2-way joining algorithm attempts to simultaneously cluster cases and variables.  The threshold parameter determines when the algorithm will consider two numbers in the data matrix to be equal, and thus satisfactorily classified in the same cluster.  If this value is very large (relative to the numbers in the data matrix), then only one cluster will be formed; if it is very small, then each data point will represent a cluster by itself.  The default value (the overall standard deviation divided by 2) is recommended for most cases.


  Two-way Joining (Block Clustering) Startup Panel - Missing Data Deletion

This combo box allows you to select one of two ways of treating missing data:

Casewise deletion of missing data:  When you select this option, a case will be deleted from the analysis if it has missing data for any variable selected for the analysis.

Substitution by means:  When you select this option, the missing data are substituted by the means for the respective dimensions.


  Two-way Joining (Block Clustering) Startup Panel - Batch Processing and Printing

This option is only available if printer, disk file, and/or Text/output Window was selected as the output destination in the Page/Output Setup dialog.  If checked, STATISTICA will automatically perform the entire analysis, print the results (either to the printer, disk file, and/or Text/output Window, whichever was selected in the Page/Output Setup dialog), and then return to this dialog.


  Joining (Tree Clustering) - Results Dialog

The Joining Results dialog provides options to review the results of the Joining (Tree Clustering) method of Cluster Analysis.

Joining Results dialog:

Hierarchical Tree Plot options

Amalgamation Schedule

Graph of Amalgamation Schedule

Distance Matrix

Descriptive Statistics

Save Distance Matrix


  Joining (Tree Clustering) Results - Hierarchical Tree Plot

Horizontal Hierarchical Tree Plot button:  This button will bring up a horizontal tree diagram summarizing the successive clustering of objects.  Refer to the Cluster Analysis Overview for a brief discussion of how to interpret the tree diagram.

Vertical Icicle Plot button:  Click on this button to bring up a vertical tree diagram (the vertical axis denotes the linkage distance).  Again, refer to the Cluster Analysis Overview for a brief discussion of how to interpret the tree diagram.

Rectangular branches:  You can choose to display both types of tree plots (see above) with either rectangular branches (select this option) or diagonal branches (de-select this option).  The latter format may increase readability of the diagram for solutions with "balanced" joining structures.

Scale tree to dlink/dmax*100:  When you select this option, the tree plot will be scaled to a standardized scale (i.e., dlink/dmax*100).  Otherwise, if de-selected, the scale will be based on the linkage distance selected in the Startup Panel.

NOTE:  Depending on the current default scale value font-size setting (see Default Scale Options), the item (case or variable) labels in the tree plot may overlap or the display of some (e.g., every other or third) overlapping labels may be suppressed (see Filters); in such cases, click on the labels in the graph and reduce the font size.


Joining (Tree Clustering) Results - Amalgamation Schedule

  Joining (Tree Clustering) Results - Amalmagation Schedule

Clicking on this button will bring up a Scrollsheet with the amalgamation (linkage) schedule.  The first column of the Scrollsheet will contain the linkage distances at which the respective clusters (as indicated in the respective rows) were formed, and each row contains the names of the objects (cases or variables) that comprise the respective cluster.


Joining (Tree Clustering) Results - Graph of Amalgamation Schedule

  Joining (Tree Clustering) Results - Graph of Amalmagation Schedule

This option will bring up a line graph of the linkage distances across consecutive steps of the linking process.  This graph is useful for identifying plateaus where many clusters are formed at approximately the same linkage distance.  This may indicate a natural "discontinuity" in terms of distances between the observed objects.


  Joining (Tree Clustering) Results - Distance Matrix

This option will bring up a standard Scrollsheet with the matrix of distances. This matrix can be saved using the Save Distance Matrix option.


  Joining (Tree Clustering) Results - Descriptive Statistics

This option will bring up a standard Scrollsheet with means and standard deviations for each object included in the cluster analysis (i.e., for each case or variable, depending on the setting of the Cluster combo box that was chosen on the Startup Panel).


  Joining (Tree Clustering) Results - Save Distance Matrix

This option allows the user to save the current distance matrix as a standard STATISTICA matrix file.  This file can be accessed later with the Cluster Analysis or Multidimensional Scaling modules.


k-Means Clustering - Results Menu

  K-means Clustering - Results Dialog

The K-means Clustering Results dialog provides several options to review the results of the K-means Clustering method of Cluster Analysis.

K-means Clustering Results dialog:

Analysis of Variance

Means of each Cluster & Distances

Graph of Means

Descriptive Statistics for each Cluster

Members of each Cluster and Distances

Save Classifications & Distances

Note that the distance between two objects or cluster centers i and j are computed as:

                    2

D    = √{Σ[(x  - x ) /ND]}

 i,j         i    j

where the summation is over the ND dimensions in the current analysis.


  K-means Clustering Results - Analysis of Variance

The goal of the k-means clustering procedure is to classify objects (cases or variables, depending on the setting of the Cluster combo box on the Startup Panel) into a user-specified number of clusters.  To evaluate the appropriateness of the classification, one can compare the within-cluster variability (small if the classification is good) with the between-cluster variability (large if the classification is good), that is, perform a standard between-groups analysis of variance for each dimension (case or variable).  Clicking on this button will bring up a standard Scrollsheet with those ANOVA's.  Note that although the F ratios and p levels are given in the table, statistical significance's should be interpreted with caution since their meanings are not the same as in an actual ANOVA of experimental data (see the Overview section).  In short, these are not a priori tests, and we capitalize on chance by arranging the most statistically significant ANOVA's possible (see Hartigan, 1975, for a more detailed discussion of this point).


  K-means Clustering Results - Means of Each Cluster & Distances

After clicking on this button, two Scrollsheets will be displayed:

(1)	A Scrollsheet with the means for each cluster for each dimension;

(2)	A Scrollsheet with the Euclidean distances (below the diagonal) and squared Euclidean distances (above the diagonal) between "cluster centers."

Specifically, this matrix shows the Euclidean distances between clusters, computed from the respective cluster means on the dimensions used for the classification.

Distances.  The distance between two objects or cluster centers i and j are computed as:

                             2

D    = Square Root{Σ [(x -x ) /ND]}

 i,j                    i  j

where the summation is over the ND dimensions in the current analysis.


  K-means Clustering Results - Graph of Means

After clicking on this button, a line graph of the means across clusters will be displayed.  This plot is very useful for visually summarizing the differences in means between clusters.


  K-means Clustering Results - Descriptive Statistics for Each Cluster

This option will bring up Scrollsheets, one for each cluster, with the descriptive statistics.


  K-means Clustering Results - Member of Each Cluster and Distance

Via this option, the user can display the (Euclidean) distances of the objects (cases or variables, depending on the setting of the Cluster combo box on the Startup Panel) from their respective cluster center (mean).  This allows one to identify potential "bad" cluster members, that is, objects that are very distant from the cluster center, yet apparently do not belong to any other cluster (i.e., they are even further away from the centers of alternative clusters).  Those distances will be displayed in standard Scrollsheets, each Scrollsheet showing the results for one cluster.

Distances.  The distance between two objects or cluster centers i and j are computed as:

                             2

D    = Square Root{Σ [(x -x ) /ND]}

 i,j                    i  j

where the summation is over the ND dimensions in the current analysis.


  K-means Clustering Results - Save Classifications and Distances

The k-means method features an option which allows the user to save classification information and distances for clustered objects.  After clicking on the Save classifications and distances button, the program will ask you for the name of the file into which the classification results will be saved.

If you are clustering variables, then the data file will contain one case for each variable clustered and the original names of each clustered variable will be used as case names in the new file.  Three variables will be created and named: Variable (the id number of each clustered item [variable] as it appeared in the original input data set), Cluster (the cluster number to which each item [variable] was classified), and Distance (the distance of that item [variable] from its respective cluster center).

If you are clustering cases, the program will give you an option to save any of the variables (i.e., their raw values) from the current data file along with the cluster information.  If the original input data file contained case names, then they will also be used to label cases in the new file.  In addition to the (optional) variables selected from the original data file, the new data file will contain three variables, named Case_No (the consecutive id number of each clustered item [case] as it appeared in the original input data set), Cluster (the cluster number to which each item [case] was classified), and Distance (the distance of that item [case] from its respective cluster center).


Two-way Joining (Block Clustering) - Results Menu

  Two-way Joining (Block Clustering) - Results Dialog

The Two-way Joining Results dialog provides several options to review the results of the Two-way Joining method of Cluster Analysis.

Two-way Joining Results dialog:

Descriptive Statistics for Cases (Rows)

Descriptive Statistics for Variables (Columns)

Reordered Data Matrix

Two-way Joining Graph


  Two-way Joining (Block Clustering) Results - Descriptive Statistics for Cases (Rows)

This option will bring up a standard Scrollsheet with means and standard deviations for each case (i.e., row of the data matrix) across variables (columns of the data matrix).


  Two-way Joining (Block Clustering) Results - Descriptive Statistics for Variables (Columns)

Clicking on this button will bring up a standard Scrollsheet with means and standard deviations for each variable (i.e., column of the data matrix) across cases (rows of the data matrix).


  Two-way Joining (Block Clustering) Results - Reordered Data Matrix

This option will bring up a standard Scrollsheet with the complete data matrix, reordered according to the results of the Two-way joining computations.  Note that the goal of this procedure is to simultaneously cluster cases and variables, that is, to move similar data points together as closely as possible by reordering the columns and rows of the data matrix.  Refer to Hartigan (1975) for a detailed description of this procedure and its applications.

3D Box Plot of Reordered Data Matrix:  The custom graph for this Scrollsheet is the 3D box plot, which allows you to visually inspect the pattern of similar and dissimilar data points.


  Two-way Joining (Block Clustering) Results - Two-way Joining Graph

This option will bring up a graphical representation of the results of the Two-way joining procedure.  Specifically, the reordered data matrix is represented in a discrete contour plot.


  Cluster Analysis - Hierarchical Tree

The hierarchical tree diagram summarizes the results of a joining (tree clustering) analysis.  On the left we begin with each object in a class by itself.  Now imagine that, in very small steps, we "relax" our criterion as to what is and is not unique.  Put another way, we lower our threshold regarding the decision when to declare two or more objects to be members of the same cluster.  As a result we link more and more objects together and aggregate (amalgamate) larger and larger clusters of increasingly dissimilar elements.  Finally, in the last step, all objects are joined together.  In the plot, the horizontal axis denotes the linkage distance.  Thus, for each node in the graph (where a new cluster is formed) we can read off the criterion distance at which the respective elements were linked together into a new single cluster.  When the data contain a clear "structure" in terms of clusters of objects that are similar to each other, then this structure will often be reflected in the hierarchical tree as distinct branches.  As the result of a successful analysis with the joining method one is able to detect clusters (branches) and interpret those branches.


  Multidimensional Scaling - Index

Introductory Overview

Startup Panel

Parameter Estimation

Results

Notes and Technical Information


  Multidimensional Scaling - Introductory Overview

General Purpose

Logic of MDS

Computational Approach

How many dimensions to specify?

Interpreting the Dimensions

Applications

MDS and Factor Analysis


Multidimensional Scaling - General Purpose

  Multidimensional Scaling Introductory Overview - General Purpose

Multidimensional scaling (MDS) can be considered to be an alternative to factor analysis (see Factor Analysis).  In general, the goal of the analysis is to detect meaningful underlying dimensions that allow the researcher to explain observed similarities or dissimilarities (distances) between the investigated objects.  In factor analysis, the similarities between objects (e.g., variables) are expressed in the correlation matrix.  With MDS one may analyze any kind of similarity or dissimilarity matrix, in addition to correlation matrices.


Multidimensional Scaling - Logic of MDS

  Multidimensional Scaling Introductory Overview - Logic of MDS

The following simple example may demonstrate the logic of an MDS analysis.  Suppose we take a matrix of distances between major US cities from a map.  We then analyze this matrix, specifying that we want to reproduce the distances based on two dimensions.  As a result of the MDS analysis, we would most likely obtain a two-dimensional representation of the locations of the cities, that is, we would basically obtain a two-dimensional map.

In general then, MDS attempts to arrange "objects" (major cities in this example) in a space with a particular number of dimensions (two-dimensional in this example) so as to reproduce the observed distances.  As a result, we can "explain" the distances in terms of underlying dimensions; in our example, we could explain the distances in terms of the two geographical dimensions: north/south and east/west.

Orientation of axes.  As in factor analysis, the actual orientation of axes in the final solution is arbitrary.  To return to our example, we could rotate the map in any way we want, the distances between cities remain the same.  Thus, the final orientation of axes in the plane or space is mostly the result of a subjective decision by the researcher, who will choose an orientation that can be most easily explained.  To return to our example, we could have chosen an orientation of axes other than north/south and east/west; however, that orientation is most convenient because it "makes the most sense" (i.e., it is easily interpretable).


Multidimensional Scaling - Computational Approach

  Multidimensional Scaling Introductory Overview - Computational Approach

MDS is not so much an exact procedure as rather a way to "rearrange" objects in an efficient manner, so as to arrive at a configuration that best approximates the observed distances.  The program actually moves objects around in the space defined by the requested number of dimensions, and checks how well the distances between objects can be reproduced by the new configuration.  In more technical terms, the program uses a function minimization algorithm that evaluates different configurations with the goal of maximizing the goodness-of-fit (or minimizing "lack of fit").

Measures of goodness-of-fit: Stress.  The most common measure that is used to evaluate how well (or poorly) a particular configuration reproduces the observed distance matrix is the stress measure.  The raw stress value Phi of a configuration is defined by:

                   2

Phi = Σ[d  -f(δ  )]

         ij    ij

In this formula, dij stands for the reproduced distances, given the respective number of dimensions, and δij (deltaij) stands for the input data (i.e., observed distances).  The expression f(δij) indicates a nonmetric, monotone transformation of the observed input data (distances).  Thus, the program will attempt to reproduce the general rank-ordering of distances between the objects in the analysis.

There are several similar related measures that are commonly used; however, most of them amount to the computation of the sum of squared deviations of observed distances (or some monotone transformation of those distances) from the reproduced distances.  Thus, the smaller the stress value, the better is the fit of the reproduced distance matrix to the observed distance matrix.

Shepard diagram.  One can plot the reproduced distances for a particular number of dimensions against the observed input data (distances).  This scatterplot is referred to as a Shepard diagram.  This plot shows the reproduced distances plotted on the vertical (Y) axis versus the original similarities plotted on the horizontal (X) axis (hence, the generally negative slope).  This plot also shows a step-function.  This line represents the so-called D-hat values, that is, the result of the monotone transformation f(δij) of the input data.  If all reproduced distances fall onto the step-line, then the rank-ordering of distances (or similarities) would be perfectly reproduced by the respective solution (dimensional model).  Deviations from the step-line indicate lack of fit.


Multidimensional Scaling - How Many Dimensions to Specify?

  Multidimensional Scaling Introductory Overview - How Many Dimensions to Specify?

If you are familiar with factor analysis, you will be quite aware of this issue.  If you are not familiar with factor analysis, you may want to read the Introductory Overview section of the Factor Analysis chapter in the manual; however, this is not necessary in order to understand the following discussion.  In general, the more dimensions we use in order to reproduce the distance matrix, the better is the fit of the reproduced matrix to the observed matrix (i.e., the smaller is the stress).  In fact, if we use as many dimensions as there are variables, then we can perfectly reproduce the observed distance matrix.  Of course, our goal is to reduce the observed complexity of nature, that is, to explain the distance matrix in terms of fewer underlying dimensions.  To return to the example of distances between cities, once we have a two-dimensional map it is much easier to visualize the location of and navigate between cities, as compared to relying on the distance matrix only.

Sources of misfit.  Let us consider for a moment why fewer factors may produce a worse representation of a distance matrix than would more factors.  Imagine the three cities A, B, and C, and the three cities D, E, and F; shown below are their distances from each other.

    A   B   C          D   E   F

A   0              D   0

B  90   0          E  90   0

C  90  90   0      F 180  90   0

In the first matrix, all cities are exactly 90 miles apart from each other; in the second matrix, cities D and F are 180 miles apart.  Now, can we arrange the three cities (objects) on one dimension (line)?  Indeed, we can arrange cities D, E, and F on one dimension:

D---90 miles---E---90 miles---F

D is 90 miles away from E, and E is 90 miles away form F; thus, D is 90+90=180 miles away from F.  If you try to do the same thing with cities A, B, and C you will see that there is no way to arrange the three cities on one line so that the distances can be reproduced.  However, we can arrange those cities in two dimensions, in the shape of a triangle:

                 A

     90 miles         90 miles

        B     90 miles   C

Arranging the three cities in this manner, we can perfectly reproduce the distances between them.  Without going into much detail, this small example illustrates how a particular distance matrix implies a particular number of dimensions.  Of course, "real" data are never this "clean," and contain a lot of noise, that is, random variability that contributes to the differences between the reproduced and observed matrix.

Scree test.  A common way to decide how many dimensions to use is to plot the stress value against different numbers of dimensions.  This test was first proposed by Cattell (1966) in the context of the number-of-factors problem in factor analysis (see Factor Analysis); Kruskal and Wish (1978; pp. 53-60) discuss the application of this plot to MDS.

Cattell suggests to find the place where the smooth decrease of stress values (eigenvalues in factor analysis) appears to level off to the right of the plot.  To the right of this point one finds, presumably, only "factorial scree" -- "scree" is the geological term referring to the debris which collects on the lower part of a rocky slope.

Interpretability of configuration.  A second criterion for deciding how many dimensions to interpret is the clarity of the final configuration.  Sometimes, as in our example of distances between cities, the resultant dimensions are easily interpreted.  At other times, the points in the plot form a sort of "random cloud," and there is no straightforward and easy way to interpret the dimensions.  In the latter case one should try to include more or fewer dimensions and examine the resultant final configurations.  Often, more interpretable solutions emerge.  However, if the data points in the plot do not follow any pattern, and if the stress plot does not show any clear "elbow," then the data are most likely random "noise."


Multidimensional Scaling - Interpreting the Dimensions

  Multidimensional Scaling Introductory Overview - Interpreting the Dimensions

The interpretation of dimensions usually represents the final step of the analysis.  As mentioned earlier, the actual orientations of the axes from the MDS analysis are arbitrary, and can be rotated in any direction.  A first step is to produce scatterplots of the objects in the different two-dimensional planes.  Three-dimensional solutions can also be illustrated graphically, however, their interpretation is somewhat more complex.

In addition to "meaningful dimensions," one should also look for clusters of points or particular patterns and configurations (such as circles, manifolds, etc.).  For a detailed discussion of how to interpret final configurations, see Borg and Lingoes (1987), Borg and Shye (in press), or Guttman (1968).

Use of multiple regression techniques.  An analytical way of interpreting dimensions (described in Kruskal & Wish, 1978) is to use multiple regression techniques to regress some meaningful variables on the coordinates for the different dimensions.  Note that this can easily be done via Multiple Regression.


Multidimensional Scaling - Applications

  Multidimensional Scaling Introductory Overview - Applications

The "beauty" of MDS is that we can analyze any kind of distance or similarity matrix.  These similarities can represent people's ratings of similarities between objects, the percent agreement between judges, the number of times a subjects fails to discriminate between stimuli, etc.  For example, MDS methods used to be very popular in psychological research on person perception where similarities between trait descriptors were analyzed to uncover the underlying dimensionality of people's perceptions of traits (see, for example Rosenberg, 1977).  They are also very popular in marketing research, in order to detect the number and nature of dimensions underlying the perceptions of different brands or products (for detailed descriptions of various examples see, for example, Green & Carmone, 1970).

In general, MDS methods allow the researcher to ask relatively unobtrusive questions ("how similar is brand A to brand B") and to derive from those questions underlying dimensions without the respondents ever knowing what is the researcher's real interest.


Multidimensional Scaling - MDS and Factor Analysis

  Multidimensional Scaling Introductory Overview - MDS and Factor Analysis

Even though there are similarities in the type of research questions to which these two procedures can be applied, MDS and factor analysis are fundamentally different methods.  Factor analysis requires that the underlying data are distributed as multivariate normal, and that the relationships are linear.  MDS imposes no such restrictions.  As long as the rank-ordering of distances (or similarities) in the matrix is meaningful, MDS can be used.  In terms of resultant differences, factor analysis tends to extract more factors (dimensions) than MDS; as a result, MDS often yields more readily, interpretable solutions.  Most importantly, however, MDS can be applied to any kind of distances or similarities, while factor analysis requires us to first compute a correlation matrix.  MDS can be based on subjects' direct assessment of similarities between stimuli, while factor analysis requires subjects to rate those stimuli on some list of attributes (for which the factor analysis is performed).

In summary, MDS methods are applicable to a wide variety of research designs because distance measures can be obtained in any number of ways (for different examples, refer to the references provided at the beginning of this section).


Multidimensional Scaling - Startup Panel

  MDS - Startup Panel

Multidimensional Scaling is the only statistical module in STATISTICA that cannot accept raw data files as the main input file.  Instead, it requires as input a matrix file, containing either correlations, similarities, or dissimilarities (distances).

STATISTICA matrix files can be created directly (e.g., via Data Management), or they can be produced by other modules of STATISTICA.  For example, a wide variety of distance matrices can be computed from raw data and saved via Cluster Analysis (see also, MDS - Index).

Multidimensional Scaling dialog:

Variables

Number of Dimensions

Starting Configuration

Epsilon

Number of Iterations


Multidimensional Scaling Startup Panel - Variables

  MDS Startup Panel - Variables

This option will bring up the standard variable selection window in which you can select the variables for the analysis.


Multidimensional Scaling Startup Panel - Number of Dimensions

  MDS Startup Panel - Number of Dimensions

In this edit box, the user can enter the number of dimensions for the multidimensional scaling analysis.  The default value is 2.  The maximum number of dimensions that can be specified is 9, or the number of variables (objects) minus one, whichever is smaller.  Note that in consecutive analyses, by accepting the default settings the user can systematically evaluate solutions for n dimensions, n-1 dimensions, n-2 dimensions, etc.  For example, you may first specify 5 dimensions, and then, after returning from the output dialog, STATISTICA will by default compute a solution for 4 dimensions, and so on.


Multidimensional Scaling Startup Panel - Starting Configuration

  MDS Startup Panel - Starting Configuration

This combo box allows the user to select the starting configuration for the current analysis; available options are Standard Guttman-Lingoes, Last final, or From a STATISTICA file.

Standard Guttman-Lingoes:  When first entering Multidimensional Scaling, the default starting configuration is Standard Guttman-Lingoes.  This procedure amounts to a principal components analysis, and in most instances will provide an adequate starting configuration for the iterative fitting procedure.  (For a more detailed description of principal components analysis, refer to the Introductory Overview section of Factor Analysis.)

Last Final:  After returning from the Results dialog, the default starting configuration is Last final.  In this setting, STATISTICA will use as the starting configuration the configuration of the previously computed model.  For example, suppose that you have just computed a three-dimensional solution for a similarity matrix, and are now returning to the Startup Panel.  If you next want to calculate the two-dimensional solution (and you do not change the setting of the Starting configuration combo box) the program will automatically use the previous configuration for the first two dimensions as the starting configuration for the next analysis.  Of course, if you select new variables (Variables), or if you increase the number of dimensions, the Last final option is not available.

From a STATISTICA file:  If the Starting configuration combo box is set to From a STATISTICA file, the user can specify a STATISTICA raw data file with the coordinates for the starting configuration.  This file may be created via Data Management, or it can be a configuration file saved from the Multidimensional Scaling Results dialog during a previous run.  The file containing the starting configuration must have as many cases as the current matrix file, and it must have as many variables as there are dimensions specified for the current run.


Multidimensional Scaling Startup Panel - Epsilon

  MDS Startup Panel - Epsilon

All distances that are less than epsilon will be considered to be 0 (zero) by the program.  Thus, this parameter specifies the smallest distance that is to be considered "important" or significant by the program.  The smaller this value, the more iterations will be performed and the more "precise" is the solution.  Change this value only if the iterative fitting procedure cannot converge (i.e., produce a solution) even after very many iterations.


Multidimensional Scaling Startup Panel - Number of Iterations

  MDS Startup Panel - Number of Iterations

This option allows you to specify the minimum and maximum number of iterations that are to be performed during the iterative fitting procedure.  The minimum number of iterations is 6.


Multidimensional Scaling - Estimation

  MDS - Estimation

Multidimensional Scaling is an implementation of nonmetric multidimensional scaling.  After determining the starting configuration (e.g., via principal components analysis) the program will begin iterations under steepest descent (see, for example, Schiffman, Reynolds, and Young, 1981).  The goal of these iterations is to minimize the raw stress (or raw Phi) and the coefficient of alienation (see Guttman, 1968).  The raw stress is defined as:

                   2

Phi = Σ[d  -f(δ  )]

         ij    ij

where dij are the reproduced distances, given the current number of dimensions, and f(δij) represents the monotone transformation of the observed input data δij (deltaij).

The coefficient of alienation K is defined as:

                  2      2         2  1/2

K = [1-{Σd  * δ  } /Σ(d   ) * Σ(δ   )]

          ij   ij      ij        ij

In general, STATISTICA will attempt to minimize the differences between the reproduced distances and a monotone transformation of the input data, that is, the program will attempt to reproduce the rank-ordering of the input distances or similarities (hence, also the name nonmetric multidimensional scaling).

Note that under steepest descent the fitted values are calculated via the rank-image permutation procedure (see Guttman, 1968; or Schiffman, Reynolds, & Young, 1981, pp. 368-369).After each iteration under steepest descent the program will perform up to five iterations using the monotone regression transformation procedure (see Kruskal, 1964; or Schiffman, Reynolds, & Young, 1981, pp. 367-368).  This procedure is aimed at minimizing the standardized stress (S):

               2      2  1/2

S = [Σ(d  -δ  ) /Σ(d   )]

        ij  ij      ij

Before final convergence, STATISTICA will perform several monotone regression transformation iterations.

D-Stars and D-Hats:  D-stars are calculated via a procedure known as the rank-image permutation procedure (see Guttman, 1968; or Schiffman, Reynolds, & Young, 1981, pp. 368-369).  In general, this procedure attempts to reproduce the rank order of differences in the similarity or dissimilarity matrix.  D-hats are calculated via a procedure referred to as the monotone regression transformation procedure (see Kruskal, 1964; or Schiffman, Reynolds, & Young, 1981, pp. 367-368).  In this procedure, the program attempts to determine the best monotone (regression) transformation to reproduce the similarities (or dissimilarities) in the input matrix.


Multidimensional Scaling - Results

  MDS - Results

When you click OK in the MDS - Estimation window, the Results dialog will open.

Results dialog:

Final Configuration

D-hat values

D-star Values

Distance Matrix

Summary

Save Final Configuration

Graphs Final Configuration - 2D, 3D

Graph D-hat vs. Distances

Graph D-star vs. Distances

Shepard Diagram


Multidimensional Scaling Results - Final Configuration

  MDS Results - Final Configuration

This option will bring up a Scrollsheet with the coordinates of the final configuration.


Multidimensional Scaling Results - D-hat Values

  MDS Results - D-hat Values

This option will bring up a Scrollsheet with the transformed input data values calculated according to the monotone regression procedure (D-hat, see Kruskal, 1964); see also the Introductory Overview).


Multidimensional Scaling Results - D-star Values

  MDS Results - D-star Values

This option will bring up a Scrollsheet with the transformed input data values, calculated according to Guttman's rank image procedure (D-star; Guttman, 1968).


Multidimensional Scaling Results - Distance Matrix

  MDS Results - Distance Matrix

This option will bring up a Scrollsheet with the matrix of reproduced distances, given the current number of dimensions and configuration of points.


Multidimensional Scaling Results - Summary

  MDS Results - Summary

This option will display the reproduced distances along with the D-hat and D-star values.  The elements in the Scrollsheet are sorted by the transformed input data values (D-hat, D-star), and each element is referenced by its matrix subscript.  For example, the element denoted as D(4,2) refers to the element in the fourth row and the second column of the similarity (or dissimilarity) matrix.


Multidimensional Scaling Results - Save Final Configuration

  MDS Results - Save Final Configuration

The coordinates for the final configuration can be saved in a standard STATISTICA data file.  The number of variables in the new data file will always be equal to the number of dimensions specified for the current multidimensional scaling analysis.  These files can later be accessed by all other STATISTICA modules.  For example, you may specify the configuration stored in this file as the starting configuration for subsequent analyses.  You may also combine this file (via Data Management) with another data file containing additional variables.  Multiple regression techniques (regressing these auxiliary variables on the coordinates for the different dimensions) are often used to aid in the interpretation of dimensions.  Finally, these files can be used in Graphics to produce a variety of specialized 2-D and 3-D graphs of the respective solution.


Multidimensional Scaling Results - Graph Final Configuration

  MDS Results - Graph Final Configuration

This option allows the user to plot the final configuration of variables (objects).  Note that a variety of specialized 2-D and 3-D graphs can also be produced via Graphics, from a data file containing the configuration as saved via option Save final configuration.


Multidimensional Scaling Results - Graph D-hat vs. Distances

  MDS Results - Graph D-hat vs. Distances

With this option, the user can produce a plot of the transformed input data values (D-hat) against the reproduced distances.  The more closely the points in the plot cluster around the diagonal, the better is the fit of the respective model.


Multidimensional Scaling Results - Graph D-star vs. Distances

  MDS Results - Graph D-star vs. Distances

With this option, the user can produce a plot of the transformed input data values (D-star) against the reproduced distances.  The more closely the points in the plot cluster around the diagonal, the better is the fit of the respective model.


Multidimensional Results - Shepard Diagram

  MDS - Shepard Diagram

After clicking on this option, a scatterplot will be displayed where each point represents a distance - data point pair (note that the original data are plotted against the horizontal X-axis in the plot).  In addition, the D-hat values are indicated in the graph by a step function.  As described in the Introductory Overview section, STATISTICA performs nonmetric multidimensional scaling, and the D-hat values are computed by a monotone (non-linear) transformation of the original data (dissimilarities).  Thus, the step function will be monotonically increasing or decreasing.  The closer the fit of the step function to the data points plotted in the graph, the better the fit of the respective model, that is, the better is the reproduction of the distances (or, specifically, the rank order of distances) in the input data, given the respective number of dimensions.


Multidimensional Scaling - 2D Plot of Final Configuration

  MDS - 2D Plot of Final Configuration

Select the two dimensions for the scatterplot.  If data point labels overlap in the resulting plot, then see If Data Point Labels Overlap


Multidimensional Scaling - 3D Plot of Final Configuration

  MDS - 3D Plot of Final Configuration

Select the three dimensions for the 3D scatterplot.  If data point labels overlap in the resulting plot, then see If Data Point Labels Overlap


  Multidimensional Scaling - Notes and Technical Information

Multidimensional Scaling is an implementation of non-metric multidimensional scaling.  Comprehensive introductions to the computational approach used in this module can be found in Borg and Lingoes (1987), Borg and Shye (in press), Guttman (1968), Schiffman, Reynolds, and Young (1981), Young and Hamer (1987), and in Kruskal and Wish (1978).

Computational Approach

As the starting configuration, principal components of the similarity/dissimilarity matrix are computed.  The program will then begin iterations under steepest descent (see, for example, Schiffman, Reynolds, and Young, 1981).  The goal of these iterations is to minimize the raw stress (or raw Phi) and the coefficient of alienation (see Guttman, 1968).  The raw stress is defined as:

                   2

Phi = Σ[d  -f(δ  )]

         ij    ij

where dij are the reproduced distances, given the current number of dimensions, and f(δij) represents the monotone transformation of the observed input data δij (deltaij).

The coefficient of alienation K is defined as:

                  2      2         2  1/2

K = [1-{Σd  * δ  } /Σ(d   ) * Σ(δ   )]

          ij   ij      ij        ij

In general, STATISTICA will attempt to minimize the differences between the reproduced distances and a monotone transformation of the input data, that is, the program will attempt to reproduce the rank-ordering of the input distances or similarities (hence, also the name nonmetric multidimensional scaling).

Note that under steepest descent the fitted values are calculated via the rank-image permutation procedure (see Guttman, 1968; or Schiffman, Reynolds, & Young, 1981, pp. 368-369).After each iteration under steepest descent the program will perform up to five iterations using the monotone regression transformation procedure (see Kruskal, 1964; or Schiffman, Reynolds, & Young, 1981, pp. 367-368).  This procedure is aimed at minimizing the standardized stress (S):

               2      2  1/2

S = [Σ(d  -δ  ) /Σ(d   )]

        ij  ij      ij

Before final convergence, STATISTICA will perform several monotone regression transformation iterations.

D-Stars and D-Hats

D-stars are calculated via a procedure known as the rank-image permutation procedure (see Guttman, 1968; or Schiffman, Reynolds, & Young, 1981, pp. 368-369).  In general, this procedure attempts to reproduce the rank order of differences in the similarity or dissimilarity matrix.  D-hats are calculated via a procedure referred to as the monotone regression transformation procedure (see Kruskal, 1964;Schiffman, Reynolds, & Young, 1981, pp. 367-368).  In this procedure, the program attempts to determine the best monotone (regression) transformation to reproduce the similarities (or dissimilarities) in the input matrix.


  Nonlinear Estimation - Index

Introductory Overview

Startup Panel

  User-Defined Regression

Syntax

  Logistic Regression

  Probit Regression

  Exponential Growth Regression

  Breakpoint Regression

Parameter Estimation

Results


  Nonlinear Estimation - Introductory Overview

General Purpose

Estimating Linear and Nonlinear Models

Common Nonlinear Regression Models

Nonlinear Estimation Procedures

Evaluating the Fit of the Model


Nonlinear Estimation - General Purpose

  Nonlinear Estimation Introductory Overview - General Purpose

In the most general terms, Nonlinear Estimation will compute the relationship between a set of independent variables and a dependent variable.  For example, we may want to compute the relationship between the dose of a drug and its effectiveness, the relationship between training and subsequent performance on a task, the relationship between the price of a house and the time it takes to sell it, etc.  You may recognize research issues in these examples that are commonly addressed by such techniques as multiple regression (see, Multiple Regression) or analysis of variance (see, ANOVA/MANOVA).  In fact, you may think of Nonlinear Estimation as a generalization of those methods.  Specifically, multiple regression (and ANOVA) assumes that the relationship between the independent variable(s) and the dependent variable is linear in nature.  Nonlinear Estimation leaves it up to you to specify the nature of the relationship; for example, you may specify the dependent variable to be a logarithmic function of the independent variable(s), an exponential function, a function of some complex ratio of independent measures, etc.  (However, if all variables of interest are categorical in nature, or can be converted into categorical variables, you may also consider the Correspondence Analysis module.)

When allowing for any type of relationship between the independent variables and the dependent variable, two issues raise their heads.  First, what types of relationships "make sense", that is, are interpretable in a meaningful manner?  Note that the simple linear relationship is very convenient in that it allows us to make such straightforward interpretations as "the more of x (e.g., the higher the price of a house), the more there is of y (the longer it takes to sell it); and given a particular increase in x, a proportional increase in y can be expected."  Nonlinear relationships cannot usually be interpreted and verbalized in such a simple manner.  The second issue that needs to be addressed is how to exactly compute the relationship, that is, how to arrive at results that allow us to say whether or not there is a nonlinear relationship as predicted.

Let us now discuss the nonlinear regression problem in a somewhat more formal manner, that is, introduce the common terminology that will allow us to examine the nature of these techniques more closely, and how they are used to address important questions in various research domains (medicine, social sciences, physics, chemistry, pharmacology, engineering, etc.).


Nonlinear Estimation - Estimating Linear and Nonlinear Models

  Nonlinear Estimation Introductory Overview - Estimating Linear and Nonlinear Models

Technically speaking, Nonlinear Estimation is a general fitting procedure that will estimate any kind of relationship between a dependent (or response variable), and a list of independent variables.  In general, all regression models may be stated as:

y = F(x , x , ... , x )

       1   2         n

In most general terms, we are interested in whether and how a dependent variable is related to a list of independent variables; the term F(x...) in the expression above means that y, the dependent or response variable, is a function of the x's, that is, the independent variables.

An example of this type of model would be the linear multiple regression model as described in Multiple Regression.  For this model, we assume the dependent variable to be a linear function of the independent variables, that is:

y = a + b *x  + b *x  + ... + b *x

         1  1    2  2          n  n

If you are not familiar with multiple linear regression, you may want to read the Introductory Overview section to Multiple Regression at this point (however, it is not necessary to understand all of the nuances of multiple linear regression techniques in order to understand the methods discussed here).

Nonlinear Estimation allows you to specify essentially any type of continuous or discontinuous regression model.  Some of the most common nonlinear models (such as probit, logit, exponential growth, and breakpoint regression) are pre-defined in Nonlinear Estimation and can simply be requested as dialog options.  However, you can also type in any type of regression equation, which STATISTICA will then fit to your data (see User-Defined Regression).  Moreover, you can specify either standard least squares estimation, maximum likelihood estimation (where appropriate), or, again, define your own "loss function" (see below) by typing in the respective equation.

In general, whenever the simple linear regression model does not appear to adequately represent the relationships between variables, then the nonlinear regression model approach is appropriate.  Click on the following topics for overviews of the common nonlinear regression models, nonlinear estimation procedures, and evaluation of the fit of the data to the nonlinear model.

Common Nonlinear Regression Models

Nonlinear Estimation Procedures

Evaluating the Fit of the Model


  Nonlinear Estimation - Common Nonlinear Regression Models

Intrinsically Linear Regression Models

Intrinsically Nonlinear Regression Models


  Common Nonlinear Regression Models - Intrinsically Linear Regression Models

Polynomial Regression.  A common "nonlinear" model is polynomial regression.  We put the term nonlinear in quotes here because the nature of this model is actually linear.  For example, suppose we measure in a learning experiment subjects' physiological arousal and their performance on a complex tracking task.  Based on the well-known Yerkes-Dodson law we could expect a curvilinear relationship between arousal and performance; this expectation can be expressed in the regression equation:

                                           2

Performance = a + b * Arousal + b * Arousal

                   1             2

In this equation, a represents the intercept, and b1 and b2 are regression coefficients.  The non-linearity of this model is expressed in the term Arousal**2.  However, the nature of the model is still linear, except that when estimating it, we would square the measure of arousal.  The Multiple Regression fixed nonlinear option could also be used to estimate the regression coefficients for this model.  These types of models, where we include some transformation of the independent variables in a linear equation, are also referred to as models that are nonlinear in the variables.

Models that are nonlinear in the parameters.  To contrast the example above, consider the relationship between a human's age from birth (the x variable) and his or her growth rate (the y variable).  Clearly, the relationship between these two variables in the first year of a person's life (when most growth occurs) is very different than during adulthood (when almost no growth occurs).  Thus, the relationship could probably best be expressed in terms of some negative exponential function:

Growth = exp(-b *Age)

               1

Note that the nature of this model is no longer linear, that is, the expression shown above does not simply represent a linear regression model, with some transformation of the independent variable.  This type of model is said to be nonlinear in the parameters.

Making nonlinear models linear.  In general, whenever a regression model can be "made" into a linear model, this is the preferred route to pursue (for estimating the respective model).  The linear multiple regression model (see Multiple Regression) is very well understood mathematically, and, from a pragmatic standpoint, is most easily interpreted.  Therefore, returning to the simple exponential regression model of Growth as a function of Age shown above, we could convert this nonlinear regression equation into a linear one by simply taking the logarithm of both sides of the equations, so that:

log(Growth) = -b *Age

                1

If we now substitute log(Growth) with y, we have the standard linear regression model as shown earlier (without the intercept which was ignored here to simplify matters).  Thus, we could log-transform the Growth rate data (e.g., using the spreadsheet formula transformations) and then use Multiple Regression to estimate the relationship between Age and Growth, that is, compute the regression coefficient b1.

Model adequacy.  Of course, by using the "wrong" transformation, one could end up with an inadequate model.  Therefore, after "linearizing" a model such as the one shown above, it is particularly important to use the extensive residual statistics in Multiple Regression.


  Common Nonlinear Regression Models - Intrinsically Nonlinear Regression Models

Some regression models which cannot be transformed into linear ones, can only be estimated via Nonlinear Estimation.  In the growth rate example above, we purposely "forgot" about the random error in the dependent variable.  Of course, the growth rate is affected by very many other variables (other than time), and we can expect a considerable amount of random (residual) fluctuation around the fitted line.  If we add this error or residual variability to the model, we could rewrite it as follows:

Growth = exp(-b *Age) + error

               1

Additive error.  In this model we assume that the error variability is independent of age, that is, that the amount of residual error variability is the same at any age.  Because the error term in this model is additive, you can no longer linearize this model by taking the logarithm of both sides.  If for a given data set, you were to log-transform variable Growth anyway and fit the simple linear model, then you would find that the residuals from the analysis would no longer be evenly distributed over the range of variable Age; and thus, the standard linear regression analysis (via Multiple Regression) would no longer be appropriate.  Therefore, the only way to estimate the parameters for this model is via the Nonlinear Estimation module.

Multiplicative error.  To "defend" our previous example, in this particular instance it is not likely that the error variability is constant at all ages, that is, that the error is additive.  Most likely, there is more random and unpredictable fluctuation of the growth rate at the earlier ages than the later ages, when growth comes to a virtual standstill anyway.  Thus, a more realistic model including the error would be:

Growth = exp(-b *Age) * error

               1

Put in words, the greater the age, the smaller the term exp(-b1*Age), and, consequently, the smaller the resultant error variability.  If we now take the log of both sides of the equation, the residual error term will become an additive factor in a linear equation, and we can go ahead and estimate b1 via standard multiple regression.

Log (Growth) = -b *Age + error

                 1

Let us now consider some regression models (that are nonlinear in their parameters) which cannot be "made into" linear models through simple transformations of the raw data.

General Growth Model

Models for Binary Responses: Probit & Logit

General Logistic Regression Model

Drug Responsiveness and Half-Maximal Response

Discontinuous Regression Models


  Intrinsically Nonlinear Regression Models - General Growth Model

The general growth model, is similar to the example that we previously considered:

y = b  + b *exp(b *x) + error

     0    1      2

This model is commonly used in studies of any kind of growth (y), when the rate of growth at any given point in time (x) is proportional to the amount of growth remaining.  The parameter b0 in this model represents the maximum growth value.  A typical example where this model would be adequate is when one wants to describe the concentration of a substance (e.g., in water) as a function of elapsed time.


  Intrinsically Nonlinear Regression Models - Models for Binary Responses: Probit & Logit

It is not uncommon that a dependent or response variable is binary in nature, that is, that it can have only two possible values.  For example, patients either do or do not recover from an injury; job applicants either succeed or fail at an employment test, subscribers to a journal either do or do not renew a subscription, coupons may or may not be returned, etc.  In all of these cases, one may be interested in estimating a model that describes the relationship between one or more continuous independent variable(s) to the binary dependent variable.

Using linear regression.  Of course, one could use standard multiple regression procedures to compute standard regression coefficients.  For example, if one studied the renewal of journal subscriptions, one could create a y variable with 1's and 0's, where 1 indicates that the respective subscriber renewed, and 0 indicates that the subscriber did not renew.  However, there is a problem:  Multiple Regression does not "know" that the response variable is binary in nature.  Therefore, it will inevitably fit a model that leads to predicted values that are greater than 1 or less than 0.  However, predicted values that are greater than 1 or less than 0 are not valid; thus, the restriction in the range of the binary variable (e.g., between 0 and 1) is ignored if one uses the standard multiple regression procedure.

Continuous response functions.  We could rephrase the regression problem so that, rather than predicting a binary variable, we are predicting a continuous variable that naturally stays within the 0-1 bounds.  The two most common regression models that accomplish exactly this are the logit and the probit regression models.

Logit regression.  In the logit regression model, the predicted values for the dependent variable will never be less than (or equal to) 0, or greater than (or equal to) 1, regardless of the values of the independent variables.  This is accomplished by applying the following regression equation, which actually has some "deeper meaning" as we will see shortly (the term logit was first used by Berkson, 1944):

y=exp(b +b *x +...+b *x )/{1+exp(b +b *x +...+b *x )}

       0  1  1      n  n          0  1  1      n  n

One can easily recognize that, regardless of the regression coefficients or the magnitude of the x values, this model will always produce predicted values (predicted y's) in the range of 0 to 1.

The name logit stems from the fact that one can easily linearize this model via the logit transformation.  Suppose we think of the binary dependent variable y in terms of an underlying continuous probability p, ranging from 0 to 1.  We can then transform that probability p as:

p' = log {p/(1-p)}

        e

This transformation is referred to as the logit or logistic transformation.  Note that p' can theoretically assume any value between minus and plus infinity.  Since the logit transform solves the issue of the 0/1 boundaries for the original dependent variable (probability), we could use those (logit transformed) values in an ordinary linear regression equation.  In fact, if we perform the logit transform on both sides of the logit regression equation stated earlier, we obtain the standard linear regression model:

p' = b  + b *x  + b *x  + ... + b *x

      0    1  1    2  2          n  n

Probit regression.  One may consider the binary response variable to be the result of a normally distributed underlying variable that actually ranges from minus infinity to positive infinity.  For example, a subscriber to a journal can feel very strongly about not renewing a subscription, be almost undecided, "tend towards" renewing the subscription, or feel very much in favor of renewing the subscription.  In any event, all that we (the publisher of the journal) will see is the binary response of renewal or failure to renew the subscription.  However, if we set up the standard linear regression equation based on the underlying "feeling" or attitude we could write:

feeling...= b  + b *x  + ...

             0    1  1

which is, of course, the standard regression model.  It is reasonable to assume that these feelings are normally distributed, and that the probability p of renewing the subscription is about equal to the relative space under the normal curve.  Therefore, if we transform each side of the equation so as to reflect normal probabilities, we obtain:

NP(feeling...) = NP(b  + b *x  ...)

                     0    1  1

where NP stands for normal probability (space under the normal curve), as tabulated in practically all statistics texts.  The equation shown above is also referred to as the probit regression model.  (The term probit was first used by Bliss, 1934).


  Intrinsically Nonlinear Regression Models - General Logistic Regression Model

The general logistic model can be stated as:

y = b /{1+b *exp(b *x)}

     0     1      2

You can think of this model as an extension of the logit or logistic model for binary responses.  However, while the logit model restricts the dependent response variable to only two values, this model allows the response to vary within a particular lower and upper limit.  For example, suppose we are interested in the population growth of a species that is introduced to a new habitat, as a function of time.  The dependent variable would be the number of individuals of that species in the respective habitat.  Obviously, there is a lower limit on the dependent variable, since fewer than 0 individuals cannot exist in the habitat; however, there also is most likely an upper limit that will be reached at some point in time.


  Intrinsically Nonlinear Regression Models - Drug Responsiveness and Half-Maximal Response

In pharmacology, the following model is often used to describe the effects of different dose levels of a drug:

                     b1

y = b  - b /{1+(x/b )  }

     0    0        2

In this model, x is the dose level (usually in some coded form, so that x ≥ 1) and y is the responsiveness, in terms of the percent of maximum possible responsiveness.  The parameter b0 then denotes the expected response at the level of dose saturation and b2 is the concentration that produces a half-maximal response; the parameter b1 determines the slope of the function.


  Intrinsically Nonlinear Regression Models - Discontinuous Regression Models

Piecewise linear regression.  It is not uncommon that the nature of the relationship between one or more independent variables and a dependent variable changes over the range of the independent variables.  For example, suppose we monitor the per-unit manufacturing cost of a particular product as a function of the number of units manufactured (output) per month.  In general, the more units per month we produce, the lower is our per-unit cost, and this linear relationship may hold over a wide range of different levels of production output.  However, it is conceivable that above a certain point, there is a discontinuity in the relationship between these two variables.  For example, the per-unit cost may decrease relatively less quickly when older (less efficient) machines have to be put on-line in order to cope with the larger volume.  Suppose that the older machines go on-line when the production output rises above 500 units per month; we may specify a regression model for cost-per-unit as:

y = b  + b *x*(x ≤ 500) + b *x*(x > 500)

     0    1                2

In this formula, y stands for the estimated per-unit cost; x is the output per month.  The expressions (x ≤ 500) and (x > 500) denote logical conditions that evaluate to 0 if false, and to 1 if true.  Thus, this model specifies a common intercept (b0), and a slope that is either equal to b1 (if x ≤ 500 is true, that is, equal to 1) or b2 (if x > 500 is true, that is, equal to 1).

Instead of specifying the point where the discontinuity in the regression line occurs (at 500 units per months in the example above), one could also estimate that point.  For example, one might have noticed or suspected that there is a discontinuity in the cost-per-unit at one particular point; however, one may not know where that point is.  In that case, simply replace the 500 in the equation above with an additional parameter (e.g., b3).  Nonlinear Estimation would then estimate the point of discontinuity.

Breakpoint regression.  One could also adjust the equation above to reflect a "jump" in the regression line.  For example, imagine that, after the older machines are put on-line, the per-unit-cost jumps to a higher level, and then slowly goes down as volume continues to increase.  In that case, simply specify an additional intercept (b3), so that:

y = (b +b *x)*(x ≤ 500) + (b +b *x)*(x > 500)

      0  1                  3  2

Nonlinear Estimation includes a pre-defined breakpoint regression model that can be chosen as a dialog option.  However, unlike the model shown above, that option will fit different regression models to different ranges of the dependent y variable.

Comparing groups.  The method described here to estimate different regression equations in different domains of the independent variable can also be used to distinguish between groups.  For example, suppose in the example above, there are three different plants; to simplify the example, let us ignore the breakpoint for now.  If we coded the three plants in a grouping variable by using the values 1, 2, and 3, we could simultaneously estimate three different regression equations by specifying:

y = (x =1)*(b  +b  *x)+(x =2)*(b  +b  *x)+(x =3)*(b  +b  *x)

      p      10  11      p      20  21      p      30  31

In this equation, xp denotes the grouping variable containing the codes that identify each plant, b10, b20, and b30 are the three different intercepts, and b11, b21, and b31 refer to the slope parameters (regression coefficients) for each plant.  One could compare the fit of the common regression model without considering the different groups (plants) with this model in order to determine which model is more appropriate.


  Nonlinear Estimation Procedures

Least Squares Estimation

Loss Functions

Weighted Least Squares

Maximum Likelihood

Maximum likelihood and probit/logit models

Function Minimization Algorithms

Start Values, Step Sizes, Convergence Criteria

Penalty Functions, Constraining Parameters

Local Minima

Quasi-Newton Method

Simplex Procedure

Hooke-Jeeves Pattern Moves

Rosenbrock Pattern Search

Hessian Matrix and Standard Errors

Click on the following topics for overviews of the common nonlinear regression models and evaluation of the fit of the data to the nonlinear model.

Common Nonlinear Regression Models

Evaluating the Fit of the Model


  Nonlinear Estimation Procedures - Least Squares Estimation

Some of the more common nonlinear regression models are reviewed in Common Nonlinear Regression Models.  Now, the question arises as to how these models are estimated.  If you are familiar with linear regression techniques (as described in Multiple Regression) or analysis of variance (ANOVA) techniques (as described in ANOVA/MANOVA), then you may be aware of the fact that all of those methods use so-called least squares estimation procedures.  In the most general terms, least squares estimation is aimed at minimizing the sum of squared deviations of the observed values for the dependent variable from those predicted by the model.  (The term least squares was first used by Legendre, 1805.)


  Nonlinear Estimation Procedures - Loss Functions

In standard multiple regression we estimate the regression coefficients by "finding" those coefficients that minimize the residual variance (sum of squared residuals) around the regression line.  Any deviation of an observed score from a predicted score signifies some loss in the accuracy of our prediction, for example, due to random noise (error).  Therefore, we can say that the goal of least squares estimation is to minimize a loss function; specifically, this loss function is defined as the sum of the squared deviation about the predicted values (the term loss was first used by Wald, 1939).  When this function is at its minimum, then we get the same parameter estimates (intercept, regression coefficients) as we would in Multiple Regression; because of the particular loss functions that yielded those estimates, we can call the estimates least squares estimates.

Phrased in this manner, there is no reason why you cannot consider other loss functions.  For example, rather than minimizing the sum of squared deviations, why not minimize the sum of absolute deviations?  Indeed, this is sometimes useful in order to "de-emphasize" outliers.  Relative to all other residuals, a large residual will become much larger when squared.  However, if one only takes the absolute value of the deviations, then the resulting regression line will most likely be less affected by outliers.

Nonlinear Estimation contains several function minimization methods that can be used to minimize any kind of loss function.  For more information, see:

Weighted Least Squares

Maximum Likelihood

Maximum likelihood and probit/logit models

Function Minimization Algorithms

Start Values, Step Sizes, Convergence Criteria

Penalty Functions, Constraining Parameters

Local Minima

Quasi-Newton Method

Simplex Procedure

Hooke-Jeeves Pattern Moves

Rosenbrock Pattern Search

Hessian Matrix and Standard Errors


  Nonlinear Estimation Procedures - Weighted Least Squares

In addition to least squares and absolute deviation regression (see above), weighted least squares estimation is probably the most commonly used technique.  Ordinary least squares techniques assume that the residual variance around the regression line is the same across all values of the independent variable(s).  Put another way, it is assumed that the error variance in the measurement of each case is identical.  Often, this is not a realistic assumption; in particular, violations frequently occur in business, economic, or biological applications.

For example, suppose we wanted to study the relationship between the projected cost of construction projects, and the actual cost.  This may be useful in order to gage the expected cost overruns.  In this case it is reasonable to assume that the absolute magnitude (dollar amount) by which the estimates are off, is proportional to the size of the project.  Thus, we would use a weighted least squares loss function to fit a linear regression model.  Specifically, the loss function would be (see, for example, Neter, Wasserman, & Kutner, 1985, p. 168):

                 2       2

Loss = (Obs-Pred)  * (1/x )

In this equation, the loss function first specifies the standard least squares loss function (Observed minus Predicted squared; i.e., the squared residual), and then weighs this loss by the inverse of the squared value of the independent variable (x) for each case.  In the actual estimation, the program will sum up the value of the loss function for each case (e.g., construction project), as specified above, and estimate the parameters that minimize that sum.  To return to our example, the larger the project (x) the less weight is placed on the deviation from the predicted value (cost).  This method will yield more stable estimates of the regression parameters (for more details, see Neter, Wasserman, & Kutner, 1985).


  Nonlinear Estimation Procedures - Maximum Likelihood

An alternative to the least squares loss function (see above) is to maximize the likelihood or log-likelihood function (or to minimize the negative log-likelihood function; the term maximum likelihood was first used by Fisher, 1922a).  In most general terms, the likelihood function is defined as:

                   n

L = F(Y,Model) = ∏   { p[y , Model Parameters(x )]}

                  i=1     i                    i

In theory, we can compute the probability (now called L, the likelihood) of the specific dependent variable values to occur in our sample, given the respective regression model.  Provided that all observations are independent of each other, this likelihood is the geometric sum (∏, across i = 1 to n cases) of probabilities for each individual observation (i) to occur, given the respective model and parameters for the x values.  (The geometric sum means that we would multiply out the individual probabilities across cases.)  It is also customary to express this function as a natural logarithm, in which case the geometric sum becomes a regular arithmetic sum (Σ, across i = 1 to n cases).

Given the respective model, the larger the likelihood of the model, the larger is the probability of the dependent variable values to occur in the sample.  Therefore, the greater the likelihood, the better is the fit of the model to the data.  The actual computations for particular models here can become quite complicated because we need to "track" (compute) the probabilities of the y-values to occur (given the model and the respective x-values).  As it turns out, if all assumptions for standard multiple regression are met (as described in the Multiple Regression chapter in the manual), then the standard least squares estimation method (see above) will yield results identical to the maximum likelihood method.  If the assumption of equal error variances across the range of the x variable(s) is violated, then the weighted least squares method described earlier will yield maximum likelihood estimates.


  Nonlinear Estimation Procedures - Maximum Likelihood and Probit/Logit Models

The maximum likelihood function has been "worked out" for probit and logit regression models.  Specifically, the loss function for these models is computed as the sum of the natural log of the logit or probit likelihood L1 so that:

            n

log(L ) = Σ   [y *log(p ) + (1-y )*log(1-p )]

     1     i=1  i      i        i         i

where

log(L1)	is the natural log of the (logit or probit) likelihood (log-likelihood) for the current model

yi	is the observed value for case i

pi	is the expected (predicted or fitted) probability (between 0 and 1)

The log-likelihood of the null model (L0), that is, the model containing the intercept only (and no regression coefficients) is computed as:

log(L ) = n *(log(n /n)) + n *(log(n /n))

     0     0       0        1       1

where

log(L0)	is the natural log of the (logit or probit) likelihood of the null model (intercept only)

n0	is the number of observations with a value of 0 (zero)

n1	is the number of observations with a value of 1

n	is the total number of observations

These formulas are provided here for your reference; maximum likelihood estimation will automatically be used for probit and logit models so you do not need to type in this complex formula into the loss function editor.


  Nonlinear Estimation Procedures - Function Minimization Algorithms

Now that we have discussed different regression models, and the loss functions that can be used to estimate them, the only "mystery" that is left is how to minimize the loss functions (to find the best fitting set of parameters), and how to estimate the standard errors of the parameter estimates.  Nonlinear Estimation uses one very efficient algorithm (quasi-Newton) that approximates the second-order derivatives of the loss function to guide the search for the minimum (i.e., for the best parameter estimates, given the respective loss function).  In addition, Nonlinear Estimation offers several more general function minimization algorithms that follow different search strategies (which do not depend on the second-order derivatives).  These strategies are sometimes more effective for estimating loss functions with local minima; therefore, these methods are often particularly useful to find appropriate start values for the estimation via the quasi-Newton method.

In all cases, STATISTICA can compute (if requested by the user) the standard errors of the parameter estimates (see Estimation Procedure).  These standard errors are based on the second-order partial derivatives for the parameters, which are computed via finite difference approximation.

If you are not interested in how the minimization of the loss function is done, only that it can be done, you may skip the following paragraphs.  However, you may find it useful to know a little about these procedures in case your regression model "refuses" to be fit to the data.  In that case, the iterative estimation procedure will fail to converge, producing ever "stranger" (e.g., very large or very small) parameter estimates.

In the following paragraphs we will first discuss some general issues involved in unconstrained optimization, and then briefly review the methods used in this module.  For more detailed discussions of these procedures you may refer to Brent (1973), Gill and Murray (1974), Peressini, Sullivan, and Uhl (1988), and Wilde and Beightler (1967).  For specific algorithms, see Dennis and Schnabel (1983), Eason and Fenton (1974), Fletcher (1969), Fletcher and Powell (1963), Fletcher and Reeves (1964), Hooke and Jeeves (1961), Jacoby, Kowalik, and Pizzo (1972), and Nelder and Mead (1964).


  Nonlinear Estimation Procedures - Start Values, Step Sizes, Convergence Criteria

A common aspect of all estimation procedures is that they require the user to specify some start values, initial step sizes, and a criterion for convergence (see Estimation Procedure).  All methods will begin with a particular set of initial estimates (start values), which will be changed in some systematic manner from iteration to iteration; in the first iteration, the step size determines by how much the parameters will be moved.  Finally, the convergence criterion determines when the iteration process will stop.  For example, the process may stop when the improvements in the loss function from iteration to iteration are less than a specific amount.  Nonlinear Estimation has preset defaults for all of these parameters, which are appropriate in most cases.


  Nonlinear Estimation Procedures - Penalty Functions, Constraining Parameters

All estimation procedures in Nonlinear Estimation are unconstrained in nature.  That means that the program will move parameters around without any regard for whether or not permissible values result.  For example, in the course of logit regression we may get estimated values that are equal to 0.0, in which case the logarithm cannot be computed (since the log of 0 is undefined).  When this happens, the program will assign a penalty to the loss function, that is, a very large value.  As a result, the various estimation procedures usually move away from the regions that produce those functions.  However, in some circumstances, the estimation will "get stuck," and as a result, you would see a very large value of the loss function.  This could happen, if, for example, the regression equation involves taking the logarithm of an independent variable which has a value of zero for some cases (in which case the logarithm cannot be computed).

If the user wishes to constrain a procedure in Nonlinear Estimation, then this constraint must be specified in the loss function as a penalty function (assessment).  By doing this, the user may control what permissible values of the parameters to be estimated may be manipulated by the program.  For example, if two parameters (a and b) are to be constrained to be greater than or equal to zero, then one must assess a large penalty to these parameters if this condition is not met.  Below is an example of a user-specified regression and loss function, including a penalty assessment designed to "penalize" the parameters a and/or b if either one is not greater than or equal to zero (see also General Syntax Conventions:  Loss Function):

Estimated function:  v3 = a + b*v1 + (c*v2)

Loss function:  L = (obs - pred)**2 + (a<0)*100000 + (b<0)*100000


  Nonlinear Estimation Procedures - Local Minima

The most "treacherous" threat to unconstrained function minimization are local minima.  For example, a particular loss function may become slightly larger, regardless of how a particular parameter is moved.  However, if the parameter were to be moved into a completely different place, the loss function may actually become smaller.  You can think of such local minima as local "valleys" or minor "dents" in the loss function.  However, in most practical applications, local minima will produce "outrageous" and extremely large or small parameter estimates with very large standard errors.  In those cases, specify different start values and try again.  Also note, that the Simplex method (see below) is particularly "smart" in avoiding such minima; therefore, this method may be particularly suited in order to find appropriate start values for complex functions.


  Nonlinear Estimation Procedures - Quasi-Newton Method

As you may remember, the slope of a function at a particular point can be computed as the first-order derivative of the function (at that point).  The "slope of the slope" is the second-order derivative, which tells us how fast the slope is changing at the respective point, and in which direction.  The quasi-Newton method will, at each step, evaluate the function at different points in order to estimate the first-order derivatives and second-order derivatives.  It will then use this information to follow a path towards the minimum of the loss function.


  Nonlinear Estimation Procedures - Simplex Procedure

This algorithm does not rely on the computation or estimation of the derivatives of the loss function.  Instead, at each iteration the function will be evaluated at m+1 points in the m dimensional parameter space.  For example, in two dimensions (i.e., when there are two parameters to be estimated), the program will evaluate the function at three points around the current optimum.  These three points would define a triangle; in more than two dimensions, the "figure" produced by these points is called a Simplex.  Intuitively, in two dimensions, three points will allow us to determine "which way to go," that is, in which direction in the two dimensional space to proceed in order to minimize the function.  The same principle can be applied to the multidimensional parameter space, that is, the Simplex will "move" downhill; when the current step sizes become too "crude" to detect a clear downhill direction, (i.e., the Simplex is too large), the Simplex will "contract" and try again.

An additional strength of this method is that when a minimum appears to have been found, the Simplex will again be expanded to a larger size to see whether the respective minimum is a local minimum.  Thus, in a way, the Simplex moves like a smooth single cell organism down the loss function, contracting and expanding as local minima or significant ridges are encountered.


  Nonlinear Estimation Procedures - Hooke-Jeeves Pattern Moves

In a sense this is the simplest of all algorithms.  At each iteration, this method first defines a pattern of points by moving each parameter one by one, so as to optimize the current loss function.  The entire pattern of points is then shifted or moved to a new location; this new location is determined by extrapolating the line from the old base point in the m dimensional parameter space to the new base point.  The step sizes in this process are constantly adjusted to "zero in" on the respective optimum.  This method is usually quite effective, and should be tried if both the quasi-Newton and Simplex methods (see above) fail to produce reasonable estimates.


  Nonlinear Estimation Procedures - Rosenbrock Pattern Search

Where all other methods fail, the Rosenbrock Pattern Search method often succeeds.  This method will rotate the parameter space and align one axis with a ridge (this method is also called the method of rotating coordinates); all other axes will remain orthogonal to this axis.  If the loss function is unimodal and has detectable ridges pointing towards the minimum of the function, then this method will proceed with sure-footed accuracy towards the minimum of the function.  However, note that this search algorithm may terminate early when there are several constraint boundaries (resulting in the penalty value; see above) that intersect, leading to a discontinuity in the ridges.


  Nonlinear Estimation Procedures - Hessian Matrix and Standard Errors

The matrix of second-order (partial) derivatives is also called the Hessian matrix.  It turns out that the inverse of the Hessian matrix approximates the variance/covariance matrix of parameter estimates.  Intuitively, there should be an inverse relationship between the second-order derivative for a parameter and its standard error:  If the change of the slope around the minimum of the function is very sharp, then the second-order derivative will be large; however, the parameter estimate will be quite stable in the sense that the minimum with respect to the parameter is clearly identifiable.  If the second-order derivative is nearly zero, then the change in the slope around the minimum is zero, meaning that we can practically move the parameter in any direction without greatly affecting the loss function.  Thus, the standard error of the parameter will be very large.

The Hessian matrix (and asymptotic standard errors for the parameters) are computed separately via finite difference approximation by selecting the option Asymptotic Standard Errors from the Model Estimation dialog.  This procedure yields very precise asymptotic standard errors for all estimation methods.


  Nonlinear Estimation - Evaluating the Fit of the Model

After estimating the regression parameters, an essential aspect of the analysis is to test the appropriateness of the overall model.  For example, if one specified a linear regression model, but the relationship is intrinsically non-linear, then the parameter estimates (regression coefficients) and the estimated standard errors of those estimates may be significantly "off."  Let us review some of the ways to evaluate the appropriateness of a model.

Proportion of Variance Explained

Goodness-of-fit Chi-square

Plot of Observed vs. Predicted Values

Normal and Half-Normal Probability Plots

Variance/Covariance Matrix for Parameters

Click on the following topics for overviews of the common nonlinear regression models and nonlinear estimation procedures.

Common Nonlinear Regression Models

Nonlinear Estimation Procedures


Evaluating the Fit of the Model - Proportion of Variance Explained

  Nonlinear Estimation Evaluating the Fit of the Model - Proportion of Variance Explained

Regardless of the model, one can always compute the total variance of the dependent variable (total sum of squares, SST), the proportion of variance due to the residuals (error sum of squares, SSE), and the proportion of variance due to the regression model (regression sum of squares, SSR=SST-SSE).  The ratio of the regression sum of squares to the total sum of squares (SSR/SST) explains the proportion of variance accounted for in the dependent variable (y) by the model; thus, this ratio is equivalent to the R-square (0 ≤ R-square ≤ 1, the coefficient of determination).  Even when the dependent variable is not normally distributed across cases, this measure may help evaluate how well the model fits the data.


Evaluating the Fit of the Model - Goodness-of-Fit Chi-square

  Nonlinear Estimation Evaluating the Fit of the Model - Goodness-of-fit Chi-square

For probit and logit regression models, the Nonlinear Estimation module will use maximum likelihood estimation (i.e., maximize the likelihood function; see Probit/Logit Regression).  As it turns out, one can directly compare the likelihood L0 for the null model where all slope parameters are zero, with the likelihood L1 of the fitted model.  Specifically, one can compute the Chi-square statistic for this comparison as:

Chi-square = -2 * (log(L ) - log(L ))

                        0         1

The degrees of freedom for this Chi-square value are equal to the difference in the number of parameters for the null and the fitted model; thus, the degrees of freedom will be equal to the number of independent variables in the logit or probit regression.  If the p-level associated with this Chi-square is significant, then we can say that the estimated model yields a significantly better fit to the data than the null model, that is, that the regression parameters are statistically significant.


Evaluating the Fit of the Model - Plot of Observed vs. Predicted Values

  Nonlinear Estimation Evaluating the Fit of the Model - Plot of Observed vs. Predicted Values

It is always a good idea to inspect a scatterplot of predicted vs. observed values.  If the model is appropriate for the data, then we would expect the points to roughly follow a straight line; if the model is incorrectly specified, then this plot will indicate a non-linear pattern.


Evaluating the Fit of the Model - Normal and Half-Normal Probability Plots

  Nonlinear Estimation Evaluating the Fit of the Model - Normal and Half-Normal Probability Plots

The normal probability plot of residuals will give us an indication of whether or not the residuals (i.e., errors) are normally distributed.  For more information on how the standard normal probability plot is constructed, see Normal Probability Plots.  For more information on how the half-normal probability plot is constructed, see Half-Normal Probability Plots.


Evaluating the Fit of the Model - Variance/Covariance Matrix for Paramters

  Nonlinear Estimation Evaluating the Fit of the Model - Variance/Covariance Matrix for Parameters

When a model is grossly misspecified, or the estimation procedure gets "hung up" in a local minimum, the standard errors for the parameter estimates (which are optionally computed by the program via finite difference approximation) can become very large.  This means that regardless of how the parameters were moved around the final values, the resulting loss function did not change much.  Also, the correlations between parameters may become very large, indicating that parameters are very redundant; put another way, when the estimation algorithm moved one parameter away from the final value, then the increase in the loss function could be almost entirely compensated for by moving another parameter.  Thus, the effect of those two parameters on the loss function was very redundant.


  Nonlinear Estimation - Startup Panel

Select the desired regression model from this dialog (see also, Nonlinear Estimation - Index).  When you select the User-specified regression (default) option, you will be able to type in a formula to specify the relationship between the independent variables and the dependent variable.

For details concerning the different nonlinear models, see Common Nonlinear Regression Models.


    Nonlinear Estimation - Probit/Logit Regression

When you click on either the Logistic Regression or the Probit Regression options from the Nonlinear Regression Startup Panel, you will be able to make some selections in the Probit or Logit Regression dialogs.  For more information on Probit and Logit regressions, see Common Nonlinear Regression Models.

Loss function:  To estimate the parameters of logit and probit models, the program will maximize the likelihood for the data (i.e., compute maximum likelihood parameter estimates).  To use other loss functions (e.g., weighted least squares), choose option User-specified regression; you can then specify the model by typing in the model equation, and the loss function by specifying the equation that describes the quantity that is to be minimized during the parameter estimation process.

Probit/Logit Regression dialog:

Input file

Variables

Codes

Missing data


    Probit/Logit Regression - Input File

There are two ways to set up a data file for a probit or logit regression analysis.  First, a data file may contain raw data, with a coding variable as the dependent variable (containing the two codes that indicate the two levels of the dichotomous dependent variable).  If the data are arranged in this manner, then set this combo box to Codes and no counts.

Alternatively, one may enter frequencies directly into the file.  This way of arranging the data file is often more efficient when the data contain failure (or survival) rates as a function of time.  For example, Cox (1970) reported the following data on tests of objects for failures after certain times.  Variable Failure is an indicator variable (0=no failure, 1=failure), and variable Count represents the respective number of objects that did or did not fail in the respective time interval:

Time  Failure  Count

----  -------  -----

  7        0     55

 14        0    155

 14        1      2

 27        0    152

 27        1      7

 51        0     13

 51        1      3

Thus, at time 7 there were no failures among 55 objects.  At time 14, there were 2 failures (coded 1) and 155 non-failures (coded 0, for a total of 157 objects).  At time 27 there were 7 failures and 152 non-failures, etc.  To analyze this data set, one would set the Input file combo box to Codes and counts, specify Time as the independent variable (in the first list of the Specify Variables dialog), Failure as the dependent variable (in the second list), and variable Count as the variable containing the counts (in the third list).  Note that the total frequencies reported on the Results dialog will be the actual frequencies, that is, taking into account the counting variable.


    Probit/Logit Regression - Variables

This option will bring up the standard variable selection dialog in which you can select one dependent variable and a set of independent or predictor variables.  In addition, if the Input file combo box is set to Codes and counts, then STATISTICA expects you to specify the Count variable containing the frequency counts.


    Probit/Logit Regression - Codes

Logit and probit regression models in a sense, predict probabilities underlying the dichotomous dependent variable, and these methods will produce predicted (expected) values in the range between 0 and 1 (for details, see Common Nonlinear Regression Models).  If the dependent variable is not coded in this way, that is, as 0 and 1, then the user must specify the respective codes in the Codes edit boxes.  As the data are read, the dependent variable will then be transformed so that all values that match the first code become 0 (zero), and all values that match the second code become 1.


    Probit/Logit Regression - Missing Data

Missing data can either be deleted casewise or substituted by the means for the respective variables.  If Casewise deletion of missing data is selected, a case will be deleted from the analysis if it has missing data for any of the selected variables.  If Mean substitution is specified, a missing data point will be replaced by the mean for the respective variable.


  Nonlinear Estimation - Exponential Regression

STATISTICA will estimate, using least squares, the model:

y = c + exp(b  + b *x  + b *x  + ... + b *x )

             0    1  1    2  2          m  m

where

c, bi are parameters (for the m independent variables)

This model is commonly used in order to study the growth of populations.

Exponential Regression dialog:

Variables button:  When you click on this button, the standard variable selection dialog will open in which you will be able to select the independent or predictor variables, and a dependent variable.

Missing data:  Missing data can either be deleted casewise or substituted by the means for the respective variables.  If Casewise deletion of missing data is selected, a case will be deleted from the analysis if it has missing data for any of the selected variables.  If Mean substitution is specified, a missing data point will be replaced by the mean for the respective variable.


  Nonlinear Estimation - Breakpoint Regression

When you select the Piecewise Linear Regression option from the Nonlinear Regression startup panel, STATISTICA will estimate, using least squares, the model:

y = (b  +b  *x +...+b  *x )*(y ≤ b ) + (b  +b  *x +...+b  *x )*(y > b )

      01  11  1      m1  m        n      02  12  1      m2  m        n

Thus, the program will estimate two separate linear regression equations; one for the y values that are less than or equal to the breakpoint (b0) and one for the y values that are greater than the breakpoint.  (For a general description of these types of models, see Common Nonlinear Regression Models).

To estimate models with breakpoints (discontinuities) in the independent variables, choose option User-specified regression from the Startup Panel and then use logical operators in the model equation to define the breakpoints)

Breakpoint Regression dialog:

Variables button:  When you click on this button, the standard variable selection dialog will open in which you will be able to select the independent or predictor variables, and a dependent variable.

Breakpoint:  By default, STATISTICA will estimate the breakpoint (starting at the mean for the dependent variable; the Estimated by Program radio button is selected).  You can specify a breakpoint for the regression by checking the User-defined radio button (in which case, the breakpoint value that you enter in the edit box will be treated as a constant in the estimation procedure, rather than as a parameter to be estimated).

Missing data:  Missing data can either be deleted casewise or substituted by the means for the respective variables.  If Casewise deletion of missing data is selected, a case will be deleted from the analysis if it has missing data for any of the selected variables.  If Mean substitution is specified, a missing data point will be replaced by the mean for the respective variable.


  Nonlinear Estimation - User-Defined Models

You can specify a regression model and loss function by first clicking on the User-specified Regression option in the Nonlinear Regression Startup Panel to open the User-Specified Regression Function dialog.

User-Specified Regression Function dialog:

Function to be estimated & loss function button:  When you click on this button, the Estimated Function and Loss Function dialog will open in which you can specify the regression model and the loss function.  Different regression models are described in the Common Nonlinear Regression Models and loss functions are described in Nonlinear Estimation Procedures.

Missing data:  Missing data can either be deleted casewise or substituted by the means for the respective variables.  If Casewise deletion of missing data is selected, a case will be deleted from the analysis if it has missing data for any of the selected variables.  If Mean substitution is specified, a missing data point will be replaced by the mean for the respective variable.


  Nonlinear Estimation - Syntax (User Functions)

The syntax for specifying regression models and loss functions is straightforward, because it follows the standard notation for mathematical expressions.  The fastest way to familiarize yourself with the syntax is to review the examples provided in the Examples section of the manual (see also the examples below).  Note that you can save the equation specifying a model and loss function using the Save As button (see below).  The file will be saved in a standard text format, so that it can also be edited via other editors (e.g., Notepad); it consists of two lines of text:  the model and the loss function.

Shown below the edit fields in this dialog is a summary of the syntax.  The general conventions for the equations and syntax reference are given below.

General Syntax Conventions:  Regression Equations

General Syntax Conventions:  Loss Function

Examples:

Example 1:  Specifying a regression model that will evaluate differences across groups.

Example 2:  Using logical expressions to estimate regression parameters.


  Nonlinear Estimation - General Syntax Conventions:  Regression Equations

All regression models have the same form; in general:

dependent variable = expression including independent variables

On the left side of the equation specify the dependent variable, on the right side specify the expression including independent variables and the parameters to be estimated.

•	Refer to variables either by their numbers (e.g., = v1 - v2) or name (e.g., = Retail - Cost)

•	All names that are not recognized by the program as variable names or valid reserved keywords are interpreted to be parameters.

•	Equations may contain logical expressions that involve constants, variables, parameters, or any mixture of the three.  Logical expressions evaluate to 0 if they are false, and to 1 if they are true thus models containing conditional expressions can be evaluated; (see Example 2 above for an example of a model with logical expressions).

•	Operators:  Use parentheses to specify complex logical conditions (see above) or change the default precedence of the arithmetic and logical operators shown below.

•	Arithmetic Operators:

+, -, *, /, ** (exponentiation)

•	Logical Operators:

<, >, >=, <=, <> (unequal)

For logical and/or/not operators, use arithmetic operators (see Summary of STATISTICA Formula Syntax)

•	Parenthesis:

( )

•	Constants:

Pi = 3.14..., Euler (e) = 2.71...

•	Functions:

abs(x) - absolute value of x	log10(x) - common logarithm of x

arcsin(x) - arc sine of x	sign(x) - sign of x:  if x>0 then +1, if x<0 then -1, if x=0 remains 0

cos(x) - cosine of x	sin(x) - sine of x

exp(x) - e to the power of x	sinh(x) - hyperbolic sine of x

log(x) - natural logarithm of x	sqrt(x) - square root of x

log2(x) - binary logarithm of x	tan(x) - tangent of x

•	Distributions and their integrals:  Distribution functions can be used in custom regression models.  For example:

y = b0 + b1*normal(log(x), 1, 2)

where b0 and b1 are the regression parameters to be estimated.  For more information on the types of distributions available, see Distributions and their integrals.

NOTES:  If the value of any variable used in the formula is missing (in the current case), then the expression evaluates to missing data (for the current case).

If any of the variables to be used in the model need to be transformed or rescaled before the estimation procedure, use the spreadsheet features.  For more extensive data transformations, use STATISTICA BASIC (a programming language available in the Data Management module which supports a variety of special facilities for statistical data management and transformations).

For data recoding, use the Recode Values of Variable dialog accessible from the spreadsheet.


General Syntax Conventions:  Regression Equations - Distributions and their Integrals

  Nonlinear Estimation General Syntax Conventions:  Regression Equations - Distributions and their Integrals

Note that the meaning of the distribution parameters, as well as the number of parameters, depends on the respective distribution function.  Here is a listing of all available functions.  Only the probability density functions are described; for each density function, there is a probability distribution function (e.g., inormal, ibeta, etc.) with the same number and type of parameters.

Density or	Inverse

Probability	Distribution	Distribution

Distribution	Function	Function	Function

Beta Distribution	beta(x,ν,ω)	ibeta(x,ν,ω)	vbeta(x,ν,ω)

Binomial Distribution	binom(x,p,n)	ibinom(x,p,n)

Cauchy Distribution	cauchy(x,η,θ)	icauchy(x,η,θ)	vcauchy(x,η,θ)

Chi-square Distribution	chi2(x,ν)	ichi2(x,ν)	vchi2(x,ν)

Exponential Distribution	expon(x,λ)	iexpon(x,λ)	vexpon(x,λ)

Extreme Distribution	extreme(x,a,b)	iextreme(x,a,b)	vextreme(x,a,b)

F Distribution	F(x,ν,ω)	iF(x,ν,ω)	vF(x,ν,ω)

Gamma Distribution	gamma(x,c)	igamma(x,c)	vgamma(x,c)

Geometric Distribution	geom(x,p)	igeom(x,p)

Laplace Distribution	laplace(x,a,b)	ilaplace(x,a,b)	vlaplace(x,a,b)

Logistic Distribution	logis(x,a,b)	ilogis(x,a,b)	vlogis(x,a,b)

Lognormal Distribution	lognorm(x,μ,σ)	ilognorm(x,μ,σ)	vlognorm(x,μ,σ)

Normal Distribution	normal(x,μ,σ)	inormal(x,μ,σ)	vnormal(x,μ,σ)

Pareto Distribution	pareto(x,c)	ipareto(x,c)	vpareto(x,c)

Poisson Distribution	poisson(x,λ)	ipoisson(x,λ)

Rayleigh Distribution	rayleigh(x,b)	irayleigh(x,b)	vrayleigh(x,b)

(In Nonlinear functions	rayl(x,b)	irayl(x,b)	vrayl(x,b)

and loss functions)

Student's t Distribution 	student(x,df)	istudent(x,df)	vstudent(x,df)

Weibull Distribution	weibull(x,b,c,θ)	iweibull(x,b,c,θ)	vweibull(x,b,c,θ)


General Syntax Conventions:  Loss Function

  Nonlinear Estimation - General Syntax Conventions:  Loss Function

The specification of the loss function is also quite straightforward.  In the estimation procedure, the specified value will be computed for each case in the data file; the estimation procedure will then attempt to find parameters that minimize the sum of those values across all cases.

In general, all rules apply as outlined for the specification of the regression equation for the model.  In addition, the two keywords Pred and Obs (the case is ignored) are available to allow you to refer to the predicted and observed values, respectively, for the dependent variable.  For example, the default least squares loss function can be specified as:

L = (Obs - Pred)**2

Constraining Parameters (Penalty Function)

When specifying regression functions, you can assess a penalty function in the loss function in order to constrain parameter values (see Penalty Functions).  The following example will demonstrate how one can constrain the parameters b0 and b1 to be greater than or equal to zero.

Step 1:  In the Estimated Function & Loss Function dialog, specify the regression model:

v3 = b  + b *v1 + b *exp(b *v2)

      0    1       3      1

Step 2:  Now, specify the desired loss function with a penalty assessment as follows:

L = (obs-pred)**2 + (b <0)*100000 + (b <0)*10000

                      0               1

Note how the logical operators are used in this loss function.  If either b0 or b1 is less than zero, then the program adds a large number, thus assessing a penalty to the loss function.  As a result, the various estimation procedures move away from the regions that produce those functions.

Math Errors

If a math error such as division by zero or square root of a negative number is detected during the evaluation of an equation, then the program will automatically assign a very large number to the loss function.  This way of dealing with invalid parameter estimates is also referred to as assigning a penalty function (see Introductory Overview).  In most cases, the penalty function will "entice" the parameters back into the realm of valid values.


  Nonlinear Estimation - Syntax Example 1

In this example, we will specify a regression model that will evaluate differences across groups.  For this example, the groups represent two different manufacturing plants (plant locations A and B, variable v1) at two different time periods (week 1 and week 2, variable v2) and variable v3 is the dependent variable (an efficiency measurement).

Step 1:  In the Estimated Function and Loss Function dialog, first specify the desired regression model in the general form for models:

v3 = b0 + b1*v1 + b3*exp(b2*v2)

Step 2:  Now specify the desired loss function.  For example:

L = (obs - pred)**2

the standard least squares loss function (this is the default entry in the loss function field).

Step 3:  Once you have entered the desired model and loss function, click OK to exit this dialog and proceed with the analysis.  STATISTICA will automatically check the syntax of the expressions for errors and notify you if there are any.


  Nonlinear Estimation - Syntax Example 2

When specifying regression functions, you can use logical expressions that will evaluate to 0 if they are false, and to 1 if they are true.  This example will demonstrate how one can estimate separate regression parameters for each of the plants in the above example.  Specifically, instead of using the b1 parameter as in the model in Example 1, we will use logical operators to estimate the different b0 parameters directly.

Step 1:  In the Estimated Function and Loss Function dialog, first specify the regression model:

v3 = b  *(v1=1) + b  *(v1=0) + b *exp(b *v2)

      0A           0B           3      2

Note how the logical operators are used in this example.  If v1 (Plant Location) is equal to 1 then the program will estimate b0A, that is, the constant for plant A; if v1 is equal to 0 then the program will estimate b0B.

Step 2:  Now specify the desired loss function.  For example:

L = (obs - pred)**2

the standard (default) least squares loss function.

Step 3:  Once you have entered the desired model and loss function, click OK to exit this dialog and proceed with the analysis.  STATISTICA will automatically check the syntax of the expressions for errors and notify you if there are any.


  Nonlinear Estimation - Estimation Procedure

Once you have specified the regression model, the Model Estimation dialog will open.  Here, you can specify the estimation method, number of iterations, convergence criterion, and other options.  Also given in this dialog is a summary of the model and parameters established so far in the analysis.

Model Estimation dialog:

Summary Box

Estimation method

Asymptotic standard errors

Eta for finite difference approximation

Maximum number of iterations

Convergence criterion

Start values

Initial step size

Means and standard deviations

Matrix plot for all variables

Box & whisker plot for all variables


  Estimation Procedure - Summary Box

The summary box lists your choices for the regression model, i.e., number of parameters, loss function, dependent variable, codes, independent variables, missing data deletion, and the number of valid cases.  You can review those choices here and if they are not appropriate, click on the Cancel button to return to the previous dialog in order to make any corrections.


  Estimation Procedure - Estimation Method

There are four different estimation procedures available in Nonlinear Estimation which can also be combined.  This combo box allows you to select a particular estimation procedure.  Nonlinear Estimation provides four estimation methods (listed below).  These methods, their strengths and weaknesses, are described in Nonlinear Estimation Procedures.  The Parameter Estimation - When the Estimation Process Does Not Converge topic contains several practical guidelines that you may follow (involving the choice of the estimation method) if the estimation procedure fails to converge.

(1) quasi-Newton:  For most applications, the default quasi-Newton method will yield the best performance, that is, it is the fastest method to converge.  In this method the second-order (partial) derivatives of the loss function are asymptotically estimated, and used to determine the movement of parameters from iteration to iteration.  To the extent that the second-order derivatives of the loss function are meaningful (and they usually are), this procedure is more efficient than any of the others.

The following procedures do not estimate the second-order derivatives of the loss function but rather use various geometrical approaches to function minimization.  They have the general advantage of being more "robust," that is, they are less likely to converge on local minima, and are less sensitive to "bad" (i.e., grossly inadequate) start values.

(2) Simplex:  This algorithm does not rely on the computation or estimation of the derivatives of the loss function.  Instead, at each iteration the function will be evaluated at m+1 points in the m dimensional parameter space.

(3) Hooke-Jeeves pattern moves:  At each iteration, this method first defines a pattern of points by moving each parameter one by one, so as to optimize the current loss function.  The entire pattern of points is then shifted or moved to a new location; this new location is determined by extrapolating the line from the old base point in the m dimensional parameter space to the new base point.  The step sizes in this process are constantly adjusted to "zero in" on the respective optimum.  This method is usually quite effective, and should be tried if both the quasi-Newton and Simplex methods (see above) fail to produce reasonable estimates.

(4) Rosenbrock pattern search (or method of rotating coordinates):This method will rotate the parameter space and align one axis with a ridge (this method is also called the method of rotating coordinates); all other axes will remain orthogonal to this axis.  If the loss function is unimodal and has detectable ridges pointing towards the minimum of the function, then this method will proceed with sure-footed accuracy towards the minimum of the function.  However, note that this search algorithm may terminate early when there are several constraint boundaries (resulting in the penalty value; see above) that intersect, leading to a discontinuity in the ridges.

Choosing combinations of methods:  Because the Simplex, Hooke-Jeeves, and Rosenbrock methods are generally less sensitive to local minima, you may use any one of these methods with the quasi-Newton method.  This is particularly useful if you are not sure about the appropriate start values for the estimation.  In that case, the first method may generate initial parameter estimates, that will then be used in subsequent quasi-Newton iterations.


  Estimation Procedure - Asymptotic Standard Errors

Set this check box if you want to compute the standard errors for the parameter estimates (and the variance/covariance matrix of parameter estimates).  These standard errors are computed via finite difference approximation of the second-order partial derivatives (i.e., the Hessian matrix; refer to Nonlinear Estimation Procedures for details).  Note that the Parameter Estimates and Standard Errors option in the Results dialog is only available if this check box is set.


  Estimation Procedure - Eta for Finite Difference Approximation

This option is only available if Asymptotic standard errors were requested.  As described in the overview section , the standard errors for the parameter estimates are computed via finite differencing.  Specifically, the matrix of second-order partial derivatives is approximated.  In order to obtain accurate estimates for the derivatives, some a priori knowledge is necessary of the reliability of the loss value.  This reliability can be expressed as parameter η (Eta ) so that η = 10**-DIGITS; where Digits is the number of reliable base-10 digits computed from the loss function.  By default (i.e., when this check box is not set) η will be estimated automatically by the program (by checking the "responsiveness" of the loss function to small changes in the parameter values).  However, in some cases, when the magnitudes of the first order partial derivatives for two or more parameters are very different, the default estimation of η may not be optimal.  In that case, you may enter a user-defined constant; specifically, the integer value entered into the edit field to the right of this check box will be interpreted as the Digits in η.

In practice, experiment with this parameter (start with the default value of 10**-8) in cases when the parameter estimation converges with reasonable values, but when requesting the Scrollsheet with parameter values and their standard errors (from the Results menu) the message appears: Matrix ill-conditioned; cannot compute standard errors.


  Estimation Procedure - Maximum Number of Iterations

The estimation of parameters in nonlinear regression is an iterative procedure (see Nonlinear Estimation Procedures).  At each iteration, the program evaluates whether the fit of the model (to the data) has improved from the previous iteration.  This edit box allows you to specify the maximum number of iterations that are to be performed.


  Estimation Procedure - Convergence Criterion

This edit box allows you to change the convergence criterion value (by default, 0.0001).  The exact meaning of this parameter depends, among other things, on the estimation method that is chosen.  Refer to Fletcher (1972) for details about the quasi-Newton method; refer to O'Neill (1971) or Nelder and Mead (1965) for a discussion of the Simplex procedure; refer to Fletcher and Reeves (1964), and Hooke and Jeeves (1961) for details concerning the Hooke-Jeeves method and the Rosenbrock pattern method.  The Parameter Estimation - When the Estimation Process Does Not Converge topic contains several practical guidelines that you may follow (involving the choice of the estimation method) if the estimation procedure fails to converge.


  Estimation Procedure - Start Values

The start values are used in the first iteration of each estimation method to determine the initial value of the loss function (see also, Nonlinear Estimation Procedures).  This option allows you to change the start values (by default, 0.1).  Clicking on this button will bring up the Specify Start Values dialog in which you can enter the individual start values for each parameter, or one common value for all parameters.


  Estimation Procedure - Initial Step Sizes

This option will allow you to change the default step size (0.5 for quasi-Newton, 1.0 for Simplex and Rosenbrock, 2.0 for Hooke-Jeeves).  Clicking on this button will bring up the Specify Initial Step Sizes dialog in which you can enter the individual step size values for each parameter or one common step size for all parameters.  The step size values are used during the initial iterations to "scale" the problem, that is, to determine by how much to move each parameter.  The exact impact of these values on the estimation depends, among other things, on the estimation method that is chosen.


  Estimation Procedure - Means and Standard Deviations

This option will bring up a Scrollsheet with the means and standard deviations for all selected variables (i.e., including the variable containing counts, if one was chosen).  The default graph for this Scrollsheet is the histogram.  The histograms will show the observed frequency distribution for the respective variable, and the expected frequencies for the normal distribution.


  Estimation Procedure - Matrix Plot for all Variables

This option will bring up a scatterplot matrix for all variables selected for the analysis.


  Estimation Procedure - Box & Whisker Plot for all Variables

This option allows the user to produce a box and whisker plot for the variables selected for the analysis.


  Nonlinear Estimation - Start Values

The start values are used in the first iteration of each estimation method to determine the initial value of the loss function.  The importance of appropriate start values for rapid convergence is explained in Nonlinear Estimation Procedures.  In this dialog window specify the desired start values.

Specify Start Values dialog:

Individual Start Values:  This box lists the parameters currently in the model.  You can change the start values for each of these parameters individually in the appropriate edit boxes or specify a common start value (see below).

Common Values:  Specify a start value that will be used for each of the parameters.

Apply button:  Once you have specified a common start value (see above), you can click on the Apply button to copy it to the individual start values edit boxes (see above).


  Nonlinear estimation - Step Sizes

The step size values are used during the initial iterations to "scale" the problem, that is, to determine by how much to move each parameter.  The exact impact of these values on the estimation depends, among other things, on the estimation method that is chosen.  In this dialog window specify the desired step size values.

Specify Initial Step Sizes dialog:

Individual Step Size Values:  This box lists a constant (B0) and each of the independent variables.  You can change the step size values for each of these variables individually in the appropriate edit boxes or specify a common step size value (see below).

Common Values:  Specify a step size value that will be used for each of the independent variables and B0.

Apply button:  Once you have specified a common step size value (see above), you can click on the Apply button to copy it to the individual step size values edit boxes (see above).


  Nonlinear Estimation - Parameter Estimation

When you click OK in the Model Estimation dialog, STATISTICA will begin the iterative estimation process and display the resulting iterations, loss values, and parameter estimates in the Parameter Estimation window.  Clicking OK in this window will open the Results dialog.

When the Estimation Process Does Not Converge

In general, follow these steps to estimate the parameters for any nonlinear regression model:

1.	First, accept the default values for the starting parameters, step sizes, and convergence criterion.

2.	If the estimation procedure does not converge, set the convergence criterion to 0.1, and then experiment with the start values (try different sets of reasonable values).

3.	If the estimation process continues to "go astray," change the step sizes to smaller values (e.g., 0.05).

4.	The different estimation procedures in Nonlinear Estimation use very different minimization algorithms (see Nonlinear Estimation Procedures), each with its own strengths and weaknesses.  If problems persist, switch to a different estimation procedure.  Try them in the order suggested by the respective dialog, that is, begin with the Simplex method.  Start with the default settings for all parameters.  However, you may want to increase the maximum number of iterations (Simplex usually requires more, but each iteration is faster).  Next use the Hooke-Jeeves method, and finally, try the Rosenbrock method.

5.	Continue to experiment with the starting values and step sizes.  For example, Simplex sometimes converges more easily when the convergence criterion is set to the minimum (0.0000001).  If Simplex returns a very large loss value (e.g., 1E+37), it indicates that the estimation got "trapped" with illegal parameters; continue to change the start values and step sizes.

6.	Try combining the methods of estimation.  Because the Simplex, Hooke-Jeeves, and Rosenbrock methods are generally less sensitive to local minima, you may use any one of these methods with the quasi-Newton method.  This is particularly useful if you are not sure about the appropriate start values for the estimation.  In that case, the first method may generate initial parameter estimates, that will then be used in subsequent quasi-Newton iterations.

Nonlinear regression is not well suited for exploratory data analysis purposes.  Rather, the researcher should bring to the analysis some understanding of the nature of and relationships between variables.  Such understanding will suggest appropriate models that can be estimated, and start values that are fairly close to the actual parameters.  Given such prior understanding of one's data, and some experience with the different estimation methods, it is usually not difficult to fit models that "make sense" and satisfactorily reproduce the data.


  Nonlinear Estimation - Results

This is the final dialog in the Nonlinear Regression process.  In this dialog, you can selectively review the results of the regression as well as other options (described below).  This dialog also summarizes the choices that you have made in previous dialogs.

Results dialog:

Summary Box

Parameter estimates (and standard errors)

Cov./corrs. of parameters

Scale MS-error to 1

Residual, Predicted, Observed Values

Classification of Cases and Odds Ratios

Means & standard deviations

Difference (previous model)

Save predicted and residual values

Plot options


  Nonlinear Estimation Results - Summary Box

The summary box lists your choices for the regression analysis, i.e., the regression model, dependent variable, loss function; proportion of variance accounted for by the model, R, number of 0's and 1's, independent variables and final value.


  Nonlinear Estimation Results - Parameter Estimates

This option will bring up a Scrollsheet with the parameter estimates for the current model.  Summary statistics for the current analysis will be displayed in the headers of the Scrollsheet.  If the standard errors were requested on the previous dialog (see Estimation Procedure), then the Scrollsheet will also show the (asymptotic) standard errors of the parameter estimates, the respective t-values (parameters divided by standard errors), and the associated p-levels.


  Nonlinear Estimation Results - Cov/Corrs of Parameters

This option is only available if you have selected the Asymptotic Standard Errors option in the Estimation Procedure dialog.  Clicking this button will first bring up a Scrollsheet with the (asymptotic) variance/covariance matrix for the parameter estimates, and then a Scrollsheet with the correlations between parameter estimates.


  Nonlinear Estimation Results - Scale Mean Square Error to 1

For maximum likelihood estimates, it is recommended to rescale the mean square error to 1.  The resulting standard deviations for the parameter estimates are then the usual information theory standard errors (Jennrich & Moore, 1975).  When using maximum likelihood estimation for probit or logit models, this check box will automatically be set.


  Nonlinear Estimation Results - Residual, Predicted, Observed Values

Residual Values button:  Clicking on this button will bring up a Scrollsheet with the residual values (i.e., observed values minus predicted values).

Predicted Values button:  Clicking on this button will bring up a Scrollsheet with the predicted values.

Observed Values button:  Clicking on this button will bring up a Scrollsheet with the observed values.


  Nonlinear Estimation Results - Classification of Cases and Odds Ratios

This option is only available when fitting logit and probit regression models.  After clicking on this button, a Scrollsheet will be displayed with the observed and predicted classifications, and the so-called odds ratio.

        Classification of Cases

---------------------------------------

Odds ratio: 9.7778 Perc.Correct 76.00%

            Pred.     Pred.    Percent

Observed   FAILURE   SUCCESS   Correct

---------------------------------------

FAILURE      11          3     78.57143

SUCCESS       3         11     72.72727

---------------------------------------

A case is assigned to (classified as belonging to) the first group if the predicted value is less than or equal to 0.5, and it is assigned to the second group if the respective predicted value is greater than 0.5.  The odds ratio is computed as (f11*f22)/(f12*f21); where fij. stands for the respective frequencies in the 2 by 2 table.  The percentages of correctly classified cases are also reported.


  Nonlinear Estimation Results - Means and Standard Deviations

Clicking on this button will bring up a Scrollsheet with the means and standard deviations for all selected variables (i.e., including the variable containing counts, if one was chosen).


  Nonlinear Estimation Results - Difference (Previous Model)

This option is only available if logit or probit regression was selected, when the current model is hierarchically related to the previous model that was estimated.  "Hierarchically related" means that the current model is identical to the previous model with the exception of an addition or deletion of one or more independent variables.  In that case, comparisons between the goodness-of-fit for the two models are meaningful, and can be reviewed by clicking on this button.  For logit and probit models, this Scrollsheet will also show the incremental maximum likelihood Chi-square value for the difference between the two hierarchically related models, and the respective degrees of freedom and p-level.


  Nonlinear Estimation Results - Save Predicted and Residual Values

Predicted and residual scores (as well as all variables in the current data file) can be saved together in a data file for further analysis.


  Nonlinear Estimation Results - Plot Options

After clicking on any of the graphics buttons, the respective graph will be displayed

Fitted 2D function & observed values:  This plot allows a 2-dimensional visual examination (i.e., qualitative evaluation) of the fit of the data to the model.  It is useful for identification of outliers, which can then be marked in the Graph Data Editor using the Brushing Tool.

Fitted 3D function & observed values:  This plot allows a 3-dimensional visual examination (i.e., qualitative evaluation) of the fit of the data to the model.  It is useful for identification of outliers, which can then be marked in the Graph Data Editor using the Brushing Tool.

Distribution of residuals:  Click on this button to display a plot of the frequency distribution (Histogram) of the residuals, overlaid with the normal curve (the expected frequencies for the normal distribution).

Normal probability plot of residuals:  Normal probability plots provide a quick way to visually inspect to what extent the pattern of residuals follows a normal distribution.  If the residuals are not normally distributed, they will deviate from the line.  Outliers may also become evident in this plot.  If there is a general lack of fit, and the data seem to form a clear pattern (e.g., an S shape) around the line, then the dependent variable may have to be transformed in some way (e.g., a log transformation to "pull in" the tail of the distribution, etc.; refer to the manual for additional details).

Half-normal probability plot of residuals:  The half-normal probability plot is constructed in the same way as the standard normal probability plot, except that only the positive half of the normal curve is considered.  Consequently, only positive normal values will be plotted on the Y axis.  This plot is used when one wants to ignore the sign of the residual, that is, when one is mostly interested in the distribution of absolute residuals, regardless of the sign.

Predicted vs. observed values:  Choose this option when you want a plot of the predicted values vs. the observed values.

Predicted vs. residual values:  Choose this option when you want a plot of the predicted values vs. the residual values.

Matrix plot for all variables:  Select this option to produce a visual (scatterplot) representation of the correlations between several variables in a matrix format.  When you click on this button, the Select Variables dialog will open in which you can select the variables to be plotted against each other (one scatterplot is generated for each pair of variables) in a square matrix of scatterplots.

Box & whisker plot for all variables:  The box plot resulting from this option represents the central tendencies and variability's of the selected variables.  As measures of central tendency, you can choose between plotting the means and medians and their respective measures of variability; standard deviations or standard errors (associated with the means), and ranges (associated with the medians).  Choose one of four types of box plots to represent the distribution of the values of the currently highlighted variable in the Box and Whisker Plot Type dialog.


Principal Components and Factor Analysis - Index
  Principal Components & Factor Analysis - Index

Introductory Overview

Basic Idea of Factor Analysis as a Data Reduction Method

Factor Analysis as a Classification Method

Miscellaneous Other Issues and Statistics

Hierarchical Factor Analysis

Startup Panel

Factor Extraction

Descriptive Statistics

Multiple Regression

Factor Analysis Results

Factor Rotation

Notes and Technical Information


Principal Components and Factor Analysis - Overview

  Principal Components and Factor Analysis - Introductory Overview

General Purpose

Basic Idea of Factor Analysis as a Data Reduction Method

Factor Analysis as a Classification Method

Miscellaneous Other Issues and Statistics


Principal Components and Factor Analysis Overview - General Purpose

  Principal Components and Factor Analysis Introductory Overview - General Purpose

The main applications of factor analytic techniques are: (1) to reduce the number of variables and (2) to detect structure in the relationships between variables, that is to classify variables.  Therefore, factor analysis is applied as a data reduction or structure detection method (the term factor analysis was first introduced by Thurstone, 1931).  The topics listed below will describe the principles of factor analysis, and how it can be applied towards these two purposes.  We will assume that you are familiar with the basic logic of statistical reasoning as described in Elementary Concepts.  Moreover, we will also assume that you are familiar with the concepts of variance and correlation; if not, we advise that you read the Basic Statistics chapter at this point.

There are many excellent books on factor analysis.  For example, a hands-on how-to approach can be found in Stevens (1986); more detailed technical descriptions are provided in Cooley and Lohnes (1971); Harman (1976); Kim and Mueller, (1978a, 1978b); Lawley and Maxwell (1971); Lindeman, Merenda, and Gold (1980); Morrison (1967); or Mulaik (1972).  The interpretation of secondary factors in hierarchical factor analysis, as an alternative to traditional oblique rotational strategies, is explained in detail by Wherry (1984).

Confirmatory factor analysis.  STATISTICA also includes the general Structural Equation Modeling (SEPATH) module.  The procedures available in that module allow you to test specific hypotheses about the factor structure for a set of variables, in one or several samples (e.g., you can compare factor structures across samples).  The Examples section SEPATH discusses several examples of such analyses.

Correspondence analysis.  Correspondence analysis is a descriptive/exploratory technique designed to analyze two-way and multi-way tables containing some measure of correspondence between the rows and columns.  The results provide information which is similar in nature to those produced by factor analysis techniques, and they allow one to explore the structure of categorical variables included in the table.  For more information regarding these methods, refer to the description of the Correspondence Analysis module.


  Basic Idea of Factor Analysis as a Data Reduction Method

Suppose we conducted a (rather "silly") study in which we measure 100 people's height in inches and centimeters.  Thus, we would have two variables that measure height.  If in future studies, we want to research, for example, the effect of different nutritional food supplements on height, would we continue to use both measures?  Probably not; height is one characteristic of a person, regardless of how it is measured.

Let us now extrapolate from this "silly" study to something that one might actually do as a researcher.  Suppose we want to measure people's satisfaction with their lives.  We design a satisfaction questionnaire with various items; among other things we ask our subjects how satisfied they are with their hobbies (item 1) and how intensely they are pursuing a hobby (item 2).  Most likely, the responses to the two items are highly correlated with each other.  (If you are not familiar with the correlation coefficient, we recommend that you read the description in Basic Statistics - Correlations)  Given a high correlation between the two items, we can conclude that they are quite redundant.

Combining Two Variables into a Single Factor

Principal Components Analysis

Extracting Principal Components

Generalizing to the Case of Multiple Variables

How many Factors to Extract?

Reviewing the Results of a Principal Components Analysis


Factor Analysis as a Data Reduction Method - Combining Two Variables into a Single Factor

  Basic Idea of Factor Analysis as a Data Reduction Method - Combining Two Variables into a Single Factor

One can summarize the correlation between two variables in a scatterplot.  A regression line can then be fitted that represents the "best" summary of the linear relationship between the variables.  If we could define a variable that would approximate the regression line in such a plot, then that variable would capture most of the "essence" of the two items.  Subjects' single scores on that new factor, represented by the regression line, could then be used in future data analyses to represent that essence of the two items.  In a sense we have reduced the two variables to one factor.  Note that the new factor is actually a linear combination of the two variables.


Factor Analysis as a Data Reduction Method - Principal Components Analysis

  Basic Idea of Factor Analysis as a Data Reduction Method - Principal Components Analysis

The example described above, combining two correlated variables into one factor, illustrates the basic idea of factor analysis, or of principal components analysis to be precise (we will return to this later).  If we extend the two-variable example to multiple variables, then the computations become more involved, but the basic principle of expressing two or more variables by a single factor remains the same.


Factor Analysis as a Data Reduction Method - Extracting Principal Components

  Basic Idea of Factor Analysis as a Data Reduction Method - Extracting Principal Components

We do not want to go into the details about the computational aspects of principal components analysis here, which can be found elsewhere (references were provided at the beginning of this section).  However, basically, the extraction of principal components amounts to a variance maximizing (varimax) rotation of the original variable space.  For example, in a scatterplot we can think of the regression line as the original X axis, rotated so that it approximates the regression line.  This type of rotation is called variance maximizing because the criterion for (goal of) the rotation is to maximize the variance (variability) of the "new" variable (factor), while minimizing the variance around the new variable (see Rotational Strategies).


Factor Analysis as a Data Reduction Method - Generalizing to the Case of Multiple Variables

  Basic Idea of Factor Analysis as a Data Reduction Method - Generalizing to the Case of Multiple Variables

When there are more than two variables, we can think of them as defining a "space," just as two variables defined a plane.  Thus, when we have three variables, we could plot a three-dimensional scatterplot, and, again we could fit a plane through the data.  With more than three variables it becomes impossible to illustrate the points in a scatterplot, however, the logic of rotating the axes so as to maximize the variance of the new factor remains the same.

Multiple orthogonal factors.  After we have found the line on which the variance is maximal, there remains some variability around this line.  In principal components analysis, after the first factor has been extracted, that is, after the first line has been drawn through the data, we continue and define another line that maximizes the remaining variability, and so on.  In this manner, consecutive factors are extracted.  Because each consecutive factor is defined to maximize the variability that is not captured by the preceding factor, consecutive factors are independent of each other.  Put another way, consecutive factors are uncorrelated or orthogonal to each other.


Factor Analysis as a Data Reduction Method - How many Factors to Extract?

  Basic Idea of Factor Analysis as a Data Reduction Method - How many Factors to Extract?

Remember that, so far, we are considering principal components analysis as a data reduction method, that is, as a method for reducing the number of variables.  The question then is, how many factors do we want to extract?  Note that as we extract consecutive factors, they account for less and less variability.  The decision of when to stop extracting factors basically depends on when there is only very little "random" variability left.  The nature of this decision is arbitrary; however, various guidelines have been developed, and they are reviewed in Reviewing the Results of a Principal Components Analysis under Eigenvalues and the Number-of-Factors Problem.


Factor Analysis as a Data Reduction Method - Reviewing the Results of a Principal Components analysis

  Basic Idea of Factor Analysis as a Data Reduction Method - Reviewing the Results of a Principal Components Analysis

Without further ado, let us now look at some of the standard results from a principal components analysis.  To reiterate, we are extracting factors that account for less and less variance.  To simplify matters, one usually starts with the correlation matrix, where the variances of all variables are equal to 1.0.  Therefore, the total variance in that matrix is equal to the number of variables.  For example, if we have 10 variables each with a variance of 1 then the total variability that can potentially be extracted is equal to 10 times 1.  Suppose that in the satisfaction study introduced earlier we included 10 items to measure different aspects of satisfaction at home and at work.  The variance accounted for by successive factors would be summarized as follows:

+----------+-------------------------------------------+

| STAT.    |         Eigenvalues (factor.sta)          |

| FACTOR   |     Extraction: Principal components      |

| ANALYSIS |                                           |

+----------+----------+----------+----------+----------+

|          |          |  % total |  Cumul.  |  Cumul.  |

| Value    | Eigenval | Variance | Eigenval |      %   |

+----------+----------+----------+----------+----------+

|      1   | 6.118369 | 61.18369 |  6.11837 |  61.1837 |

|      2   | 1.800682 | 18.00682 |  7.91905 |  79.1905 |

|      3   |  .472888 |  4.72888 |  8.39194 |  83.9194 |

|      4   |  .407996 |  4.07996 |  8.79993 |  87.9993 |

|      5   |  .317222 |  3.17222 |  9.11716 |  91.1716 |

|      6   |  .293300 |  2.93300 |  9.41046 |  94.1046 |

|      7   |  .195808 |  1.95808 |  9.60626 |  96.0626 |

|      8   |  .170431 |  1.70431 |  9.77670 |  97.7670 |

|      9   |  .137970 |  1.37970 |  9.91467 |  99.1467 |

|     10   |  .085334 |   .85334 | 10.00000 | 100.0000 |

+----------+-------------------------------------------+

Eigenvalues

In the second column (Eigenvalue) in the Scrollsheet above, we find the variance on the new factors that were successively extracted.  In the third column, these values are expressed as a percent of the total variance (in this example, 10).  As we can see, factor 1 accounts for 61 percent of the variance, factor 2 for 18 percent, and so on.  As expected, the sum of the eigenvalues is equal to the number of variables.  The third column contains the cumulative variance extracted.  The variances extracted by the factors are called the eigenvalues.  This name derives from the computational issues involved (solving the so-called Eigenvalue problem, see also the Technical Notes section in the manual).

Eigenvalues and the Number-of-Factors Problem

Now that we have a measure of how much variance each successive factor extracts, we can return to the question of how many factors to retain.  As mentioned earlier, by its nature this is an arbitrary decision.  However, there are some guidelines that are commonly used, and that, in practice, seem to yield the best results.

The Kaiser criterion.  First, we can retain only factors with eigenvalues greater than 1.  In essence this is like saying that, unless a factor extracts at least as much as the equivalent of one original variable, we drop it.  This criterion was proposed by Kaiser (1960), and is probably the one most widely used.  In our example above, using this criterion, we would retain 2 factors (principal components).

The scree test.  A graphical method is the scree test first proposed by Cattell (1966).  We can plot the eigenvalues shown in the Scrollsheet above in a simple line plot.  Cattell suggests to find the place where the smooth decrease of eigenvalues appears to level off to the right of the plot.  To the right of this point, presumably, one finds only "factorial scree" -- "scree" is the geological term referring to the debris which collects on the lower part of a rocky slope.  According to this criterion, we would probably retain 2 or 3 factors in our example.

Which criterion to use.  Both criteria have been studied in detail (Browne, 1968; Cattell & Jaspers, 1967; Hakstian, Rogers, & Cattell, 1982; Linn, 1968; Tucker, Koopman & Linn, 1969).  Theoretically, one can evaluate those criteria by generating random data based on a particular number of factors.  One can then see whether the number of factors is accurately detected by those criteria.  Using this general technique, the first method (Kaiser criterion) sometimes retains too many factors, while the second technique (scree test) sometimes retains too few; however, both do quite well under normal conditions, that is, when there are relatively few factors and many cases.  In practice, an additional important aspect is the extent to which a solution is interpretable.  Therefore, one usually examines several solutions with more or fewer factors, and chooses the one that makes the best "sense."  We will discuss this issue in the context of factor rotations below.

Principal Factors Analysis

Before we continue to examine the different aspects of the typical output from a principal components analysis, let us now introduce principal factors analysis.  Let us return to our satisfaction questionnaire example to conceive of another "mental model" for factor analysis.  We can think of subjects' responses as being dependent on two components.  First, there are some underlying common factors, such as the "satisfaction-with-hobbies" factor we looked at before.  Each item measures some part of this common aspect of satisfaction.  Second, each item also captures a unique aspect of satisfaction that is not addressed by any other item.

Communalities.  If this model is correct, then we should not expect that the factors will extract all variance from our items; rather, only that proportion that is due to the common factors and shared by several items.  In the language of factor analysis, the proportion of variance of a particular item that is due to common factors (shared with other items) is called communality.  Therefore, an additional task facing us when applying this model is to estimate the communalities for each variable, that is, the proportion of variance that each item has in common with other items.  The proportion of variance that is unique to each item is then the respective item's total variance minus the communality.  A common starting point is to use the squared multiple correlation of an item with all other items as an estimate of the communality (refer to Multiple Regression for details about multiple regression).  Some authors have suggested various iterative "post-solution improvements" to the initial multiple regression communality estimate; for example, the so-called MINRES method (minimum residual factor method; Harman & Jones, 1966) will try various modifications to the factor loadings with the goal to minimize the residual (unexplained) sums of squares.  Refer to the description of the Extraction dialog for the different methods available in the Factor Analysis module.

Principal factors vs. principal components.  The defining characteristic then that distinguishes between the two factor analytic models is that in principal components analysis we assume that all variability in an item should be used in the analysis, while in principal factors analysis we only use the variability in an item that it has in common with the other items.  A detailed discussion of the pros and cons of each approach is beyond the scope of this introduction (refer to the general references provided in Principal components and Factor Analysis - Introductory Overview).  In most cases, these two methods usually yield very similar results.  However, principal components analysis is often preferred as a method for data reduction, while principal factors analysis is often preferred when the goal of the analysis is to detect structure (see Factor Analysis as a Classification Method).


  Factor Analysis as a Classification Method

Let us now return to the interpretation of the standard results from a factor analysis (see Reviewing the Results of a Principal Components Analysis).  We will henceforth use the term factor analysis generically to encompass both principal components and principal factors analysis.  Let us assume that we are at the point in our analysis where we basically know how many factors to extract.  We may now want to know the meaning of the factors, that is, whether and how we can interpret them in a meaningful manner.  To illustrate how this can be accomplished, let us work "backwards," that is, begin with a meaningful structure and then see how it is reflected in the results of a factor analysis.  Let us return to our satisfaction example; shown below is the correlation matrix for items pertaining to satisfaction at work and items pertaining to satisfaction at home.

+----------+-----------------------------------------+

| STAT.    |        Correlations (factor.sta)        |

| FACTOR   |         Casewise deletion of MD         |

| ANALYSIS |                  n=100                  |

+----------+------+------+------+------+------+------+

|          |      |      |      |      |      |      |

| Variable |WORK_1|WORK_2|WORK_3|HOME_1|HOME_2|HOME_3|

+----------+------+------+------+------+------+------+

| WORK_1   | 1.00 |  .65 |  .65 |  .14 |  .15 |  .14 |

| WORK_2   |  .65 | 1.00 |  .73 |  .14 |  .18 |  .24 |

| WORK_3   |  .65 |  .73 | 1.00 |  .16 |  .24 |  .25 |

| HOME_1   |  .14 |  .14 |  .16 | 1.00 |  .66 |  .59 |

| HOME_2   |  .15 |  .18 |  .24 |  .66 | 1.00 |  .73 |

| HOME_3   |  .14 |  .24 |  .25 |  .59 |  .73 | 1.00 |

+----------+------+------+------+------+------+------+

The work satisfaction items are highly correlated amongst themselves, and the home satisfaction items are highly intercorrelated amongst themselves.  The correlations across these two types of items (work satisfaction items with home satisfaction items) is comparatively small.  It thus seems that there are two relatively independent factors reflected in the correlation matrix, one related to satisfaction at work, the other related to satisfaction at home.

Factor Loadings

Rotating the Factor Structure

Interpreting the Factor Structure

Oblique Factors

Hierarchical Factor Analysis


  Factor Analysis as a Classification Method - Factor Loadings

Let us now perform a principal components analysis and look at the two-factor solution.  Specifically, let us look at the correlations between the variables and the two factors (or "new" variables), as they are extracted by default; these correlations are also called factor loadings.

+----------+-----------------------------+

| STAT.    | Factor Loadings (Unrotated) |

| FACTOR   | Principal components        |

| ANALYSIS |                             |

+----------+----------+----------+-------+

|          |   Factor |   Factor |

| Variable |       1  |       2  |

+----------+----------+----------+

| WORK_1   |  .654384 |  .564143 |

| WORK_2   |  .715256 |  .541444 |

| WORK_3   |  .741688 |  .508212 |

| HOME_1   |  .634120 | -.563123 |

| HOME_2   |  .706267 | -.572658 |

| HOME_3   |  .707446 | -.525602 |

+----------+----------+----------+

| Expl.Var | 2.891313 | 1.791000 |

| Prp.Totl |  .481885 |  .298500 |

+----------+----------+----------+

Apparently, the first factor is generally more highly correlated with the variables than the second factor.  This is to be expected because, as previously described, these factors are extracted successively and will account for less and less variance overall.


Factor Analysis as a Classification Method - Rotating the Factor Structure

  Factor Analysis as a Classification Method - Roataing the Factor Structure

We could plot the factor loadings shown above in a scatterplot.  In that plot, each variable is represented as a point.  In this plot we could rotate the axes in any direction without changing the relative locations of the points to each other; however, the actual coordinates of the points, that is, the factor loadings would of course change.  In this example, if you produce the plot it will be evident that if we were to rotate the axes by about 45 degrees we might attain a clear pattern of loadings identifying the work satisfaction items and the home satisfaction items.

Rotational strategies.  There are various rotational strategies that have been proposed.  The goal of all of these strategies is to obtain a clear pattern of loadings, that is, factors that are somehow clearly marked by high loadings for some variables and low loadings for others.  This general pattern is also sometimes referred to as simple structure (a more formalized definition can be found in most standard textbooks).  Typical rotational strategies are varimax, quartimax, and equamax; these are described in greater detail in the context of the Rotation dialog.

We have described the idea of the varimax rotation before (see Extracting Principal Components), and it can be applied to this problem as well.  As before, we want to find a rotation that maximizes the variance on the new axes; put another way, we want to obtain a pattern of loadings on each factor that is as diverse as possible, lending itself to easier interpretation.  Below is the table of rotated factor loadings.

+----------+--------------------------------------+

| STAT.    | Factor Loadings (Varimax normalized) |

| FACTOR   | Extraction: Principal components     |

| ANALYSIS |                                      |

+----------+----------+----------+----------------+

|          |   Factor |   Factor |

| Variable |       1  |       2  |

+----------+----------+----------+

| WORK_1   |  .862443 |  .051643 |

| WORK_2   |  .890267 |  .110351 |

| WORK_3   |  .886055 |  .152603 |

| HOME_1   |  .062145 |  .845786 |

| HOME_2   |  .107230 |  .902913 |

| HOME_3   |  .140876 |  .869995 |

+----------+----------+----------+

| Expl.Var | 2.356684 | 2.325629 |

| Prp.Totl |  .392781 |  .387605 |

+----------+----------+----------+


  Factor Analysis as a Classification Method - Interpreting the Factor Structure

Now the pattern is much clearer.  As expected, the first factor is marked by high loadings on the work satisfaction items, the second factor is marked by high loadings on the home satisfaction items.  We would thus conclude that satisfaction, as measured by our questionnaire, is composed of those two aspects; hence we have arrived at a classification of the variables.


  Factor Analysis as a Classification Method - Oblique Factors

Some authors (e.g., Catell & Khanna; Harman, 1976; Jennrich & Sampson, 1966; Clarkson & Jennrich, 1988) have discussed in some detail the concept of oblique (non-orthogonal) factors, in order to achieve more interpretable simple structure.  Specifically, computational strategies have been developed to rotate factors so as to best represent "clusters" of variables, without the constraint of orthogonality of factors.  However, the oblique factors produced by such rotations are often not easily interpreted.  To return to the example discussed above, suppose we would have included in the satisfaction questionnaire above four items that measured other, "miscellaneous" types of satisfaction.  Let us assume that people's responses to those items were affected about equally by their satisfaction at home (Factor 1) and at work (Factor 2).  An oblique rotation will likely produce two correlated factors with less-than-obvious meaning, that is, with many cross-loadings.


  Factor Analysis as a Classification Method - Hierarchical Factor Analysis

Instead of computing loadings for often difficult to interpret oblique factors, the Factor Analysis module in STATISTICA uses a strategy first proposed by Thompson (1951) and Schmid and Leiman (1957), which has been elaborated and popularized in the detailed discussions by Wherry (1959, 1975, 1984).  In this strategy, STATISTICA first identifies clusters of items and rotates axes through those clusters; next the correlations between those (oblique) factors is computed, and that correlation matrix of oblique factors is further factor-analyzed to yield a set of orthogonal factors that divide the variability in the items into that due to shared or common variance (secondary factors), and unique variance due to the clusters of similar variables (items) in the analysis (primary factors).  To return to the example above, such a hierarchical analysis might yield the following factor loadings:

+----------+-------------------------------------+

| STAT.    | Secondary & Primary Factor Loadings |

| FACTOR   |                                     |

| ANALYSIS |                                     |

+----------+----------+---------+---------+------+

|          |  Second. | Primary | Primary |

| Factor   |      1   |     1   |     2   |

+----------+----------+---------+---------+

| WORK_1   |  .483178 | .649499 | .187074 |

| WORK_2   |  .570953 | .687056 | .140627 |

| WORK_3   |  .565624 | .656790 | .115461 |

| HOME_1   |  .535812 | .117278 | .630076 |

| HOME_2   |  .615403 | .079910 | .668880 |

| HOME_3   |  .586405 | .065512 | .626730 |

| MISCEL_1 |  .780488 | .466823 | .280141 |

| MISCEL_2 |  .734854 | .464779 | .238512 |

| MISCEL_3 |  .776013 | .439010 | .303672 |

| MISCEL_4 |  .714183 | .455157 | .228351 |

+----------+----------+---------+---------+

Careful examination of these loadings would lead to the following conclusions:

(1)  There is a general (secondary) satisfaction factor that likely affects all types of satisfaction measured by the 10 items;

(2)  There appear to be two primary unique areas of satisfaction that can best be described as satisfaction with work and satisfaction with home life.

Wherry (1984) discusses in great detail examples of such hierarchical analyses, and how meaningful and interpretable secondary factors can be derived.

Confirmatory Factor Analysis.  Over the past 15 years, so-called confirmatory methods have become increasingly popular (e.g., see Jöreskog and Sörbom, 1979).  In general, one can specify a priori, a pattern of factor loadings for a particular number of orthogonal or oblique factors, and then test whether the observed correlation matrix can be reproduced given these specifications.  Confirmatory factor analyses can be performed via STATISTICA's general Structural Equation Modeling (SEPATH) module.  Note that the Examples section of SEPATH discusses several examples of such analyses.


  Miscellaneous Other Issues and Statistics

Factor Scores

Reproduced and Residual Correlations

Matrix Ill-Conditioning


  Miscellaneous Other Issues and Statistics - Factor Scores

We can estimate the actual values of individual cases (observations) for the factors.  In the Factor Analysis module of STATISTICA, these scores may be displayed in a Scrollsheet or Text/output Window, and also saved to a disk file (whichever you choose in the Page/Output Setup dialog).  These factor scores are particularly useful when one wants to perform further analyses involving the factors that one has identified in the factor analysis.


  Miscellaneous Other Issues and Statistics - Reproduced and Residual Correlations

An additional check for the appropriateness of the respective number of factors that were extracted is to compute the correlation matrix that would result if those were indeed the only factors.  That matrix is called the reproduced correlation matrix.  To see how this matrix deviates from the observed correlation matrix, one can compute the difference between the two; that matrix is called the matrix of residual correlations.  The residual matrix may point to "misfits," that is, to particular correlation coefficients that cannot be reproduced appropriately by the current number of factors.


  Miscellaneous Other Issues and Statistics - Matrix Ill-conditioning

Computationally, in order to perform a factor analysis, STATISTICA needs to invert the correlation matrix.  If, in this correlation matrix there are variables that are 100% redundant, then the inverse of the matrix cannot be computed.  For example, if a variable is the sum of two other variables selected for the analysis, then the correlation matrix of those variables cannot be inverted, and the factor analysis can basically not be performed.  In practice this happens when you are attempting to factor analyze a set of highly intercorrelated variables, as it, for example, sometimes occurs in correlational research with questionnaires.  The Factor Analysis module will detect matrix ill-conditioning and issue a respective warning.  Then STATISTICA will artificially lower all correlations in the correlation matrix by adding a small constant to the diagonal of the matrix, and then restandardizing it.  This procedure will usually yield a matrix that now can be inverted and thus factor-analyzed; moreover, the factor patterns should not be affected by this procedure.  However, note that the resulting estimates are not exact.


  Factor Analysis - Hierarchical Factor Analysis

Oblique Factors

Some authors (e.g., Catell & Khanna; Harman, 1976; Jennrich & Sampson, 1966; Clarkson & Jennrich, 1988) have discussed in some detail the concept of oblique (non-orthogonal) factors, in order to achieve more interpretable simple structure (refer to the Introductory Overview section).  Specifically, computer (algorithmic) strategies have been developed to rotate factors so as to best represent "clusters" of variables, without the constraint of orthogonality of factors.  However, the oblique factors produced by such rotations are often not easily interpreted.  For example, suppose we analyzed the responses to a questionnaire asking about people's satisfaction with various aspects of their lives.  Let us assume that the questionnaire contains 3 items designed to measure satisfaction with one's work, 3 items designed to measure satisfaction with one's home life, and 4 items designed to measure overall (miscellaneous) satisfaction.  Let us also assume that people's responses to those last 4 items are affected about equally by their satisfaction at home (Factor 1) and at work (Factor 2).  In this case, an oblique rotation will likely produce two correlated factors with less-than-obvious meaning, that is, with generally many cross-loadings.

Hierarchical Factor Analysis

Instead of computing loadings for often difficult to interpret oblique factors, the Factor Analysis module in STATISTICA uses a strategy first proposed by Thompson (1951) and Schmid and Leiman (1957), which has been elaborated and popularized in the detailed discussions by Wherry (1959, 1975, 1984).  In this strategy, STATISTICA first identifies clusters of items and rotates axes through those clusters; next the correlations between those (oblique) factors are computed, and that correlation matrix of oblique factors is further factor-analyzed to yield a set of orthogonal factors that divide the variability in the items into that due to shared or common variance (secondary factors), and unique variance due to the clusters of similar variables (items) in the analysis (primary factors).  To return to the example above, such a hierarchical analysis might yield the following factor loadings:

+----------+-------------------------------------+

| STAT.    | Secondary & Primary Factor Loadings |

| FACTOR   |                                     |

| ANALYSIS |                                     |

+----------+----------+---------+---------+------+

|          |  Second. | Primary | Primary |

| Factor   |      1   |     1   |     2   |

+----------+----------+---------+---------+

| WORK_1   |  .483178 | .649499 | .187074 |

| WORK_2   |  .570953 | .687056 | .140627 |

| WORK_3   |  .565624 | .656790 | .115461 |

| HOME_1   |  .535812 | .117278 | .630076 |

| HOME_2   |  .615403 | .079910 | .668880 |

| HOME_3   |  .586405 | .065512 | .626730 |

| MISCEL_1 |  .780488 | .466823 | .280141 |

| MISCEL_2 |  .734854 | .464779 | .238512 |

| MISCEL_3 |  .776013 | .439010 | .303672 |

| MISCEL_4 |  .714183 | .455157 | .228351 |

+----------+----------+---------+---------+

Careful examination of these loadings would lead to the following conclusions:

(1) there is a general (secondary) satisfaction factor that likely affects all types of satisfaction measured by the 10 items;

(2) there appear to be two primary unique areas of satisfaction that can best be described as satisfaction with work and satisfaction with home life.

Wherry (1984) discusses in great detail, examples of such hierarchical analyses and how meaningful and interpretable secondary factors can be derived.


Factor Analysis - Opening Menu

  Factor Analysis - Startup Panel

In this dialog, you can select all variables that are to be included in the analysis (see also, Factor Analysis - Index).  Note that the Factor Analysis module can analyze extremely large problems (up to 300 variables, correlation matrices with up to 90,000 elements can be analyzed).

Factor Analysis dialog:

Variables:  Click on this button to bring up the standard variable selection window.  Select all variables that are to be included in the factor analysis.

Input File.  Input is either raw data or a correlation matrix previously created via Factor Analysis or another STATISTICA module (e.g., Basic Statistics, Multiple Regression, Canonical Analysis, Reliability, or directly via Data Management, see also, Matrix File Format).

Missing data deletion.  This combo box is only active if a raw data file has been specified (see above).  Missing data can be deleted casewise, pairwise, or substituted by means.


  Factor Analysis - Factor Extraction

The choices on this dialog will determine (1) the manner in which factors are extracted, and (2) how many factors will be extracted.  Both issues are discussed in greater detail in the Introductory Overview section.

NOTE:  Matrix ill-conditioning and the modified correlation matrix.  The Introductory Overview section discusses the issue of matrix ill-conditioning.  If during the factoring process you received the message that the correlation matrix cannot be inverted, then, the correlation matrix will be modified (to allow inversion).  Specifically, a small constant is added to the diagonal of the correlation matrix until the determinant of that matrix is greater than 1.e-50.  All subsequent computations will be performed based on the modified (slightly lowered) correlations; to restore the original exact correlation matrix, click Cancel to return to the startup panel and then click OK to reread the data file.

Define Method of Factor Extraction dialog:

Review correlations/means/SD

Perform multiple regression

Extraction method

Maximum no. of factors

Minimum eigenvalue

Min. change in communality

Maximum number of iterations


  Factor Analysis Factor Extraction - Review correlations/means/SD

This button will bring up a dialog for reviewing various descriptive statistics and graphs.  You can also use this option in order to save the current correlation matrix in a matrix file.


  Factor Analysis Factor Extraction - Perform Multiple Regression

This button will bring up a dialog for performing multiple regression analyses with the currently selected variables.  Regression equations with up to 299 independent variables can be evaluated.  Note that extensive options for multiple regression are available in the Multiple Regression module of STATISTICA.


  Factor Analysis Factor Extraction - Extraction Methods

The choice of radio buttons in this box will determine the procedure that is used for extracting the factors from the correlation matrix.

Principal components:  The first option, Principal components, will factor the original correlation matrix (with 1's on the diagonal, i.e., for communalities); all other options will result in principal factor analyses.  This distinction is also discussed in the Introductory Overview section.

Communalities=multiple R-square:  If this radio button is set, then, prior to factoring, the diagonal of the correlation matrix (communalities) will be computed as the multiple R-square of the respective variable with all other variables.  This is a common default method for estimating the communalities for principal factor analysis.

Iterated communalities (MINRES):  This method was originally proposed by Harman & Jones (1966).  First, multiple R-square estimates are used for the communalities.  After the initial extraction of factors, the method adjusts the loadings over several iterations and evaluates the goodness-of-fit of the resulting solution in terms of the residual sums of squares.

Maximum likelihood factors:  This method of factoring was first proposed by Lawley (1940), and it is discussed in detail in Harman (1976).  Unlike in the other methods, it is assumed that the underlying number of factors is known (that is, as set in the Maximum number of factors edit box).  STATISTICA will then estimate the loadings and communalities that maximize the probability of the observed correlation matrix to occur (hence the term maximum likelihood).  On the results dialog, a Chi-square test of the goodness-of-fit is available.

Centroid method:  This method of factoring a correlation matrix was originally developed by Thurstone (1931), and represents a geometrical approach to factor analysis.  It is the least "modern" method for factor analysis.  Refer to Harman (1976) or Wherry (1984) for additional details.

Principal axis method:  In this method, in each iteration, the eigenvalues are computed from current communalities; next the communalities are recomputed based on the extracted eigenvalues and eigenvectors.  The new communalities are then placed in the diagonal of the correlation matrix, and the next iteration begins.  Iterations will continue until either (1) the Maximum number of iterations are exceeded, or (2) the Min. change in communalities is less than that specified in the respective edit box.


  Factor Analysis Factor Extraction - Maximum Number of Factors

This number will determine how many factors will be extracted.  Note that this edit field works in conjunction with the Minimum eigenvalue field below, that is, STATISTICA will extract either as many factors as requested, or as many as have eigenvalues greater than that specified in the Minimum eigenvalue field, whichever criterion yields fewer numbers of factors.


Factor Analysis Factor Extraction - Minimum Eigenvalue

  Factor Analysis Factor Extraction - Minumum Eigenvalue

This number will determine how many factors are extracted, that is, STATISTICA will extract as many factors as there are eigenvalues greater than the number specified in this field.  Note that this edit field works in conjunction with the Maximum no. of factors field.


Factor Analysis Factor Extraction - Minimum Change in Communality

  Factor Analysis Factor Extraction - Min. Change in Communality

This option is only available if principal axis factoring or centroid factoring are requested.  Those procedures will recompute the communalities in successive iterations until some criterion is met.  Specifically, iterations will stop when the change in the successively computed communalities is less than the value specified in this edit field, or when the Maximum no. of factors have been exceeded.


  Factor Analysis Factor Extraction - Maximum Number of Iterations

This option is also only available if principal axis factoring or centroid factoring are requested.  Those procedures will recompute the communalities in successive iterations; iterations will stop when the change in the successively computed communalities is less than the value specified in the Min. change in communality field, or when the Maximum number of iterations have been exceeded.


  Factor Analysis - Descriptive Statistics

This dialog allows you to compute detailed descriptive statistics for the variables in the current analysis.  Note that two important underlying assumption of factor analysis are (1) that the distributions of variables follow the normal distribution, and (2) that the correlations between variables are linear.  The graphics options on this dialog allow you to visually test both of those assumptions.  (The graphics options are not available if a correlation matrix input file is currently analyzed).

NOTE:  Matrix ill-conditioning and the modified correlation matrix.  The Introductory Overview section discusses the issue of matrix ill-conditioning.  If during the factoring process you received the message that the correlation matrix could not be inverted, then, when subsequently calling this dialog (descriptive statistics), the correlation matrix will have been modified (to allow inversion).  Specifically, a small constant was added to the diagonal of the correlation matrix until the determinant of that matrix was greater than 1.e-50.  The modified (slightly lowered) correlations will be reported here if matrix ill conditioning was detected and the modification performed.

Reviewing Descriptive Statistics dialog:

Means & SD

Correlations

Scatterplot matrix

Covariances

Save correlations

Summary statistics for pairwise deletion of missing data

Pairwise means

Pairwise standard deviations

Pairwise n

Box & whisker plots

Histograms

Normal probability plots

3D Bivariate distribution plot

2D Scatterplots

3D Scatterplots

Surface plots


Factor Analysis - A Note on Matrix Ill-Conditioning and the Modified Correlation Matrix

  Factor Analysis Descriptive Statistics - A Note on Matrix Ill-conditioning and the Modified Correlation Matrix

The Introductory Overview section discusses the issue of matrix ill-conditioning.  If during the factoring process you received the message that the correlation matrix could not be inverted, then, when subsequently calling this dialog (descriptive statistics), the correlation matrix will have been modified (to allow inversion).  Specifically, a small constant was added to the diagonal of the correlation matrix until the determinant of that matrix was greater than 1.e-50.  The modified (slightly lowered) correlations will be reported here if matrix ill conditioning was detected and the modification performed.


  Factor Analysis Descriptive Statistics - Means and Standard Deviations

This option will bring up a Scrollsheet with the descriptive statistics for the variables in the analysis.  If a raw data file is analyzed, then the default statistical graph for that Scrollsheet is the histogram with fitted normal distribution.


  Factor Analysis Descriptive Statistics - Correlations

This option will bring up a Scrollsheet with the current correlation matrix.  If a raw data file is analyzed, then the default statistical graph for that Scrollsheet is the scatterplot with the fitted regression line.  If matrix ill-conditioning was detected during the factoring process, then this matrix will have been slightly modified (see Note).


  Factor Analysis Descriptive Statistics - Scatterplot Matrix

This option is only available if a raw data file is being analyzed.  This button will bring up a scatterplot matrix for the variables in the current analysis.


  Factor Analysis Descriptive Statistics - Covariances

This option will bring up a Scrollsheet with the current covariance matrix.  If a raw data file is analyzed, the default statistical graph for that Scrollsheet is the scatterplot with the fitted regression line.  If matrix ill-conditioning was detected during the factoring process, then this matrix will have been slightly modified (see Note).


  Factor Analysis Descriptive Statistics - Save Correlations

This option allows you to save the current correlation matrix in STATISTICA Matrix File Format.  The correlation matrix can then be directly read in subsequent factor analyses (or analyses via Multiple Regression, Canonical Correlation, Reliability and Item Analysis, Cluster Analysis, Multidimensional Scaling, etc.).


  Factor Analysis Descriptive Statistics - Summary Statistics for Pairwise Deletion of Missing Data

These options are only available if Pairwise deletion of missing data was selected on the Startup Panel, and if this dialog was called immediately after reading the data (these various matrices are no longer needed in the actual factor analysis computations, and are thus discarded when the factor extraction process begins).  Note that in pairwise deletion of missing data, the different correlations in the correlation matrix can be based on unequal numbers of (different) cases.  Thus, for each correlation coefficient there can be:

(1)	A unique n (valid number of cases);

(2)	Unique means for the two respective variables;

(3)	Unique standard deviations for the two variables.

If large discrepancies are evident for the values for different correlations (pairs of variables), then the different correlations may have been computed from different actual cases.  Before reaching final conclusions from the factor analysis, it is advisable to repeat the analysis either with casewise deletion of missing data or mean substitution.


  Factor Analysis Descriptive Statistics - Pairwise Means

This option will bring up a Scrollsheet with the pairwise means.  The Scrollsheet will show the means for the row variables, when they are paired (correlated) with the respective column variables.


  Factor Analysis Descriptive Statistics - Pairwise Standard Deviations

This option will bring up a Scrollsheet with the pairwise standard deviations.  The Scrollsheet will show the standard deviations for the row variables, when they are paired (correlated) with the respective column variables.


  Factor Analysis Descriptive Statistics - Pairwise n

This option will bring up a Scrollsheet with the pairwise n (valid number of cases).


  Factor Analysis Descriptive Statistics - Box and Whisker Plots

This option allows you to produce box and whisker plots for the variables in the current analysis.  The box and whisker plot will summarize each variable by three components:

(1)	A central line to indicate central tendency or location;

(2)	A box to indicate variability around this central tendency;

(3)	Whiskers around the box to indicate the range of the variable.

After clicking on this button you can choose to plot for each variable:

(1)	Medians (central line), quartiles (box), and ranges (whiskers); note that the specific method that is used to compute medians and quartiles can be configured in the STATISTICA Defaults: General dialog.

(2)	Means, standard errors of the means, and standard deviations;

(3)	Means, standard deviations, and 1.96 times the standard deviations (95% normal confidence interval for individual observations around the mean);

(4)	Means standard errors of the means, and 1.96 times the standard errors of the means (95% normal confidence interval for means).


  Factor Analysis Descriptive Statistics - Histograms

This option allows you to produce histograms of the distributions of variables in the current analysis.  The plots will also include the expected normal distribution curves.


  Factor Analysis Descriptive Statistics - Normal Probability Plots

This option will produce a cascade of normal probability plots for the selected variables, one plot per selected variable.  For more information on how the standard normal probability plot is constructed, see Computation Note for Normal Probability Plots.


  Factor Analysis Descriptive Statistics - 3D Bivariate Distribution Plot

This option will produce a cascade of 3D histograms for selected pairs of variables, one plot per pair.  After clicking on this button, the user is first prompted to select two lists of variables (from among those originally selected via the Variables option).  3D histograms will be produced for each variable in the first list with each variable in the second list.


  Factor Analysis Descriptive Statistics - 2D Scatterplot

This option will produce a cascade of scatterplots for selected pairs of variables, one plot per variable pair (i.e., correlation).  Each plot will also show the regression line and the standard error of the predicted values (as error lines).


  Factor Analysis Descriptive Statistics - 3D Scatterplot

This option will produce a 3D scatterplot for a selected triplet of variables.


  Factor Analysis Descriptive Statistics - Surface Plot

This option will produce a 3D scatterplot for a selected triplet of variables, and fit a quadratic surface to the data.


  Factor Analysis - Multiple Regression

This dialog allows you to perform multiple regression analyses for the variables in the current analysis.  Note that STATISTICA includes a designated Multiple Regression module, which contains numerous additional options and extensive residual analysis facilities.

NOTE:  Matrix ill-conditioning and the modified correlation matrix.  The Introductory Overview section discusses the issue of matrix ill-conditioning.  If during the factoring process you received the message that the correlation matrix could not be inverted, then, when subsequently calling this dialog (multiple regression), the correlation matrix will have been modified (to allow inversion).  Specifically, a small constant was added to the diagonal of the correlation matrix until the determinant of that matrix was greater than 1.e-50.  If matrix ill conditioning was detected and the modification performed, then all estimates here will be based on the modified correlation matrix.  If this dialog is called immediately after the data have been read, then all computations will be based on the actual (exact) correlation matrix.

Multiple Regression Analysis dialog:

Variables

Tolerance

Review corrs/means/SD

Regression coefficients

Partial correlations

Save pred/residuals


  Factor Analysis Multiple Regression - Variables

This option will bring up a standard two-variable lists selection dialog in which you can select the independent variables and the dependent variable.


  Factor Analysis Multiple Regression - Tolerance

The tolerance of a variable is defined as 1 minus the squared multiple correlation of this variable with all other independent variables in the regression equation.  Therefore, the smaller the tolerance of a variable, the more redundant is its contribution to the regression (i.e., it is redundant with the contribution of other independent variables).  If the tolerance of any of the variables in the regression equation is equal to zero (or very close to zero) then the regression equation cannot be evaluated (the matrix is said to be ill-conditioned, and it cannot be inverted, see the above Note).  This option allows you to specify the minimum tolerance that is considered acceptable by STATISTICA.  The minimum value that can be specified here is 1.00E-25 (i.e., a number with 24 zeros past the decimal point).  However, it is not recommended to reset this switch to such an extremely low value.  If the tolerance of a variable entered into the regression equation is less than the default tolerance value (.01) it means that this variable is 99 percent redundant with (identical to) the variables already in the equation.  Forcing very redundant variables into the regression equation is not only questionable in terms of relevance of results, but the resultant estimates (regression coefficients) will become increasingly unreliable.


  Factor Analysis Multiple Regression - Review Correlations/Means/SD

This option will bring up the Descriptive statistics dialog window.


  Factor Analysis Multiple Regression - Regression Coefficients

This option will bring up a Scrollsheet with the standardized (beta) and nonstandardized (B) regression coefficients (weights), their standard error, and statistical significance.  The summary statistics for the regression analysis (e.g., R, R-square, etc.) will be shown in the headers of the Scrollsheet.


  Factor Analysis Multiple Regression - Partial Correlations

Clicking on this button will bring up Scrollsheets with:

(1)	The beta in (standard regression coefficient for the respective variable if it were to enter into the regression equation as an independent variable);

(2)	The partial correlation (between the respective variable and the dependent variable, after controlling for all other independent variables in the equation);

(3)	The semi-partial (part) correlation (the correlation between the unadjusted dependent variable with the respective variable after controlling for all independent variables in the equation);

(4)	The tolerance for the respective variable (defined as 1 minus the squared multiple correlation between the respective variable and all independent variables in the regression equation);

(5)	The minimum tolerance (the smallest tolerance among all independent variables in the equation if the respective variable were to be entered as an additional independent variable);

(6)	The t value associated with these statistics for the respective variable;

(7)	The statistical significance of the t value.

These statistics will first be displayed separately for variables not currently in the regression equation (if any), and for the variables in the regression equation.


  Factor Analysis Multiple Regression - Save Predicted/Residuals

This option is only available if a raw data file is analyzed (not a matrix file).  This option allows you to save the predicted and residual values for the current regression equation.


Factor Analysis - Alpha Level (Highlighting)

  Factor Analysis - Alpha Level for Highlighting

The default value for alpha is .05.  This value is used to determine the significance of a specific effect.  If the p-value is less than or equal to the designated value for alpha then we say that the effect is significant and it is highlighted in the window.  Set the desired alpha level (.0001 < α < .5) that is to be used for highlighting significant results in the Scrollsheet.


  Factor Analysis - Iterated Communalities

The iterative computation of communalities is in progress.  Click the Cancel button to interrupt the computations.

NOTE:  Matrix ill-conditioning and the modified correlation matrix.  The Introductory Overview section discusses the issue of matrix ill-conditioning.  If during the factoring process you received the message that the correlation matrix cannot be inverted, then, the correlation matrix will be modified (to allow inversion).  Specifically, a small constant is added to the diagonal of the correlation matrix until the determinant of that matrix is greater than 1.e-50.  All subsequent computations will be performed based on the modified (slightly lowered) correlations; to restore the original exact correlation matrix, click Cancel to return to the startup panel and then click OK to reread the data file.


  Factor Analysis - Results

The following options are available from the Factor Analysis Results dialog.

NOTE:  Matrix ill-conditioning and the modified correlation matrix

Factor Analysis Results dialog:

Eigenvalues

Communalities

Goodness-of-fit test

Scree plot

Reproduced/residual corrs

Factor rotation

Factor loadings

Plot of loadings, 2D & 3D

Hierarchical analysis of oblique factors

Factor score coefficients

Factor scores

Save factor scores

Review correlations/means/SD

Perform multiple regression


  Factor Analysis Results - Matrix Ill-Conditioning and the Modified Correlation Matrix

The Introductory Overview section discusses the issue of matrix ill-conditioning.  If during the factoring process you received the message that the correlation matrix cannot be inverted, then, the correlation matrix will be modified (to allow inversion).  Specifically, a small constant is added to the diagonal of the correlation matrix until the determinant of that matrix is greater than 1.e-50.  All subsequent computations will be performed based on the modified (slightly lowered) correlations.


  Factor Analysis Results - Eigenvalues

This option will bring up a Scrollsheet with the eigenvalues.  The relative (percent) and cumulative eigenvalues are also reported.  The interpretation of eigenvalues is described in the Introductory Overview section.  In general, the eigenvalues reflect the amount of common variance accounted for by the respective number of factors.


  Factor Analysis Results - Communalities

This option will bring up a Scrollsheet with the communalities, computed from the respective number of factors extracted in the current analysis.  Again, refer to the Introductory Overview section for a discussion of communalities; in general, the communalities can be interpreted as the proportion of variance accounted for in the respective variables by the current number of factors.


  Factor Analysis Results - Goodness-of-Fit

This option is only available if Maximum Likelihood factoring was selected.  This option will bring up a Scrollsheet with the U test (Lawley, 1940) of fit for the current number of factors.  In general, when the variables in the analysis come from a multivariate normal distribution, then the distribution of covariances follows the Wishart distribution (Wishart, 1928).  Based on these assumptions, a Chi-square test can be constructed testing whether all residual correlations are equal to zero, that is, whether or not the residual correlation matrix is a diagonal matrix.  If statistically significant, it can be concluded that the residual correlation matrix is significantly different from the diagonal matrix, and therefore, that significant correlations between variables are still not accounted for.  Also, Chi-square tests of incremental models (with increasing numbers of factors) can be performed, allowing for statistical significance testing of the number of factors "contained" in the correlation matrix.  However, note that the sensitivity of the Chi-square test is greatly affected by the sample size (n); refer to Harman (1976), Mulaik (1972), or Wherry (1984) for additional details.


  Factor Analysis Results - Scree Plot

This option will bring up the so-called scree plot (Cattell, 1966).  Specifically, the successive eigenvalues will be shown in a simple line plot.  Cattell suggests to find the place where the smooth decrease of eigenvalues appears to level off to the right of the plot.  To the right of this point, presumably, one finds only "factorial scree" -- "scree" is the geological term referring to the debris which collects on the lower part of a rocky slope.  Thus, no more than the number of factors to the left of this point should be extracted.  Refer to the Introductory Overview section for a more detailed discussion of the number-of-factors issue in factor analysis.


  Factor Analysis Results - Reproduced/Resid. Corrs.

This option will bring up Scrollsheets with the reproduced and residual (observed minus reproduced) correlation matrices.


  Factor Analysis Results - Factor Rotation

As discussed in the Introductory Overview section, the rotational orientation of axes in factor analysis is more or less arbitrary.  However, numerous rotational strategies have been proposed to choose an orientation of axes that is most interpretable (i.e., approximates simple structure).  Several of such strategies are available in the Factor Analysis module (refer to the Factor Rotation menu).  The current orientation of axes is indicated to the right of this button.


  Factor Analysis Results - Factor Loadings

This option will bring up a Scrollsheet with the current factor loadings, that is, rotated in the manner indicated next to the Factor rotation button.  The default statistical plot for this Scrollsheet is the 2D or 3D scatterplot of factor loadings.  Factor loadings can be interpreted as correlations between the respective variables and factors; thus they represent the most important information for the interpretation of factors.  Refer to the manual or the Introductory Overview section for additional details.  Initially, factor loadings greater than 0.7 are highlighted in the Scrollsheet.


  Factor Analysis Results - Plot of Loadings

These options will produce 2D or 3D scatterplots of the current factor loadings; often, visual inspection of loadings suggests a clearer interpretation of factors.


  Factor Analysis Results - Hierarchical Analysis of Oblique Factors

This option is only available if more than one factor was extracted.  In that case, a hierarchical factor analysis (see Thompson, 1951; Schmid & Leiman, 1957; Wherry, 1959, 1975, 1984) can be performed.  In short, STATISTICA will first identify clusters of marker variables (with high unique factor loadings, and low cross-loadings) and rotate axes through those clusters.  If no such clear clusters of "marker variables" can be identified for each oblique factor; the hierarchical analysis will not be performed.  Next the correlations between those (oblique) factors is computed, and that correlation matrix of oblique factors is further factor-analyzed to yield a set of orthogonal factors that divide the variability in the items into that due to shared or common variance (secondary factors), and unique variance due to the clusters of similar variables (items) in the analysis (primary factors).  After clicking on this button, Scrollsheets with the complete results will automatically be generated.


  Factor Analysis Results - Factor Score Coefficients

This option will bring up a Scrollsheet with the factor score coefficients.  For principal components analysis, exact coefficients can be computed from the (rotated or unrotated) factor loadings.  For principal factors analysis (with estimated communalities), regression estimates of the factor score coefficients are computed; see Harman (1976, p. 368).


  Factor Analysis Results - Factor Scores

This option is only available if a raw data file is currently being analyzed.  This option will bring up a Scrollsheet with factor scores, based on the factor score coefficients computed as described above.  If casewise or pairwise deletion of missing data was selected, then factor scores can only be computed for complete cases (without missing data on any of the variables in the current analysis); if mean substitution was selected, then missing data will be substituted by the respective variable means in the computations (since factor scores are computed from normal z values, missing data will in effect be substituted by zero).


  Factor Analysis Results - Save Factor Scores

This option is only available if a raw data file is currently being analyzed.  This option allows you to save the factor scores, which are computed as described above.


  Factor Analysis Results - Review Correlations/Means/SD

This button will bring up a dialog for reviewing various descriptive statistics and graphs.  Also use this option in order to save the current correlation matrix in a matrix file.


  Factor Analysis Results - Perform Multiple Regression

This button will bring up a dialog for performing multiple regression analyses with the currently selected variables.  Regression equations with up to 299 independent variables can be evaluated.  Note that extensive options for multiple regression are available in the Multiple Regression module of STATISTICA.


  Factor Analysis - Residual Correlations

Enter the cut-off value for the residual correlations that are to be highlighted in the Scrollsheet.


  Factor Analysis - Factor Loadings

Enter the cut-off value for factor loadings that are to be highlighted in the Scrollsheet.  Factor loadings can be interpreted as correlations between the respective variables and factors; thus they represent the most important information for the interpretation of factors.  Refer to the manual or the Introductory Overview section for additional details.


  Factor Analysis - Rotation

There are various rotational strategies that have been proposed.  The goal of all of these strategies is to obtain a clear pattern of loadings, that is, factors that are somehow clearly marked by high loadings for some variables and low loadings for others.  This general pattern is also sometimes referred to as simple structure (a more formalized definition can be found in most standard textbooks).  Typical rotational strategies are varimax, biquartimax, quartimax, and equamax.  Some authors (e.g., Catell & Khanna; Harman, 1976; Jennrich & Sampson, 1966; Clarkson & Jennrich, 1988) have discussed in some detail the concept of oblique (non-orthogonal) factors, in order to achieve more interpretable simple structure.  Specifically, computer (algorithmic) strategies have been developed to rotate factors so as to best represent "clusters" of variables, without the constraint of orthogonality of factors.  However, the oblique factors produced by such rotations are often not easily interpreted.  Use the Hierarchical analysis of oblique factors option instead in order to identify (correlated, oblique) clusters of variables (see also hierarchical factor analysis).

Note that you can use the Structural Equation Modeling (SEPATH) module to test the adequacy (goodness of fit) of specific orthogonal or oblique factor solutions.

Varimax raw

Varimax normalized

Biquartimax raw

Biquartimax normalized

Quartimax raw

Quartimax normalized

Equamax raw

Equamax normalized


  Factor Analysis Rotation - Varimax Raw

This option will perform a varimax rotation of the factor loadings.  This rotation is aimed at maximizing the variances of the squared raw factor loadings across variables for each factor; this is equivalent to maximizing the variances in the columns of the matrix of the squared raw factor loadings.


  Factor Analysis Rotation - Varimax Normalized

This option will perform a varimax rotation of the normalized factor loadings (raw factor loadings divided by the square roots of the respective communalities).  This rotation is aimed at maximizing the variances of the squared normalized factor loadings across variables for each factor; this is equivalent to maximizing the variances in the columns of the matrix of the squared normalized factor loadings.  This is the method that is most commonly used and referred to as varimax rotation.


  Factor Analysis Rotation - Biquartimax Raw

This option will perform a biquartimax rotation of the raw factor loadings.  This rotation can be considered to be an "even mixture" of the varimax and quartimax rotation.  Specifically, it is aimed at simultaneously maximizing the sum of variances of the squared raw factor loadings across factors and maximizing the sum of variances of the squared raw factor loadings across variables; this is equivalent to simultaneously maximizing the variances in the rows and columns of the matrix of the squared raw factor loadings.


  Factor Analysis Rotation - Biquartimax Normalized

This rotation is equivalent to the biquartimax raw rotation, except that it is performed on normalized (standardized) factor loadings.


  Factor Analysis Rotation - Quartimax Raw

This option will perform a quartimax rotation of the (raw) factor loadings.  This rotation is aimed at maximizing the variances of (the squared raw) factor loadings across factors for each variable; this is equivalent to maximizing the variances in the rows of the matrix of the squared raw factor loadings.


  Factor Analysis Rotation - Quartimax Normalized

This option will perform a quartimax rotation of the normalized factor loadings, that is, the raw factor loadings divided by the square roots of the respective communalities.  This rotation is aimed at maximizing the variances of the squared normalized factor loadings across factors for each variable; this is equivalent to maximizing the variances in the rows of the matrix of the squared normalized factor loadings.  This is the method that is commonly referred to as quartimax rotation.


  Factor Analysis Rotation - Equamax Raw

This option will perform an equamax rotation of the raw factor loadings.  This rotation can be considered to be a "weighted mixture" of the varimax and quartimax rotation.  Specifically, it is aimed at simultaneously maximizing the sum of variances of the squared raw factor loadings across factors and maximizing the sum of variances of the squared raw factor loadings across variables; this is equivalent to simultaneously maximizing the variances in the rows and columns of the matrix of the squared raw factor loadings.  However, unlike the biquartimax rotation, the relative weight assigned to the varimax criterion in the rotation is equal to the number of factors divided by 2.


  Factor Analysis Rotation - Equamax Normalized

This option will perform an equamax rotation, as described for Equamax raw; however, this rotation will be performed on the normalized factor loadings.


  Factor Analysis - 3D Plot of Loadings

Select the variables for the 3D scatterplot of factor loadings.  The points in the scatterplot represent individual variables and are labeled with their respective names (de-select the Display variable numbers option) or numbers (select the Display variable numbers option).  If the labels overlap, try to rotate the graph (see Perspective and Rotation) or double-click on any variable label to access the Font dialog which will allow you to adjust (reduce) the size of font used to label the points.

See also:  If Data Point Labels Overlap


  Factor Analysis - 2D Plot of Loadings

Select the variables for the 2D scatterplot of factor loadings.  The points in the scatterplot represent individual variables and are labeled with their respective names.  If the labels overlap, double-click on any variable label to access the Font dialog which will allow you to adjust (reduce) the size of font used to label the points.

See also:  If Data Point Labels Overlap


  Factor Analysis - Notes and Technical Information

Eigenvalues

At the "heart" of factor analysis is the eigenvalue problem that is solved in this program via the Householder method; see, for example, Golub and Van Loan (1983), Jacobs (1977), or Ralston and Wilf (1967, Vol. II).  Eigenvalues are calculated via least squares procedures.  The sum of the eigenvalues is equal to the sum of the diagonal elements of the matrix (correlations or covariances) that is analyzed, that is:

Σλ = trace/S/ = Σs

  j               ij

where

λj	is the j'th eigenvalue

/S/	is the variance/covariance matrix or correlation matrix

sij	are the diagonal elements of the variance/covariance matrix or the correlation matrix

Matrix Ill-Conditioning and the Modified Correlation Matrix

The Introductory Overview section discusses the issue of matrix ill-conditioning.  If during the factoring process you received the message that the correlation matrix cannot be inverted, then the correlation matrix will be modified (to allow inversion).  Specifically, a small constant is added to the diagonal elements of the correlation matrix until the determinant of that matrix is greater than 1.E-50.  All subsequent computations will be performed based on the modified (slightly lowered) correlations; to restore the original exact correlation matrix, click Cancel to return to the Startup Panel and then click OK to re-read the data file.

Analyzing covariance or moment matrices

STATISTICA includes the example STATISTICA BASIC program file Factor.stb (in the STBASIC sub-directory).  That program will compute a principal components analysis based on either the correlation matrix, covariance matrix, or moment matrix.


  ANOVA/MANOVA - Index

Introductory Overview

Basic Ideas

Complex Designs

Analysis of Covariance (ANCOVA)

Multivariate Designs:  MANOVA/MANCOVA

Contrast Analysis and Post hoc Tests

Assumptions and Effects of Violating Assumptions

Notes

Specifying Between Uni/Multivariate Designs

Specifying Within (Repeated Measures) Uni/Multivariate Designs

Multiple Dependent Measures (MANOVA)

Nested Designs and Latin Squares

Other Special Designs

Type I, II, III Sums of Squares

Analyzing Designs with Missing Cells (Type IV Sums of Squares)

Random Factors

Fixed and Changing covariates

Startup Panel

Specifying Within-SS (Repeated Measures) Designs

Specifying the Code for an Isolated Control Group

Specifying a Nested Design

Specifying Random Factors (effects)

Changing vs. Fixed Covariates

Results Dialog

Output Options (Detail of Reported Results)

Testing Specific Effects

Regression Results (Covariates)

Post hoc Tests

Descriptive Statistics and Graphs

Pooled Effects and Error Terms

Means and Graphs of Means (Interaction Plots)

Contrast Analysis, Entering Contrasts For Each Effect

Specifying Pre-defined Sets of Contrasts

Entering Contrast Vectors (for all Factors Together)

Notes and Technical Information


  ANOVA/MANOVA - Introductory Overview

The following discussions are a "primer" on the basic logic, assumptions, and terminology of analysis of variance techniques.  To learn how to specify particular designs in ANOVA/MANOVA, refer to the Notes section (between-group designs, repeated measures designs) where the general conventions for specifying designs are explained.  For detailed examples of selected common designs, refer to the Examples section of the manual.

Basic Ideas

Complex Designs

Analysis of Covariance (ANCOVA)

Multivariate Designs:  MANOVA/MANCOVA

Contrast Analysis and Post hoc Tests

Assumptions and Effects of Violating Assumptions

See also, ANOVA/MANOVA Notes


ANOVA/MANOVA - Basic Ideas

  ANOVA/MANOVA Introductory Overview - Basic Ideas

The Purpose of Analysis of Variance.  In general, the purpose of analysis of variance (ANOVA) is to test for significant differences between means.  Elementary Concepts provides a brief introduction into the basics of statistical significance testing.  If we are only comparing two means, then ANOVA will give the same results as the t test for independent samples (if we are comparing two different groups of cases or observations), or the t test for dependent samples (if we are comparing two variables in one set of cases or observations).  If you are not familiar with those tests you may at this point want to "brush up" on your knowledge about those tests by reading Basic Statistics and Tables.

Why the name analysis of variance?  It may seem odd to you that a procedure that compares means is called analysis of variance.  However, this name is derived from the fact that in order to test for statistical significance between means, we are actually comparing (i.e., analyzing) variances.

The Partitioning of Sums of Squares

Multi-Factor ANOVA

Interaction Effects

For more Introductory Overview topics, click on the topic name.

Complex Designs

Analysis of Covariance (ANCOVA)

Multivariate Designs:  MANOVA/MANCOVA

Contrast Analysis and Post hoc Tests

Assumptions and Effects of Violating Assumptions

See also, ANOVA/MANOVA Notes


ANOVA/MANOVA-Basic Ideas - The Partitioning of Sums of Squares

  ANOVA/MANOVA Introductory Overview-Basic Ideas - The Partioning of Sums of Squares

At the heart of ANOVA is the fact that variances can be divided up, that is, partitioned.  Remember that the variance is computed as the sum of squared deviations from the overall mean, divided by n-1 (sample size minus one).  Thus, given a certain n, the variance is a function of the sums of (deviation) squares, or SS for short.  Partitioning of variance works as follows.  Consider the following data set:

                          Group 1      Group 2

                          -------      -------

Observation 1               2            6

Observation 2               3            7

Observation 3               1            5

----------------------------------------------

Mean                        2            6

Sums of Squares (SS)        2            2

----------------------------------------------

Overall Mean                       4

Total Sums of Squares             28

The means for the two groups are quite different (2 and 6, respectively).  The sums of squares within each group are equal to 2.  Adding them together, we get 4.  If we now repeat these computations, ignoring group membership, that is, if we compute the total SS based on the overall mean, we get the number 28.  In other words, computing the variance (sums of squares) based on the within-group variability yields a much smaller estimate of variance than computing it based on the total variability (the overall mean).  The reason for this in the above example is of course that there is a large difference between means, and it is this difference that accounts for the difference in the SS.  In fact, if we were to perform an ANOVA on the above data, we would get the following result:

+----------+--------------------------------+

| STAT.    |         MAIN EFFECT            |

|          +------+----+------+------+------+

|          |  SS  | df |  MS  |  F   |  p   |

+----------+------+----+------+------+------+

| Effect   | 24.0 |  1 | 24.0 | 24.0 | .008 |

| Error    |  4.0 |  4 |  1.0 |      |      |

+----------+------+----+------+------+------+

As you can see, in the above table the total SS (28) was partitioned into the SS due to within-group variability (2+2=4; see the second row of the Scrollsheet) and variability due to differences between means (28-(2+2)=24; see the first row of the Scrollsheet).

SS Error and SS Effect.  The within-group variability (SS) is usually referred to as Error variance.  This term denotes the fact that we cannot readily explain or account for it in the current design.  However, the SS Effect we can explain.  Namely, it is due to the differences in means between the groups.  Put another way, group membership explains this variability because we know that it is due to the differences in means.

Significance testing.  The basic idea of statistical significance testing is discussed in Elementary Concepts.  Elementary Concepts also explains why very many statistical test represent ratios of explained to unexplained variability.  ANOVA is a good example of this.  Here, we base this test on a comparison of the variance due to the between-groups variability (called Mean Square Effect, or MSeffect) with the within-group variability (called Mean Square Error, or Mserror; this term was first used by Edgeworth, 1885).  Under the null hypothesis (that there are no mean differences between groups in the population), we would still expect some minor random fluctuation in the means for the two groups when taking small samples (as in our example).  Therefore, under the null hypothesis, the variance estimated based on within-group variability should be about the same as the variance due to between-groups variability.  We can compare those two estimates of variance via the F test, which tests whether the ratio of the two variance estimates is significantly greater than 1.  In our example above, that test is highly significant, and we would in fact conclude that the means for the two groups are significantly different from each other.

Summary of the basic logic of ANOVA.  To summarize the discussion up to this point, the purpose of analysis of variance is to test differences in means (for groups or variables) for statistical significance.  This is accomplished by analyzing the variance, that is, by partitioning the total variance into the component that is due to true random error (i.e., within-group SS) and the components that are due to differences between means.  These latter variance components are then tested for statistical significance, and, if significant, we reject the null hypothesis of no differences between means, and accept the alternative hypothesis that the means (in the population) are different from each other.

Dependent and independent variables.  The variables that are measured (e.g., a test score) are called dependent variables.  The variables that are manipulated or controlled (e.g., a teaching method or some other criterion used to divide observations into groups that are compared) are called factors or independent variables.  For more information on this important distinction, refer to Elementary Concepts.


ANOVA/MANOVA-Basic Ideas - Multi-Factor Anova

  ANOVA/MANOVA Introductory Overview-Basic Ideas - Multi-Factor ANOVA

In the simple example above, it may have occurred to you that we could have simply computed a t test for independent samples with Basic Statistics and Tables to arrive at the same conclusion.  And, indeed, we would get the identical result if we were to compare the two groups using this test.  However, ANOVA is a much more flexible and powerful technique that can be applied to much more complex research issues.

Multiple factors.  The world is complex and multivariate in nature, and instances when a single variable completely explains a phenomenon are rare.  For example, when trying to explore how to grow a bigger tomato, we would need to consider factors that have to do with the plants' genetic makeup, soil conditions, lighting, temperature, etc.  Thus, in a typical experiment, many factors are taken into account.  One important reason for using ANOVA methods rather than multiple two-group studies analyzed via t tests is that the former method is more efficient, and with fewer observations we can gain more information.  Let us expand on this statement.

Controlling for factors.  Suppose that in the above two-group example we introduce another grouping factor, for example, Gender.  Imagine that in each group we have 3 males and 3 females.  We could summarize this design in a 2 by 2 table:

            Experimental   Experimental

               Group 1        Group 2

--------------------------------------

Males            2              6

                 3              7

                 1              5

               -----          -----

          Mean   2              6

--------------------------------------

Females          4              8

                 5              9

                 3              7

               -----          -----

          Mean   4              8

--------------------------------------

Before performing any computations, it appears that we can partition the total variance into at least 3 sources: (1) error (within-group) variability, (2) variability due to experimental group membership, and (3) variability due to gender.  (Note that there is an additional source -- interaction -- that we will discuss shortly.)  What would have happened had we not included gender as a factor in the study but rather computed a simple t test?  If you compute the SS ignoring the gender factor (use the within-group means ignoring or collapsing across gender; the result is SS=10+10=20), you will see that the resulting within-group SS is larger than it is when we include gender (use the within-group, within-gender means to compute those SS; they will be equal to 2 in each group, thus the combined SS-within is equal to 2+2+2+2=8).  This difference is due to the fact that the means for males are systematically lower than those for females, and this difference in means adds variability if we ignore this factor.  Controlling for error variance increases the sensitivity (power) of a test.  This example demonstrates another principal of ANOVA that makes it preferable over simple two-group t test studies:  In ANOVA we can test each factor while controlling for all others; this is actually the reason why ANOVA is more statistically powerful (i.e., we need fewer observations to find a significant effect) than the simple t test.


ANOVA/MANOVA-Basic Ideas - Interaction Effects

  ANOVA/MANOVA Introductory Overview-Basic Ideas - Interaction Effects

There is another advantage of ANOVA over simple t-tests:  ANOVA allows us to detect interaction effects between variables, and, therefore, to test more complex hypotheses about reality.  Let us consider another example to illustrate this point.  (The term interaction was first used by Fisher, 1926)

Main effects, two-way interaction.  Imagine that we have a sample of highly achievement-oriented students and another of achievement "avoiders."  We now create two random halves in each sample, and give one half of each sample a challenging test, the other an easy test.  We measure how hard the students work on the test.  The means of this (fictitious) study are as follows:

                   Achievement-    Achievement-

                    oriented        avoiders

                   ------------    ------------

Challenging Test      10              5

       Easy Test       5             10

How can we summarize these results?  Is it appropriate to conclude that (1) challenging tests make students work harder, (2) achievement-oriented students work harder than achievement-avoiders?  None of these statements captures the essence of this clearly systematic pattern of means.  The appropriate way to summarize the result would be to say that challenging tests make only achievement-oriented students work harder, while easy tests make only achievement-avoiders work harder.  In other words, the type of achievement orientation and test difficulty interact in their effect on effort; specifically, this is an example of a two-way interaction between achievement orientation and test difficulty.  Note that statements 1 and 2 above describe so-called main effects.

Higher order interactions.  While the previous two-way interaction can be put into words relatively easily, higher order interactions are increasingly difficult to verbalize.  Imagine that we had included factor Gender in the achievement study above, and we had obtained the following pattern of means:

FEMALES                Achievement-   Achievement-

                        oriented        avoiders

        ------------------------------------------

        Challenging Test     10              5

               Easy Test      5             10

--------------------------------------------------

MALES                  Achievement-   Achievement-

                        oriented        avoiders

        ------------------------------------------

        Challenging Test      1              6

               Easy Test      6              1

How could we now summarize the results of our study?  ANOVA/MANOVA allows you to produce graphs of means for all effects with basically a single click of the mouse; those graphs greatly facilitate the interpretation of complex effects.  The pattern shown in the table above represents a three-way interaction between factors.  Thus we may summarize this pattern by saying that for females there is a two-way interaction between achievement-orientation type and test difficulty:  Achievement-oriented females work harder on challenging tests than on easy tests, achievement-avoiding females work harder on easy tests than on difficult tests.  For males, this interaction is reversed.  As you can see, the description of the interaction has become much more involved.

A general way to express interactions.  A general way to express all interactions is to say that an effect is modified (qualified) by another effect.  Let us try this with the two-way interaction above.  The main effect for test difficulty is modified by achievement orientation.  For the three-way interaction in the previous paragraph, we may summarize that the two-way interaction between test difficulty and achievement orientation is modified (qualified) by gender.  If we have a four-way interaction, we may say that the three-way interaction is modified by the fourth variable, that is, that there are different types of interactions in the different levels of the fourth variable.  As it turns out, in many areas of research five- or higher-way interactions are not that uncommon.


ANOVA/MANOVA - Complex Designs

  ANOVA/MANOVA Introductory Overview - Complex Designs

The Notes section (between-group designs, repeated measures designs) discusses numerous examples of complex designs.  Let us review the basic "building blocks" of complex designs.

Between-Groups and Repeated Measures

Incomplete (Nested) Designs

For more Introductory Overview topics, click on the topic name.

Basic Ideas

Analysis of Covariance (ANCOVA)

Multivariate Designs:  MANOVA/MANCOVA

Contrast Analysis and Post hoc Tests

Assumptions and Effects of Violating Assumptions

See also, ANOVA/MANOVA Notes


ANOVA/MANOVA-Complex Designs - Between-Groups and Repeated Measures

  ANOVA/MANOVA Introductory Overview-Complex Designs - Between-Groups and Repeated Measures

When we want to compare two groups, we would use the t test for independent samples (in Basic Statistics and Tables); when we want to compare two variables given the same subjects (observations), we would use the t test for dependent samples.  This distinction -- dependent and independent samples -- is important for ANOVA as well.  Basically, if we have repeated measurements of the same variable (under different conditions or at different points in time) on the same subjects, then the factor is a repeated measures factor (also called a within-subjects factor, because to estimate its significance we compute the within-subjects SS).  If we compare different groups of subjects (e.g., males and females; three strains of bacteria, etc.) then we refer to the factor as a between-groups factor.  The computations of significance tests are different for these different types of factors; however, the logic of computations and interpretations is the same.

Between-within designs.  In many instances, experiments call for the inclusion of between-groups and repeated measures factors.  For example, we may measure math skills in male and female students (gender, a between-groups factor) at the beginning and the end of the semester.  The two measurements on each student would constitute a within-subjects (repeated measures) factor.  The interpretation of main effects and interactions is not affected by whether a factor is between-groups or repeated measures, and both factors may obviously interact with each other (e.g., females improve over the semester while males deteriorate).


ANOVA/MANOVA -Complex Designs - Incomplete (Nested) Designs

  ANOVA/MANOVA Introductory Overview-Complex Designs - Incomplete (Nested) Designs

There are instances where we may decide to ignore interaction effects.  This happens when (1) we know that in the population the interaction effect is negligible, or (2) when a complete factorial design (this term was first introduced by Fisher, 1935a) cannot be used for economic reasons.  Imagine a study where we want to evaluate the effect of four fuel additives on gas mileage.  For our test, our company has provided us with four cars and four drivers.  A complete factorial experiment, that is, one in which each combination of driver, additive, and car appears at least once, would require 4 x 4 x 4 = 64 individual test conditions (groups).  However, we may not have the resources (time) to run all of these conditions; moreover, it seems unlikely that the type of driver would interact with the fuel additive to an extent that would be of practical relevance.  Given these considerations, one could actually run a so-called Latin square design and "get away" with only 16 individual groups (the four additives are denoted by letters A, B, C, and D):

                   Car

               ----------

               1  2  3  4

-------------------------

Driver 1       A  B  C  D

Driver 2       B  C  D  A

Driver 3       C  D  A  B

Driver 4       D  A  B  C

Latin square designs (this term was first used by Euler, 1782) are described in most textbooks on experimental methods (e.g., Hays, 1988; Lindman, 1974; Milliken & Johnson, 1984; Winer, 1962), and we do not want to discuss here the details of how they are constructed.  Suffice it to say that this design is incomplete insofar as not all combinations of factor levels occur in the design.  For example, Driver 1 will only drive Car 1 with additive A, while Driver 3 will drive that car with additive C.  In a sense, the levels of the additives factor (A, B, C, and D) are placed into the cells of the car by driver matrix like "eggs into a nest."  This mnemonic device is sometimes useful for remembering the nature of nested designs.  ANOVA/MANOVA will easily analyze these types of designs.


ANOVA/MANOVA - Analysis of Covariance (ANCOVA)

  ANOVA/MANOVA Introductory Overview - Analysis of Covariance (ANCOVA)

General Idea

The Basic Ideas section discussed briefly the idea of "controlling" for factors and how the inclusion of additional factors can reduce the error SS and increase the statistical power (sensitivity) of our design.  This idea can be extended to continuous variables, and when such continuous variables are included as factors in the design they are called covariates.

Fixed Covariates

Changing Covariates

For more Introductory Overview topics, click on the topic name.

Basic Ideas

Complex Designs

Multivariate Designs:  MANOVA/MANCOVA

Contrast Analysis and Post hoc Tests

Assumptions and Effects of Violating Assumptions

See also, ANOVA/MANOVA Notes


  Analysis of Covariance (ANCOVA) - Fixed Covariates

Suppose that we want to compare the math skills of students who were randomly assigned to one of two alternative textbooks.  Imagine that we also have data about the general intelligence (IQ) for each student in the study.  We would suspect that general intelligence is related to math skills, and we can use this information to make our test more sensitive.  Specifically, imagine that in each one of the two groups we can compute the correlation coefficient (see Basic Statistics and Tables) between IQ and math skills.  Remember that once we have computed the correlation coefficient we can estimate the amount of variance in math skills that is accounted for by IQ, and the amount of (residual) variance that we cannot explain with IQ (refer also to Elementary Concepts and Basic Statistics and Tables).  We may use this residual variance in the ANOVA as an estimate of the true error SS after controlling for IQ.  If the correlation between IQ and math skills is substantial, then a large reduction in the error SS may be achieved.

Effect of a covariate on the F test.  In the F test, to evaluate the statistical significance of between-groups differences, we compute the ratio of the between-groups variance (MSeffect) over the error variance (MSerror).  If MSerror becomes smaller, due to the explanatory power of IQ, then the overall F value will become larger.

Multiple covariates.  The logic described above for the case of a single covariate (IQ) can easily be extended to the case of multiple covariates.  For example, in addition to IQ, we might include measures of motivation, spatial reasoning, etc., and instead of a simple correlation, compute the multiple correlation coefficient (see Multiple Regression).

When the F value gets smaller.  In some studies with covariates it happens that the F value actually becomes smaller (less significant) after including covariates in the design.  This is usually an indication that the covariates are not only correlated with the dependent variable (e.g., math skills), but also with the between-groups factors (e.g., the two different textbooks).  For example, imagine that we measured IQ at the end of the semester, after the students in the different experimental groups had used the respective textbook for almost one year.  It is possible that, even though students were initially randomly assigned to one of the two textbooks, the different books were so different that both math skills and IQ improved differentially in the two groups.  In that case, the covariate will not only partition variance away from the error variance, but also from the variance due to the between-groups factor.  Put another way, after controlling for the differences in IQ that were produced by the two textbooks, the math skills are not that different.  Put in yet a third way, by "eliminating" the effects of IQ, we have inadvertently eliminated the true effect of the textbooks on students' math skills.

Adjusted means.  When the latter case happens, that is, when the covariate is affected by the between-groups factor, then it is appropriate to compute so-called adjusted means.  These are the means that one would get after removing all differences that can be accounted for by the covariate.

Interactions between covariates and factors.  Just as we can test for interactions between factors, we can also test for the interactions between covariates and between-groups factors.  Specifically, imagine that one of the textbooks is particularly suited for intelligent students, while the other actually bores those students but challenges the less intelligent ones.  As a result, we may find a positive correlation in the first group (the more intelligent, the better the performance), but a zero or slightly negative correlation in the second group (the more intelligent the student, the less likely he or she is to acquire math skills from the particular textbook).  In some older statistics textbooks this condition is discussed as a case where the assumptions for analysis of covariance are violated (see Assumptions and Effects of Violating Assumptions).  However, because ANOVA/MANOVA uses a very general approach to analysis of covariance, you can specifically estimate the statistical significance of interactions between factors and covariates.


  Analysis of Covariance (ANCOVA) - Changing Covariates

While fixed covariates are commonly discussed in textbooks on ANOVA, changing covariates are discussed less frequently.  In general, when we have repeated measures, we are interested in testing the differences in repeated measurements on the same subjects.  Thus we are actually interested in evaluating the significance of changes.  If we have a covariate that is also measured at each point when the dependent variable is measured, then we can compute the correlation between the changes in the covariate and the changes in the dependent variable.  For example, we could study math anxiety and math skills at the beginning and at the end of the semester.  It would be interesting to see whether any changes in math anxiety over the semester correlate with changes in math skills.  The ANOVA/MANOVA module will automatically evaluate the statistical significance of changing covariates when the design allows it.


ANOVA/MANOVA - Multivariate Designs:  MANOVA/MANCOVA

  ANOVA/MANOVA Introductory Overview - Multivariate Designs:  MANOVA/MANCOVA

Between-Groups Designs

Repeated Measures Designs

Sum Scores versus MANOVA

For more Introductory Overview topics, click on the topic name.

Basic Ideas

Complex Designs

Analysis of Covariance (ANCOVA)

Contrast Analysis and Post hoc Tests

Assumptions and Effects of Violating Assumptions

See also, ANOVA/MANOVA Notes


  Multivariate Designs:  MANOVA/MANCOVA - Between-Groups Designs

All examples discussed so far have involved only one dependent variable.  Even though the computations become increasingly complex, the logic and nature of the computations do not change when there is more than one dependent variable at a time.  For example, we may conduct a study where we try two different textbooks, and we are interested in the students' improvements in math and physics.  In that case, we have two dependent variables, and our hypothesis is that both together are affected by the difference in textbooks.  We could now perform a multivariate analysis of variance (MANOVA) to test this hypothesis.  Instead of a univariate F value, we would obtain a multivariate F value (Wilks' lambda) based on a comparison of the error variance/covariance matrix and the effect variance/covariance matrix.  The "covariance" here is included because the two measures are probably correlated and we must take this correlation into account when performing the significance test.  Obviously, if we were to take the same measure twice, then we would really not learn anything new.  If we take a correlated measure, we gain some new information, but the new variable will also contain redundant information that is expressed in the covariance between the variables.

Interpreting results.  If the overall multivariate test is significant, we conclude that the respective effect (e.g., textbook) is significant.  However, our next question would of course be whether only math skills improved, only physics skills improved, or both.  In fact, after obtaining a significant multivariate test for a particular main effect or interaction, customarily one would examine the univariate F tests for each variable to interpret the respective effect.  In other words, one would identify the specific dependent variables that contributed to the significant overall effect.


  Multivariate Designs:  MANOVA/MANCOVA - Repeated Measures Designs

If we were to measure math and physics skills at the beginning of the semester and the end of the semester, we would have a multivariate repeated measure.  Again, the logic of significance testing in such designs is simply an extension of the univariate case.  Note that MANOVA methods are also commonly used to test the significance of univariate repeated measures factors with more than two levels; this application will be discussed later in this section.


  Multivariate Designs:  MANOVA/MANCOVA - Sum Scores versus MANOVA

Even experienced users of ANOVA and MANOVA techniques are often puzzled by the differences in results that sometimes occur when performing a MANOVA on, for example, three variables as compared to a univariate ANOVA on the sum of the three variables.  The logic underlying the summing of variables is that each variable contains some "true" value of the variable in question, as well as some random measurement error.  Therefore, by summing up variables, the measurement error will sum to approximately 0 across all measurements, and the sum score will become more and more reliable (increasingly equal to the sum of true scores).  In fact, under these circumstances, ANOVA on sums is appropriate and represents a very sensitive (powerful) method.  However, if the dependent variable is truly multi-dimensional in nature, then summing is inappropriate.  For example, suppose that my dependent measure consists of four indicators of success in society, and each indicator represents a completely independent way in which a person could "make it" in life (e.g., successful professional, successful entrepreneur, successful homemaker, etc.).  Now, summing up the scores on those variables would be like adding apples to oranges, and the resulting sum score will not be a reliable indicator of a single underlying dimension.  Thus, one should treat such data as multivariate indicators of success in a MANOVA.


ANOVA/MANOVA - Contrast Analysis and Post-hoc Tests

  ANOVA/MANOVA Introductory Overview - Contrast Analysis and Post hoc Tests

Why Compare Individual Sets of Means?

Usually, experimental hypotheses are stated in terms that are more specific than simply main effects or interactions.  We may have the specific hypothesis that a particular textbook will improve math skills in males, but not in females, while another book would be about equally effective for both genders, but less effective overall for males.  Now generally, we are predicting an interaction here: the effectiveness of the book is modified (qualified) by the student's gender.  However, we have a particular prediction concerning the nature of the interaction: we expect a significant difference between genders for one book, but not the other.  This type of specific prediction is usually tested via contrast analysis.

Contrast Analysis

Briefly, contrast analysis allows us to test the statistical significance of predicted specific differences in particular parts of our complex design.  It is a major and indispensable component of the analysis of every complex ANOVA design.  ANOVA/MANOVA has a uniquely flexible contrast analysis facility that allows the user to specify and analyze practically any type of desired comparison (see the Notes section for a description of how to specify contrasts).

Post hoc Comparisons

Sometimes we find effects in our experiment that were not expected.  Even though in most cases a creative experimenter will be able to explain almost any pattern of means, it would not be appropriate to analyze and evaluate that pattern as if one had predicted it all along.  The problem here is one of capitalizing on chance when performing multiple tests post hoc, that is, without a priori hypotheses.  To illustrate this point, let us consider the following "experiment."  Imagine we were to write down a number between 1 and 10 on 100 pieces of paper.  We then put all of those pieces into a hat and draw 20 samples (of pieces of paper) of 5 observations each, and compute the means (from the numbers written on the pieces of paper) for each group.  How likely do you think it is that we will find two sample means that are significantly different from each other?  It is very likely!  Selecting the extreme means obtained from 20 samples is very different from taking only 2 samples from the hat in the first place, which is what the test via the contrast analysis implies.  Without going into further detail, there are several so-called post hoc tests that are explicitly based on the first scenario (taking the extremes from 20 samples), that is, they are based on the assumption that we have chosen for our comparison the most extreme (different) means out of k total means in the design.  Those tests apply "corrections" that are designed to offset the advantage of post hoc selection of the most extreme comparisons.  ANOVA/MANOVA offers a wide selection of those tests. Whenever one finds unexpected results in an experiment one should use those post hoc procedures to test their statistical significance.

For more Introductory Overview topics, click on the topic name.

Basic Ideas

Complex Designs

Analysis of Covariance (ANCOVA)

Multivariate Designs:  MANOVA/MANCOVA

Assumptions and Effects of Violating Assumptions

See also, ANOVA/MANOVA Notes


ANOVA/MANOVA - Assumptions and Effects of Violating Assumptions

  ANOVA/MANOVA Introductory Overview - Assumptions and Effects of Violating Assumptions

Deviation from Normal Distribution

Homogeneity of Variances

Homogeneity of Variances and Covariances

Sphericity and Compound Symmetry

For more Introductory Overview topics, click on the topic name.

Basic Ideas

Complex Designs

Analysis of Covariance (ANCOVA)

Multivariate Designs:  MANOVA/MANCOVA

Contrast Analysis and Post hoc Tests

See also, ANOVA/MANOVA Notes


Assumptions and Effects of Violating Assumptions - Deviation form Normal Distribution

  Assumptions and Effects of Violating Assumptions - Deviation from Normal Distribution

Assumptions.  It is assumed that the dependent variable is measured on at least an interval scale level (see Elementary Concepts).  Moreover, the dependent variable should be normally distributed within groups.  ANOVA/MANOVA contains extensive diagnostic graphics as well as statistics to test the validity of this assumption.

Effects of violations.  Overall, the F test is remarkably robust to deviations from normality (see Lindman, 1974, for a summary).  If the kurtosis (see Basic Statistics and Tables) is greater than 0, then the F tends to be too small and we cannot reject the null hypothesis even though it is incorrect.  The opposite is the case when the kurtosis is less than 0.  The skewness of the distribution usually does not have a sizable effect on the F statistic.  If the n per cell is fairly large, then deviations from normality do not matter much at all because of the central limit theorem, according to which the sampling distribution of the mean approximates the normal distribution, regardless of the distribution of the variable in the population.  A detailed discussion of the robustness of the F statistic can be found in Box and Anderson (1955), or Lindman (1974).


  Assumptions and Effects of Violating Assumptions - Homogeneity of Variances

Assumptions.  It is assumed that the variances in the different groups of the design are identical; this assumption is called the homogeneity of variances assumption.  Remember that at the beginning of this section we computed the error variance (SS error) by adding up the sums of squares within each group.  If the variances in the two groups are different from each other, then adding the two together is not appropriate, and will not yield an estimate of the common within-group variance (since no common variance exists).  ANOVA/MANOVA contains a wide variety of statistical tests to detect violations of this assumption.

Effects of violations.  Lindman (1974, p. 33) shows that the F statistic is quite robust against violations of this assumption (heterogeneity of variances; see also Box, 1954a, 1954b; Hsu, 1938).

Special case: correlated means and variances.  However, one instance when the F statistic is very misleading is when the means are correlated with variances across cells of the design.  ANOVA/MANOVA allows you to plot a scatterplot of variances or standard deviations against the means to detect such correlations.  The reason why this is a "dangerous" violation is the following:  Imagine that you have 8 cells in the design, 7 with about equal means but one with a much higher mean.  The F statistic may suggest to you a statistically significant effect.  However, suppose that there also is a much larger variance in the cell with the highest mean, that is, the means and the variances are correlated across cells (the higher the mean the larger the variance).  In that case, the high mean in the one cell is actually quite unreliable, as is indicated by the large variance.  However, because the overall F statistic is based on a pooled within-cell variance estimate, the high mean is identified as significantly different from the others, when in fact it is not at all significantly different if one based the test on the within-cell variance in that cell alone.

This pattern -- a high mean and a large variance in one cell -- frequently occurs when there are outliers present in the data. One or two extreme cases in a cell with only 10 cases can greatly bias the mean, and will dramatically increase the variance.


  Assumptions and Effects of Violating Assumptions - Homogeneity of Variances and Covariances

Assumptions.  In multivariate designs, with multiple dependent measures, the homogeneity of variances assumption described earlier also applies.  However, since there are multiple dependent variables, it is also required that their intercorrelations (covariances) are homogeneous across the cells of the design.  ANOVA/MANOVA offers various specific tests of this assumption.

Effects of violations.  The multivariate equivalent of the F test is Wilks' lambda.  Not much is known about the robustness of Wilks' lambda to violations of this assumption.  However, because the interpretation of MANOVA results usually rests on the interpretation of significant univariate effects (after the overall test is significant), the above discussion concerning univariate ANOVA basically applies, and important significant univariate effects should be carefully scrutinized.

Special case: ANCOVA.  A special serious violation of the homogeneity of variances/covariances assumption may occur when covariates are involved in the design.  Specifically, if the correlations of the covariates with the dependent measure(s) are very different in different cells of the design, gross misinterpretations of results may occur.  Remember that in ANCOVA, we in essence perform a regression analysis within each cell to partition out the variance component due to the covariates.  The homogeneity of variances/covariances assumption implies that we perform this regression analysis subject to the constraint that all regression equations (slopes) across the cells of the design are the same.  If this is not the case, serious biases may occur.  ANOVA/MANOVA provides specific tests of this assumption, and it is advisable to look at those tests to ensure that the regression equations in different cells are approximately the same.


  Assumptions and Effects of Violating Assumptions - Sphericity and Compound Symmetry

Reasons for Using the Multivariate Approach to Repeated Measures ANOVA

In repeated measures ANOVA containing repeated measures factors with more than two levels, additional special assumptions enter the picture: The compound symmetry assumption and the assumption of sphericity.  Because these assumptions rarely hold (see below), the MANOVA approach to repeated measures ANOVA has gained popularity in recent years (both tests are automatically computed in ANOVA/MANOVA).

The compound symmetry assumption requires that the variances (pooled within-group) and covariances (across subjects) of the different repeated measures are homogeneous (identical).  This is a sufficient condition for the univariate F test for repeated measures to be valid (i.e., for the reported F values to actually follow the F distribution).  However, it is not a necessary condition.  The sphericity assumption is a necessary and sufficient condition for the F test to be valid; it states that the within-subject "model" consists of independent (orthogonal) components.  The nature of these assumptions, and the effects of violations are usually not well-described in ANOVA textbooks; in the following paragraphs we will try to clarify this matter and explain what it means when the results of the univariate approach differ from the multivariate approach to repeated measures ANOVA.

The necessity of independent hypotheses.  One general way of looking at ANOVA is to consider it a model fitting procedure.  In a sense we bring to our data a set of a priori hypotheses; we then partition the variance (test main effects, interactions) to test those hypotheses.  Computationally, this approach translates into generating a set of contrasts (comparisons between means in the design) that specify the main effect and interaction hypotheses.  However, if these contrasts are not independent of each other, then the partitioning of variances runs afoul.  For example, if two contrasts A and B are identical to each other and we partition out their components from the total variance, then we take the same thing out twice.  Intuitively, specifying the two (not independent) hypotheses "the mean in Cell 1 is higher than the mean in Cell 2" and "the mean in Cell 1 is higher than the mean in Cell 2" is silly and simply makes no sense.  Thus, hypotheses must be independent of each other, or orthogonal (the term orthogonality was first used by Yates, 1933).

Independent hypotheses in repeated measures.  The general algorithm implemented in ANOVA/MANOVA will attempt to generate, for each effect, a set of independent (orthogonal) contrasts (see the Technical Information chapter in the manual).  In repeated measures ANOVA, these contrasts specify a set of hypotheses about differences between the levels of the repeated measures factor.  However, if these differences are correlated across subjects, then the resulting contrasts are no longer independent.  For example, in a study where we measured learning at three times during the experimental session, it may happen that the changes from time 1 to time 2 are negatively correlated with the changes from time 2 to time 3:  subjects who learn most of the material between time 1 and time 2 improve less from time 2 to time 3.  In fact, in most instances where a repeated measures ANOVA is used, one would probably suspect that the changes across levels are correlated across subjects.  However, when this happens, the compound symmetry and sphericity assumptions have been violated, and independent contrasts cannot be computed.

Effects of violations and remedies.  When the compound symmetry or sphericity assumptions have been violated, the univariate ANOVA table will give erroneous results.  Before multivariate procedures were well understood, various approximations were introduced to compensate for the violations (e.g., Greenhouse & Geisser, 1959; Huynh & Feldt, 1970), and these techniques are still widely used (therefore, ANOVA/MANOVA provides those methods).

MANOVA approach to repeated measures.  To summarize, the problem of compound symmetry and sphericity pertains to the fact that multiple contrasts involved in testing repeated measures effects (with more than two levels) are not independent of each other.  However, they do not need to be independent of each other if we use multivariate criteria to simultaneously test the statistical significance of the two or more repeated measures contrasts.  This "insight" is the reason why MANOVA methods are increasingly applied to test the significance of univariate repeated measures factors with more than two levels.  We wholeheartedly endorse this approach because it simply bypasses the assumption of compound symmetry and sphericity altogether.

Cases when the MANOVA approach cannot be used.  There are instances (designs) when the MANOVA approach cannot be applied; specifically, when there are few subjects in the design and many levels on the repeated measures factor, there may not be enough degrees of freedom to perform the multivariate analysis.  For example, if we have 12 subjects and p = 4 repeated measures factors, each at k = 3 levels, then the four-way interaction would "consume" (k1)p = 24 = 16 degrees of freedom.  However, we have only 12 subjects, so in this instance the multivariate test cannot be performed.  ANOVA/MANOVA will detect those instances and only compute the univariate tests.

Differences in univariate and multivariate results.  Anyone whose research involves extensive repeated measures designs has seen cases when the univariate approach to repeated measures ANOVA gives clearly different results from the multivariate approach.  To repeat the point, this means that the differences between the levels of the respective repeated measures factors are in some way correlated across subjects.  Sometimes, this insight by itself is of considerable interest.


  ANOVA/MANOVA Notes - Specifying Univariate and Multivariate Between-Groups Designs

One-way Between-Groups ANOVA and Contrast Analysis

Multi-way Between-Groups ANOVA and Contrast Analysis

Isolated ("hanging") Control Group

For more information, see:

Specifying Within (Repeated Measures) Uni/Multivariate Designs

Multiple Dependent Measures (MANOVA)

Nested Designs and Latin Squares

Other Special Designs

Type I, II, III Sums of Squares

Analyzing Designs with Missing Cells (Type IV Sums of Squares)

Random Factors

Fixed and Changing covariates

See also, ANOVA/MANOVA Introductory Overview


  Specifying Univariate and Multivariate Between-Groups Designs - One-way Between-Groups ANOVA and Contrast Analysis

Summary.  Between-groups designs are ANOVA designs with several distinct groups of subjects (or observations).  For example, one may use three different algebra textbooks, one in each of three classes, and subsequently measure students' performance on a standardized algebra test.  The three classes would then represent three distinct groups, and if one wanted to compare their performance, a one-way between-groups analysis of variance would be specified.  Each group in this design was "exposed" to a different algebra textbook; thus, the type of algebra book used represents the between-groups factor.  Because three different textbooks were used, this between-groups factor contains three levels.

Setting up the data file.  When entering the data for this study, the user must create a data file with at least two variables.  One variable should contain students' scores on the standardized algebra test.  This variable is referred to as the dependent variable.  Another variable that needs to be included in the data file should contain code numbers or text codes that uniquely identify the group membership of each case in the data file; this variable is referred to as the independent or grouping variable.

For example, one may assign the text value Book_1 to a student if he or she was in the class in which the first algebra textbook was used; one may assign the text value Book_2 if the respective student was in the class in which the second algebra textbook was used, and one may assign the text value Book_3 if the student participated in the class in which the third algebra textbook was used.  The resulting data file may look like this:

Independent     Dependent

variable        variable

-----------     ---------

  Book_1           23

  Book_3           48

  Book_3           26

  Book_2           27

  Book_1           43

  Book_1           39

  Book_2           30

    .               .

    .               .

    .               .

In this example, the grouping variable only contains the three different text codes that the user entered in order to code the between-groups factor.  If a data file contains cases with numeric or text values for the grouping variable that were not specified in the list of valid codes, those cases are excluded from the analysis.  Note that when entering data into the file, it is not necessary to enter the subjects (cases) in any particular order.

Analyzing the design.  In order to analyze these data, one would first select the Variables option from the ANOVA/MANOVA main dialog, and specify as the between-groups factor or independent variable the variable number 1.  Then variable 2 would be specified as the dependent variable.  Next, one would specify (via option Codes) the independent variable codes as entered in the data file.  Note that it is not necessary to explicitly enter into the codes window all integer codes representing the text values; you could also simply click OK at this point and let the program select all codes by default.

After clicking OK the program will process the data and display the results dialog.

Testing planned comparisons.  Planned comparisons are useful if one wants to compare specific groups in the design.  The program expects the user to enter a set of contrasts that identifies the desired comparisons.  If, in the present example, one wants to compare the group taught with the first algebra textbook (i.e., group 1) with the group that was taught with the third algebra textbook (i.e., group 3) and ignore group 2 in this particular comparison, one set of contrasts would be entered, namely 1, 0, and -1.

Rules for generating contrasts.  The rules for generating these contrasts are as follows.

(1)	The contrast must have as many coefficients as there are levels for the respective factor.

(2)	Groups to be omitted in the contrast are given a 0 (zero).

(3)	Groups that are to be compared against each other are assigned positive or negative integer values, respectively; however, it is important that the sum of such contrast coefficients is equal to zero.

(4)	Groups that are to be collapsed in the contrast are assigned identical integer values.

For example, if one wanted to compare group 1 with groups 2 and 3 combined, the proper set of contrast coefficients would be 2, -1, -1.  If one wanted to compare group 2 against groups 1 and 3 combined, the proper contrast would be 1, -2, and 1.  If one wanted to compare group 2 with group 3 (ignoring group 1), the proper contrast would be 0, 1, and -1.

Multivariate analysis of variance.  The discussion so far has been restricted to univariate analysis of variance.  However, if one selects multiple dependent variables on the ANOVA/MANOVA dialog, then a multivariate analysis of variance will automatically be performed (unless the multiple dependent variables are specified to be levels of repeated measures factors).  For example, if in the previous example students' algebra ability had been measured with three tests rather than just one, the data file could look like this:

Independent    Dependent variables

variable

-----------    -------------------

  Book_1          23   24   28

  Book_3          48   43   40

  Book_3          26   38   21

  Book_2          27   29   35

  Book_1          43   42   42

  Book_1          39   40   31

  Book_2          30   29   27

    .              .    .    .

    .              .    .    .

    .              .    .    .

In order to perform a multivariate analysis of variance (MANOVA) of the three test scores, enter all three variables into the dependent variable list.  When subsequently testing the main effect or planned comparisons, both multivariate test results (for all dependent variables simultaneously) and the results of the univariate tests (testing one variable at a time) will be calculated.

The manner in which planned comparisons are specified is basically identical to the univariate case.  However, when entering contrast coefficients for a planned comparison, the user also has the option to enter contrasts for the dependent variables.  Click on the Options button next to the Planned comparisons button (see Results Dialog) and select Contrasts for dependent variables; the program will then allow you to specify contrasts for the dependent variables.  For example, the user may choose to ignore some of the dependent variables in the comparison by assigning 0's (zeros) to them when specifying the contrast.


  Specifying Univariate and Multivariate Between-Groups Designs - Multi-way Between-Groups ANOVA and Contrast Analysis

Summary.  When an analysis of variance design contains more than one between-groups factor, the design is referred to as a multi-way or multi-factor between-groups design.  For example, one may try three different algebra textbooks (between-groups factor number 1), and, in addition, evaluate gender differences (between-groups factor number 2).  The dependent variable would be students' scores on a standardized algebra test.

Setting up the data file.  In addition to the dependent variable (scores on the standardized algebra test), two independent or grouping variables must be included in the data file.  One independent or grouping variable should contain code numbers or text values that uniquely identify to which textbook group the respective subject belongs (i.e., which algebra textbook was used to teach the respective student); the other independent or grouping variable should contain code numbers or text values that uniquely identify the respective student's gender.  The data file may look like this:

Independent variables   Dependent

                        variable

---------------------   ---------

  Book_1    Male           23

  Book_3    Female         48

  Book_3    Male           26

  Book_2    Female         27

  Book_1    Male           43

  Book_1    Male           39

  Book_2    Female         30

    .         .             .

    .         .             .

    .         .             .

The first variable (column) contains the values Book_1, Book_2, and Book_3.  This variable is the independent or grouping variable that uniquely identifies which algebra textbook was used.  The second variable (column) contains only the values Male and Female.  This variable is the independent or grouping variable that uniquely identifies students' gender.  The third variable (column) contains students' scores on the standardized algebra test.

Specifying the design.  The design that needs to be specified is a 3 (textbook) by 2 (gender) between-groups analysis of variance design.  From the ANOVA/MANOVA startup panel, specify variables 1 and 2 as the independent variables (between-groups factors), and variable 3 as the dependent variable.

Testing main effects and interactions.  In this design, there are three effects that can be tested:  The interaction effect between students' gender and the type of textbook used, the main effect for textbook, and the main effect for students' gender.  If you use option All effects or Means/Graphs from the Results Dialog, all effects will be computed.  If you want to examine the effects in detail, use option Specific effect/means from the Results Dialog and specify the desired effect.

Testing planned comparisons.  Planned comparisons are specified in exactly the same manner as in one-way between-groups ANOVA.  However, instead of specifying a set of contrasts for just one factor, one has to specify sets of contrasts for each factor in the design.

In addition to the rules for specifying contrasts that were introduced in the discussion of one-way between-groups ANOVA designs, it is also possible (and often necessary) to enter contrast coefficients that do not sum to zero (0).  For example, in order to specify a set of contrasts that is equivalent to the test of the main effect of students' gender, one could enter the following set of contrasts:

For factor 1 (type of algebra text):

1    1    1

For factor 2 (gender):

1   -1

Thus, all levels of the first factor (type of algebra textbook) are given the same weight, whereas the contrast coefficients for the second factor contrast males versus females.

There are many specific comparisons that may be "composed".  For example, if one wants to test the main effect for the type of algebra text, but only for males (level 1 of the gender factor), one may enter the following set of contrasts:

For factor 1 (type of algebra text) the following two contrasts:

1     0    -1

0     1    -1

For factor 2 (gender):

1     0

For factor 1, two independent contrasts were entered that will be tested simultaneously.  These two contrasts represent an exhaustive set of contrasts, i.e., they simultaneously compare all levels of factor 1 (omnibus set of contrasts).  For factor 2, one contrast was entered that assigns a zero to the second level of the gender factor (females).  Thus, females will be ignored, and the resulting analysis is a test of the main effect of textbook, for males only.

In a similar manner, more complex contrasts may be specified in higher order (three-way, four-way, etc.) designs (e.g., interactions within one level of another variable).  It is recommended to refer to a specialized ANOVA textbook (e.g., Lindman, 1974; Keppel, 1973; Winer, 1962, 1971) to learn more about how to specify complex contrasts via contrast coefficients (e.g., simple effects, linear and nonlinear effects and interactions).  Note that the dialog window for entering contrast coefficients (Specify Contrasts for this Factor) also contains options for specifying appropriate predefined contrasts; of particular interest are often the so-called Polynomial contrasts which let you test linear and nonlinear trends across the levels of the respective factor.

Multivariate multi-way between-groups ANOVA (MANOVA).  The specifications for a multi-way between-groups ANOVA with multiple dependent variables (MANOVA) are identical to those necessary for a univariate analysis.  Independent or grouping variables must be specified which contain code numbers to uniquely identify the group membership of each case in the data file.  If more than one dependent variable is specified for the dependent variable list, a multivariate analysis of variance will automatically be performed (unless the dependent variables can be interpreted as the levels of repeated measures factors).  By default, univariate tests are also performed for each dependent variable in the list.

The manner in which planned comparisons are specified is basically identical to the univariate case.  However, when entering contrast coefficients for a planned comparison, the user also has the option to enter contrasts for the dependent variables.  Click on the Options button next to the Planned comparisons button (see Results Dialog) and select Contrasts for dependent variables; STATISTICA will then allow you to specify contrasts for the dependent variables.  For example, the user may choose to ignore some of the dependent variables in the comparison by assigning 0's (zeros) to them when specifying the contrast.


  Specifying Univariate and Multivariate Between-Groups Designs - Isolated ("hanging") Control Group

Sometimes, experimental designs require the inclusion of control groups that did not receive any treatment.  For example, imagine an experimental test of the effectiveness of two different drugs (factor 1) for treating infections with two different strains of a particular virus (factor 2).  In the experiment, two groups of laboratory animals were infected with one of the two types of viruses, and treated with one of the two drugs.  The primary dependent variable is the animals' performance on a learning task, e.g., after how many trials the animal learns to distinguish reliably between different geometric shapes.

In this experiment it may be desirable to compare the performance of the animals in the different experimental conditions with the performance of animals that were not affected with any virus and not exposed to any drug.  Without this comparison, the experiment could be described as a 2 (type of drug) by 2 (strain of virus) experimental design.  Adding to the experimental design a group of animals that were not exposed to any level of any of the independent variables means adding an isolated or hanging control group.  The resulting design could be described as a 2 by 2 design with a "hanging control group."

Setting up the data file.  The file containing the data from the experiment in this example should be arranged as follows (note that, for simplicity, we are not using text values in the coding variable):

Independent variables   Dependent

                        variable

---------------------   ---------

      1       1            45

      2       1            29

      9       9            35

      2       2            38

      2       1            20

      9       9            26

      1       1            25

      2       1            39

      1       2            37

      1       2            34

      9       9            25

The first variable (column) contains the codes that identify which one of two drugs was administered (codes 1 and 2).  The second variable (column) contains codes that identify with which one of the two viruses the respective animal had been infected (codes 1 and 2).  Both variables also contain the code number 9.  This is the code number that was entered for both independent variables to indicate that the respective case "belongs" to the isolated control group.

In general, an isolated control group must be identified by one unique code number that is entered for all independent variables in order to identify that a case belongs to the isolated control group.

Specifying the design.  When specifying this example design on the ANOVA/MANOVA Startup Panel, one would first specify the 2 by 2 between-groups design as usual.  As the independent variable codes, 1 and 2 would be entered.  Then click on the Isolated control group button to specify the code number that was used to uniquely identify the cases that belong to the isolated control group (i.e., 9 in this example) is entered.

The test of main effects and interactions will proceed as usual, i.e., as if a simple 2 by 2 ANOVA design was specified.  However, the sum of squares for the error term (and the degrees of freedom for the error term) will be estimated based on the four experimental groups in the design and the isolated control group (i.e., pooled within-group variance across all groups).

In order to see the mean(s) for the isolated control group, use the Specific effect option on the Results dialog and select the test of the highest order interaction between the factors (i.e., the two-way interaction in the present example); after exiting the Scrollsheet with the means for the part of the design that is completely crossed, the program will display the mean(s) for the isolated control group.

Planned comparisons.  To evaluate differences between the isolated control group and the other groups in the design, one must enter an appropriate set of contrast vectors; that is, rather than entering contrasts factor by factor separately, we must enter contrast coefficients for all groups together.  Click on the Options button next to the Planned comparison button (see Results Dialog), and on the subsequent dialog set the Together (contrast vectors) radio button.  Then select Planned comparisons; the isolated control group is referred to (i.e., "weighted") by the last contrast coefficient that is entered.  For example, if in the present example one wanted to compare the isolated control group with all other groups in the experimental design, the proper set of contrasts (entered as one vector or set, i.e., all coefficients are entered together) would be:

Factor 1, level:       1   1   2   2
Factor 2, level:       1   2   1   2
                       -------------
Enter these
Contrast Coefficients: 1   1   1   1   -4

If one wanted to compare the performance of animals that were treated with the first drug (level 1 of the first independent variable) with the performance of animals in the isolated group, the set of coefficients would look like this:

Factor 1, level:       1   1   2   2
Factor 2, level:       1   2   1   2
                       -------------
Enter these
Contrast Coefficients: 1   1   0   0   -2

If one wanted to compare the performance of animals that were infected with the first virus (level 1 of the second independent variable) and treated with the second drug (level 2 of the first independent variable) to the performance of animals in the isolated control group, the set of coefficients would look like this:

Factor 1, level:       1   1   2   2

Factor 2, level:       1   2   1   2

                       -------------

Enter these

Contrast Coefficients: 0   0   1   0   -1

In general, when entering a set of contrasts all at once, the program will assign contrast coefficients to subsequent levels of factors; the fastest moving (changing) levels are those of the last factor that was specified, the second fastest moving (changing) levels are those of the next to the last factor, and so on.  The coefficient that refers to the isolated control group is always entered as the last one.


  ANOVA/MANOVA Notes - Specifying Within-Subjects (Repeated Measures) Univariate and Multivariate Designs

One-way Within-Subjects (Repeated Measures) ANOVA

One-way Within-Subjects (Repeated Measures) ANOVA with Multiple Dependent Measures (MANOVA)

Multi-Way Within-Subjects (Repeated Measures) ANOVA Designs

Multivariate (MANOVA) Multi-Way Within-Subjects (Repeated Measures) Designs

Between-Within Univariate (ANOVA) and Multivariate (MANOVA) Designs

For more information, see:

Specifying Between Uni/Multivariate Designs

Multiple Dependent Measures (MANOVA)

Nested Designs and Latin Squares

Other Special Designs

Type I, II, III Sums of Squares

Analyzing Designs with Missing Cells (Type IV Sums of Squares)

Random Factors

Fixed and Changing covariates

See also, ANOVA/MANOVA Introductory Overview


Specifying Within-Subjects Univariate and Multivariate Designs - One-way Within-Subjects ANOVA

  Specifying Within-Subjects (Repeated Measures) Univariate and Multivariate Designs - One-way Within-Subjects ANOVA

Often, one wants to administer the same test to the same subjects repeatedly over a period of time or under different circumstances.  In essence, one is interested in examining differences within each subject, for example, subjects' improvement over time.  Such designs are referred to as within-subjects designs or repeated measures designs.

For example, imagine that one wants to monitor the improvement of students' algebra skills over three months of instruction.  A standardized algebra test is administered after one month (level 1 of the repeated measures factor), and comparable tests are administered after two months (level 2 of the repeated measures factor) and after three months (level 3 of the repeated measures factor).  Thus, the repeated measures factor (Time) has three levels.

Setting up the data file.  In order to analyze such a data set, one needs to perform a within-subjects (or repeated measures) analysis of variance.  First, a data file should be created that contains the test scores for all subjects; this file should be arranged as follows:

              Test administered after

          -------------------------------

          1 Month    2 Months    3 Months

          -------    --------    --------

Case 1       24         26          28

Case 2       30         30          32

Case 3       30         29          28

Case 4       30         29          34

Case 5       35         36          32

  .          .          .           .

  .          .          .           .

  .          .          .           .

The first variable (column) contains subjects' scores on the algebra test after one month of instruction, the second variable (column 2) contains the respective subjects' scores on the algebra test after two months of instruction, and variable 3 (column 3) contains the respective subjects' scores after three months of instruction.

Specifying the design.  In order to analyze this data set, one would first specify variables 1 to 3 as the dependent variable list (leave the independent variable list empty).  Next one needs to specify the Repeated measures (within-SS) design.  After clicking on that button, specify one repeated measures factor with three levels (the default in this case).

Testing effects.  Effects involving repeated measures factors are tested in exactly the same manner as in between-groups ANOVA.  If a repeated measures factor has more than two levels, then there are two alternative ways of assessing the significance of effects involving that factor.  The traditional way (see Winer, 1962, 1971) is to perform a univariate test; however, in recent years it has become common practice to use multivariate analysis of variance to analyze such designs.  The advantage of the latter approach is discussed in the Introductory Overview  section; in short, the multivariate approach requires less restrictive assumptions.  In practice, the two approaches usually yield similar results, unless the changes (differences) across the levels are correlated with each other across subjects.  In our example, this would be the case if students' improvement from 1 to 2 months is correlated with their improvement from 2 to 3 months.

In any event, it is prudent to carefully evaluate the univariate and multivariate solutions.  The second example in this ANOVA/MANOVA chapter of the manual presents data where the univariate and multivariate approach to repeated measures ANOVA yield discrepant results; that example also discusses how to locate the source of the discrepancy.

Testing planned comparisons.  The user can test planned comparisons between particular levels of the repeated measures factor in exactly the same manner as one would test planned comparisons in between-groups designs.  After choosing Planned comparisons from the results dialog, the user is asked to enter a set of contrast coefficients.

The rules for generating contrast coefficients are as follows.

(1)  The contrast must have as many coefficients as there are levels for the respective factor.

(2)  Levels that are to be omitted in the contrast are assigned a 0 (zero).

(3)  Levels that are to be compared against each other are assigned positive or negative integer values; however, it is important that the sum of such contrasts is equal to zero.

(4)  Levels that are to be collapsed are assigned identical integer values.

Referring back to the example, if one wanted to compare the students' performance on the algebra test after one month of instruction with their performance after three months of instructions, the following contrast coefficients would be appropriate:

          1    0    -1

If one wanted to compare subjects' performance after three months of instruction with their performance after one and two months of instruction combined, one would enter the coefficients:

          -1    -1    2

Example 2 in the Examples section in the manual provides an illustration of how to specify and interpret contrast coefficients.


Specifying Within-Subjects Univariate and Multivariate Designs - One-way Within-Subjects ANOVA

  Specifying Within-Subjects (Repeated Measures) Univariate and Multivariate Designs - One-way Within-Subjects ANOVA

One-way Within-Subjects (Repeated Measures) ANOVA with Multiple Dependent Measures (MANOVA)

If, in the example described above, one had administered two different tests of algebra skills at each time, it would be appropriate to perform a multivariate analysis of variance with repeated measures.

Setting up the data file.  The data file could be arranged like this:

           Test administered after

    -------------------------------------

    1 Month       2 Months       3 Months

    --------      --------       --------

      Test          Test           Test

     1     2       1     2        1     2

    --    --      --    --       --    --

    24    30      26    34       28    28

    30    32      30    28       32    34

    30    27      29    28       28    33

    30    28      29    26       34    35

    35    25      36    27       32    36

    .     .       .     .        .     .

    .     .       .     .        .     .

    .     .       .     .        .     .

In this example, the first variable (first column) contains the data for the first test that was administered after one month of instruction, the second variable (second column) contains the respective subjects' scores on the second test that was administered after one month of instruction.  The third variable contains the respective subjects' scores on the first test after two months of instruction, the fourth variable contains subjects' scores on the second test after two months of instruction, etc.

Specifying the design.  In order to analyze these data as a one-way repeated measures MANOVA design with multiple dependent variables (two tests), all variables (i.e., 1-6) would be selected into the dependent variable list (via option Variables on the startup panel).  Then the Repeated measures (within SS) design would be specified as before, i.e., one repeated measures factor with three levels.

In general, STATISTICA will cycle through the list of dependent variables and attempt to divide it evenly.  The assignment of variables to levels of the repeated measures factor is determined by the order in which dependent variables appear in the dependent variable list, not by the order in which variables were entered into the file.  For example, imagine that the data in the above example were entered into a data file in the following manner:

      Test 1                Test 2

 -----------------     -----------------

 Test administered     Test administered

   after month           after month

    1   2   3             1   2   3

    --  --  --            --  --  --

    24  26  28            30  34  28

    30  30  32            32  28  34

    30  29  28            27  28  33

    30  29  34            28  26  35

    35  36  32            25  27  36

    .   .   .             .   .   .

    .   .   .             .   .   .

    .   .   .             .   .   .

In this case, the data were entered such that the first variable contains the scores for the first test after one month of instruction, the second variable contains the scores for the first test after two months of instruction, the third variable contains the scores for the first test after three months of instruction, the fourth variable contains the scores for the second test after one month of instruction, the fifth variable contains the scores for the second test after two months of instruction, and the sixth variable contains the scores for the second test after three months of instruction.  When specifying the dependent variable list, the variables have to be "reordered," i.e., the user should enter 1 4 2 5 3 6 as the dependent variable list, in exactly this order.  The within-subjects design can then be specified as before.


Specifying Within-Subjects Univariate and Multivariate Designs - Multi-way Within-Subjects ANOVA

  Specifying Within-Subjects (Repeated Measures) Univariate and Multivariate Designs - Multi-way Within-Subjects ANOVA

Summary.  In experimental designs, it is not uncommon to include more than one repeated measures factor.  Example 2 in the Example section of the manual describes such a study.  For example, in a memory experiment one may compare subjects' recall of words that were presented at the beginning of a list of words, in the middle of the list, and at the end of the list (first repeated measures factor with three levels); in addition, the words either contained four letters or five letters (second repeated measures factor with two levels); finally, the words were either meaningful words in the English language, or were not meaningful (third repeated measures factor with two levels).  The resultant design is a 3 (position of words) by 2 (length of words) by 2 (meaningful vs. nonsense words) ANOVA design where all factors are repeated measures factors.

Setting up the data file.  Let us assume that the data were entered into a file as follows:

Rep. measures               Level:

  factor:

-------------      -----------------------

1 (Position)          1       2       3

                   ------- ------- -------

2 (Length)          1   2   1   2   1   2

                   --- --- --- --- --- ---

3 (Meaning)        1 2 1 2 1 2 1 2 1 2 1 2

                   - - - - - - - - - - - -

Subject 1          9 4 3 4 3 4 5 4 3 4 5 4

Subject 2          7 4 3 4 6 4 3 7 6 5 4 3

Subject 3          6 5 7 8 7 6 8 5 6 4 5 2

   .               . . . . . . . . . . . .

   .               . . . . . . . . . . . .

   .               . . . . . . . . . . . .

The first variable in the data file contains the data for the first level of all repeated measures factors.  The second variable contains the data for the second level of the third repeated measures factor, and the first levels of the first and second repeated measures factors, and so on.

Specifying the design.  In order to specify the design for the example data, one would first select all variables into the dependent variable list, in exactly the same order in which the variables appear in the file (in this example the variables do not have to be reordered); i.e., enter 1-12 into the dependent variable list selection window.  Then specify the Repeated measures (within SS) design as follows:  Specify three repeated measures factors.  First specify the factor Position with 3 levels, then specify the factor Length with 2 levels, and then specify the factor Meaning with 2 levels.

In general, the program will assign variables to levels of the repeated measures factors in the following manner:  The program will "cycle" through the list of dependent variables and assign the variables to consecutive levels of the repeated measures factors.  In this procedure, the fastest "moving" (changing) levels are those of the repeated measures factor that was specified last; the next-fastest moving (changing) levels are those of the factor that was specified next to the last, and so on.  When the program cycles through the list of dependent variables, the assignment of variables to levels is determined by the order in which dependent variables appear in the list of dependent variables (not by the order in which variables appear in the file).  For example, if a 2 x 2 x 3 repeated measures ANOVA is specified, the program would assign consecutive variables from the dependent variable list to levels of repeated measures factors in the following manner:

Rep. measures                Level:

  factor:

--------------------------------------------------

1st Factor:          1                   2

             -----------------   -----------------

2nd Factor:     1         2         1         2

             -------   -------   -------   -------

3rd Factor:  1  2  3   1  2  3   1  2  3   1  2  3

             -  -  -   -  -  -   -  -  -   -  -  -

Position in

dependent

var. list:   1  2  3   4  5  6   7  8  9  10 11 12

Note that the last row of numbers refers to the position of the respective dependent variable in the list of dependent variables (not the position of the variable in the file).  Thus, when specifying complex multi-way within-subjects designs, there are two things that determine how variables are assigned to levels of the repeated measures factors:  (1) the order in which repeated measures factors are specified, and (2) the order in which dependent variables are specified in the dependent variable list.

Examining specific effects.  Specific effects (option Specific effect/means on the results dialog) are specified in the usual manner.  Referring back to the example, in order to specify the three-way interaction between all three factors, click on the Specific effect/means button and select all three factors.  In order to specify the two-way interaction between the first and the third factor, select those two factors.  In order to test the main effect for the second factor, only select the second factor, and so on.  Again, the user has the choice of computing the multivariate or univariate test (or both) when evaluating effects that involve repeated measures factors with more than two levels (use Output options to determine the detail of reported results).

Testing planned comparisons.  Planned comparisons can be performed in exactly the same manner as in between-groups designs, that is, the program expects the user to enter a set of contrast coefficients.  It is usually easier to enter these contrasts separately for each factor rather than together for all effects.  In general, the same rules introduced for the one-way repeated measures ANOVA apply when specifying contrasts for multi-way repeated measures designs.  However, in addition it is admissible (and often necessary) to enter contrast coefficients for a factor that do not sum to zero (0).  Referring back to the example of a 3 x 2 x 2 repeated measures design, if one wanted to evaluate the interaction of the second and third factor, but only for the first level of the first factor, the following coefficients would be entered:

Factor 1 (Position):  1  0  0

Factor 2 (Length)  :  1 -1

Factor 3 (Meaning) :  1 -1

In this case, the second and third level of the first repeated measures factor will be ignored, and the interaction between factors 2 and 3 will be evaluated only within level 1 of the first repeated measures factor.  If one wanted to evaluate the main effect for Meaning (third factor) within the first level of the first repeated measures factor, the following set of coefficients should be entered:

Factor 1 (Position):  1  0  0

Factor 2 (Length)  :  1  1

Factor 3 (Meaning) :  1 -1

Again, the second and third level of the first repeated measures factor will be ignored.  Both the first and second level of the second repeated measures factor will be "weighted" equally, i.e., not contrasted against each other, while the two levels of the third repeated measures factor will be compared.

If one wanted to evaluate the interaction of the first two factors within the first level of the third factor, the appropriate set of coefficients would be:

Factor 1 (Position):  1  0 -1

               and :  0  1 -1

Factor 2 (Length)  :  1 -1

Factor 3 (Meaning) :  1  0

Note that in this set of contrasts, one has to specify two sets of coefficients (an omnibus set of contrasts) for the first repeated measures factor because the first factor contains three levels, allowing for two independent comparisons.  A detailed discussion of contrast analysis and the issue of independence (orthogonality) is beyond the scope of this introduction.  The user should refer to an ANOVA textbook (e.g., Lindman, 1978; Winer, 1962, 1971) to learn more about how to set up contrasts to test specific hypotheses (e.g., linear and nonlinear trends, with equal or unequal spacing, etc.).  Note that the dialog window for entering contrast coefficients also contains options for specifying appropriate predefined contrasts; of particular interest are often the so-called Polynomial contrasts which let you test linear and nonlinear trends across the levels of the respective factor.


Specifying Within-Subjects Univariate and Multivariate Designs - Multi-way Within-Subjects ANOVA

  Specifying Within-Subjects (Repeated Measures) Univariate and Multivariate Designs - Multi-way Within-Subjects ANOVA

Multivariate (MANOVA) Multi-Way Within-Subjects (Repeated Measures) Designs

As described earlier, the program will "cycle" through the list of dependent variables in order to assign dependent variables to levels of the repeated measures factor.  If there are more variables in the dependent variable list than the total number of levels, a multivariate analysis of variance will automatically be performed.  The program will assign variables to consecutive levels of repeated measures factors as before, however, for each level of each repeated measures factor, the program will cycle through the number of dependent variables and assign them to one of the multiple dependent measures.

For example, if one wants to specify a 2 x 3 repeated measures ANOVA with 2 dependent variables, then the program would assign consecutive variables in the dependent variable list as follows:

Rep. measures                 level:

   factor:

-------------   ----------------------------------

First:                  1                 2

                ----------------  ----------------

Second:           1     2     3     1     2     3

                ----  ----  ----  ----  ----  ----

Dep. Var.       1  2  1  2  1  2  1  2  1  2  1  2

                -  -  -  -  -  -  -  -  -  -  -  -

Position in dep.

var. list:      1  2  3  4  5  6  7  8  9 10 11 12

Again, please note that what is important is the position of the dependent variables in the list of dependent variables, not their position in the data file.


Specifying Within-Subjects Univariate and Multivariate Designs - Between-Within Univariate ANOVA

  Specifying Within-Subjects (Repeated Measures) Univariate and Multivariate Designs - Between-Within Univariate ANOVA

Between-Within Univariate (ANOVA) and Multivariate (MANOVA) Designs

Summary.  In experimental research it is very common to administer different treatments to different groups of subjects (between-groups factors), and then to monitor a dependent variable over time or under different circumstances (within-subjects or repeated measures factor).  This type of design combines repeated measures factors and between-groups factors into a single design.

For example, a researcher may infect laboratory animals with two types of viruses (between-groups factor 1 with 2 levels) and then administer two different drugs (between-groups factor 2 with 2 levels).  Then the researcher may monitor the animals' activity levels 1 day after the drugs were administered, after 2 days, and after 3 days (repeated measures factor Time with 3 levels).  The resulting design is 2 x 2 x 3 ANOVA design, where the third factor is a repeated measures factor.

Setting up the data file.  To specify this design, the user must separately specify the between-groups part of the design and the within-subjects part of the design.  For example, imagine that data were entered into a data file as follows:

                Variable:

           -------------------

           1  2    3    4    5

           -  -   --   --   --

Case 1     1  1   23   34   32

Case 2     1  2   40   43   45

Case 3     2  2   23   24   23

Case 4     2  1   54   34   54

Case 5     1  2   23   24   25

Case 6     2  1   34   23   34

  .        .  .   .    .    .

  .        .  .   .    .    .

  .        .  .   .    .    .

The first two variables (columns) are the independent or grouping variables that uniquely identify to which experimental group the respective case (laboratory animal) "belongs" (to simplify matters, integer codes rather than text values are shown here).  Variables 3 to 5 contain the dependent variables, i.e., the activity measures that were obtained after one, two, and three days.  Thus, variable 3 contains the data for the first level of the repeated measures factor, variable 4 contains the data for the second level of the repeated measures factor, and variable 5 contains the data for the third level of the repeated measures factor.

Specifying the design.  In order to specify the 2 x 2 x 3 between-within design, use option Variables (on the startup panel) to select variables 1 and 2 as the independent variables, and variables 3, 4, and 5 as the dependent variables.  Next, select the independent variable codes for the independent variables; in this example, the codes 1 and 2 were used to specify with which virus the respective animal had been infected (independent variable 1), and with which drug it had been treated (independent variable 2).

The between-groups part of the ANOVA design is now completely specified.  Next specify the Repeated measures (within ss) part of the design, that is, specify one repeated measures factor (you may call it Time) with 3 levels.

In general, one can specify between-within ANOVA designs of any complexity by separately specifying the between-groups part of the design and the within-subjects part of the design.

Examining specific effects and testing planned comparisons.  On the Results dialog you may select specific effects (Specific effect/means) and Planned comparisons in exactly the same manner as in multi-way between-groups designs or in within-subjects designs.  Between-groups factors and within-subjects (repeated measures) factors are listed consecutively.


  ANOVA/MANOVA Notes - Multiple Dependent Measures (MANOVA)

ANOVA/MANOVA will automatically perform a multivariate analysis of variance when multiple dependent variables are specified (i.e., dependent variables that are not levels of repeated measures factors).  For example, if the user specified a between-groups design with three dependent variables, a multivariate analysis of variance (MANOVA) with three dependent variables would automatically be performed.  However, if in addition, a within-subjects factor with three levels is specified, then a univariate analysis of variance would be performed because the three dependent variables would be interpreted as representing the levels of the repeated measures factor.  If six dependent variables were specified, then once again a multivariate analysis of variance would be performed, with 2 dependent variables for each level of the repeated measures factor.

In general, ANOVA/MANOVA will divide the number of dependent variables that are specified by the product of numbers of levels of all repeated measures factors.  If the result of this division is greater than 1, then a multivariate analysis of variance is performed (if the result of the division is not an integer value, then an error message will be displayed).  For example, if a design is specified with 2 repeated measures factors, the first with 3 levels and the second with 2 levels, then at least 6 dependent variables must be specified (since there is a total of 2 x 3 = 6 levels).  However, if the user specifies 12 dependent variables, then the program will perform a multivariate analysis of variance with 2 dependent variables (since 12 divided by 6 is equal to 2).

In all other respects, the analysis of designs with multiple dependent variables (i.e., calculation of major effects and planned comparisons) proceeds in exactly the same manner as in the univariate case.  However, when entering contrast coefficients for a planned comparison, the user also has the option of entering contrasts for the dependent variables.  For example, the user may choose to ignore some of the dependent variables in the comparison by assigning 0's (zeros) to them when specifying the contrast.  In order to specify contrasts for the dependent variables, set the respective button on the Planned comparisons Options dialog.

Refer to the Notes section (repeated measures) for more detailed examples of how to specify multivariate repeated measures designs.

For more information, see:

Specifying Between Uni/Multivariate Designs

Specifying Within (Repeated Measures) Uni/Multivariate Designs

Nested Designs and Latin Squares

Other Special Designs

Type I, II, III Sums of Squares

Analyzing Designs with Missing Cells (Type IV Sums of Squares)

Random Factors

Fixed and Changing covariates

See also, ANOVA/MANOVA Overview


  ANOVA/MANOVA Notes - Nested Designs

Simple Between-Groups Nested Designs

Simple Within-Subjects (Repeated Measures) Designs

Latin Squares, Greco-Latin Squares, Generalized Latin Squares

For more information, see:

Specifying Between Uni/Multivariate Designs

Specifying Within (Repeated Measures) Uni/Multivariate Designs

Multiple Dependent Measures (MANOVA)

Other Special Designs

Type I, II, III Sums of Squares

Analyzing Designs with Missing Cells (Type IV Sums of Squares)

Random Factors

Fixed and Changing covariates

See also, ANOVA/MANOVA Introductory Overview


  ANOVA/MANOVA Notes Nested Designs - Simple Between-Groups Nested Designs

In some studies it is not feasible to implement a complete factorial design, i.e., a design where each level of each factor co-occurs with each level of all others (the term factorial design was first introduced by Fisher, 1935a).  For example, suppose one wanted to evaluate the effects of 4 different fertilizers (between-groups factor 1 with 4 levels) on the growth of corn.  Imagine that the researcher used two fertilizers on each one of two different fields (between-groups factor 2 with 2 levels).  The resulting design would be a 4 (Fertilizer) by 2 (Field) design; however, because only two levels of the first factor occur within each of the two levels of the second factor, the design is actually a 4 (nested within factor 2) by 2 design.

In general, designs are nested (the term was first used by Ganguli, 1941) when only some levels of a factor occur within the levels of another factor.  In a sense, the levels of one factor are "placed" within the levels of the other factor like "eggs into a nest," hence the name "nested" design.

To return to the example, the data for this design may be entered as follows:

Fertilizer   Field          Growth

                     (dependent variable)

----------   -----   --------------------

    1          1              24

    1          1              34

    2          1              25

    2          1              28

    3          2              45

    3          2              42

    4          2              33

    4          2              31

Let us assume that the researcher took two samples of corn from each field and measured their size (on some arbitrary scale).  Each row in the data set represents the data for one of those samples.  The first variable (column) contains code numbers that uniquely identify what fertilizer was used for the respective corn sample, therefore this is an independent or grouping variable.  The second variable (columns) contains codes that uniquely identify the field from which the respective corn sample was taken; thus this is the second independent or grouping variable.

Note that levels 1 and 2 of the first between-groups factor (Fertilizer) only appear within the first level (i.e., within level 1) of the second factor (Field), whereas levels 3 and 4 of the first factor only appear within level 2 of the second factor.  Therefore, the first factor (Fertilizer) is nested within the second factor (Field).

Specifying the design.  In order to specify this design, first select the dependent variable (variable 3) and the independent or grouping variables (variables 1 and 2) as usual (in the Startup Panel.  When specifying the code values that were used to indicate the four levels of the first between-groups factor, enter 1-4, i.e., specify the four values that were actually used in the data file.

Next, click on the Nested design button.  For each factor, specify (1) whether or not the factor is nested, (2) in which other factors the respective factor is nested, and (3) how many levels the respective factor has within the factors in which it is nested.  In this example, the first factor is nested in only one other factor; namely, it is nested in factor 2.  There are 2 levels of the first factor within each level of the second factor; therefore, enter 2 in the respective field.

Testing main effects and interactions.  Because of nesting, interactions of the nested factor with the factor(s) in which it is nested cannot be evaluated.  Thus, in the present example one cannot test the hypothesis that the type of fertilizer and the particular field interact in their effect on the size of corn:  It is simply impossible to determine, based on the current study, to what size the corn would have grown on field 1 (i.e., level 1 of the Field factor) had the third and fourth fertilizer (i.e., level 3 and level 4 of the Fertilizer factor) been used.


ANOVA/MANOVA Notes Nested Designs - Simple Within-Subjects (Repeated Measures) Designs

  ANOVA/MANOVA Notes Nested Designs - Simple Within-Subects (Repeated Measures) Designs

In some instances, one may want to analyze designs where a repeated measures factor is nested in other repeated measures factors.  For example, one may administer to subjects 4 different memory tests (repeated measures factor 1 with 4 levels) over 2 days (repeated measures factor 2 with 2 levels).  If 2 memory tests were administered on the first day, and the 2 remaining tests on the second day, one may consider the 4 levels of the first repeated measures factor to be nested in the 2 levels of the second repeated measures factor.  In the present example, the data file may be arranged as follows:

Repeated measures factor:

------------------------------------------

Factor 1 (Test), level    1    2    3    4

Factor 2 (Day) , level    1    1    2    2

                         --   --   --   --

Case 1                   23   24   23   25

Case 2                   25   23   25   28

Case 3                   29   38   37   29

Case 4                   48   47   48   47

  .                      .    .    .    .

  .                      .    .    .    .

  .                      .    .    .    .

The first variable (column) contains the data for the first level of the first repeated measures factor and the first level of the second repeated measures factor.  The second variable (column) contains the data for the second level of the first repeated measures factor and the first level of the second repeated measures factor, and so on.  Note that in this example, levels 1 and 2 of the first repeated measures factor are only paired with level 1 of the second repeated measures factor, while levels 3 and 4 of the first repeated measures factor are only paired with level 2 of the second repeated measures factor; thus this design is a nested repeated measures design.

In order to specify this design (in the Startup Panel), first enter all variables into the dependent variable list in the same order in which they appear in the data file, i.e., enter 1-4 into the dependent variable list selection window.  Next specify the Repeated measures (within ss) design.  First, specify the first repeated measures factor (Test), however, specify that this factor contains 2 levels; then specify the second repeated measures factor (Day) to contain 2 levels.  At this point the program "does not know yet" that there are going to be nested factors.  Consequently, it expects the number of variables to divide evenly by the total number of levels.  If one were to specify the first factor as having 4 levels and the second factor with 2 levels, the program would expect to find at least 8 variables (total number of levels:  2 x 4 = 8) in the dependent variable list.

Next, specify the nesting:  The first repeated measures factor is nested within the second repeated measures factor, and it contains 2 levels within each level of the second factor.

Testing main effects and interactions.  Testing for main effects and interactions in nested repeated measures designs is done in exactly the same manner as if a complete factorial within-subjects design had been analyzed.  However, note that interactions between nested factors and the factors in which they are nested cannot be evaluated.  In the present example, it is simply impossible to know how subjects would have performed on the first and second memory test (levels 1 and 2 of the first repeated measures factor) had they been administered on the second day (i.e., level 2 of the second repeated measures factor); this study does not provide the information necessary to estimate such interaction.

Between-within designs.  In designs that contain both between-groups and within-subjects (repeated measures) factors, one may specify nesting of factors both in the between-groups part of the design and the within-subjects part of the design.  Note that between-groups factors can only be nested in other between-groups factors, and that within-subjects (repeated measures) factors can only be nested in other repeated measures factors.


  ANOVA/MANOVA Notes Nested Designs - Latin Squares, Greco-Latin Squares, Generalized Latin Squares

A general class of balanced nested designs are the Latin squares (see for example Hays, 1988; Lindman, 1974; Milliken & Johnson, 1984; Winer, 1962; the term Latin square was first used by Euler, 1782).  An example of a Latin square design is also discussed in the Introductory Overview section.  In nested designs, the combination of treatment levels is arranged so as to yield unconfounded main effect estimates with a minimum number of observations.  To analyze these types of designs, use the Pooled effect/error term option from the results dialog.

First select the desired Effect in the Pooled Effects and Error Terms dialog.  Next click on the Error button and pool all main effects into the error term; then click on the Error button again to set this switch to SS Total minus customized.  In this manner the selected effect will be evaluated against the SS total minus the SS due to all effects that can be estimated.


  ANOVA/MANOVA Notes - Other Special Designs

Designs with Cell n of 1

Randomized Block Designs

For more information, see:

Specifying Between Uni/Multivariate Designs

Specifying Within (Repeated Measures) Uni/Multivariate Designs

Multiple Dependent Measures (MANOVA)

Nested Designs and Latin Squares

Type I, II, III Sums of Squares

Analyzing Designs with Missing Cells (Type IV Sums of Squares)

Random Factors

Fixed and Changing covariates

See also, ANOVA/MANOVA Introductory Overview


  ANOVA/MANOVA Notes Other Special Designs - Designs with Cell n of 1

In some instances the observations for the study are not easy to come by, and costs are associated with obtaining an observation.  Economic aspects then have to be weighed against design aspects.  One way to design economical experiments is to select only single observations for different cells in the design.  If the design is a full factorial design with an n of 1 in each cell, then estimating the sums of squares for all effects exhausts the degrees of freedom, and no SS error can be computed.  To analyze such designs, first compute the complete table of all effects; of course, because no SS-error can be computed, no F tests can be computed either.  Then examine the reported Means Squares (MS; SS divided by the respective degrees of freedom).  Their size is an estimate of the size of the respective effect.  Use that information to decide which effects to pool into the error term (the small, non-significant effects).  Usually, one discards higher order interactions in these types of designs.  Finally, use the Pooled effect/error option on the results dialog to "build" the chosen error term and to test the statistical significance of effects.  However, remember that the statistical significance tests here are not to be taken too "literally" because this procedure capitalizes on chance (only small effects are pooled into the error).


  ANOVA/MANOVA Notes Other Special Designs - Randomized Block Designs

Sometimes, experiments with an n of 1 are designed deliberately in order to reduce the SS error, yielding a more sensitive ANOVA design.  Specifically, the observations in the design can be arranged in blocks, in a manner that allows computation of an unconfounded main effect estimate of the blocking factor.  The error term is then reduced by the SS due to the blocking factor.  (The term randomized blocks was first used by Fisher, 1926.)

Example.  Suppose we want to test the yield of different varieties of wheat under three types of fertilizer.  We have four different fields available for our research, and decide to treat them as an additional blocking factor in the design.  The design could be summarized as follows:

                            Field (Block)

                      -------------------------

Fertilizer  Variety    I      II     III    IV

----------  -------   ----   ----   ----   ----

   1           A      10.2   10.1   11.1   12.3

               B      11.1    9.8    8.6    9.4

               C       .      .      .      .

               D       .      .      .      .

   2           A       .      .      .      .

               B       .      .      .      .

               C       .      .      .      .

               D       .      .      .      .

   3           A       .      .      .      .

               B       .      .      .      .

               C       .      .      .      .

               D       .      .      .      .

In this example, we are actually not interested in the effect of the blocking variable itself, that is, any significant differences between fields are of no theoretical interest to us.  However, by estimating the SS due to the blocking factor (Field), we may be able to reduce the error variance, allowing for more sensitive tests for the effect of Fertilizer, Variety, and the interaction between the two.  Also note that in this type of design one also decides to ignore any interactions of the blocking variable with the variables of interest.

Setting up the data file.  The data file for this experiment is set up in the same way as one would set up the file from a regular full factorial between-groups experiment.  The file should contain three grouping variables (Fertilizer, Variety, and Field) with codes that uniquely identify to which cell in the design each case belongs.  The fourth variable in the file would be the dependent variable (Yield).

Specifying and analyzing the design.  One would specify this design as if it were a regular full factorial design.  When testing for the statistical significance of the effects of interest, we would use the Pooled effect/error option to build the appropriate error term for the test.  Remember that the effects of interest are the main effects for Fertilizer and Variety, and the interaction between the two.  In addition, we can estimate the main effect for the blocking variable (Field).  To specify the error term, first select to pool all of these effects together, and then click on the Error button again to set this switch to SS-Total minus customized.


  ANOVA/MANOVA Notes - Type I, II, III, and IV Sums of Squares

Multiple Regression and ANOVA

Unbalanced and Balanced Designs

Type I, II, III, and IV Sums of Squares

Regression approach option

Determining the Order of Entry for Type I SS

Interpreting Type I, II, and III Hypotheses

For more information, see:

Specifying Between Uni/Multivariate Designs

Specifying Within (Repeated Measures) Uni/Multivariate Designs

Multiple Dependent Measures (MANOVA)

Nested Designs and Latin Squares

Other Special Designs

Analyzing Designs with Missing Cells (Type IV Sums of Squares)

Random Factors

Fixed and Changing covariates

See also, ANOVA/MANOVA Introductory Overview


Type I, II, III, and IV Sums of Squares - Multiple Regression and ANOVA

  ANOVA/MANOVA Notes Type I, II, III, and IV Sums of Squares - Multiple Regression and ANOVA

There is a close relationship between the multiple regression method and analysis of variance.  In fact, both are special cases of the general linear model.  For a detailed discussion of the linear model you should refer to the references provided in the ANOVA/MANOVA chapter of the manual.  In short, practically all experimental designs can be analyzed via multiple regression.

           Factor B

Factor   ------------

  A       B1      B2

---------------------

A1       3, 4    4, 5

A2       6, 6    3, 2

Let us consider a simple 2 x 2 between-groups design.  Suppose that the entries in the table above are the data (for the dependent variable or DV) collected in the experiment.  One could set up a data file in the following manner:

DV  A  B  AxB

-- -- --  ---

3   1  1   1

4   1  1   1

4   1 -1  -1

5   1 -1  -1

6  -1  1  -1

6  -1  1  -1

3  -1 -1   1

2  -1 -1   1

Columns A and B contain the codes that identify the levels of factors A and B; the column denoted as AxB contains the product of the two columns A and B.  You can analyze these data via multiple regression; specify variable DV as the dependent variable, and variables A through AxB as the independent variables.  The significance tests for the regression coefficients will be identical to those computed via ANOVA for the main effects (A and B) and the interaction (AxB).


Type I, II, III, and IV Sums of Squares - Unbalanced and Balanced Designs

  ANOVA/MANOVA Notes Type I, II, III, and IV Sums of Squares - Unbalanced and Balanced Designs

If you compute the correlation matrix for all variables for the example data shown above, you will notice that the main effects (A and B) and interaction (AxB) are all uncorrelated.  This property of the effects is usually also referred to as orthogonality, that is, effects A and B are said to be orthogonal or independent of each other.  Because all effects in the design shown above are orthogonal to each other, the design is said to be balanced.

Balanced designs have some "nice" properties; specifically, the computations to analyze such designs are quite simple.  For example, all we would have to do is compute the simple correlations between the effects and the dependent variable.  Since the effects are orthogonal, partial correlations (i.e., the full multiple regression) does not have to be computed.  However, in real research, designs are not always balanced.

Consider the following data set with unequal numbers of observations in different cells.

            Factor B

Factor  ----------------

 A        B1         B2

------------------------

A1      3           4, 5

A2      6, 6, 7     2

If you again coded these data as before, and compute the correlation matrix for all variables you would find that the factors in the design are now correlated with each other.  Thus, the factors in the design are no longer orthogonal, and the design is said to be unbalanced.  Note that the correlation among the factors is entirely due to the different frequencies of the 1's and -1's in the effect columns of the data matrix.  Put another way, experimental designs with unequal cell sizes (or non-proportional cell sizes to be exact) will be unbalanced, that is, the main effects and interactions will be confounded.  Thus, in order to evaluate the statistical significance of effects, we have to compute the complete multiple regression.  In fact there are several strategies that one can follow.


  ANOVA/MANOVA Notes Type I, II, III, and IV Sums of Squares

In general, we can test the significance of partial correlations, in effect controlling for other effects, or we can enter the variables in a stepwise fashion, controlling for all other factors that were previously entered and ignoring those that have not yet been entered.  In essence, this is the difference between Type III and Type I Sums of Squares (the terminology was introduced in SAS, e.g., see SAS 1982; detailed discussions can also be found in Searle, p. 461; Woodward, Bonett, & Brecht, 1990, p. 216; or Milliken & Johnson, p. 138).  Another "intermediate" strategy would be to control for all other main effects when testing a particular main effect, for all main effects and two-way interactions when testing a particular two-way interaction, for all main effects, two-way interactions, and three-way interactions when testing a particular three-way interaction, and so on.  Sums of squares for effects computed in this manner are called Type II sums of squares.  Thus, Type II sums of squares control for all effects of the same or lower order, while ignoring all effects of higher order.  Finally, for some special designs with missing cells (incomplete designs), one can also compute so-called Type IV sums of squares; this method is discussed in the context of incomplete (missing cell) designs.


Type I, II, III, and IV Sums of Squares - Regression Approach Option

  ANOVA/MANOVA Notes Type I, II, III, and IV Sums of Squares - Regression Approach Option

A check box is available on the Startup Panel of ANOVA/MANOVA to request the regression approach to ANOVA.  If this check box is set, then the program will perform additional computations while reading the data, and the user can later request to test all effects, specific hypotheses, or pooled effects, using Type I, II, or III sums of squares.

After the data are read, open the Output options dialog.  The first option (Hypothesis type) allows you to select the type of hypothesis that will be tested if you subsequently choose option Specific effect/mean, Table of all effects, Means/Graphs, or Pooled effect/error.

Type I SS and the Specific effect option.  After requesting Type I sums of squares, you can test specific effects via the Specific effect/mean option.  If you choose to test a main effect, then that effect will be tested, ignoring all other effects.  If you select to test a two-way interaction, then the respective interaction will be tested, controlling for all main effects and ignoring all other interactions; that is, all main effects will first be entered into the "model," and then the sums of squares due to the respective two-way interaction will be computed.  If you specify a three-way interaction, then that interaction will be tested after controlling for all main effects and two-way interactions, and ignoring all other three-way or higher order interactions.  In general, all effects will be tested after controlling for all effects of lower order.  In order to compute Type I sums of squares while controlling for some specific factors (e.g., same-order interactions), choose option Table of all effects or Means/Graphs, and then specify the desired order of entry into the model (see below).


Type I, II, III, and IV Sums of Squares - Determining the Order of Entry for Type I SS

  ANOVA/MANOVA Notes Type I, II, III, and IV Sums of Squares - Determining the Order of Entry for Type I SS

As mentioned earlier, Type I sums of squares test effects sequentially, that is, all effects that were previously entered into the model are controlled for, and all effects not yet entered into the model are ignored.  If you selected Type I sums of squares from the Output Options dialog, then after selecting the Table of all effects or Means/Graphs option, a dialog window (see Sequential (Type I) Sums of Squares) will come up that allows you to specify the order in which effects are to be tested.


Type I, II, III, and IV Sums of Squares - Interpreting Type I, II, and III Hypothesis

  ANOVA/MANOVA Notes Type I, II, III, and IV Sums of Squares - Interpreting Type I, II, and III Hypotheses

Type III sums of squares are most easily interpreted.  Remember that Type III sums of squares are tests of effects after controlling for all other effects.  For example, after finding a statistically significant Type III effect for factor A, one can say that after controlling for all other effects (factors) in the experimental design, there is a unique significant effect for factor A.  In terms of marginal means, one can simply look at the (unweighted) marginal means for factor A as reported by ANOVA/MANOVA and interpret the effect accordingly.  Probably, in 99% of all ANOVA applications this is the type of test that the researcher is interested in.  This, incidentally, is also the type of sums of squares that is usually computed by default in ANOVA/MANOVA, regardless of whether or not the Regression approach option was set.

Significant effects based on Type I or Type II sums of squares cannot be interpreted as easily.  One best considers such results in the context of stepwise multiple regression (e.g., as discussed in Multiple Regression).  If, using Type I sums of squares, a main effect B is significant (after A was already entered into the model, but before the AxB interaction was added), one should conclude that there is a significant main effect for factor B, provided that there is no interaction between A and B.  (Of course, if the Type III test for factor B is also significant, then we can conclude that there is a significant unique main effect for B, after controlling for all other factors and their interactions.)

In terms of marginal means, Type I and Type II hypotheses have usually no simple interpretation.  That is to say, one cannot interpret significant effects by looking simply at marginal means.  Rather, the reported p-values pertain to complex hypotheses that combine means and sample sizes.  For example, the Type II hypothesis for factor A in the simple 2 x 2 example shown above would be (see Woodward, Bonett, and Brecht, 1990, p. 219):

         2

Σ(n  - n   /n  )*u   = Σ   [Σ( n  *n   /n   * u   )]

j  ij   ji   .j   ij   i'≠j j   ij  i'j  .j    i'j

Here the nij's are the cell n's, the uij's are the cell means, and the dots (e.g., n.j) refer to the respective marginal elements (e.g., marginal n's or marginal means).  Without going into further detail (for a thorough discussion see Milliken & Johnson, 1984, Chapter 10), it is clear that this is not a simple hypothesis, and in most cases not one that is of particular interest to the researcher.  However, there are cases when Type I hypotheses may be of interest.


  ANOVA/MANOVA Notes - Analyzing Designs with Missing Cells (Incomplete Designs)

Factorial designs that contain some missing cells (treatment combinations where there are no observations) are said to be incomplete.  In such designs, some factors are usually not orthogonal, and some interactions cannot be computed.  In general, there is no one best method to analyze such designs.

Regression Approach

Cell Means ANOVA Approach

Missing Cells and the Specific Effect Option

Missing Cells and the Pooled Effect/Error Option

For more information, see:

Specifying Between Uni/Multivariate Designs

Specifying Within (Repeated Measures) Uni/Multivariate Designs

Multiple Dependent Measures (MANOVA)

Nested Designs and Latin Squares

Other Special Designs

Type I, II, III Sums of Squares

Random Factors

Fixed and Changing covariates

See also, ANOVA/MANOVA Introductory Overview


  Analyzing Designs with Missing Cells (Incomplete Designs) - Regression Approach

In some older programs, which basically analyze ANOVA designs via multiple regression, the default way of handling incomplete designs is to code the factors in the design in the usual manner (as if the design were complete), and then to perform the multiple regression analysis for those dummy-coded factors that can be estimated.  Unfortunately, this method will yield results that are very difficult, if not impossible, to interpret because it is not clear how each effect translates in terms of linear combinations of means.  Consider the following simple example:

              Factor B

Factor  ------------------

 A        B1          B2

--------------------------

A1      3            4, 5

A2      6, 6, 7    Missing

If you were to perform a multiple regression of the form Dependent variable = Intercept + Factor A + Factor B, the actual hypotheses being tested in terms of linear combinations of means would be:

Factor A: Cell A1,B1 = Cell A2,B1

Factor B: Cell A1,B1 = Cell A1,B2

While this case is simple, when the design is more complicated it is virtually impossible to determine what exactly is being tested.


  ANOVA/MANOVA Notes Analyzing Designs with Missing Cells (Incomplete Designs) - Cell Means ANOVA Approach

The approach that we recommend, and which seems to be preferred in the literature on this subject, is to test meaningful (with regard to the research question) a priori hypotheses about the means observed in the cells of the design.  Detailed discussions of this approach can be found in Dodge (1985), Heiberger (1989), Milliken and  Johnson (1984), Searle (1987), or Woodward, Bonett, and Brecht (1990).  The sums of squares associated with hypotheses about linear combinations of means in incomplete designs, testing the estimable portions of effects, are also called Type IV sums of squares.

Automatic generation of Type IV hypotheses.  When a multi-factorial design contains a complex pattern of missing cells it can be quite challenging to identify orthogonal (independent) hypotheses that test something equivalent to main effects or interactions.  Algorithmic (computer) strategies (based on the generalized inverse of the design matrix) have been developed to generate the appropriate weights for such comparisons; unfortunately, the resulting hypotheses are not unique.  Instead, they depend on the order in which the effects were specified, and they rarely allow for simple interpretation.  Therefore, we rather recommend that you carefully study the pattern of missing cells in the design, and then formulate Type IV hypotheses that are most meaningful given the research question at hand.  Then, test those hypotheses using the Planned comparison option from the Results dialog.  The easiest way to specify planned comparisons in this case is to request to enter contrast vectors for all factors together on the Planned comparisons options dialog; the dialog that will appear after you then request Planned comparisons will show all groups in the current design, and mark those that are missing.


  Analyzing Designs with Missing Cells (Incomplete Designs) - Missing Cells, Specific Effect Option

There are several types of designs in which the pattern of missing cells is not haphazard, but rather carefully planned to allow for simple tests of main effects which are not confounded by other main effects.  For example, Latin Squares designs are often used to evaluate main effects for several factors with many levels; if complete designs were used for that purpose the number of necessary cells in the design would quickly get out of hand. For example, consider a 4 x 4 x 4 x 4 factorial design which would require 256 cells; at the same time one can use a Greco Latin Square design to estimate main effects from only 16 cells in the design (Experimental Design also discusses such designs in detail).  In general, incomplete designs in which main effects (and some interactions) can be estimated from simple linear combinations of means are said to be balanced incomplete designs.

When designs are balanced, the standard (default) method of generating the contrasts (weights) for the main effects and interactions will produce an analysis of variance table in which the sums of squares for the respective effects are not confounded with each other.  The Specific effect option on the Results dialog will generate such default contrasts assigning zeros to the cells that are missing in the design.  To inform the user regarding the specific hypothesis that is being tested, a Scrollsheet with the actual weights will be displayed right after an effect was requested (via option Specific effect).  However, note that the sums of squares computed for the respective effect are only orthogonal (independent) to other main effect (or interaction) hypotheses if the design is balanced!  Otherwise one should use the Planned comparison option to test meaningful comparisons between means.


  Analyzing Designs with Missing Cells (Incomplete Designs) - MIssing Cells, Pooled Effect/Error

When the Regression approach option in the startup panel of ANOVA/MANOVA is not set (default setting), then the cell means model will be used to compute the sums of squares for the effects.  If the design is unbalanced, and one pools effects that are not orthogonal (see discussion under Missing Cells and the Specific Effect option above), then the resulting pooled sums of squares may consist of non-orthogonal (or overlapping) components.  The results are then basically not interpretable (note that the sums of squares for effects that are to be pooled are computed successively, not simultaneously).  Therefore, be careful in your choice and implementation of a complex incomplete experimental design.  There are many textbooks that offer detailed discussion of different types of designs (e.g., Dodge, 1985; Heiberger, 1989; Lindman, 1974; Milliken & Johnson, 1984; Searle, 1987; Woodward & Bonett, 1990), and such advice is beyond the scope of this overview.


  ANOVA/MANOVA Notes - Random Effects

Some research questions require the assessment of the significance of random effects.  For example, one may want to test the hypothesis that there are significant differences in students' algebra skills across different high schools in the state (i.e., the high school factor would represent a random effect).  Note that if one's hypothesis were more specific (e.g., algebra skills in rural high schools are better than in urban schools) the high school factor would be a fixed effect (the terms fixed effect and random effect were first used by Eisenhart, 1947).  However, the hypothesis as it stands requires that one draw a random sample of high schools from the population of high schools in the state.  Then a sample of students within each selected high school would be tested.  Thus, each level of the high school factor (i.e., each high school that was selected into the random sample of high schools) does not represent a distinct level of the factor, but instead represents one possible level chosen from a population of levels, and one is interested in generalizing from the chosen levels to the population of levels (i.e., the hypothesis pertains to any differences between high schools in the state).

As a rule of thumb, a factor should probably be treated as a random factor if one would not choose the same levels of the factor for a replication of the study.  In the present example, if we wanted to replicate the study, we would not test students in exactly the same high schools; rather, we would draw a new sample of high schools, that is, a new sample of levels of the high school factor.  Thus, the high school factor is a random effect.  On the other hand, if we wanted to replicate a learning experiment where subjects had to memorize lists of either 10 words or 20 words (level 1 and level 2, respectively, of a between-groups factor) we would again expose subjects to exactly the same levels, i.e., to lists of 10 words or lists of 20 words.  Thus, this factor is a fixed effect.  Please refer to ANOVA textbooks (e.g., Lindman, 1974; Winer, 1962, 1971) if you are not familiar with the distinction between fixed and random effects.

Comparing Experiments

Another example of when one may specify a factor as random is in comparisons across different experiments.  Sometimes, one may want to compare the results of different experiments that used identical designs.  In that case, it is advisable to treat the between-groups factor "Experiment" as a random effect, because one is interested in drawing inferences about the entire "population of experiments" that could have been performed.

Specifying the Design

In order to specify a random factor, first specify all (between-groups and within-subjects) factors.  Then click on Random factors on the startup panel and select the factors in the design that should be treated as random factors.

Tests of Main Effects and Interactions

Main effects that are completely crossed with random effects have as their error term the interaction of the respective fixed factor with the random factor.  Technically, planned comparisons cannot be evaluated in designs with random effects (see Kirk, 1982).  If you try to do so, ANOVA/MANOVA will issue a warning message to this effect and then proceed as if the design contained no random effects.

For more information, see:

Specifying Between Uni/Multivariate Designs

Specifying Within (Repeated Measures) Uni/Multivariate Designs

Multiple Dependent Measures (MANOVA)

Nested Designs and Latin Squares

Other Special Designs

Type I, II, III Sums of Squares

Analyzing Designs with Missing Cells (Type IV Sums of Squares)

Fixed and Changing covariates

See also, ANOVA/MANOVA Introductory Overview


  ANOVA/MANOVA Notes - Fixed (Static) and Changing Covariates in Between-Groups and Within-Subjects Designs

In general, covariates represent continuous factors in the design.  They are usually included in order to reduce the SS error term, resulting in a more sensitive design.

Fixed Covariates

Changing Covariates

For more information, see:

Specifying Between Uni/Multivariate Designs

Specifying Within (Repeated Measures) Uni/Multivariate Designs

Multiple Dependent Measures (MANOVA)

Nested Designs and Latin Squares

Other Special Designs

Type I, II, III Sums of Squares

Analyzing Designs with Missing Cells (Type IV Sums of Squares)

Random Factors

See also, ANOVA/MANOVA Introductory Overview


Fixed (Static) and Changing Covariates - Fixed Covariates

  Fixed (Static) and Changing Covariates in Between-Groups and Within-Subjects Designs - Fixed Covariates

The most common application of covariates is in between-groups designs, in cases when one has continuous variables that are likely to be correlated with the dependent variable of interest.  For example, before beginning a special math training course, the IQ (Intelligence Quotient) of all participating students can be measured.  Students are then randomly assigned to one of two courses, and their improvement in that course is measured as the major dependent variable of interest.  In this study one might suspect that the large differences in intelligence among participating students contributes a lot of "random" variability to the dependent measure.  In fact, this variability (due to differences in intelligence) may be so large that it will "mask" the differential effectiveness of the two training courses.  In that case, one could specify the IQ measure as the covariate.  If related to students' improvements in the math course, the covariate may significantly reduce the error variance.

Adjusted means.  When the covariate is not only correlated with the dependent variable within each group in the design, but also correlated with the between-groups factors themselves, then we need to adjust the means before interpreting any effects.  A covariate can be correlated with the between-groups factors if it is affected by them; for example, if in the above study we were to have measured IQ after the math training courses, then it is conceivable that the covariate (IQ) could have been affected by the different courses.  In those cases, you will see that the inclusion of the covariate will not only affect the SS error term in the analysis but also SS effect terms for the between-groups factors.  Also, the adjusted means (computed by ANOVA/MANOVA if requested via Output options on the results dialog) will be different from the raw observed means.  When this happens, the inclusion of a covariate sometimes actually decreases the statistical significance of effects.

Contrast analysis.  Many textbooks on ANOVA are somewhat "evasive" on the issue of contrast analysis in designs with covariates.  In ANOVA/MANOVA simply specify contrasts as usual; because of the general computational approach used in the program the results of contrast analyses automatically take into account the covariates.  Note that, in effect, the contrast analysis is performed on the adjusted means.


Fixed (Static) and Changing Covariates - Changing Covariates

  Fixed (Static) and Changing Covariates in Between-Groups and Within-Subjects Designs - Changing Covariates

These types of covariates can only occur in repeated measures designs.  The general idea of changing covariates can be illustrated as follows:  Imagine that, in a repeated measures design, we measure a covariate at each point of repeated measurement of the dependent variable.  We can now ask two questions:  (1) Overall, is the covariate related to the dependent variable; and (2) are the changes in the covariate across the repeated measurements related to the changes in the dependent variable?  The first question amounts to an analysis equivalent to that of fixed covariates.  The second question requires that the SS for the repeated measures design be adjusted by the respective covariates.

Computational approach.  ANOVA/MANOVA employs the general linear model approach to ANOVA.  The adjustment of within-subjects effects for covariates is handled practically automatically.  After the respective within-subjects hypothesis and error matrices have been computed, and before the final results statistics are computed, the hypothesis and error matrices are adjusted by the covariates.  However, this procedure is multivariate by its very nature, and one should definitely rely on the multivariate test for repeated measures (and covariates) with more than two levels.  Note that the regression results for the changing covariates are only reported when requesting those results via Output options from the results dialog, and then examining a specific effect involving the repeated measures factor.  If you choose option Within-cell regression, the within-cell (group) regression analyses are performed by treating each level of the repeated measures factor as a dependent variable.

Between-groups and within-subjects ANOVA.  If the design contains between-groups as well as repeated measures factors, the results for the covariates regarding the between-groups model are the same as if we had analyzed the sum scores across all levels of the repeated measures factor.

Specifying changing covariates.  The logic of specifying changing covariates follows exactly that of specifying repeated measures factors.  The program will cycle through the list of covariates (entered via option Covariates on the startup panel) and assign the successive levels of repeated measures factors to the variables.  As is the case when specifying repeated measures factors, the fastest-changing levels are those of the repeated measures factor specified last; the next-fastest changing levels are those of the repeated measures factor specified next to the last, etc.  If there are multiple changing covariates, then the fastest-changing factor is the covariate number ("adjacent" variables in the list of covariates will be treated as "belonging" to different covariates).  For example, suppose we had two tests that were measured at three times (month 1, 2, and 3), and we wanted to specify the two tests as changing covariates.  Imagine the data for the covariates were entered in the file as follows:

           Test administered after

    -------------------------------------

    1 Month       2 Months       3 Months

    --------      --------       --------

      Test          Test           Test

     1     2       1     2        1     2

    --    --      --    --       --    --

    24    30      26    34       28    28

    30    32      30    28       32    34

    30    27      29    28       28    33

    30    28      29    26       34    35

    35    25      36    27       32    36

    .     .       .     .        .     .

    .     .       .     .        .     .

    .     .       .     .        .     .

Specify the list of covariates in this order.  (Of course, you also need to specify the within-subjects model as a single factor, three-level repeated measures design.)  Upon exiting the startup panel, you will be prompted to specify whether this list represents a set of fixed covariates or changing covariates.

If you select Changing, then the list of covariates will be interpreted as intended, that is, in our example, as two changing covariates.  Note that the question concerning the nature of the covariate will only appear if the number of specified covariates can be divided evenly by the total number of repeated measurements; otherwise, the list of covariates can of course not be interpreted in any other way but as fixed covariates.


  ANOVA/MANOVA - Startup Panel

When you first open the ANOVA/MANOVA module, the General ANOVA/MANOVA dialog will open (see also, ANOVA/MANOVA - Index).  In order to specify a between-groups design in this dialog, at least one dependent variable must be selected, at least one independent or grouping variable must be selected, and at least two independent variable codes must be specified (via the Codes option) for each between-groups factor (note that if you do not explicitly specify the codes, by default, the program will use as codes, all values encountered in the specified independent variables).

In order to specify a repeated measures factor design in this opening dialog, at least two dependent variables must be selected, and the repeated measures factor has to be identified via the Repeated measures (within ss) design option.  Multiple dependent variables that cannot be interpreted (by the program, given the design you specified) as levels of repeated measures factors are interpreted as multiple dependent variables in a MANOVA design (this will occur if, for example you select two or more dependent variables and do not define them as repeated measures, or whenever you select more dependent variables than can be accounted for by the currently defined repeated measure factors and their levels).

ANOVA/MANOVA will automatically handle designs with empty cells.  To analyze Latin squares, Greco-Latin squares, or other balanced incomplete designs, simply specify them as if they were complete factorial designs.  Then use the option Pooled effect/error on the Results dialog to build the appropriate error term for testing the effects.  Designs with complex patterns of missing cells should be analyzed via specific planned comparisons.

General ANOVA/MANOVA dialog:

Variables (independent and dependent)

Covariates

Codes for between-groups factors

Repeated measures (within-SS) design

Nested design

Random factors

Isolated control group

Regression approach


  ANOVA/MANOVA Startup Panel - Variables

Choosing this option will bring up a window for selecting a list of independent variables (between-groups factors) and a list of dependent variables.  Independent (or grouping) variables are the variables that contain codes that uniquely identify to which group (cell) in the between-groups design a case belongs.  Up to 8 independent variables can be specified; if the design has no between-groups factors, leave the first list blank.

If a repeated measures analysis is desired, specify as dependent variables all variables that contain the data for the different levels for the repeated measures factor(s).  The assignment of variables to levels of the repeated measures factor(s) is determined by the order in which dependent variables appear in the dependent variable list, not by the order in which variables were entered into the file.


  ANOVA/MANOVA Startup Panel - Covariates

After choosing this option a standard three-variable-lists selection window will be displayed.  The first two lists allow you to select the independent or grouping variables and dependent variables (as described under option Variables).  The third list is for covariates in the design.  At this point select all covariates, regardless of whether they represent fixed (static) covariates (each covariate was measured once for each subject) or changing covariates (each covariate was measured at each repeated measurement of the dependent variable).  If the number of covariates is an even multiple of the total number of levels in the within-subjects (repeated measures) design, then upon exiting this dialog via OK, the user will be asked whether the covariates are to be interpreted as changing covariates or as fixed covariates.


  ANOVA/MANOVA Startup Panel - Codes for Between-Groups Factors

Clicking on this button will bring up the independent variable codes selection windows.  Independent variable codes are the code numbers or names (text codes) that were entered for the independent variables in order to uniquely identify the group membership of each case (e.g., a 1 or Male was entered if a subject was male, a 2 or Female was entered if a subject was female).  You may also refer to the Examples section of the manual to see how codes are used to specify the between-groups ANOVA design.

If you do not explicitly specify codes for the independent variables, but simply click OK to continue on from the startup panel, the program will automatically use all codes in the respective independent variables.


  ANOVA/MANOVA Startup Panel - Repeated Measures Designs

This option allows you to specify the within-subjects or repeated measures part of the design.  After choosing this option, a dialog window will come up for specifying repeated measures factors.  For each repeated measures factor, specify a name up to 8 characters long, and the number of levels that the factor contains.  For more information on specifying a repeated measures design see Specifying Repeated Measures Designs.


  ANOVA/MANOVA Startup Panel - Nested Design

This option allows the user to specify nested designs.  In nested designs, the levels of a factor are nested within the levels of another factor.  For example, if one were to administer four different tests to four high school classes (i.e., a between-groups factor with 4 levels), and two of those four classes are in high school A, whereas the other two classes are in high school B, then the levels of the first factor (4 different tests) would be nested in the second factor (2 different high schools).  Note that not all nested designs must be (or, in fact, can be) set up via this option.

After choosing this option, the Nesting for Between-group Factors dialog will come up where the user can select (1) the nested factors, (2) the factors in which they are nested, and (3) the number of levels the respective factors have within the factors in which they are nested.  Repeated measures factors can only be nested in other repeated measures factors, and between-groups factors can only be nested in other between-groups factors.


  ANOVA/MANOVA Startup Panel - Random Factor

After choosing this option, the user can select the factors in the design that are to be treated as random factors.  For more information about selecting random factors see Random Effects (mixed models).


  ANOVA/MANOVA Startup Panel - Isolated Control Group

This option allows the user to specify an independent variable code that identifies an isolated control group (or "hanging" control group).  For more information on specifying the isolated control group, see Specifying the Isolated Control Group.


  ANOVA/MANOVA Startup Panel - Regression Approach

If the Regression approach check box is set, then the program will perform additional computations while reading the data, and the user can later request to test all effects, specific hypotheses, or pooled effects, using Type I, II, or III sums of squares.


  ANOVA/MANOVA - Specifying Repeated Measures Designs

To specify a repeated measures factor enter a label and the number of levels for the factor.  The program will interpret the variables in the dependent variable list as levels of the repeated measures factors.  Thus, the number of dependent variables must be evenly divisible by the total number of repeated measures factors.  If there are more (twice or three times as many) dependent variables than levels for the repeated measures factors, then adjacent variables in the dependent variable list will be interpreted as multiple dependent measures in a repeated measures MANOVA.

Specifying more than one repeated measures factor

Multivariate repeated measures designs


  Specifying Repeated Measures Designs - Specifying more than One Repeated Measures Factor

If a design contains more than one repeated measures factor, the order in which they are specified will determine the assignment of dependent variables to levels of the repeated measures factors.  The program will "cycle" through the dependent variable list, assigning variables to subsequent levels of the repeated measures factor.  Specifically, the fastest-moving (changing) levels are those of the repeated measures factor which was specified last, the next-fastest moving (changing) levels are those of the repeated measures factor which was specified next to last, and so on.  If one or more changing covariates were specified (covariates that were measured at each level of the repeated measures factors), the list of covariates will be assigned to levels of the repeated measures factors in the same manner.

Example.  If 12 dependent variables were selected, and the user wants to specify a 2 x 2 x 3 repeated measures design, then the assignment of variables to levels should be as follows:

Rep. measures
factor        levels of repeated measures factors
------------- -----------------------------------
First         1  1  1  1  1  1  2  2  2  2  2  2
              ----------------  ----------------
Second        1  1  1  2  2  2  1  1  1  2  2  2
              -------  -------  -------  -------
Third         1  2  3  1  2  3  1  2  3  1  2  3
              -  -  -  -  -  -  -  -  -  -  -  -
Dep. Var.     1  2  3  4  5  6  7  8  9 10 11 12

Note that the numbers in the last row of the example table above represent the consecutive numbers of variables in the list of dependent variables specified by the user, and not the numbers of those variables in the data file (e.g., the number 1 above, may represent variable number 256 in the data file).

See also:

Multivariate repeated measures designs


  Specifying Repeated Measures Designs - Multivariate Repeated Measures Designs

If, in the example given in Specifying more than one repeated measures factor, the dependent variable list had consisted of 24 rather than 12 dependent variables, a 2 x 2 x 3 multivariate analysis of variance (MANOVA) with repeated measures would be performed (with two dependent variables at each level of the repeated measures factors).  When cycling through the dependent variable list, the fastest changing levels (i.e., adjacent variables in the dependent variable list) always represent the multiple dependent variables.  Refer to the Notes section for other examples and more detailed explanations of how the program assigns variables from the dependent variable list to levels of repeated measures factors.

See also:

Specifying more than one repeated measures factor


  ANOVA/MANOVA - Specifying Code for Isolated ("Hanging") Control Group

Specify here the code that is used in the independent (grouping) variables to identify the cases that belong to the isolated ("hanging") control group.

Isolated Control Group Designs

Experimental designs are usually completely crossed (factorial designs), that is, each level of each factor appears with each level of all others.  For example, in a 2 (types of drug) x 2 (types of virus) design, each type of drug would be used with each type of virus.  However, in order to establish an appropriate control group (e.g., a group of healthy animals that were not exposed to any virus or drug) experimental designs sometimes require the addition of a single group, i.e., an isolated control group (or "hanging" control group).

ANOVA/MANOVA expects that the isolated control group is identified by one common code value in all independent (or grouping) variables.  Valid code values that may be entered are integer values in the range from 999 to +999.  Later in the computations of the sums of squares, ANOVA/MANOVA will take the isolated control group into account in the calculation of the error sums of squares.  Specific comparisons involving the isolated control group can be specified via the Planned comparisons option on the results dialog.  Refer to the Notes section for a more detailed discussion of how to prepare data files, and how to analyze isolated control group designs.


  ANOVA/MANOVA - Specifying Nested Designs

Specify the nested factors in the Nesting For Between-Groups Factors dialog.  When you open this dialog, several columns will be displayed (one for each within-subjects factor) with a factor name at the top and the remaining factors listed below.  To specify a nested factor:

(1)	Go to the column with the name of the factor (at the top of the column) that you want to designate as the nested variable;

(2)	In this column, select the factor(s) in which this factor is nested by clicking on the factor names to highlight them.  The column will now refer to the first factor (listed at the top of the column) as "nested in" the selected factor(s);

(3)	Specify the number of levels of this factor within each of the factor(s) in which it is nested;

(4)	Repeat this process for each of the nested factors (in their respective columns).

(Note that you can de-select a nested factor by holding down the CTRL key and then clicking on that factor with the left-mouse-button.)

Nested designs

In nested designs the levels of a factor are nested within the levels of another factor.  For example, if one were to administer four different tests to four high school classes (i.e., a between-groups factor with 4 levels), and two of those four classes are in high school A, whereas the other two classes are in high school B, then the levels of the first factor (4 different tests) would be nested in the second factor (2 different high schools).


  ANOVA/MANOVA - Specifying Random Factors (Effects)

Select the factors that are to be treated as random factors in the design, in the Random Effects (Mixed Model) dialog.

Random effects

Fixed and random effects differ in that the levels for fixed effects are especially selected or "fixed" by the researcher (e.g., manipulation in an experiment), whereas the levels for random effects are selected by the researcher via some random selection procedure from a population of possible levels (e.g., three different schools in which an experiment was conducted).

Designs with multiple random effects

If an ANOVA design contains several random factors or random and repeated measures factors, the sums of squares (and F values) for some effects are not determined, and they cannot be estimated.


  ANOVA/MANOVA - Fixed vs. Changing Covariates

Because the number of covariates selected in this design is evenly divisible by the total number of levels of the repeated measures factors, the list of variables selected as covariates can be treated as fixed or changing covariates.

Changing covariates

While fixed covariates are commonly discussed in textbooks on ANOVA, changing covariates are discussed less frequently.  In general, when we have repeated measures, we are interested in testing the differences in repeated measurements on the same subjects.  Thus we are actually interested in evaluating the significance of changes.  If we have a covariate that is also measured at each point when the dependent variable is measured, then we can compute the correlation between the changes in the covariate and the changes in the dependent variable.  For example, we could study math anxiety and math skills at the beginning and at the end of the semester.  It would be interesting to see whether any changes in math anxiety over the semester correlate with changes in math skills.


  ANOVA/MANOVA - Results Dialog

After you make your selections and click OK in the Startup Panel, the ANOVA Results dialog will open.  In this dialog you can choose from several options to review specific results.

ANOVA Results dialog:

Table of all effects	Post hoc comparisons

Means/Graphs	Descriptive stats & graphs

Specific effect/Means/Graphs	Within-cell regression

Planned comparisons	Output options

Options	Print Design

Pooled effect/error


ANOVA/MANOVA Results - Table of All Effects

  ANOVA/MANOVA Results Dialog - Table of All Effects

This option will automatically compute the complete table of all effects and display a summary Scrollsheet.  In that Scrollsheet, significant effects will by highlighted; the alpha-level criterion for highlighting can be changed via the Options Scrollsheet Toolbar button.

The summary statistics reported in this Scrollsheet include:

Wilks Lambda:  This column contains the Wilks lambda for each effect.  Wilks lambda can assume values in the range of 0 (perfect discrimination) to 1 (no discrimination).

Raos R:  This column contains the Raos R for each effect.  Raos R is a transformed value of Wilks lambda which is used to determine the significance of the given effect.  See Distribution of Raos R, below, for more information on how Raos R is calculated.

df 1, df 2:  These are the degrees of freedom for the F-test statistic (Raos R) used to determine the significance of the effect.

p-value:  This column contains the p-levels associated with the Raos R statistics for each effect.

Distribution of Raos R:    When the analysis is based on (1) any number of groups with two dependent variables, (2) two groups with any number of dependent variables or (3) three groups with any number of variables, the distribution of Raos R (a transformation of Wilks lambda) follows an F distribution exactly, with the degrees of freedom given in the Table of All Effects.  Under all other circumstances, the transformation used to calculate Raos R (see Lindeman, Merenda, & Gold, 1980; Rao, 1952; Tatsuoka, 1971) follows an approximate F distribution with the degrees of freedom given in the Table of All Effects.


ANOVA/MANOVA Results - Means/Graphs

  ANOVA/MANOVA Results Dialog - Means/Graphs

This option will also automatically compute the complete table of all effects.  A dialog will subsequently be displayed allowing you to select specific effects and to display either a plot of means (interaction) or a Scrollsheet of (unweighted) means.  This option is the quickest way to explore patterns of significant effects from complex ANOVA designs.


ANOVA/MANOVA Results - Specific Effect/Means/Graphs

  ANOVA/MANOVA Results Dialog - Specific Effect/Means/Graphs

Click on this button to open a dialog where you can select the effect that you want to examine more closely.  You can choose the results reported here by clicking on the Output options button to specify the detail of results to be reported.

The rules for specifying effects in this dialog is straightforward:

•	To examine a main effect, select (highlight) the respective (single) factor;

•	To examine an interaction between two factors, highlight the respective two factors;

•	To examine three-way interactions, select (highlight) the three factors, and so on.


ANOVA/MANOVA Results - Planned Comparisons

  ANOVA/MANOVA Results Dialog - Planned Comparisons

This option allows you to test specific contrasts (contrast analysis).  The type of contrasts (separate or together) that you choose in the Option for Planned Comparisons Facility dialog (accessible from the Options) determines which contrast dialog will open when you click on the Planned Comparisons button.

If Separate Contrasts is selected, then after you click on this button, you will be prompted to enter the contrast coefficients factor by factor in the Specify Contrasts dialog.

If you elected to enter the contrasts Together, then you will be prompted to enter the contrast coefficients for the factors in the Contrasts for Between-Group (Within-Subjects) Factors dialog.

The general logic and rules for "building" contrasts are described in the Notes section for both between-group designs as well as repeated measures designs.


ANOVA/MANOVA Results - Options

  ANOVA/MANOVA Results Dialog - Options

When you click on this button, the Option for Planned Comparisons Facility dialog will open in which you can select the manner in which contrasts will be entered in the Planned Comparison option.  Contrasts can be entered separately for each factor (choose Enter Contrasts Separately for Each Factor), or for all factors combined (together, as a contrast vector; choose Enter Contrasts for Factors Together); in multivariate designs the user can also choose to enter contrasts for the dependent variables.


ANOVA/MANOVA Results - Pooled Effect/Error

  ANOVA/MANOVA Results Dialog - Pooled Effect/Error

After choosing this option, the user can specify effects that are to be pooled together, and effects that are to be pooled into the error term in the Pooled Effects & Error Terms dialog.  This option is particularly useful for testing effects in incomplete designs.


ANOVA/MANOVA Results - Post Hoc Comparisons

  ANOVA/MANOVA Results Dialog - Post Hoc Comparisons

After choosing this option, the Specify Effect for Post hoc Tests dialog window will open, prompting the user to specify the effect for which to perform the Post hoc tests.  The conventions for specifying effects in this window are identical to those for specifying effects after choosing option Specific effect/means/graphs.  The Post hoc tests will be performed on the marginal (unweighted) means for the respective effect.  Available Post hoc tests are the LSD (Least Significant Difference) test, the Newman-Keuls test, Duncan's multiple range test, the Scheffé test, Tukey's HSD (Honest Significant Difference) test, and the Spjotvoll & Stoline HSD test.  These tests can be chosen from the Post hoc Comparisons of Means dialog that will be displayed after specifying the effect.


ANOVA/MANOVA Results - Descriptive Stats and Graphs

  ANOVA/MANOVA Results Dialog - Descriptive Stats and Graphs

This option will bring up the Descriptive Statistics & Graphs dialog with a wide variety of options for computing descriptive statistics, for testing ANOVA assumptions, and for plotting various aspects of the data.


ANOVA/MANOVA Results - Within-Cell Regression

  ANOVA/MANOVA Results Dialog - Within-Cell Regression

This option will perform a regression analysis for the covariates.  Results can be viewed for each dependent variable separately (univariate), or for all dependent variables simultaneously (multivariate).  Note that this option will always perform the analyses separately for each variable in the dependent variable list, even if those variables represent levels of a repeated measures factor.  If, in a repeated measures design, you want to review the results for a dependent variable that is actually comprised of many levels, use the Output options to request Regression results; then use option Specific effect/means/graphs to look at the effect of interest.


ANOVA/MANOVA Results - Output Options

  ANOVA/MANOVA Results Dialog - Output Options

This option will bring up the Output Options dialog for selecting the specific output options that are to be displayed when examining a specific effect via option Specific effect/means/graphs.  Note that not all options here may be applicable to your specific design, and the settings of those options will be ignored.


ANOVA/MANOVA Results - Print Design

  ANOVA/MANOVA Results Dialog - Print Design

Click on this button to print the ANOVA/MANOVA design either to the printer, output file, and/or Text/output Window (as specified in the Page/Output Setup dialog).


  ANOVA/MANOVA - Output options

The selections on this dialog will determine the detail of the results displayed when examining specific effects via option Specific effect/means/graphs on the results dialog.  Note that not all options on this dialog are applicable to all designs.

Output Option dialog:

Hypothesis Type

Tests for Within-Subjects (Repeated Measures) Designs

Analysis of Covariance

Multivariate Analysis


  ANOVA/MANOVA Output Options - Hypothesis Type

Select the type of hypothesis for the analysis.

Means Model:  By default, when the Regression approach check box on the startup panel is not set, ANOVA/MANOVA uses the Cell Means ANOVA Model.  Specifically, the sums of squares for the different effects in the design are computed for linear combinations of the cell means.  For complete factorial designs, this yields sums of squares that are identical to those discussed below as Type III.  However, with the Planned comparison option the user can test hypotheses about any weighted or unweighted linear combination of cell means.  In this manner, the user can test not only Type III hypotheses, but any type of hypothesis (including Type IV).  This general approach proves particularly useful when analyzing designs with missing cells (so-called incomplete designs).

Type I, II, and III Hypotheses:  These options are only available if the Regression approach check box on the startup panel was set.  In general, we can test the significance of partial correlations, in effect controlling for other effects, or we can enter the variables in a stepwise fashion, controlling for all other factors that were previously entered and ignoring those that have not yet been entered.  In essence, this is the difference between Type III and Type I Sums of Squares.  Another "intermediate" strategy would be to control for all other main effects when testing a particular main effect, for all main effects and two-way interactions when testing a particular two-way interaction, for all main effects, two-way interactions, and three-way interactions when testing a particular three-way interaction, and so on.  Sums of squares for effects computed in this manner are called Type II sums of squares.  Thus, Type II sums of squares control for all effects of the same or lower order, while ignoring all effects of higher order.


  ANOVA/MANOVA Output Options - Designs

This switch is only applicable in designs containing repeated measures factors with more than two levels.  The Overview section discusses the advantage of multivariate tests of effects involving those factors over the traditional univariate approach.  Briefly, an important assumption underlying the use of univariate test statistics for repeated measures factors with more than two levels is the so-called compound symmetry assumption.  This assumption, which is frequently violated, is not implied by the multivariate approach.  This switch allows users to compute the univariate only tests, the multivariate only tests, or both (default).

Greenhouse-Geisser & Huynh-Feldt:  The purpose of these tests is to adjust the univariate results of repeated measures ANOVA (for factors with more than two levels) for violations of the compound symmetry assumption.  This assumption, as well as these tests, are discussed in the Overview section.

Mauchley's Sphericity Test:  This test is only applicable to designs with repeated measures factors with more than two levels.  The sphericity assumption is related to the compound symmetry assumption; both are concerned with the conditions under which the univariate approach to repeated measures ANOVA yields valid statistical significance tests.  These assumptions are discussed in the Overview section.

The Mauchley test of sphericity evaluates the hypothesis that the sphericity assumption holds (null hypothesis); if the test is significant, then we reject the hypothesis of sphericity and declare the assumption violated.  However, Monte Carlo studies (Rogan, Keselman & Mendoza, 1979; Keselman, Rogan, Mendoza & Breen, 1980) have shown the Mauchley test to be very sensitive to departures from multivariate normality; yet, even minor (non-significant) violations of the sphericity assumption can lead to erroneous conclusions in the ANOVA (see Bock, 1975; Box, 1954; Kirk, 1982).  Therefore, we advise the user to always compute the multivariate statistics for repeated measures, just in case.


  ANOVA/MANOVA Output Options - Analysis of Covariance

The following two options are only applicable when the design contains covariates and (in the case of Adjusted Means) between-groups factors.

Regression Results:  This option controls whether or not the regression results for the covariates are reported (click on this option in order to include regression results in the output).

Adjusted means:  This option controls whether or not the adjusted means (adjusted for covariates) will be reported (click on this option in order to include adjusted means in the output).


  ANOVA/MANOVA Output Options - Multivariate Analysis

The following two options are available when performing multivariate analysis.

Discriminant Analysis:  In multivariate designs with between-groups factors, a discriminant function analysis can be performed (see also Discriminant Analysis for details concerning this procedure).  This check box controls whether or not these results are reported.  If requested, the program will compute the linear combination of dependent variables that results in the best discrimination between groups.  The maximum number of those linear combinations (or roots) that can be computed is equal to the minimum of (1) the number of groups minus one, or (2) the number of dependent variables.

Display Sums of Squares Matrices:  When this check box is set, the sums of squares matrices for the hypothesis and the error are displayed.  When the design is between-groups multivariate in nature (multiple dependent variables), the rows and columns of these matrices contain the hypothesis or error SS for each dependent variable in the diagonal, and the respective sums of cross-products in the off-diagonal locations.  If the design is univariate but contains repeated measures factors with more than two levels, then when evaluating hypotheses involving those repeated measures, these matrices will contain the respective sums of squares and cross-products (SSCP) for the within-subject model.


  ANOVA/MANOVA - Testing Specific Effects

Specify the effect that you wish to examine more closely.  You can click on the Output options button to specify the detail of results that will be reported for the effect that you select here.

The rules for specifying effects is straightforward:

•	To examine a main effect select (highlight) the respective factor;

•	To examine an interaction between two factors highlight the respective two factors;

•	To examine three-way interactions select the three respective factors, and so on.


  ANOVA/MANOVA - Results for Covariates (Regression Results)

This dialog is only available if the design contains covariates and will be displayed when either of the following two cases occur:

(1)	If the user chooses Within-cell Regression from the results dialog;

(2)	If the user chooses Regression Results from the Output Options dialog, and then examines a specific effect (via the Specific effect/Means/Graphs option).

Covariates and repeated measures

The results displayed in the two instances described above will be different if the design includes repeated measures factors.  If the user chooses the option Within-cell Regression from the results dialog, then the displayed regression results pertain to the regression of the covariates on each variable in the dependent variable list, even though they specify levels of a repeated measures factor.  In the second case (via Specific Effect), the regression results pertain to regression of the covariates on the logical respective dependent variable.  If the covariates are fixed (static) then this logical dependent variable is always the sum across all levels of all repeated measures factors.  If the covariates are changing covariates, then the regression results pertain to the regression of the respective orthonormal effect/error matrices for the covariates on the orthonormal effect/error matrices for the dependent variables.

Regression Results (Covariates) dialog:

Summary of Results for Covariates:  If there is only one dependent variable in the design, the univariate ANOVA table for all covariates will be displayed.  In the multivariate case, the respective multivariate tests will be displayed.

B-weights and beta weights:  This option allows the user to review the raw and standardized regression coefficients (B and beta weights, respectively) and their statistical significance, for each covariate and for each dependent variable.


  ANOVA/MANOVA - Selecting Variables for Means (Interaction) Plot

When you click on the Means/Graphs button in the results dialog, the Table of all Effects dialog will open in which you can select the variables or their interactions to be included in either a plot of means or Scrollsheet of (unweighted) means (click on the Graph or Scrollsheet radio button in the Display option).  This dialog gives a summary of the analysis of variance so that you can decide which effect to look at (for example, you may only want to look at the significant effects which are marked with an  *  , asterisk).  To select the desired main effect or interaction, click on the variable name or interaction to highlight it and then click OK to display the graph or Scrollsheet.


  ANOVA/MANOVA - Assignment of Factors to Axes of the Plot

When plotting interactions (see Means/Graphs), you can control the assignment of design factors to the line patterns, upper X-axis, and lower X-axis.  For a 3-way or higher order interaction, you also have the option to display all plots in one graph (select the Display all segments of the graph in one "line" option to display the plots side by side in one row) or not (de-select this option to display the plots in more than one row).  However, if more than three factors need to be plotted, then the plot is produced in "chunks" within the levels of the other (not-selected) factors.


  ANOVA/MANOVA - Post hoc Comparisons

This dialog provides a choice of various post hoc procedures.  You may refer to the Overview section for a discussion of the basic logic behind these tests.  Discussions of post hoc procedures are also provided in Winer (1962), Hays (1988), or Milliken and Johnson (1984).  The tests will be computed for the (unweighted) marginal means involved in the selected effect.  For example, if a main effect was specified, then the post hoc tests are performed on the (unweighted) marginal means for each level of the respective factor; if the post hoc test was requested for a 2 x 2 interaction effect then the post hoc tests will be performed on the four means of the 2 x 2 table that make up the interaction.

Choice of error term.  The post hoc tests are performed based on the error terms from the respective overall analysis.  Thus, post hoc tests for both repeated measures as well as between-groups factors can be performed.

Post hoc Comparisons of Means dialog:

Means

LSD Test or Planned Comparison

Scheffé test

Newman-Keuls test & Critical Ranges

Duncan's Multiple Range Test & Critical Ranges

Tukey HSD (Honest Significant Difference) Test

Tukey HSD for Unequal Sample Sizes (Spjotvoll & Stoline test)


  Post hoc Comparisons - Means

This option will bring up a Scrollsheet with the (unweighted) marginal means for the respective effect.  As in all other Scrollsheets of marginal means in ANOVA/MANOVA, these means can be plotted via the Stats Graph option.


  Post hoc Comparisons - LSD Test or Planned Comparison

This test is equivalent to the t-test for independent or dependent samples (see also Basic Statistics and Tables), based on the n in the respective cells of the design involved in the comparison.  It offers the least amount of protection against the increased alpha error rate due to multiple post hoc comparisons.  After choosing this option, a matrix of p-values will be displayed in a Scrollsheet.  These p-values indicate the post hoc significance levels for the respective pairs of means.


  Post hoc Comparisons - Scheffé Test

This option will bring up a Scrollsheet with the post hoc p-levels for the Scheffé test.  The Scheffé test is usually more conservative than the Newman-Keuls or Duncan test (see Winer, 1962).


  Post hoc Comparisons - Newman-Keuls test & Critical Ranges

This test is based on the studentized range statistic.  Computationally, the program first sorts the means into ascending order.  For each pair of means the program then assesses the probability under the null hypothesis (no differences between means in the population) of obtaining differences between means of this (or greater) magnitude, given the respective number of samples.  Thus, it actually tests the significance of ranges, given the respective number of samples.  Note that ANOVA/MANOVA does not merely report cut-off values for p, but will compute the actual probabilities based on the distribution of the studentized range statistics.

After exiting from the Scrollsheet which displays the matrix of p-values for pairs of means, the program will compute the critical ranges between ordered means, given the respective alpha level (by default p < .05).  You can change this alpha level using the Alpha Level for Critical Ranges option.


  Post hoc Comparisons - Duncan's Multiple Range Test & Critical Ranges

This test is based on the same logic as the Newman-Keuls procedure; however, it uses a less conservative test criterion (see, for example, Milliken & Johnson, 1984).


  Post hoc Comparisons - Tukey HSD (Honest Significant Difference) Test

The Tukey HSD test falls between the Newman-Keuls and Scheffé procedures with regard to conservatism.


  Post hoc Comparisons - Tukey HSD for Unequal Sample Sizes (Spjotvoll & Stoline test)

This test is a generalization of Tukey's test to the case of unequal samples sizes (see Spjotvoll & Stoline, 1973, p. 975).


  ANOVA/MANOVA - Descriptive Statistics & Tests of ANOVA Assumptions

When you click on the Descriptive Stats & Graphs button in the ANOVA/MANOVA results dialog, the Descriptive Statistics & Graphs dialog will open.

Descriptive Statistics & Graphs dialog:

Descriptive Statistics

Descriptive Graphs

Tests of ANOVA Assumptions


  Descriptive Statistics & Tests of ANOVA Assumptions - Tests of ANOVA Assumptions

The following options are available for testing specific assumptions.  For more general discussion of these assumptions, see the Assumptions and the Effects of Violating Assumptions section.

Homogeneity of Variances/Covariances button:  One of the assumptions of univariate ANOVA is that the variances are equal (homogeneous) across the cells of the between-groups design.  In the multivariate case (MANOVA), this assumption applies to the variance/covariance matrix of dependent variables (and covariates).  Those assumptions, and the effect of their violation, are discussed in the Overview.  After choosing this option the Tests of Homogeneity of Variances/Covariances dialog will be displayed from which the user can choose a specific univariate (Cochran C, Hartley, Bartlett, or Leven's test) or multivariate (Box M or Sen & Puri's Nonparametric test) test.

Parallelism of Regression lines/planes (interactions by covariates) button:  One of the common assumptions of analysis of covariance is that the regression models in each cell of the between-groups design are equal.  With this option, this assumption can be specifically tested.  Basically, the test amounts to comparing the residual variance/covariance matrices within each cell based on a common regression model (common beta coefficients) with the within-cell residual matrix based on separate models.  If there is more than one between-group factor, then the user can specify which factor(s) to ignore (i.e., which cells in the design to constrain to identical regression models), and which factors to include (for which cells in the design to allow for separate regression models).  Put another way, the user can specifically test interactions of the covariates with the between-groups factors.

After choosing this option, if there is more than one between-groups factor in the design, an effects specification window will open.  As the default, the highest order between-groups interaction is specified.  Accepting this default will result in the test of whether or not there are differences in the regression lines or planes across any of the cells of the between-groups design.  If there are multiple dependent variables, both the univariate results (for each dependent variable) as well as the multivariate results (for all variables simultaneously) are reported.

Plot of means versus standard deviations/variances/standard errors buttons:  These options allow you to plot the (unweighted) means for the dependent variables against the respective measure of variability (select either standard deviations, variances, or standard errors), across the between-groups cells of the design.  The Overview discusses how the overall F tests in the ANOVA table can be very misleading if the means are correlated with the variability.  Briefly, if extreme (large or small) means occur in cells with larger variances, then there are usually outliers present in those cells.  As a result, the confidence limits of the respective means would be much larger if estimated from those cells alone, while the overall ANOVA result makes those means appear more reliable, leading to statistically significant results.  This happens quite often in actual research, and one is well-advised to produce this plot before accepting critical results.  If the means are correlated with the variability across the cells of the design, one can (1) try to identify outliers and exclude them from the analysis, (2) use nonparametric tests, or (3) use transformations (such as a log transformation) on the data to "pull in the long tails" of the distributions with the larger variances.

Distribution of Dep. Variables and Covariates button:  This option allows you to produce a histogram for the selected dependent variables and covariates, either for selected groups or all groups combined.  First, a Scrollsheet with the observed distribution will be displayed; the expected frequencies under the normal distribution will also be reported in that Scrollsheet.  In addition, the Kolmogorov-Smirnov one-sample test and the Chi-square Goodness-of-fit test will be reported.  Next the plot of the histogram will be displayed; the normal curve will be superimposed over the observed data.

Usually only severe deviations from normality pose problems for the validity of the F statistic.  Lindman (1974, p. 32) discusses the impact of deviations from the normal distribution with regard to the Kurtosis of the distribution; after reviewing evidence from Monte-Carlo research, he concludes that the F statistic is quite robust in this respect.  However, "odd" systematic shapes in this plot may be very useful for identifying outliers or multi-modality in the distribution.

Stem & Leaf Plot for Dep. Vars & Covariates button:  This is an alternative to the histogram (above).  Like the histogram, the stem and leaf plot (Tukey, 1972) can be produced for selected variables, either for selected groups only, or for all groups combined.

In this plot, each stem represents an interval, just like in a regular histogram.  However, unlike in the histogram where we plot a vertical "bar" to indicate the number of cases that fall into the respective interval, here we plot the actual values as leaves of the stem.

Normal and Half-Normal Probability Plots buttons:  These options allow you to plot the within-cell deviations from the respective cell means in a normal probability plot (click on the Normal Plot of Within-Cell Residuals button), half-normal probability plot (click on the Half-Normal button), or a detrended half-normal probability plot (click on the Detrended Normal Plot of Within-Cell Residuals button).  These options provide another "visual" check of whether or not the normality assumption is violated.  For more information on how each of these plots is constructed, see Spreadsheet and Scrollsheet Stats Graphs - Probability Plot of . . ..

Scatterplot of Dep.Vars and Covariates button:  This option allows you to compute scatterplots between any two dependent variables or covariates.  These plots can be produced for all groups (between-groups cells in the design) combined, or for selected groups only.  The program will first prompt you to select the two variables for the plot, and then ask you to specify whether to produce the plot for a specific group or all groups combined.

Half-Normal Prob. Plot of z-transformed Within-Cell Correlations button:  This option is only available if there are multiple dependent variables or covariates in the design.  It is useful for exploring the distribution of the within-cell (group) correlations between variables.  If the correlations are homogeneous across groups in the population (a MANOVA assumption), then we would expect the correlations to be normally distributed across the samples in our study.  Because correlation coefficients generally do not follow the normal distribution, the z-transformed correlations are used for the plot instead.  The half-normal probability plot is constructed from those z-transformed within-cell correlations as explained under Normal and half-normal probability plots in Spreadsheet and Scrollsheet Stats Graphs - Probability Plot of . . ..

Matrix Scatterplot for all Variables button:  This option will bring up a matrix scatterplot for all dependent variables and covariates in the current design.


  Descriptive Statistics & Tests of ANOVA Assumptions - Descriptive Statistics

The following options are available under the Descriptive Statistics heading in this dialog.

Pooled Within-Groups Covariances & Correlations button:  Via this option you can display the pooled within-group variance/covariance matrix and the correlation matrix of dependent variables and covariates.  First, the covariance matrix will be displayed, then the pooled within-group correlation matrix will be displayed.

Total Covariances & Correlations button:  This option will display the total variance/covariance matrix and correlation matrix of dependent variables and covariates.

Covariances & Correlations for Selected Groups button:  This option is useful for examining the variance/covariance matrices for selected groups (cells in the between-groups design).  After choosing this option the list of cells in the between-groups design will be displayed.  From that list select the group for which to display the variance/covariance and correlation matrix of dependent variables and covariates.

Means & Number of Cases button:  This option will bring up a Scrollsheet of (unweighted) means for each dependent variable and covariate, and the number of cases (valid n) for each cell of the between-groups design.  The overall means and total n are also reported.

Standard Deviations button:  This option will bring up a Scrollsheet of standard deviations for each dependent variable and covariate and the number of cases (valid n) for each cell of the between-groups design.  The overall standard deviations and total n are also reported.


  Descriptive Statistics & Tests of ANOVA Assumptions - Descriptive Graphs

The following options allow you to plot specific descriptive graphs.  After you click on any of these options, a dialog window will be displayed prompting you to select the "effect" for which to produce the plot.  The plot will be categorized by the selected factors, collapsing across those that were not selected.

Categorized Histogram (by group) button:  This option will allow you to visually examine the distribution of values of the currently highlighted variable broken down (categorized) by the levels of the previously selected grouping factor(s) (see also, Categorized Histograms).

Categorized Normal Probability Plot button:  When you click on this button, a plot displaying separate probability plots for each category of the previously selected grouping factor will be produced.  These categorized probability plots visualize the normality of the distribution of the currently selected factor categorized by the grouping factor.  The assumption of normality (the data follow a normal distribution) is a very important assumption in statistics (see Elementary Concepts), and normal probability plots are often used to visually verify this assumption.

Categorized Box-Whisker Plot button:  You can choose one of four types of categorized box and whisker plots to represent the distribution of categorized values of the selected factor.  The box plots resulting from this option represent the selected factor's central tendency and variability for each category of the previously selected grouping factor(s).  As measures of central tendency, you can choose between plotting the means and medians of the values in each category and for each, their respective measures of variability; standard deviations or standard errors, and ranges in the Box and Whisker Plot Type dialog.

Categorized Scatterplot button:  Click on this button in order to plot the values of one factor against the values of another, categorized by the levels of the grouping factor(s).  The Categorized Scatterplot visualizes a relation between two variables X and Y (e.g., weight and height).  Individual data points are represented in two-dimensional space, where axes represent the variables.  The two coordinates (X and Y) that determine the location of each point correspond to its specific values on the two variables.


  ANOVA/MANOVA - Selecting a Group for the Scrollsheet or Plot

This window lists all groups in the current between-group design.  Select a group by clicking on it.


  ANOVA/MANOVA - Tests of Homogeneity of Variances

One of the assumptions of univariate ANOVA is that the variances are equal (homogeneous) across the cells of the between-groups design.  In the multivariate case (MANOVA), this assumption applies to the variance/covariance matrix of dependent variables (and covariates).  Those assumptions, and the effect of their violation, are discussed in the Overview.

Univariate Test Options

Multivariate Test Options


  Tests of Homogeneity of Variances - Univariate Tests

Univariate Tests:  This option will bring up a Scrollsheet with the Hartley F-max statistic, Cochran C statistic, and the Bartlett Chi-square test (with appropriate degrees of freedom and p-level).  All of these statistics test the homogeneity of variances assumption in the univariate case.  If there are multiple dependent variables or covariates, the tests are displayed for each dependent variable and for each covariate.  All of these tests are described in most standard ANOVA textbooks (e.g., see Winer, 1962, p. 94).  As described in the Overview section, the consequences of even quite major violations of the homogeneity of variances assumption are not that critical.  Lindman (1974, p. 33) summarizes the results of various studies of this issue, and shows that only under the most severe violations do we need to be concerned about the validity of the F statistic.  It is, however, very important to examine any correlations between the means and the variances (or standard deviations; use option Plot of Means versus standard deviations... to look at those correlations).

Levene's test:  Levene's test for the homogeneity of variances amounts to performing a one-way ANOVA on the absolute deviation scores (from the respective cell means).  The logic of this test is that the greater the variance in a cell, the larger are the absolute deviations from the respective cell mean.  This test is discussed in Milliken and Johnson (1984).


  Tests of Homogeneity of Variances - Multivariate Tests

Box M:  This is a multivariate test of the homogeneity of variances and covariances for multiple dependent variables or covariates.  Use the Variables radio buttons to specify whether or not to include the covariates in this tests.  The Box M test is very sensitive to deviations from the normal distribution and its results should be viewed with some skepticism.  If this test is significant, then it means that the variance/covariance matrices in the different between-group cells in the design are significantly different from each other (see Anderson, 1958).  In that case, one should probably examine the within-group variance/covariance matrices for any major heterogeneity problems; however, violations of this homogeneity of variances/covariances assumption usually do not seriously threaten the validity of the multivariate results.

Sen & Puri's Nonparametric Test:  This nonparametric alternative to the Box M test (Sen & Puri, 1968) has recently gained in popularity.  In essence, the test is based only on the rank-order information in the data, and therefore it is not affected by deviations from the normal distribution.  However, it is also not a very sensitive test.


  ANOVA/MANOVA - Compress/Spread Stem-and-Leaf Plot

This option affects the number of intervals that is created for the stem-and-leaf plot.


  ANOVA/MANOVA - Selecting Two Variables

Select one variable from each list of variables by clicking on the variable name to highlight it.


  ANOVA/MANOVA - Selecting a Variable

Select one variable from this list by clicking on it.


  ANOVA/MANOVA - Selecting a List of Variables

Select a variable list by highlighting the respective variables.  To highlight a block of variables, hold down the left-mouse-button while moving the mouse over the list.  To select/deselect single variables into or from the list, hold down the CTRL key while clicking on the respective variable.


  ANOVA/MANOVA - Assignment of Factors to Axes in Categorized Plots

The selected plot will be produced categorized by the selected factors.  Select the factors by which the plot is to be categorized within each plot, that is, the factors that are to be denoted by the x (horizontal) and the y axes (vertical) in the plot.  If there are more than two factors, then a separate plot will be produced for each level of the factors that were not assigned to any axes.


  ANOVA/MANOVA - Pooled Effects & Error Terms

This dialog allows the user to build customized effects or error terms.  In some cases, a researcher may want to perform a summary test of all main effects.  Another common practice is to pool into the error term higher order interactions that are of little theoretical or practical interest.  Via this method, a wide variety of incomplete designs (including Latin squares) can be analyzed (see below).  Note that only effect and error terms involving between-groups factors can be pooled.

Pooled Effect and Error Term dialog:

Effect

Error

Latin squares


  Pooled Effects & Error Terms - Effect

After clicking on this button, the Between-group Effect dialog will open with all between-groups effects in the design.  Select all effects that are to be pooled together in this dialog and then click OK.


  Pooled Effects & Error Terms - Error

This button actually represents a switch with three settings: Within, Customized, and SS-Total minus customized.

Within:  In the first setting, the standard within-group error term is used to test the pooled effect selected via option Effect.  Click OK in this dialog (once you have selected the pooled effects) to complete the test.

Customized:  In order to define a customized (pooled) error term, click on the Error button (while it is still on the Within setting) to open the Between-group Effect dialog.  Select in this dialog, the effects to be pooled into the error term (e.g., a 3-way interaction and the within error terms) just as in option Effect above, and after closing this window, the Error switch will be set to Customized.  Click OK in this dialog to complete the test using the pooled error term.

SS-Total minus customized:  Once you have selected the variables to pool into the customized error term in the Between-group Effect dialog, click OK to exit the dialog and then click on the Error button to change the setting to SS-Total minus customized.  In that setting, the error term used in the analysis is the total sums of squares minus the sums of squares attributable to the effects pooled into the customized error term (as selected in the previous setting of the switch).  This latter setting of the switch is particularly useful for analyzing Latin square type designs or randomized block designs.


  Pooled Effects & Error Terms - Latin Square

To analyze a (univariate or multivariate) Latin square, Greco-Latin square, Hyper-Greco Latin square, etc., first define the design as if it were a full factorial design.  Next bring up this dialog and select the desired main effect to be tested (via option Effect).  As the error term, select the sums of squares total minus all main effects.  This will result in the appropriate significance tests for the main effects.  Note that a comprehensive implementation of Latin, Greco-Latin, and Hyper-Greco Latin square designs is also available in Experimental Design.


  ANOVA/MANOVA - Specifying Pooled Effects (Combining Effects)

Select the effects that are to be pooled together (combined).  Highlight an effect by clicking on it; highlight a group of effects by moving the mouse over them while holding down the left-mouse-button.  To select/deselect individual effects press the CTRL key and click on the respective effect.


  ANOVA/MANOVA - Sequential (Type I) Sums of Squares

Type I sums of squares test effects sequentially, in a way similar to stepwise multiple regression (see the Notes section; see also Multiple Regression).  All effects that were previously entered into the model are controlled for, and all effects not yet entered into the model are ignored.

When you select Type I Sums of Squares in the Output Options dialog and then click on the All Effects button in the results dialog, the Order of Effects for Type I Sums of Squares dialog will open.  You can elect to test the effects in the default order (click on the Default radio button) or in a customized order (click on the Customized radio button).


  ANOVA/MANOVA - Order of Effects (Sequential Sums of Squares)

Type I sums of squares test effects sequentially, in a way similar to stepwise multiple regression (see the Notes section; see also Multiple Regression).  All effects that were previously entered into the model are controlled for, and all effects not yet entered into the model are ignored.

On this dialog, specify the order in which the effects are to be tested (entered into the model).  The left column show the effects in the default order.  You can select single or multiple effects in that column in the standard manner, that is, by clicking on them.  Then click on the >> button to append the selected effects to the right column, which shows the order in which the effects will be tested (entered into the model).  If you make a mistake, you can also move effects out of the right column.

You do not have to select all effects into the right column.  After you click OK all effects that were not selected will automatically be tested last, in the default order.

You can click on the Sort Sel. button to sort the list of effects in the right column according to the default order.


  ANOVA/MANOVA - Alpha Level for Table of All Effects

Enter the alpha error probability that is to be used for highlighting effects in the table of all effects.  The default value for alpha is .05.  This value is used as a "cut-off" for statistical significance (i.e., if the p-value is less than alpha, then the effect is highlighted in the Scrollsheet to indicate significance).  In this dialog, you can edit this "cut-off" value (.0001 < α < .5) and then click OK to immediately apply this change to the next copy of the current Scrollsheet.


  ANOVA/MANOVA - Plots of Means/Interactions & Tables of Means

In order to produce a plot of means (interaction plot) or Scrollsheet of (unweighted) means (depending on the setting of the Display radio buttons), first select either a main effect or interaction by highlighting it (clicking on it).  Then click Ok to exit this dialog and display the Scrollsheet or graph.


  ANOVA/MANOVA - Entering Contrasts for Each Factor Separately

To specify a contrast for an effect in this intermediate dialog, first click on the desired effect and then enter the respective contrast coefficients in the Entering Contrasts for this Factor dialog.  The currently specified set(s) of contrasts are listed under each factor.

To learn more about the logic and interpretation of contrast analysis refer to the Overview section; examples of how to specify contrasts are also discussed in the Notes section, for between-group designs as well as repeated measures designs.


ANOVA/MANOVA - Specifying a Set of Contrast

  ANOVA/MANOVA - Specifying a Set of Contrasts

Specify the contrast coefficients for the highlighted factor.  To learn more about the logic and interpretation of contrast analysis refer to the Overview section; examples of how to specify contrasts are also discussed in the Notes section, for between-group designs as well as repeated measures designs.

The general rules for generating contrast coefficients are as follows:

(1)	The contrast must have as many coefficients as there are levels for the respective factor.

(2)	Levels that are to be omitted in the contrast are assigned a 0 (zero).

(3)	Levels that are to be compared against each other are assigned positive or negative integer values; however, it is important that the sum of such contrasts is equal to zero.

(4)	Levels that are to be collapsed are assigned identical integer values (e.g., all 1's).

If the highlighted factor has more than two levels, then several pre-defined sets of contrasts are also available, including contrast coefficients for testing orthogonal polynomials (trend analysis).

Quick Fill:  The Quick Fill option allows you to quickly enter contrast coefficients.  When you select Cell and click on one of the number buttons, the coefficient in the cell for the highlighted variable will be replaced by that number (i.e., only that cell will be replaced).  If you select Column, then clicking on one of the number buttons will replace the coefficients for all of the variables with the selected number (i.e., the entire column of contrast coefficients will be replaced with this number).  If you select Row, then clicking on one of the number buttons will replace all of the coefficients for a variable with the selected number (i.e., the entire row of contrast coefficients will be replaced with this number).

Predefined Contrasts:  If desired, you can click on either the Polynomial or Other buttons under this option in order to select a predefined contrast.


  ANOVA/MANOVA - Specifying Contrast Vectors

Enter the desired contrast coefficients for the respective combination of treatment levels (cells of the between-group or within-subject design).  To learn more about the logic and interpretation of contrast analysis refer to the Overview section; examples of how to specify contrasts are also discussed in the Notes section, for between-group designs as well as repeated measures designs.

The general rules for generating contrast coefficients are as follows.

(1)	The contrast must have as many coefficients as there are combined number of levels (cells in the design).

(2)	Cells that are to be omitted in the contrast are assigned a 0 (zero).

(3)	Cells that are to be compared against each other are assigned positive or negative integer values; however, it is important that the sum of such contrasts is equal to zero.

(4)	Levels that are to be collapsed are assigned identical integer values (e.g., all 1's).

If there are missing cells in the between-group design then asterisks are shown next to the respective rows.  Only 0's may be entered for those cells.


  ANOVA/MANOVA - Predefined Types of Contrasts

When you click on either the Polynomial or Other buttons in the Specify Contrasts for this Factor the respective Polynomial Coefficients dialog or Predefined Contrasts dialog will open from which you can select one of the predefined sets of contrasts.

Polynomial Coefficients dialog:  Select in this dialog, the degree of polynomial (up to a fifth order polynomial, if applicable) for the contrast coefficients.

Predefined Contrasts dialog:  Choose from the following predefined contrasts in this dialog:

Deviation:  This type of contrast compares the deviations from the grand mean of the dependent variable, for example for a factor with 3 levels, the following matrix of contrasts would be created:

 2 -1 -1

-1  2 -1

Difference:  This type of contrast compares the levels of a variable with the mean of the preceding levels of that variable, for example for a factor with 3 levels, the following matrix of contrasts would be created:

-1  1  0

-1 -1  2

Helmert:  This is the Helmert contrast matrix, for example for a factor with 3 levels, the following matrix of contrasts would be created:

 2 -1 -1

 0  1 -1

Simple:  This type of contrast compares a preceding level of a variable with the last level of that variable, for example for a factor with 3 levels, the following matrix of contrasts would be created:

 1  0 -1

 0  1 -1

Repeated:  This type of contrast compares adjacent levels of a variable, for example for a factor with 3 levels, the following matrix of contrasts would be created:

 1 -1  0

 0  1 -1


  ANOVA/MANOVA - Options for Planned Comparison Facility

Contrasts can be entered separately for each factor, or for all factors combined (together, as a contrast vector);  in multivariate designs the user can also choose to enter contrasts for the dependent variables.

To learn more about the logic and interpretation of contrast analysis refer to the Overview section; examples of how to specify contrasts are also discussed in the Notes section, for between-group designs as well as repeated measures designs.


  ANOVA/MANOVA - Reordering Effects for Type I (Sequential) SS

Type I sums of squares test effects sequentially, in a way similar to stepwise multiple regression (see the Notes section; see also Multiple Regression).  All effects that were previously entered into the model are controlled for, and all effects not yet entered into the model are ignored.

On this dialog specify the order in which the effects are to be tested (entered into the model).  The left columns show the effects in the default order.  You can select single or multiple effects in that column in the standard manner, that is, by clicking on them.  Then click on the >> button to append the selected effects to the right column, which shows the order in which the effects will be tested (entered into the model).  If you make a mistake, you can also move effects out of the right column.

You do not have to select all effects into the right column.  After you click OK all effects that were not selected will automatically be tested last, in the default order.

You can click on the Sort Sel. button to sort the list of effects in the right column according to the default order.


  ANOVA/MANOVA - Notes and Technical Information

General

ANOVA/MANOVA is an implementation of the general linear model (see Bock, 1975; Finn, 1974, 1977; Hays, 1981; Lindman, Merenda, & Gold, 1980).  The program will first compute the within-cell variance/covariance matrix of dependent variables (and covariates, see below).  The design matrix of main effects and interactions (or the matrix of contrasts coefficients) is first orthonormalized (see Bjorck, 1967), and then used to compute the sums of squares hypothesis (from the cell means) and sums of squares error (from the within-cell variance/covariance matrix).  If the design contains covariates, they are appended to the within-cell variance/covariance matrix of dependent variables and treated as such; before the computation of the statistical tests, the hypothesis and error matrices are reduced (adjusted by covariates) via sweeping (Dempster, 1969).  These procedures are described in detail by Finn (1974, 1977).

The General Linear Model

Detailed treatments of this model can be found in numerous sources.  A few examples are Bock (1975); Finn (1974); Hocking and Speed (1975); Morrison (1967); Timm (1975); or Timm and Carlson (1973, 1975).


  STATISTICA Command Language (SCL)

Introductory Overview and Global Options

Introductory Overview of STATISTICA Command Language

Writing an SCL Program

Verifying the SCL Program

Running the SCL Program

Interrupting SCL Programs

Error Trapping: If Something Goes Wrong

Reviewing Output

SENDKEYS Command

Run-time User-interface for SCL Programs

Menus

Examples

Syntax

General Conventions & Global Options

Specifying Variables

Specifying Values of Variables (codes)

Selection Conditions

Structure of SCL Language

Description of Syntax

Output (Saving, Printing)

Sendkeys

Data Management

STATISTICA BASIC

Basic Statistics

Nonparametric Statistics & Distribution Fitting

Multiple Regression

Nonlinear Estimation

Time Series and Forecasting

Factor Analysis

Cluster Analysis

Canonical Correlation Analysis

Correspondence Analysis

Multidimensional Scaling

Reliability and Item Analysis

General ANOVA/MANOVA

Discriminant Function Analysis

Log-linear Analysis

Survival Analysis

Quality Control

Process Analysis

Design of Experiments

SEPATH

Graphics

STATISTICA Command Language - Run Module


  STATISTICA Command Language - Introductory Overview

Introductory Overview of STATISTICA Command Language

Writing an SCL Program

Verifying the SCL Program

Running the SCL Program

Interrupting SCL Programs

Error Trapping: If Something Goes Wrong

Reviewing Output

SENDKEYS Command


  Introductory Overview of STATISTICA Command Language

The STATISTICA Command Language (SCL for short) allows you to run STATISTICA in batch mode, that is, you can develop "programs" that will instruct STATISTICA in what to do (see also Command Language - Index).  Those SCL programs can then be executed in any module of STATISTICA without requiring any additional input.  SCL programs can also be saved for later repeated use via the Save As option in the File pull-down menu.  You can use the STATISTICA Command Language as a "turn-key" system in order to speed up invoking already tested or repeatedly executed SCL programs or to develop "fail-safe" programs for persons unfamiliar with STATISTICA.  Alternatively, you can assign SCL programs to buttons on the customizable Auto Tasks Buttons floating toolbar.

You can create or execute an SCL program in any module of STATISTICA (via the Analysis pull-down menu option Command Language (SCL) or the File pull-down menu option Open Other - Command Language).  STATISTICA provides a Command Wizard in which you can select specific SCL commands to help you build your program.  When you highlight a command, a brief description will be displayed and the command will appear in the edit field of the dialog.  You can edit the command (e.g., add variable names, enter specific codes, etc.) in this edit field and click Insert to enter the command at the current cursor position in the program.

During execution, if the SCL program calls a currently open module (e.g., you want to perform a regression analysis and you are currently in the Multiple Regression module), then you will be prompted to close the module (automatically) before proceeding with the analysis.  If you choose not to close the module, the SCL program will be halted.  The STATISTICA File Server will be used to perform all graphics and general spreadsheet commands.  Since multiple File Server modules can be open at the same time, you will not be prompted to close an open File Server module.

STATISTICA maintains a log of messages for non-fatal errors which may occur during execution of the program.  After the program is executed, these messages (if any) will be displayed in a text window for your review.  In order to save or print these messages, highlight the desired text and copy it to the Clipboard (via CTRL+C) and then paste (via CTRL+V) the contents of the Clipboard into a new Text/output Window.

Now, consider the following simple SCL program:

OUTPUTSETUP SCROLLSHEETS = PRINTER AND WINDOW

DESCRIPTIVES VARIABLES=ALL

CORRELATION VARIABLES=ALL/PAIRWISE

This SCL program will compute descriptive statistics (using Basic Statistics) for all variables in the current data file and then compute the correlation matrix for all variables, using pairwise deletion of missing data.  The first line of the "program" directs the output from both tasks to the printer and Text/output Window (see OUTPUTSETUP).

SCL supports abbreviations of long keywords; for example, the above program can also use short equivalents of DESCRIPTIVES, VARIABLES, and CORRELATION:

OUTPUTSETUP SCROLLSHEETS = PRINTER AND WINDOW

DESC VARS=ALL

CORR VARS=ALL/PAIRWISE

All common tasks and procedures can be run via the STATISTICA Command Language.  For information about the general syntax rules, see STATISTICA Command Language - Syntax, and for example programs see, STATISTICA Command Language - Examples.  See also Order of SCL Commands.

Your SCL programs may be integrated with STATISTICA BASIC programs.  One or multiple BASIC programs can be included in an SCL program to perform data transformations, custom computations, produce custom output (e.g., additional graphs, Scrollsheets), or provide user interface for the SCL program (see next paragraph).  Also, STATISTICA BASIC programs can be fully integrated with the SCL programs in which they are embedded; for example, the BASIC programs can use as input (and then process) Scrollsheets and graphs produced by SCL.  Moreover, the output produced by the BASIC programs can be used as input by the subsequent tasks of the SCL program.

Although SCL command programs do not offer (directly) designated run-time user-interface, you can use STATISTICA BASIC programs (to be called from an SCL command program) to design dialog boxes and other elements of the user-interface which will allow users of the SCL program to select variables, data files, etc. in run-time.  An example is given in Calling STATISTICA BASIC from within SCL.

For other Overview topics, see:

Writing an SCL Program	Error Trapping: If Something Goes Wrong

Verifying the SCL Program	Reviewing Output

Running the SCL Program	SENDKEYS Command

Interrupting SCL Programs


STATISTICA Command Language - Writing an SCL Program

  STATISTICA Command Language Introductory Overview - Writing an SCL Program

In order to write an SCL program, choose the option Command Language (SCL) from the Analysis pull-down menu of any module.  Additionally, you can open a previously saved SCL file by clicking on the Open Other - Command Language option from the File pull-down menu of every module.

In order to create a new program, you can either type in the commands in the current SCL window or click on the [image] button from the SCL toolbar to open the Command Wizard in which you can select specific SCL commands to help you build your program.  Note that you can have more than one SCL window open at a time so that you can compare programs, copy and paste between programs, etc.  If you want to use a previously saved program, you can bring it up in the current SCL window using the Open option from the File pull-down menu.  Note that the order of SCL statements is very important and you should refer to the appropriate topic for examples in writing SCL programs (see also Order of SCL Statements).

In order to direct STATISTICA to the appropriate data file, you will need to precede the program with the line: FILE="filename", where filename refers to a STATISTICA raw data or matrix file and its path (e.g., c:\stat\examples\adstudy.sta).

For other Overview topics, see:

Introductory Overview of STATISTICA Command Language

Verifying the SCL Program

Running the SCL Program

Interrupting SCL Programs

Error Trapping: If Something Goes Wrong

Reviewing Output

SENDKEYS Command


STATISTICA Command Language - Verifying the SCL Program

  STATISTICA Command Language Introductory Overview - Verifying the SCL Program

After you have typed in the SCL program, you can either Verify it (that is, check the formal correctness of the syntax; select the Verify option from the Analysis pull-down menu) without executing the program, or Execute the program while simultaneously verifying the syntax (click on the Execute toolbar button).

For other Overview topics, see:

Introductory Overview of STATISTICA Command Language

Writing an SCL Program

Running the SCL Program

Interrupting SCL Programs

Error Trapping: If Something Goes Wrong

Reviewing Output

SENDKEYS Command


STATISTICA Command Language - Running the SCL Program

  STATISTICA Command Language Introductory Overview - Running the SCL Program

In order to run the SCL program, click on the Execute button on the SCL toolbar.  If the program has no syntax errors, execution of the commands will begin.

During execution, if the SCL program calls a currently open module (e.g., you want to perform a regression analysis and you are currently in the Multiple Regression module), then you will be prompted to close the module (automatically) before proceeding with the analysis.  If you choose not to close the module, the SCL program will be halted.  The STATISTICA File Server will be used to perform all graphics and general spreadsheet commands.  Since multiple File Server modules can be open at the same time, you will not be prompted to close an open File Server module.

STATISTICA maintains a log of messages for non-fatal errors which may occur during execution of the program.  After the program is executed, these messages (if any) will be displayed in a text window for your review.  In order to save or print these messages, highlight the desired text and copy it to the Clipboard (via CTRL+C) and then paste (via CTRL+V) the contents of the Clipboard into a new Text/output Window.

For other Overview topics, see:

Introductory Overview of STATISTICA Command Language

Writing an SCL Program

Verifying the SCL Program

Interrupting SCL Programs

Error Trapping: If Something Goes Wrong

Reviewing Output

SENDKEYS Command


STATISTICA Command Language - Interrupting SCL Programs

  STATISTICA Command Language Introductory Overview - Interrupting SCL Programs

Note that you can interrupt the execution of an SCL at any point by clicking the mouse or pressing the ESC or CTRL+BREAK keys.  The program will stop and ask you if you want to interrupt the program.  If you answer Yes, the execution will stop and you will be returned to the STATISTICA Command Language window; if you answer no, then the execution will continue.

For other Overview topics, see:

Introductory Overview of STATISTICA Command Language

Writing an SCL Program

Verifying the SCL Program

Running the SCL Program

Error Trapping: If Something Goes Wrong

Reviewing Output

SENDKEYS Command


STATISTICA Command Language - Error Trapping: If Something Goes Wrong

  STATISTICA Command Language Introductory Overview - Error Trapping: If Something Goes Wrong

If, during the processing of an SCL program, a major interruption occurs (e.g., a wrong parameter is specified in the program), then the execution of that task will be terminated and the remainder of the SCL commands (if any) will be executed.  At the completion of the program, all error messages will appear in an SCL Log window.  You can review the error messages in this dialog in order to determine the source of the problem.

For other Overview topics, see:

Introductory Overview of STATISTICA Command Language

Writing an SCL Program

Verifying the SCL Program

Running the SCL Program

Interrupting SCL Programs

Reviewing Output

SENDKEYS Command


STATISTICA Command Language - Reviewing Output

  STATISTICA Command Language Introductory Overview - Reviewing Output

As you will see, the execution of SCL programs is usually very fast.  To view the results of the requested analyses, you can do one of the following:

•	STOP the program before exiting module (this will return the control to the user and allow you to review the output or continue the analysis interactively).

•	Use the OUTPUTSETUP command to specify the global output destination.

•	Use the SAVEGRAPH and SAVESCROLLSH commands to save the individual output objects into separate files.

For other Overview topics, see:

Introductory Overview of STATISTICA Command Language

Writing an SCL Program

Verifying the SCL Program

Running the SCL Program

Interrupting SCL Programs

Error Trapping: If Something Goes Wrong

SENDKEYS Command


SCLReviewing Output - STOP Command

  STATISTICA Command Language Reviewing Output - STOP Command

You can stop the SCL program execution after the final output has been computed.  To do so, place the command STOP after the last program command line.  After the SCL program has been executed, the module that performed the last task will remain active, so the user can review any Scrollsheets and graphs which have been created and interactively select additional output, change parameters, etc.


SCLReviewing Output - OUTPUTSETUP Command

  STATISTICA Command Language Reviewing Output - OUTPUTSETUP Command

You can specify the global output destination according to the following commands that correspond to the options available in the Page/Output Setup dialog (see below for information on saving individual objects, e.g., graphs):

OUTPUTSETUP

   [SCROLLSHEETS [=] {OFF                           }   {specifies the output channel for Scrollsheets}

                     {PRINTER [AND WINDOW]          }

                     {FILE = "Filename" [AND WINDOW]}

                     {WINDOW                        } ]

   [GRAPHS [=] {OFF                 }   {specifies the output channel for graphs}

               {PRINTER [AND WINDOW]}

               {WINDOW              } ]

   [REPORTFILE [=] "Filename"]   {specifies the RTF file for the Text/output window}

   [OUTPUT [=] { BRIEF  }   {specifies the amount of supplimental output}

               { SHORT  }

               { MEDIUM }

               { LONG   }]

   [PAGE [=] page_no ]   {specifies the desired page number}

   [LINE [=] {0} ... {7} ]   {specifies line thickness for printed output page}

   [HEADER [=] "Job_Header" ]   {}

   [DATETIME [=] {YES}         {prints date and time at the top of each output page}

                 {NO} ]

   [CENTERTITLES [=] {YES}     {centers the output header}

                     {NO} ]

   [METAFILEMODE [=] {PRINTER}   {specifies the printer resolution for creating metafiles}

                     {SCREEN} ]

   [GRAPHSIZE [=] {cy BY cx {INCH} {CM} }   {Specifies the size of the graph when printed to the Text/output window}

                  {FULL}                 ]

If OFF is specified, then no output will be printed (or in the case of Scrollsheets, sent to an output file).  Select PRINTER to send the output to the printer.  Optionally, you can specify AND WINDOW to send the output both to the printer and Text/output Window or specify only WINDOW to send the output to the Text/output Window.  For Scrollsheet output, you can also send the output to a text file (and optionally the WINDOW).  The REPORTFILE option specifies the name of the RTF file which will be opened (or created if it does not currently exist) in a Text/output Window.

Example

Saving graphs and Scrollsheets as individual objects.  The OUTPUTSETUP commands listed above control (globally) the management of the entire output.  If you intend to save graphs or Scrollsheets as individual objects (in separate files, one file per object), use the SAVEGRAPH and/or SAVESCROLLSH commands.

NOTE:  In order to maintain a backward compatibility with previous versions of STATISTICA/w, you can use the following output commands.  However, it is recommended that you use the OUTPUTSETUP commands.

PRINTER [=] { ON                  }

            { YES                 }

            { FILE [=] "FileName" }

            { OFF                 }

            { NO                  }

OUTPUT [=] { BRIEF  }

           { SHORT  }

           { MEDIUM }

           { LONG   }

The PRINTER=ON command will direct all output (Scrollsheet and graph) to the printer.  PRINTER=OFF will turn off both the Scrollsheet and graph output.  PRINTER=FILE will direct the Scrollsheet output to the specified file.  Instead of ON and OFF, the keywords YES and NO (respectively) can be used.

Valid Abbreviations:

SCROLLSHEET, GRAPH


SCL OUTPUTSETUP Command - Example

  STATISTICA Command Language OUTPUTSETUP Command - Example

This example SCL program will perform 4 tasks by calling the following STATISTICA modules:  Basic Statistics (for descriptives), Time Series (for autocorrelations), Time Series (for cross-spectrum analysis) and File Server (to produce a histogram).  All statistical results (text and Scrollsheets) as well as graphs will be directed to the RTF file ('D:\report.RTF') specified in the REPORTFILE statement which will be opened at the very beginning of execution and then saved automatically on exit from each module in order to preserve the changes and collect all output in one file.

outputsetup

scrollsheets = window

graphs = window

reportfile = 'D:\report.RTF'

file = 'd:\STAT\EXAMPLES\10items.sta'

descr

vars = 1-6

statistics = 1,3

autocorr

VAR = item7

/lag = 15

/whitenoise = OFF

cospectrum

VAR = ITEM3

dependent = item1

/window = 7

/smoothing = bartlett

/append quaddensity gain phase

/plot sine by logperiod

HISTogram

REG

VAR = 1 3

/FIT = NORMAL


SCLReviewing Output - SAVEGRAPH and SAVESCROLLSH Commands

  STATISTICA Command Language Reviewing Output - SAVEGRAPH and SAVESCROLLSH Commands

You can use the following commands at the beginning of the SCL program in order to direct the output to the desired destination:

You can choose to save the Scrollsheet output created during analysis into separate Scrollsheet files (one Scrollsheet per file) via the SAVESCROLLSH command.

SAVESCROLLSH = "Filename"

Note that if more than one Scrollsheet is produced during the analysis, then STATISTICA will number the Scrollsheets sequentially as they are being saved (e.g., sheet1.scr, sheet2.scr, sheet3.scr, etc.).

You can choose to save the graph output created during analysis into separate STATISTICA graphic files (one graph per file) via the SAVEGRAPH command.

SAVEGRAPH = "Filename"

Note that if more than one graph is produced during the analysis, then STATISTICA will number the graphs sequentially as they are being saved (e.g., graph1.stg, graph2.stg, graph3.stg, etc.).


STATISTICA Command Language - SENDKEYS Command

  STATISTICA Command Language Introductory Overview - SENDKEYS Command

The STATISTICA Command Language allows you to execute standard STATISTICA keyboard operations (SENDKEYS commands) from within batch programs.  The SENDKEYS commands can be used as custom "extensions" or shortcut commands in your SCL programs.  Thus, via this feature, all specialized options in all modules can be referenced in SCL programs.  For more information on Sendkeys commands, see SCL Syntax - Sendkeys.

For other Overview topics, see:

Introductory Overview of STATISTICA Command Language

Writing an SCL Program

Verifying the SCL Program

Running the SCL Program

Interrupting SCL Programs

Error Trapping: If Something Goes Wrong

Reviewing Output


  STATISTICA Command Language - Menus

The SCL window pull-down menus contain options specific to creating and executing SCL commands.  For more information, See:

SCL Window Toolbar buttons

File

Edit

View

Character

Paragraph

Analysis

Options

Window

Help


  SCL Window Toolbar buttons

The following toolbar buttons are specific to the SCL window:

  Execute the current SCL program.

  Bring up the Command Wizard (keyboard shortcut ALT+I).

  Help: Examples - quick access to simple examples.

  Help: Syntax - quick access to common syntax conventions.

For information on the other toolbar buttons available in this window, see Text/output Window Toolbar


  SCL Window File Menu

These options are available from the File pull-down menu.  Choose an option below for more information about that option.

New

Open Text

Open Other

New Data

Data File

Graph File

Scrollsheet

Text/Output

STATISTICA BASIC

Command Language (SCL)

Save

Save As

Print All

Print Selection

Page/Output Setup

Print Files

Printer Setup

Exit


  SCL Window - New

Selecting this option from the File pull-down menu will open a new (blank) text document in a new SCL window.


  SCL Window - Open

Selecting this option from the File pull-down menu will open a selected text document in a new SCL window.


  SCL Window Edit Menu

Choose an option below for more information about that option.

  Undo	Find

  Cut	Find Next

  Copy	Replace

  Paste	Go To

Paste Special	Insert Bitmap from File

Clear	Object Size

Select All	Screen Catcher


  SCL Window Analysis Menu

These general options are available from the Analysis pull-down menu.  Choose an option to obtain more information about that option.

Execute

Verify

Startup Panel

Resume Analysis

STATISTICA BASIC

Command Language (SCL)

Quick Basic Stats

  Descriptive Statistics

  Correlation Matrices

  Frequency Tables

  Probability Calculator

  More....


  SCL Window - Execute

Select this option from either the Analysis pull-down menu or the Execute toolbar button to automatically verify and execute the SCL program.  To verify the program without executing it, see Verify.


  SCL Window - Verify

Select this option from the Analysis pull-down menu in order to verify the syntax of the SCL program without executing it.


  SCL Window Options Menu

Choose an option for more information about that option.

Check Files	General

Check Variables	Display

Check Text Values	Print

Macro

Command Language (SCL)	Keyboard Macro

STATISTICA BASIC	Recorded Show Macro

Quick Open File	Customize Auto Task Buttons


  SCL Window - Check Files

This option determines whether or not STATISTICA will check (during verification) that all files referenced in the SCL program actually exist in the specified path.  Note that files created via the SCL SAVEAS option in Data Management will not be verfied.

Click on this option in the Options pull-down menu to toggle between verifying (option is checked) or not verifying (option is not checked) the files.


  SCL Window - Check Variables

The setting of the Check Variables option determines whether or not STATISTICA will check (during verification) that all variables referenced in the SCL program actually exist in the respective data file  Note that variables in files created via the SCL SAVEAS option in Data Management will not be verified (the specific variable names in such files are unknown before the program is executed, e.g., they depend on the contents of a foreign file to be imported).

Click on this option in the Options pull-down menu to toggle between verifying (option is checked) or not verifying (option is not checked) the variables.


  SCL Window - Check Text Values

The setting of the Check Text Values option determines whether or not STATISTICA will check (during verification) that all text values (codes) referenced in the SCL program actually exist in the respective data file.  Click on this option in the Options pull-down menu to toggle between verifying (option is checked) or not verifying (option is not checked) the text values.


  SCL Syntax - SAVEAS

[ SAVEAS [=] "FileName" ]

This SCL option will allow you to create a new file during execution of the program in order to save data which have been manipulated by Data Management operations (e.g., import, merge, sort, subset, etc.; for examples, see Data Management Examples).

Example:

FILE = "C:\STAT\EXAMPLES\ADSTUDY.STA"

SUBSET VARS GENDER-MEASUR2

SAVEAS "C:\STAT\EXAMPLES\ADNEW.STA"

FILE = "C:\STAT\EXAMPLES\ADNEW.STA"

T_TEST GROUPS=1(1,2)

        VARS = 3-4

The first part of this example creates a subset of data file Adstudy.sta and saves the subset as Adnew.sta.  Then, this new file is opened and used to perform a t-test.

NOTE:  Because in most instances, the specific file to be created via the SAVEAS option does not exist before the SCL program is executed (and thus, its variable names and/or text values cannot be verified), later in the program when you perform analyses on the data in the newly created file, you will need to refer to the variables in this file by the variable number (e.g., 1, 2, 5-7, etc.; see also Syntax) and any text values of variables in the file by their numeric equivalents.  If variable names and text values from this file are used in SCL statements a syntax error will result.


  SCL Window Window Menu

These options are available from the Window pull-down menu.

Scrollsheet Manager	Tile Vertically

Graph Manager	Arrange Icons

Cascade	Close All but Data File

Tile Horizontally


  SCL Window Help Menu

These options are available from the Help pull-down menu.

SCL Syntax	Search Help On

SCL Examples	Glossary

Index	Keyboard

Spreadsheet	Text/Output

Scrollsheet	Advisor

Graph	About


  STATISTICA Command Language - Examples

The examples below give (in most cases) incomplete programs because they do not specify the output destination (e.g., printer or disk file).  If you would like to try these programs, simply complete them by adding one or two more lines of commands to specify the OUTPUTSETUP.  Optionally, you can also place the command STOP at the end of the example in order to interrupt the analysis and return control to the last used module.  (See also, STATISTICA Command Language - Introductory Overview, and Order of SCL Statements.)

To turn on printer output, use the OUTPUTSETUP command at the beginning of the program.  For example, the following program directs Scrollsheet and graphic output to the printer and Text/output Window.

FILE = "C:\STAT\EXAMPLES\ADSTUDY.STA"

OUTPUTSETUP

   SCROLLSHEETS = PRINTER AND WINDOW

   GRAPHS = PRINTER AND WINDOW

DESC VARS = ALL

STOP

To direct the Scrollsheet output to the disk, use the command FILE = "filename" after the OUTPUTSETUP SCROLLSHEET command.  For example, the output from the following program is directed to the disk file Adstudy.txt.

FILE = "C:\STAT\EXAMPLES\ADSTUDY.STA"

OUTPUTSETUP

   SCROLLSHEET FILE "C:\STAT\EXAMPLES\ADSTUDY.TXT"

DESC VARS = ALL

STOP

Alternatively, file output (graphs or Scrollsheets) can be created using the SAVEGRAPH and SAVESCROLLSH commands, respectively.

For more examples, see below.

Data Management Examples

Basic Statistics Examples

Nonparametrics and Distributions Examples

Multiple Regression Examples

Nonlinear Estimation Examples

Factor Analysis Example

Cluster Analysis Examples

Canonical Correlation Examples

ANOVA/MANOVA Examples

Discriminant Function Analysis Examples

Log-linear Analysis Example

Survival Analysis Examples


  SCL Data Management Examples

For more information, see Data Management, Order of SCL Statements, and SCL - Data Management (for syntax help).

Example 1:  This program will import the 1-2-3 spreadsheet file DATA.WK1, and save it under the file name NEWDATA.STA.  If SAVEAS is not used, the file will be saved under the file name of the imported file, with extension *.sta.

IMPORT FILE = "D:\EXAMPLES\DATA.WK1"

   SAVEAS "D:\EXAMPLES\NEWDATA.STA"

For help with syntax, see SCL - Data Management.

Example 2:  This example program will first select the STATISTICA raw data file EXP.STA, and then export it to the Lotus 1-2-3 file EXP.WK1 (LOTUS2 refers to the 1-2-3 file format for release 2.x; LOTUS1 refers to the file format used in 1-2-3 release 1).

FILE = "EXP.STA"

EXPORT LOTUS2

For help with syntax, see SCL - Data Management.

Example 3:  This example will sort data file EXP.STA by Variable 1 (GROUP) in ascending order, and "within" Variable 1 by Variable 2 (GENDER) in descending order.  The text representations of values are used for the sort.

FILE = "D:\EXAMPLES\EXP.STA"

SORT KEYS = (GROUP, ASCEN, ALPHA)

            (GENDER, DESCEN, ALPHA)

For help with syntax, see SCL - Data Management.

Example 4:  This example will merge the files EXP.STA and EXP2.STA by variable number 1 in the first file, and variable number 3 in the second file.  Records will be merged if they contain the same values in variable number 1 in file EXP.STA and variable number 3 in EXP2.STA.  If those variables contain text values, the merge will be based on those values.  The file will be saved under the file name NEWDATA.STA.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

MERGE SECFILE = "C:\STAT\EXAMPLES\EXP2.STA"

  MODE = VARS

    /RELATIONAL

    KEYS = 1,3

    COMP = ALPHA

  SAVEAS "D:\OUTPUT\NEWDATA.STA"

For help with syntax, see SCL - Data Management.

Example 5:  This example will create a subset of 4 variables from file EXP.STA, and save it under the file EXPNEW.STA.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

SUBSET VARS CORRECT1-CORRECT3

       SAVEAS "C:\DATA\EXPNEW.STA"

For help with syntax, see SCL - Data Management.

Example 6:  The following example will standardize variable CORRECT1 in file EXP.STA.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

STANDARDIZE VARS = CORRECT1

For help with syntax, see SCL - Data Management.

Example 7:  The following example will execute a STATISTICA BASIC program that was previously created and saved under the name PROGRAM.STB.  The program will be executed on the raw data file EXP.STA.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

STBASIC PROGRAM = "C:\STAT\EXAMPLES\PROGRAM.STB"

For help with syntax, see SCL - Data Management.

Example 8:  The following example will perform several editing operations on the variables and cases in the file EXP.STA.  Note that the operations will be performed in the order in which they are listed.  The transformed data will be saved in a new data file (EXP2.STA).

FILE = "C:\STAT\EXAMPLES\EXP.STA"

EDIT

/MOVEVAR 1-4 AFTER 8

/RENAMEVAR (5, "TRTMNT")

/LONGVARNAME (5, "TREATMENT GROUP")

/DELCASE 41-48

SAVEAS "C:\STAT\EXAMPLES\EXP2.STA"

For help with syntax, see SCL - Data Management.


  SCL Basic Statistics Examples

For more information on these commands, see Basic Statistics & Tables, Order of SCL Statements, and SCL - Basic Statistics (for syntax help).

Example 1:  The following example will compute descriptive statistics for 3 variables in the data file EXP.STA.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

DESCRIPTIVES VARS=CORRECT1-CORRECT3

STATISTICS = ALL

For help with syntax, see SCL - Basic Statistics.

Example 2:  The following example will compute correlations for all of the variables in the data file EXP.STA; missing data deletion will be pairwise.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

CORRELATION VARS=ALL

/EXTENDED

/PAIRWISE

/DETAILED

STATISTICS = 2

For help with syntax, see SCL - Basic Statistics.

Example 3:  The following example will compute a t-test for Dependent Samples for variables CORRECT1 through CORRECT3 in the data file EXP.STA.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

T_PAIRS VARS CORRECT1-CORRECT3

/PAIRWISE

/MATRIX

STATISTICS = ALL

For help with syntax, see SCL - Basic Statistics.

Example 4:  The following example will compute a t-test for Independent Samples for variables CORRECT1 through CORRECT3 in the data file EXP.STA.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

T_TEST GROUPS=GENDER(MALE,FEMALE)

VARS = CORRECT1-CORRECT3

/CASEWISE

/HOTELLING

STATISTICS = 1,3,4

For help with syntax, see SCL - Basic Statistics.

Example 5:  The following example will compute descriptive statistics by groups for the groups GROUP, GENDER, and TIME.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

BREAKDOWN

   GROUPS=GROUP (ALL) GENDER (ALL) TIME (ALL)

   VARS=CORRECT1-CORRECT3

STATISTICS = 1,2,8,10

For help with syntax, see SCL - Basic Statistics.

Example 6:  The following example will compute Crosstabulation Tables for the variables FOOTBALL by BASEBALL through SWIMMING and by TRACK.

FILE = "C:\STAT\EXAMPLES\SPORTS.STA"

TABLES

VARS FOOTBALL BY

     BASEBALL-SWIMMING BY

     TRACK

/PERCENT = ROW,COLUMN

/FREQUENCIES

STATISTICS = ALL

For help with syntax, see SCL - Basic Statistics.

Example 7:  The following example will compute stub-and-banner tables for the variablesFOOTBALL and BASEBALL by TRACK through MARATHON.  The option PERCENT (or PERC) specifies that the relative (as well as raw) frequencies will be included in the output.

FILE = "C:\STAT\EXAMPLES\SPORTS.STA"

BANNERS

VARS FOOTBALL BASEBALL BY TRACK-MARATHON

/PERCENT = ALL

/STATS2WAY

STATISTICS = 1,2,3

For help with syntax, see SCL - Basic Statistics.

Example 8:  The following example will compute Frequency Tables with 10 intervals for the variables CORRECT1 through CORRECT3 in the data file EXP.STA.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

FREQUENCY

VARS=CORRECT1-CORRECT3

/MODE=10 INTERVALS

/NORMALEXPECTED

STATISTICS = ALL

For help with syntax, see SCL - Basic Statistics.


  SCL Nonparametrics Examples

For more information, see Nonparametrics and Distribution Fitting, aOrder of SCL Statements, and SCL - Nonparametric Statistics & Distribution Fitting (for syntax help).

Example:  The following example will fit the normal distribution to the data.  You can specify the parameters or have the program calculate them from the data.  For more commands for fitting other distributions, see SCL General Conventions - Nonparametrics and Distribution Fitting.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

NORMAL VAR CORRECT1

  /CATEGORIES = 12

  /MINMAX = (2,20)

  /MEAN = 9.0

  /VARIANCE = 14.0

For help with syntax, see SCL - Nonparametric Statistics & Distribution Fitting.


  SCL Multiple Regression Examples

For more information, see Multiple Regression, Order of SCL Statements, and SCL - Multiple Regression (for syntax help).

Example 1:  The following example will compute a standard multiple regression analysis using file POVERTY.STA, using variable PT_POOR as the dependent variable (see also the Example section of the Multiple Regression chapter).  The correlation matrix for all variables in the file is also requested.

FILE = "C:\STAT\EXAMPLES\POVERTY.STA"

REGRESSION

DEPENDENT=PT_POOR

INDEPENDENT=POP_CHNG N_EMPLD TAX_RATE AFR_AM

/CASEWISE

/METHOD = STANDARD

/INTERCEPT = YES

STATISTICS = ALL

For help with syntax, see SCL - Multiple Regression.

Example 2:  The next example will compute a stepwise forward regression analysis using file POVERTY.STA with the same variables.  Note that the F to enter value is also set; the F to remove value (FOUT) is left at the default (0.0).

FILE = "C:\STAT\EXAMPLES\POVERTY.STA"

REGRESSION

 DEPENDENT=PT_POOR

 INDEPENDENT=POP_CHNG N_EMPLD TAX_RATE AFR_AM

 /METHOD FORWARD FIN = 3.0

/INTERCEPT = YES

For help with syntax, see SCL - Multiple Regression.


  SCL Nonlinear Estimation Examples

For more information, see Nonlinear Estimation, Order of SCL Statements, and SCL - Nonlinear Estimation (for syntax help).

Example 1:  The following example program will perform a logit regression, with variable SUCCESS as the dependent variable and variable EXPERNCE as the independent variable.

FILE = "C:\STAT\EXAMPLES\PROGRAM.STA"

LOGIT INDEPENDENT=EXPERNCE

        DEPENDENT=SUCCESS

For help with syntax, see SCL - Nonlinear Estimation.

Example 2:  The following example performs a user-defined regression by specifying the regression model and the loss function.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

NONLINEAR

  FUNCTION="STRESS_R=INTERC+B*CORRECT1"

  /LOSS="ABS(PRED-OBS)"

For help with syntax, see SCL - Nonlinear Estimation.


  SCL Factor Analysis Example

For more information, see Factor Analysis, Order of SCL Statements, and SCL - Factor Analysis (for syntax help).

Example:  Choosing METHOD=COMPONENTS will set the communalities equal to the variances during the analysis.

FILE = "C:\STAT\EXAMPLES\FACTOR.STA"

FACTOR VARS=ALL

  /METHOD COMPONENTS=3

  /ROTATION=VARIMAX

For help with syntax, see SCL - Factor Analysis.


  SCL Cluster Analysis Examples

For more information, see Cluster Analysis, Order of SCL Statements, and SCL - Cluster Analysis (for syntax help).

Example 1:  The following example will compute a joining (or tree clustering) analysis in Cluster Analysis.

FILE = "C:\STAT\EXAMPLES\CARS.STA"

JOINING VARS = ALL

  /CLUSTER = CASES

  /DISTANCE = MANHATTAN

  /LINKAGE = COMPLETE

For help with syntax, see SCL - Cluster Analysis.

Example 2:  The following example will compute a k-Means clustering in Cluster Analysis.

FILE = "C:\STAT\EXAMPLES\CARS.STA"

K_MEANS VARS = ALL

  /CLUSTER = CASES

  /NCLUSTER = 3

For help with syntax, see SCL - Cluster Analysis.


  SCL Canonical Correlation Analysis Example

For more information, see Canonical Correlation Analysis, Order of SCL Statements, and SCL - Canonical Correlation Analysis (for syntax help).

Example:  The following example will compute a canonical correlation analysis.

FILE = "C:\STAT\EXAMPLES\FACTOR.STA"

CANONICAL

  VARS WORK_1-WORK_3 BY HOBBY_1-MISCEL_2

For help with syntax, see SCL - Canonical Correlation Analysis.


  SCL ANOVA/MANOVA Analysis Example

For more information, see ANOVA/MANOVA, Order of SCL Statements, and SCL - General ANOVA/MANOVA (for syntax help).

Example:  The following example will compute a 2 x 2 x 3 x 2 between x 3 within (repeated) analysis of variance.  Refer to ANOVA/MANOVA for details on how to specify different designs.  Note that the name or label of the repeated measures factor is enclosed in quotation marks.

FILE = "EXP.STA"

MANOVA

 VARS = CORRECT1-CORRECT3

 /GROUPS GROUP  (EXPERMTL,CONTROL)

         GENDER (1,2)

         TIME   (BEFORE,AFTER_1,AFTER_2)

         PAID   (NOT_PAID,PAID)

 /REPEATED "REPFACT" (3)

 /POSTHOC (GROUP, GENDER, TIME, PAID)

    /ALL

 STATISTICS = 2,3

For help with syntax, see SCL - General ANOVA/MANOVA.


  SCL Discriminant Function Analysis Examples

For more information, see Discriminant Function Analysis, Order of SCL Statements, and SCL - Discriminant Function Analysis (for syntax help).

Example 1:  The following example performs a standard discriminant function analysis on the data in file IRISDAT.STA.  Note the use of the ALL convention to select all codes in variable IRISTYPE.

FILE = "C:\STAT\EXAMPLES\IRISDAT.STA"

DISCRIMINANT

  GROUPS IRISTYPE (ALL)

  VARS = SEPALLEN-PETALWID

For help with syntax, see SCL - Discriminant Function Analysis.

Example 2:  The following example performs a forward stepwise discriminant function analysis on the data in file IRISDAT.STA.

FILE = "C:\STAT\EXAMPLES\IRISDAT.STA"

DISCRIMINANT

  GROUPS IRISTYPE (ALL)

  VARS = SEPALLEN-PETALWID

  /METHOD=FORWARD

For help with syntax, see SCL - Discriminant Function Analysis.


  SCL Log-linear Analysis Example

For more information, see Log-linear Analysis, Order of SCL Statements, and SCL - Log-linear Analysis (for syntax help).

Example:  The following example performs a log-linear analysis on the data in the file CENTER2.STA.

FILE = "C:\STAT\EXAMPLES\CENTER2.STA"

LOGLINEAR

  INPUT = CODES

    FREQ = FREQUNCY

    GROUPS = APPEARNC(ALL)

             SURVIVAL('YES','NO')

             AGE (ALL)

             LOCATION(ALL)

For help with syntax, see SCL - Log-linear Analysis.


  SCL Survival Analysis Examples

For more information, see Survival Analysis, Order of SCL Statements, and SCL - Survival Analysis (for syntax help).

Example 1:  The following example computes a lifetable analysis on the data in the file HEART.STA.

FILE = "C:\STAT\EXAMPLES\HEART.STA"

LIFETABLE INPUT=RAWDATA

  VARS=1-6

  CENSOR=CENSORED CENSORED=1 COMPLETE=0

For help with syntax, see SCL - Survival Analysis.

Example 2:  The following example computes an explanatory regression model for survival/failure times.

FILE = "C:\STAT\EXAMPLES\HEART.STA"

SURV_REG

  DEPENDENT=1-6

  INDEPENDENT=AGE ANTIGEN MISMATCH

  METHOD=COX

  CENSOR=CENSORED CENSORED=1 COMPLETE=0

For help with syntax, see SCL - Survival Analysis.


  STATISTICA Command Language - Syntax

The syntax of STATISTICA Command Language is described in the following three general topics.  For more information on a topic, click on the topic name.

General Conventions & Global Options

Structure of SCL Language

Description of Syntax

Index

For specific syntax descriptions and some examples, see the following topics:

Order of SCL Statements

Data Management

STATISTICA BASIC

Basic Statistics

Nonparametric Statistics & Distribution Fitting

ANOVA/MANOVA

Multiple Regression

Nonlinear Estimation

Time Series and Forecasting

Factor Analysis

Cluster Analysis

Canonical Correlation Analysis

Multidimensional Scaling

Reliability and Item Analysis

General ANOVA/MANOVA

Discriminant Function Analysis

Log-linear Analysis

Survival Analysis

Quality Control

Process Analysis

Design of Experiments

SEPATH

Graphics


SCL Syntax - General Conventions & Global Operations

  SCL Syntax - General Conventions & Global Options

General Conventions

Upper and lower case.  The STATISTICA Command Language does not distinguish between upper and lowercase letters.  Therefore, the command DESC is equivalent to desc or Desc.

Comments.  You may include comments in SCL programs; those comments will be ignored by the program.  Enclose comments in curly brackets: {this is my comment}.  (Note, text enclosed within curly brackets within quotes will be read as part of the program; e.g., "{tab}".)

Commands and lines.  SCL does not assign any special meaning to line breaks.  Thus, you may enter commands, one to a line, or you may type several commands on a single line.

Text.  When referring to text (e.g., file names, headers), those texts must be enclosed in either single apostrophes (e.g., FILE='EXP.STA') or quotation marks (FILE="EXP.STA").

Variables.  Variables can be referred to by name or number. To define lists of variables you may use the dash (-) convention.  For example, VARS = 1 3 4-6 12 would specify variables 1, 3, 4 to 6, and 12.  Suppose the variable name for variable 3 is Gender.  One could then also type: VARS = 1 GENDER 4-6 12.  To select all variables in the data file, you can either use the word ALL or use the STATISTICA star convention; for example, you could type VARS= ALL or VARS = *.

You can use variable names that are also valid SCL commands.  However, you may have to take special precautions to make sure that STATISTICA Command Language properly interprets the respective variable names.  Specifically, if you follow a variable list specification by a SCL keyword that is also a valid variable name in the current data file, then you must place a semicolon or the word END after the respective task specification (to instruct the program where the variable list ends, and an additional task begins).  For example:

CORR VARS TEST1 TEST2 CORR;

CORR VARS TEST5-TEST9

In this example, the first CORR command will compute a correlation matrix for the three variables TEST1, TEST2, and CORR.  Next, the keyword CORR is used again to compute an additional correlation matrix.

Codes.  Several statistical techniques require you to specify numeric or text codes, for example, in order to identify groups.  Such codes can be specified by typing in a number (numeric value) or the respective text value.  Text values must be enclosed in single ( ' ) or double ( " ) quotation marks if they contain characters other than uppercase letters, underscores and numbers, (e.g., spaces, commas, hyphens, lowercase letters), or if they start with a number.  When lists of codes are requested, the dash option (-), the * option, and the ALL keyword can also be used.  For example, all of the following specifications would be valid: GENDER (MALE,FEMALE); GENDER ('MALE', 'FEMALE'); GENDER ("MALE", "FEMALE"); GENDER (1,2); GENDER (1-2); GENDER (*); GENDER (ALL).  The following ANOVA design specification illustrates the use of these conventions.

MANOVA

  VARS = CORRECT1-CORRECT3

  /GROUPS GROUP  (EXPERMTL,CONTROL)

          GENDER (1,2)

          TIME   (ALL)

          PAID   (NOT_PAID,PAID)

          LEVEL  ('ONE-UP', 'ONE-DOWN')

Abbreviations (alternative words).  To allow you to write "transparent" SCL programs, many keywords and commands are relatively long.  For example, to compute descriptive statistics you could use the DESCRIPTIVES command.  However, most of those commands can also be abbreviated; for examples, you could also use the command DESC.  Valid abbreviations for long keywords are listed in the description of the SCL syntax below.

For more information on SCL syntax see also:

Order of SCL Statements

Structure of SCL Language

Description of Syntax

Global Options

In the following description of the SCL syntax it is assumed that you are familiar with the general conventions of STATISTICA as well as the (menu) options offered by the respective STATISTICA modules(s).  Please refer to the Menus & Options sections of the respective chapters.  Each of the following topics address specific SCL syntax conventions.  For more information on those conventions, click on the topic name.

Input file

Printer (output) Options

Save Graph

Save Scrollsheet

Selection Conditions

Specifying a Weight Variable

Job Header Specification

Sendkeys


  SCL Syntax - Input File

FILE [=] "FileName"

FileName can be up to 128 characters long, and can include drive and path designators (e.g., D:\STAT\MYDATA.STA).  If no file name extension such as *.sta is specified, the program will assume the extension *.sta.

For more SCL syntax conventions, see also:

Printer (output) Options

Save Graph

Save Scrollsheet

Selection Conditions

Specifying a Weight Variable

Job Header Specification

Sendkeys


  SCL Syntax - Save Graph

SAVEGRAPH [=] { "FileName" }

              { OFF        }

You can choose to save the graphs created during analysis using this SCL option.  At the beginning of a task, use the SAVEGRAPH keyword and specify a file name (file name extension *.stg; if the extension is not specified, then the default extension *.stg will be used by the program) under which the graph(s) will be saved.  If more than one graph is created during the analysis, STATISTICA will save each graph in a separate file and number the files sequentially (e.g., Graph.stg, Graph1.stg, Graph2.stg, Graph3.stg, etc.).  If the specified file name is 8 characters long, the last character(s) will be replaced by the consecutive number(s).  This SCL option is global in that once it is invoked at the beginning of a task, it will remain in effect for each subsequent task (until you turn it off using the SAVEGRAPH = OFF statement).  Saved graphs can later be opened for review or further analysis, customization, etc.; they can also be printed in batch using the Print Files facility.

Example:  The example below will produce two graphs - a histogram and a scatterplot.  A SAVEGRAPH statement is included before each graph in order to save each one under a specific file name (instead of sequentially under the file name specified in the first SAVEGRAPH statement).

FILE = "D:\STAT\ADSTUDY.STA"

SAVEGRAPH = "D:\STAT\HIST.STG"

HIST

VAR = 3

SAVEGRAPH = "D:\STAT\SCATT.STG"

SCATT

X=3

Y=4

For more SCL syntax conventions, see also:

Input file

Printer (output) Options

Save Scrollsheet

Selection Conditions

Specifying a Weight Variable

Job Header Specification

Sendkeys


  SCL Syntax - Save Scrollsheet

SAVESCROLLSH [=] { "FileName" }

                 { OFF        }

Instead of directing the text output to the printer, textfile, or Text/output Window, you can choose to save the Scrollsheets of output created during analysis into separate Scrollsheet files (one Scrollsheet per file).  Those files can later be opened for review, converted into data files, etc. (see Scrollsheet Save as Data).  Saved Scrollsheets can also be printed in batch using the Print Files facility.  At the beginning of a task, use the SAVESCROLLSH keyword and specify a file name (file name extension *.scr; if the extension is not specified, then the default extension *.scr will be used by the program) under which the Scrollsheet(s) will be saved.  If more than one Scrollsheet is created during the analysis, STATISTICA will save each Scrollsheet in a separate file and number the files sequentially (e.g., Output.scr, Output1.scr, Output2.scr, Output3.scr, etc.).  If the specified file name is 8 characters long, the last character(s) will be replaced by the consecutive number(s).  This SCL option is global in that once it is invoked at the beginning of a task, it will remain in effect for each subsequent task (until you turn it off using the SAVESCROLLSH = OFF statement).

Example:  The example below will produce three Scrollsheets containing frequency tables for each of the specified variables and these Scrollsheets will be saved (sequentially) under the file names Freq.scr, Freq1.scr, and Freq2.scr.

FILE = "D:\STAT\EXP.STA"

SAVESCROLLSH = "D:\STAT\FREQ.SCR"

FREQ

VARS=CORRECT1-CORRECT3

/MODE=10 INTERVALS

For more SCL syntax conventions, see also:

Input file

Printer (output) Options

Save Graph

Selection Conditions

Specifying a Weight Variable

Job Header Specification

Sendkeys


  SCL Syntax - Selection Conditions

The following commands allow you to specify selection conditions in order to include only a subset of cases in an analysis.  Once a selection condition has been specified, it will remain in effect until you turn it OFF.

SELECT { OFF                 }

       { FILE [=] "FileName" }

{ INCLUDE } [IF] "ConditionText"

{ EXCLUDE }

ConditionText has to be placed in quotes (as text). For example:

INCLUDE IF "(v1=1 and v2=1) or v3=2"

To specify a selection condition file, you could, for example, type:

SELECT FILE = "C:\STAT\EXAMPLES\EXP.SEL"

For more SCL syntax conventions, see also:

Input file

Printer (output) Options

Save Graph

Save Scrollsheet

Specifying a Weight Variable

Job Header Specification

Sendkeys


  SCL Syntax - Specifying a Weight Variable

The following commands allow you to "adjust" the contribution of individual cases to the outcome of an analysis by "weighting" those cases in proportion to the values of a selected variable.  Once a weighting variable has been specified, it will remain in effect until you turn it OFF.

WEIGHT [=] { OFF      }

           { Variable }

For more SCL syntax conventions, see also:

Input file

Printer (output) Options

Save Graph

Save Scrollsheet

Selection Conditions

Specifying a Weight Variable

Job Header Specification

Sendkeys


  SCL Syntax - Job Header Specification

You can specify an output header via the HEADER command.  This header will be included as the title on every printed page when at least a SHORT output format is specified.

OUTPUTSETUP

    HEADER [=] "HeaderText"

HeaderText can be up to 80 characters long.

For more SCL syntax conventions, see also:

Input file

Printer (output) Options

Save Graph

Save Scrollsheet

Selection Conditions

Specifying a Weight Variable

Sendkeys


  SCL Syntax - Specifying Statistical Results

Optional output from statistical procedures can be requested using the STATISTICS = command followed by a numerical designation of the requested output (for information about the available output options please refer to the reference section for the specific analysis).

STATISTICS = ALL   all available results for the specified task in SCL will be created.

STATISTICS = number [,...,number]   only the specified statistical results will be created.

For example, the command STATISTICS = 1,3,7 specifies that statistical results 1,3 and 7 will be created.

NOTE:  The STATISTICS = command is optional.  If it is not explicitly specified, a default set of results will be produced for the given task.

Valid Abbreviation:

STATS

For more information on the types of results available for each procedure, see the following topics:

Data Management

Basic Statistics

Nonparametric Statistics & Distribution Fitting

Multiple Regression

Nonlinear Estimation

Time Series and Forecasting

Factor Analysis

Cluster Analysis

Canonical Correlation Analysis

Correspondence Analysis

Multidimensional Scaling

Reliability and Item Analysis

General ANOVA/MANOVA

Discriminant Function Analysis

Log-linear Analysis

SEPATH

Survival Analysis

Quality Control

Process Analysis

Design of Experiments

Graphics


  SCL Syntax - Sendkeys

SENDKEYS Command

The STATISTICA Command Language allows you to execute standard STATISTICA keyboard operations (SENDKEYS command) from within batch programs.  The SENDKEYS commands can be used as custom "extensions" or shortcut commands in your SCL programs.  Thus, via this feature, all specialized options in all modules can be referenced in SCL programs.

Each SENDKEYS command line is limited to 80 characters and must be placed at the end of each task (multiple SENDKEYS commands can be specified).  For example, suppose you want to produce a scatterplot for selected pairs of variables from within a correlation matrix produced via Basic Statistics.  First, enter the SCL program to create the correlation matrix, then at the end of that task, enter the STOP command (see below).

FILE = "C:\STAT\EXAMPLES\ADSTUDY.STA"

OUTPUTSETUP

   SCROLLSHEETS = WINDOW

DESC VARS = ALL

CORR VARS = ALL/PAIRWISE

STOP

Now, Execute the program and when it stops, record the keystrokes that it takes to produce the desired scatterplot.  Return to the STATISTICA Command Language program and enter at the end of the task (before STOP), the SENDKEYS command that will detail the keystrokes necessary to create the scatterplot (see below).

FILE = "C:\STAT\EXAMPLES\ADSTUDY.STA"

OUTPUTSETUP

   SCROLLSHEETS = FILE "C:\STAT\OUTPUT\RESULTS.TXT"

DESC VARS = ALL

CORR VARS = ALL/PAIRWISE

SENDKEYS "%21{TAB}3%O"

STOP

Note that the ALT key is represented by a % sign, the SHIFT key by a + sign, and the CTRL key by a ^ sign in these commands.  Text names of keys are placed inside curly brackets {}, (e.g., {TAB}).  The SENDKEYS commands are useful in cases when the same graphs or options (that cannot be programmed using Command Language keywords) need to be created or executed over and over again.  The SENDKEYS commands used here follow the same logic as those used in other Windows applications (e.g., Excel, Word for Windows, MS Test, batch language in Norton Desktop for Windows, MS Visual Basic).

SENDKEYS Syntax

When specifying SENDKEYS keystrokes commands, use the syntax outlined below.

SENDKEYS [=] "keystrokes"

Keystrokes is the sequence of keystrokes required to produce the desired output.  For example:

SENDKEYS = "%D%E{DOWN 2}%O"

The above example represents the keystrokes necessary to create a specific graph in the ANOVA/MANOVA module.  Note that the ALT key is represented by a % sign in these commands.  Text names of keys are placed inside curly brackets {}, (e.g., {TAB}, {ENTER}, {DOWN}).  In the above example:

%D	represents the selection of the Descriptive Statistics & Graphs option in the ANOVA Results dialog.

%E	represents the selection of the Plot Means vs. Standard Deviations option in the Descriptive Statistics & Graphs dialog.

{DOWN 2} 	represents the movement of the cursor down two rows in order to select the third variable in the variable selection list.

%O	represents the selection of the OK button in order to leave the variable selection dialog and produce the graph.

The SENDKEYS commands used here follow the same logic as those used in other Windows applications (e.g., Excel, Word for Windows).  The codes used to represent specific keyboard characters are listed below.

Keyboard Characters	Code

Alt	%

Ctrl 	^

Shift	+

Enter	~ or {Enter}

Keyboard Character	type in that key (e.g., abc@!)

Backspace	{Backspace}

Break	{Break}

CapsLock	{Capslock}

Clear	{Clear}

Delete	{Del}

Down	{Down}

End 	{End}

Escape 	{Esc}

Help	{Help}

Home	{Home}

Insert	{Insert}

Left 	{Left}

Page Down	{Pgdn}

Page Up	{Pgup}

Print Screen	{Prtsc}

Right	{Right}

Tab 	{Tab}

Up	{Up}

Single quotes	{ ' }'

Double quotes	{ " }

F1, ..., F12  	{Fnumber} (e.g., {F11})

You can instruct STATISTICA to repeat specific key sequences by specifying the number of times that you want it repeated (e.g., {DOWN 4}, {RIGHT 2}).  (Note:  be sure to leave a space between the code word and the number.)

Use parenthesis, brackets, or curly brackets to define the order of keystrokes.  For example, if you want to hold down the CTRL key while pressing the SHIFT and C keys, specify this "string" as:  ^(+C).  To hold down the SHIFT and CTRL keys while pressing two other keys, specify this string as:  +(^(AB)).

To specify a character that is normally used as a special character (e.g., ~, ^, %, +, (), {}, []), place it in curly brackets (e.g., {~}, will be read as the character ~ and not as the keyboard code for ENTER).

For examples of Sendkeys, see Examples with SENDKEYS.

For more SCL syntax conventions, see also:

Input file

Printer (output) Options

Save Graph

Save Scrollsheet

Selection Conditions

Specifying a Weight Variable

Job Header Specification


  SCL Syntax - Structure of SCL Language

Tasks.  A STATISTICA Command Language program consists of one or more tasks.  A task is some particular statistical technique or operation.  For example, DESCRIPTIVES is a task, that is, it will compute descriptive statistics.  Each task usually requires additional necessary or optional specifications, such as the specification of a variable list.

Global options.  Global options refer to specifications that will affect all tasks, or until they are explicitly reset.  For example, the SCROLLSHEETS = PRINTER command in the OUTPUTSETUP block will affect all subsequent tasks, that is, scrollsheets and text results from all subsequent tasks will be printed unless you change this option later.  Other global options are the specification of the input file, the disk output file, selection conditions, a weight variable, or a header text for the printed output.

All global options may appear more than once in a program.  For example:

FILE = "C:\STAT\EXAMPLES\EXP.STA"

OUTPUTSETUP

   SCROLLSHEETS = FILE "C:\STAT\EXAMPLES\OUTPUT.TXT"

DESC VARS = ALL

FILE = "C:\STAT\EXAMPLES\ADSTUDY.STA"

OUTPUTSETUP

   SCROLLSHEETS = PRINTER

DESC VARS = ALL

This example program would first compute descriptive statistics for all variables in file Exp.sta, and print the results to the output file Output.txt.  Next, the program would compute descriptive statistics for all variables in file Adstudy.sta, and send the results to the printer.

For more information on SCL syntax see also:

Order of SCL Statements

General Conventions

Description of Syntax


  SCL Syntax - Description of Syntax

In the description of the STATISTICA Command Language syntax, the following conventions will be used to refer to required, optional, or alternative specifications:

Keywords and commands.  All capitalized words denote SCL keywords.

Required input.  Required keywords or commands are those that are not enclosed in any parentheses or brackets.

User specified selection.  Specifications that have to be chosen by the user are printed in upper and lower case letters.  For example, VAR = VarList means that VAR is a required keyword, and that the user must choose the respective variable list.  For example, you might type in VAR = GENDER INCOME LOCATION.

Optional specifications.  Optional syntax is enclosed in square brackets.  For example, in the task CORRELATION VARS [=] VarList [ BY VarList], the required input is CORRELATION VARS VarList.  The equal sign is optional, and so is the second variable list.  However, if a second variable list is to be specified, it must be preceded by BY.  Usually additional options are preceded by slash (/).  For example [/ PAIRWISE] which specifies pairwise deletion of missing data.

Alternative specifications.  When there are several alternatives, they are presented inside curly brackets {}.  For example, consider the specification:

OUTPUT [=]	{ BRIEF  }

{ SHORT  }

{ MEDIUM }

{ LONG   }

Here, the word OUTPUT is required, followed by one of the four specifications BRIEF, SHORT, MEDIUM, and LONG.

Repeatable specifications.  "Ellipses" indicate that an element of syntax may be repeated.  For example, consider the syntax:

MANOVA

VARS = VarList

/GROUPS = Variable ( CodesList ) ...

In this case the specification of the respective variable can be repeated, that is, you can specify more than one grouping variable and the respective codes.  For example you can use:

MANOVA

VARS = 10-20

/GROUPS = Gender(ALL)

as well as:

MANOVA

VARS = 10-20

/GROUPS = Gender(ALL) Educat(ALL) State(ALL)

For more information on SCL syntax see also:

Order of SCL Statements

General Conventions

Structure of SCL Language


  SCL General Conventions - Overview

For a brief description of the SCL syntax, see Syntax Description.  See also Order of SCL Statements.

Specifying Variables

Specifying Values of Variables (codes)


SCL General Conventions - Specifying Variables

  SCL General Conventions Overview - Specifying Variables

Single variables can be defined either by number or by name:

Variable

{ number }

{ name   }

Lists of variables are defined as follows:

[/] { VARIABLES } [=] VarList

    { VARLIST   }

    { VARS      }

    { VAR       }

VarList

{ ALL                             }

{ *                               }

{ { Variable - Variable } [,] ... }

  { Variable            }

Examples:

SUBSET VARS CORRECT1-CORRECT3

DESC VARS = ALL

CORR VARIABLES = *

Variable names that are also SCL keywords.  You can use variable names that are also valid SCL commands.  However, you may have to take special precautions to make sure that STATISTICA Command Language properly interprets the respective variable names.  Specifically, if you follow a variable list specification by a SCL keyword that is also a valid variable name in the current data file, then you must place a semicolon or the word END after the respective task specification (to instruct the program where the variable list ends, and an additional task begins).  For example:

CORR VARS TEST1 TEST2 CORR;

CORR VARS TEST5-TEST9

In this example, the first CORR command will compute a correlation matrix for the three variables TEST1, TEST2, and CORR.  Next, the keyword CORR is used again to compute an additional correlation matrix.

See also:

Specifying Values of Variables (codes)

For more information on specific tasks, see the following topics:

Data Management

Basic Statistics

Nonparametric Statistics & Distribution Fitting

Multiple Regression

Nonlinear Estimation

Time Series and Forecasting

Factor Analysis

Cluster Analysis

Canonical Correlation Analysis

Correspondence Analysis

Multidimensional Scaling

Reliability and Item Analysis

General ANOVA/MANOVA

Discriminant Function Analysis

Log-linear Analysis

Survival Analysis

Quality Control

Process Analysis

Design of Experiments

Graphics


SCL General Conventions - Specifying Values of Variables (codes)

  SCL General Conventions Overview - Specifying Values of Variables (codes)

To define values or codes for variables, use the following convention:

Value

{ number }

{ text   }

{ "text" }

{ 'text' }

In other words, you can use either values or text equivalents.  Text values that consist of uppercase letters, underscores and numbers, but do not start with a number, can be used without quotation marks.  Otherwise, they have to be enclosed in single or double quotes (see the text values 'ONE-UP', 'ONE-DOWN' in the example below).

Lists of values or codes are specified as follows:

CodesList

{ ALL                       }

{ *                         }

{ { Value - Value } [,] ... }

  { Value         }

For example:

MANOVA

  VARS = CORRECT1-CORRECT3

  /GROUPS GROUP  (EXPERMTL,CONTROL)

          GENDER (1,2)

          TIME   (ALL)

          PAID   (NOT_PAID,PAID)

          LEVEL  ('ONE-UP', 'ONE-DOWN')

Note that text values for factor LEVEL in the above example ('ONE-UP', 'ONE-DOWN') are enclosed in single quotes because they contain a character (hyphen) which is interpreted by SCL as a separator.

See also:

Specifying Variables

For more information on specific tasks, see the following topics:

Data Management

Basic Statistics

Nonparametric Statistics & Distribution Fitting

Multiple Regression

Nonlinear Estimation

Time Series and Forecasting

Factor Analysis

Cluster Analysis

Canonical Correlation Analysis

Correspondence Analysis

Multidimensional Scaling

Reliability and Item Analysis

General ANOVA/MANOVA

Discriminant Function Analysis

Log-linear Analysis

Survival Analysis

Quality Control

Process Analysis

Design of Experiments

Graphics


SCL General Conventions - Data Management

  SCL - Data Management

For more information on these and related topics, see Data Management.  See also Order of SCL Statements.

Spreadsheet operations on variables or cases

Importing data files

Exporting data files

Sorting data files

Merging data files

Creating subsets of variables

Standardizing variables

Replacing missing data by respective variable mean


  SCL - Spreadsheet Operations on Variables or Cases

Several specific editing operations (listed below) can be performed on cases or variables.  The STATISTICA File Server will be used to perform all of these general spreadsheet commands.

    ADDVAR	{adds specified number of variables}

    COPYVAR	{copies specified variables to a specific location in the data file}

    MOVEVAR	{moves specified variables to a specific location in the data file}

    DELVAR	{deletes specified variables}

    RENAMEVAR	{renames specified variable}

    LONGVARNAME	{changes or specifies a new long variable name or formula}

    RECALCVAR	{recalculates specified variable when a formula is entered in the long variable name}

    ADDCASE	{adds specified number of cases}

    COPYCASE	{copies specified number of cases}

    MOVECASE	{moves specified cases}

    DELCASE	{deletes specified cases}

EDIT

{ /ADDVAR "NewName" AFTER Variable [HM = number]   }

{ /COPYVAR Variable1 [- Variable2] AFTER Variable3 }

{ /MOVEVAR Variable1 [-Variable2] AFTER Variable3  }

{ /DELVAR Variable1 [-Variable2]                   }

{ /RENAMEVAR (Variable, "NewName")                 }

{ /LONGVARNAME (Variable, "NewLongName")           }

{ /RECALCVAR Variable                              }

{ /ADDCASE number AFTER Case                       }

{ /COPYCASE Case1 [- Case2] AFTER Case3            }

{ /MOVECASE Case1 [- Case2] AFTER Case3            }

{ /DELCASE Case1 [- Case2]                         }

...

[SAVEAS [=] "FileName"]

You can use up to 64 editing options under one EDIT task statement in your program and the options will be executed in the order in which they are listed in your SCL program.  Since each of these editing operations will change the structure of the file as they are performed, it is advised that you specify only variable numbers (e.g., 1, 2, 3, etc.) and not variable names.

For information on long variable name formulas and syntax, see spreadsheet formulas.  Note that when a you use the LONGVARNAME statement to specify a transformation on a variable, you will need to use the RECALCVAR statement after it in order to recalculate that variable (i.e., perform the transformation).  If you want to save the edited file under a different name, use the SAVEAS option (see below).

Example

For other spreadsheet procedures, see:

Importing data files

Exporting data files

Sorting data files

Merging data files

Creating subsets of variables

Standardizing variables

Replacing missing data by respective variable mean


  SCL - Importing Data Files

The syntax for importing foreign data files to STATISTICA is given below.  (See also SCL - ODBC Import.)

IMPORT

FILE [=] "FileName"

{/EXCEL

/TEXTCOLS [=] {YES}

              {NO }

/CASENAME [=] {YES}

              {NO }

/VARS [=] Variable1 [- Variable2]

/CASES [=] Case1 [- Case2]

/SHEET [=] Sheet_No

/VARNAMES [=] {ORIGINAL}

              {FIRSTROW}

              {CREATE  }             }

Note that the above /SHEET = Sheet_No option is applicable only for Excel 5 files.  If the Excel 5 file you wish to import has more than one sheet, then you must specify the number of the sheet to import.

{/LOTUS

/TEXTCOLS [=] {YES}

              {NO }

/CASENAME [=] {YES}

              {NO }

/VARS [=] Variable1 [- Variable2]

/CASES [=] Case1 [- Case2]

/SHEETS [=] Sheet1 [-Sheet2]

/VARNAMES [=] {ORIGINAL}

              {FIRSTROW}

              {CREATE  }             }

{/DBASE

/TEXTCOLS [=] {YES}

              {NO }

/CASENAME [=] {YES}

              {NO }

/VARS [=] Variable1 [- Variable2]

/CASES [=] Case1 [- Case2]           }

{/PARADOX

/TEXTCOLS [=] {YES}

              {NO }

/CASENAME [=] {YES}

              {NO }

/VARS [=] Variable1 [- Variable2]

/CASES [=] Case1 [- Case2]           }

{/MFM

/TEXTCOLS [=] {YES}

              {NO }

/CASENAME [=] {YES}

              {NO }

/VARS [=] Variable1 [- Variable2]

/CASES [=] Case1 [- Case2]           }

{/SPSS

/TEXTCOLS [=] {YES}

              {NO }

/CASENAME [=] {YES}

              {NO }

/VALLABS [=]  {YES}

              {NO }                  }

{/ASCIIFIX

Vars Cases "FormatStatement"

/TEXTCOLS [=] {YES}

              {NO }

/CASENAME [=] {YES}

              {NO }                  }

{/ASCIIFREE

Vars Cases "FormatStatement"

/TEXTCOLS [=] {YES}

              {NO }

/CASENAME [=] {YES}

              {NO }

/BASICSEP [=] {UNDEFINED}

              {STANDARD }

              {BLANK    }

              {NONNUM   }

/ADDSEP [=] {TAB        }

            {SPACE      }

            {CR         }

            {'Separator'}             }

{/ASCIIQUICK

/CASENAME [=] {YES}

              {NO }

/VARNAMES [=] {FIRSTROW}

              {CREATE  }

/SEPARATOR [=] {TAB        }

               {SPACE      }

               {COMMA      }

               {SEMICOLON  }

               {'Separator'}          }

[SAVEAS [=] "FileName"]

To import non-ASCII files, you can either specify the file name of the import file and the program will automatically identify the file type (see Example 1), or you can specify the file type and other import options specific to that file type (see Example 2).  Note that the importing options must be specified in the order shown below.  If an option is not explicitly specified, then the default setting will be used during import.

To import an ASCII file specify either free-format ASCII or a fixed format (in this case you also have to specify the numbers of variables and cases in the file, and a format describing the lengths of fields, see Data Management) or you can use the Quick Import facility.  The quick import of ASCII files is based on their line structure (equivalent to using the Quick Import option available in every module of STATISTICA).  In this case, each line is treated as one record and the number of cases and variables are determined automatically.

For information on the import options, please refer to the respective section on importing data in the manual or Electronic Manual (see Data Management and Quick Import).

Examples

For other Data Management procedures, see:

Spreadsheet operations on variables or cases

Exporting data files

Sorting data files

Merging data files

Creating subsets of variables

Standardizing variables

Replacing missing data by respective variable mean


  SCL - Exporting Data Files

The syntax for exporting STATISTICA data files to a foreign file format is given below.

FILE [=] "FileName"

EXPORT [=] { STG                           }

           { MFM                           }

           { EXCEL

              [/ { QUICK } ]

                 { /MORE }                 }

           { LOTUS1

           { LOTUS2

              [/ { QUICK } ]

                 { /MORE }                 }

           { SYMPHONY                      }

           { LOTUS3

              [/ { QUICK } ]

                 { /MORE }                 }

           { LOTUS                         }

              [/ { QUICK } ]

                 { /MORE }                 }

           { DBASEIII                      }

           { DBASEIV                       }

           { SPSS                          }

           { ASCIIFIX                      }

           { ASCIIFREE                     }

           { ASCIIQUICK

              [/SEPARATOR [=] {TAB        }

                              {SPACE      }

                              {COMMA      }

                              {SEMICOLON  }

                              {'Separator'}]}

[ SAVEAS [=] "FileName"]

To export non-ASCII files, simply specify the name of the program to which the file will be exported.  You can use either the quick or extended export facilities to export to an ASCII, Lotus, or Excel file (see Quick Export).  If you do not specify the type of export for these three file types, then by default, a quick export will be performed (note that the default separator for the ASCII export is TAB).  (Note that the LOTUS option refers to Lotus 1-2-3 for Windows.)

To export an ASCII file specify either free-format or fixed format ASCII (see Data Management) or you can use the Quick Export option described below.

For information on the exporting data files, please refer to the respective section in the manual or Electronic Manual (see Data Management and Quick Export).

Example

For other Data Management procedures, see:

Spreadsheet operations on variables or cases

Importing data files

Sorting data files

Merging data files

Creating subsets of variables

Standardizing variables

Replacing missing data by respective variable mean


  SCL - Sorting Data Files

To sort a data file, first identify the key variables by which to sort the file.  Files can be sorted in ascending or descending order.  You can specify whether to use the text or respective numeric representations for the sort.

SORT

KEYS = (Variable, { ASCEN  }, { ALPHA  }) ...

                  { DESCEN }  { NUMERIC}

[ SAVEAS [=] "FileName"]

Example

For other Data Management procedures, see:

Spreadsheet operations on variables or cases

Importing data files

Exporting data files

Merging data files

Creating subsets of variables

Standardizing variables

Replacing missing data by respective variable mean


  SCL - Merging Data Files

This option allows you to merge two raw data files.  The general rules for different types of merges are described in Data Management.

MERGE

  SECFILE [=] "FileName"

  MODE [=]

   { VARS [{ RELATIONAL   }

           { HIERARCHICAL }

           KEYS [=] Variable,Variable

           COMP [=] { ALPHA   }

                    { NUMERIC } ] }

   { CASES }

   { ALPHA [ { CONCATENATE } ] }

             { REPLACE     }

  [ SAVEAS [=] "FileName"]

Example

For other Data Management procedures, see:

Spreadsheet operations on variables or cases

Importing data files

Exporting data files

Sorting data files

Creating subsets of variables

Standardizing variables

Replacing missing data by respective variable mean


  SCL - ODBC Import

This option allows you to import database files using ODBC.  You can either provide all ODBC specifications (as listed below);

ODBC

  DATASOURCE [=] "Data_Source_Name"

  [LOGIN [=] "User_ID"]

  [PASSWORD [=] "Password"]

  [OTHER [=] "Other_Attributes"]

  SQL [=] "SQL_Statement"

  SAVEAS [=] "FileName"

or use a a pre-defined (i.e., previously saved) template of ODBC specifications.

ODBC

  OPENSPECS [=] "FileName"

  SAVEAS [=] "FileName"

The ODBC/Templates specifications file must contain all necessary connection attributes and a correct SQL statement.

For more information, see ODBC Import - Templates; for other Data Management procedures, see:

Spreadsheet operations on variables or cases

Importing data files

Exporting data files

Sorting data files

Creating subsets of variables

Standardizing variables

Replacing missing data by respective variable mean


  SCL - Creating Subsets of Variables

SUBSET

VARS [=] VarList

[ SAVEAS [=] "FileName" ]

Example

For other Data Management procedures, see:

Spreadsheet operations on variables or cases

Importing data files

Exporting data files

Sorting data files

Merging data files

Standardizing variables

Replacing missing data by respective variable mean


  SCL - Standardizing Variables

When standardizing variables, you may either ignore any text values in the respective variables, or include their numeric equivalents in the computations.  Refer to Data Management for details.

STANDARDIZE

VARS [=] VarList

[ SAVEAS [=] "FileName" ]

Example

Valid Abbreviation:

STAND

For other Data Management procedures, see:

Spreadsheet operations on variables or cases

Importing data files

Exporting data files

Sorting data files

Merging data files

Creating subsets of variables

Replacing missing data by respective variable mean


SCL - Replace Missing Data by Respective Variable Mean

  SCL - Replacing Missing Data by Respective Variable Mean

REPLACE_MD

VARS [=] VarList

[ SAVEAS [=] "FileName"]

For other Data Management procedures, see:

Spreadsheet operations on variables or cases

Importing data files

Exporting data files

Sorting data files

Merging data files

Creating subsets of variables

Standardizing variables


  SCL - Executing STATISTICA BASIC Programs

The optional keywords MEMORY, ERRLEVEL, and MATHERR pertain to the settings of options on the STATISTICA BASIC options dialog.  Refer to STATISTICA BASIC for details.

STBASIC

PROGRAM [=] "FileName"

[/ MEMORY [=] Number ]

[/ ERRLEVEL [=] Number ]

[/ MATHERR [=] { STOP  }]

               { SETMD }

[ SAVEAS [=] "FileName" ]

Example

Accessing Scrollsheets via STATISTICA BASIC:  If you need to perform follow-up analyses on the output created in SCL, you can save each Scrollsheet into separate Scrollsheet files (one Scrollsheet per file) via the SCL command SAVESCROLLSH.  Then, using STATISTICA BASIC from within your SCL program, you can open the previously-saved Scrollsheets via option OpenScrollsheet (for more information on Scrollsheet commands in STATISTICA BASIC, see STATISTICA BASIC Scrollsheet Library).

Accessing Graphs via STATISTICA BASIC:  Graphs created in SCL (see SCL - Graphics), can be saved (via the SAVEGRAPH) option and then re-opened via STATISTICA BASIC from within your SCL program (see option OpenGraph; see also, Graphics Library of STATISTICA BASIC).

Using STATISTICA BASIC to create run-time user-interface for SCL command programs:  Although SCL command programs do not offer (directly) designated run-time user-interface, you can use STATISTICA BASIC programs (to be called from an SCL command program) to design dialog boxes and other elements of the user-interface which will allow users of the SCL program to select variables, data files, etc. in run-time.  An example is given in Calling STATISTICA BASIC from within SCL.


  SCL - Editing Data Files, an Example

This program will first add two variables (HM=2) with the variable name prefix NEW.  Then, a long variable name formula will be entered for each new variable and the variables will be recalculated.  The resulting file will then be saved under the file name "10ITEMSB.STA".

FILE = "C:\STAT\EXAMPLES\10ITEMS.STA"

EDIT

/ADDVAR "NEW" AFTER 10 HM = 2

SAVEAS = "C:\STAT\EXAMPLES\10ITEMSB.STA"

FILE = "C:\STAT\EXAMPLES\10ITEMSB.STA"

EDIT

/LONGVARNAME (11, "=(v1+v2+v3)/3; the mean of the first three vars")

/RECALCVAR 11

/LONGVARNAME (12, "=trunc(rnd(9)); generate random numbers between 0 and 9")

/RECALCVAR 12


  SCL - Importing Data Files

Example 1:  This program will import the 1-2-3 spreadsheet file Data.wk1, and save it under the file name Newdata.sta.  If SAVEAS is not used, the file will be saved under the file name of the imported file, with extension *.sta.

IMPORT FILE = "C:\LOTUS\DATA.WK1"

SAVEAS "C:\STAT\NEWDATA.STA"

Example 2:  This program will import the 1-2-3 spreadsheet file Data.wk1 using the following options, and save it under the file name NEWDATA2.STA.  If SAVEAS is not used, the file will be saved under the file name of the imported file, with extension *.sta.

IMPORT FILE = "C:\LOTUS\DATA.WK1"

/LOTUS

/TEXTCOLS = YES

/CASENAME = YES

/VARS = 1-4

/VARNAMES = FIRSTROW

SAVEAS "C:\STAT\NEWDATA2.STA"

Example 3:  This program will import the ASCII free file AD.FRE using the following options, and save it under the file name ADFREE.STA.  If SAVEAS is not used, the file will be saved under the file name of the imported file, with extension *.sta.  For more information on specifying the format statement, see Import ASCII free file.

IMPORT

FILE = "D:\AD.FRE"

/ASCIIFREE 28 50 "A11 2(S A8) 23S"

/TEXTCOLS = YES

/CASENAME = YES

/BASICSEP = UNDEFINED

/ADDSEP = '$'

SAVEAS "C:\STAT\ADFREE.STA"

Example 4:  This program will import the ASCII fixed file AD.FIX using the following options, and save it under the file name ADFIX.STA.  If SAVEAS is not used, the file will be saved under the file name of the imported file, with extension *.sta.  For more information on this type of import, see Import ASCII fix file.

IMPORT

FILE = "D:\AD.FIX"

/ASCIIFIX 25 50 "A8 A10 13S4 10S2"

/TEXTCOLS = NO

/CASENAME = YES

SAVEAS "C:\STAT\ADFIX.STA"


  SCL - Exporting Data Files

This example program will first select the STATISTICA raw data file EXP.STA, and then export it to the Lotus 1-2-3 file EXP.WK1 (LOTUS2 refers to the 1-2-3 file format for release 2.x).

FILE = "C:\STAT\EXAMPLES\EXP.STA"

EXPORT LOTUS2


  SCL - Sorting Data Files

This example will sort data file EXP.STA by Variable 1 (GROUP) in ascending order, and "within" Variable 1 by Variable 2 (GENDER) in descending order.  The text representations of values are used for the sort.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

SORT KEYS = (GROUP, ASCEN, ALPHA)

            (GENDER, DESCEN, ALPHA)


  SCL - Merging Data Files

This example will merge the files EXP.STA and EXP2.STA by variable number 1 in the first file, and variable number 3 in the second file.  Records will be merged if they contain the same values in variable number 1 in file EXP.STA and variable number 3 in EXP2.STA.  If those variables contain text values, the merge will be based on those values.  The file will be saved under the file name NEWDATA.STA.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

MERGE SECFILE = "C:\STAT\EXAMPLES\EXP2.STA"

  MODE = VARS

  RELATIONAL

  KEYS = 1,3

  COMP = ALPHA

  SAVEAS "D:\NEWDATA.STA"


  SCL - Creating Subsets of Variables

This example will create a subset of 4 variables from file EXP.STA, and save it under the file EXPNEW.STA.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

SUBSET VARS CORRECT1-CORRECT3

  SAVEAS "C:\STAT\EXPNEW.STA"


  SCL - Standardizing Variables

The following example will standardize variable CORRECT1 in file EXP.STA.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

STANDARDIZE VARS = CORRECT1


  SCL - Executing STATISTICA BASIC Programs

The following example will execute a STATISTICA BASIC program that was previously created and saved under the name PROGRAM.STB.  The program will be executed on the raw data file EXP.STA.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

STBASIC PROGRAM = "C:\STAT\EXAMPLES\PROGRAM.STB"


  SCL - Calling STATISTICA BASIC from within SCL

Interactive selection of data files to be processed within SCL:  This program demonstrates how one can mix STATISTICA BASIC programs and SCL (STATISTICA Command Language) programs.  This program will first execute a previously saved STATISTICA BASIC program opendata.stb.  That program will prompt the user to select a data file to be used for further analysis.  The BASIC program will copy the selected data file to a temporary data file scldata.sta.  Then this SCL program will continue by opening scldata.sta and running the DESC procedure on all variables.

STBASIC

PROGRAM = 'd:\stat\tech_dat\opendata.stb'

FILE = 'c:\scldata.sta'

DESC

VARS = all

STOP

The STATISTICA BASIC file, opendata.stb, which is called in the SCL program above is as follows:

SelectOpenFileName ('Select the File to Open', fname$, 'sta');

CopyFile(fname$, 'c:\scldata.sta');

Interactive selection of variables to be processed within SCL:  This program also demonstrates how one can mix STATISTICA BASIC programs and SCL (STATISTICA Command Language) programs.  This program will first append a variable (new variable 26) to the example data file Adstudy.sta; then the previously saved STATISTICA BASIC program sclhelp.stb is executed; that program will prompt the user to select a variable that is to be used as the dependent variable in a multiple regression analysis.  The BASIC program will copy the selected variable to the new variable 26; then this SCL program will continue by running the REGRESSION procedure with variable 26 as the dependent variable.

FILE = 'c:\stat\examples\adstudy.sta'

EDIT

/ADDVAR 'Depend' AFTER 25 HM = 1

SAVEAS = 'c:\stat\examples\temp.sta'

FILE = 'c:\stat\examples\temp.sta'

STBASIC

PROGRAM = 'c:\stat\examples\stbasic\sclhelp.stb'

REGR

DEP = 26

INDEP = 3 4 5

/INTERCEPT = NO

STATS = 1 2 7

STOP

The STATISTICA BASIC file, sclhelp.stb, which is called in the SCL program above is as follows:

RandomAccess;

NoDataFileVariableNames;

Var:=1;

SelectVariables1 ('Select dependent variable', 1, 1, Var, nbVar, 'Dependent variable:');

MatrixCopy (DATA, 1, Var, NCases, 1, DATA, 1, NVars);


SCL General Conventions - Basic Statistics

  SCL - Basic Statistics

For more information on these and related topics, see Basic Statistics and Tables.

Descriptive statistics

Correlation matrices

T-test for dependent samples

T-test for independent samples

Breakdown tables

Frequency tables

Crosstabulation tables

Banner tables


  SCL - Descriptive Statistics

DESCRIPTIVES

   VARS [=] VarList

   [{/QUARTILES

     /ALPHAERROR [=] number }

    {/ALL } ]

   [STATISTICS [=] {number [, ... , number] }

                   {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Detailed descriptive statistics

2 - Frequency tables and Histograms

3 - Box & Whisker plot for all variables

4 - Normal probability plots and Detrended normal probab. plots

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

For more information on the options given above, see Descriptive Statistics.

Example:  The following example will compute descriptive statistics for the specified variables.  In addition, frequency tables and histograms and a box & whisker plot for all variables will be produced.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

DESCRIPTIVES VARS=CORRECT1-CORRECT3

STATS = ALL

Valid Abbreviations:

DESC, DESCR, STATS

For other Basic Statistics procedures, see:

Correlation matrices

T-test for dependent samples

T-test for independent samples

Breakdown tables

Frequency tables

Crosstabulation tables

Banner tables


  SCL - Correlation Matrices

When a single variable list is specified, a square matrix of correlations will be computed; if two lists are specified (via the BY keyword), then a rectangular correlation matrix will be computed.  The display format options STANDARD and EXTENDED correspond to the respective options described in Basic Statistics.

CORRELATION

   VARS [=] VarList [ BY VarList ]

   [/ { STANDARD   } ]

      { EXTENDED   }

   [/ { CASEWISE } ]

      { PAIRWISE }

   [/{MATRIX_P }

     {MATRIX_PN }

     {DETAILED } ]

   [STATISTICS [=] {number [, ... , number] }

                   {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Correlations

2 - Matrix plot

3 - 2D Scatterplot (for two-lists only)

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

For more information on the options given above, see Correlations.

Example:  The following program will compute a matrix of correlations for all the variables in the specified data file.  In addition, a matrix scatterplot will be produced.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

CORRELATION VARS=ALL/PAIRWISE

STATS = ALL

Valid Abbreviation:

CORR, STATS

For other Basic Statistics procedures, see:

Descriptive statistics

T-test for dependent samples

T-test for independent samples

Breakdown tables

Frequency tables

Crosstabulation tables

Banner tables


  SCL - t-test for Dependent Samples

TPAIRS

   VARS [=] VarList [ BY VarList ]

   [ / { CASEWISE } ]

       { PAIRWISE }

   [/{MATRIX }

     {DETAILED } ]

   [STATISTICS [=] {number [, ... , number] }

                   {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - T-tests

2 - Box & Whisker plot

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

For more information on the options given above, see t-test for Dependent Samples.

Example:  The following example will perform a t-test for the specified variables.  In addition, a box & whisker plot will be produced.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

T_PAIRS VARS CORRECT1-CORRECT3

STATS = ALL

Valid Abbreviation:

TPAIRS, STATS

For other Basic Statistics procedures, see:

Descriptive statistics

Correlation matrices

T-test for independent samples

Breakdown tables

Frequency tables

Crosstabulation tables

Banner tables


SCL - T-test for Dependent Samples

  SCL - t-test for Independent Samples

TTEST

   GROUPS [=] Variable (Value [,] Value)

   VARS [=] VarList

   [ / { CASEWISE } ]

       { PAIRWISE }

   [/SEPARATE]

   [/HOTELLING]

   [/LEVENE]

   [STATISTICS [=] {number [, ... , number] }

                   {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - T-tests

2 - Box & Whisker plot

3 - Categorized histograms

4 - Categorized normal plots

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

For more information on the options given above, see t-test for Independent Samples.

Example:  The following example will perform a t-test between groups for the specified variables.  In addition, a box & whisker plot, categorized histogram and categorized normal probability plot will be produced.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

T_TEST GROUPS=GENDER(MALE,FEMALE)

        VARS = CORRECT1-CORRECT3

STATS = ALL

Valid Abbreviation:

TTEST, STATS

For other Basic Statistics procedures, see:

Descriptive statistics

Correlation matrices

T-test for dependent samples

Breakdown tables

Frequency tables

Crosstabulation tables

Banner tables


  SCL - Breakdown Tables

BREAKDOWN

   GROUPS [=] Variable (CodeList) ...

   VARS [=] VarList

   [/{CASEWISE }

     {PAIRWISE } ]

   [STATISTICS [=] {number [, ... , number] }

                   {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Summary table of means

2 - Detailed two-way tables

3 - Analysis of variance

4 - Levene's test (homogeneity of var.)

5 - Categorized box & whisker plot (for all variables)

6 - Categorized histograms (for all variables)

7 - Categorized normal prob. plots (for all variables)

8 - Interaction plots (for all variables)

9 - Plot of means vs. std.devs (for all variables)

10 - Within-group correlations (for all variables); available only if number of specified vars > 1;

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

For more information on the options given above, see Breakdown: Descriptive statistics by groups.

Example:  The following example will produce summary tables for the specified variables.  In addition, an interaction plot and plot of means vs. standard deviations will be produced.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

BREAKDOWN

GROUPS=GROUP (ALL) GENDER (ALL) TIME (ALL)

VARS=CORRECT1-CORRECT3

STATS = 1,8,9

Valid Abbreviation:

BREAKD, STATS

For other Basic Statistics procedures, see:

Descriptive statistics

Correlation matrices

T-test for dependent samples

T-test for independent samples

Frequency tables

Crosstabulation tables

Banner tables


  SCL - Frequency Tables

FREQUENCY

   VARS [=] Varlist

   [/MODE [=] {INTEGER         }

              {number INTERVALS}

              {VALUES          }

              {number NEATINTERV}

              {STEP [=] number} ]

   [/{CASEWISE }

     {PAIRWISE } ]

   [/IGNOREMD

   [/NORMALEXPECTED]

   [STATISTICS [=] {number [, ... , number] }

                   {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Frequency tables

2 - Histograms

3 - Test for normality

4 - Box & Whisker plot for all vars

5 - Normal probab. plots

6 - Half-normal & Detrended normal probab. plots

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

For more information on the options given above, see Frequency Tables.

Example:  The following example will produce frequency tables for the specified variables.  In addition, tests for normality will be performed and a histogram, box & whisker, and probability plots will be produced.

FILE = "C:\STAT\EXAMPLES\EXP.STA"

FREQUENCY

VARS=CORRECT1-CORRECT3

/MODE=10 INTERVALS

STATS = ALL

Valid Abbreviation:

FREQ, STATS

For other Basic Statistics procedures, see:

Descriptive statistics

Correlation matrices

T-test for dependent samples

T-test for independent samples

Breakdown tables

Crosstabulation tables

Banner tables


  SCL - Crosstabulation Tables

TABLES

   VARS [=] VarList BY VarList

                 [BY VarList] [BY VarList]

                 [BY VarList] [BY VarList]

   [/PERCENT [=] { {TOTAL} [,] ... }

                   {ROW}

                   {COLUMN}

                 {ALL} ]

   [/FREQUENCIES]

   [/INCLUDEMD]

   [/STATS2WAY]

   [STATISTICS [=] {number [, ... , number] }

                   {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Review summary tables

2 - Detailed two-way tables

3 - Categorized histograms

4 - Interaction plots of frequencies

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

For more information on the options given above, see Crosstqabulation Tables.

NOTE:  When option PERCENT (or PERC) is used, then the output will include the relative (as well as raw) frequencies.

Example:  The following example will produce crosstabulation tables for the specified variables.  In addition, categorized histograms and interaction plots of frequencies will be produced.

FILE = "C:\STAT\EXAMPLES\SPORTS.STA"

TABLES

  VARS FOOTBALL BY

       BASEBALL-SWIMMING BY

       TRACK

  /FREQUENCIES

STATS = 1,3,4

Valid Abbreviation:

PERC, FREQ, STATS

For other Basic Statistics procedures, see:

Descriptive statistics

Correlation matrices

T-test for dependent samples

T-test for independent samples

Breakdown tables

Frequency tables

Banner tables


  SCL - Banner Tables

BANNERS

   VARS [=] VarList BY VarList

   [/PERCENT [=] { {TOTAL} [,] ... }

                   {ROW}

                   {COLUMN}

                 {ALL} ]

   [/FREQUENCIES]

   [/INCLUDEMD]

   [/STATS2WAY]

   [STATISTICS [=] {number [, ... , number] }

                   {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Review summary tables

2 - Detailed two-way tables

3 - Stub and Banner table

4 - Categorized histograms

5 - Interaction plots of frequencies

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

For more information on the options given above, see Stub-and-Banner Tables.

NOTE:  For the following example, when option PERCENT (or PERC) is used, then the output will include the relative (as well as raw) frequencies.

Example:  The following example will produce banner tables with row and column percents for the specified variables.  In addition, a stub and banner table and interaction plots of frequencies will be produced.

FILE = "C:\STAT\EXAMPLES\SPORTS.STA"

BANNERS

  VARS FOOTBALL BASEBALL BY TRACK-MARATHON

  /PERCENT = ROW, COLUMN

  STATS = 3,5

Valid Abbreviation:

PERC, FREQ, STATS

For other Basic Statistics procedures, see:

Descriptive statistics

Correlation matrices

T-test for dependent samples

T-test for independent samples

Breakdown tables

Frequency tables

Crosstabulation tables


SCL General Conventions - Nonparametric Statistics & Distribution Fitting

  SCL - Nonparametric Statistics & Distribution Fitting

For more information on these and related topics, see Nonparametrics and Distribution Fitting.

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Sign Test

SIGNTEST

VARS [=] VarList BY VarList

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Sign Test

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviation:

SIGN, STATS

For other Nonparametric procedures, see:

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Comparing Expected vs. Observed Frequencies

FITEXPECTED

OBSERVED [=] Variable

EXPECTED [=] Variable

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Expected vs. Observed

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviation:

FITEXP, STATS

For other Nonparametric procedures, see:

Sign Test

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Nonparametric Correlations

RANKCORR

VARS [=] VarList BY VarList

METHOD [=] { SPEARMAN }

           { KENDALL  }

           { GAMMA    }

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Correlation table

2 - Matrix plot

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviation:

STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Wald-Wolfowitz Runs Test

WW_TEST

GROUPS [=] Variable ( Value [,] Value )

VARS [=] VarList

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Wald-Wolfowitz test

2 - Box & Whisker plot

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviation:

STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Mann-Whitney U test

MW_UTEST

GROUPS [=] Variable ( Value [,] Value )

VARS [=] VarList

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Mann-Whitney test

2 - Box & Whisker plot

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviation:

STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Kolmogorov-Smirnov Two Sample Test

KS_TEST

GROUPS [=] Variable ( Value [,] Value )

VARS [=] VarList

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Kolmogorov-Smirnov Two Sample Test

2 - Box & Whisker plot

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviation:

STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Kruskal-Wallis ANOVA and Median Test

KW_TEST

GROUPS [=] Variable ( CodesList )

VARS [=] VarList

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Kruskal-Wallis ANOVA and Median Test

2 - Box & Whisker plot

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviation:

STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Friedman ANOVA and Kendall Concordance Coefficient

FRIEDMAN

VARS [=] VarList

KENDALL

VARS [=] VarList

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Friedman ANOVA and Kendall Concordance Coefficient

2 - Box & Whisker plot

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviation:

STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Wilcoxon Matched Pairs Test

WILCOXON_TEST

VARS [=] VarList BY VarList

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Wilcoxon test

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

WILCOX,STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Cochran Q Test

COCHRAN_TEST

VARS [=] VarList

[/ CODES [=] ( Number, Number ) ]

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Cochran Q test

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

COCHRAN, STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Extended Descriptive Statistics

EXT_DESC

VARS [=] VarList

[/ PERCENTILES [=] ( Number, Number ) ]

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Extended Descriptive Statistics

2 - Box & Whisker plot

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

PERC, PERCENT, STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Fitting the Normal Distribution to Data

By default, the program will compute the parameters for the normal distribution (mean, standard deviation) from the data; however, you may enter specific parameters (use keywords MEAN, VARIANCE).  CATEGORIES controls the number of categories for the frequency distribution table and histogram, MINMAX determines the minimum and maximum for the frequency distribution table and histogram.

NORMAL

VAR [=] Variable

[/ CATEGORIES [=] Number ]

[/ MINMAX [=] ( Number, Number ) ]

[/ MEAN [=] Number ]

[/ VARIANCE [=] Number ]

[/ KS_TEST = { CATEGORIZED }

                 { CONTINUOUS }

                 { NO }         ]

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Scrollsheet of observed and expected frequencies

2 - Graph - frequency distribution

3 - Graph - cumulative distribution

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

CAT (for categories), CONT, STATS

Example:

FILE = "C:\STAT\EXAMPLES\EXP.STA"

NORMAL VAR CORRECT1

  /CATEGORIES = 12

  /MINMAX = (2,20)

  /MEAN = 9.0

  /VARIANCE = 14.0

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Fitting a Rectangular Distribution to Data

RECTANGULAR

VAR [=] Variable

[/ CATEGORIES [=] Number ]

[/ MINMAX [=] ( Number, Number ) ]

[/ MEAN [=] Number ]

[/ KS_TEST = { CATEGORIZED }

                 { CONTINUOUS }

                 { NO }         ]

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Scrollsheet of observed and expected frequencies

2 - Graph - frequency distribution

3 - Graph - cumulative distribution

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

RECTANG, CAT (for categories), CONT, STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Fitting the Exponential Distribution to Data

EXPONENTIAL

VAR [=] Variable

[/ CATEGORIES [=] Number ]

[/ MINMAX [=] ( Number, Number ) ]

[/ LAMBDA [=] Number ]

[/ KS_TEST = { CATEGORIZED }

                 { CONTINUOUS }

                 { NO }         ]

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Scrollsheet of observed and expected frequencies

2 - Graph - frequency distribution

3 - Graph - cumulative distribution

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

EXPONENT, CAT (for categories), CONT, STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Fitting the Gamma Distribution to Data

GAMMA

VAR [=] Variable

[/ CATEGORIES [=] Number ]

[/ MINMAX [=] ( Number, Number ) ]

[/ SCALE [=] Number ]

[/ SHAPE [=] Number ]

[/ KS_TEST = { CATEGORIZED }

                 { CONTINUOUS }

                 { NO }         ]

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Scrollsheet of observed and expected frequencies

2 - Graph - frequency distribution

3 - Graph - cumulative distribution

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

CAT (for categories), CONT, STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Fitting the Log-normal Distribution to Data

LOGNORMAL

VAR [=] Variable

[/ CATEGORIES [=] Number ]

[/ MINMAX [=] ( Number, Number ) ]

[/ MEAN [=] Number ]

[/ VARIANCE [=] Number ]

[/ KS_TEST = { CATEGORIZED }

                 { CONTINUOUS }

                 { NO }         ]

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Scrollsheet of observed and expected frequencies

2 - Graph - frequency distribution

3 - Graph - cumulative distribution

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

CAT (for categories), CONT, STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Fitting the Chi-square Distribution to Data

CHI_SQUARE

VAR [=] Variable

[/ CATEGORIES [=] Number ]

[/ MINMAX [=] ( Number, Number ) ]

[/ DF [=] Number]

[/ KS_TEST = { CATEGORIZED }

                 { CONTINUOUS }

                 { NO }         ]

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Scrollsheet of observed and expected frequencies

2 - Graph - frequency distribution

3 - Graph - cumulative distribution

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

CHISQ, CAT (for categories), CONT, STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Fitting the Binomial Distribution to Data

BINOMIAL

VAR [=] Variable

[/ CATEGORIES [=] Number ]

[/ MINMAX [=] ( Number, Number ) ]

[/ TRIALS [=] Number ]

[/ KS_TEST = { CATEGORIZED }

                 { CONTINUOUS }

                 { NO }         ]

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Scrollsheet of observed and expected frequencies

2 - Graph - frequency distribution

3 - Graph - cumulative distribution

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

CAT (for categories), CONT, STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Fitting the Poisson Distribution to Data

POISSON

VAR [=] Variable

[/ CATEGORIES [=] Number ]

[/ MINMAX [=] ( Number, Number ) ]

[/ LAMBDA [=] Number ]

[/ KS_TEST = { CATEGORIZED }

                 { CONTINUOUS }

                 { NO }         ]

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Scrollsheet of observed and expected frequencies

2 - Graph - frequency distribution

3 - Graph - cumulative distribution

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

CAT (for categories), CONT, STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Geometric Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Fitting the Geometric Distribution to Data

GEOMETRIC

VAR [=] Variable

[/ CATEGORIES [=] Number ]

[/ MINMAX [=] ( Number, Number ) ]

[/ P [=] Number ]

[/ KS_TEST = { CATEGORIZED }

                 { CONTINUOUS }

                 { NO }         ]

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Scrollsheet of observed and expected frequencies

2 - Graph - frequency distribution

3 - Graph - cumulative distribution

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

CAT (for categories), CONT, STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Bernoulli Distribution to Data


  SCL - Fitting the Bernoulli Distribution to Data

BERNOULLI

VAR [=] Variable

[/ CATEGORIES [=] Number ]

[/ MINMAX [=] ( Number, Number ) ]

[/ P [=] Number ]

[/ KS_TEST = { CATEGORIZED }

                 { CONTINUOUS }

                 { NO }         ]

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Scrollsheet of observed and expected frequencies

2 - Graph - frequency distribution

3 - Graph - cumulative distribution

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

CAT (for categories), CONT, STATS

For other Nonparametric procedures, see:

Sign Test

Comparing Expected vs. Observed Frequencies

Nonparametric Correlations

Wald-Wolfowitz Runs Test

Mann-Whitney U Test

Kolmogorov-Smirnov Two Sample Test

Kruskal-Wallis ANOVA and Median Test

Friedman ANOVA and Kendall Concordance Coefficient

Wilcoxon Matched Pairs Test

Cochran Q Test

Extended Descriptive Statistics

Fitting the Normal Distribution to Data

Fitting the Rectangular Distribution to Data

Fitting the Exponential Distribution to Data

Fitting the Gamma Distribution to Data

Fitting the Log-normal Distribution to Data

Fitting the Chi-square Distribution to Data

Fitting the Binomial Distribution to Data

Fitting the Poisson Distribution to Data

Fitting the Geometric Distribution to Data


SCL General Conventions - Multiple Regression

  SCL - Multiple Regression

For more information on these and related topics, see Multiple Regression.  See also Order of SCL Statements.

REGRESSION

   DEPENDENT [=] VarList

   INDEPENDENT [=] VarList

   [/{CASEWISE}

     {PAIRWISE}

     {MEANSUBST} ]

   [/METHOD [=] {STANDARD}

                {FORWARD [FIN [=] Number]

                         [FOUT [=] Number]

                         [MAXSTEPS [=] Number] }

                {BACKWARD [FIN [=] Number]

                          [FOUT [=] Number]

                          [MAXSTEPS [=] Number] }

   [/INTERCEPT [=] {YES} {NO} ]

   [/TOLERANCE [=] Number ]

   [STATISTICS [=] {number [, ... , number] }

                   {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Regression summary, analysis of variance, partial correlation, redundancy

2 - Covariance of regression coefficient, current sweep matrix

3 - ANOVA, adjusted for means; available only if INTERCEPT=NO;

4 - Display residuals & pred.

5 - Durbin-Watson statistic

6 - Casewise plots (plots of residuals, plots of outliers, plots of predicted)

7 - Scatterplots (predicted & residual, predicted & observed, observed & residual)

8 - Probability plots (normal plot, half-normal plot, and detrended normal plot of residuals)

9 - Means and standard deviations, correlations

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

NOTE: If the FORWARD or BACKWARD stepwise method is specified, then the specification of statistical results/graphs will be disregarded (except for number 4) and a predefined batch of statistics will be produced for each step of the analysis.  The predefined batch of statistics includes:

•	a regression summary,

•	a summary of partial correlations and redundancies for all variables which are in and not in the equation at each step of the analysis, and

•	a summary of the stepwise regression at each step, up to the current step.

For more information on the above options, see Multiple Regression.

Example 1

Example 2

Valid Abbreviations:

REGR,DEP,INDEP,TOLER, STATS


  SCL - Performing Multiple Regression (Example 1)

The following example will compute a standard multiple regression analysis using file Poverty.sta, using variable Pt_Poor as the dependent variable (see also the Example section of the Multiple Regression chapter).  In addition, the covariance matrix, sweep matrix, plots of residuals, plots of outliers, plots of predicted values, and a series of scatterplots will be produced.

FILE = "C:\STAT\EXAMPLES\POVERTY.STA"

REGRESSION

 DEPENDENT=PT_POOR

 INDEPENDENT=POP_CHNG N_EMPLD TAX_RATE AFR_AM

 /CASEWISE

 /METHOD = STANDARD

 STATS = 1,2,6,7


  SCL - Performing Multiple Regression (Example 2)

This example will compute a stepwise forward regression analysis using file Poverty.sta with the same variables as in Example 1.  (MAXSTEPS is left at the default value.)  Note that a predefined batch of statistics is produced when performing a stepwise regression analysis (see Multiple Regression).

FILE = "C:\STAT\EXAMPLES\POVERTY.STA"

REGRESSION

 DEPENDENT=PT_POOR

 INDEPENDENT=POP_CHNG N_EMPLD TAX_RATE AFR_AM

 /METHOD FORWARD FIN = 3.0

                 FOUT = 2.5

 /INTERCEPT = YES

 /TOLERANCE = .01


SCL General Conventions - Nonlinear Estimation

  SCL - Nonlinear Estimation

For more information on these and related topics, see Nonlinear Estimation.  See also Order of SCL Statements.

Logit and Probit Regression

General Nonlinear Regression


  SCL - Logit and Probit Regression

LOGIT

PROBIT

INDEPENDENT [=] VarList

DEPENDENT [=] Variable (Value,Value)

[/ COUNTS = Variable ]

[/ { CASEWISE   } ]

   { MEANSUBST  }

[/ ITERATIONS [=] Number ]

[/ CONVERG [=] Number ]

[/ METHOD [=] { QUASINEWTON } ]

              { SIMPLEX     }

              { HOOKEJEEVES }

              { ROSENBROCK  }

[/ START [=] ( Number [,] ... ) ]

[/ STEP [=] ( Number [,] ... ) ]

[/SAVE [=] 'FileName' ]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Parameters & standard errors, covariances & correlations of parameters

2 - Means & standard deviations

3 - Classification of cases & odds ratio

4 - Residuals, predicted values

5 - Graphs:  Distribution of residuals, half-normal probability plot, predicted vs. observed values, predicted vs. residual values

6 - Fitted 2D or 3D functions & observed values (applicable only if you have selected 1 or 2 independent variable(s), respectively)

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Example

Valid Abbreviations:

INDEP,DEP,MAXL,LEASTSQ,ITERAT,QUASIN,HOOKEJ,

ROSENB,STATS

See also,

General Nonlinear Regression


  SCL - General Nonlinear Regression

Refer to Nonlinear Estimation for details on how to specify nonlinear regression functions, and how to specify loss functions.

NONLINEAR

FUNCTION [=] "EstFunction"

[/ LOSS [=] "LossFunction" ]

[/ { CASEWISE   } ]

   { MEANSUBST  }

[/ PRINT MEANS ]

[/ ITERATIONS [=] Number ]

[/ CONVERG [=] Number ]

[/ METHOD [=] { QUASINEWTON } ]

              { SIMPLEX     }

              { HOOKEJEEVES }

              { ROSENBROCK  }

[/ NPAR [=] Number ]

[/ START [=] ( Number ... ) ]

[/ STEP [=] ( Number ... ) ]

[/SAVE [=] 'FileName' ]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

Note that in order to specify start values or step sizes for NONLINEAR, always first specify the number of parameters in the model equation (i.e., in EstFunction) via the NPAR keyword.

STATISTICS:  Choose from the following selection of statistical results:

1 - Parameters & standard errors, covariances and correlations of parameters

2 - Means & standard deviations

3 - Classification of cases & odds ratio

4 - Residuals, predicted values

5 - Graphs:  Distribution of residuals, half-normal probability plot, predicted vs. observed values, predicted vs. residual values

6 - Fitted 2D or 3D functions & observed values (applicable only if you have selected 1 or 2 independent variable(s), respectively)

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Example:

FILE = "C:\STAT\EXAMPLES\EXP.STA"

NONLINEAR

  FUNCTION="STRESS_R=INTERC+B*CORRECT1"

  /LOSS="ABS(PRED-OBS)"

Valid Abbreviations:

NONLIN,ITERAT,QUASIN,HOOKEJ,ROSENB,STATS

See also,

Logit and Probit Regression


  SCL - Performing Nonlinear Estimation

The following example program will perform a logit regression, with variable SUCCESS as the dependent variable and variable EXPERNCE as the independent variable.

FILE = "PROGRAM.STA"

LOGIT INDEPENDENT=EXPERNCE

        DEPENDENT=SUCCESS


SCL General Conventions - Time Series and Forecasting

  SCL - Time Series and Forecasting

For more information on these and related topics, see Time Series and Forecasting.  See also Order of SCL Statements.

A Time Series and Forecasting analysis may be specified in the following manner:

(1)  State the method name (e.g., ARIMA)

(2)  Specify the variable (e.g., VAR = 1)

(3)  Specify the transformations (optional)

(4)  Specify any options

Example:

FILE = "C:\STAT\EXAMPLES\TIME.STA"

ARIMA

VAR = 1

/TRANSFORM EXP

/TRANSFORM DIFFERENCE = 2

MODEL = (0,1,1)(0,1,1)  SEASON = 12

/METHOD = EXACT

STOP

Time Series Options

The following options are applicable to any Time Series and Forecasting method (listed below).  In the SCL statement explanations (below), the statement TimeSeriesOptions will be used to indicate that one or more of the following options can be used at that point in the SCL program.  Please refer to the Time Series topics (listed below) for examples containing these options.

    [/SCALE MIN [=] Number STEP [=] Number]

    [/NBACKUPS [=] Number]

    [/DATES [=] Variable]

    [/SAVEAS [=] FIleName]

    [/TRANSFORM  { ADD [=] Number                            } ]

                 { POWER [=] Number                          }

                 { IPOWER [=] Number                         }

                 { LOG                                       }

                 { EXP                                       }

                 { MEAN                                      }

                 { STANDARDIZE                               }

                 { DETREND                                   }

                 { AUTOCORR [=] Number                       }

                 { MAVERAGE [=] Number [PRIOR]               }

                 { MMEDIAN [=] Number [PRIOR]                }

                 { EXPONENTIALSMOOTHING [=] Number           }

                 { SUBTRACT [=] Number VAR [=] Variable      }

                 { RESIDUAL [=] Number VAR [=] Variable      }

                 { FORWARD [=] Number                        }

                 { BACKWARD [=] Number                       }

                 { F4253H                                    }

                 { DIFFERENCE [=] Number                     }

                 { INTEGRATE [=] Number VAR [=] Variable     }

    ...

    [/TRANSFORM  ...                                           ]

Time Series Methods

The following Time Series and Forecasting methods can be sepcified using SCL commands.  For more information about the SCL statements for a particular method, click on the method name.

Transformations

ARIMA

Interrupted Time Series

Exponential Smoothing

Seasonal Decomposition

X-11 Census Method II Seasonal Adjustment (Monthly)

X-11 Census Method II Seasonal Adjustment (Quarterly)

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis


  SCL - Time Series Transformations

For more information about Time Series Transformations, see:

Transformations

Transformation Functions

Transformations for Spectrum Analysis

See also Order of SCL Statements.

TRANSFORMATIONS

   VAR [=] Variable

   TimeSeriesOptions

AUTOCORR

   VAR [=] Variable

   TimeSeriesOptions

   [/LAG [=] Number ]

   [/WHITENOISE [=] { ON  } ]

                    { OFF }

CROSSCORR

   VAR [=] Variable BY Variable

   TimeSeriesOptions

   [/LAG [=] Number ]

PARTIALCORR

   VAR [=] Variable

   TimeSeriesOptions

   [/LAG [=] Number ]

Example

See also:

Time Series Options

ARIMA

Interrupted Time Series

Exponential Smoothing

Seasonal Decomposition

X-11 Census Method II Seasonal Adjustment (Monthly)

X-11 Census Method II Seasonal Adjustment (Quarterly)

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis


  SCL - Performing Time Series Transformations

The following example program will perform an autocorrelation analysis on the variable STOCK1 and save the variables in the data file TSRESULT.STA.  Next, a 5-point moving average transformation will be performed.

FILE = "C:\STAT\EXAMPLES\STOCKS.STA"

   AUTOCORR

       VAR = STOCK1

          /NBACKUPS = 5

          /SAVEAS = "C:\STAT\EXAMPLES\TSRESULT.STA"

          /TRANSFORM   MAVERAGE = 5 PRIOR

       /LAG = 25

       /WHITENOISE =  ON

STOP


  SCL Time Series - ARIMA

For more information about Time Series ARIMA, see:

ARIMA Overview

ARIMA Models

Specifying ARIMA Models

ARIMA Results

See also Order of SCL Statements.

     ARIMA

          VAR [=] Variable

          TimeSeriesOptions

          MODEL [=] (p,d,q) [ (ps,ds,qs) SEASON [=] Number ]

          [/CONSTANT [=] { ON  } ]

                         { OFF }

          [/LOG [=] { ON  } ]

                    { OFF }

          [/POWER [=] Number ]

          [/METHOD [=] { APRROXIMATE [ BACKCAST [=] Number ] } ]

                       { EXACT                               }

          [/ITERATIONS [=] Number ]

          [/FORECAST [=] Number ]

          [/START [=] Number ]

          [/CONFID [=] Number ]

          [STATISTICS [=] {number [, ... , number] }

                          {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Parameter estimates, autocorrelations, partial autocorrelations

2 - Forecast cases, plot series and forecast.

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

STATS, ITERAT

Example

See also:

Time Series Options

Transformations

Interrupted Time Series

Exponential Smoothing

Seasonal Decomposition

X-11 Census Method II Seasonal Adjustment (Monthly)

X-11 Census Method II Seasonal Adjustment (Quarterly)

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis


  SCL - Performing ARIMA

The following example program will perform a log transformation of the variable SERIES_G and then difference the resulting transformed variable by a lag of 1.  An ARIMA analysis will be performed on the final transformed variable.

FILE = "C:\STAT\EXAMPLES\SERIES_G.STA"

   ARIMA

       VAR = SERIES_G

       /TRANSFORM LOG

       /TRANSFORM DIFFERENCE = 1

       MODEL = (0,1,1)(0,1,1)  SEASON = 12

       /METHOD = EXACT

STOP


  SCL Time Series - Interrupted Time Series

For more information about Interrupted Time Series, see:

Interrupted Time Series

Interrupted ARIMA Models

Specifying ARIMA Models

ARIMA Results

See also Order of SCL Statements.

INTERRUPTEDARIMA

     VAR [=] Variable

     TimeSeriesOptions

     MODEL [=] (p,d,q) [ (ps,ds,qs) SEASON [=] Number ]

     [/CONSTANT [=] { ON  } ]

                    { OFF }

     [/INTERVENTION [=] (CaseNumber, { ABRUPTPERMANENT  } )

                                     { GRADUALPERMANENT }

                                     { ABRUPTTEMPORARY  }

                        (CaseNumber, { ABRUPTPERMANENT  } )

                                     { GRADUALPERMANENT }

                                     { ABRUPTTEMPORARY  }

                        ...

     [/LOG [=] { ON  } ]

               { OFF }

     [/POWER [=] Number ]

     [/METHOD [=] { APPROXIMATE [ BACKCAST [=] Number ] } ]

                  { EXACT                               }

     [/ITERATIONS [=] Number ]

     [/FORECAST [=] Number ]

     [/START [=] Number ]

     [/CONFID [=] Number ]

     [STATISTICS [=] {number [, ... , number] }

                     {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Interrupted time series

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

STATS, ITERAT

Example

See also:

Time Series Options

Transformations

ARIMA

Exponential Smoothing

Seasonal Decomposition

X-11 Census Method II Seasonal Adjustment (Monthly)

X-11 Census Method II Seasonal Adjustment (Quarterly)

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis


  SCL - Performing Interrupted Time Series

The following example program will perform an Interrupted ARIMA analysis on the variable CALLS.

FILE = "C:\STAT\EXAMPLES\DIRECTOR.STA"

   INTERRUPTEDARIMA

       VAR = CALLS

       MODEL = (0,1,0) (0,1,1) SEASON = 12

       /INTERVENTION = (147,  ABRUPTPERMANENT )

       /LOG = OFF

       /METHOD = APPROXIMATE  BACKCAST = 0

STOP


  SCL Time Series - Exponential Smoothing

For more information about Exponential Smoothing Time Series, see:

Exponential Smoothing

See also Order of SCL Statements.

EXPONENTIALSMOOTHING

          VAR [=] Variable

          TimeSeriesOptions

          TREND [=] { NONE   }

                    { LINEAR }

                    { EXP    }

                    { DAMPED }

          SEASONALITY [=] { NONE           }

                          { ADDITIVE       }

                          { MULTIPLICATIVE }

          [/SEASON [=] Number ]

          [/PARAMETERS [=] { AUTO                                      }

                           { GRIDSEARCH                                }

                           { [ALPHA [=] Number ] [DELTA [=] Number ]

                             [GAMMA [=] Number ] [PHI [=] Number ]     }

          [/INITVALUE [=] Number ]

          [/INITTREND [=] Number ]

          [/FORECAST [=] Number ]

          [STATISTICS [=] {number [, ... , number] }

                          {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Exponential smoothing

2 - Exponential smoothing and summary plot for each smooth.

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

STATS

Example

See also:

Time Series Options

Transformations

ARIMA

Interrupted Time Series

Seasonal Decomposition

X-11 Census Method II Seasonal Adjustment (Monthly)

X-11 Census Method II Seasonal Adjustment (Quarterly)

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis


  SCL - Performing Exponential Smoothing

The following example program will perform an Exponential Smoothing analysis on the variable SERIES_G.

FILE = "C:\STAT\EXAMPLES\SERIES_G.STA"

   EXPONENTIALSMOOTHING

       VAR = SERIES_G

       TREND = LINEAR

       SEASONALITY = MULTIPLICATIVE

       /FORECAST = 12

STOP


  SCL Time Series - Seasonal Decomposition

For more information about Seasonal Decomposition Time Series, see:

Seasonal Decomposition (Census I)

See also Order of SCL Statements.

CENSUS1

     VAR [=] Variable

     TimeSeriesOptions

     SEASONALITY [=] { ADDITIVE       }

                     { MULTIPLICATIVE }

     [/SEASON [=] Number ]

     [/CENTERED [=] { ON  } ]

                    { OFF }

     [/APPEND { ALL }

              { [ MAVERAGE ] [ RATIOS ] [ SEASON ] [ ADJUSTED ]

                [ TRENDCYCLE ] [ IRREGULAR ] } ]

     [STATISTICS [=] {number [, ... , number] }

                     {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Seasonal decomposition

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

STATS

Example

See also:

Time Series Options

Transformations

ARIMA

Interrupted Time Series

Exponential Smoothing

X-11 Census Method II Seasonal Adjustment (Monthly)

X-11 Census Method II Seasonal Adjustment (Quarterly)

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis


  SCL - Performing Seasonal Decomposition

The following example program will perform a Seasonal Decomposition (Census I) on the variable SALES.

FILE = "C:\STAT\EXAMPLES\RETAIL.STA"

   CENSUS1

       VAR = SALES

       /SCALE MIN = 1 STEP = 12

       /NBACKUPS = 6

       /DATES = DATE

       SEASONALITY = MULTIPLICATIVE

       /APPEND ALL

STOP


  SCL Time Series - X-11 Census Method II Seasonal Adjustment (Monthly)

For more information about X-11 Census Method II Seasonal Adjustment (Monthly) Time Series, see:

X-11 Census Method II Seasonal Adjustment

Seasonal Adjustment: Basic Ideas and Terms

The Census II Method

Results Tables Computed by the X-11 Method

Specific Description of all Results Tables Computed by the X-11 Method

X-11 monthly seasonal adjustment

See also Order of SCL Statements.

X11MONTHLY

     VAR [=] Variable

     TimeSeriesOptions

     SEASONALITY [=] { ADDITIVE       }

                     { MULTIPLICATIVE }

     [/FROMMONTH [=] Number ]

     [/FROMYEAR [=] Number ]

     [/SUMMARY [=] { ON  } ]

                   { OFF }

     [/PRINT [=] { STANDARD } ]

                 { LONG     }

                 { FULL     }

     [/CHARTS [=] { NONE     } ]

                  { STANDARD }

                  { FULL     }

     [/PRIORDAILY [=] ( Number, Number, Number, Number, Number, Number, Number ) ]

     [/REGRESSION [=] { NONE    } ]

                      { COMPUTE }

                      { ADJUST  }

                      { TEST    }

     [/LENGTH [=] { ON  } ]

                  { OFF }

     [/START [=] Number ]

     [/ADJUST [=] Number ]

     [/SIGMA  [=] Number ]

     [/PRIOR VAR [=] Variable ]

     [/FULL [=] Number ]

     [/ZERO [=] Number ]

     [/MAVERAGE [=] { AUTO     } { AUTO     }  ...  { AUTO     } ]

                    { MA_3TERM } { MA_3TERM }  ...  { MA_3TERM }

                    { MA_3x3   } { MA_3x3   }  ...  { MA_3x3   }

                    { MA_3x5   } { MA_3x5   }  ...  { MA_3x5   }

                    { MA_3x9   } { MA_3x9   }  ...  { MA_3x9   }

                    { STABLE   } { STABLE   }  ...  { STABLE   }

     [/HENDERSON [=] { AUTO     } ]

                     { H_9TERM  }

                     { H_13TERM }

                     { H_23TERM }

     [/ADJUSTEXTREMES [=] { ON  } ]

                          { OFF }

     [STATISTICS [=] {number [, ... , number] }

                     {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - X-11 census method II seasonal adjustement (monthly).

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

STATS

Example

See also:

Time Series Options

Transformations

ARIMA

Interrupted Time Series

Exponential Smoothing

Seasonal Decomposition

X-11 Census Method II Seasonal Adjustment (Quarterly)

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis


  SCL - Performing X-11 Census Method II Seasonal Adjustment (Monthly)

The following example program will perform a X-11(Census Method II) Monthly Seasonal Adjustment on the variable SALES.

FILE = "C:\STAT\EXAMPLES\RETAIL.STA"

   X11MONTHLY

       VAR = SALES

       /SCALE MIN = 1 STEP = 12

       /NBACKUPS = 4

       /DATES = DATE

       SEASONALITY = MULTIPLICATIVE

       /PRINT = STANDARD

       /CHARTS = STANDARD

       /REGRESSION = TEST

   STOP


SCL Time Series - X-11 Census Mehtod II Seasonal Adjustment (Quarterly)

  SCL Time Series - X-11 Census Method II Seasonal Adjustment (Quarterly)

For more information about X-11 Census Method II Seasonal Adjustment (Quarterly) Time Series, see:

X-11 Census Method II Seasonal Adjustment

Seasonal Adjustment: Basic Ideas and Terms

The Census II Method

Results Tables Computed by the X-11 Method

Specific Description of all Results Tables Computed by the X-11 Method

X-11 quarterly seasonal adjustment

See also Order of SCL Statements.

X11QUARTERLY

     VAR [=] Variable

     TimeSeriesOptions

     SEASONALITY [=] { ADDITIVE       }

                     { MULTIPLICATIVE }

     [/FROMQUARTER [=] Number ]

     [/FROMYEAR [=] Number ]

     [/SUMMARY [=] { ON  } ]

                   { OFF }

     [/PRINT [=] { STANDARD } ]

                 { LONG     }

                 { FULL     }

     [/CHARTS [=] { NONE     } ]

                  { STANDARD }

                  { FULL     }

     [/FULL [=] Number ]

     [/ZERO [=] Number ]

     [/ADJUSTEXTREMES [=] { ON  } ]

                          { OFF }

     [STATISTICS [=] {number [, ... , number] }

                     {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - X-11 census method II seasonal adjustement (quarterly).

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

STATS

Example

See also:

Time Series Options

Transformations

ARIMA

Interrupted Time Series

Exponential Smoothing

Seasonal Decomposition

X-11 Census Method II Seasonal Adjustment (Monthly)

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis


SCL - Performing X-11 Census Mehtod II Seasonal Adjustment (Quarterly)

  SCL - PerformingX-11 Census Method II Seasonal Adjustment (Quarterly)

The following example program will perform a X-11(Census Method II) Quarterly Seasonal Adjustment on the variable SALES.

FILE = "C:\STAT\EXAMPLES\RETAIL.STA"

   X11MONTHLY

       VAR = SALES

       /SCALE MIN = 1 STEP = 12

       /NBACKUPS = 4

       /DATES = DATE

       SEASONALITY = MULTIPLICATIVE

       /PRINT = STANDARD

       /CHARTS = STANDARD

STOP


  SCL Time Series - Distributed Lags Analysis

For more information about Time Series Distributed Lags Analysis, see:

Distributed Lags Analysis

See also Order of SCL Statements.

DISTRIBUTEDLAGS

     VAR [=] Variable

     INDEPENDENT [=] Variable

     TimeSeriesOptions

     LAG [=] Number

     METHOD [=] { UNCONSTRAINED    }

                { ALMON [=] Number }

     [STATISTICS [=] {number [, ... , number] }

                     {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Distributed lags analysis.

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

STATS

Example

See also:

Time Series Options

Transformations

ARIMA

Interrupted Time Series

Exponential Smoothing

Seasonal Decomposition

X-11 Census Method II Seasonal Adjustment (Monthly)

X-11 Census Method II Seasonal Adjustment (Quarterly)

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis


  SCL - Performing Distributed Lags Analysis

The following example program will perform a Distributed Lags Analysis.

FILE = "C:\STAT\EXAMPLES\TEACHERS.STA"

   DISTRIBUTEDLAGS

       VAR = TEACHERS

       INDEPENDENT = CHILDREN

       LAG = 2

       METHOD = UNCONSTRAINED

   STOP


  SCL Time Series - Single Spectrum (Fourier) Analysis

For more information about Time Series Single Spectrum (Fourier) Analysis, see:

Single Spectrum (Fourier) Analysis

See also Order of SCL Statements.

SPECTRUM

     VAR [=] Variable

     TimeSeriesOptions

     [/TAPER [=] Number ]

     [/MEANSUBTRACT [=] { ON  } ]

                        { OFF }

     [/DETREND [=] { ON  } ]

                   { OFF }

     [/PAD [=] Number ]

     [/WINDOW [=] Number ]

     [/SMOOTHING [=] { DANIELL                          } ]

                     { TUKEY                            }

                     { HAMMING                          }

                     { PARZEN                           }

                     { BARTLETT                         }

                     { USER [=] ( Number, ..., Number ) }

     [/KOLMOGOROV [=] { ON  } ]

                      { OFF }

     [/APPEND { ALL }

              { [ FREQUENCY ] [ PERIOD ] [ COSINE ]

                [ SINE ] [ PERIODOGRAM ] [ DENSITY ] } ]

     [/PLOT { ALL }

            { [ COSINE ] [ SINE ] [ PERIODOGRAM ]

              [ DENSITY ] [ LOGPERIODOGRAM ] [ LOGDENSITY ] }

            BY { FREQUENCY }

               { PERIOD    }

               { LOGPERIOD } ]

     [STATISTICS [=] {number [, ... , number] }

                     {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Single spectrum (Fourier) analysis.

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

STATS

Example

See also:

Time Series Options

Transformations

ARIMA

Interrupted Time Series

Exponential Smoothing

Seasonal Decomposition

X-11 Census Method II Seasonal Adjustment (Monthly)

X-11 Census Method II Seasonal Adjustment (Quarterly)

Distributed Lags Analysis

Cross-spectrum Analysis


  SCL - Performing Single Spectrum (Fourier) Analysis

The following example program will perform a Single Spectrum (Fourier) Analysis.

FILE = "C:\STAT\EXAMPLES\SUNSPOT.STA"

   SPECTRUM

       VAR = SPOTS

       /SCALE MIN = 1 STEP = 12

       /MEANSUBTRACT = ON

       /DETREND = ON

       /WINDOW = 5

   /SMOOTHING 	= HAMMING

       /KOLMOGOROV = ON

       /APPEND PERIODOGRAM DENSITY

       /PLOT  ALL

       BY FREQUENCY

STOP


  SCL Time Series - Cross-spectrum Analysis

For more information about Time Series Cross-spectrum Analysis, see:

Cross-spectrum Analysis

See also Order of SCL Statements.

COSPECTRUM

     VAR [=] Variable

     DEPENDENT [=] Variable

     TimeSeriesOptions

     [/TAPER [=] Number ]

     [/MEANSUBTRACT [=] { ON  } ]

                        { OFF }

     [/DETREND [=] { ON  } ]

                   { OFF }

     [/PAD [=] Number ]

     [/WINDOW [=] Number ]

     [/SMOOTHING [=] { DANIELL                          } ]

                     { TUKEY                            }

                     { HAMMING                          }

                     { PARZEN                           }

                     { BARTLETT                         }

                     { USER [=] ( Number, ..., Number ) }

     [/APPEND { ALL }

              { [ FREQUENCY ] [ PERIOD ] [ COSINE ] [ SINE ]

                [ PERIODOGRAM ] [ DENSITY ] [ CROSSPERIODOGRAM ]

                [ CODENSITY ] [ QUADDENSITY ] [ AMPLITUDE ]

                [ COHERENCY ] [ GAIN ] [ PHASE ] } ]

     [/PLOT { ALL }

            { [ COSINE ] [ SINE ] [ PERIODOGRAM ] [ DENSITY ]

              [ LOGPERIODOGRAM ] [ LOGDENSITY ]

              [ CROSSPERIODOGRAM ] [ CODENSITY ] [ QUADDENSITY ]

              [ AMPLITUDE ] [ COHERENCY ] [ GAIN ] [ PHASE ] }

            BY { FREQUENCY }

               { PERIOD    }

               { LOGPERIOD } ]

     [STATISTICS [=] {number [, ... , number] }

                     {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Cross spectrum analysis.

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

STATS

Example

See also:

Time Series Options

Transformations

ARIMA

Interrupted Time Series

Exponential Smoothing

Seasonal Decomposition

X-11 Census Method II Seasonal Adjustment (Monthly)

X-11 Census Method II Seasonal Adjustment (Quarterly)

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis


  SCL - Performing Cross-spectrum Analysis

The following example program will perform a Cross-spectrum Analysis.

   FILE = "C:\STAT\EXAMPLES\STOCKS.STA"

   COSPECTRUM

       VAR = STOCK1

       DEPENDENT = STOCK2

       /SCALE MIN = 1 STEP = 12

       /MEANSUBTRACT = ON

       /DETREND = ON

       /WINDOW = 5

   /SMOOTHING 	= HAMMING

       /APPEND PERIODOGRAM DENSITY

       /PLOT  ALL

       BY FREQUENCY

STOP


  SCL - Factor Analysis

For more information on these and related topics, see Factor Analysis.  See also Order of SCL Statements.

FACTOR

VARS [=] VarList

[/ METHOD [=] {COMPONENTS}  [= Number] ]

              {MULTR2}

              {MINRES}

              {MAXLIKELIHOOD}

              {CENTROID}

              {PRINCAXIS}

[/ MINEIGEN [=] Number ]

[/ ROTATION [=] {VARIMAX}

                {BIQUARTIMAX}

                {EQUIMAX}

                {QUARTIMAX}

[/ {CASEWISE}

   {PAIRWISE}

   {MEANSUBST} ]

[/ PLOT2D [=] (FactorNumber , FactorNumber) ... ]

[/ SAVE [=] 'FileName' ]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Eigenvalues, communalities, factor loadings (before and after rotation, if applicable), factor score coefficients; for Maximum Likelihood method - also Goodness of fit

2 - Means & standard deviations, correlations, reproduced & residual correlations

3 - Scree plot

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Notes:	If MINEIGEN (minimun eigenvalue) is specified and not equal to zero, then the 2D plots of loadings will not be created (even if requested in the program).

For backward compatibility, MULTR2 may be substituted with FACTOR; in both cases, "Communalities = multiple R-square" will be selected as the extraction method.

Example:

FILE = "C:\STAT\EXAMPLES\FACTOR.STA"

FACTOR VARS=ALL

  /METHOD COMPONENTS=3

  /ROTATION=VARIMAX

Valid Abbreviations:

MAXL, STATS


  SCL - Correspondence Analysis

For more information on these and related topics, see Correspondence Analysis.  See also Order of SCL Statements.

Regular Correspondence Analysis

Multiple Correspondence Analysis


  SCL - Correspondence Analysis - Regular

For more information on these and related topics, see Correspondence Analysis.  See also Order of SCL Statements.

CORRESPONDENCE

INPUT [=]

{ RAWDATA

ROWS [=] Variable ( CodesList ) ...

COLUMNS [=] Variable ( CodesList ) ...}

{ GROUPS

ROWS [=] Variable ( CodesList ) ...

COLUMNS [=] Variable ( CodesList ) ...

FREQ [=] Variable                }

{ FREQUENCIES

VARS [=] VarList          }

[/DIM { NUMBER [=] number }

          { PERCENT [=] number } ]

[/STANDARDIZE [=] { ROWCOL }

                      { CANONICAL }

                      { ROW }

                      {COLUMN } ]

[/TRUNCATE [=] number ]

[/IDENTICAL ]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Eigenvalues, row and column coordinates

2 - Unstandardized matrices

3 - Observed frequencies, row percentages, column percentages, total percentages

4 - Expected (chi-square), observed minus expected, contribution to chi-square, standardized deviates

5 - Row and column plots of coordinates, 1D

6 - Row and column plots of coordinates, 2D

7 - Row and column plots of coordinates, 3D

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

CA,FREQ,PERC,STATS


  SCL - Correspondence Analysis - Multiple

For more information on these and related topics, see Correspondence Analysis.  See also Order of SCL Statements.

MULTCORRESP

INPUT [=]

{ RAWDATA

VARS [=] Variable ( CodesList ) ...  }

{ GROUPS

VARS [=] Variable ( CodesList ) ...

FREQ [=] Variable        }

{ FREQUENCIES

VARS [=] VarList

FACTORS [=] "Label" ( Number ) ...}

[/SUPPLEMENT [=] VarList ]     }

[/DIM { NUMBER [=] number }

          { PERCENT [=] number } ]

[/TRUNCATE [=] number ]

[/IDENTICAL ]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

NOTE: The SUPPLEMENT variables must constitute a subset of the main variable list.  This feature is not verified by SCL, but will be checked at execution time and the SCL program will not be executed if the list is specified incorrectly.

STATISTICS:  Choose from the following selection of statistical results:

1 - Eigenvalues, row and column coordinates

2 - Unstandardized matrices

3 - Observed frequencies, row percentages, column percentages, total percentages

4 - Expected (chi-square), observed minus expected, contribution to chi-square, standardized deviates

5 - Row and column plots of coordinates, 1D

6 - Row and column plots of coordinates, 2D

7 - Row and column plots of coordinates, 3D

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

MCA,FREQ,PERC,STATS


  SCL - Cluster Analysis

For more information on these and related topics, see Cluster Analysis.  See also Order of SCL Statements.

Joining or Tree Clustering

K-means Clustering


  SCL - Joining or Tree Clustering

Refer to Cluster Analysis for details concerning the different distance measures and linkage rules available in this module.

JOINING

VARS [=] VarList

[/ INPUT [=]   { RAWDATA}

               { MATRIX}  ]

[/ CLUSTER [=] { VARS  } ]

               { CASES }

[/DISTANCE [=] { SQUARED                   }

               ( EUCLIDEAN                 }

               { MANHATTAN                 }

               { CHEBYSHEV                 }

               { POWER [=] (Number,Number) }

               { PERCENT                   }

               { PEARSON                   }

[/ LINKAGE [=] { SINGLE                    }]

               { COMPLETE                }

               { UNWEIGHTED { AVERAGE  } }

                            { CENTROID }

               { WEIGHTED { AVERAGE  }  }

                          { CENTROID }

               { WARD }

[/ { CASEWISE   } ]

   { MEANSUBST  }

[/ SAVEMATRIX [=] 'FileName' ]

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Descriptive statistics for cases, descriptive statistics for variables, reordered data matrix

2 - Two way joining graph

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Example:

FILE = "C:\STAT\EXAMPLES\CARS.STA"

JOINING VARS = ALL

  /CLUSTER = CASES

  /DISTANCE = MANHATTAN

  /LINKAGE = COMPLETE

Valid Abbreviation:

STATS

See also,

K-means Clustering


  SCL - K-means Clustering

K_MEANS

VARS [=] VarList

[/ CLUSTER [=] { VARS  } ]

               { CASES }

[/ NCLUSTER [=] Number } ]

[/ ITERATIONS [=] Number } ]

[/ { CASEWISE   } ]

   { MEANSUBST  }

[/INITCENTERS [=] {MAXINIT}

                  {SORTDIST}

                  {FIRSTNOBS} ]

[/SAVE [=] 'FileName' ]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Analysis of variance, cluster means and Euclidean distances, descriptive statistics for each cluster, members of each cluster and distances

2 - Graph of means

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Example:

FILE = "C:\STAT\EXAMPLES\CARS.STA"

K_MEANS VARS = ALL

  /CLUSTER = CASES

  /NCLUSTER = 3

Valid Abbreviations:

ITERAT, STATS

See also,

Joining or Tree Clustering


  SCL - Two-Way Joining

TWOWAYJOIN

VARS [=] VarList

[/THRESHOLD [=] Number ]

[/{CASEWISE}

  {MEANSUBST} ]

[STATISTICS [=] {number [, ... , number] }

        {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Descriptive statistics for cases, descriptive statistics for variables, reordered data matrix.

2 - Two-way joining graph

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviation:

STATS


  SCL - Canonical Correlation Analysis

For more information on these and related topics, see Canonical Correlation.  See also Order of SCL Statements.

CANONICAL

  VARS [=] VarList BY VarList

  [/ { CASEWISE   } ]

     { MEANSUBST  }

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Result summary

2 - Correlations within/between sets, eigenvalues, canonical weights, factor structures & redundancies, Chi-square tests of canonical roots

3 - Graph of eigenvalues

4 - Means & standard deviations, correlation matrix

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Example:

FILE = "C:\STAT\EXAMPLES\FACTOR.STA"

CANONICAL

  VARS WORK_1-WORK_3 BY HOBBY_1-MISCEL_2

Valid Abbreviation:

CANON, STATS


  SCL - Multidimensional Scaling

For more information on these and related topics, see Multidimensional Scaling.  See also Order of SCL Statements.

MDSCALING

[/ VARS [=] VarList ]

[/ DIMENSIONS [=] Number ]

[/ ITERATIONS [=] Number ]

[/ SAVE [=] 'FileName' ]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Final configuration

2 - D-hat values, D-star values, distance matrix, summary

3 - Graphs: D-hat vs. distances, D-star vs. distances, Shepard diagram

4 - 2D graphs of final configuration

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Example:

FILE = "C:\STAT\EXAMPLES\NATIONS.STA"

MDS

/VARS = ALL

/DIM = 3

Valid Abbreviations:

MDS, DIM, ITERAT, STATS


  SCL - Reliability and Item Analysis

For more information on these and related topics, see Reliability and Item Analysis.  See also Order of SCL Statements.

RELIABILITY

VARS [=] VarList

[/ FIRST [=] VarList

   SECOND [=] VarList ]

[/ { CASEWISE  }

   { MEANSUBST } ]

[/ REGRESSION ]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Item-total statistics; additionally, for split-half reliability: means & standard deviations for 1st and 2nd half, summary (Cronbach's alpha, summary statistics for full scale, etc.)

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Example:

FILE = "C:\STAT\EXAMPLES\10ITEMS.STA"

RELIABILITY VARS=ALL

Valid Abbreviations:

RELIAB, REGR, STATS


  SCL - General ANOVA/MANOVA

For more information on these and related topics, see ANOVA/MANOVA.  See also Order of SCL Statements.

MANOVA

   VARS [=] VarList

   [/GROUPS [=] Variable (CodesList) ... ]

   [/REPEATED [=] "Name" (Number) ... ]

   [/COVARIATES [=] VarList ]

   [/{FIXEDCOV}

     {CHANGINGCOV} ]

   [/NESTED [=] (Variable (Level) IN Variable [,] ... ) ... ]

   [/RANDOM [=] FactorName [,] ... ]

   [/REGRAPPROACH

   [/POSTHOC (List of Factor Names)

            /{LSD} ...

             {SCHEFFE}

             {NEWMAN}

             {DUNCAN}

             {HSD}

             {SS}

             {ALL} ] ...

   [/SPECEFFECT (List of Factor Names) ] ...

   [/OPTIONS [=]

        {GREENHOUSE }...

        {MAUCHLEY }

        {REGRRES }

        {ADJUSTED } ]

   [STATISTICS [=] {number [, ... , number] }

                   {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - All effects

2 - Means and number. of cases for each group and standard deviations for each group

3 - Pooled within group covariances and correlations, and total covariances and correlations

4 - Marginal means (detailed results for all effects)

5 - Graphs (for all effects)

6 - Tests for homogeneity of variances/covariances

7 - Plot of means versus standard deviation

8 - Stem & leaf plots for all dependent variables and covariates

9 - Normal plot of within-cell residuals

If no STATISTICS are explicitly specified, then the default set of results will be: 1 and 2.

For more information on the above options, see ANOVA/MANOVA.

Example

Valid Abbreviations:

STATS


  SCL - Performing General ANOVA/MANOVA

The following example will compute a 2 x 2 x 3 x 2 between x 3 within (repeated measures) analysis of variance.  In addition, a Scrollsheet of marginal means, a plot of means vs. standard deviations and stem & leaf plots will be produced.  Refer to ANOVA/MANOVA for details on how to specify different designs.  Note that the name or label of the repeated measures factor is enclosed in quotation marks.

FILE = "EXP.STA"

MANOVA

 VARS = CORRECT1-CORRECT3

 /GROUPS GROUP  (EXPERMTL,CONTROL)

         GENDER (1,2)

         TIME   (BEFORE,AFTER_1,AFTER_2)

         PAID   (NOT_PAID,PAID)

 /REPEATED "REPFACT" (3)

 /POSTHOC (GROUP, GENDER, TIME, PAID)

    /LSD

 STATISTICS = 1,4,7,8


  SCL - Discriminant Function Analysis

For more information on these and related topics, see Discriminant Function Analysis.  See also Order of SCL Statements.

DISCRIMINANT

GROUPS [=] Variable ( CodesList ) ...

VARS [=] VarList

[/ METHOD [=] { STANDARD}

              { FORWARD  [FIN  [=] Number]

                         [FOUT [=] Number]

                         [MAXSTEPS [=] Number] }

              { BACKWARD [FIN [=] Number]

                         [FOUT [=] Number]

                         [MAXSTEPS [=] Number] }

[/ TOLERANCE [=] Number]

[/ { CASEWISE   }

   { MEANSUBST } ]

[/ CLASSIFICATION PRIOR [=] { EQUAL }

                            { SIZE  } ]

[/ SAVE [=] 'FileName']

  [STATISTICS [=] {number [, ... , number] }

                  {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - for Standard method:  summary statistics for variables in the model, distances between groups;
for Forward/Backward method:  summary of stepwise analysis

2 - Descriptive statistics (means & number of cases, pooled within-groups covariances & correlations, total covariances & correlations)

3 - Canonical analysis results (Chi-squared tests, coefficients for canonical variables, factor structure, means of canonical variables); this set of results will be created only if the number of groups is greater than 2 and at least 2 independent variables are specified;

4 - Classification function & matrix

5 - Classification of cases, squared Mahalanobis distances, posterior probabilities

6 - Descriptive stats graphs (graph of correlations, Box & Whisker plot)

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Example 1

Example 2

Valid Abbreviations:

DISC, TOLER, CLASS, STATS


  SCL - Performing Discriminant Function Analysis (Example 1)

The following example performs a standard discriminant function analysis on the data in file IRISDAT.STA.  Note the use of the ALL convention to select all codes in variable IRISTYPE.

FILE = "IRISDAT.STA"

DISCRIMINANT

  GROUPS IRISTYPE (ALL)

  VARS = SEPALLEN-PETALWID


  SCL - Performing Discriminant Function Analysis (Example 2)

The following example performs a forward stepwise discriminant function analysis on the data in file IRISDAT.STA.

FILE = "IRISDAT.STA"

DISCRIMINANT

  GROUPS IRISTYPE (ALL)

  VARS = SEPALLEN-PETALWID

  /METHOD=FORWARD


  SCL - Log-linear Analysis of Frequency Tables

Refer to Log-linear Analysis for details on how to specify tables in this module.  See also Order of SCL Statements.

LOGLINEAR

INPUT [=]

  { RAWDATA

      GROUPS [=] Variable( CodesList ) ... }

  { FREQUENCIES

      FACTORS [=] "Label" ( Number ) ...   }

      VARS [=] VarList

  { CODES

      FREQ [=] Variable

      GROUPS [=] Variable( CodesList ) ... }

[/ MODEL [=] 'ModelDefinition' ]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Complete observed table, test all marginal & partial association models, marginal tables

2 - Fitted table, residuals (observed - fitted), components of Maximum Likelihood Chi-square)

3 - Graphs: observed vs. fitted, fitted vs. residuals, fitted vs. standard residuals, fitted vs. Maximum Likelihood Chi-Square components, and fitted vs. Freeman-Tukey deviates

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Note: The 'ModelDefinition' parameter for MODEL command must be a string of up to 52 characters specifying the desired model.

Example:

FILE = "CENTER2.STA"

LOGLINEAR

  INPUT = CODES

    FREQ = FREQUNCY

    GROUPS = APPEARNC(ALL)

             SURVIVAL('YES','NO')

             AGE(ALL)

             LOCATION(ALL)

Valid Abbreviations:

LOGLIN, STATS


  SCL - Survival Analysis

For more information on these and related topics, see Survival Analysis.  See also Order of SCL Statements.

Life Tables and Fitting Survival Distributions

Kaplan Meier Product Limit Method

Comparison of Survivial in Two or More Groups

Explanatory Regression Models for Survival/Failure Times

Regression Models with Time Dependent Covariates


  SCL - Life Tables and Fitting Survival Distributions

LIFETABLE

INPUT [=]

     { RAWDATA

            VARS [=] VarList

            CENSOR [=] Variable

            CENSORED [=] Value

            COMPLETE [=] Value

         [/ INTERVALS [=] Number] }

     { TABLE

            INTERVALS [=] Variable ( Number )

            CENSORED [=] Variable

            FAILED [=] Variable   }

[/CORRECTINTERV [=] {YES} {NO} ]

[/MODEL [=] {EXPONENTIAL}

            {LINEAR}

            {GOMPERTZ}

            {WEIBULL} ]

[STATISTICS [=] {number [, ... , number] }

                    {ALL} ]

Note that when INPUT is equal to TABLE, then you must specify the number of observations ("alive") entering the first interval; specify this number following the INTERVALS variable (e.g., INTERVALS = PERIODS (678)).  Refer to Survival Analysis for details.

STATISTICS:  Choose from the following selection of statistical results:

1 - Life table

2 - Parameter estimates, Estimates of hazard function, Estimates of survival function, Estimates of probability density function

3 - Graphs: Hazard function, Survival function, Probability density function

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Example:

FILE = "C:\STAT\EXAMPLES\HEART.STA"

LIFETABLE INPUT=RAWDATA

  VARS=1-6

  CENSOR=CENSORED CENSORED=1 COMPLETE=0

Valid Abbreviations:

LIFET,INTERV,EXP,STATS

For other Survival Analysis procedures, see:

Kaplan Meier Product Limit Method

Comparison of Survivial in Two or More Groups

Explanatory Regression Models for Survival/Failure Times

Regression Models with Time Dependent Covariates


  SCL - Kaplan-Meier Product Limit Method

KAPLAN_MEIER

VARS = VarList

CENSOR [=] Variable

CENSORED [=] Value

COMPLETE [=] Value

[STATISTICS [=] {number [, ... , number] }

                    {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Product-limit estimate, percentiles of survival distribution

2 - Graphs: survival times vs. cumulative proportion surviving, log-survival times vs. cumulative proportion surviving, log-survival times vs. log cumulative proportion surviving

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

KAPLAN,STATS

For other Survival Analysis procedures, see:

Life Tables and Fitting Survival Distributions

Comparison of Survivial in Two or More Groups

Explanatory Regression Models for Survival/Failure Times

Regression Models with Time Dependent Covariates


  SCL - Comparison of Survival in Two or More Groups

SURV_COMP

VARS = VarList

CENSOR [=] Variable

CENSORED [=] Value

COMPLETE [=] Value

GROUPS [=] Variable( CodesList )

[/ TESTS [=] { ALL      } ]

             { GEHAN   }

             { FTEST   }

             { COX     }

             { LOGRANK }

             { PETO    }

[STATISTICS [=] {number [, ... , number] }

                    {ALL} ]

Note that the TESTS option is only applicable (available) when two groups are being compared.  Refer to Survival Analysis for details.

STATISTICS:  Choose from the following selection of statistical results:

For 2-group comparison:

1 - Selected test (or all tests, if not explicitly specified in the program)

2 - Graph of proportion surviving for each group, Cumulative proportion surviving by group (Kaplan-Meier estimate)

For multiple comparisons:

1 - Survival times & scores, Scores for each group, Descriptive stats

2 - Graph of proportion surviving for each group, Cumulative proportion surviving by group (Kaplan-Meier estimate)

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviation:

STATS

For other Survival Analysis procedures, see:

Life Tables and Fitting Survival Distributions

Kaplan Meier Product Limit Method

Explanatory Regression Models for Survival/Failure Times

Regression Models with Time Dependent Covariates


  SCL - Regression Models with Time Dependent Covariates

Refer to Survival Analysis for details.

TIMEDEP

DEPENDENT [=] VarList

CENSOR [=] Variable

CENSORED [=] Value

COMPLETE [=] Value

COVARIATES [=] 'Expression' [,] ...

[/ITERATIONS [=] Number ]

[/CONVERG [=] Number ]

[/START [=] ( Number [,] ... ) ]

[/{CASEWISE}

  {MEANSUBST} ]

[STATISTICS [=] {number [, ... , number] }

                    {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Parameter estimates, parameter covariances & correlations

2 - Means & standard deviations

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviation:

DEP,ITERAT,STATS

For other Survival Analysis procedures, see:

Life Tables and Fitting Survival Distributions

Kaplan Meier Product Limit Method

Explanatory Regression Models for Survival/Failure Times

Regression Models with Time Dependent Covariates


  SCL - Explanatory Regression Models for Survival/Failure Times

SURV_REG

DEPENDENT [=] VarList

INDEPENDENT [=] VarList

METHOD [=] { COX       }

           { EXP       }

           { LOGNORMAL }

           { NORMAL    }

CENSOR [=] Variable

CENSORED [=] Value

COMPLETE [=] Value

[/ ITERATIONS [=] Number ]

[/ CONVERG [=] Number ]

[/ START [=] ( Number ... ) ]

[/{ MEANSUBST }

  { CASEWISE  }]

[STATISTICS [=] {number [, ... , number] }

                    {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Parameter estimates, parameter covariances & correlations

2 - Means & standard deviations

3 - Graphs: survival function for means (for Cox); for all other methods: residuals vs. alpha, residuals vs. theta, residuals vs. log(t)

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Example:

FILE = "C:\STAT\EXAMPLES\HEART.STA"

SURV_REG

  DEPENDENT=1-6

  INDEPENDENT=AGE ANTIGEN MISMATCH

  METHOD=COX

  CENSOR=CENSORED CENSORED=1 COMPLETE=0

Valid Abbreviations:

INDEP,DEP,ITERAT,STATS

For other Survival Analysis procedures, see:

Life Tables and Fitting Survival Distributions

Kaplan Meier Product Limit Method

Comparison of Survivial in Two or More Groups


  SCL - Quality Control

For more information on these and related topics, see Quality Control.  See also Order of SCL Statements.

Shewhart Control Charts

C chart for Poisson Frequencies

Attributes Control Charts for Rates and Proportions

CUSUM Chart for Variables

Moving Average Chart for Variables

Exponentially Weighted Moving Average Chart for Variables

Regression Control Chart

Pareto Chart Analysis


  SCL - Standard Control Charts for Variables

For more information on these and related topics, see Quality Control.  See also Order of SCL Statements.

X_RCHART

X_SCHART

X_VCHART

INPUT [=]

     {RAWDATA

         {SAMPLES [=] Variable (CodesList)}

         {SAMPLESIZE [=] Number}

         MEASURES [=] Variable }

     {AGGREGATED

         MEANS [=] Variable

         VARIABILITY [=] Variable

         {SIZES [=] Variable

         {SAMPLESIZE [=] Number} }

{

[/X_CENTERLINE [=] Number]

[/SIGMA [=] Number]

[/X_UCL [=] Number]

[/X_LCL [=] Number]

[/X_WARNING [=] Number, Number ]

[/X_UNEQUALN [=] {AVERAGE}

                 {SEPARATE}

                 {NORMALIZED} ]

[/{R_UCL} [=] Number]

  {S_UCL}

   {V_UCL}

[/{R_LCL} [=] Number]

  {S_LCL}

  {V_LCL}

[/{R_WARNING} [=] Number, Number ]

  {S_WARNING}

[/{R_UNEQUALN}

  {S_UNEQUALN}

  {V_UNEQUALN} [=] {AVERAGE}

                   {SEPARATE}

                   {NORMALIZED} ]

[/MAVERAGE [=] {NPOINT (Number) }

               {EXP (Number) }

               {NONE} ]

[/RUNSTESTS]

[/PROCESSCAPABILITY ( NOMINAL [=] Number, {DELTA [=] Number}

                    {LOWER [=] Number}

                    {UPPER [=] Number}

                    {LOWER [=] Number  UPPER [=] Number} ) ]

[/HISTOGRAM [=] {ON}

                {OFF} ]

[/BREAKS [=] {OFF}

             {Number} ]

}

{[/OPENSPECS [=] 'FileName' ]}

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - X-bar & Sigma chart; runs tests, if requested; process capability, if requested

2 - X-bar chart

3 - Sigma chart

4 - Descriptive statistics

5 - Operating characteristic curve

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

PROCCAPAB,STATS

For other Quality Control procedures, see:

C chart for Poisson Frequencies

Attributes Control Charts for Rates and Proportions

CUSUM Chart for Variables

Moving Average Chart for Variables

Exponentially Weighted Moving Average Chart for Variables

Regression Control Chart

Pareto Chart Analysis


  SCL - C chart for Poisson Frequencies

For more information on these and related topics, see Quality Control.  See also Order of SCL Statements.

C_CHART

COUNTS [=] Variable

{

[/CENTERLINE [=] Number]

[/UCL [=] Number]

[/LCL [=] Number]

[/WARNING [=] Number, Number ]

[/MAVERAGE [=] {NPOINT (Number) }

               {EXP (Number) }

               {NONE} ]

[/RUNSTESTS]

[/HISTOGRAM [=] {ON}

                {OFF} ]

[/BREAKS [=] {OFF}

             {Number} ]

}

{[/OPENSPECS [=] 'FileName' ]}

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Current chart

2 - Descriptive statistics; runs tests, if requested

3 - Operating characteristic curve

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviation:

STATS

For other Quality Control procedures, see:

Shewhart Control Charts

Attributes Control Charts for Rates and Proportions

CUSUM Chart for Variables

Moving Average Chart for Variables

Exponentially Weighted Moving Average Chart for Variables

Regression Control Chart

Pareto Chart Analysis


  SCL - Attribute Control Charts for Rates and Proportions

For more information on these and related topics, see Quality Control.  See also Order of SCL Statements.

U_CHART

NP_CHART

P_CHART

       COUNTS [=] Variable

       {SIZES [=] Variable}

       {SAMPLESIZE [=] Number}

       {

       [/CENTERLINE [=] Number]

       [/UCL [=] Number]

       [/LCL [=] Number]

       [/WARNING [=] Number, Number ]

       [/MAVERAGE [=] {NPOINT (Number) }

                      {EXP (Number) }

                      {NONE} ]

       [/RUNSTESTS]

       [/HISTOGRAM [=] {ON}

                       {OFF} ]

       [/BREAKS [=] {OFF}

                    {Number} ]

       }

       {[/OPENSPECS [=] 'FileName' ]}

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Current chart

2 - Descriptive statistics; runs tests, if requested

3 - Operating characteristic curve

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviation:

STATS

For other Quality Control procedures, see:

Shewhart Control Charts

C chart for Poisson Frequencies

CUSUM Chart for Variables

Moving Average Chart for Variables

Exponentially Weighted Moving Average Chart for Variables

Regression Control Chart

Pareto Chart Analysis


  SCL - CUSUM Chart for Variables

For more information on these and related topics, see Quality Control.  See also Order of SCL Statements.

CUSUM

INPUT [=]

        {RAWDATA

              {SAMPLES [=] Variable (CodesList)}

              {SAMPLESIZE [=] Number}

              MEASURES [=] Variable

        }

        {AGGREGATED

              MEANS [=] Variable

              VARIABILITY [=] Variable

              {SIZES [=] Variable}

              {SAMPLESIZE [=] Number}

        }

{

[/CENTERLINE [=] Number]

[/SIGMA [=] Number]

[/ALPHA [=] Number]

[/BETA [=] Number]

[/SHIFT[=] Number]

[/VMASK [=] Number]

[/PROCESSCAPABILITY ( NOMINAL [=] Number, {DELTA [=] Number}

                                          {LOWER [=] Number}

                                          {UPPER [=] Number}

                                          {LOWER [=] Number  UPPER [=] Number} ) ]

[/BREAKS [=] {OFF}

             {Number} ]

}

{[/OPENSPECS [=] 'FileName' ]}

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Current chart

2 - Descriptive statistics;process capability indices if requested

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

PROCCAPAB, STATS

For other Quality Control procedures, see:

Shewhart Control Charts

C chart for Poisson Frequencies

Attributes Control Charts for Rates and Proportions

Moving Average Chart for Variables

Exponentially Weighted Moving Average Chart for Variables

Regression Control Chart

Pareto Chart Analysis


  SCL - Moving Average Chart for Variables

For more information on these and related topics, see Quality Control.  See also Order of SCL Statements.

MA_CHART

INPUT [=]

        {RAWDATA

               {SAMPLES [=] Variable (CodesList)}

               {SAMPLESIZE [=] Number}

               MEASURES [=] Variable

        }

        {AGGREGATED

               MEANS [=] Variable

               VARIABILITY [=] Variable

               {SIZES [=] Variable}

               {SAMPLESIZE [=] Number}

        }

{

[/NPOINT [=] Number]

[/CENTERLINE [=] Number]

[/SIGMA [=] Number]

[/UCL [=] Number]

[/LCL [=] Number]

[/WARNING[=] Number, Number]

[/RUNSTESTS]

[/PROCESSCAPABILITY ( NOMINAL [=] Number, {DELTA [=] Number}

                                          {LOWER [=] Number}

                                          {UPPER [=] Number}

                                          {LOWER [=] Number  UPPER [=] Number} ) ]

[/HISTOGRAM [=] {ON}

                {OFF} ]

[/BREAKS [=] {OFF}

             {Number} ]

}

{[/OPENSPECS [=] 'FileName' ]}

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Current chart

2 - Descriptive statistics; process capability indices, if requested; and runs tests, if requested

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

PROCCAPAB, STATS

For other Quality Control procedures, see:

Shewhart Control Charts

C chart for Poisson Frequencies

Attributes Control Charts for Rates and Proportions

CUSUM Chart for Variables

Exponentially Weighted Moving Average Chart for Variables

Regression Control Chart

Pareto Chart Analysis


  SCL - Exponentially Weighted Moving Average Chart for Variables

For more information on these and related topics, see Quality Control.  See also Order of SCL Statements.

EWMA_CHART

INPUT [=]

           {RAWDATA

                {SAMPLES [=] Variable (CodesList)}

                {SAMPLESIZE [=] Number}

                MEASURES [=] Variable

           }

           {AGGREGATED

                MEANS [=] Variable

                VARIABILITY [=] Variable

                {SIZES [=] Variable}

                {SAMPLESIZE [=] Number}

           }

{

[/EXP [=] Number]

[/CENTERLINE [=] Number]

[/SIGMA [=] Number]

[/UCL [=] Number]

[/LCL [=] Number]

[/WARNING[=] Number, Number]

[/RUNSTESTS]

[/PROCESSCAPABILITY ( NOMINAL [=] Number, {DELTA [=] Number}

                                              {LOWER [=] Number}

                                              {UPPER [=] Number}

                                              {LOWER [=] Number  UPPER [=] Number} ) ]

}

[/HISTOGRAM [=] {ON}

                {OFF} ]

[/BREAKS [=] {OFF}

             {Number} ]

{[/OPENSPECS [=] 'FileName' ]}

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Current chart

2 - Descriptive statistics; process capability indices, if requested; and runs tests, if requested

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

PROCCAPAB, STATS

For other Quality Control procedures, see:

Shewhart Control Charts

C chart for Poisson Frequencies

Attributes Control Charts for Rates and Proportions

CUSUM Chart for Variables

Moving Average Chart for Variables

Regression Control Chart

Pareto Chart Analysis


  SCL - Regression Control Chart

For more information on these and related topics, see Quality Control.  See also Order of SCL Statements.

REGRCONTROL

       INDEPENDENT [=] Variable

       DEPENDENT [=] Variable

       [/INTERCEPT [=] Number]

       [/SLOPE [=] Number]

       [/SIGMA [=] Number]

       [/UCL [=] Number]

       [/LCL [=] Number]

       [/WARNING [=] Number, Number ]

       [/CONFID [=] {Number}

                    {NONE} ]

 [STATISTICS [=] {number [, ... , number] }

                 {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Current chart

2 - Descriptive statistics

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

INDEP, DEP, STATS

For other Quality Control procedures, see:

Shewhart Control Charts

C chart for Poisson Frequencies

Attributes Control Charts for Rates and Proportions

CUSUM Chart for Variables

Moving Average Chart for Variables

Exponentially Weighted Moving Average Chart for Variables

Pareto Chart Analysis


  SCL - Pareto Chart Analysis

For more information on these and related topics, see Quality Control.  See also Order of SCL Statements.

PARETO

    {INPUT [=] RAWDATA

     VAR [=] Variable (CodesList) }

    {INPUT [=] AGGREGATED

     VAR [=] Variable }

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Pareto chart

2 - Chart summary

If no STATISTICS are explicitly specified, then the default set of results will be: 1.

Valid Abbreviations:

STATS

For other Quality Control procedures, see:

Shewhart Control Charts

C chart for Poisson Frequencies

Attributes Control Charts for Rates and Proportions

CUSUM Chart for Variables

Moving Average Chart for Variables

Exponentially Weighted Moving Average Chart for Variables

Regression Control Chart


  SCL - Process Analysis

For more information on these and related topics, see Process Analysis.  See also Order of SCL Statements.

Sampling Plans

Process (machine) Capability Analysis and Tolerance Intervals

Fitting all Distributions

Gage Repeatability and Reproducibility


  SCL - Sampling Plans

For more information on these and related topics, see Process Analysis.  See also Order of SCL Statements.

SAMPLING

[/TEST [=] {TWOTAIL}

           {RIGHT}

           {LEFT} ]

[/DISTR [=]	{NORMAL}

           {BINOMIAL}

           {POISSON} ]

[/ALPHA = Number]

[/BETA [=] Number]

[/H0 [=] Number]

[/H1 [=] Number]

[/SIGMA [=] Number]

[/SEQUENTIAL [=] Variable]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

Note that the SIGMA parameter is not applicable if DISTR is set to BINOMIAL or POISSON.

STATISTICS:  Choose from the following selection of statistical results:

1 - Results and operating characteristic curve for fixed sampling plan

2 - Results and plot of sequential sampling plan

If no STATISTICS are explicitly specified, the default set of results will be: 1.

Valid Abbreviation:

STATS

For other Process Analysis procedures, see:

Process (machine) Capability Analysis and Tolerance Intervals

Fitting all Distributions

Gage Repeatability and Reproducibility


  SCL - Process (machine) Capability Analysis and Tolerance Intervals

For more information on these and related topics, see Process Analysis.  See also Order of SCL Statements.

CAPABILITY

VAR [=] Variable [BY Variable]

[/DISTR [=]	{BETA (Number, Number) }

           {EXP (Number) }

           {EXTREME}

           {GAMMA (Number) }

           {LOGNORMAL (Number) }

           {NORMAL}

           {RAYLEIGH (Number) }

           {WEIBULL (Number) } ]

[/NOMINAL [=] Number

       {DELTA [=] Number}

       {LOWER [=] Number}

       {UPPER [=] Number}

       {LOWER [=] Number  UPPER [=] Number} ]

[/PARAM1 [=] Number]

[/PARAM2 [=] Number]

[/LIMITS [=] Number]

[/SCALING [=] ( Number, Number, Number, NEAT [=] {YES} {NO} ) ]

[/NONNORMAL]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

If DISTR is set to NORMAL, PARAM1 and PARAM2 may be substituted with MEAN and SIGMA, respectively.

Note that the PARAM2 parameter is not applicable if DISTR is set to RAYLEIGH or EXP.

Note that the SCALING option applies to the histogram and frequency distribution Scrollsheet.  If the scaling option is not specified, then the default scaling values will be used.

Note that the NONNORMAL command is applicable only if DISTR is set to NORMAL.  If you select the NONNORMAL option, then results for a non-normal distribution will be produced (see Non-Normal Distributions).

STATISTICS:  Choose from the following selection of statistical results:

1 - Descriptive statistics, process capability indices, process capability indices for non-normal distribution (if requested)

2 - Frequency distribution, number beyond specs, expected frequencies for non-normal distribution (if requested)

3 - Histogram (summary of process capability), histogram for non-normal distribution (if requested)

4 - for normal distribution: Q-Q and P-P plot, Q-Q and P-P plot for non-normal distribution (if requested);

 for other distributions: Q-Q and P-P plot, normal probability (Q-Q) plot

If no STATISTICS are explicitly specified, the default set of results will be: 1.

Example:

OUTPUTSETUP

   SCROLLSHEETS = PRINTER AND WINDOW

OUTPUT =  BRIEF

FILE = "C:\STAT\EXAMPLES\PISTONS2.STA"

CAPABILITY

VAR = SAMPLE_1

NOMINAL = 74

DELTA = .05

Valid Abbreviation:

STATS

For other Process Analysis procedures, see:

Sampling Plans

Fitting all Distributions

Gage Repeatability and Reproducibility


  SCL - Fitting All Distributions

For more information on these and related topics, see Process Analysis.  See also Order of SCL Statements.

FITALLDISTR

VAR [=] Variable

BETA [=] Number, Number

EXP [=] Number

GAMMA [=] Number

LOGNORMAL [=] Number

RAYLEIGH [=] Number

WEIBULL [=] Number

Generates the results of fitting all available distributions: Beta, Exponential, Extreme Value, Gamma, Log-Normal, Normal (including general Non-Normal), Rayleigh and Weibull.

The syntax for this task allows the user to specify threshold parameters where applicable (and sigma for the Beta distribution).

For other Process Analysis procedures, see:

Sampling Plans

Process (machine) Capability Analysis and Tolerance Intervals

Gage Repeatability and Reproducibility


  SCL - Gage Repeatability and Reproducibility

For more information on these and related topics, see Process Analysis.  See also Order of SCL Statements.

R_AND_R

INPUT [=]

{STANDARD

       OPERATORS [=] Variable (CodesList)

       PARTS [=] Variable (CodesList)

       MEASURES [=] Variable

       [/TRIALS [=] Variable (CodesList) ]

}

{DATASHEET

       OPERATORS [=] Number

       PARTS [=] Number

       TRIALS [=] Number

       VARS [=] VarList

}

[/TOLERANCE [=] Number [ (INTERVALS [=] Number) ] ]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Descriptive statistics, variance estimates - range method, variance estimates - ANOVA method (if number of trials is greater than 1), percent tolerance - range method (if TOLERANCE specified), percent tolerance - ANOVA method (if TOLERANCE specified, and number of trials is greater than 1)

2 - Complete ANOVA table

3 - Repeatability & reproducibility plot

4 - Combined plot, box & whisker plot

5 - Range charts: by operators, by parts (if number of trials is greater than 1)

6 - Sigma charts: by operators, by parts (if number of trials is greater than 1)

If no STATISTICS are explicitly specified, the default set of results will be: 1.

Valid Abbreviations:

TOLER,INTERV,STATS

For other Process Analysis procedures, see:

Sampling Plans

Process (machine) Capability Analysis and Tolerance Intervals

Fitting all Distributions


  SCL - Design of Experiments

For more information on these and related topics, see Design of Experiments.  See also Order of SCL Statements.

2**(K-p) Designs (Two-level Factorial Design)

Two-level Screening (Plackett-Burman) Designs

3**(k-p) and Box-Behnken Designs

Mixed 2 and 3 Level Designs

Central Composite and Non-Factorial Response Surface Designs

Latin Squares Designs

Taguchi Robust Design Experiments

Mixture Designs

D- and A- (T-) Optimal Designs


  SCL - 2**(K-p) Designs (Two-level Factorial Design)

For more information on these and related topics, see Design of Experiments.  See also Order of SCL Statements.

TWO_KP

    DEPENDENT [=] VarList

    INDEPENDENT [=] VarList

    [/BLOCK [=] Variable]

    [/MODEL [=] {MAINEFFECT}

                {TWOWAY}

                {THREEWAY} ]

    [/MEANS [=] (Factor [, Factor [, Factor] ] ) ...]

    [/SQUARE [=] (Factor , Factor) ... ]

    [/CUBE [=] (Factor , Factor , Factor) ... ]

    [/SURFACE [=] (Factor , Factor) ... ]

    [/CONTOUR [=] (Factor , Factor) ... ]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

In the MEANS option, one of the factors may be substituted by the keyword BLOCK, if a BLOCK variable was specified (i.e., if the design is blocked).

If only two independent variables (factors) are specified, no factor specification is required for SURFACE and CONTOUR plots (the factors will be selected automatically).

STATISTICS:  Choose from the following selection of statistical results:

1 - Display design, main effects and interactions

2 - Regression coefficients

3 - Main effects and regression coefficients, effects sorted by size

4 - Complete ANOVA table

5 - Normal probability plot of effects

6 - Pareto chart of effects

7 - Graph of predicted vs. observed values

8 - Histogram and normal probability plot of residuals

9 - Correlation matrix, correlation matrix of effects

If no STATISTICS are explicitly specified, the default set of results will be: 1and 4.

Valid Abbreviations:

DEP,INDEP,STATS

For other Process Analysis procedures, see:

Two-level Screening (Plackett-Burman) Designs

3**(k-p) and Box-Behnken Designs

Mixed 2 and 3 Level Designs

Central Composite and Non-Factorial Response Surface Designs

Latin Squares Designs

Taguchi Robust Design Experiments

Mixture Designs

D- and A- (T-) Optimal Designs


  SCL - Two-level Screening (Plackett-Burman) Designs

For more information on these and related topics, see Design of Experiments.  See also Order of SCL Statements.

SCREENING

    DEPENDENT [=] VarList

    INDEPENDENT [=] VarList

    [/BLOCK [=] Variable]

    [/MODEL [=] {MAINEFFECT}

                {TWOWAY} ]

    [/MEANS [=] (Factor [, Factor [, Factor] ] ) ...]

    [/SQUARE [=] (Factor , Factor) ... ]

    [/CUBE [=] (Factor , Factor , Factor) ... ]

    [/SURFACE [=] (Factor , Factor) ... ]

    [/CONTOUR [=] (Factor , Factor) ... ]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

In the MEANS option, one of the factors may be substituted by the keyword BLOCK, if a BLOCK variable was specified (i.e., if the design is blocked).

If only two independent variables (factors) are specified, no factor specification is required for SURFACE and CONTOUR plots (the factors will be selected automatically).

STATISTICS:  Choose from the following selection of statistical results:

1 - Display design, main effects and interactions

2 - Regression coefficients

3 - Main effects and regression coefficients, effects sorted by size

4 - Complete ANOVA table

5 - Normal probability plot of effects

6 - Pareto chart of effects

7 - Graph of predicted vs. observed values

8 - Histogram and normal probability plot of residuals

9 - Correlation matrix, correlation matrix of effects

If no STATISTICS are explicitly specified, the default set of results will be: 1and 4.

Valid Abbreviations:

DEP,INDEP,STATS

For other Process Analysis procedures, see:

2**(K-p) Designs (Two-level Factorial Design)

3**(k-p) and Box-Behnken Designs

Mixed 2 and 3 Level Designs

Central Composite and Non-Factorial Response Surface Designs

Latin Squares Designs

Taguchi Robust Design Experiments

Mixture Designs

D- and A- (T-) Optimal Designs


  SCL - 3**(k-p) and Box-Behnken Designs

For more information on these and related topics, see Design of Experiments.  See also Order of SCL Statements.

THREE_LEVEL

    DEPENDENT [=] VarList

    INDEPENDENT [=] VarList

    [/BLOCK [=] Variable]

    [/MODEL [=] {MAINEFFECT}

                {TWOWAYLINEAR}

                {TWOWAYQUADRATIC} ]

    [/CENTEREDPOLYNOMIAL [=] {YES}

                             {NO} ]

    [/MEANS [=] (Factor [, Factor [, Factor] ] ) ...]

    [/SURFACE [=] (Factor , Factor) ... ]

    [/CONTOUR [=] (Factor , Factor) ... ]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

In the MEANS option, one of the factors may be substituted by the keyword BLOCK, if a BLOCK variable was specified (i.e., if the design is blocked).

If only two independent variables (factors) are specified, no factor specification is required for SURFACE and CONTOUR plots (the factors will be selected automatically).

STATISTICS:  Choose from the following selection of statistical results:

1 - Display design, main effects and interactions

2 - Regression coefficients

3 - Main effects and regression coefficients, effects sorted by size

4 - Complete ANOVA table

5 - Normal probability plot of effects

6 - Pareto chart of effects

7 - Graph of predicted vs. observed values

8 - Histogram and normal probability plot of residuals

9 - Correlation matrix, correlation matrix of effects

If no STATISTICS are explicitly specified, the default set of results will be: 1and 4.

Valid Abbreviations:

CENTPOLY,DEP,INDEP,STATS

For other Process Analysis procedures, see:

2**(K-p) Designs (Two-level Factorial Design)

Two-level Screening (Plackett-Burman) Designs

Mixed 2 and 3 Level Designs

Central Composite and Non-Factorial Response Surface Designs

Latin Squares Designs

Taguchi Robust Design Experiments

Mixture Designs

D- and A- (T-) Optimal Designs


  SCL - Mixed 2 and 3 Level Designs

For more information on these and related topics, see Design of Experiments.  See also Order of SCL Statements.

MIXED2AND3

    DEPENDENT [=] VarList

    INDEPENDENT [=] VarList

    [/BLOCK [=] Variable]

    [/MODEL [=] {MAINEFFECT}

                {TWOWAYLINEAR}

                {TWOWAYQUADRATIC} ]

    [/CENTEREDPOLYNOMIAL [=] {YES}

                             {NO} ]

    [/MEANS [=] (Factor [, Factor [, Factor] ] ) ...]

    [/SURFACE [=] (Factor , Factor) ... ]

    [/CONTOUR [=] (Factor , Factor) ... ]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

In the MEANS option, one of the factors may be substituted by the keyword BLOCK, if a BLOCK variable was specified (i.e., if the design is blocked).

If only two independent variables (factors) are specified, no factor specification is required for SURFACE and CONTOUR plots (the factors will be selected automatically).

STATISTICS:  Choose from the following selection of statistical results:

1 - Display design, main effects and interactions

2 - Regression coefficients

3 - Main effects and regression coefficients, effects sorted by size

4 - Complete ANOVA table

5 - Normal probability plot of effects

6 - Pareto chart of effects

7 - Graph of predicted vs. observed values

8 - Histogram and normal probability plot of residuals

9 - Correlation matrix, correlation matrix of effects

If no STATISTICS are explicitly specified, the default set of results will be: 1and 4.

Valid Abbreviations:

CENTPOLY,DEP,INDEP,STATS

For other Process Analysis procedures, see:

2**(K-p) Designs (Two-level Factorial Design)

Two-level Screening (Plackett-Burman) Designs

3**(k-p) and Box-Behnken Designs

Central Composite and Non-Factorial Response Surface Designs

Latin Squares Designs

Taguchi Robust Design Experiments

Mixture Designs

D- and A- (T-) Optimal Designs


  SCL - Central Composite and Non-Factorial Response Surface Designs

For more information on these and related topics, see Design of Experiments.  See also Order of SCL Statements.

CENTRALCOMPOSITE

    DEPENDENT [=] VarList

    INDEPENDENT [=] VarList

    [/BLOCK [=] Variable]

    [/MODEL [=] {MAINLINEAR}

                {MAINQUADRATIC}

                {TWOWAYLINEAR}

                {TWOWAYQUADRATIC} ]

    [/SURFACE [=] (Factor , Factor) ... ]

    [/CONTOUR [=] (Factor , Factor) ... ]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

If only two independent variables (factors) are specified, no factor specification is required for SURFACE and CONTOUR plots (the factors will be selected automatically).

STATISTICS:  Choose from the following selection of statistical results:

1 - Display design, main effects and interactions

2 - Regression coefficients

3 - Main effects and regression coefficients, effects sorted by size

4 - Complete ANOVA table

5 - Normal probability plot of effects

6 - Pareto chart of effects

7 - Graph of predicted vs. observed values

8 - Histogram and normal probability plot of residuals

9 - Correlation matrix, correlation matrix of effects

If no STATISTICS are explicitly specified, the default set of results will be: 1and 4.

Valid Abbreviations:

CENTCOMP,DEP,INDEP,STATS

For other Process Analysis procedures, see:

2**(K-p) Designs (Two-level Factorial Design)

Two-level Screening (Plackett-Burman) Designs

3**(k-p) and Box-Behnken Designs

Mixed 2 and 3 Level Designs

Latin Squares Designs

Taguchi Robust Design Experiments

Mixture Designs

D- and A- (T-) Optimal Designs


  SCL - Latin Squares Designs

For more information on these and related topics, see Design of Experiments.  See also Order of SCL Statements.

LATINSQUARES

    DEPENDENT [=] Variable

    INDEPENDENT [=] VarList

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Display design

2 - Display Latin square arrangement

3 - Marginal means

4 - Analysis of variance

5 - Plot of means

If no STATISTICS are explicitly specified, the default set of results will be: 1and 4.

Valid Abbreviations:

LATINSQ,DEP,INDEP,STATS

For other Process Analysis procedures, see:

2**(K-p) Designs (Two-level Factorial Design)

Two-level Screening (Plackett-Burman) Designs

3**(k-p) and Box-Behnken Designs

Mixed 2 and 3 Level Designs

Central Composite and Non-Factorial Response Surface Designs

Latin Squares Designs

Taguchi Robust Design Experiments

Mixture Designs

D- and A- (T-) Optimal Designs


  SCL - Taguchi Robust Design Experiments

For more information on these and related topics, see Design of Experiments.  See also Order of SCL Statements.

TAGUCHI

    DEPENDENT [=] VarList

    INDEPENDENT [=] VarList

    [/PROBLEMTYPE [=] {MAXIMIZE}

                      {SMALLER}

                      {NOMINAL}

                      {LARGER}

                      {SIGNED}

                      {FRACTION}

                      {ACCUMULATION} ]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

STATISTICS:  Choose from the following selection of statistical results:

1 - Display design and S/N ratios

2 - Alias structure

3 - Descriptive statistics for untransformed variables

4 - Marginal means

5 - Eta under optimum conditions

For ACCUMULATION analysis:

6 - Bar plot of cumulative proportions

7 - Line graph by factors

For all other problem types:

6 - Analysis of variance

7 - Plot of means

If no STATISTICS are explicitly specified, the default set of results will be: 1,4 and 6.

Valid Abbreviations:

DEP,INDEP,PROBLEM,ACCUM,STATS

For other Process Analysis procedures, see:

2**(K-p) Designs (Two-level Factorial Design)

Two-level Screening (Plackett-Burman) Designs

3**(k-p) and Box-Behnken Designs

Mixed 2 and 3 Level Designs

Central Composite and Non-Factorial Response Surface Designs

Latin Squares Designs

Mixture Designs

D- and A- (T-) Optimal Designs


  SCL - Mixture Designs

For more information on these and related topics, see Design of Experiments.  See also Order of SCL Statements.

MIXTURES

    DEPENDENT [=] VarList

    INDEPENDENT [=] VarList

    [/TOLERANCE [=] Number]

    [/MODEL [=] {LINEAR}

                {QUADRATIC}

                {SPECIALCUBIC}

                {FULLCUBIC} ]

    [/SURFACE [=] (Factor , Factor , Factor) ... ]

    [/CONTOUR [=] (Factor , Factor , Factor) ... ]

    [/TRACE [=] (list of numbers separated with commas) ... ]

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

If only three independent variables (factors) are specified, no factor specification is required for SURFACE and CONTOUR plots (the factors will be selected automatically).

For each TRACE plot, you need to specify as many numbers (reference blend values) as there are independent variables (factors) in the analysis.

STATISTICS:  Choose from the following selection of statistical results:

1 - Display design, factor highs and lows

2 - Parameter stimates for pseudo components and original components

3 - Parameter stimates for pseudo components and original components, effects sorted by size

4 - Complete ANOVA table

5 - Normal probability plot of parameter estimates

6 - Pareto chart of parameter estimates

7 - Graph of predicted vs. observed values

8 - Histogram and normal probability plot of residuals

9 - Correlation matrix, correlation matrix of coefficients

If no STATISTICS are explicitly specified, the default set of results will be: 1 and 4.

Valid Abbreviations:

DEP,INDEP,TOLER,STATS

For other Process Analysis procedures, see:

2**(K-p) Designs (Two-level Factorial Design)

Two-level Screening (Plackett-Burman) Designs

3**(k-p) and Box-Behnken Designs

Mixed 2 and 3 Level Designs

Central Composite and Non-Factorial Response Surface Designs

Latin Squares Designs

Taguchi Robust Design Experiments

D- and A- (T-) Optimal Designs


  SCL - D- and A- (T-) Optimal Designs

For more information on these and related topics, see Design of Experiments.  See also Order of SCL Statements.

OPTIMALDESIGN

    VARS [=] VarList

    MODEL [=] {RESPONSE ( {MAINLINEAR}

                          {MAINQUADRATIC}

                          {TWOWAYLINEAR}

                          {TWOWAYQUADRATIC} ) }

              {MIXTURE  ( {LINEAR}

                          {QUADRATIC}

                          {SPECIALCUBIC}

                          {FULLCUBIC} ) }

    [/NPOINT [=] Number ]

    [/CRITERION [=] { D } { A } ]

    [/ITERATIONS [=] Number ]

    [/RECODE [=] {YES}  {NO} ]

    [/INITIAL [=] {FIRSTN}

                  {SEQUENTIAL}

                  {RANDOM (Number) } ]

    [/ALPHA [=] Number ]

    [/DA_TOLER [=] Number ]

    [/MIX_TOLER [=] Number ]

    [/METHOD [=] {DYKSTRA}

                 {EXCHANGE}

                 {DETMAX (Number) }

                 {MODIFIEDFEDOROV}

                 {FEDOROV} ]

    [/SCATTER2D [=] (Factor, Factor) ... ]              {for RESPONSE models only}

    [/SCATTER3D [=] (Factor, Factor, Factor) ... ]      {for RESPONSE models only}

    [/TRIANGULAR [=] (Factor, Factor, Factor) ... ]     {for MIXTURE models only}

[STATISTICS [=] {number [, ... , number] }

                {ALL} ]

Note that 2- and 3-D scatterplots are available only for RESPONSE surface models, while triangular scatterplots are available only for MIXTURE models.

If only two independent variables (factors) are specified, no factor specification is required for SCATTER2D plots (the factors will be selected automatically); respectively, if three independent variables (factors) are specified, no factor specification is required for SCATTER3D or TRIANGULAR plots.

STATISTICS:  Choose from the following selection of statistical results:

1 - Display design

2 - Summary of efficiency measures

3 - Correlation matrix for columns of design matrix

4 - Inverse of correlation matrix

If no STATISTICS are explicitly specified, the default set of results will be: 1.

Valid Abbreviations:

CRIT,ITERAT,MODFED,TRIANG,STATS

For other Process Analysis procedures, see:

2**(K-p) Designs (Two-level Factorial Design)

Two-level Screening (Plackett-Burman) Designs

3**(k-p) and Box-Behnken Designs

Mixed 2 and 3 Level Designs

Central Composite and Non-Factorial Response Surface Designs

Latin Squares Designs

Taguchi Robust Design Experiments

Mixture Designs


  SCL - SEPATH (Structural Equation Modeling)

For more information on these and related topics, see Structural Equation Modeling.  See also Order of SCL Statements.

   SEPATH

   MODEL [=] "model_file_name"

   [/{COVARIANCES}

     {CORRELATIONS}

     {MOMENTS} ]

   [/MANIFESTEXOGENOUS [=] {FREE}

                           {FIXED}

                           {USER} ]

   [/ITERATIONS [=] number]

   [/STEP [=] number]

   [/DESCENT [=] number]

   [/TOLERANCE [=] number]

   [/INITIAL [=] {DEFAULT}

                 {AUTOMATIC} ]

   [STATISTICS [=] {number [, ... , number] }

                   {ALL}

STATISTICS:  Choose from the following selection of statistical results:

1 - Model summary

2 - Noncentrality-based fit indices

3 - Other single sample fit indices

4 - LaGrange multiplier statistics

5 - Basic summary statistics

6 - Residuals: Standardized and normalized

7 - Normal probability plot

8 - Matrix: Input and reproduced

9 - Univariate skewness

10 - Kurtosis: Uni- and Multivariate

11 - Reflector matrix

12 - Iteration history

If no STATISTICS are explicitly specified, then the default set of results will be: 1, 2, 3.

Example 1

Example 2

Valid Abbreviations:

COVAR, CORR, MANIFEXO, ITERAT, STATS


SCL - SEPATH (Structural Equation Modeling) - Example 1

  SCL SEPATH (Structural Equation Modeling) - Example 1

In this example, we will fit the model specified in the file LAWLEY.CMD to the data (correlation matrix) in LAWLEY.STA.  The default results will be generated and saved in the report file LAWLEY.RTF.

FILE = "F:\STAT\EXAMPLES\LAWLEY.STA"

OUTPUTSETUP

  OUTPUT LONG

  SCROLLSHEETS WINDOW

  REPORTFILE = "F:\STAT\EXAMPLES\LAWLEY.RTF"    {The printed report file is saved.}

SAVESCROLLSH = "F:\STAT\EXAMPLES\LAWLEY.SCR"

SEPATH

MODEL "F:\STAT\EXAMPLES\LAWLEY.CMD"

   / CORRELATION


SCL - SEPATH (Structural Equation Modeling) - Example 2

  SCL SEPATH (Structural Equation Modeling) - Example 2

In this more complex example, we will analyze two different models (WHEATONA.CMD and WHEATONB.CMD) on the same data file (WHEATON.STA).  This capability can be very useful when the model is a large one, and takes a considerable amount of time to execute.

The option /STATISTICS=1,2,3,5,6 selects:

1 - Model Summary

2 - Noncentrality-Based Indices

3 - Other Single Sample Indices

5 - Basic Summary Statistics

6 - Residuals: Standardized & Normalized

FILE = "F:\STAT\EXAMPLES\WHEATON.STA"

SAVESCROLLSH = "F:\STAT\EXAMPLES\WHEATA.SCR"

OUTPUTSETUP

  OUTPUT LONG

  SCROLLSHEETS WINDOW

  REPORTFILE = "F:\STAT\EXAMPLES\WHEATONA.RTF"    {The printed report file is saved.}

SEPATH

MODEL "F:\STAT\EXAMPLES\WHEATONA.CMD"

  /STATISTICS = 1,2,3,5,6

SENDKEYS  "{Esc}%F4"              {These Keystrokes quit SEPATH, so it can be restarted for the second analysis}

SAVESCROLLSH = "F:\STAT\EXAMPLES\WHEATB.SCR"

OUTPUTSETUP

  OUTPUT LONG

  SCROLLSHEETS WINDOW

  REPORTFILE = "F:\STAT\EXAMPLES\WHEATONB.RTF"

SEPATH

MODEL "F:\STAT\EXAMPLES\WHEATONB.CMD"

  /STATISTICS=1,2,3,5,6

SENDKEYS  "{Esc}%F4"


  SCL - GRAPHICS

Every Stats Graph available in STATISTICA, can be built from specific graph keywords and general options applicable to all graphs (described below).  For example, the following keywords will produce a standard Scatterplot of variable 1 by variable 2 (for the first 25 cases) with a logarithmic fit to the data and the job header "My job header" as the graph title:

SCATTERPLOT

X = 1

Y = 2

/Fitting = log

/Cases 1, 25

/Jobheader = "My job header"

STOP

Output.  If you want to view the graph use the keyword STOP at the end (STOP will return control to the user and allow you to view the graph).  If you want to print specified graphs, use OUTPUTSETUP GRAPHS = PRINTER; to save graphs, use the SAVEGRAPH = "filename" option.

Other general options.  See Options available in all graphs, Examples with SENDKEYS, and SENDKEYS syntax.

Order of keywords.  The order of the keywords and options is significant and must be the same as described in each graph topic (see also Order of SCL Statements).

For more information on each of these graphs, see the respective topic.

Available graphs:

2D Graphs

  Stats 2D Graphs - Histograms

  Stats 2D Graphs - Scatterplots

  Scatterplots w/Histograms

  Scatterplots w/Box Plots

  Stats 2D Graphs - Probability Plots

  Stats 2D Graphs - Range Plots

  Stats 2D Graphs - Box Plots

  Stats 2D Graphs - Line Plots (Variables)

  Stats 2D Graphs - Line Plots (Case Profiles)

  Stats 2D Graphs - Sequential/Stacked Plots

  Stats 2D Graphs - Mixed Sequential/Stacked Plots

  Stats 2D Graphs - Quantile-Quantile Plots

  Stats 2D Graphs - Probability-Probability Plots

  Stats 2D Graphs - Missing/Range Data Points

  Stats 2D Graphs - Pie Charts

  Stats 2D Graphs - Custom Function Plots

3D Sequential Graphs

  Stats 3D Sequential Graphs - Raw Data Plots

  Stats 3D Sequential Graphs - Bivariate Histograms

  Stats 3D Sequential Graphs - Range Plots

  Stats 3D Sequential Graphs - Box Plots

3D XYZ Graphs

  Stats 3D XYZ Graphs - Scatterplots

  Stats 3D XYZ Graphs - Surface Plots

  Stats 3D XYZ Graphs - Contour Plots

  Stats 3D XYZ Graphs - Trace Plots

  Stats 3D XYZ Graphs - Ternary Plots

  Stats 3D XYZ Graphs - Custom Function Plots

Matrix and Icon Plots

  Stats Graphs - Matrix Plots

  Stats Graphs - Icon Plots

Categorized Graphs

  Stats Categorized Graphs - Histograms

  Stats Categorized Graphs - Scatterplots

  Stats Categorized Graphs - Probability Plots

  Stats Categorized Graphs - Line Plots

  Stats Categorized Graphs - Box Plots

  Stats Categorized Graphs - Quantile-Quantile Plots

  Stats Categorized Graphs - Probability-Probability Plots

  Stats Categorized Graphs - Missing/Range Data Plots

  Stats Categorized Graphs - Pie Charts

  Stats Categorized Graphs - 3D Scatterplot

  Stats Categorized Graphs - 3D Contour Plots

  Stats Categorized Graphs - 3D Surface Plots

  Stats Categorized Graphs - Ternary Plots


Options Common to all Graphs

  Options Common to all Graphs:

The following options are available in all STATISTICA Command Language graphs.

   [/ CASES [=] { ALL                   } ]   {Specifies the range of cases to be plotted}

                { NumberFrom , NumberTo }

   [/ OPTIMIZE [=] { OFF    } ]      {Selects specified number of cases at random}

                   { Number }

   [/ LABELS [=] { OFF          } ]   {Specifies data point labels}

                 { CASES        }

                 { VAR Variable }

   [/ TEXTVALUES [=] { ON  } ]   {Displays text labels for scale values}

                     { OFF }

   [/ FITTEDFUNCTIONS [=] { OFF        } ]   {Displays fitted function in title (REGULAR) or movable legend (CUSTOMTEXT)}

                          { REGULAR    }

                          { CUSTOMTEXT }

   [/ MSUBSETLEGENDS [=] { OFF } ]   {Displays multiple subset legends as movable (ON) or fixed (OFF)}

                         { ON  }

   [/ JOBHEADER [=] "Text" ]   {Displays specified text as first title in graph}

   [/ GRAPHHEADER [=] "Text" ]   {Displays specified text as second title in graph}

   [/ CATEGDECIMALS [=] Number ]   {Displays specified number of decimal places in category labels}

   [/ ORIENTATION [=] { STANDARD } ]   {Specifies orientation of variables in 2D graph}

                      { REVERSED }

   [ /COORDINATES [=] {NORMAL } ]   {Specifies the type of graph coordinates}

                      {POLAR  }

                      {LAYERED}

   [/ POLYNOMIAL [=] Number }   {Specifies the order of polynomial fit (2nd, 3rd, 4th, or 5th order)}

Output.  If you want to view the graph use the keyword STOP at the end (STOP will return control to the user and allow you to view the graph).  If you want to print specified graphs, use OUTPUTSETUP GRAPHS = PRINTER; to save graphs, use the SAVEGRAPH = "filename" option.

Settings in the General Layout Dialog.  See Examples with SENDKEYS.

Saving Graphs.  See Examples with SENDKEYS.

See also Order of SCL Statements.

For other options, see SENDKEYS.


  SCL - Stats 2D Graphs - Line Plots (Case Profiles)

For more information on this type of graph, see 2D Line Plots (Case Profiles).  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

   CASEPROFILEPLOT

   [ {REGULAR}

     {MULTIPLE} ]

   VARS [=] VarList

   [/IGNOREMD [=] {YES}

                  {NO} ]

   [/FITTING [=] {OFF}

                 {LINEAR}

                 {LOG}

                 {EXP}

                 {SPLINE}

                 {POLYNOMIAL}

                 {LSQUARES}

                 {NEGEXP}

                 {"Function"} ]

   [/LIMITS [=] {OFF}

                {LINE}

                {BOX}

       /Y1 [=] number  Y2 [=] number  X1 [=] number  X2 [=] number ]

Example:

The following example will create a multiple Line Plot of Case Profiles with a polynomial fit for the specified variables.

   FILE = "D:\DATA\SAMPLE.STA"

   OUTPUTSETUP

   GRAPHS = WINDOW

   CASEPROFILEPLOT

     MULTIPLE

   VARS = 1-20

   /FITTING = POLYNOMIAL

   STOP

Valid Abbreviations:

REG, MULT, FIT, POL, LSQ, NEG


  SCL - Stats 2D Graphs - Quantile-Quantile Plots

For more information on this type of graph, see 2D Quantile-Quantile Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

   QQPLOT

   VARS [=] VarList

   {BETA

         {SHAPE1 [=] number  SHAPE2 [=] number}

         {THRESHOLD [=] number  SCALE [=] number

                    [/{MAXLIKELIHOOD}

                      {MATCHMOMENTS}]           } }

   {EXPONENTIAL}

   {EXTREME}

   {GAMMA

          {SHAPE [=] number}

          {THRESHOLD [=] number

                     [/{MAXLIKELIHOOD}

                       {MATCHMOMENTS}]  } }

   {LOGNORMAL

             {SHAPE [=] number}

             {THRESHOLD [=] number} }

   {NORMAL}

   {RAYLEIGH}

   {WEIBULL

            {SHAPE [=] number}

            {THRESHOLD [=] number

                       [/{MAXLIKELIHOOD}

                         {MATCHMOMENTS}] } }

   [/LINEARFIT [=] {YES}

                   {NO} ]

   [/CUSTOMFIT [=] {NO}

                   {YES

                     [/SCALE [=] number]

                     [/THRESHOLD [=] number] } ]

   [/RANKADJ [=] number]

   [/NADJ [=] number]

   [/PROBABSCALE [=] {OFF}

                     {ON}

                     { (list_of_numbers_separated_with_commas) } ]

Example:

The following example will create a Quantile-Quantile Plot for variables 1 and 2 for the Extreme distribution and add a linear fitting line to the graph.

   FILE = "D:\DATA\SAMPLE.STA"

   OUTPUTSETUP

   GRAPHS = WINDOW

   QQPLOT

     VARS = 1 2

     EXTREME

   /LINEARFIT = YES

   STOP


  SCL - Stats 2D Graphs - Probability-Probability Plots

For more information on this type of graph, see 2D Probability-Probability Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

   PPPLOT

   VARS [=] VarList

   {BETA

        {SHAPE1 [=] number  SHAPE2 [=] number  THRESHOLD [=] number  SCALE [=] number }

        {THRESHOLD [=] number  SCALE [=] number

                   [/{MAXLIKELIHOOD}

                     {MATCHMOMENTS} ] } }

   {EXPONENTIAL

                {SCALE [=] number  THRESHOLD [=] number }

                {THRESHOLD [=] number } }

   {EXTREME

            [THRESHOLD [=] number  SCALE [=] number]  }

   {GAMMA

          {SHAPE [=] number  SCALE [=] number  THRESHOLD [=] number }

          {THRESHOLD [=] number

                     [/{MAXLIKELIHOOD}

                       {MATCHMOMENTS}] } }

   {LOGNORMAL

             {SHAPE [=] number  SCALE [=] number  THRESHOLD [=] number }

             {THRESHOLD [=] number } }

   {NORMAL

          [MU [=] number  SIGMA [=] number] }

   {RAYLEIGH

             {SCALE [=] number  THRESHOLD [=] number }

             {THRESHOLD [=] number } }

   {WEIBULL

           {SHAPE [=] number  SCALE [=] number  THRESHOLD [=] number }

           {THRESHOLD [=] number

                      [/{MAXLIKELIHOOD}

                        {MATCHMOMENTS}] }

Example:

The following example will create a Probability-Probability Plot for variable 14 for the Normal distribution (with a mean of 15 and standard deviation of 2.5).

   FILE = "D:\DATA\SAMPLE.STA"

   OUTPUTSETUP

   GRAPHS = WINDOW

   PPPLOT

     VARS = 14

   NORMAL

          MU = 15

          SIGMA = 2.5

   STOP


  SCL - Stats 2D Graphs - Missing/Range Data Plots

For more information on this type of graph, see 2D Missing/Range Data Points Plot.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

   MDRANGEPLOT

   VARS [=] VarList

   [/MISSINGDATA [=] {YES}

                     {NO} ]

   [/OUTOFRANGEPOINTS

        (MIN [=] number [,] MAX [=] number [,] VARS = VarList) ... ]

Note:  You may specify up to 8 out-of-range criteria.

Example:

The following example will create a Missing/Range Data Points Plot for variables 1-4.  The 'out of range' points are defined by specifying the valid range (min and max values) for each variable.  Values which fall outside of this defined range will be plotted in the graph.  Missing data values will also be displayed in the graph.

   FILE = "D:\DATA\SAMPLE.STA"

   OUTPUTSETUP

   GRAPHS = WINDOW

   MDRANGEPLOT

   VARS = 1-4

     /MISSINGDATA = YES

     /OUTOFRANGEPOINTS

        (MIN = 5  MAX = 25  VARS = 1)

        (MIN = 0  MAX = 4  VARS = 2)

        (MIN = -9  MAX = 9  VARS = 3)

        (MIN = 15  MAX = 20  VARS = 4)

   STOP


  SCL - Stats 2D Graphs - Histograms

For more information on this type of graph, see 2D Histograms.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

HISTOGRAM

[ { REGULAR    } ]

{ MULTIPLE   }

{ DOUBLE     }

{ HANGING    }

VAR [=] VarList [ BY VarList ]

[/CAT [=] { INTEGER                } ]

{ Number INTERVALS       }

{ "Boundaries"           }

{ CODES [=] (CodesList)  }

{ MSUBSET [=] "FileName" }

[/ CUMULATIVE [=] { YES } ]

{ NO  }

[/ BREAKS [=] { YES } ]

{ NO  }

[/ FITTING [=] { NORMAL    }

               { OFF       }

               { BETA      }

               { EXP       }

               { EXTREME   }

               { GAMMA     }

               { GEOMETRIC }

               { LAPLACE   }

               { LOGISTIC  }

               { LOGNORMAL }

               { POISSON   }

               { RAYLEIGH  }

               { SPLINE    }

               { WEIBULL   }]

Example:

The following example will create a 2D Histogram for variable 5.  The values of variable 5 will be divided into 6 intervals (categories) and the Laplace distribution will be fit to the histogram.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

HISTOGRAM

VAR = 5

/CAT = 6 INTERVALS

/FITTING = LAPLACE

STOP

Valid Abbreviations:

HIST, INTERV, REG, CUM, FIT, MULT


SCL - Stats 2D Graphs - Scatterplots w/Histogram

  SCL - Stats 2D Graphs - Scatterplots w/Histograms

For more information on this type of graph, see 2D Scatterplots w/Histograms.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

   SCATTERHISTOGRAM

   X [=] variable_x

   [/ [=] {INTEGER}

          {Number INTERVALS}

          {"Boundaries"}

          {CODES [=] (CodesList)}

   Y [=] variable_y

   [/ [=] {INTEGER}

          {Number INTERVALS}

          {"Boundaries"}

          {CODES [=] (CodesList)}

   [/SCATTERFIT [=] {OFF}

                    {LINEAR}

                    {LOG}

                    {EXP}

                    {SPLINE}

                    {POLYNOMIAL}

                    {LSQUARES}

                    {NEGEXP}

                    {"Function"} ]

   [/HISTOFIT [=] {OFF}

                  {NORMAL}

                  { BETA      }

                  { EXP       }

                  { EXTREME   }

                  { GAMMA     }

                  { GEOMETRIC }

                  { LAPLACE   }

                  { LOGISTIC  }

                  { LOGNORMAL }

                  { POISSON   }

                  { RAYLEIGH  }

                  { SPLINE    }

                  { WEIBULL   }]

   [/BREAKS [=] {YES}

                {NO} ]

   [/SIZEX [=] number ]

   [/SIZEY [=] number ]

Example:

The following example will create a Scatterplot with Histograms for variable 1 (on the X-axis) and variable 2 (on the Y-axis).  This compound graph contains a regular scatterplot of the specified two (X and Y) variables and frequency distribution histograms for the X and Y variables displayed along the X- and Y-axis of the scatterplot, respectively.

   FILE = "D:\DATA\SAMPLE.STA"

   OUTPUTSETUP

   GRAPHS = WINDOW

   SCATTERHISTOGRAM

   X = 1

   /INTEGER

   Y = 2

   /INTEGER

   /SCATTERFIT = LINEAR

   STOP

Valid Abbreviations:

INTERV, POL, LSQ, NEG


SCL - Stats 2D Graphs - Scatterplots w/Box Plot

  SCL - Stats 2D Graphs - Scatterplots w/Box Plots

For more information on this type of graph, see 2D Scatterplots w/Box Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

   SCATTERBOXPLOT

   X [=] variable_x

   Y [=] variable_y

   [/SCATTERFIT [=] {OFF}

                    {LINEAR}

                    {LOG}

                    {EXP}

                    {SPLINE}

                    {POLYNOMIAL}

                    {LSQUARES}

                    {NEGEXP}

                    {"Function"} ]

   [/{BOXWHISKERS}

     {WHISKERS}

     {BOXES}

     {COLUMNS} ]

   [/ MODE = { 1 } ] {see description below}

             { 2 }

             { 3 }

             { 4 }

   [/OUTLIERS [=] {OFF}

                  {OUTLIERS}

                  {EXTREMES}

                  {ALL}

      LEVEL [=] number      ]

   [/SIZEX [=] number ]

   [/SIZEY [=] number ]

The combination of options available when you select a Mode category (see above) is described below:

Mode:  Middle Point:       Box:            Whisker:

-----  -------------  ---------------  -----------------

  1       Median      25/75 percent    Non-Outlier Range

  2       Median      25/75 percent    Min/Max

  3       Mean        Mean-SE,Mean+SE  Mean-SD,Mean+SD

  4       Mean        Mean-SE,Mean+SE  Min/Max

Example:

The following example will create a Scatterplot w/Box Plot for variable 1 (on the X-axis) and variable 2 (on the Y-axis).  This compound graph contains a regular scatterplot of the specified two (X and Y) variables and box plots for the X and Y variables displayed along the X- and Y-axis of the Scatterplot, respectively.

   FILE = "D:\DATA\SAMPLE.STA"

   OUTPUTSETUP

   GRAPHS = WINDOW

   SCATTERBOXPLOT

   X = 1

   Y = 2

   /SCATTERFIT = LINEAR

   /BOXWHISKERS

   /MODE = 1

   /OUTLIERS = OFF

   STOP

Valid Abbreviations:

POL, LSQ, NEG


  SCL - Stats 2D Graphs - Scatterplots

For more information on this type of graph, see 2D Scatterplots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

SCATTERPLOT

[ { REGULAR                 } ]

{ MULTIPLE                }

{ DOUBLE                  }

{ FREQ [ = NumberOfFreq ] }

{ VORONOI                 }

X [=] VarList

Y [=] VarList [ BY VarList ]

    [/ FITTING [=] { OFF                              } ]

                   { LINEAR     [ CONFID [=] Number ] }

                   { LOG                              }

                   { EXP                              }

                   { SPLINE                           }

                   { POLYNOMIAL [ CONFID [=] Number ] }

                   { LSQUARES                         }

                   { NEGEXP                           }

                   { "Function"                       }

Example:

The following example will create a multiple 2D Scatterplot for variable 1 on the X-axis and variables 7 and 8 on the Y-axis.  A linear fitting line and 90 % confidence interval will be included in the graph.

FILE = "D:\DATA\SAMPLE.STA"

SCATTERPLOT

MULTIPLE

X = VAR1

Y = VAR7 VAR8

/FITTING = LINEAR CONFID = .9

/LABELS = CASES

STOP

Valid Abbreviations:

SCATTPLOT, SCATT, REG, MULT, FREQ, FIT, POL, LSQ, NEG


  SCL - Stats 2D Graphs - Probability Plots

For more information on this type of graph, see Probability Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

NORMALPLOT

[ { REGULAR    } ]

{ HALFNORMAL }

{ DETRENDED  }

VAR [=] VarList

Example:

The following example will create a Normal Probability Plot for variables 1-3.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

NORMALPLOT

VAR = 1 2 3

STOP


  SCL - Stats 2D Graphs - Range Plots

For more information on this type of graph, see 2D Range Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

   RANGEPLOT

   [ { WHISKERS } ]

     { BOXES    }

     { COLUMNS  }

   MIN [=] VarList

   MAX [=] VarList

   VALUE [=] VarList

   [/ MODE [=] { ABSOLUTE } ]

               { RELATIVE }

   [/ FITTING [=]  { OFF         } ]

                   { LINEAR      }

                   { LOG         }

                   { EXP         }

                   { SPLINE      }

                   { POLYNOMIAL  }

                   { LSQUARES    }

                   { NEGEXP      }

                   { "Function"  }

Example:

The following example will create a 2D Range Plot.  Errvar1 is the variable containing the minimum values, Errvar1 is the variable containing the maximum values to be plotted, and variable Measure contains the mid-point values to be plotted.  The range will be displayed relative to the mid-point (see MODE below).

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER

RANGEPLOT

BOXES

MIN = ERRVAR1

MAX = ERRVAR2

VALUE = MEASURE

/MODE = RELATIVE

STOP

Valid Abbreviations:

FIT, POL, LSQ, NEG


  SCL - Stats 2D Graphs - Box Plot

For more information on this type of graph, see 2D Box Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

   BOXPLOT

     [ { BOXWHISKERS } ]

       { WHISKERS    }

       { BOXES       }

       { COLUMNS     }

   VAR [=] VarList [BY Variable]

     [/CAT [=] { INTEGER                } ]

               { Number INTERVALS       }

               { "Boundaries"           }

               { CODES [=] (CodesList)  }

               { MSUBSET [=] "FileName" }

     [/ MODE = { 1 } ] {see description below}

               { 2 }

               { 3 }

               { 4 }

     [/ OUTLIERS [=] { OFF      } LEVEL [=] Number ]

                     { OUTLIERS }

                     { EXTREMES }

                     { ALL      }

     [/ TRIM [=] Number ] TRIM_SYM NEW

     [/ FITTING [=] { OFF        } ]

                    { LINEAR     }

                    { LOG        }

                    { EXP        }

                    { SPLINE     }

                    { POLYNOMIAL }

                    { LSQUARES   }

                    { NEGEXP     }

The combination of options available when you select a Mode category (see above) is described below:

Mode:  Middle Point:       Box:            Whisker:

-----  -------------  ---------------  -----------------

  1       Median      25/75 percent    Non-Outlier Range

  2       Median      25/75 percent    Min/Max

  3       Mean        Mean-SE,Mean+SE  Mean-SD,Mean+SD

  4       Mean        Mean-SE,Mean+SE  Min/Max

Example:

The following example will create a columns 2D Box Plot for the variable Score as categorized by the variable Gender.  A MODE of 2 is specified (see above) and outliers and extremes will be displayed in the graph.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = WINDOW

BOXPLOT

COLUMNS

VAR = SCORE BY GENDER

/CAT = CODES = (MALE,FEMALE)

/MODE = 2

/OUTLIERS = ALL LEVEL = 1.7

STOP

Valid Abbreviations:

FIT, POL, LSQ, NEG


  SCL - Stats 2D Graphs - Bar/Column Plots

For more information on this type of graph, see 2D Bar/Column Plots.  See also Order of SCL Statements.

BARCOLUMNPLOT

  [ { REGULAR  }

    { MULTIPLE } ]

  VARS [=] VarList

  [ / { VERTICAL   }

      { HORIZONTAL } ]

  [/LIMITS [=] { OFF  }

               { LINE }

               { BOX  }

    /Y1 [=] number  Y2 [=] number

     X1 [=] number  X2 [=] number ]

Example.  The following example will produce a HORIZONTAL MULTIPLE bar plot.  The SCL keyword STOP will stop execution of the program after the last task and return control of the module to the user in order to interactively edit, change parameters, etc.

FILE = "C:\STAT\EXAMPLES\ACCIDENT.STA"

BARCOLUMNPLOT

  MULTIPLE

  VARS Y_1983 Y_1985

  / HORIZONTAL


  SCL - Stats 2D Graphs - Line Plots (Variables)

For more information on this type of graph, see 2D Line Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

LINEPLOT

[ { REGULAR   } ]

{ MULTIPLE  }

{ DOUBLE    }

{ AGGREGATED }

{ TRACEPLOT  }

VAR [=] VarList [ BY VarList ]

[/ IGNOREMD ]

[/ FITTING [=] { OFF        } ]

{ LINEAR     }

{ LOG        }

{ EXP        }

{ SPLINE     }

{ POLYNOMIAL }

{ LSQUARES   }

{ NEGEXP     }

{ "Function" }

Example:

The following example will create a double-Y 2D Line Plot for the specified variables and for cases 13-33.  Missing data will be ignored and a spline fit will be fitted to the data.

FILE = "D:\DATA\SAMPLE.STA"

LINEPLOT

DOUBLE

VAR = 5 6 BY 10 11

/IGNOREMD

/FITTING = SPLINE

/CASES 13,33

STOP

Valid Abbreviations:

LINEP, REG, MULT, AGGR, FIT, POL, LSQ, NEG, TRACE


  SCL - Stats 2D Graphs - Sequential/Stacked Plots

For more information on this type of graph, see Sequential/Stacked Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

SEQUENTIALPLOT

{ LINE   }

{ AREA   }

{ STEP   }

{ COLUMN }

VAR [=] VarList

Example:

The following example will create an area Sequential/Stacked Plot for the specified variables.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

   HEADER = "Graph Header"

SEQUENTIALPLOT

AREA

VAR = SC1 SC2 SC3

STOP

Valid Abbreviation:

SEQPLOT


  SCL - Stats 2D Graphs - Mixed Sequential/Stacked Plots

For more information on this type of graph, see Sequential/Stacked Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

SEQUENTIALMIXEDPLOT

  { LINE }

  { STEP }

  AREA [=] VarList

  LINE [=] VarList

Example:

The following example will create a step Mixed Sequential/Stacked Plot for the specified variables.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

SEQUENTIALMIXEDPLOT

STEP

AREA = 5 6

LINE = 15 16

STOP

Valid Abbreviation:

SEQMIXPLOT


  SCL - Stats 2D Graphs - Pie Charts

For more information on this type of graph, see Pie Charts.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

PIECHART

[ { COUNTS } ]

{ VALUES }

VAR [=] VarList

[/CAT [=] { INTEGER                } ]

{ Number INTERVALS       }

{ "Boundaries"           }

{ CODES [=] (CodesList)  }

{ MSUBSET [=] "FileName" }

[/ { STYLE2D } ]

{ STYLE3D }

[/ { CIRCLE  } ]

{ ELLIPSE }

[/ LEGEND [=] { OFF            } ]

{ PERCENT        }

{ VALUES         }

{ TEXTVALUES     }

{ TEXTANDPERCENT }

{ TEXTANDVALUE   }

[/ EXPLODED [=] Number ]

Example:

The following example will create a 3D Pie Chart of counts for variable Measure.  The legend will include text and values and slice number 2 will be expoloded.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = WINDOW

PIECHART

COUNTS

VAR = MEASURE

/CAT = INTEGER

/STYLE3D

/LEGEND = TEXTANDVALUE

/EXPLODED = 2

STOP

Valid Abbreviations:

INTERV, PERC


  SCL - Stats 2D Graphs - Custom Function Plots

For more information on this type of graph, see 2D Custom Function Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

FUNCTION2D

"Function text"

[/ RANGE [=] (NumberMin, NumberMax) ]

Example:

The following example will create a 2D Custom Function Plot custom function plot for the specified function.

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

   HEADER = "Function display"

FUNCTION2D

"y = sin (exp (2*x+1))"

/RANGE = (-2, 2)

STOP


SCL - Stats 3D Sequential Graph -Raw Data Plots

  SCL - Stats 3D Sequential Graphs - Raw Data Plots

For more information on this type of graph, see 3D Sequential Graphs.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

SEQUENTIAL3D

[ { BOXES           } ]

  { BLOCKS          }

  { RIBBONS         }

  { LINES           }

  { SPIKES          }

  { CONTOURDISCRETE }

  { SURFACE         }

  { CONTOUR         }

VAR [=] VarList

Example:

The following example will create a 3D Sequential Graph of blocks for the specified variables and for cases 1-10.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

SEQUENTIAL3D

BLOCKS

VAR = 10 - 15

/CASES 1, 10

STOP

Valid Abbreviation:

SEQ3D


  SCL - Stats 3D Sequential Graphs - Bivariate Histograms

For more information on this type of graph, see 3D Sequential Graphs - Bivariate Histograms.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

HISTOGRAM3D

X [=] Variable

[/CAT [=] { INTEGER                } ]

          { Number INTERVALS       }

          { "Boundaries"           }

          { CODES [=] (CodesList)  }

          { MSUBSET [=] "FileName" }

Y [=] Variable

[/CAT [=] { INTEGER                } ]

          { Number INTERVALS       }

          { "Boundaries"           }

          { CODES [=] (CodesList)  }

          { MSUBSET [=] "FileName" }

Example:

The following example will create a Bivariate Histogram for the specified variables and categorization.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

HISTOGRAM3D

X = GENDER

/CAT = CODES = (MALE,FEMALE)

Y = SCORE

/CAT = 6 INTERVALS

STOP

Valid Abbreviations:

HIST3D, INTERV


  SCL - Stats 3D Sequential Graphs - Range Plots

For more information on this type of graph, see 3D Sequential Graphs - Range Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

RANGEPLOT3D

[ { POINTS    } ]

{ BORDERS   }

{ ERRORBARS }

{ RIBBONS   }

{ BOXES     }

{ BLOCKS    }

MIN [=] VarList

MAX [=] VarList

VALUE [=] VarList

[/ MODE [=] { ABSOLUTE } ]

{ RELATIVE }

[/ SPIKES [=] { YES }

{ NO  } ]

Example:

The following example will create a 3D Range Plot with error bars.  Errvar1 is the variable containing the minimum values, Errvar1 is the variable containing the maximum values to be plotted, and variable Measure contains the mid-point values to be plotted.  The range will be displayed absolute to the mid-point (see MODE below).  Spikes will connect the error bars to the base.

FILE = "D:\DATA\SAMPLE.STA"

RANGEPLOT3D

ERRORBARS

MIN = ERRVAR1

MAX = ERRVAR2

VALUE = MEASURE

/MODE = ABSOLUTE

/SPIKES = YES

STOP


  SCL - Stats 3D Sequential Graphs - Box Plots

For more information on this type of graph, see 3D Sequential Graphs - Box Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

BOXPLOT3D

[ { POINTS    } ]

  { BORDERS   }

  { ERRORBARS }

  { RIBBONS   }

  { BOXES     }

  { BLOCKS    }

VAR [=] VarList BY Variable

[/CAT [=] { INTEGER                } ]

          { Number INTERVALS       }

          { "Boundaries"           }

          { CODES [=] (CodesList)  }

          { MSUBSET [=] "FileName" }

[/ MODE = { 1 } ] {described below}

          { 2 }

          { 3 }

          { 4 }

[/ TRIM [=] Number ]

[/ SPIKES [=] { YES } ]

              { NO  }

The combination of options available when you select a Mode category (see above) is described below:

Mode:   Middle Point:  Bottom/Top:

-----   -------------  ---------------

  1        Median      25/75 percent

  2        Median      Min/Max

  3        Mean        Mean-SD,Mean+SD

  4        Mean        Min/Max

Example:

The following example will create a 3D Box Plot for the variable VAR5 as categorized by the variable VAR10.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

BOXPLOT3D

VAR = VAR5 BY VAR10

/CAT = "-2 0 1 10 100 500"

STOP


  SCL - Stats 3D XYZ Graphs - Scatterplots

For more information on this type of graph, see 3D XYZ Graphs - Scatterplots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

SCATTERPLOT3D

[ { REGULAR                      } ]

{ SPACE {LEVEL [=] Number}     }

{ SPECTRAL (PLANES [=] Number} }

{ DEVIATION {LEVEL [=] Number} }

X [=] Variable

Y [=] Variable

Z [=] VarList

[/ MSUBSET [=] "FileName" ]

Example:

The following example will create a 3D Scatterplot for the specified variables.  The MSUBSET option allows you to mark specific subsets of data with different point markers.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER

SCATTERPLOT3D

X = 1

Y = 2

Z = 3

/MSUBSET = "D:\DATA\MSUB.TXT"

STOP

Valid Abbreviations:

SCATT3D, REG


  SCL - Stats 3D XYZ Graphs - Surface Plots

For more information on this type of graph, see 3D XYZ Graphs - Surface Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

SURFACE3D

X [=] Variable

Y [=] Variable

Z [=] Variable

[/ FITTING [=] { LINEAR     } ]

               { QUADRATIC  }

               { LSQUARES   }

               { NEGEXP     }

               { SPLINE     }

               { "Function" }

[/ RAWDATA ]

Example:

The following example will create a Surface Plot with a negative exponential fit for the specified variables.  Raw data points will also be displayed.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

SURFACE3D

X = 1

Y = 2

Z = 3

/FITTING = NEGEXP

/RAWDATA

STOP

Valid Abbreviations:

FIT, LSQ, NEG


  SCL - Stats 3D XYZ Graphs - Contour Plots

For more information on this type of graph, see 3D XYZ Graphs - Contour Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

CONTOURPLOT

[ { AREA  } ]

{ LINES }

X [=] Variable

Y [=] Variable

Z [=] Variable

[/ FITTING [=] { LINEAR     } ]

               { QUADRATIC  }

               { LSQUARES   }

               { NEGEXP     }

               { SPLINE     }

               { "Function" }

[/ RAWDATA ]

Example:

The following example will create an area Contour Plot with a least squares fit for the specified variables.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

CONTOURPLOT

AREA

X = 1

Y = 2

Z = 3

/FITTING = LSQUARES

STOP

Valid Abbreviations:

CONTOUR, FIT, LSQ, NEG


  SCL - Stats 3D XYZ Graphs - Trace Plots

For more information on this type of graph, see 3D XYZ Graphs - Trace Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

TRACEPLOT

X [=] Variable

Y [=] Variable

Z [=] VarList

[/ MSUBSET [=] "FileName" ]

Example:

The following example will create a Trace Plot for the specified variables.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

TRACEPLOT

X = 1

Y = 2

Z = 3

STOP

Valid Abbreviation:

TRACE


SCL - Stats 3D XYZ Graphs - Ternary Graphs

  SCL - Stats 3D XYZ Graphs - Ternary Plots

For more information on this type of graph, see 3D XYZ Graphs - Ternary Graphs.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

TERNARY { SCATTER2D }

        { SCATTER3D }

        { SURFACE   }

        { CONTLINES }

        { CONTAREAS }

        { TRACE     }

X [=] Variable

Y [=] Variable

Z [=] Variable

V [=] Varlist {only if not SCATTER2D}

[/ FITTING [=] { OFF          } ]

{ LINEAR       }

{ QUADRATIC    }

{ FULLCUBIC    }

{ SPECIALCUBIC }

{ "Function"   }

Note that for SCATTER2D and TRACE ternary graphs, the FITTING option may only be set to OFF or not specified at all.  If SCATTER2D is selected, then V = Varlist is not applicable.

Example:

The following example will create a Ternary Graph with a special cubic fit for the specified variables.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

TERNARY SCATTER3D

X = 1

Y = 2

Z = 3

V = 4 5 6

/FITTING = SPECIALCUBIC

STOP

Valid Abbreviations:

FIT


  SCL - Stats 3D XYZ Graphs - Custom Function Plots

For more information on this type of graph, see 3D XYZ Graphs - Custom Function Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

FUNCTION3D

"Function text"

[/ RANGE [=] (XMin, XMax, YMin, YMax) ]

Example:

The following example will create a 3D Custom Function Plot for the specified function.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

FUNCTION3D

"z = sqrt (x**2 + y**2)"

STOP


SCL - Stats Graphs - Matrix Plot

  SCL - Stats Graphs - Matrix Plots

For more information on this type of graph, see Matrix Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

MATRIXPLOT

[ { SCATTERPLOT } ]

{ LINES       }

{ COLUMNS     }

VAR [=] VarList [ BY VarList ]

[/ FITTING [=]  { OFF         } ]

                { LINEAR      }

                { LOG         }

                { EXP         }

                { SPLINE      }

                { POLYNOMIAL  }

                { LSQUARES    }

                { NEGEXP      }

                { "Function"  }

[/ MSUBSET [=] "FileName" ]

Example:

The following example will create a scatterplot Matrix Plot for all of the variables in the specified data file.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

MATRIXPLOT

  SCATTERPLOT

  VAR = ALL

  /FITTING = OFF

STOP

Valid Abbreviations:

MATRIXP, FIT, POL, LSQ, NEG


  SCL - Stats Graphs - Icon Plots

For more information on this type of graph, see Icon Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

ICONPLOT

[ { FACES    } ]

{ STARS    }

{ SUNRAYS  }

{ POLYGONS }

{ PIES     }

{ COLUMNS  }

{ LINES    }

{ PROFILES }

VAR [=] VarList

[/ STANDARDIZE [=] { OFF   } ]

                   { CASES }

                   { VARS  }

                   { ALL   }

[/ MSUBSET [=] "FileName" ]

Example:

The following example will create a star Icon Plot for all of the variables in the specified data file.  The values will be standardized across cases as well as within each case (star icon).

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

ICONPLOT

STARS

VAR = ALL

/STANDARDIZE = ALL

STOP

Valid Abbreviations:

ICON, STAND, FACE, STAR, SUN, POLYGON, PIE, LINE, PROFILE


  SCL - Stats Categorized Graphs - Missing/Range Data Plot

For more information on this type of graph, see Categorized Missing/Range Data Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

   CATMDRANGEPLOT

   CATEGORIES [=] cat_var

   [/ [=] {INTEGER}

          {Number INTERVALS}

          {"Boundaries"}

          {CODES [=] (CodesList)}

          {MSUBSET [=] "FileName"}]

   VARS [=] list_of_vars

   [/MISSINGDATA [=] {YES}

                    {NO} ]

   [/OUTOFRANGEPOINTS

      (MIN [=] number [,] MAX [=] number [,] VARS = VarList) ... ]

Note:  You may specify up to 8 out-of-range criteria.

Example:

The following example will create a Missing/Range Data Plot for variables 1-4 as categorized by variable 6.  The 'out of range' points are defined by specifying the valid range (min and max values) for each variable.  Values which fall outside of this defined range will be plotted in the graph.  Missing data values will also be displayed in the graph.

   FILE = "D:\DATA\SAMPLE.STA"

   OUTPUTSETUP

   GRAPHS = WINDOW

   CATMDRANGEPLOT

   CAT = 6

     /10 INTERVALS

   VARS = 1-4

     /MISSINGDATA = YES

     /OUTOFRANGEPOINTS

        (MIN = 5  MAX = 25  VARS = 1)

        (MIN = 0  MAX = 4  VARS = 2)

        (MIN = -9  MAX = 9  VARS = 3)

        (MIN = 15  MAX = 20  VARS = 4)

   STOP

Valid Abbreviations:

CAT (for CATEGORIES), INTERV


  SCL - Stats Categorized Graphs - Quantile-Quantile Plot

For more information on this type of graph, see Categorized Quantile-Quantile Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

   CATQQPLOT

   CATX [=] catx_var

   [/ [=] {INTEGER}

          {Number INTERVALS}

          {"Boundaries"}

          {CODES [=] (CodesList)}

          {MSUBSET [=] "FileName"}]

   [CATY [=] caty_var

   [/ [=] {INTEGER}

          {Number INTERVALS}

          {"Boundaries"}

          {CODES [=] (CodesList)}

          {MSUBSET [=] "FileName"}] ]

   VARS [=] VarList

   {BETA

        {SHAPE1 [=] number  SHAPE2 [=] number}

        {THRESHOLD [=] number  SCALE [=] number

                   [/{MAXLIKELIHOOD}

                     {MATCHMOMENTS}] } }

   {EXPONENTIAL}

   {EXTREME}

   {GAMMA

          {SHAPE [=] number}

          {THRESHOLD [=] number

                     [/{MAXLIKELIHOOD}

                       {MATCHMOMENTS}] } }

   {LOGNORMAL

             {SHAPE [=] number}

             {THRESHOLD [=] number} }

   {NORMAL}

   {RAYLEIGH}

   {WEIBULL

           {SHAPE [=] number}

           {THRESHOLD [=] number

                      [/{MAXLIKELIHOOD}

                        {MATCHMOMENTS}] } }

   [/LINEARFIT [=] {YES}

                   {NO} ]

   [/CUSTOMFIT [=] {NO}

                   {YES

                       [/SCALE [=] number]

                       [/THRESHOLD [=] number] } ]

   [/RANKADJ [=] number]

   [/NADJ [=] number]

   [/PROBABSCALE [=] {OFF}

                     {ON }

                     { (list_of_numbers_separated_with_commas) } ]

Example:

The following example will create a Quantile-Quantile Plot for variables 4 and 5 as categorized by variable 1.

   FILE = "D:\DATA\SAMPLE.STA"

   OUTPUTSETUP

   GRAPHS = WINDOW

   CATQQPLOT

   CATX = 1

     /CODES = (MALE,FEMALE)

   VARS = 4 5

   EXTREME

   /LINEARFIT = YES

   STOP


  SCL - Stats Categorized Graphs - Probability-Probability Plot

For more information on this type of graph, see Categorized Probability-Probability Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

   CATPPPLOT

   CATX [=] catx_var

   [/ [=] {INTEGER}

          {Number INTERVALS}

          {"Boundaries"}

          {CODES [=] (CodesList)}

          {MSUBSET [=] "FileName"}]

   [CATY [=] caty_var

   [/ [=] {INTEGER}

          {Number INTERVALS}

          {"Boundaries"}

          {CODES [=] (CodesList)}

          {MSUBSET [=] "FileName"}] ]

   VARS [=] VarList

   {BETA

        {SHAPE1 [=] number  SHAPE2 [=] number  THRESHOLD [=] number  SCALE [=] number }

        {THRESHOLD [=] number  SCALE [=] number

                   [/{MAXLIKELIHOOD}

                     {MATCHMOMENTS} ] } }

   {EXPONENTIAL

               {SCALE [=] number  THRESHOLD [=] number }

               {THRESHOLD [=] number } }

   {EXTREME

            [THRESHOLD [=] number  SCALE [=] number] }

   {GAMMA

          {SHAPE [=] number  SCALE [=] number  THRESHOLD [=] number }

          {THRESHOLD [=] number

                     [/{MAXLIKELIHOOD}

                       {MATCHMOMENTS}] } }

   {LOGNORMAL

             {SHAPE [=] number  SCALE [=] number  THRESHOLD [=] number }

             {THRESHOLD [=] number } }

   {NORMAL

          [MU [=] number  SIGMA [=] number] }

   {RAYLEIGH

             {SCALE [=] number  THRESHOLD [=] number }

             {THRESHOLD [=] number } }

   {WEIBULL

           {SHAPE [=] number  SCALE [=] number  THRESHOLD [=] number }

           {THRESHOLD [=] number

                      [/{MAXLIKELIHOOD}

                        {MATCHMOMENTS}] } }

Example:

The following example will create a Probability-Probability Plot for variable 14 for the Normal distribution (with a mean of 1.5 and standard deviation of .025) as categorized by variable 2.

   FILE = "D:\DATA\SAMPLE.STA"

   OUTPUTSETUP

   GRAPHS = WINDOW

   CATPPPLOT

   CATX = 2

     /INTEGER

   VARS = 14

   NORMAL

          MU = 1.5

          SIGMA = .025

   STOP


SCL - Stats Categorized Graphs - Histograms

  SCL - Stats Categorized Graphs - Histogram

For more information on this type of graph, see Categorized Histograms.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

CATHISTOGRAM

[ { SEPARATE } ]

{ OVERLAID }

CATX [=] Variable

[/[=] { INTEGER                } ]

      { Number INTERVALS       }

      { "Boundaries"           }

      { CODES [=] (CodesList)  }

      { MSUBSET [=] "FileName" }

[CATY [=] Variable               ]

[/[=] { INTEGER                } ]

      { Number INTERVALS       }

      { "Boundaries"           }

      { CODES [=] (CodesList)  }

{ MSUBSET [=] "FileName" }

VAR [=] VarList

[/CAT [=] { INTEGER                } ]

          { Number INTERVALS       }

          { "Boundaries"           }

          { CODES [=] (CodesList)  }

          { MSUBSET [=] "FileName" }

[/ CUMULATIVE [=] { YES } ]

                  { NO  }

[/ BREAKS [=] { YES } ]

              { NO  }

[/ FITTING [=] { NORMAL    }

               { OFF       }

               { BETA      }

               { EXP       }

               { EXTREME   }

               { GAMMA     }

               { GEOMETRIC }

               { LAPLACE   }

               { LOGISTIC  }

               { LOGNORMAL }

               { POISSON   }

               { RAYLEIGH  }

               { SPLINE    }

               { WEIBULL   }]

Example:

The following example will create a Histogram for variable 5 as categorized by the levels of variable Gender.  The CUMULATIVE option results in cumulative frequencies in consecutive columns.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = WINDOW

CATHISTOGRAM

CATX = GENDER

VAR = 5

/CAT = 6 INTERVALS

/CUMULATIVE = YES

STOP

Valid Abbreviations:

INTERV, CUM, FIT


  SCL - Stats Categorized Graphs - Scatterplots

For more information on this type of graph, see Categorized Scatterplots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

CATSCATTERPLOT

[ { SEPARATE } ]

{ OVERLAID }

CATX [=] Variable

[/[=] { INTEGER                } ]

      { Number INTERVALS       }

      { "Boundaries"           }

      { CODES [=] (CodesList)  }

      { MSUBSET [=] "FileName" }

[CATY [=] Variable               ]

[/[=] { INTEGER                } ]

      { Number INTERVALS       }

      { "Boundaries"           }

      { CODES [=] (CodesList)  }

      { MSUBSET [=] "FileName" }

X [=] Variable

Y [=] Variable

[/ FITTING [=] { OFF        } ]

               { LINEAR     }

               { LOG        }

               { EXP        }

               { SPLINE     }

               { POLYNOMIAL }

               { LSQUARES   }

               { NEGEXP     }

               { "Function" }

Example:

The following example will create an overlaid Scatterplot for the specified variable as categorized by variables VAR1 (on the X-axis) and VAR2 (on the Y-axis).

FILE = "D:\DATA\SAMPLE.STA"

CATSCATTERPLOT

OVERLAID

CATX = VAR1

CATY = VAR2

X = VAR7

Y = VAR8

STOP

Valid Abbreviations:

INTERV, FIT, POL, LSQ, NEG


  SCL - Stats Categorized Graphs - Probability Plots

For more information on this type of graph, see Categorized Probability Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

CATNORMALPLOT

[ { REGULAR    } ]

  { HALFNORMAL }

  { DETRENDED  }

CATX [=] Variable

[/[=] { INTEGER                } ]

      { Number INTERVALS       }

      { "Boundaries"           }

      { CODES [=] (CodesList)  }

      { MSUBSET [=] "FileName" }

[CATY [=] Variable               ]

[/[=] { INTEGER                } ]

      { Number INTERVALS       }

      { "Boundaries"           }

      { CODES [=] (CodesList)  }

      { MSUBSET [=] "FileName" }

VAR [=] VarList

Example:

The following example will create a Normal Probability Plot for the specified variable as categorized by variable Catvar (on the X-axis) according to the specified boundaries.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER

CATNORMALPLOT

CATX = CATVAR

/= "-10 0 1 2 3 4 20 56"

VAR = HPQ

STOP

Valid Abbreviation:

INTERV


  SCL - Stats Categorized Graphs - Line Plots

For more information on this type of graph, see Categorized Line Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

CATLINEPLOT

CATX [=] Variable

[/[=] { INTEGER                } ]

{ Number INTERVALS       }

{ "Boundaries"           }

{ CODES [=] (CodesList)  }

{ MSUBSET [=] "FileName" }

[CATY [=] Variable               ]

[/[=] { INTEGER                } ]

{ Number INTERVALS       }

{ "Boundaries"           }

{ CODES [=] (CodesList)  }

{ MSUBSET [=] "FileName" }

VAR [=] VarList

Example:

The following example will create a Line Plot for the specified variable as categorized by variable 1 (on the X-axis).

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

CATLINEPLOT

CATX = 1

/=INTEGER

VAR = 2

STOP

Valid Abbreviation:

INTERV


  SCL - Stats Categorized Graphs - Box Plots

For more information on this type of graph, see Categorized Box Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

CATBOXPLOT

[ { BOXWHISKERS } ]

{ WHISKERS    }

{ BOXES       }

{ COLUMNS     }

CATX [=] Variable

[/[=] { INTEGER                } ]

      { Number INTERVALS       }

      { "Boundaries"           }

      { CODES [=] (CodesList)  }

      { MSUBSET [=] "FileName" }

[CATY [=] Variable               ]

[/[=] { INTEGER                } ]

      { Number INTERVALS       }

      { "Boundaries"           }

      { CODES [=] (CodesList)  }

      { MSUBSET [=] "FileName" }

VAR [=] VarList [BY Variable]

[/CAT [=] { INTEGER                } ]

          { Number INTERVALS       }

          { "Boundaries"           }

          { CODES [=] (CodesList)  }

          { MSUBSET [=] "FileName" }

          [/ MODE = { 1 } ]  {described below}

                    { 2 }

                    { 3 }

                    { 4 }

[/ OUTLIERS [=] { OFF      } LEVEL [=] Number ]

                { OUTLIERS }

                { EXTREMES }

                { ALL      }

[/ TRIM [=] Number ]

[/ FITTING [=] { OFF        } ]

               { LINEAR     }

               { LOG        }

               { EXP        }

               { SPLINE     }

               { POLYNOMIAL }

               { LSQUARES   }

               { NEGEXP     }

The combination of options available when you select a Mode category (see above) is described below:

Mode:  Middle Point:      Box:            Whisker:

-----  ------------- ---------------  -----------------

  1       Median     25/75 percent    Non-Outlier Rangeg_non_outlier

  2       Median     25/75 percent    Min/Max

  3       Mean       Mean-SE,Mean+SE  Mean-SD,Mean+SD

  4       Mean       Mean-SE,Mean+SE  Min/Max

Example:

The following example will create a box and whisker Box Plot for the variable Score as categorized by the variable Gender.  The box plots will be further categorized by variable Income (on the X-axis).  Extreme values will be displayed in the graph.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

   HEADER = "Project XYZ"

CATBOXPLOT

BOXWHISKERS

CATX = INCOME

/CAT = CODES (LOW,MEDIAN,HIGH)

VAR = SCORE BY GENDER

/CAT = CODES = (MALE,FEMALE)

/OUTLIERS = EXREMES LEVEL = 1.3

STOP

Valid Abbreviations:

INTERV, FIT, POL, LSQ, NEG


  SCL - Stats Categorized Graphs - Pie Charts

For more information on this type of graph, see Categorized Pie Charts.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

CATPIECHART

CATX [=] Variable

[/[=] { INTEGER                } ]

      { Number INTERVALS       }

      { "Boundaries"           }

      { CODES [=] (CodesList)  }

      { MSUBSET [=] "FileName" }

[CATY [=] Variable               ]

[/[=] { INTEGER                } ]

      { Number INTERVALS       }

      { "Boundaries"           }

      { CODES [=] (CodesList)  }

      { MSUBSET [=] "FileName" }

VAR [=] VarList

[/CAT [=] { INTEGER                } ]

          { Number INTERVALS       }

          { "Boundaries"           }

          { CODES [=] (CodesList)  }

          { MSUBSET [=] "FileName" }

[/ { STYLE2D } ]

{ STYLE3D }

[/ { CIRCLE  } ]

{ ELLIPSE }

[/ LEGEND [=] { OFF            } ]

              { PERCENT        }

              { VALUES         }

              { TEXTVALUES     }

              { TEXTANDPERCENT }

              { TEXTANDVALUE   }

[/ EXPLODED [=] Number ]

Example:

The following example will create a 3D Pie Chart for variable Measure as categorized by variable Depart.  The legend will include text and values and slice number 2 will be expoloded.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER

CATPIECHART

CATX = DEPART

VAR = MEASURE

/CAT = INTEGER

/STYLE3D

/LEGEND = TEXTANDVALUE

/EXPLODED = 2

STOP

Valid Abbreviation:

INTERV


  SCL - Stats Categorized Graphs - 3D Scatterplots

For more information on this type of graph, see Categorized 3D Scatterplot.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

CATSCATTERPLOT3D

[ { REGULAR                      } ]

{ SPACE {LEVEL [=] Number}     }

{ SPECTRAL (PLANES [=] Number} }

{ DEVIATION {LEVEL [=] Number} }

CAT [=] Variable

[/[=] { INTEGER                } ]

{ Number INTERVALS       }

{ "Boundaries"           }

{ CODES [=] (CodesList)  }

{ MSUBSET [=] "FileName" }

X [=] Variable

Y [=] Variable

Z [=] VarList

Example:

The following example will create a 3D Scatterplot with 2 spectral planes for the specified variables as categorized by variable 10.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = WINDOW

CATSCATTERPLOT3D

SPECTRAL PLANES = 2

CAT = 10

X = 1

Y = 2

Z = 3

STOP

Valid Abbreviations:

INTERV, REG


  SCL - Stats Categorized Graphs - 3D Surface Plots

For more information on this type of graph, see 3D Categorized Surface Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

CATSURFACE3D

CAT [=] Variable

[/[=] { INTEGER                } ]

{ Number INTERVALS       }

{ "Boundaries"           }

{ CODES [=] (CodesList)  }

{ MSUBSET [=] "FileName" }

X [=] Variable

Y [=] Variable

Z [=] Variable

[/ FITTING [=] { LINEAR     } ]

{ QUADRATIC  }

{ LSQUARES   }

{ NEGEXP     }

{ SPLINE     }

{ "Function" }

Example:

The following example will create a Surface Plot with a quadratic fit for the specified variables as categorized by variable 7.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

CATSURFACE3D

CAT = 7

X = 1

Y = 2

Z = 3

/FITTING = QUADRATIC

STOP

Valid Abbreviations:

FIT, LSQ, NEG


SCL - Stats Categorized Graphs - 3D Contour Plots

  SCL - 3D Categorized Contour Plots

For more information on this type of graph, see 3D Categorized Contour Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

CATCONTUR3D

[ { AREA  } ]

{ LINES }

CAT [=] Variable

[/[=] { INTEGER                } ]

      { Number INTERVALS       }

      { "Boundaries"           }

      { CODES [=] (CodesList)  }

      { MSUBSET [=] "FileName" }

X [=] Variable

Y [=] Variable

Z [=] Variable

[/ FITTING [=] { LINEAR     } ]

               { QUADRATIC  }

               { LSQUARES   }

               { NEGEXP     }

               { SPLINE     }

               { "Function" }

Example:

The following example will create a Contour Plot with a quadratic fit for the specified variables as categorized by variable 7.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

CATCONTOUR3D

CAT = 7

X = 1

Y = 2

Z = 3

/FITTING = QUADRATIC

Valid Abbreviations:

FIT, LSQ, NEG


SCL - Stats Categorized Graphs - Ternary Graphs

  SCL - Stats Categorized Graphs - Ternary Plots

For more information on this type of graph, see Categorized Ternary Plots.  See also Order of SCL Statements.  For other options, see SENDKEYS and Examples with SENDKEYS.

CATTERNARY { SCATTER2D }

           { SCATTER3D }

           { SURFACE   }

           { CONTLINES }

           { CONTAREAS }

           { TRACE     }

CATEGORIES [=] Variable

[/[=]	{ INTEGER                } ]

{ Number INTERVALS       }

{ "Boundaries"           }

{ CODES [=] (CodesList)  }

{ MSUBSET [=] "FileName" }

X [=] Variable

Y [=] Variable

Z [=] Variable

V [=] Varlist {only if not SCATTER2D}

[/ FITTING [=] { OFF          } ]

{ LINEAR       }

{ QUADRATIC    }

{ FULLCUBIC    }

{ SPECIALCUBIC }

{ "Function"   }

Note that for SCATTER2D and TRACE ternary graphs, the FITTING option may only be set to OFF or not specified at all.  If SCATTER2D is selected, then V = Varlist is not applicable.

Example:

The following example will create a Ternary Plot with a special cubic fit for the specified variables as categorized by variable 1.

FILE = "D:\DATA\SAMPLE.STA"

OUTPUTSETUP

   GRAPHS = PRINTER AND WINDOW

CATTERNARY SCATTER3D

CAT = 1

    /= CODES (M,F)

X = 3

Y = 4

Z = 5

V = 6

/FITTING = SPECIALCUBIC

STOP

Valid Abbreviations:

CAT (for CATEGORIES), INTERV, FIT


SCL - Creating Run-time User-interface for SCL programs

Although the SCL command language does not offer (directly) designated run-time user-interface, you can use STATISTICA BASIC programs (to be called from an SCL command program) to design dialog boxes and other elements of the user-interface which will allow users of the SCL program to select variables, data files, etc. in run-time.  An example is given in Calling STATISTICA BASIC from within SCL.


  Examples with SENDKEYS

These examples show how to use the SENDKEYS facility to perform specific, non-standard operations on the graphs.  See also Order of SCL Statements and SCL Syntax - Sendkeys.  The SENDKEYS command follows the syntax conventions of Microsoft macro languages (e.g., see MS Excel, MS Word, MS Visual Basic).

1) How to save a graph using SENDKEYS

2) How to change scales for the graph


  How to Change Scales for the Graph Using SENDKEYS

The following SENDKEYS sequence will change the scaling on the Y axis to manual from 0 to 20 with a step size 5 (see the sequence of keys:  %x20%p5%n0).

SCATTERPLOT

X = 1

Y = 2

SENDKEYS "{F10}l~%s{DOWN}%p%g{END}%x20%p5%n0~%o{F10}fa%nnew2~"


  How to Save a Graph Using SENDKEYS

In most cases, the SAVEGRAPH command should be used to save graphs; however, individual graphs can also be saved using the Sendkeys facility.  For example, the following SENDKEYS sequence will save the graph from the current (active) window under the file name E:\Graph1.stg (see the sequence of keys:  e:\graph1.stg).

SCATTERPLOT

X = 1

Y = 2

SENDKEYS "{F12}%ne:\graph1.stg~"


  STATISTICA Command Language - Run Module

The SCL Run Module is the "work horse" of the STATISTICA Command Language.  The Run Module can be used in three different ways:

Batch Programming

The Run Module verifies the syntax of the SCL commands if the Verify option was selected, or it verifies and executes the SCL commands if the Execute option was selected.

Turn-key System

You can use the Run Module as a "turn-key" system in order to speed up invoking already tested or repeatedly executed SCL programs or to develop "fail-safe" programs for persons unfamiliar with STATISTICA.  In order to run a SCL program in this manner, you will need to create a "custom application" icon in your STATISTICA Program Group (one for each turn-key program that you want; see the New option in the Windows Program Manager File pull-down menu for help on creating a new Program Item).  Specify in the Program Item Properties window command line, the drive and directory for the STA_RUN.EXE file as well as the appropriate path and file name of the previously saved SCL program (e.g., enter in the command line the following:  c:\STAT\STA_RUN.EXE c:\STAT\EXAMPLES\SCL_file.SCL).  You can also give this icon a meaningful name in the description line of this window.  Now whenever you click on this icon, the Run Module will execute the specified SCL program in a "turn-key" fashion.

Alternatively, you can assign SCL programs to buttons on the customizable Auto Tasks Buttons floating toolbar.

Use in Other Applications

Because STATISTICA supports the Microsoft Windows DDE/API interface standard, you can build SCL commands or entire SCL programs into macros created within and run from other Windows applications (e.g., Excel, MS Word, Ami Pro, Quattro Pro).  For example, an Excel macro may include SCL commands which will call STATISTICA from within Excel, perform a specified set of analysis via the Run Module, and then transfer and integrate specific parts of the output and/or graphs created by STATISTICA within your current Excel worksheet or workbook.  For more information on DDE links and an example of an Excel macro using the Run Module, see Creating Links (Dynamic Data Exchange).


  Time Series Analysis - Index

Introductory Overview

Identifying Patterns in Time Series Data

ARIMA (Box & Jenkins) and Autocorrelations

ARIMA Introductory Overview

Interrupted Time Series

Exponential Smoothing

Seasonal Decomposition (Census I)

X-11 Census Method II Seasonal Adjustment

Seasonal Adjustment: Basic Ideas and Terms

The Census II Method

Results Tables Computed by the X-11 Method

Specific Description of all Results Tables Computed by the X-11 Method

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis

Basic Notations and Principles

Fast Fourier Transformations

Startup Panel

Transformations

Transformation Functions

Transformations for Spectrum Analysis

ARIMA (Box & Jenkins) and Autocorrelations

ARIMA Models

Interrupted ARIMA Models

Specifying ARIMA Models

ARIMA Results

Exponential Smoothing

Seasonal Decomposition (Census I)

X-11 monthly seasonal adjustment

X-11 quarterly seasonal adjustment

Specifying Distributed Lags Analysis

Spectrum (Fourier) Analysis

Single Spectrum Analysis Results

Cross-spectrum Analysis Results


  Time Series Analysis - Introductory Overview

General Introduction

Two main goals

In the following topics, we will first review techniques used to identify patterns in time series data (such as smoothing and curve fitting techniques and autocorrelations), then we will introduce a general class of models that can be used to represent time series data and generate predictions (autoregressive and moving average models).  Finally, we will review some simple but commonly used modeling and forecasting techniques based on linear regression.  For more information on these topics, click on the topic name below.

Identifying Patterns in Time Series Data

ARIMA (Box & Jenkins) and Autocorrelations

ARIMA Introductory Overview

Interrupted Time Series

Exponential Smoothing

Seasonal Decomposition (Census I)

X-11 Census method II seasonal adjustment

X-11 Census method II result tables

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis

Basic Notations and Principles

Fast Fourier Transformations


  Time Series Analysis Introductory Overview - General Introduction

In the following topics, we will review techniques that are useful for analyzing time series data, that is, sequences of measurements that follow non-random orders.  Unlike the analyses of random samples of observations that are discussed in the context of most other statistics, the analysis of time series is based on the assumption that successive values in the data file represent consecutive measurements taken at equally spaced time intervals.

Detailed discussions of the methods described in this section can be found in Anderson (1976), Box and Jenkins (1976), Kendall (1984), Kendall and Ord (1990), Montgomery, Johnson, and Gardiner (1990), Pankratz (1983), Shumway (1988), Vandaele (1983), Walker (1991), and Wei (1989).


  Time Series Analysis Introductory Overview - Two Main Goals

There are two main goals of time series analysis: (a) identifying the nature of the phenomenon represented by the sequence of observations, and (b) forecasting (predicting future values of the time series variable).  Both of these goals require that the pattern of observed time series data is identified and more or less formally described.  Once the pattern is established, we can interpret and integrate it with other data (i.e., use it in our theory of the investigated phenomenon, e.g., sesonal commodity prices).  Regardless of the depth of our understanding and the validity of our interpretation (theory) of the phenomenon, we can extrapolate the identified pattern to predict future events.


  Time Series Analysis - Identifying Patterns in Time Series Data

Systematic pattern and random noise

Two general aspects of time series patterns

Trend Analysis

Analysis of Seasonality

For more information on simple autocorrelations (introduced in this section) and other autocorrelations, see the Examples and Dialogs, Options, Statistics sections of this chapter in the manual; see also Anderson (1976), Box and Jenkins (1976), Kendall (1984), Pankratz (1983), and Vandaele (1983).

See also:

ARIMA (Box & Jenkins) and Autocorrelations

ARIMA Introductory Overview

Interrupted Time Series

Exponential Smoothing

Seasonal Decomposition (Census I)

X-11 Census method II seasonal adjustment

X-11 Census method II result tables

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis

Basic Notations and Principles

Fast Fourier Transformations


Identifying Patterns in Time Series Data - Systematic Pattern and Random Noise

  Time Series Analysis - Identifying Patterns in Time Series Data - Systematic Pattern and Random Noise

As in most other analyses, in time series analysis it is assumed that the data consist of a systematic pattern (usually a set of identifiable components) and random noise (error) which usually makes the pattern difficult to identify.  Most time series analysis techniques involve some form of filtering out noise in order to make the pattern more salient.


Identifying Patterns in Time Series Data - Two general aspects of time series patterns

  Time Series Analysis - Identifying Patterns in Time Series Data - Two General Aspects of Time Series Patterns

Most time series patterns can be described in terms of two basic classes of components: trend and seasonality.  The former represents a general systematic linear or (most often) nonlinear component that changes over time and does not repeat or at least does not repeat within the time range captured by our data (e.g., a plateau followed by a period of exponential growth).  The latter may have a formally similar nature (e.g., a plateau followed by a period of exponential growth), however, it repeats itself in systematic intervals over time.  Those two general classes of time series components may coexist in real-life data.  For example, sales of a company can rapidly grow over years but they still follow consistent seasonal patterns (e.g., as much as 25% of yearly sales each year are made in December, whereas only 4% in August).

This general pattern is well illustrated in a "classic" Series G data set (Box and Jenkins, 1976, p. 531) representing monthly international airline passenger totals (measured in thousands) in twelve consecutive years from 1949 to 1960 (see example data file G.sta).  If you plot the successive observations (months) of airline passenger totals, a clear, almost linear trend emerges, indicating that the airline industry enjoyed a steady growth over the years (approximately 4 times more passengers traveled in 1960 than in 1949).  At the same time, the monthly figures will follow an almost identical pattern each year (e.g., more people travel during holidays then during any other time of the year).  This example data file also illustrates a very common general type of pattern in time series data, where the amplitude of the seasonal changes increases with the overall trend (i.e., the variance is correlated with the mean over the segments of the series).  This pattern which is called multiplicative seasonality indicates that the relative amplitude of seasonal changes is constant over time, thus it is related to the trend.


Identifying Patterns in Time Series Data - Trend Analysis

  Time Series Analysis - Identifying Patterns in Time Series Data - Trend Analysis

There are no proven "automatic" techniques to identify trend components in the time series data; however, as long as the trend is monotonous (consistently increasing or decreasing) that part of data analysis is typically not very difficult.  If the time series data contain considerable error, then the first step in the process of trend identification is smoothing.

Smoothing.  Smoothing always involves some form of local averaging of data such that the nonsystematic components of individual observations cancel each other out.  The most common technique is moving average smoothing which replaces each element of the series by either the simple or weighted average of n surrounding elements, where n is the width of the smoothing "window" (see Box & Jenkins, 1976; Velleman & Hoaglin, 1981).  Medians can be used instead of means.  The main advantage of median as compared to moving average smoothing is that its results are less biased by outliers (within the smoothing window).  Thus, if there are outliers in the data (e.g., due to measurement errors), median smoothing typically produces smoother or at least more "reliable" curves than moving average based on the same window width.  The main disadvantage of median smoothing is that in the absence of clear outliers it may produce more "jagged" curves than moving average and it does not allow for weighting.

All of these techniques are included among the interactive transformations in the Time Series module.  In the relatively less common cases (in time series data), when the measurement error is very large, the distance weighted least squares smoothing or negative exponentially weighted smoothing techniques described in the chapters on Graphics (Volume II) can be used.  All those methods will filter out the noise and convert the data into a smooth curve that is relatively unbiased by outliers (see the respective sections on each of those methods for more details).  Series with relatively few and systematically distributed points can be smoothed with bicubic splines (also described in the chapters on Graphics, Volume II).

Fitting a function.  Many monotonous time series data can be adequately approximated by a linear function; if there is a clear monotonous nonlinear component, the data first need to be transformed to remove the nonlinearity.  Usually a logarithmic, exponential, or (less often) polynomial function can be used.  There are several ways to do this in STATISTICA.  You can experiment with transformations of unlimited complexity using spreadsheet formulas (or Quick MML in the Data Management module), and later submit the transformed series to linear regression (either via the Multiple Regression or the Time Series module) and generate forecasts (in Multiple Regression).  Nonlinear functions of practically unlimited complexity including piecewise estimations with break points (where different functions can be simultaneously fitted to different ranges of the series) can be performed with the Nonlinear Estimation module.  Finally, the Graphics options include general purpose curve fitting procedures that can be used to fit polynomial functions (of user-specified order), logarithmic functions (with user-specified bases), exponential and other functions.


Time Series Analysis Identifying Patterns in Time Series Data - Analysis of Seasonality

  Time Series Analysis - Identifying Patterns in Time Series Data - Analysis of Seasonality

Seasonal dependency (seasonality) is another general component of the time series pattern.  The concept was illustrated in the example of the airline passengers data above.  It is formally defined as correlational dependency of order k between each i'th element of the series and the (ik)'th element (Kendall, 1976) and measured by autocorrelation (i.e., a correlation between the two terms); k is usually called the lag.  If the measurement error is not too large, seasonality can be visually identified in the series as a pattern that repeats every k elements.

Autocorrelation correlogram.  Seasonal patterns of time series can be examined via correlograms.  The correlogram (autocorrelogram) displays graphically and numerically the autocorrelation function (ACF), that is, serial correlation coefficients (and their standard errors) for consecutive lags in a specified range of lags (e.g., 1 through 30).  Ranges of two standard errors for each lag are usually marked in correlograms but typically the size of autocorrelation is of more interest than its reliability (see Elementary Concepts) because we are usually interested only in very strong (and thus highly significant) autocorrelations.

Examining correlograms.  While examining correlograms one should keep in mind that autocorrelations for consecutive lags are formally dependent.  Consider the following example.  If the first element is closely related to the second, and the second to the third, then the first element must also be somewhat related to the third one, etc.  This implies that the pattern of serial dependencies can change considerably after removing the first order autocorrelation (i.e., after differencing the series with a lag of 1).

Partial autocorrelations.  Another useful method to examine serial dependencies is to examine the partial autocorrelation function (PACF) - an extension of autocorrelation, where the dependence on the intermediate elements (those within the lag) is removed.  In other words the partial autocorrelation is similar to autocorrelation, except that when calculating it, the (auto) correlations with all the elements within the lag are partialled out (Box & Jenkins, 1976; see also McDowall, McCleary, Meidinger, & Hay, 1980).  If a lag of 1 is specified (i.e., there are no intermediate elements within the lag), then the partial autocorrelation is equivalent to autocorrelation.  In a sense, the partial autocorrelation provides a "cleaner" picture of serial dependencies for individual lags (not confounded by other serial dependencies).

Removing serial dependency.  Serial dependency for a particular lag of k can be removed by differencing the series, that is converting each i'th element of the series into its difference from the (i-k)''th element.  There are two major reasons for such transformations.

First, one can identify the hidden nature of seasonal dependencies in the series.  Remember that, as mentioned in the previous paragraph, autocorrelations for consecutive lags are interdependent.  Therefore, removing some of the autocorrelations will change other autocorrelations, that is, it may eliminate them or it may make some other seasonalities more apparent.

The other reason for removing seasonal dependencies is to make the series stationary which is necessary for ARIMA and other techniques.


  Time Series Analysis - ARIMA Introductory Overview

General Introduction

Two Common Processes

ARIMA Methodology

Identification Phase

Parameter Estimation

Evaluation of the Model

For more information on Time Series methods, see also:

Identifying Patterns in Time Series Data

Interrupted Time Series

Exponential Smoothing

Seasonal Decomposition (Census I)

X-11 Census method II seasonal adjustment

X-11 Census method II result tables

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis

Basic Notations and Principles

Fast Fourier Transformations


ARIMA Introductory Overview - General Introduction

  Time Series Analysis ARIMA Introductory Overview - General Introduction

The modeling and forecasting procedures discussed in the Identifying Patterns in Time Series Data topic, involved knowledge about the mathematical model of the process.  However, in real-life research and practice, patterns of the data are unclear, individual observations involve considerable error, and we still need not only to uncover the hidden patterns in the data but also generate forecasts.  The ARIMA methodology developed by Box and Jenkins (1976) allows us to do just that; it has gained enormous popularity in many areas and research practice confirms its power and flexibility (Hoff, 1983; Pankratz, 1983; Vandaele, 1983).  However, because of its power and flexibility, ARIMA is a complex technique; it is not easy to use, it requires a great deal of experience, and although it often produces satisfactory results, those results depend on the researcher's level of expertise (Bails & Peppers, 1982).  The following sections will introduce the basic ideas of this methodology.  For those interested in a brief, applications-oriented (non-mathematical), introduction to ARIMA methods, we recommend McDowall, McCleary, Meidinger, and Hay (1980).


ARIMA Introductory Overview - Two Common Processes

  Time Series Analysis ARIMA Introductory Overview - Two Common Processes

Autoregressive process.  Most time series consist of elements that are serially dependent in the sense that one can estimate a coefficient or a set of coefficients that describe consecutive elements of the series from specific, time-lagged (previous) elements.  This can be summarized in the equation:

x = ξ+φ *x     +φ *x     +φ *x     ...+ε

 t     1   (t-1)  2  (t-2)  3  (t-3)

Where:

ξ 	is a constant (intercept), and

φ1, φ2, φ3 	are the autoregressive model parameters.

Put in words, each observation is made up of a random error component (random shock, ε) and a linear combination of prior observations.

Stationarity requirement.  Note that an autoregressive process will only be stable if the parameters are within a certain range; for example, if there is only one autoregressive parameter then is must fall within the interval of -1<φ1<+1.  Otherwise, past effects would accumulate and the values of successive xt' s would move towards infinity, that is, the series would not be stationary.  If there is more than one autoregressive parameter, similar (general) restrictions on the parameter values can be defined (e.g., see Box & Jenkins, 1976; Montgomery, 1990).  The Time Series program will automatically check whether the stationarity requirement is met.

Moving average process.  Independent from the autoregressive process, each element in the series can also be affected by the past error (or random shock) that cannot be accounted for by the autoregressive component, that is:

x = μ+ε -θ *ε     -θ *ε     -θ *ε     ...

 t     t   1  (t-1)  2  (t-2)  3  (t-3)

Where:

μ 	is a constant, and

θ1, θ2, θ3	are the moving average model parameters.

Put in words, each observation is made up of a random error component (random shock, ε) and a linear combination of prior random shocks.

Invertibility requirement.  Without going into too much detail, there is a "duality" between the moving average process and the autoregressive process (e.g., see Box & Jenkins, 1976; Montgomery, Johnson, & Gardiner, 1990), that is, the moving average equation above can be rewritten (inverted) into an autoregressive form (of infinite order).  However, analogous to the stationarity condition described above, this can only be done if the moving average parameters follow certain conditions, that is, if the model is invertible.  Otherwise, the series will not be stationary.  Again, the Time Series program will automatically check whether the invertibility requirement is met.


ARIMA Introductory Overview - ARIMA Methodology

  Time Series Analysis ARIMA Introductory Overview - ARIMA Methodology

Autoregressive moving average model.  The general model introduced by Box and Jenkins (1976) includes autoregressive as well as moving average parameters, and explicitly includes differencing in the formulation of the model.  Specifically, the three types of parameters in the model are: the autoregressive parameters (p), the number of differencing passes (d), and moving average parameters (q).  In the notation introduced by Box and Jenkins, models are summarized as ARIMA (p, d, q); so, for example, a model described as (0, 1, 2) means that it contains 0 (zero) autoregressive (p) parameters and 2 moving average (q) parameters which were computed for the series after it was differenced once.

Identification.  As mentioned earlier, the input series for ARIMA needs to be stationary, that is, it should have a constant mean, variance, and autocorrelation through time.  Therefore, usually the series first needs to be differenced until it is stationary (this also often requires log transforming the data to stabilize the variance).  The number of times the series needs to be differenced to achieve stationarity is reflected in the d parameter (see the previous paragraph).  In order to determine the necessary level of differencing, one should examine the plot of the data and autocorrelogram.  Significant changes in level (strong upward or downward changes) usually require first order non seasonal (lag=1) differencing; strong changes of slope usually require second order non seasonal differencing.  Seasonal patterns require respective seasonal differencing (see below).  If the estimated autocorrelation coefficients decline slowly at longer lags, first order differencing is usually needed.  However, one should keep in mind that some time series may require little or no differencing, and that over differenced series produce less stable coefficient estimates.

At this stage (which is usually called Identification phase, see below) we also need to decide how many autoregressive (p) and moving average (q) parameters are necessary to yield an effective but still parsimonious model of the process (parsimonious means that it has the fewest parameters and greatest number of degrees of freedom among all models that fit the data).  In practice, the numbers of the p or q parameters very rarely need to be greater than 2 (see below for more specific recommendations).

Estimation and Forecasting.  At the next step (Estimation), the parameters are estimated (using function minimization procedures, see below; for more information on minimization procedures see also Nonlinear Estimation), so that the sum of squared residuals is minimized.  The estimates of the parameters are used in the last stage (Forecasting) to calculate new values of the series (beyond those included in the input data set) and confidence intervals for those predicted values.  The estimation process is performed on transformed (differenced) data; before the forecasts are generated, the series needs to be integrated (integration is the inverse of differencing) so that the forecasts are expressed in values compatible with the input data.  This automatic integration feature is represented by the letter I in the name of the methodology (ARIMA = Auto-Regressive Integrated Moving Average).

The constant in ARIMA models.  In addition to the standard autoregressive and moving average parameters, ARIMA models may also include a constant, as described above.  The interpretation of a (statistically significant) constant depends on the model that is fit.  Specifically, (1) if there are no autoregressive parameters in the model, then the expected value of the constant is μ, the mean of the series; (2) if there are autoregressive parameters in the series, then the constant represents the intercept.  If the series is differenced, then the constant represents the mean or intercept of the differenced series; For example, if the series is differenced once, and there are no autoregressive parameters in the model, then the constant represents the mean of the differenced series, and therefore the linear trend slope of the un-differenced series.


ARIMA Introductory Overview - Identification Phase

  Time Series Analysis ARIMA Introductory Overview - Identification

Number of parameters to be estimated.  Before the estimation can begin, we need to decide on (identify) the specific number and type of ARIMA parameters to be estimated.  The major tools used in the identification phase are plots of the series, correlograms of autocorrelation (ACF), and partial autocorrelation (PACF).  The decision is not straightforward and in less typical cases requires not only experience but also a good deal of experimentation with alternative models (as well as the technical parameters of ARIMA).  However, a majority of empirical time series patterns can be sufficiently approximated using one of the 5 basic models that can be identified based on the shape of the autocorrelogram (ACF) and partial autocorrelogram (PACF).  The following brief summary is based on practical recommendations of Pankratz (1983); for additional practical advice, see also Hoff (1983), McCleary and Hay (1980), McDowall, McCleary, Meidinger, and Hay (1980), and Vandaele (1983).  Also, note that since the number of parameters (to be estimated) of each kind is almost never greater than 2, it is often practical to try alternative models on the same data.

(1) One autoregressive (p) parameter:  ACF - exponential decay; PACF - spike at lag 1, no correlation for other lags.

(2)	Two autoregressive (p) parameters:  ACF - a sine-wave shape pattern or a set of exponential decays; PACF - spikes at lags 1 and 2, no correlation for other lags.

(3)	One moving average (q) parameter:  ACF - spike at lag 1, no correlation for other lags; PACF - damps out exponentially.

(4)	Two moving average (q) parameters:  ACF - spikes at lags 1 and 2, no correlation for other lags; PACF - a sine-wave shape pattern or a set of exponential decays.

(5)	One autoregressive (p) and one moving average (q) parameter:  ACF - exponential decay starting at lag 1; PACF - exponential decay starting at lag 1.

Seasonal models.  Multiplicative seasonal ARIMA is a generalization and extension of the method introduced in the previous paragraphs to series in which a pattern repeats seasonally over time.  In addition to the non-seasonal parameters, seasonal parameters for a specified lag (established in the identification phase) need to be estimated.  Analogous to the simple ARIMA parameters, these are: seasonal autoregressive (ps), seasonal differencing (ds), and seasonal moving average parameters (qs).  For example, the model (0,1,2)(0,1,1) describes a model that includes no autoregressive parameters, 2 regular moving average parameters and 1 seasonal moving average parameter, and these parameters were computed for the series after it was differenced once with lag 1, and once seasonally differenced.  The seasonal lag used for the seasonal parameters is usually determined during the identification phase and must be explicitly specified.

The general recommendations concerning the selection of parameters to be estimated (based on ACF and PACF) also apply to seasonal models (for an illustration of seasonal ARIMA, see the Example in the ARIMA section of the chapter).  The main difference is that in seasonal series, ACF and PACF will show sizable coefficients at multiples of the seasonal lag (in addition to their overall patterns reflecting the non seasonal components of the series).


ARIMA Introductory Overview - Parameter Estimation

  Time Series Analysis ARIMA Introductory Overview - Parameter Estimation

The Time Series module of STATISTICA includes different methods for estimating the parameters.  All of them should produce very similar estimates, but may be more or less efficient for any given model.  In general, during the parameter estimation phase a function minimization algorithm is used (the so-called quasi-Newton method; refer to the description of the Nonlinear Estimation method) to maximize the likelihood (probability) of the observed series, given the parameter values.  In practice, this requires the calculation of the (conditional) sums of squares (SS) of the residuals, given the respective parameters.  Different methods have been proposed to compute the SS for the residuals; in STATISTICA you can choose between: (1) the approximate maximum likelihood method according to McLeod and Sales (1983), (2) the approximate maximum likelihood method with backcasting, and (3) the exact maximum likelihood method according to Melard (1984).

Comparison of methods.  In general, all methods should yield very similar parameter estimates.  Also, all methods are about equally efficient in most real-world time series applications.  However, method 1 above, (approximate maximum likelihood, no backcasts) is the fastest, and should be used in particular for very long time series (e.g., with more than 30,000 observations; note that the Time Series module is unique in that it will take full advantage of your computer's memory, and it will not impose fixed limitations on the lengths of time series that can be analyzed).  Melard's exact maximum likelihood method (number 3 above) may also become inefficient when used to estimate parameters for seasonal models with long seasonal lags (e.g., with yearly lags of 365 days).  On the other hand, the Time Series module will always use the approximate maximum likelihood method first in order to establish initial parameter estimates that are very close to the actual final values; thus, usually only a few iterations with the exact maximum likelihood method (3, above) are necessary to finalize the parameter estimates.

Parameter standard errors.  For all parameter estimates, the Time Series module will compute so-called asymptotic standard errors.  These are computed from the matrix of second-order partial derivatives that is approximated via finite differencing (see also the respective discussion in Nonlinear Estimation).

Penalty value.  As mentioned above, the estimation procedure requires that the (conditional) sums of squares of the ARIMA residuals be minimized.  If the model is inappropriate, it may happen during the iterative estimation process that the parameter estimates become very large, and, in fact, invalid.  In that case, the program will assign a very large value (a so-called penalty value) to the SS.  This usually "entices" the iteration process to move the parameters away from invalid ranges.  However, in some cases even this strategy fails, and you may see on the screen (during the Estimation procedure) very large values for the SS in consecutive iterations.  In that case, carefully evaluate the appropriateness of your model.  If your model contains many parameters, and perhaps an intervention component (see below), you may try again with different parameter start values.


ARIMA Introductory Overview - Evaluation of the Model

  Time Series Analysis ARIMA Introductory Overview - Evaluation of the Model

Parameter estimates.  The Time Series module will report approximate t values, computed from the parameter standard errors (see above).  If not significant, the respective parameter can in most cases be dropped from the model without affecting substantially the overall fit of the model.

Other quality criteria.  Another straightforward and common measure of the reliability of the model is the accuracy of its forecasts generated based on partial data so that the forecasts can be compared with known (original) observations; this test is illustrated in the ARIMA Example  in the manual.  However, a good model should not only provide sufficiently accurate forecasts, it should also be parsimonious and produce statistically independent residuals that contain only noise and no systematic components (e.g., the correlogram of residuals should not reveal any serial dependencies).  A good test of the model is (a) to plot the residuals and inspect them for any systematic trends, and (b) to examine the autocorrelogram of residuals (there should be no serial dependency between residuals).

Analysis of residuals.  The major concern here is that the residuals are systematically distributed across the series (e.g., they could be negative in the first part of the series and approach zero in the second part) or that they contain some serial dependency which may suggest that the ARIMA model is inadequate.  The analysis of ARIMA residuals constitutes an important test of the model.  The estimation procedure assumes that the residual are not (auto-) correlated and that they are normally distributed.  The Time Series module will automatically compute the residuals, and make them available for further analyses with all other methods available in this module; residuals can also be saved to a data file, together with the original series or its transformations.

Limitations.  The ARIMA method is appropriate only for a time series that is stationary (i.e., its mean, variance, and autocorrelation should be approximately constant through time) and it is recommended that there are at least 50 observations in the input data.  It is also assumed that the values of the estimated parameters are constant throughout the series.


  Time Series Analysis - Interrupted Time Series ARIMA

A common research questions in time series analysis is whether an outside event affected subsequent observations.  For example, did the implementation of a new economic policy improve economic performance; did the a new anti-crime law affect subsequent crime rates; and so on.  In general, we would like to evaluate the impact of one or more discrete events on the values in the time series.  This type of interrupted time series analysis is described in detail in McDowall, McCleary, Meidinger, & Hay (1980).  McDowall, et. al., distinguish between three major types of impacts that are possible: (1) permanent abrupt, (2) permanent gradual, and (3) abrupt temporary.  These different impact patterns can be reviewed in the Impact patterns dialog.

Abrupt Permanent Impact

Gradual Permanent Impact

Abrupt Temporary Impact

See also:

Identifying Patterns in Time Series Data

ARIMA Introductory Overview

Exponential Smoothing

Seasonal Decomposition (Census I)

X-11 Census method II seasonal adjustment

X-11 Census method II result tables

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis

Basic Notations and Principles

Fast Fourier Transformations


  Time Series Analysis - Exponential Smoothing

General Introduction

Simple Exponential Smoothing

Choosing the Best Value for Parameter α (alpha)

Indices of Lack of Fit (Error)

Seasonal and Non-seasonal Models With or Without Trend

Summary of Available Exponential Smoothing Models

See also:

Identifying Patterns in Time Series Data

ARIMA (Box & Jenkins) and Autocorrelations

ARIMA Introductory Overview

Interrupted Time Series

Seasonal Decomposition (Census I)

X-11 Census method II seasonal adjustment

X-11 Census method II result tables

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis

Basic Notations and Principles

Fast Fourier Transformations


Exponential Smoothing - General Introduction

  Time Series Analysis Exponential Smoothing - General Introduction

Exponential smoothing has become very popular as a forecasting method for a wide variety of time series data.  Historically, the method was independently developed by Brown and Holt.  Brown worked for the US Navy during World War II, where his assignment was to design a tracking system for fire-control information to compute the location of submarines.  Later, he applied this technique to the forecasting of demand for spare parts (an inventory control problem).  He described those ideas in his 1959 book on inventory control.  Holt's research was sponsored by the Office of Naval Research; independently, he developed exponential smoothing models for constant processes, processes with linear trends, and for seasonal data.

The implementation of exponential smoothing methods in STATISTICA follows closely the survey of techniques presented by Gardner (1985), who proposed a "unified" classification of exponential smoothing methods.  Excellent introductions can also be found in Makridakis, Wheelwright, and McGee (1983), Makridakis and Wheelwright (1989), Montgomery, Johnson, & Gardiner (1990).


Exponential Smoothing - Simple Exponential Smoothing

  Time Series Analysis Exponential Smoothing - Simple Exponential Smoothing

A simple and pragmatic model for a time series would be to consider each observation as consisting of a constant (b) and an error component ε (epsilon), that is: Xt=b+εt.  The constant b is relatively stable in each segment of the series, but may change slowly over time.  If appropriate, then one way to isolate the true value of b, and thus the systematic or predictable part of the series, is to compute a kind of moving average, where the current and immediately preceding ("younger") observations are assigned greater weight than the respective older observations.  Simple exponential smoothing accomplishes exactly such weighting, where exponentially smaller weights are assigned to older observations.  The specific formula for simple exponential smoothing is:

S = α*X +(1-α)*S

 t     t        t-1

When applied recursively to each successive observation in the series, each new smoothed value (forecast) is computed as the weighted average of the current observation and the previous smoothed observation; the previous smoothed observation was computed in turn from the previous observed value and the smoothed value before the previous observation, and so on.  Thus, in effect, each smoothed value is the weighted average of the previous observations, where the weights decrease exponentially depending on the value of parameter α (alpha).  If α is equal to 1 (one) then the previous observations are ignored entirely; if α is equal to 0 (zero), then the current observation is ignored entirely, and the smoothed value consists entirely of the previous smoothed value (which in turn is computed from the smoothed observation before it, and so on; thus all smoothed values will be equal to the initial smoothed value S0).  Values of α in-between will produce intermediate results.

Even though significant work has been done to study the theoretical properties of (simple and complex) exponential smoothing (e.g., see Gardner, 1985; Muth, 1960; see also McKenzie, 1984, 1985), the method has gained popularity mostly because of its usefulness as a forecasting tool.  For example, empirical research by Makridakis et al. (1982, Makridakis, 1983), has shown simple exponential smoothing to be the best choice for one-period-ahead forecasting, from among 24 other time series methods and using a variety of accuracy measures (see also Gross and Craig, 1974, for additional empirical evidence).  Thus, regardless of the theoretical model for the process underlying the observed time series, simple exponential smoothing will often produce quite accurate forecasts.


Exponential Smoothing - Choosing the Best Value for Parameter Alpha

  Time Series Analysis Exponential Smoothing - Choosing the Best Value for Parameter α (alpha)

Gardner (1985) discusses various theoretical and empirical arguments for selecting an appropriate smoothing parameter.  Obviously, looking at the formula presented above, α should fall into the interval between 0 (zero) and 1 (although, see Brenner et al., 1968, for an ARIMA perspective, implying 0<α<2).  Gardner (1985) reports that among practitioners, an α smaller than .30 is usually recommended.  However, in the study by Makridakis et al. (1982), α values above .30 frequently yielded the best forecasts.  After reviewing the literature on this topic, Gardner (1985) concludes that it is best to estimate an optimum α from the data (see below), rather than to "guess" and set an artificially low value.

Estimating the best α value from the data.  In practice, the smoothing parameter is often chosen by a grid search of the parameter space; that is, different solutions for α are tried starting, for example, with α = 0.1 to α = 0.9, with increments of 0.1.  Then α is chosen so as to produce the smallest sums of squares (or mean squares) for the residuals (i.e., observed values minus one-step-ahead forecasts; this mean squared error is also referred to as ex post mean squared error, ex post MSE for short).  The Time Series module provides an option to perform a grid search, and also allows the user to automatically search for the best α parameter via a general function minimization procedure (see below).


Exponential Smoothing - Indices of Lack of Fit (Error)

  Time Series Analysis Exponential Smoothing - Indices of Lack of Fit (Error)

The most straightforward way of evaluating the accuracy of the forecasts based on a particular α value is to simply plot the observed values and the one-step-ahead forecasts.  In the Time Series module, this plot will also include the residuals (scaled against the right Y-axis), so that regions of better or worst fit can also easily be identified.  This visual check of the accuracy of forecasts is often the most powerful method for determining whether or not the current exponential smoothing model fits the data.  In addition, besides the ex post MSE criterion (see previous paragraph), there are other statistical measures of error that can be used to determine the optimum α parameter (see Makridakis, Wheelwright, and McGee, 1983; all measures will automatically be computed by the Time Series module):

Mean error:  The mean error (ME) value is simply computed as the average error value (average of observed minus one-step-ahead forecast).  Obviously, a drawback of this measure is that positive and negative error values can cancel each other out, so this measure is not a very good indicator of overall fit.

Mean absolute error:  The mean absolute error (MAE) value is computed as the average absolute error value.  If this value is 0 (zero), the fit (forecast) is perfect.  As compared to the mean squared error value, this measure of fit will "de-emphasize" outliers, that is, unique or rare large error values will affect the MAE less than the MSE value.

Sum of squared error (SSE), Mean squared error.  These values are computed as the sum (or average) of the squared error values.  This is the most commonly used lack-of-fit indicator in statistical fitting procedures.

Percentage error (PE).  All the above measures rely on the actual error value.  It may seem reasonable to rather express the lack of fit in terms of the relative deviation of the one-step-ahead forecasts from the observed values, that is, relative to the magnitude of the observed values.  For example, when trying to predict monthly sales that may fluctuate widely (e.g., seasonally) from month to month, we may be satisfied if our prediction "hits the target" with about ±10% accuracy.  In other words, the absolute errors may be not so much of interest as are the relative errors in the forecasts.  To assess the relative error, various indices have been proposed (see Makridakis, Wheelwright, and McGee, 1983).  The first one, the percentage error value, is computed as:

PE  = 100*(X -F )/X

  t         t  t   t

where Xt is the observed value at time t, and Ft is the forecasts (smoothed values).

Mean percentage error (MPE).  This value is computed as the average of the PE values.

Mean absolute percentage error (MAPE).  As is the case with the mean error value (ME, see above), a mean percentage error near 0 (zero) can be produced by large positive and negative percentage errors that cancel each other out.  Thus, a better measure of relative overall fit is the mean absolute percentage error.  Also, this measure is usually more meaningful than the mean squared error.  For example, knowing that the average forecast is "off" by ±5% is a useful result in and of itself, whereas a mean squared error of 30.8 is not immediately interpretable.

Automatic search for best parameter.  The Time Series module effectively takes the guessing out of the parameter search process.  A quasi-Newton function minimization procedure (the same as in ARIMA, see also Automatic parameter search) is used to minimize either the mean squared error, mean absolute error, or mean absolute percentage error.  In most cases, this procedure is more efficient than the grid search (particularly when more than one parameter must be determined), and the optimum α parameter can quickly be identified.

The first smoothed value S0.  A final issue that we have neglected up to this point is the problem of the initial value, or how to start the smoothing process.  If you look back at the formula above, it is evident that one needs an S0 value in order to compute the smoothed value (forecast) for the first observation in the series.  Depending on the choice of the α parameter (i.e., when α is close to zero), the initial value for the smoothing process can affect the quality of the forecasts for many observations.  As with most other aspects of exponential smoothing it is recommended to choose the initial value that produces the best forecasts.  On the other hand, in practice, when there are many leading observations prior to a crucial actual forecast, the initial value will not affect that forecast by much, since its effect will have long "faded" from the smoothed series (due to the exponentially decreasing weights, the older an observation the less it will influence the forecast).  The Time Series module allows for user-defined initial values, but will also automatically compute initial values (see description of actual smoothing methods below).


Exponential Smoothing - Seasonal and Non-seasonal Models With or Without Trend

  Time Series Analysis Exponential Smoothing - Seasonal and Non-seasonal Models With or Without Trend

The discussion above in the context of simple exponential smoothing introduced the basic procedure for identifying a smoothing parameter, and for evaluating the goodness-of-fit of a model.  In addition to simple exponential smoothing, more complex models have been developed to accommodate time series with seasonal and trend components.  The general idea here is that forecasts are not only computed from consecutive previous observations (as in simple exponential smoothing), but an independent (smoothed) trend and seasonal component can be added.  The STATISTICA Time Series module follows the two-way classification system proposed by Gardner (1985), who discusses the different models in terms of seasonality (none, additive, or multiplicative) and trend (none, linear, exponential, or damped).

Additive and multiplicative seasonality.  Many time series data follow recurring seasonal patterns (see also Classical Seasonal Decomposition).  For example, annual sales of toys will probably peak in the months of November and December, and perhaps during the summer (with a much smaller peak) when children are on their summer break.  This pattern will likely repeat every year, however, the relative amount of increase in sales during December may slowly change from year to year.  Thus, it may be useful to smooth the seasonal component independently with an extra parameter, usually denoted as δ (delta).  Seasonal components can be additive in nature or multiplicative.  For example, during the month of December the sales for a particular toy may increase by 1 million dollars every year.  Thus, we could add to our forecasts for every December the amount of 1 million dollars (over the respective annual average) to account for this seasonal fluctuation.  In this case, the seasonality is additive.  Alternatively, during the month of December the sales for a particular toy may increase by 40%, that is, increase by a factor of 1.4.  Thus, when the sales for the toy are generally weak, than the absolute (dollar) increase in sales during December will be relatively weak (but the percentage will be constant); if the sales of the toy are strong, than the absolute (dollar) increase in sales will be proportionately greater.  Again, in this case the sales increase by a certain factor, and the seasonal component is thus multiplicative in nature (i.e., the multiplicative seasonal component in this case would be 1.4).  In plots of the series, the distinguishing characteristic between these two types of seasonal components is that in the additive case, the series shows steady seasonal fluctuations, regardless of the overall level of the series; in the multiplicative case, the size of the seasonal fluctuations vary, depending on the overall level of the series.

The seasonal smoothing parameter δ.  In general the one-step-ahead forecasts are computed as (for no trend models, for linear and exponential trend models a trend component is added to the model; see below):

Additive model:

Forecast  = S +I

        t    t  t-p

Multiplicative model:

Forecast  = S *I

        t    t  t-p

In this formula, St stands for the (simple) exponentially smoothed value of the series at time t, and It-p stands for the smoothed seasonal factor at time t minus p (the length of the season).  Thus, compared to simple exponential smoothing, the forecast is "enhanced" by adding or multiplying the simple smoothed value by the predicted seasonal component.  This seasonal component is derived analogous to the St value from simple exponential smoothing as:

Additive model:

I  = I   +δ*(1-α)*e

 t    t-p          t

Multiplicative model:

I  = I   +δ*(1-α)*e /S

 t    t-p          t  t

Put in words, the predicted seasonal component at time t is computed as the respective seasonal component in the last seasonal cycle plus a portion of the error (et; the observed minus the forecast value at time t).  Considering the formulas above, it is clear that parameter δ can assume values between 0 and 1.  If it is zero, then the seasonal component for a particular point in time is predicted to be identical to the predicted seasonal component for the respective time during the previous seasonal cycle, which in turn is predicted to be identical to that from the previous cycle, and so on.  Thus, if δ is zero, a constant unchanging seasonal component is used to generate the one-step-ahead forecasts.  If the δ parameter is equal to 1, then the seasonal component is modified "maximally" at every step by the respective forecast error (times 1-α, which we will ignore for the purpose of this brief introduction).  In most cases, when seasonality is present in the time series, the optimum δ parameter will fall somewhere between 0 (zero) and 1(one).

Linear, exponential, and damped trend.  To remain with the toy example above, the sales for a toy can show a linear upward trend (e.g., each year, sales increase by 1 million dollars), exponential growth (e.g., each year, sales increase by a factor of 1.3), or a damped trend (during the first year sales increase by 1 million dollars; during the second year the increase is only 80% over the previous year, i.e., $800,000; during the next year it is again 80% less than the previous year, i.e., $800,000 * .8 = $640,000; etc.).  Each type of trend leaves a clear "signature" that can usually be identified in the series; shown below in the brief discussion of the different models are icons that illustrate the general patterns.  In general, the trend factor may change slowly over time, and, again, it may make sense to smooth the trend component with a separate parameter (denoted γ [gamma] for linear and exponential trend models, and φ [phi] for damped trend models).

The trend smoothing parameters γ (linear and exponential trend) and φ (damped trend).  Analogous to the seasonal component, when a trend component is included in the exponential smoothing process, an independent trend component is computed for each time, and modified as a function of the forecast error and the respective parameter.  If the γ parameter is 0 (zero), than the trend component is constant across all values of the time series (and for all forecasts).  If the parameter is 1, then the trend component is modified "maximally" from observation to observation by the respective forecast error.  Parameter values that fall in-between represent mixtures of those two extremes.  Parameter φ is a trend modification parameter, and affects how strongly changes in the trend will affect estimates of the trend for subsequent forecasts, that is, how quickly the trend will be "damped" or increased.


Exponential Smoothing - Summary of Available Exponential Smoothing Models

  Time Series Analysis Exponential Smoothing - Summary of Available Exponential Smoothing Models

A listing of available exponential smoothing models (as described in Gardner, 1985) is given in Exponential Smoothing Models.  The specific formulas for computing the one-step-ahead forecasts are also provided in the Gardner reference, and will not be repeated in the Exponential Smoothing Models topic.


Time Series Analysis - Classical Seasonal Decomposition (Census Method I)

  Time Series Analysis - Classical Seasonal Decomposition (Census Method 1)

General Introduction

Computations

See also:

Identifying Patterns in Time Series Data

ARIMA (Box & Jenkins) and Autocorrelations

ARIMA Introductory Overview

Interrupted Time Series

Exponential Smoothing

X-11 Census method II seasonal adjustment

X-11 Census method II result tables

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis

Basic Notations and Principles

Fast Fourier Transformations


Classical Seasonal Decomposition (Census Method I) - General Introduction

  Time Series Analysis Classical Seasonal Decomposition (Census Method 1) - General Introduction

Suppose you recorded the monthly passenger load on international flights for a period of 12 years (such data are included in the example data file Series_g.sta, see also Box & Jenkins, 1976).  If you plot those data, it is apparent that (1) there appears to be a linear upwards trend in the passenger loads over the years, and (2) there is a recurring pattern or seasonality within each year (i.e., most travel occurs during the summer months, and a minor peak occurs during the December holidays).  The purpose of the seasonal decomposition method is to isolate those components, that is, to de-compose the series into the trend effect, seasonal effects, and remaining variability.  The "classic" technique designed to accomplish this decomposition is known as the Census I method.  This technique is described and discussed in detail in Makridakis, Wheelwright, and McGee (1983), and Makridakis and Wheelwright (1989).

General model.  The general idea of seasonal decomposition is straightforward.  In general, a time series like the one described above can be thought of as consisting of four different components: (1) A seasonal component (denoted as St, where t stands for the particular point in time) (2) a trend component (Tt), (3) a cyclical component (Ct), and (4) a random, error, or irregular component (It).  The difference between a cyclical and a seasonal component is that the latter occurs at regular (seasonal) intervals, while cyclical factors have usually a longer duration that varies from cycle to cycle.  In the Census I method, the trend and cyclical components are customarily combined into a trend-cycle component (TCt).  The specific functional relationship between these components can assume different forms.  However, two straightforward possibilities are that they combine in an additive or a multiplicative fashion:

Additive model:

X  = TC +S +I

 t     t  t  t

Multiplicative model:

X  = T *C *S *I

 t    t  t  t  t

Here Xt stands for the observed value of the time series at time t.  Given some a priori knowledge about the cyclical factors affecting the series (e.g., business cycles), the estimates for the different components can be used to compute forecasts for future observations.  (However, the Exponential smoothing method, which can also incorporate seasonality and trend components, is the preferred technique for forecasting purposes.)

Additive and multiplicative seasonality.  Let us consider the difference between an additive and multiplicative seasonal component in an example:  The annual sales of toys will probably peak in the months of November and December, and perhaps during the summer (with a much smaller peak) when children are on their summer break.  This seasonal pattern will likely repeat every year.  Seasonal components can be additive or multiplicative in nature.  For example, during the month of December the sales for a particular toy may increase by 3 million dollars every year.  Thus, we could add to our forecasts for every December the amount of 3 million to account for this seasonal fluctuation.  In this case, the seasonality is additive.  Alternatively, during the month of December the sales for a particular toy may increase by 40%, that is, increase by a factor of 1.4.  Thus, when the sales for the toy are generally weak, then the absolute (dollar) increase in sales during December will be relatively weak (but the percentage will be constant); if the sales of the toy are strong, then the absolute (dollar) increase in sales will be proportionately greater.  Again, in this case the sales increase by a certain factor, and the seasonal component is thus multiplicative in nature (i.e., the multiplicative seasonal component in this case would be 1.4).  In plots of series, the distinguishing characteristic between these two types of seasonal components is that in the additive case, the series shows steady seasonal fluctuations, regardless of the overall level of the series; in the multiplicative case, the size of the seasonal fluctuations vary, depending on the overall level of the series.

Additive and multiplicative trend-cycle.  We can extend the previous example to illustrate the additive and multiplicative trend-cycle components.  In terms of our toy example, a "fashion" trend may produce a steady increase in sales (e.g., a trend towards more educational toys in general); as with the seasonal component, this trend may be additive (sales increase by 3 million dollars per year) or multiplicative (sales increase by 30%, or by a factor of 1.3, annually) in nature.  In addition, cyclical components may impact sales; to reiterate, a cyclical component is different from a seasonal component in that it usually is of longer duration, and that it occurs at irregular intervals.  For example, a particular toy may be particularly "hot" during a summer season (e.g., a particular doll which is tied to the release of a major children's movie, and is promoted with extensive advertising).  Again such a cyclical component can effect sales in an additive manner or multiplicative manner.


Classical Seasonal Decomposition (Census Method I) - Computations

  Time Series Analysis Classical Seasonal Decomposition (Census Method 1) - Computations

Computationally, the Seasonal Decomposition (Census I) procedure of the Time Series module closely follows the standard formulas, as shown in Makridakis, Wheelwright, and McGee (1983), and Makridakis and Wheelwright (1989).

Moving average.  First a moving average is computed for the series, with the moving average window width equal to the length of one season.  If the length of the season is even, then the user can choose to use either equal weights for the moving average or unequal weights can be used, where the first and last observation in the moving average window are averaged (select the Centered option in the Seasonal Decomposition (Census I) dialog).

Ratios or differences.  In the moving average series, all seasonal (within-season) variability will be eliminated; thus, the differences (in additive models) or ratios (in multiplicative models) of the observed and smoothed series will isolate the seasonal component (plus irregular component).  Specifically, the moving average is subtracted from the observed series (for additive models) or the observed series is divided by the moving average values (for multiplicative models).

Seasonal components.  The seasonal component is then computed as the average (for additive models) or medial average (for multiplicative models) for each point in the season.  (The medial average of a set of values is the mean after the smallest and largest values are excluded).  The resulting values represent the (average) seasonal component of the series.

Seasonally adjusted series.  The original series can be adjusted by subtracting from it (additive models) or dividing it by (multiplicative models) the seasonal component.  The resulting series is the seasonally adjusted series (i.e., the seasonal component will be removed).

Trend-cycle component.  Remember that the cyclical component is different from the seasonal component in that it is usually longer than one season, and different cycles can be of different lengths.  The combined trend and cyclical component can be approximated by applying to the seasonally adjusted series a 5 point (centered) weighed moving average smoothing transformation with the weights of 1, 2, 3, 2, 1.

Random or irregular component.  Finally, the random or irregular (error) component can be isolated by subtracting from the seasonally adjusted series (additive models) or dividing the adjusted series by (multiplicative models) the trend-cycle component.


  Time Series Analysis - X-11 Census Method II Seasonal Adjustment

The general ideas of seasonal decomposition and adjustment are discussed in the context of the Census I seasonal adjustment method (Seasonal Decomposition (Census I)).  The Census method II (2) is an extension and refinement of the simple adjustment method.  Over the years, different versions of the Census method II evolved at the Census Bureau; the method that has become most popular and is used most widely in government and business is the so-called X-11 variant of the Census method II (see Hiskin, Young, & Musgrave, 1967).  Subsequently, the term X-11 has become synonymous with this refined version of the Census method II.  In addition to the documentation that can be obtained from the Census Bureau, a detailed summary of this method is also provided in Makridakis, Wheelwright, and McGee (1983) and Makridakis and Wheelwright (1989).

For more information on this method, see the following topics:

Seasonal Adjustment: Basic Ideas and Terms

The Census II Method

Results Tables Computed by the X-11 Method

Specific Description of all Results Tables Computed by the X-11 Method

For more information on other Time Series methods, see Time Series Analysis - Index and the following topics:

Identifying Patterns in Time Series Data

ARIMA (Box & Jenkins) and Autocorrelations

ARIMA Introductory Overview

Interrupted Time Series

Exponential Smoothing

Seasonal Decomposition (Census I)

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis

Basic Notations and Principles

Fast Fourier Transformations


  Time Series Analysis - Seasonal Adjustment: Basic Ideas and Terms

Suppose you recorded the monthly passenger load on international flights for a period of 12 years (such data are included in the example data file Series_g.sta, see also Box & Jenkins, 1976).  If you plot those data, it is apparent that (1) there appears to be an upwards linear trend in the passenger loads over the years, and (2) there is a recurring pattern or seasonality within each year (i.e., most travel occurs during the summer months, and a minor peak occurs during the December holidays).  The purpose of seasonal decomposition and adjustment is to isolate those components, that is, to de-compose the series into the trend effect, seasonal effects, and remaining variability.  The "classic" technique designed to accomplish this decomposition was developed in the 1920's and is also known as the Census I method (see the Census I overview section).  This technique is also described and discussed in detail in Makridakis, Wheelwright, and McGee (1983), and Makridakis and Wheelwright (1989).

General model.  The general idea of seasonal decomposition is straightforward.  In general, a time series like the one described above can be thought of as consisting of four different components: (1) A seasonal component (denoted as St, where t stands for the particular point in time) (2) a trend component (Tt), (3) a cyclical component (Ct), and (4) a random, error, or irregular component (It).  The difference between a cyclical and a seasonal component is that the latter occurs at regular (seasonal) intervals, while cyclical factors usually have a longer duration that varies from cycle to cycle.  The trend and cyclical components are customarily combined into a trend-cycle component (TCt).  The specific functional relationship between these components can assume different forms.  However, two straightforward possibilities are that they combine in an additive or a multiplicative fashion:

Additive Model:

X  = TC +S +I

 t     t  t  t

Multiplicative Model:

X  = T *C *S *I

 t    t  t  t  t

Where:

Xt	represents the observed value of the time series at time t.

Given some a priori knowledge about the cyclical factors affecting the series (e.g., business cycles), the estimates for the different components can be used to compute forecasts for future observations.  (However, the Exponential smoothing method, which can also incorporate seasonality and trend components, is the preferred technique for forecasting purposes.)

Additive and multiplicative seasonality.  Consider the difference between an additive and multiplicative seasonal component in an example:  The annual sales of toys will probably peak in the months of November and December, and perhaps during the summer (with a much smaller peak) when children are on their summer break.  This seasonal pattern will likely repeat every year.  Seasonal components can be additive or multiplicative in nature.  For example, during the month of December the sales for a particular toy may increase by 3 million dollars every year.  Thus, you could add to your forecasts for every December the amount of 3 million to account for this seasonal fluctuation.  In this case, the seasonality is additive.  Alternatively, during the month of December the sales for a particular toy may increase by 40%, that is, increase by a factor of 1.4.  Thus, when the sales for the toy are generally weak, then the absolute (dollar) increase in sales during December will be relatively weak (but the percentage will be constant); if the sales of the toy are strong, then the absolute (dollar) increase in sales will be proportionately greater.  Again, in this case the sales increase by a certain factor, and the seasonal component is thus multiplicative in nature (i.e., the multiplicative seasonal component in this case would be 1.4).  In plots of series, the distinguishing characteristic between these two types of seasonal components is that in the additive case, the series shows steady seasonal fluctuations, regardless of the overall level of the series; in the multiplicative case, the size of the seasonal fluctuations vary, depending on the overall level of the series.

Additive and multiplicative trend-cycle.  The previous example can be extended to illustrate the additive and multiplicative trend-cycle components.  In terms of the toy example, a "fashion" trend may produce a steady increase in sales (e.g., a trend towards more educational toys in general); as with the seasonal component, this trend may be additive (sales increase by 3 million dollars per year) or multiplicative (sales increase by 30%, or by a factor of 1.3, annually) in nature.  In addition, cyclical components may impact sales.  To reiterate, a cyclical component is different from a seasonal component in that it usually is of longer duration, and that it occurs at irregular intervals.  For example, a particular toy may be particularly "hot" during a summer season (e.g., a particular doll which is tied to the release of a major children's movie, and is promoted with extensive advertising).  Again such a cyclical component can effect sales in an additive manner or multiplicative manner.


  Time Series Analysis - The Census II Method

The basic method for seasonal decomposition and adjustment outlined in the Basic Ideas and Terms topic can be refined in several ways.  In fact, unlike many other time-series modeling techniques (e.g., ARIMA) which are grounded in some theoretical model of an underlying process, the X-11 variant of the Census II method simply contains many ad hoc features and refinements, that over the years have proven to provide excellent estimates for many real-world applications (see Burman, 1979, Kendal & Ord, 1990, Makridakis & Wheelwright, 1989; Wallis, 1974).  Some of the major refinements are listed below.

Trading-day adjustment.  Different months have different numbers of days, and different numbers of trading-days (i.e., Mondays, Tuesdays, etc.).  When analyzing, for example, monthly revenue figures for an amusement park, the fluctuation in the different numbers of Saturdays and Sundays (peak days) in the different months will surely contribute significantly to the variability in monthly revenues.  The X-11 variant of the Census II method allows the user to test whether such trading-day variability exists in the series, and, if so, to adjust the series accordingly.

Extreme values.  Most real-world time series contain outliers, that is, extreme fluctuations due to rare events.  For example, a strike may affect production in a particular month of one year.  Such extreme outliers may bias the estimates of the seasonal and trend components.  The X-11 procedure includes provisions to deal with extreme values through the use of "statistical control principles," that is, values that are above or below a certain range (expressed in terms of multiples of sigma, the standard deviation) can be modified or dropped before final estimates for the seasonality are computed.

Multiple refinements.  The refinement for outliers, extreme values, and different numbers of trading-days can be applied more than once, in order to obtain successively improved estimates of the components.  The X-11 method applies a series of successive refinements of the estimates to arrive at the final trend-cycle, seasonal, and irregular components, and the seasonally adjusted series.

Tests and summary statistics.  In addition to estimating the major components of the series, various summary statistics can be computed.  For example, analysis of variance tables can be prepared to test the significance of seasonal variability and trading-day variability (see above) in the series; the X-11 procedure will also compute the percentage change from month to month in the random and trend-cycle components.  As the duration or span in terms of months (or quarters for quarterly X-11) increases, the change in the trend-cycle component will likely also increase, while the change in the random component should remain about the same.  The width of the average span at which the changes in the random component are about equal to the changes in the trend-cycle component is called the month (quarter) for cyclical dominance, or MCD (QCD) for short.  For example, if the MCD is equal to 2 then one can infer that over a 2 month span the trend-cycle will dominate the fluctuations of the irregular (random) component.  These and various other results are discussed in greater detail below.


  Time Series Analysis - Result Tables Computed by the X-11 Method

The computations performed by the X-11 procedure are best discussed in the context of the results tables that are reported.  The adjustment process is divided into seven major steps, which are customarily labeled with consecutive letters A through G.

A    Prior adjustment (monthly seasonal adjustment only).

Before any seasonal adjustment is performed on the monthly time series, various prior user-defined adjustments can be incorporated.  The user can specify a second series that contains prior adjustment factors; the values in that series will either be subtracted (additive model) from the original series, or the original series will be divided by these values (multiplicative model).  For multiplicative models, user-specified trading-day adjustment weights can also be specified.  These weights will be used to adjust the monthly observations depending on the number of respective trading-days represented by the observation.

B    Preliminary estimation of trading-day variation (monthly X-11) and weights.

Next, preliminary trading-day adjustment factors (monthly X-11 only) and weights for reducing the effect of extreme observations are computed.

C    Final estimation of trading-day variation and irregular weights (monthly X-11).

The adjustments and weights computed in B above are then used to derive improved trend-cycle and seasonal estimates.  These improved estimates are used to compute the final trading-day factors (monthly X-11 only) and weights.

D    Final estimation of seasonal factors, trend-cycle, irregular, and seasonally adjusted series.  The final trading-day factors and weights computed in C above are used to compute the final estimates of the components.

E    Modified original, seasonally adjusted, and irregular series.

The original and final seasonally adjusted series, and the irregular component are modified for extremes.  The resulting modified series allow the user to examine the stability of the seasonal adjustment.

F    Month (quarter) for cyclical dominance (MCD, QCD), moving average, and summary measures.

In this part of the computations, various summary measures (see below) are computed to allow the user to examine the relative importance of the different components, the average fluctuation from month-to-month (quarter-to-quarter), the average number of consecutive changes in the same direction (average number of runs), etc.

G   Charts.

Finally, the program will compute various charts (graphs) to summarize the results.  For example, the final seasonally adjusted series will be plotted, in chronological order, or by month (see below).

For a specific description of the tables and charts, see Specific Description of all Results Tables Computed by the X-11 Method.


  Time Series Analysis - Specific Description of all Result Tables Computed by the X-11 Method

In each part A through G of the analysis (see Results Tables Computed by the X-11 Method), different result tables are computed.  Customarily, these tables are numbered, and also identified by a letter to indicate the respective part of the analysis.  For example, table B 11 shows the initial seasonally adjusted series; C 11 is the refined seasonally adjusted series, and D 11 is the final seasonally adjusted series.  Shown below is a list of all available tables.  Those tables identified by an asterisk (*) are not available (applicable) when analyzing quarterly series.  (Also, for quarterly adjustment, some of the computations outlined below are slightly different; for example instead of a 12-term [monthly] moving average, a 4-term [quarterly] moving average is applied to compute the seasonal factors; the initial trend-cycle estimate is computed via a centered 4-term moving average, the final trend-cycle estimate in each part is computed by a 5-term Henderson average.)

Following the convention of the Bureau of the Census version of the X-11 method, the STATISTICA implementation offers three levels of printout detail: Standard (17 to 27 tables), Long (27 to 39 tables), and Full (44 to 59 tables).  An option to only produce selected tables (Scrollsheets) is also provided (see the descriptions of the X-11 monthly seasonal adjustment and X-11 quarterly seasonal adjustment dialogs).  In the description of each table below, the letters S, L, and F are used next to each title to indicate, which tables will be displayed and/or printed at the respective setting of the output option.  (For the charts, two levels of detail are available: Standard and All.)

Click on the table name below, to obtain more information about that table.

*A 1.  Original series (S)

*A 2.  Prior monthly adjustment factors (S)

*A 3.  Original series adjusted by prior monthly adjustment factors (S)

*A 4. Prior trading-day adjustment factors (S)

B 1. Prior adjusted series or original series (S)

B 2. Trend-cycle (L)

B 3. Unmodified S-I differences or ratios (F)

B 4. Replacement values for extreme S-I differences (ratios) (F)

B 5. Seasonal factors (F)

B 6. Seasonally adjusted series (F)

B 7. Trend-cycle (L)

B 8. Unmodified S-I differences (ratios) (F)

B 9. Replacement values for extreme S-I differences (ratios) (F)

B 10.  Seasonal factors (L)

B 11. Seasonally adjusted series (F)

B 12. (not used)

B 13. Irregular series (L)

Tables B 14 through B 16, B18, and B19: Adjustment for trading-day variation.  These tables are only available when analyzing monthly series.  Different months contain different numbers of days of the week (i.e., Mondays, Tuesdays, etc.).  In some series, the variation in the different numbers of trading-days may contribute significantly to monthly fluctuations (e.g., the monthly revenues of an amusement park will be greatly influenced by the number of Saturdays/Sundays in each month).  The user can specify initial weights for each trading-day (see A 4), and/or these weights can be estimated from the data (the user can also choose to apply those weights conditionally, i.e., only if they explain a significant proportion of variance; see the description of the X-11 monthly seasonal adjustment dialog).

*B 14. Extreme Irregular Values Excluded from Trading-day Regression (L)

*B 15.  Preliminary trading-day regression (L)

*B 16. Trading-day adjustment factors derived from regression coefficients (F)

B 17. Preliminary weights for irregular component (L)

*B 18. Trading-day factors derived from combined daily weights (F)

*B 19. Original series adjusted for trading-day and prior variation (F)

C 1. Original series modified by preliminary weights and adjusted for trading-day and prior variation (L)

C 2. Trend-cycle (F)

C 3. (not used)

C 4. Modified S-I differences (ratios) (F)

C 5. Seasonal factors (F)

C 6. Seasonally adjusted series (F)

C 7. Trend-cycle (L)

C 8. (not used)

C 9. Modified S-I differences (ratios) (F)

C 10. Seasonal factors (L)

C 11. Seasonally adjusted series (F)

C 12. (not used)

C 13. Irregular series (S)

Tables C 14 through C 16, C 18, and C 19: Adjustment for trading-day variation.  These tables are only available when analyzing monthly series, and when adjustment for trading-day variation is requested.  In that case, the trading-day adjustment factors are computed from the refined adjusted series, analogous to the adjustment performed in part B (B 14 through B 16, B 18 and B 19).

*C 14. Extreme irregular values excluded from trading-day regression (S)

*C 15.  Final trading-day regression (S)

*C 16. Final trading-day adjustment factors derived from regression coefficients (S)

C 17. Final weights for irregular component (S)

*C 18. Final trading-day factors derived from combined daily weights (S)

*C 19. Original series adjusted for trading-day and prior variation (S)

D 1. Original series modified by final weights and adjusted for trading-day and prior variation (L)

D 2. Trend-cycle (F)

D 3. (not used)

D 4. Modified S-I differences (ratios) (F)

D 5. Seasonal factors (F)

D 6. Seasonally adjusted series. (F)

D 7. Trend-cycle (L)

D 8. Final unmodified S-I differences (ratios) (S)

D 9. Final replacement values for extreme S-I differences (ratios) (S)

D 10. Final seasonal factors (S)

D 11. Final seasonally adjusted series (S)

D 12. Final trend-cycle (S)

D 13. Final irregular (S)

E 1. Modified original series (S)

E 2. Modified seasonally adjusted series (S)

E 3. Modified irregular series (S)

E 4. Differences (ratios) of annual totals (S)

E 5. Differences (percent changes) in original series (S)

E 6. Differences (percent changes) in final seasonally adjusted series (S)

F 1. MCD (QCD) moving average (S)

F 2. Summary measures (S)

G 1. Chart (S)

G 2. Chart (S)

G 3. Chart (A)

G 4. Chart (A)


  Time Series Analysis - Distributed Lags Analysis Introductory Overview

General Purpose

General Model

Almon Distributed Lag

For more information on other Time Series methods, see Time Series Analysis - Index and the following topics:

Identifying Patterns in Time Series Data

ARIMA (Box & Jenkins) and Autocorrelations

ARIMA Introductory Overview

Interrupted Time Series

Exponential Smoothing

Seasonal Decomposition (Census I)

X-11 Census method II seasonal adjustment

X-11 Census method II result tables

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis

Basic Notations and Principles

Fast Fourier Transformations


Distributed Lags Analysis - General Purpose

  Time Series Analysis Distributed Lags Analysis Introductory Overview - General Purpose

Distributed lags analysis is a specialized technique for examining the relationships between variables that involve some delay.  For example, suppose that you are a manufacturer of computer software, and you want to determine the relationship between the number of inquiries that are received, and the number of orders that are placed by your customers.  You could record those numbers monthly for a one year period, and then correlate the two variables.  However, obviously inquiries will precede actual orders, and one can expect that the number of orders will follow the number of inquiries with some delay.  Put another way, there will be a (time) lagged correlation between the number of inquiries and the number of orders that are received (see also autocorrelation and crosscorrelation).

Time-lagged correlations are particularly common in econometrics.  For example, the benefits of investments in new machinery usually only become evident after some time.  Higher income will change people's choice of rental apartments, however, this relationship will be lagged because it will take some time for people to terminate their current leases, find new apartments, and move.  In general, the relationship between capital appropriations and capital expenditures will be lagged, because it will require some time before investment decisions are actually acted upon.

In all of these cases, we have an independent or explanatory variable that affects the dependent variables with some lag.  The distributed lags method allows you to investigate those lags.

Detailed discussions of distributed lags correlation can be found in most econometrics textbooks, for example, in Judge, Griffith, Hill, Luetkepohl, and Lee (1985), Maddala (1977), and Fomby, Hill, and Johnson (1984).  In the following paragraphs we will present a brief description of these methods.  We will assume that you are familiar with the concept of correlation (see Basic Statistics), lagged cross-correlation, and the basic ideas of multiple regression (see Multiple Regression).


Distributed Lags Analysis - General Model

  Time Series Analysis Distributed Lags Analysis Introductory Overview - General Model

Suppose we have a dependent variable y and an independent or explanatory variable x which are both measured repeatedly over time.  In some textbooks, the dependent variable is also referred to as the endogenous variable, and the independent or explanatory variable the exogenous variable.  The simplest way to describe the relationship between the two would be in a simple linear relationship:

y  = Σ β *x

 t      i  t-i

In this equation, the value of the dependent variable at time t is expressed as a linear function of x measured at times t, t-1, t-2, etc.  Thus, the dependent variable is a linear function of x, and x is lagged by 1, 2, etc. time periods.  The beta weights (βi) can be considered slope parameters in this equation.  You may recognize this equation as a special case of the general linear regression equation (see the Multiple Regression overview).  If the weights for the lagged time periods are statistically significant, we can conclude that the y variable is predicted (or explained) with the respective lag.


Distributed Lags Analysis - Almon Distributed Lag

  Time Series Analysis Distributed Lags Analysis Introductory Overview - Almon Distributed Lag

A common problem that often arises when computing the weights for the multiple linear regression model shown above is that the values of adjacent (in time) values in the x variable are highly correlated.  In extreme cases, their independent contributions to the prediction of y may become so redundant that the correlation matrix of measures can no longer be inverted, and thus, the beta weights cannot be computed.  In less extreme cases, the computation of the beta weights and their standard errors can become very imprecise, due to round-off error.  In the context of Multiple Regression this general computational problem is discussed as the multicollinearity or matrix ill-conditioning issue.

Almon (1965) proposed a procedure that will reduce the multicollinearity in this case.  Specifically, suppose we express each weight in the linear regression equation in the following manner:

                            q

β  = α  + α *i + ... + α *i

 i    0    1            q

Almon could show that in many cases it is easier (i.e., it avoids the multicollinearity problem) to estimate the alpha values than the beta weights directly.  Note that with this method, the precision of the beta weight estimates is dependent on the degree or order of the polynomial approximation.

Misspecifications.  A general problem with this technique is that, of course, the lag length and correct polynomial degree are not known a priori.  The effects of misspecifications of these parameters are potentially serious (in terms of biased estimation).  This issue is discussed in greater detail in Frost (1975), Schmidt and Waud (1973), Schmidt and Sickles (1975), and Trivedi and Pagan (1979).


  Time Series Analysis - Single Spectrum (Fourier) Analysis

Spectrum analysis is concerned with the exploration of cyclical patterns of data.  The purpose of the analysis is to decompose a complex time series with cyclical components into a few underlying sinusoidal (sine and cosine) functions of particular wavelengths.  The term "spectrum" provides an appropriate metaphor for the nature of this analysis:  Suppose you study a beam of white sun light, which at first looks like a random (white noise) accumulation of light of different wavelengths.  However, when put through a prism, we can separate the different wave lengths or cyclical components that make up white sun light.  In fact, via this technique we can now identify and distinguish between different sources of light.  Thus, by identifying the important underlying cyclical components, we have learned something about the phenomenon of interest.  In essence, performing spectrum analysis on a time series is like putting the series through a prism in order to identify the wave lengths and importance of underlying cyclical components.  As a result of a successful analysis one might uncover just a few recurring cycles of different lengths in the time series of interest, which at first looked more or less like random noise.

A much cited example for spectrum analysis is the cyclical nature of sun spot activity (e.g., see Bloomfield, 1976, or Shumway, 1988).  It turns out that sun spot activity varies over 11 year cycles.  Other examples of celestial phenomena, weather patterns, fluctuations in commodity prices, economic activity, etc. are also often used in the literature to demonstrate this technique.  To contrast this technique with ARIMA or Exponential Smoothing, the purpose of spectrum analysis is to identify the seasonal fluctuations of different lengths, while in the former types of analysis, the length of the seasonal component is usually known (or guessed) a priori and then included in some theoretical model of moving averages or autocorrelations.

The classic text on spectrum analysis is Bloomfield (1976); however, other detailed discussions can be found in Jenkins and Watts (1968), Brillinger (1975), Brigham (1974), Elliott and Rao (1982), Priestley (1981), Shumway (1988), or Wei (1989).

For more information, see Time Series Analysis - Index and the following topics:

Basic Notations and Principles

Fast Fourier Transformations

Identifying Patterns in Time Series Data

ARIMA (Box & Jenkins) and Autocorrelations

ARIMA Introductory Overview

Interrupted Time Series

Distributed Lags Analysis

Seasonal Decomposition (Census I)

Exponential Smoothing

Cross-spectrum Analysis


  Time Series Analysis - Cross-spectrum Analysis

General Introduction

Basic Notation and Principles

Results for Each Variable

The Cross-periodogram, Cross-density, Quadrature-density, and Cross-amplitude

Squared Coherency, Gain, and Phase Shift

How the Example Data were Created

For more information, see Time Series Analysis - Index and the following topics:

Identifying Patterns in Time Series Data

ARIMA (Box & Jenkins) and Autocorrelations

ARIMA Introductory Overview

Interrupted Time Series

Exponential Smoothing

Seasonal Decomposition (Census I)

X-11 Census method II seasonal adjustment

X-11 Census method II result tables

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Basic Notations and Principles

Fast Fourier Transformations


Cross-spectrum analysis - General Introduction

  Time Series Analysis Cross-spectrum Analysis - General Introduction

Cross-spectrum analysis is an extension of Single Spectrum (Fourier) Analysis to the simultaneous analysis of two series.  In the following paragraphs, we will assume that you have already read the introduction to single spectrum analysis.  Detailed discussions of  this technique can be found in Bloomfield (1976), Jenkins and Watts (1968), Brillinger (1975), Brigham (1974), Elliott and Rao (1982), Priestley (1981), Shumway (1988), or Wei (1989).

Strong periodicity in the series at the respective frequency.  A much cited example for spectrum analysis is the cyclical nature of sun spot activity (e.g., see Bloomfield, 1976, or Shumway, 1988).  It turns out that sun spot activity varies over 11 year cycles.  Other examples of celestial phenomena, weather patterns, fluctuations in commodity prices, economic activity, etc. are also often used in the literature to demonstrate this technique.

The purpose of cross-spectrum analysis is to uncover the correlations between two series at different frequencies.  For example, sun spot activity may be related to weather phenomena here on earth.  If so, then if we were to record those phenomena (e.g., yearly average temperature) and submit the resulting series to a cross-spectrum analysis together with the sun spot data, we may find that the weather indeed correlates with the sunspot activity at the 11 year cycle.  That is, we may find a periodicity in the weather data that is "in-sync" with the sun spot cycles.  One can easily think of other areas of research where such knowledge could be very useful; for example, various economic indicators may show similar (correlated) cyclical behavior; various physiological measures likely will also display "coordinated" (i.e., correlated) cyclical behavior, and so on.


Cross-spectrum analysis - Basic Notation and Principles

  Time Series Analysis Cross-spectrum Analysis - Basic Notation and Principles

A simple example

Consider the following two series with 16 cases:

+--+--------+--------+

|  |    VAR1|    VAR2|

+--+--------+--------+

| 1|   1.000|   -.058|

| 2|   1.637|   -.713|

| 3|   1.148|   -.383|

| 4|   -.058|    .006|

| 5|   -.713|   -.483|

| 6|   -.383|  -1.441|

| 7|    .006|  -1.637|

| 8|   -.483|   -.707|

| 9|  -1.441|    .331|

|10|  -1.637|    .441|

|11|   -.707|   -.058|

|12|    .331|   -.006|

|13|    .441|    .924|

|14|   -.058|   1.713|

|15|   -.006|   1.365|

|16|    .924|    .266|

+--+--------+--------+

At first sight it is not easy to see the relationship between the two series.  However, as shown below the series were created so that they would contain two strong correlated periodicities.  Shown below are parts of the summary Scrollsheet from the cross-spectrum analysis (the spectral estimates were smoothed with a Parzen window of width 3).

+----------------------------------------------------------------------------+

|Indep.(X): VAR1                                                             |

|  Dep.(Y): VAR2                                                             |

+----------+----------+----------+----------+----------+----------+----------+

|          |          |     X    |     Y    |   Cross  |   Cross  |   Cross  |

| Frequncy |  Period  |  Density |  Density |  Density |   Quad   |  Amplit. |

+----------+----------+----------+----------+----------+----------+----------+

| 0.000000 |          |  .000000 |  .024292 |  -.00000 |  0.00000 |  .000000 |

|  .062500 | 16.00000 | 8.094709 | 7.798284 |  2.35583 | -7.58781 | 7.945114 |

|  .125000 |  8.00000 |  .058771 |  .100936 |  -.04755 |   .06059 |  .077020 |

|  .187500 |  5.33333 | 3.617294 | 3.845154 | -2.92645 |  2.31191 | 3.729484 |

|  .250000 |  4.00000 |  .333005 |  .278685 |  -.26941 |   .14221 |  .304637 |

|  .312500 |  3.20000 |  .091897 |  .067630 |  -.07435 |   .02622 |  .078835 |

|  .375000 |  2.66667 |  .052575 |  .036056 |  -.04253 |   .00930 |  .043539 |

|  .437500 |  2.28571 |  .040248 |  .026633 |  -.03256 |   .00342 |  .032740 |

|  .500000 |  2.00000 |  .037115 | 0.000000 |  0.00000 |  0.00000 | 0.000000 |

+----------+----------+----------+----------+----------+----------+----------+


Cross-spectrum analysis - Results for Each Variable

  Time Series Analysis Cross-spectrum Analysis - Results for Each Variable

The complete summary Scrollsheet contains all spectrum statistics computed for each variable, as described in the Single Spectrum (Fourier) Analysis overview section.  Looking at the results shown above, it is clear that both variables show strong periodicities at the frequencies .0625 and .1875.


Cross-spectrum analysis - The Cross-periodogram, Cross-density, Quadrature-density, and Cross-amplitude

  Time Series Analysis Cross-spectrum Analysis - Cross-periodogram, Cross-Density, Quadrature-density, Cross-amplitude

Analogous to the results for the single variables, the complete summary Scrollsheet will also display periodogram values for the cross periodogram.  However, the cross-spectrum consists of complex numbers that can be divided into a real and an imaginary part.  These can be smoothed to obtain the cross-density and quadrature density (quad density for short) estimates, respectively.  (The reasons for smoothing, and the different common weight functions for smoothing are discussed in the Single Spectrum (Fourier) Analysis section.)  The square root of the sum of the squared cross-density and quad-density values is called the cross-amplitude.  The cross-amplitude can be interpreted as a measure of covariance between the respective frequency components in the two series.  Thus we can conclude from the results shown in the table above that the .0625 and .1875 frequency components in the two series covary.


Cross-spectrum analysis - Squared Coherency, Gain, and Phase Shift

  Time Series Analysis Cross-spectrum Analysis - Squared Coherency, Gain, and Phase Shift

There are additional statistics that will be displayed in the complete summary Scrollsheet.

Squared coherency.  One can standardize the cross-amplitude values by squaring them and dividing by the product of the spectrum density estimates for each series.  The result is called the squared coherency, which can be interpreted similar to the squared correlation coefficient (see Correlations - Overview), that is, the coherency value is the squared correlation between the cyclical components in the two series at the respective frequency.  However, the coherency values should not be interpreted by themselves; for example, when the spectral density estimates in both series are very small, large coherency values may result (the divisor in the computation of the coherency values will be very small), even though there are no strong cyclical components in either series at the respective frequencies.

Gain.  The gain value is computed by dividing the cross-amplitude value by the spectrum density estimates for one of the two series in the analysis.  Consequently, two gain values are computed, which can be interpreted as the standard least squares regression coefficients for the respective frequencies

Phase shift.  Finally, the phase shift estimates are computed as tan**-1 of the ratio of the quad density estimates over the cross-density estimate.  The phase shift estimates (usually denoted by the Greek letter ) are measures of the extent to which each frequency component of one series leads the other.


Cross-spectrum analysis - How the Example Data were Created

  Time Series Analysis Cross-spectrum Analysis - How the Example Data were Created

Now, let us return to the example data set presented above.  The large spectral density estimates for both series, and the cross-amplitude values at frequencies ν = 0.0625 and ν = .1875 suggest two strong synchronized periodicities in both series at those frequencies.  In fact, the two series were created as:

v1 = cos(2*π*.0625*(v0-1)) + .75*sin(2*π*.2*(v0-1))

v2 = cos(2*π*.0625*(v0+2)) + .75*sin(2*π*.2*(v0+2))

(where v0 is the case number).  Indeed, the analysis presented in this overview reproduced the periodicity "inserted" into the data very well.


  Spectrum Analysis - Basic Notation and Principles

Frequency and Period

The General Structural Model

A Simple Example

Periodogram

The Problem of Leakage

Padding the Time Series

Tapering

Data Windows and Spectral Density Estimates

Preparing the Data for Analysis

Results when no Periodicity in the Series Exists

For more information, see Time Series Analysis - Index and the following topics:

Identifying Patterns in Time Series Data

ARIMA (Box & Jenkins) and Autocorrelations

ARIMA Introductory Overview

Interrupted Time Series

Exponential Smoothing

Seasonal Decomposition (Census I)

X-11 Census method II seasonal adjustment

X-11 Census method II result tables

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis

Fast Fourier Transformations


  Spectrum Analysis Basic Notation and Principles - Frequency and Period

The "wave length" of a sine or cosine function is typically expressed in terms of the number of cycles per unit time (Frequency), often denoted by the Greek letter nu (ν; some text books also use f).  For example, the number of letters handled in a post office may show 12 cycles per year: On the first of every month a large amount of mail is sent (many bills come due on the first of the month), then the amount of mail decreases in the middle of the month, then it increases again towards the end of the month.  Therefore, every month the fluctuation in the amount of mail handled by the post office will go through a full cycle.  Thus, if the unit of analysis is one year, then ν would be equal to 12, as there would be 12 cycles per year.  Of course, there will likely be other cycles with different frequencies.  For example, there might be annual cycles (ν=1), and perhaps weekly cycles (ν=52 weeks per year).

The period T of a sine or cosine function is defined as the length of time required for one full cycle.  Thus, it is the reciprocal of the frequency, or: T = 1/ν.  To return to the mail example in the previous paragraph, the monthly cycle, expressed in yearly terms, would be equal to 1/12 = 0.0833.  Put into words, there is a period in the series of length 0.0833 years.

In the Time Series module the frequency is computed in terms of cycles per observations, since each observation represents one unit of time.


  Spectrum Analysis Basic Notation and Principles - The General Structural Model

As mentioned before, the purpose of spectrum analysis is to decompose the original series into underlying sine and cosine functions of different frequencies, in order to determine those that appear particularly strong or important.  One way to do so would be to cast the issue as a linear Multiple Regression problem, where the dependent variable is the observed time series, and the independent variables are the sine functions of all possible (discrete) frequencies.  Such a linear multiple regression model may be written as:

x  = a +Σ[a *cos(λ  *t)+b *sin(λ  *t)]      (for k=1 to q)

 t    0    k      k     k      k

Following the common notation from classical harmonic analysis, in this equation λ (lambda) is the frequency expressed in terms of radians per unit time, that is: λ = 2*π*νk, where π is the constant pi=3.1415... and νk = k/q.  What is important here is to recognize that the computational problem of fitting sine and cosine functions of different lengths to the data can be considered in terms of multiple linear regression.  Note that the cosine parameters ak and sine parameters bk are regression coefficients that tell us the degree to which the respective functions are correlated with the data.  Overall there are q different sine and cosine functions; intuitively (as also discussed in Multiple Regression), it should be clear that we cannot have more sine and cosine functions than there are data points in the series.  Without going into detail, if there are N data points in the series, then there will be N/2+1 cosine functions and N/2-1 sine functions.  In other words, there will be as many different sinusoidal waves as there are data points, and we will be able to completely reproduce the series from the underlying functions.  (Note that if the number of cases in the series is odd, then the last data point will usually be ignored; in order for a sinusoidal function to be identified, you need at least two points: the high peak and the low peak.)

To summarize, spectrum analysis will identify the correlation of sine and cosine functions of different frequency with the observed data.  If a large correlation (sine or cosine coefficient) is identified, one can conclude that there is a strong periodicity of the respective frequency (or period) in the data.

Complex numbers (real and imaginary numbers).  In many text books on spectrum analysis, the structural model shown above is presented in terms of complex numbers, that is, the parameter estimation process is described in terms of the Fourier transform of a series into real and imaginary parts.  Complex numbers are the superset that includes all real and imaginary numbers.  Imaginary numbers, by definition, are numbers that are multiplied by the constant i, where i is defined as the square root of -1.  Obviously, the square root of -1 does not exist, hence the term imaginary number; however, meaningful arithmetic operations on imaginary numbers can still be performed (e.g., [i*2]**2= -4).  It is useful to think of real and imaginary numbers as forming a two dimensional plane, where the horizontal or X-axis represents all real numbers, and the vertical or Y-axis represents all imaginary numbers.  Complex numbers can then be represented as points in the two-dimensional plane.  For example, the complex number 3+i*2 can be represented by a point with coordinates {3,2} in this plane.  One can also think of complex numbers as angles, for example, one can connect the point representing a complex number in the plane with the origin (complex number 0+i*0), and measure the angle of that vector to the horizontal line.  Thus, intuitively one can see how the spectrum decomposition formula shown above, consisting of sine and cosine functions, can be rewritten in terms of operations on complex numbers.  In fact, in this manner the mathematical discussion and required computations are often more elegant and easier to perform; which is why many text books prefer the presentation of spectrum analysis in terms of complex numbers.


  Spectrum Analysis Basic Notation and Principles - A Simple Example

Shumway (1988) presents a simple example to clarify the underlying "mechanics" of spectrum analysis.  Let us create a series with 16 cases following the equation shown above, and then see how we may "extract" the information that was put in it.  First, create a variable and define it as:

x = 1*cos(2*π*.0625*(v0-1)) + .75*sin(2*π*.2*(v0-1))

You can produce this variable by typing in the formula as the long variable label.  This variable is made up of two underlying periodicities:  The first at the frequency of ν=.0625 (or period 1/ν=16; one observation completes 1/16'th of a full cycle, and a full cycle is completed every 16 observations) and the second at the frequency of ν=.2 (or period of 5).  The cosine coefficient (1.0) is larger than the sine coefficient (.75).  The spectrum analysis summary results Scrollsheet computed by the Time Series module is shown below.

+---+---------------------------------------+

|   | Spectral analysis:VAR1 (shumex.sta)   |

|   | No. of cases: 16                      |

| t |                                       |

+---+-------+-------+-------+-------+-------+

|   | Freq- |       |Cosine | Sine  |Period-|

|   | uency |Period |Coeffs |Coeffs |ogram  |

+---+-------+-------+-------+-------+-------+

| 0 | .0000 |       |  .000 | 0.000 |  .000 |

| 1 | .0625 | 16.00 | 1.006 |  .028 | 8.095 |

| 2 | .1250 |  8.00 |  .033 |  .079 |  .059 |

| 3 | .1875 |  5.33 |  .374 |  .559 | 3.617 |

| 4 | .2500 |  4.00 | -.144 | -.144 |  .333 |

| 5 | .3125 |  3.20 | -.089 | -.060 |  .092 |

| 6 | .3750 |  2.67 | -.075 | -.031 |  .053 |

| 7 | .4375 |  2.29 | -.070 | -.014 |  .040 |

| 8 | .5000 |  2.00 | -.068 | 0.000 |  .037 |

+---+-------+-------+-------+-------+-------+

Let us now review the columns of this Scrollsheet.  Clearly, the largest cosine coefficient can be found for the .0625 frequency.  A smaller sine coefficient can be found at frequency = .1875.  Thus, clearly the two sine/cosine frequencies which were "inserted" into the example data file are reflected in the Scrollsheet.


  Spectrum Analysis Basic Notation and Principles - Periodogram

The sine and cosine functions are mutually independent (or orthogonal); thus we may sum the squared coefficients for each frequency to obtain the periodogram.  Specifically, the periodogram values above are computed as:

                      2                      2

P  = sine coefficient   * cosine coefficient   * N/2

 k                   k                      k

where Pk is the periodogram value at frequency νk and N is the overall length of the series.  The periodogram values can be interpreted in terms of variance (sums of squares) of the data at the respective frequency or period.  Customarily, the periodogram values are plotted against the frequencies or periods, and many such plots are available in the Time Series module (see the Spectrum Analysis Results dialog).


  Spectrum Analysis Basic Notation and Principles - The Problem of Leakage

In the example above, a sine function with a frequency of 0.2 was "inserted" into the series.  However, because of the length of the series (16), none of the frequencies reported in the Scrollsheet exactly "hits" on that frequency.  In practice, what often happens in those cases is that the respective frequency will "leak" into adjacent frequencies.  For example, one may find large periodogram values for two adjacent frequencies, when, in fact, there is only one strong underlying sine or cosine function at a frequency that falls in-between those implied by the length of the series.  There are three ways in which one can approach the problem of leakage:

(1)  By padding the series one may apply a finer frequency "roster" to the data,

(2)  By tapering the series prior to the analysis one may reduce leakage, or

(3)  By smoothing the periodogram one may identify the general frequency "regions" or (spectral densities) that significantly contribute to the cyclical behavior of the series.

See below for descriptions of each of these approaches.


  Spectrum Analysis Basic Notation and Principles - Padding the Time Series

Because the frequency values are computed as N/t (the number of units of times) one may simply pad the series with a constant (e.g., zeros) and thereby introduce smaller increments in the frequency values.  In a sense, padding allows one to apply a finer roster to the data.  In fact, if we padded the example data file described in the example above with ten zeros, the results would not change, that is, the largest periodogram peaks would still occur at the frequency values closest to .0625 and .2.  (Padding is also often desirable for computational efficiency reasons; see below.)


  Spectrum Analysis Basic Notation and Principles - Tapering

The so-called process of split-cosine-bell tapering is a recommended transformation of the series prior to the spectrum analysis.  It usually leads to a reduction of leakage in the periodogram.  The rationale for this transformation is explained in detail in Bloomfield (1976, p. 80-94).  In essence, a proportion (p) of the data at the beginning and at the end of the series is transformed via multiplication by the weights:

w  = 0.5*{1-cos[π*(t-0.5)/m]}

 t

(for t=0 to m-1)

w  = 0.5*{1-cos[π*(N-t+0.5)/m]}

 t

(for t=N-m to N-1)

where m is chosen so that 2*m/N is equal to the proportion of data to be tapered (p).


  Spectrum Analysis Basic Notation and Principles - Data Windows and Spectral Density Estimates

In practice, when analyzing actual data, it is usually not of crucial importance to identify exactly the frequencies for particular underlying sine or cosine functions.  Rather, because the periodogram values are subject to substantial random fluctuation, one is faced with the problem of very many "chaotic" periodogram spikes.  In that case, one would like to find the frequencies with the greatest spectral densities, that is, the frequency regions, consisting of many adjacent frequencies, that contribute most to the overall periodic behavior of the series.  This can be accomplished by smoothing the periodogram values via a weighted moving average transformation.  Suppose the moving average window is of width m (which must be an odd number); the following are the most commonly used smoothers (note: p = (m-1)/2).

Daniell (or equal weight) window.  The Daniell window (Daniell 1946) amounts to a simple (equal weight) moving average transformation of the periodogram values, that is, each spectral density estimate is computed as the mean of the m/2 preceding and subsequent periodogram values.

Tukey window.  In the Tukey (Blackman and Tukey, 1958) or Tukey-Hanning window (named after Julius Von Hann), for each frequency, the weights for the weighted moving average of the periodogram values are computed as:

w  = 0.5+0.5*cos(π*j/p) (for j=0 to p)

 j

w   = w  (for j0)

 -j    j

Hamming window.  In the Hamming (named after R. W. Hamming) window or Tukey-Hamming window (Blackman and Tukey, 1958), for each frequency, the weights for the weighted moving average of the periodogram values are computed as:

w  = 0.54+0.46*cos(π*j/p) (for j=0 to p)

 j

w   = w  (for j0)

 -j    j

Parzen window.  In the Parzen window (Parzen, 1961), for each frequency, the weights for the weighted moving average of the periodogram values are computed as:

              2        3

w  = 1-6*(j/p) +6*(j/p)  (for j=0 to p/2)

 j

             3

w  = 2*(1-j/p)  (for j=p/2+1 to p)

 j

w   = w  (for j0)

 -j    j

Bartlett window.  In the Bartlett window (Bartlett, 1950) the weights are computed as:

w  = 1-(j/p) (for j=0 to p)

 j

w   = w  (for j0)

 -j    j

With the exception of the Daniell window, all weight functions will assign the greatest weight to the observation being smoothed in the center of the window, and increasingly smaller weights to values that are further away from the center. (Note also that the Time Series module will standardize the weights so that they sum to 1.)  In many cases, all of these data windows will produce very similar results; in the Time Series module it is very easy to experiment with different windows and different widths, and to see the effect on the interpretability of results.


  Spectrum Analysis Basic Notation and Principles - Preparing the Data for Analysis

Let us now consider a few other practical points in spectrum analysis.  Usually, one wants to subtract the mean from the series, and detrend the series (so that it is stationary) prior to the analysis.  Otherwise the periodogram and density spectrum will mostly be "overwhelmed" by a very large value for the first cosine coefficient (for frequency 0.0).  In a sense, the mean is a cycle of frequency 0 (zero) per unit time; that is, it is a constant.  Similarly, a trend is also of little interest when one wants to uncover the periodicities in the series.  In fact, both of those potentially strong effects may mask the more interesting periodicities in the data, and thus both the mean and the trend (linear) should be removed from the series prior to the analysis (by default, they will be removed in the Time Series module).  Sometimes, it is also useful to smooth the data prior to the analysis, in order to "tame" the random noise that may obscure meaningful periodic cycles in the periodogram.


Spectrum Analysis Basic Notation and Principles - Results when no Periodicity in the Series Exists

  Spectrum Analysis Basic Notation and Principles - Results when no Periodity in the Series Exist

Finally, what if there are no recurring cycles in the data, that is, if each observation is completely independent of all other observations?  If the distribution of the observations follows the normal distribution, such a time series is also referred to as a white noise series (like the white noise one hears on the radio when tuned in-between stations).  A white noise input series will result in periodogram values that follow an exponential distribution.  Thus, by testing the distribution of periodogram values against the exponential distribution, one may test whether the input series is different from a white noise series.  The Time Series module will produce a histogram of the periodogram values, and fit the exponential distribution to the histogram.  In addition, the user can also request to compute the Kolmogorov-Smirnov one-sample d statistic (see also Nonparametrics and Distributions for more details).

Testing for white noise in certain frequency bands.  Note that you can also plot the periodogram values for a particular frequency range only.  Again, if the input is a white noise series with respect to those frequencies (i.e., it there are no significant periodic cycles of those frequencies), then the distribution of the periodogram values should again follow an exponential distribution.


Time Series Analysis - Fast Fourier Transformations (FFT)

  Fast Fourier Transforms (FFT)

General Introduction

Computation of FFT in Time Series

For more information, see Time Series Analysis - Index and the following topics:

Identifying Patterns in Time Series Data

ARIMA (Box & Jenkins) and Autocorrelations

ARIMA Introductory Overview

Interrupted Time Series

Exponential Smoothing

Seasonal Decomposition (Census I)

X-11 Census method II seasonal adjustment

X-11 Census method II result tables

Distributed Lags Analysis

Single Spectrum (Fourier) Analysis

Cross-spectrum Analysis

Basic Notations and Principles


Fast Fourier Transformations (FFT) - General Introduction

  Fast Fourier Transforms (FFT) - General Introduction

The interpretation of the results of spectrum analysis is discussed in the Basic Notation and Principles topic, however, we have not described how it is done computationally.  Up until the mid-1960s the standard way of performing the spectrum decomposition was to use explicit formulae to solve for the sine and cosine parameters.  The computations involved required at least N**2 (complex) multiplications.  Thus, even with today's high-speed computers , it would be very time consuming to analyze even small time series (e.g., 8,000 observations would result in at least 64 million multiplications).

The time requirements changed drastically with the development of the so-called fast Fourier transform algorithm, or FFT for short.  In the mid-1960s, J.W. Cooley and J.W. Tukey (1965) popularized this algorithm which, in retrospect, had in fact been discovered independently by various individuals.  Various refinements and improvements of this algorithm can be found in Monro (1975) and Monro and Branch (1976).  Readers interested in the computational details of this algorithm may refer to any of the texts cited in the overview.  Suffice it to say that via the FFT algorithm, the time to perform a spectral analysis is proportional to N*log2(N) -- a huge improvement.

However, a draw-back of the standard FFT algorithm is that the number of cases in the series must be equal to a power of 2 (i.e., 16, 64, 128, 256, ...).  Usually, this necessitated padding of the series, which, as described above, will in most cases not change the characteristic peaks of the periodogram or the spectral density estimates.  In cases, however, where the time units are meaningful, such padding may make the interpretation of results more cumbersome.  As described below, the implementation of spectral analysis in the Time Series module does not impose any restrictions on the length of the input series.


Fast Fourier Transformations (FFT) - Compuation of FFT in Time Series

  Fast Fourier Transforms (FFT) - Computation of FFT in Time Series

The implementation of the FFT algorithm in the Time Series module allows the user to take full advantage of the savings afforded by this algorithm.  On most standard computers, series with over 100,000 cases can easily be analyzed.  However, there are a few things to remember when analyzing series of that size.

As mentioned above, the standard (and most efficient) FFT algorithm requires that the length of the input series is equal to a power of 2.  If this is not the case, additional computations have to be performed.  The Time Series module will use the simple explicit computational formulas as long as the input series is relatively small, and the number of computations can be performed in a relatively short amount of time.  For long time series, in order to still utilize the FFT algorithm, an implementation of the general approach described by Monro and Branch (1976) is used.  This method requires significantly more storage space, however, series of considerable length can still be analyzed very quickly, even if the number of observations is not equal to a power of 2.

For time series of lengths not equal to a power of 2, we would like to make the following recommendations:  If the input series is small to moderately sized (e.g., only a few thousand cases), then do not worry.  The analysis will typically only take a few seconds anyway.  In order to analyze moderately large and large series (e.g., over 100,000 cases), pad the series to a power of 2 (choose the respective option on the Spectrum (Fourier) Analysis dialog) and then taper the series during the exploratory part of your data analysis.  If necessary, you may later use the Do not pad series, use exact length option from the Spectrum (Fourier) Analysis dialog, to derive the final estimates.


  Time Series Analysis - Startup Panel

This dialog lists all general procedures available in the Time Series module (see also Time Series Analysis - Index).  For all analyses, first select one or more variables (time series).  Refer to the Overview for an introduction to all procedures accessible from this panel.

General Logic of Memory Management

After you select one or more variables (time series), they will be read into the active work area.  Transformations of variables, forecasts, residuals, etc. are later also appended to the active work area.  The number of backups (i.e., previous versions of the series) per original variable (series) that is maintained in the active work area is determined by the Number of backups per variable (series) parameter (see below).  When a new transformation is about to be appended, and the maximum number of backups for the respective original variable (by default 3) has already been exceeded, then the "oldest" previous backup will be replaced.  You can lock a variable (prevent it from being overwritten) by double-clicking on the respective variable in the Lock column.  Double-click on the Variable column and the Long variable (series) name column to edit the respective names.  For more details, refer to the active work area section.

Time Series Analysis startup panel:

Variables

OK (transformations, autocorrelations, crosscorrelations, plots)

Number of backups per variable

Save variables

Delete highlighted variable

ARIMA & autocorrelation functions

Interrupted time series analysis

Exponential smoothing & forecasting

X-11 monthly seasonal adjustment

X-11 quarterly seasonal adjustment

Seasonal decomposition

Distributed lags analysis

Spectral (Fourier) analysis

Replace missing data


  Time Series Analysis Startup Panel - Variables

This button will bring up a standard single variable selection window.  Note that, after clicking on this button, the active work area will be cleared before the selected variables are read in.  After selecting the variables, they will be loaded into the active work area, and, if necessary, missing data will be replaced according to the setting of the radio buttons in the box entitled Replace missing data... (see missing data).


  Time Series Analysis Startup Panel - OK (Transformations, Autocorrelations, Crosscorrelations, Plots)

This button will bring up the Transformations dialog.  From that dialog you can select from among all common time series transformation, review plots or listings of one or more series, and review autocorrelations, partial autocorrelations, and crosscorrelations.


  Time Series Analysis Startup Panel - Number of Backups per Variable

This parameter determines the maximum number of backups (i.e., previous versions of the series) that is kept in the active work area for each variable.  When a new transformation is about to be appended, and the maximum number of backups for the respective original variable has already been exceeded, the "oldest" previous backup will be replaced.  You can lock a variable (prevent it from being overwritten) by double-clicking on the respective variable in the Lock column.  For more details, refer to the active work area section.


  Time Series Analysis Startup Panel - Save Variables

This option allows you to save the variables (series) that are currently available in the active work area into a standard STATISTICA data file (which can be used as input for subsequent analyses).


  Time Series Analysis Startup Panel - Delete Highlighted Variable

This option allows you to delete the currently highlighted variable.  To highlight a variable, click on it either in the Lock, Variable, or Long variable (series) name column.


  Time Series Analysis Startup Panel - ARIMA and Autocorrelation Functions

This option will bring up the dialog for Specifying the ARIMA model.  This option allows you to test seasonal and non-seasonal ARIMA models.  Refer to the Overview section for details concerning this method.


  Time Series Analysis Startup Panel - Interrupted Time Series Analysis

This option will bring up the dialog for specifying Interrupted time series models.  In general, these models allow you to test whether and how events at specific points in time affect subsequent observations in the time series. Refer to the Overview section for details concerning this method.


  Time Series Analysis Startup Panel - Exponential Smoothing and Forecasting

This option is described in the Exponential Smoothing topic.


  Time Series Analysis Startup Panel - X-11 Monthly Seasonal Adjustment

This option is described in the X-11 monthly seasonal decomposition (Census II) topic.


  Time Series Analysis Startup Panel - X-11 Quarterly Seasonal Adjustment

This option is described in the X-11 quarterly seasonal decomposition (Census II) topic.


  Time Series Analysis Startup Panel - Seasonal Decomposition

This option is described in the Seasonal Decomposition (Census I) topic.


  Time Series Analysis Startup Panel - Distributed Lags Analysis

Select this option to open the Distributed Lags Analysis dialog in which you can specify the variables and other aspects of this analysis.  Refer to the Distributed Lags Analysis section for details concerning this method.


  Time Series Analysis Startup Panel - Spectral (Fourier) Analysis

This option is described in the Single Spectrum (Fourier) Analysis and Cross-spectrum Analysis topics.


  Time Series Analysis Startup Panel - Replace Missing Data

The Time Series module offers a range of different methods for dealing with missing data.  For more information, see Missing Data.


  Time Series Analysis - Active Work Area

All variables (series) and their transformations that are currently available for analysis are stored in the active work area, and listed in the edit fields at the top of the dialog.  When you select new variables, the active work area will first be cleared, and then the selected variables will be read into the active work area (after all "holes" with missing data have been "patched").  The following information applies to the active work area.

Highlighted variable

Naming conventions

Editing variable names

Number of backups per variable (series)

Locking variables (series)

Deleting variables (series) from the current work area

Saving variables (series) in the current work area


  Time Series Analysis Active Work Area - Highlighted Variable

All subsequent analyses will be performed on the highlighted variable.  For example, when you perform a transformation, then the currently highlighted variable will be transformed, and a new (transformed) variable will be appended to the active work area.  To highlight a variable, simply click on it in any of the edit fields.


  Time Series Analysis Active Work Area - Naming Conventions

When a new (e.g., transformed) variable is appended to the active work area, it is assigned (1) the same short variable name as the original variable (that was transformed), and (2) a new long variable name that consists of the old long variable name (as much of it as will fit) and a brief description of the respective transformation that was performed.  In this manner, as you perform successive transformations or analyses (e.g., successively difference a series), an automatic log of transformations will be maintained in the long variable names.  For example:

SERIES_G	[The original series]

SERIES_G  x+3;	[After adding a constant]

SERIES_G  x+3;ln(x);	[After the logarithmic transformation was performed]

SERIES_G  x+3;ln(x);D(-12)	[After the series was differenced with the lag of 12]


  Time Series Analysis Active Work Area - Editing Variable Names

Double-click in the column labeled Variable or Long variable (series) name to edit the short or long variable name for the series in the active work area.  Note that the short and long names will only be changed in the active work area, not in the file (use the respective data spreadsheet operations to permanently change those names).


  Time Series Analysis Active Work Area - Number of Backups per Variable (Series)

All dialogs that contain the edit fields for highlighting a variable (series) for analysis also contain a field for specifying the desired Number of backups per variable (series).  After a transformation (or other analysis) was performed on a series, the resulting transformed series (or residuals, forecasts, etc. in ARIMA) will be appended to the active work area, and the values of the series prior to the transformation will be maintained as a backup.  The number of such backups that will be maintained in the active work area is controlled by this parameter.  Thus, for example, if this parameter is set to 3 (default), and you have just performed the fourth transformation of an original variable, then the series with the data after the first transformation will be dropped from the active work area, and replaced by the new (fourth) transformation.  Thus, successive transformations will be appended to the active work area until there are as many backups as specified in this parameter; at that point the respective "oldest" transformation will be replaced by the new one.  Up to 99 backups can be kept of a single original variable.


  Time Series Analysis Active Work Area - Locking Variables (Series)

The first column of the edit fields carries the header Lock.  When you double-click in that column for a transformed variable, that variable will be locked in the active work area (or unlocked, if it was previously locked).  An L will appear in that column to indicate that the variable is now locked.  Locked variables will not be replaced as successive transformations exceed the current maximum number of backups.  Note that original (untransformed) variables are always locked, and they cannot be unlocked.


  Time Series Analysis Active Work Area - Deleting Variables (Series) from the Current Work Area

To delete a transformed variable from the active work area, use the Delete highlighted variable button.  Original (untransformed) variables cannot be deleted.


  Time Series Analysis Active Work Area - Saving Variables (Series) from the Current Work Area

Use the Save variables button to save the variables (series) in the active work area into a standard STATISTICA data file.  You can save all variables or only selected variables.


  Time Series Analysis - Missing Data

Practically all time series analyses require that all data are observed, and that there are no "holes" with missing data in the time series.  As long as the missing data are at the end of the series (trailing missing data) or the beginning of the series (leading missing data), the missing data will simply be ignored.  Missing data embedded in the series have to be replaced in some way.  Time Series offers a range of different methods for dealing with missing data in that case:

Overall mean

Interpolation from adjacent points

Mean of N adjacent points

Median of N adjacent points

Predicted values from linear trend regression


  Time Series Analysis Missing Data - Overall Mean

In this method, all missing data will simply be replaced by the overall mean of the series.  Very often, when the series is not stationary, or when there are large systematic fluctuations in the values of the series, this method may not be appropriate.  On the other hand, the overall mean is often the best a priori (unbiased) guess for the missing data.


  Time Series Analysis Missing Data - Interpolation from Adjacent Points

In this method, the missing data are computed by interpolation from the adjacent non-missing points.  Graphically, this method amounts to replacing missing data by connecting with a straight line the point just prior to the missing data with the point just following the missing data.  Thus, this method in a sense assumes that there is some serial correlation in the data, that is, that each observation is to some extent related to and therefore most similar to the previous observation.


  Time Series Analysis Missing Data - Mean of N Adjacent Points

In this method the missing data are computed from the mean of the N adjacent points on both sides of the "hole" of missing data.  For example, when N is left at its default value of 1, then missing data will be replaced by the average of the value just prior to the missing data and the value immediately following the missing data.  In general, this method implies that the data in the region or window specified by the N parameter are more similar to each other than points that are further away.


  Time Series Analysis Missing Data - Median of N Adjacent Points

This method is essentially the same as that described above, except that missing data are replaced by the median of the N non-missing adjacent point.


  Time Series Analysis Missing Data - Predicted Values from Linear Trend Regression

In this method, the program will fit a least-squares regression line to the time series.  The missing data will then be replaced by the values predicted by this regression line.  This method implies, that the most salient (or strongest) feature of the series is its linear trend across time.


   Time Series Analysis - Transformations of Variables

Click on the Variable or Long variable (series) name column to highlight the variable (series) in the active work area that is to be transformed or analyzed.  Click OK to select a transformation.  Transformed variables will be appended to the active work area.  The number of backups that will be kept for any one variable is determined by the Number of backups per variable (series) parameter (see below).  (See also, Time Series Analysis - Index.)

Transformation of Variables dialog:

Number of backups per variable

Delete

Save variables

Review and plot variables

Plot variables (series) after each transformation

Display/plot subset of cases only

Review/Plot highlighted variable

Review/Plot multiple variables

Plot two var. lists with different scales

Label data points with...

Scale X-axis in plots manually (min, step)

Autocorrelations & crosscorrelations

Autocorrelations

Alpha for highlighting

White noise standard errors

Partial autocorrelations

Crosscorrelations

Number of lags

2D scatterplot

3D scatterplot

Label points in scatterplots

Histogram

Descriptive statistics

Normal, detrended normal, and half-normal probability plots


Transformations of Variables - Number of Backups per Variable

   Time Series Analysis Transformations of Variables - Number of Backups per Variable

This parameter determines the maximum number of backups that is kept in the active work area for each variable.  When a new transformation is about to be appended, and the maximum number of backups for the respective original variable has already been exceeded, the "oldest" previous backup will be replaced.  You can lock a variable (prevent it from being overwritten) by double-clicking on the respective variable in the Lock column.  For more details, refer to the active work area section.


Transformations of Variables - Delete

   Time Series Analysis Transformations of Variables - Delete

This option allows you to delete the currently highlighted variable.  To highlight a variable, click on it either in the Lock, Variable, or Long variable (series) name column.


Transformations of Variables - Save Variables

   Time Series Analysis Transformations of Variables - Save Variables

This option allows you to save the variables (series) that are currently available in the active work area into a standard STATISTICA data file (which can be used as input for subsequent analyses).


Transformations of Variables - Review and Plot Variables

   Time Series Analysis Transformations of Variables - Review and Plot Variables

These options allow you to review or plot the currently highlighted variable (together with other variables).  The labeling of the individual observations (that is, of the respective points in time represented by the rows in Scrollsheets or the horizontal X-axis in plots) is determined by the setting of the radio buttons in the Label  data points box.  For the plots, you can choose to Scale the X-axis in the plots manually.  This is often useful when the series consists of several regularly recurring time intervals, for example, if it is made up of 10 years with 12 (monthly) observations each.  Then it may be useful to scale the X-axis in the plot so that each major tickmark indicates exactly one year.


Transformations of Variables - Plot Variables (Series) after each Transform

   Time Series Analysis Transformations of Variables - Plot Variables (Series) after each Transform

If this check box is set, then after each transformation, the transformed variable will be plotted.


Transformations of Variables - Display/Plot Subset of Cases Only

   Time Series Analysis Transformations of Variables - Dispaly/Plot Subset of Cases Only

If this check box is set, then, before plotting or displaying one or more series, you will be prompted to select a range of observations to include in the plot or display.


Transformations of Variables - Review/Plot Highlighted Variable

   Time Series Analysis Transformations of Variables - Review/Plot Highlighted Variable

This button will bring up a Scrollsheet (or a plot) with the values for the currently highlighted variable.


Transformations of Variables - Review/Plot Multiple Variables

   Time Series Analysis Transformations of Variables - Review/Plot Multiple Variables

After clicking on this button, you will first be prompted to select a list of variables to be displayed or plotted.  When plotting multiple variables the vertical (Y) axis will have a common scale; thus, if the series that are plotted contain values of different magnitudes, then use option Plot two var lists with different scales (see below).  In that option, two variable lists are plotted against the left Y and right Y axes using different scales.


Transformations of Variables - Plot Two Var. Lists with Different Scales

   Time Series Analysis Transformations of Variables - Plot Two Var. Lists with Different Scales

This option allows you to plot two lists of variables using different scales for the vertical (Y) axes in the plot.  The first list will be plotted against the left Y-axis and the second list will be plotted against the right Y-axis.  For example, suppose you want to plot two variables (series) called S1 and S2, and that these variables contain values of different magnitudes: the values of S1 range from 1- 100 and the values of S2 range from 1000 to 10000.  If you plot S1 against the left Y-axis (scaled from 1-100) and S2 against the right Y-axis (scaled from 1000-10000), then both variables will be plotted with optimal resolution, and thus relationships between patterns across time (the X-axis) may become more clearly identifiable.


Transformations of Variables - Label Data Points With...

   Time Series Analysis Transformations of Variables - Label Data Points With...

The choice of radio button in this box determines the labeling of the data points in displays or plots.  The setting of these radio buttons will be retained across other analytical procedures in this module, for example, when displaying residuals from an ARIMA analysis.  By default (radio button Case numbers), each point will be identified by the respective case number, and case numbers will be used on the X-axis in plots of available series.  If there are Case names available in the data file, you may use them to label the data points (and the X-axis in plots).  If you choose to use Dates, a single variable selection window will come up where you can select the variable containing dates (i.e., values formatted as dates).  Those dates will then be used to label the rows in Scrollsheets and the X-axis in plots.  Finally, you may use Consecutive integers, starting from 1, to label the points and X-axis in plots.

Note that in the Consecutive integers setting, what will be displayed is the offset (plus one) of the respective data point from the first data point of any variable in the active work area.  For example, suppose you have in the active work area, two series called S1 and S2.  S1 has its first valid observation at case number 5, and S2 has its first valid observation at case number 8.  If we were to use option Review multiple variables to display both variables, and choose the Consecutive integers option, then the first valid observation for variable S1 will be labeled 1, and the first valid observation for variable S2 will be labeled 4.


Transformations of Variables - Scale X-axis in Plots Manually (min, step)

   Time Series Analysis Transformations of Variables - Scale X-axis in Plots Manually (min, step)

The setting of this check box will affect the scaling of the X-axis in line plots of single or multiple variables (series).  The choice of scaling will be retained across other analytical procedures in this module, for example, when plotting forecasts from an ARIMA analysis.  By default, if this check box is not set, the X-axis in all plots will always be scaled so that (1) all valid data points are displayed in the plot, and (2) that the tickmarks (steps) on the X-axis are "neat" (i.e., the significant digit of the step size is either 1, 2, or 5).  However, if there is a known periodicity in the data that is of interest, such as 12 months per year or 10 observations per day, etc., then it may be useful to set this check box and to scale the X-axis for plots accordingly.


Transformations of Variables - Autocorrelations & Crosscorrelations

   Time Series Analysis Transformations of Variables - Autocorrelations & Crosscorrelations

These options will compute the autocorrelations, partial autocorrelations, and crosscorrelations between two time series.


Transformations of Variables - Autocorrelations

   Time Series Analysis Transformations of Variables - Autocorrelations

This option will bring up a Scrollsheet and plot of the autocorrelations, for a lag of 1 through the number specified in the Number of lags edit field.  The Scrollsheet will report the autocorrelations, their standard errors, the so-called Box-Ljung statistic, and the significance level of that statistic.  In general, the autocorrelation is the correlation of the series with itself, lagged by a particular number of observations.  Refer to the Overview section for a brief description of how the pattern of autocorrelations aids in the determination of an appropriate ARIMA model.  For details regarding the computations of those statistics refer to the autocorrelation section.


Transformations of Variables - Alpha for Highlighting

   Time Series Analysis Transformations of Variables - Alpha for Highlighting

Significant autocorrelations (significant Box-Ljung statistics) will be highlighted in the Scrollsheet.  This edit field allows you to specify the significance level that is used for highlighting.


Transformations of Variables - White Noise Standard Error

   Time Series Analysis Transformations of Variables - White Noise Standard Errors

Under the assumption that the true moving average process in the series is of the order k-1, the approximate standard error of the autocorrelation rk is computed as:

                                2

StdErr(r ) = √{(1/N) * [1+2*Σ(r  )]}

        k                      i

(for i = 1 to k-1)

Here N is the number of observations in the series.  Under the assumption that the series is a white noise process, that is, that all autocorrelations are equal to zero, the standard error of rk is computed as:

StdErr(r ) = √{(1/N) * [(N-k)/(N+2)]}

        k

Check the White noise standard errors option to compute the standard errors in this manner.


Transformations of Variables - Partial Autocorrelations

   Time Series Analysis Transformations of Variables - Partial Autocorrelations

This option will bring up a Scrollsheet and plot of the partial autocorrelations, for a lag of 1 through the number specified in the Number of lags edit field.  The Scrollsheet will report the partial autocorrelations and their standard errors.  In general, the partial autocorrelation is the partial correlation of a series with itself, lagged by a particular number of observations, and controlling for all correlations for lags of lower order.  For example, the partial autocorrelation for a lag of 2 represents the unique correlation of the series with itself at that lag, after controlling for the correlation at lag 1.  For details regarding the computations of the partial autocorrelation and its standard error refer to the partial autocorrelation section.  Partial autocorrelations that are larger than two times their respective standard errors will be highlighted in the Scrollsheet.


Transformations of Variables - Crosscorrelations

   Time Series Analysis Transformations of Variables - Crosscorrelations

This option will bring up a Scrollsheet and plot of crosscorrelations, for a lag of -k through +k, where k is the number specified in the Number of lags edit field.  The Scrollsheet will report the crosscorrelations and their standard errors.  In general, the crosscorrelation is the correlation of a series with another series, shifted by a particular number of observations.  For details regarding the computations of the crosscorrelations and their standard errors refer to the crosscorrelation section.  In the Scrollsheet, correlations that are greater than 2 times their respective standard errors will be highlighted.


Transformations of Variables - Number of Lags

   Time Series Analysis Transformations of Variables - Number of Lags

This parameter determines the maximum number of lags for which the auto-, partial auto-, and crosscorrelations will be computed.


Transformations of Variables - 2D Scatterplot

   Time Series Analysis Transformations of Variables - 2D Scatterplot

This option will bring up a 2D scatterplot of the highlighted variable with another variable in the active work area; in this plot the values of the highlighted variable will be lagged by k observations, as specified in the field Plot highlighted variable with lag of....  After clicking on this button, you will be prompted to select the second variable for the scatterplot.  To review specific autocorrelations, choose the same variable for both axes of the plot.


Transformations of Variables - 3D Scatterplot

   Time Series Analysis Transformations of Variables - 3D Scatterplot

This option will bring up a 3D scatterplot of the highlighted variable with two other variables in the active work area; in this plot the values of the highlighted variable will be lagged by k observations, as specified in the field Plot highlighted variable with lag of...  After clicking on this button, you will be prompted to select two additional variables for the scatterplot.


Transformations of Variables - Label Points in Scatterplot

   Time Series Analysis Transformations of Variables - Label Points in Scatterplot

If this checkbox is set, the points in the scatterplot will be labeled with either case names, case numbers, dates, or consecutive integers, depending on the setting of the radio buttons in the Label data points box.


Transformations of Variables - Histogram

   Time Series Analysis Transformations of Variables - Histogram

This option will bring up a histogram of the currently highlighted variable.


Transformations of Variables - Descriptive Statistics

   Time Series Analysis Transformations of Variables - Descriptive Statistics

This option will bring up a Scrollsheet with descriptive statistics for all variables currently available in the active work area.


Transformations of Variables - Normal, Detrended Normal, and Half-Normal Probability Plots

   Time Series Analysis Transformations of Variables - Normal, Detrended Normal, and Half-Normal Probability Plots

These options will bring up the respective normal probability plot for the highlighted variable.  For more information on how these plots are constructed, see Normal Probability Plots, Half-Normal Probability Plots, and Detrended Normal Probability Plots.


  Time Series Analysis - Crosscorrelations

The crosscorrelation coefficient rxy(k) represents the correlation between two series X and Y, where X is lagged by k observations (see also, Time Series Analysis - Index).  Note that the crosscorrelation function is not symmetrical about the lag of 0, that is, different correlations will emerge depending on whether the X-axis is shifted forward or backwards. The crosscorrelation coefficient is computed following the standard formulas, as described in most time series references (e.g., Box & Jenkins, 1976):

r   = (1/N)*Σ[(X -X-bar)*(Y   -Y-bar)]

 xy             t          t+1

(for t=1 to N-l; l=0 to k)

r   = (1/N)*Σ[(Y -Y-bar)*(X   -X-bar)]

 xy             t          t+1

(for t=1 to N+l; l=-1 to -k)

Where X-bar and Y-bar are the means of the respective two series.

Standard error of rxy(k).  Under the assumption that X and Y are independent, and that one of the series consists only of white noise, then the standard error of the crosscorrelation is approximately equal to:

StdErr(r     ) = √[1/(N-k)]

        xy(k)

Where N is the number of observations in the series.


  Time Series Analysis - Autocorrelations

An autocorrelation is the correlation of a series with itself, shifted by a particular lag of k observations.  The plot of autocorrelations for various lags is a crucial tool for determining an appropriate model for ARIMA analysis (see also, Time Series Analysis - Overview and Time Series Analysis - Index).  The computations of the autocorrelation coefficients rk follow the standard formulas, as described in most time series references (e.g., Box & Jenkins, 1976).

Standard error of rk.   Under the assumption that the true moving average process in the series is of the order k-1, then the approximate standard error of rk is defined as:

                                2

StdErr(r ) = √{(1/N) * [1+2*Σ(r  )]}

        k                      i

(for i = 1 to k-1)

Here N is the number of observations in the series.  However, under the assumption that the series is a white noise process, that is, that all autocorrelations are equal to zero, the standard error of rk is defined as:

StdErr(r ) = √{(1/N) * [(N-k)/(N+2)]}

        k

Check the White noise standard errors option to compute the standard errors in this manner.

Box-Ljung Q.  At a given lag k the Box-Ljung Q statistic is defined by:

                 2

Q  = n*(n+2)*Σ[r  /(n-i)]

 k              i

(for i = 1 to k)

When the number of observations is large, then the Q statistic has a Chi-Square distribution with k-p-q degrees of freedom, where p and q are the number of autoregressive and moving average parameters, respectively.


  Time Series Analysis - Partial Autocorrelations

A partial autocorrelation is the correlation of a series with itself, shifted by a particular lag of k observations, and controlling for the correlations for all shifts of 1 through k-1.  The plot of partial autocorrelations for various lags is a crucial tool for determining an appropriate model for ARIMA analysis (see ARIMA Overview and Time Series Analysis - Index).  The computations of the partial autocorrelation coefficients φk follow the standard formulas, as described in most time series references (e.g., Box & Jenkins, 1976).

Standard error of φk.   Under the assumption that the true autoregressive process in the series is of order p  k-1, then the approximate standard error of φk is defined as:

StdErr(φ ) = √(1/N)

        k

Here N is the number of observations in the series.


  Time Series Analysis - General Transformations

Select the desired type of transformation (see also, Time Series Analysis - Index).  The new transformed variable will be appended to the active work area.  If a transformation produces an invalid value (e.g., square root of a negative value, division by zero, etc.), the program will assign a missing data value; then, in a second pass, those missing data will be replaced according to the choice in the Replace missing data box on the startup panel.

Time Series Transformations dialog:

Transformations: (x=f(x))

Smoothing

Transformations for spectrum analysis

Two-series transformations

Shift relative starting point of series

Filtering and other techniques


General Transformations - Transformations: (x=f(x))

  Time Series Analysis General Transformations - Transformations: (x=f(x))

Add a constant:  A constant C will be added to all values in the Transform variable.  By default, this constant will be equal to minus the smallest value in the series, so that after the transformation the minimum value of the series will be equal to 0 (zero).

Power:  Each value in the series will be transformed as: X=X**C.

Inverse power:  Each value in the series will be transformed as: X=X**(1/C).

Natural log:  Each value in the series will be transformed as: X=natural log(X).

Exponent:  Each value in the series will be transformed as: X=e**X (where e is Euler's constant).

Mean subtract:  Each value in the series is transformed as X=X-M; where M is either (1) the overall mean for the untransformed series, or (2) the value indicated in the M= edit field, depending on the setting of the checkbox below (Estimate mean & std. dev. from data).

Standardize:  Each value in the series is standardized: X=(X-M)/SD; where M and SD are either (1) the overall mean and standard deviation for the untransformed series, or (2) the values indicated in the respective edit fields to the right, depending on the setting of the checkbox below (Estimate mean & std. dev. from data).

Estimate mean & std. dev. from data:  This checkbox determines whether, for the two transformations described in the previous two paragraphs, the mean and/or standard deviation is to be computed from the data, or whether user-defined values are to be used.

Trend subtract:  The values in the series will be transformed to remove the trend over time: X=X-(a+b*t).  In this formula, t refers to the case number and a and b are constants which are either user-defined or computed from the data, depending on the setting of the checkbox below (Estimate a/b from data).

Autocorr:  The values in the series will be transformed to remove an autocorrelation of a particular lag: X=X-(a+b*X(lag)).  In this formula, a and b are constants which are either user-defined or computed from the data (via least squares regression), depending on the setting of the checkbox below (Estimate a/b from data).  The lag in the computations is determined by the value in the Lag edit field below.

Estimate a/b from data:  This checkbox determines whether, for the two transformations described in the previous two paragraphs, the intercept (a) and slope (b) is to be computed from the data (via least squares regression), or whether user-defined values are to be used.


General Transformations - Smoothing

  Time Series Analysis General Transformations - Smoothing

The general purpose of smoothing techniques is to "bring out" the major patterns or trends in a time series, while de-emphasizing minor fluctuations (random noise).  Visually, as a result of smoothing, a jagged line pattern should be transformed into a smooth curve.  A number of techniques are available:

N-points moving average.  Each point in the transformed series is computed as the mean of N adjacent points (the so-called moving average window).  If the N parameter is odd, then the moving average is naturally centered in the middle of the moving average window.  If N is even, the moving average is centered by averaging each pair of uncentered means.  If the Prior checkbox is set, then the moving average will be computed from the N preceding values.  If the Weighted checkbox is set then a weighted moving average will be computed.  In that case, after clicking OK, a dialog will come up for specifying the respective weights.

N points moving median.  Each point in the transformed series is computed as the median of N adjacent points. If the N parameter is odd, then the moving median is naturally centered in the middle of the moving median window.  If N is even, the moving median is centered by averaging each pair of uncentered medians.  If the Prior checkbox is set, then the moving median will be computed from the N preceding values.

Simple exponential smoothing.  In this transformation, each point is computed as a weighted average of all preceding observations, where greater weight is assigned to more recent observations (specifically, the weights decrease geometrically with the "age" of prior observations).  Algorithmically, this is accomplished by:

S  = α*X +(1-α)*S

 t      t        t-1

where St is the value of the transformed series at time t, St-1 is the value of the transformed series at time t-1, Xt is the value of the untransformed series at time t, and α (alpha) is a constant (0<α<1).  If α is close to 0 (zero), then more emphasis is placed on (greater weight is assigned to) observations prior to a particular time t, resulting in a smoother curve; if α is close to 1, then more emphasis is placed on the respective untransformed observation at time t, resulting in a curve that is less smooth, but more closely following the actual (untransformed) data.  Note that a complete implementation of exponential smoothing and forecasting is also available from the startup panel.  See also the Exponential Smoothing overview section.


General Transformations - Transformations for Spectrum Analysis

  Time Series Analysis General Transformations - Transformations for Spectrum Analysis

When you click on this button, the Transformations for Spectrum Analysis dialog will open in which you can select the type of transformation for this type of Time Series analysis.


General Transformations - Two Series Transformations

  Time Series Analysis General Transformations - Two Series Transformations

These transformations require two variables (series).  Thus, after selecting any of these transformations and clicking OK, you will be prompted to select the second (Y) variable for the respective transformation (the first or X variable will be the currently highlighted variable in the active work area)..

Difference.  The highlighted series (X) is transformed by: X=X-Y(lag).  The Lag can be specified in the edit field to the right.

Residualizing.  The highlighted series (X) is transformed by: X=X-(a+b*y(lag)).  The Lag can be specified in the edit field to the right; a and b are the intercept and slope, respectively, of the (lagged) crosscorrelation.  These parameters can either be estimated via least squares regression from the data (set the Estimate a and b from data checkbox), or they can be entered manually.


General Transformations - Shift Relative Starting Point of Series

  Time Series Analysis General Transformations - Shift Relative Starting Point of Series

These transformations allow you to shift the series forward or backward, relative to all other series currently in the active work area.

Shift (lag) series forward:  The series will be shifted forward by the number of observations specified in the Lag edit field.

Shift (lag) series backward:  The series will be shifted backward by the number of observations specified in the Lag edit field.


General Transformations - Filtering and Other Techniques

  Time Series Analysis General Transformations - Filtering and Other Techniques

4253H filter.  This transformation consists of several passes of moving average/median smoothing, and is a powerful filter for smoothing a series.  Specifically, the following transformations will be performed: (1) a 4 points moving median centered by a moving median of 2, (2) a 5 point moving median, (3) a 3 point moving median, and (4) a 3-point weighted moving average using Hanning weights (.25, .5, .25), (5) residuals are computed by subtracting the transformed series from the original series, (6) steps 1 through 4 are then repeated for the residuals, (7) the transformed residuals are added to the transformed series.  In practice, this filtering method often produces a smooth series while maintaining the salient characteristics of the original series.

Differencing.  The series will be transformed as: X=X-X(lag).  After differencing, the resulting series will be of length N-lag (where N is the length of the original series).

Integrate.  This transformation is the reverse of differencing.  The series will be transformed as: X=X+X(lag).  After clicking OK to begin the transformations you will be prompted to select a variable with the leading observations.  If none is selected, then all leading observations will be equal to 0 (zero).  For example, suppose the series consists of the values: 3, 4, 2, etc.  We integrate the series with a lag of 1, and choose no variable with leading observations.  The first value of the new series will thus be 0 (zero); the next value will be 0+3, the next 0+3+4, and so on.  The resulting series will be of length N+1, where N is the number of cases in the original series.  Suppose we selected a variable with leading observations, and that the value found in that series for case 1-lag (that is, in this example, for the case just preceding the first case in the series to be transformed) is equal to 5.  Then the first value of the new series will be 5, the next value will be 5+3, the next 5+3+2, and so on.  In this manner, one can difference a series and fully restore it to its original values by integrating it, provided one uses the values of the original (untransformed) series for leading observations.


  Time Series Analysis - Transformations for Spectrum Analysis

Select the desired type of transformation in this dialog (see also, Time Series Analysis - Index).  The new transformed variable will be appended to the active work area.  If a transformation produces an invalid value (e.g., square root of a negative value, division by zero, etc.), the program will assign a missing data value; then, in a second pass, those missing data will be replaced according to the choice in the Replace missing data box on the startup panel.

The transformations on this dialog are customarily performed on series (results) produced by a Single Spectrum (Fourier) Analysis or Cross-spectrum Analysis.  Forward Fourier analysis and inverse Fourier analysis is also used for constructing filters at particular frequencies (see below).

Transformations for Spectrum Analysis dialog:

Tapering

Smoothing window

Real & imaginary part

Inverse Fourier transform


Transformations for Spectrum Analysis - Tapering

  Time Series Analysis Transformations for Spectrum Analysis - Tapering

The so-called process of split-cosine-bell tapering is a recommended transformation of a series prior to spectrum analysis.  It usually leads to a reduction of leakage in the periodogram.  The rationale for this transformation is explained in detail in Bloomfield (1976, p. 80-94), see also Tapering.


Transformations for Spectrum Analysis - Smoothing Window

  Time Series Analysis Transformations for Spectrum Analysis - Smoothing Window

As described in greater detail in the Single Spectrum (Fourier) Analysis overview section, the periodogram values computed in a spectrum analysis are subject to substantial random fluctuation.  A clearer picture of underlying periodicities often only emerges when examining the spectral densities, that is, the frequency regions, consisting of many adjacent frequencies, that contribute most to the overall periodic behavior of the series.  The spectral density estimates can be computed by smoothing the periodogram values with a weighted moving average.  Suppose the moving average window is of width m as specified in the Span edit field (which must be an odd number, see below); the following smoothers listed below are those most commonly cited in the literature.  For more information on a particular smoothing window, click on the window name.

Daniell (or equal weight) window

Tukey window

Hamming window

Parzen window

Bartlett window

User-defined window.

If the User-defined window radio button is selected, then you are prompted to enter the weights used for smoothing directly (a dialog will open prompting you to specify the weights).

Note that in all cases the Time Series module will standardize the weights so that they always sum to 1.  For example, if you entered 1 2 3 2 1 as the user-defined weights, they will be converted to: 1/9 2/9 3/9 2/9 1/9 (so that they add up to 1).  Also, at the beginning and end of the series, the smoothing is done via reflection.

Span.  This edit field determines the width of the smoothing window.  The number entered here must be odd and greater than or equal to 3.


Transformations for Spectrum Analysis - Real and Imaginary Part

  Time Series Analysis Transformations for Spectrum Analysis - Real and Imaginary Part

This option will perform a Fourier transformation on the input series, resulting in a real and imaginary part (i.e., two new series are created, representing complex numbers).  The transformation is accomplished via the so-called fast Fourier transform algorithm, or FFT for short (first popularized by J.W. Cooley and J.W. Tukey, 1965).  The implementation of the FFT algorithm in the Time Series module allows the user to take full advantage of the savings afforded by this algorithm.  On most standard computers, series with over 100,000 cases can easily be analyzed.  However, there are a few things to remember when analyzing series of that size.

The standard (and most efficient) FFT algorithm requires that the length of the input series is a power of 2.  If this is not the case, then additional computations have to be performed.  In order to still utilize the FFT algorithm, an implementation of the general approach described by Monro and Branch (1976) is used in the Time Series module.  This method requires significantly more storage space, however, series of considerable length can still be analyzed very quickly, even if the number of observations is not equal to a power of 2.

The Fourier transform and its inverse transformation (see below) are often used to construct frequency filters (see, for example, Bloomfield. 1976).  For example, if a Single Spectrum (Fourier) Analysis of a series indicates no significant periodicities at high frequencies, then one may want to filter the series so as to completely eliminate all high frequency fluctuations.  This can be accomplished by first performing the Fourier transformation, then modifying the real and imaginary parts of the series at the respective frequencies, and finally recomputing the series via the inverse Fourier transform.


Transformations for Spectrum Analysis - Inverse Fourier Transform

  Time Series Analysis Transformations for Spectrum Analysis - Inverse Fourier Transform

This is the inverse of the Fourier transform (using the same computational algorithms).  Note that the currently highlighted variable will be interpreted as the real part of the series, and you will be prompted to select the imaginary part after clicking OK.


Time series - Inverse Fourier transform

  Time Series Analysis - Inverse Fourier Transform

Select the imaginary part of the series for the inverse Fourier transformation (see the Transformations for Spectrum Analysis dialog for a description of this transformation).  To select the variable, either double-click on the respective variable, or click once on the respective variable to highlight it and then click OK.


  Time Series Analysis - Choose Range to Transform

Select the range (in terms of case numbers) of the series to be transformed.


  Time Series Analysis - Selecting Variables

Select a variable (series) in this dialog either by highlighting one or more variables and then clicking on the OK button.

You can select a continuous block of variables by holding down the left-mouse-button and dragging the cursor over the variables that you want to highlight.  You can also highlight a continuous block of variables by clicking on the first variable name that you want to select, and while holding down the SHIFT key, clicking on the last variable name that you want to select.  This method will select (highlight) the first and last variables and all variables in-between.  You can select discontinuous blocks of variables by holding down the CTRL key and then clicking on each variable that you want to select.

De-selecting Previously Selected Variables:  You can de-select discontinuous or continuous blocks of previously selected variables by holding down the CTRL key and then clicking on each variable that you want to de-select.


  Time Series Analysis - Selecting Two Variables Lists

Select two lists of variables in this dialog by highlighting the variables and then clicking on the OK button.

You can select a continuous block of variables by holding down the left-mouse-button and dragging the cursor over the variables that you want to highlight.  You can also highlight a continuous block of variables by clicking on the first variable name that you want to select, and while holding down the SHIFT key, clicking on the last variable name that you want to select.  This method will select (highlight) the first and last variables and all variables in-between.  You can select discontinuous blocks of variables by holding down the CTRL key and then clicking on each variable that you want to select.

De-selecting Previously Selected Variables:  You can de-select discontinuous or continuous blocks of previously selected variables by holding down the CTRL key and then clicking on each variable that you want to de-select.


  Time Series Analysis - Specifying Moving Average Weights

Specify the weights to be used for the moving average smoothing transformation.  Note that only the relative magnitudes of the weights matter; for example, specifying .25, .5, .25 or 1, 2, 1 will produce exactly the same result, that is, in this case, the first and the third observation in the moving average window will be assigned half the weight as the second observation, or:

X    = (W *X +W *X +W *X )/(W +W +W )

 new     1  1  2  2  3  3    1  2  3

where W1,2,3 are the weights.  Only positive weights are allowed.


  Time Series Analysis - Selecting One Variable/Series

Select a single variable in this dialog by double-clicking on the variable name to select it and close the dialog box.


  Time Series Analysis - Selecting Variable with Leading Observations

Select a variable by clicking on it.  If you do not select a variable then all leading observations will be set to 0 (zero).

The integration transformation is the reverse of differencing.  The series will be transformed as: X=X+X(lag).  If no variable with leading observations is selected, then all leading observations will be equal to 0 (zero).  For example, suppose the series consists of the values: 3, 4, 2, etc.  We integrate the series with a lag of 1, and choose no variable with leading observations.  The first value of the new series will thus be 0 (zero); the next value will be 0+3, the next 0+3+4, and so on.  The resulting series will be of length N+1, where N is the number of cases in the original series.  Suppose we selected a variable with leading observations, and that the value found in that series for case 1-lag (that is, in this example, for the case just preceding the first case in the series to be transformed) is equal to 5.  Then the first value of the new series will be 5, the next value will be 5+3, the next 5+3+2, and so on.  In this manner, one can difference a series and fully restore it to its original values by integrating it, provided one uses the values of the original (untransformed) series for leading observations.


  Time Series Analysis - Selecting a Variable/Series for the Scatterplot

The current variable will be represented on the Y-axis (vertical) of the scatterplot.  Select a single variable in this dialog for the X-axis (horizontal) of the plot, by double-clicking on the variable name to select it and close the dialog box.


  Time Series Analysis - Selecting Variables/Series for the 3D Scatterplot

Select two variables for the 3D scatterplot by highlighting each variable and then clicking on the OK button.


  Time Series Analysis - Specifying Alpha Level

Enter the significance (α) level that is to be used for highlighting in the Scrollsheet.


  Time Series Analysis - Variable for Crosscorrelation Function

Select the second variable for the crosscorrelation function by double-clicking on it to select it and close this dialog.

After selecting the variable, a Scrollsheet and plot of crosscorrelations will come up, for a lag of -k through +k, where k is the number previously specified in the Number of lags edit field.  The Scrollsheet will report the crosscorrelations and their standard errors (correlations that are greater than 2 times their respective standard errors will be highlighted).  In general, the crosscorrelation is the correlation of a series with another series, shifted by a particular number of observations.  For details regarding the computations of the crosscorrelations and their standard errors refer to the crosscorrelation section.


  Time Series Analysis - Specifying the ARIMA Model

Click on in the Variable or Long variable (series) name column to highlight the variable (series) in the active work area that is to be analyzed (see also, Time Series Analysis - Index).  Select at least one seasonal or non-seasonal moving average or autoregressive parameter.  If seasonal parameters are specified, a seasonal lag must also be specified.  Click OK to begin parameter estimation.  Note that, when returning from the ARIMA Results dialog, up to three new series will be created, and appended to the active work area: (1) the transformed original series (e.g., differenced, logged, etc., depending on the selections in the Transform variable.... box, see below), (2) the ARIMA residuals (from the series after transformations and differencing), and (3) the original series plus forecasts.  Thus, make sure that there is sufficient "space" in the active work area for the respective variable, that is, that there are at least 3 (not locked) backups available.  Increase the Number of backups parameter if necessary.

Also, be sure to Lock all important backups of the original variable (those which you want to retain) if there are less than 3 unused backups available; otherwise, those backups will be overwritten (by the 3 series created by the ARIMA procedure).  To lock a backup, double-click in the Lock column for the respective variable.

For a general discussion of the ARIMA model, refer to the Overview section.

Single Series ARIMA Model dialog:

ARIMA Model Parameters

Transform variable (series) prior to analysis

Estimation of maximum likelihood

Options

Review and plot variables

Autocorrelations

Histogram

Descriptive statistics

Normal, detrended normal, and half-normal probability plots


Specifying the ARIMA Model - ARIMA Model Parameters

  Time Series Analysis Specifying the ARIMA Model - ARIMA Model Parameters

Estimate constant.  In addition to the autoregressive and moving average parameters, ARIMA models may also include a constant.  The interpretation of a (statistically significant) constant depends on the model that is fit.  Specifically, (1) if there are no autoregressive parameters in the model, then the expected value of the constant is μ, the mean of the series; (2) if there are autoregressive parameters in the series then the constant represents the intercept.  If the series is differenced, then the constant represents the mean or intercept of the differenced series; For example, if the series is differenced once, and there are no autoregressive parameters in the model, then the constant represents the mean of the differenced series, and therefore the linear trend slope of the un-differenced series.

Seasonal lag.  This parameter determines the seasonal lag that is applied to the seasonal autoregressive and/or moving average parameters (option P-Seasonal and Q-Seasonal, respectively).  Note that for very long seasonal lags (e.g., 365 days per year), it is recommended to use the Approximate rather than Exact maximum likelihood method, which is less efficient in those cases.  Refer to the Overview section for a discussion of the different methods for computing the likelihood for ARIMA models.

Autoregressive parameters.  Select the number of autoregressive parameters in the model.

Seasonal autoregressive parameters.  Select the number of seasonal autoregressive parameters in the model.  If any seasonal parameters are selected, a Seasonal lag must also be specified.

Moving average parameters.  Select the number of moving average parameters in the model.

Seasonal moving average parameters.  Select the number of seasonal moving average parameters in the model.  If any seasonal parameters are selected, a Seasonal lag must also be specified.


Specifying the ARIMA Model - Transform Variable/Series Prior to Analysis

  Time Series Analysis Specifying the ARIMA Model - Transform Variable/Series Prior to Analysis

The transformations that can be selected via check boxes will be performed prior to the analysis, and the ARIMA parameters will be estimated for the transformed series.  Before forecasts are computed, those transformations will be "undone" and, therefore, those forecasts can be interpreted in terms of the metric of the untransformed series.  The Other transformations & plots button will bring up the General transformations dialog, and those transformations will not automatically be undone when forecasts are computed.

Natural log.  The natural log for each value will be computed.

Power transform.  Each value in the series will be raised to the power of C, where C is the value specified in the edit field on the right.

Difference.  If this checkbox is set, then the series will be differenced.  In keeping with the standard notation introduced by Box & Jenkins (1976), non-seasonal (1) and seasonal (2) differencing can be requested.  Specify the respective Lag and the number of difference passes that are to be performed.

Other transformations.  As described above, this option will bring up the General transformations dialog which allows you to perform a wide variety of transformations on the data.  The transformed series will be appended to the active work area.


Specifying the ARIMA Model - Estimation of Maximum Likelihood

  Time Series Analysis Specifying the ARIMA Model - Estimation of Maximum Likelihood

The Overview section discusses the procedure for estimating the ARIMA model parameters.  In general, the estimation procedure will maximize the likelihood of the data, given the respective model (i.e., number and type of ARIMA parameters).  Three different approaches are implemented in the Time Series module for computing the likelihood for an ARIMA model: (1) the approximate maximum likelihood method according to McLeod and Sales (1983), (2) the approximate maximum likelihood method with backcasting, and (3) the exact maximum likelihood method according to Melard (1984).  All methods will usually yield similar parameter estimates.  Also, all methods are about equally efficient in most real-world time series applications.  However, method 1 (approximate maximum likelihood, no backcasts) is the fastest, and should be used in particular for very long time series (e.g., with more than 30,000 observations; note that the Time Series module is unique in that it will take full advantage of your computer's memory, and it will not impose fixed limitations on the lengths of time series that can be analyzed).  Melard's exact maximum likelihood method (number 3 above) may also become inefficient when used to estimate parameters for seasonal models with long seasonal lags (e.g., with yearly lags of 365 days).  On the other hand, the Time Series module will always use the approximate maximum likelihood method first in order to establish initial parameter estimates that are very close to the actual final values; thus, usually only a few iterations with the exact maximum likelihood method (3 above) are necessary to finalize the parameter estimates.

Backcast cases.  This edit field is only active if the Approximate method is chosen.  The backcast method is somewhat slower than the Approximate maximum likelihood method without backcasts; however, usually when the N in of the series is relatively small and/or some parameter values are close to 1.0 (or -1.0) the estimates derived in this manner tend to be closer to the equivalent Exact maximum likelihood parameters.  The optimum setting of this parameter depends on the type of model and the actual magnitude of the parameter values; in practice, McLeod and Sales (1983) recommend to choose the number of backcasts so that:

No.of backcasts = q+s*q +20*(p+s*p )

                       s          s

where p, ps, q, and qs are the non-seasonal and seasonal autoregressive and moving average parameters, respectively, and s is the seasonal lag.


Specifying the ARIMA Model - Options

  Time Series Analysis Specifying the ARIMA Model - Options

This option will bring up the ARIMA parameter estimation options dialog.  The estimation of ARIMA parameters is an iterative procedure.  On that dialog you can specify the maximum number of iterations, the convergence criterion, and request to specify start values for the parameter estimation.  If you request to manually specify start values, then, after clicking OK, you will be prompted to specify start values for all parameters in the model.


Specifying the ARIMA Model - Review and Plot Variables

  Time Series Analysis Specifying the ARIMA Model - Review and Plot Variables

These options allow you to review or plot the currently highlighted variable (together with other variables).  The labeling of the individual observations (that is, of the respective points in time represented by the rows in Scrollsheets or the horizontal X-axis in plots) is determined by the selections in the Display/plot options dialog (click on the Options button below; these options are also available on the Transformations dialog).  For the plots, you can choose to Scale the X axis in the plots manually.  This is often useful when the series consists of several regularly recurring time intervals, for example, if it is made up of 10 years with 12 (monthly) observations each.  Then it may be useful to scale the X-axis in the plot so that each major tickmark indicates one year.

Display/plot subset of cases only.  If this check box is set, then, before plotting or displaying one or more series, you will be prompted to select a range of observations to include in the plot or display.

Options (scaling, labels, etc.).  This option will bring up the Display/plot options dialog.  That dialog allows you to change the labeling of the observations (i.e., the rows in Scrollsheets and the X-axis in line plots can be labeled with case names, case numbers, dates from another variable, etc.) and the scaling of the X-axis in line plots (minimum, step size).

Review/Plot highlighted variable.  This button will bring up a Scrollsheet (or a plot) with the values for the currently highlighted variable.

Review/Plot multiple variables.  After clicking on this button, you will first be prompted to select a list of variables to be displayed or plotted.  When plotting multiple variables the vertical (Y) axis will have a common scale; thus, if the series that are plotted contain values of completely different magnitudes use option Plot two var lists with different scales (see below), instead.

Plot two var. lists with different scales.  This option allows you to plot two lists of variables using different scales for the vertical (Y) axes in the plot.  The first list will be plotted against the left Y-axis and the second list will be plotted against the right Y-axis.  For example, suppose you want to plot two variables (series) called S1 and S2, and that these variables contain values of different magnitudes: the values of S1 range from 1-100 and the values of S2 range from 1000 to 10000.  If you plot S1 against the left Y-axis (scaled from 1-100) and S2 against the right Y-axis (scaled from 1000-10000) then both variables will be plotted with optimal resolution, and thus relationships between patterns across time (the X-axis) may become more clearly identifiable.


Specifying the ARIMA Model - Autocorrelations

  Time Series Analysis Specifying the ARIMA Model - Autocorrelations

These options will compute the autocorrelations and partial autocorrelations for the currently highlighted variable; these statistics will be displayed in a Scrollsheet and drawn in a correlogram graph.  Refer to the Overview section for a brief description of how the pattern of (partial) autocorrelations aids in the determination of an appropriate ARIMA model.

Autocorrelations button.  This option will bring up a Scrollsheet and plot of the autocorrelations, for a lag of 1 through the number specified in the Number of lags edit field.  The Scrollsheet will report the autocorrelations, their standard errors, the so-called Box-Ljung statistic, and the significance level of that statistic.  In general, the autocorrelation is the correlation of the series with itself, lagged by a particular number of observations.  For details regarding the computations of those statistics refer to the autocorrelation section.

Alpha for highlighting.  Significant autocorrelations (significant Box-Ljung statistics) will be highlighted in the Scrollsheet.  This edit field allows you to specify the significance level that is used for highlighting.

White noise standard errors.  Under the assumption that the true moving average process in the series is of the order k-1, the approximate standard error of the autocorrelation rk is computed as:

                                2

StdErr(r ) = √{(1/N) * [1+2*Σ(r  )]}

        k                      i

(for i = 1 to k-1)

Here N is the number of observations in the series.  Under the assumption that the series is a white noise process, that is, that all autocorrelations are equal to zero, the standard error of rk is computed as:

StdErr(r ) = √{(1/N) * [(N-k)/(N+2)]}

        k

Check the White noise standard errors option to compute the standard errors in this manner.

Partial autocorrelations.  This option will bring up a Scrollsheet and plot of the partial autocorrelations, for a lag of 1 through the number specified in the Number of lags edit field.  The Scrollsheet will report the partial autocorrelations and their standard errors.  In general, the partial autocorrelation is the partial correlation of a series with itself, lagged by a particular number of observations, and controlling for all correlations for lags of lower order.  For example, the partial autocorrelation for a lag of 2 represents the unique correlation of the series with itself at that lag, after controlling for the correlation at lag 1.  For details regarding the computations of the partial autocorrelation and its standard error refer to the partial autocorrelation section.  Partial autocorrelations that are larger than two times their respective standard errors will be highlighted in the Scrollsheet.

Number of lags.  This parameter determines the maximum number of lags for which the auto-, and partial autocorrelations will be computed.


Specifying the ARIMA Model - Histogram

  Time Series Analysis Specifying the ARIMA Model - Histogram

This option will bring up a histogram of the currently highlighted variable.


Specifying the ARIMA Model - Descriptive Statistics

  Time Series Analysis Specifying the ARIMA Model - Descriptive Statistics

This option will bring up a Scrollsheet with descriptive statistics for all variables currently available in the active work area.


Specifying the ARIMA Model - Normal, Detrended Normal, Half-Normal Probability Plots

  Time Series Analysis Specifying the ARIMA Model - Normal, Detrended Normal, and Half-Normal Probability Plots

These options will bring up the respective normal probability plot for the highlighted variable.  For more information on how these plots are constructed, see Normal Probability Plots, Half-Normal Probability Plots, and Detrended Normal Probability Plots.


  Time Series Analysis - Display/Plot Options

Label data points with...:  The choice of radio button in this box determines the labeling of the data points in displays or plots.  The setting of these radio buttons will be retained across other analytical procedures in this module, for example, when displaying residuals from an ARIMA analysis.  By default (radio button Case numbers), each point will be identified by the respective case number, and case numbers will be used on the X-axis in plots of available series.  If there are Case names available in the data file, you may use them to label the data points (rows in Scrollsheets and the X-axis in plots).  If you choose to use Dates, a single variable selection dialog will come up where you can select the variable containing dates (i.e., values formatted as dates).  Those dates will then be used to label points in Scrollsheets and the X-axis in plots.  Finally, you may use Consecutive integers, starting from 1, to label the points and X-axis in plots.

Note that in the Consecutive integers setting what will be displayed is the offset (plus one) of the respective data point from the first data point of any variable in the active work area.  For example, suppose you have in the active work area two series called S1 and S2.  S1 has its first valid observation at case number 5, and S2 has its first valid observation at case number 8.  If we were to use option Review multiple variables to display both variables, and choose the Consecutive integers option, then the first valid observation for variable S1 will be labeled 1, and the first valid observation for variable S2 will be labeled 4.

Scale X-axis in plots manually (min, step):  The setting of this check box will affect the scaling of the X-axis in line plots of single or multiple variables (series).  The choice of scaling will be retained across other analytical procedures in this module, for example, when plotting forecasts from an ARIMA analysis.  By default, if this check box is not set, the X-axis in all plots will always be scaled so that (1) all valid data points are displayed in the plot, and (2) that the tickmarks (steps) on the X-axis are "neat" (i.e., the significant digit of the step size is either 1, 2, or 5).  However, if there is a known periodicity in the data that is of interest, such as 12 months per year or 10 observations per day, etc., then it may be useful to set this check box and to scale the X-axis for plots accordingly.


  Time Series Analysis - Estimation Procedure

The ARIMA parameter estimation procedure is iterative in nature, that is, parameter estimates are refined in successive iterations (see also, Time Series Analysis - Overview section and Time Series Analysis - Index).  A quasi-Newton algorithm is used to minimize the conditional residual sums of squares, given the respective ARIMA parameter estimates.  The sums of squares value is listed in the Loss column in the window; the parameter values are listed to the right.

If the parameter estimation procedure fails to converge.  There are a number of reasons why the parameter estimation procedure does not converge.  One major reason can be that the model parameters are highly redundant (and intercorrelated); thus when one parameter is moved in one direction, then another parameter becomes less than optimal and must also be moved; that move in turn may cause the first parameter to be less than optimal, and so on.  Often, this type of problem occurs when the model is misspecified.  Therefore, one should further study the patterns of (partial) autocorrelations and try to fit a simpler model with less parameters.  Also, this problem may occur when there is a local minimum in the sums of squares function, "holding" some parameter values in a place where they are very redundant with other parameters.  Therefore, you may also want to try different start values (see the Parameter estimation options panel).

Another reason for the failure to converge could be that the estimation procedure repeatedly attempts to move the parameters outside their legal bounds.  In that case, a very large value ("penalty function") is assigned to the SS to "entice" the estimation procedure to move the parameters away from the illegal values.  When that fails, you may see very large values for the sums of squares, indicating that the model is inappropriate.  This can happen, for example, when the series is clearly non-stationary, and a single autoregressive parameter is requested (see the Overview section for a discussion of the ARIMA model).


  Time Series Analysis - ARIMA Results

This dialog provides access to the ARIMA results (see also, Time Series Analysis - Index).  When exiting the dialog via Exit, the ARIMA residuals will be appended to the active work area.  Note that those residuals pertain to the differenced and transformed series.  If during the review of the results ARIMA forecasts were computed, those forecasts will also be appended to the active work area.

Single Series ARIMA Results dialog:

Parameter estimates

Parameters for interrupted time series

Print results

Parameter covariances/correlations

Forecasting

Plots of residuals

Review and plot variables

Autocorrelations of residuals


ARIMA Results - Parameter Estimates

  Time Series Analysis ARIMA Results - Parameter Estimates

This option will bring up a Scrollsheet with the parameter estimates, their standard errors, the t values (parameter estimates divided by standard errors), and the respective p levels.  Note that the standard errors are approximations, computed from the inverse of the matrix of partial derivatives approximated via finite differencing (refer to the Overview section).


ARIMA Results - Parameters for Interrupted Time Series

  Time Series Analysis ARIMA Results - Parameters For Interrupted Time Series

The general logic of interrupted time series ARIMA is described in the Overview section (refer also to the Interrupted time series dialog).  Following the standard notation discussed in McDowall, McCleary, Meidinger, & Hay (1980), three major types of impacts are possible: (1) permanent abrupt, (2) permanent gradual, and (3) abrupt temporary.

A permanent abrupt impact pattern simply implies that the overall mean of the time series shifted after the intervention; the overall shift is denoted by ω (parameter name omega(i) in the Scrollsheet).

The gradual permanent impact pattern implies that the increase or decrease due to the intervention is gradual, and that the final permanent impact becomes evident only after some time.  This type of intervention can be summarized by the expression: Impactt=δ*Impactt-1+ω (for all t  time of impact, else = 0).  The respective parameter names used in the Scrollsheet are delta(i) and omega(i).  If δ is greater than 0 and less than 1 (the bounds of system stability), the impact will be gradual and result in an asymptotic change (shift) in the overall mean by the quantity: Asymptotic change in level=ω/(1-δ).  The asymptotic change for gradual permanent impacts will also be displayed in the Scrollsheet.  Note that, when evaluating a fitted model, it is important that both parameters are statistically significant; otherwise one could reach paradoxical conclusions.  For example, suppose the ω parameter is not statistically significant from 0 (zero) but the δ parameter is; this would mean that an intervention caused a significant gradual change, the final result of which was not significantly different from zero.

The abrupt temporary impact pattern implies an initial abrupt increase or decrease due to the intervention which then slowly decays, without permanently changing the mean of the series.  This type of intervention can be summarized by the expressions:

Prior to intervention:	Impactt = 0

At time of intervention:	Impactt = ω

After intervention:	Impactt = δ*Impactt-1

Note that this impact pattern is again defined by the two parameters δ (parameter name delta(i) in the Scrollsheet) and ω (parameter name omega(i) in the Scrollsheet).  Note that, when evaluating a fitted model, it is again important that both parameters are statistically significant; otherwise one could reach paradoxical conclusions.  For example, suppose the ω parameter is not statistically significant from 0 (zero) but the δ parameter is; this would mean that an intervention did not cause an initial abrupt change, which then showed significant decay.


ARIMA Results - Print Results

  Time Series Analysis ARIMA Results - Print Results

This button will print a summary of the results to the current printer, disk file, and/or Text/output Window, depending on your choice in the Page/Output Setup dialog.


ARIMA Results - Parameter Covariances/Correlations

  Time Series Analysis ARIMA Results - Parameter Covariances/Correlations

The variance/covariance matrix of parameter estimates is computed from a finite difference approximation of the Hessian matrix of partial derivatives.  The resulting estimates are asymptotic in nature.  The higher the correlation between two parameters, the greater is their redundancy of their contribution to the fit of the model.  The parameter covariance matrix cannot be computed if the Hessian matrix cannot be inverted, which usually indicates that one or more parameters are completely redundant.  In terms of the ARIMA model, this usually means that the model is inappropriate (misspecified).  In that case, carefully review the patterns of (partial) autocorrelation and try to fit a simpler model.


ARIMA Results - Forecasting

  Time Series Analysis ARIMA Results - Forecasting

ARIMA forecasts are computed, after all transformations and differencing (selected on the ARIMA specification dialog) has been "undone;" that is, the computed forecasts will be expressed in the units of the original time series.  The computations of the forecasts and their standard errors closely follows the algorithm described in Box & Jenkins (1976; Program 4).

Forecast cases.  This button will bring up a Scrollsheet with (1) the ARIMA forecasts, (2) their standard errors (if no log or power transformation was requested), (3) their confidence limits according to the value in the Confidence level edit field, and (4) the observed values and residuals (observed minus predicted), if applicable (i.e., if forecasts are requested for cases that were also observed; see below).

Plot series & forecasts.  This button will bring up a line graph showing (1) the values of the observed series, (2) the values of the forecasts, and (3) the confidence limits around the forecasts, according to the value in the Confidence level edit field.  The scaling and labeling of the horizontal (X) axis in this plot depends on the current settings in the Display/plot options dialog (click on the Options button in the Review and plot variables box).

Number of cases...; Start at case.  These parameters determine (1) how many forecasts will be computed, and (2) at which point in the series the forecasts begin.  Ordinarily, one wants to predict the future, so by default the program will compute the forecasts starting with the first observation in the future (after the last valid observed case) through at least one seasonal cycle.  However, a very powerful visual way of evaluating the quality of the fit of the current ARIMA model to the data is to evaluate how well the predicted values follow the actual observed values.  Therefore, it is sometimes useful to compute forecasts for two or three seasonal cycles in the middle of the series.

Note that the Start at parameter should always be set in terms of the original case numbers in the file, not in terms of valid case numbers for the respective series.  For example, if the variable being analyzed has, in the data file, missing data for the first 20 cases, and then 100 valid cases, then the first future case will be 20+100+1=121 (even though there are only 80 valid cases in the series).

Confidence level.  This parameter determines the confidence band around the forecasts in the Scrollsheets and plots.

Append forecasts to original series on Exit.  If this checkbox is set (it is by default), then when exiting this dialog (via Exit) the forecasts (the ones computed the last time prior to Canceling) will be combined with the observed values (up to the forecasts), and this new series will be appended to the active work area.  So for example, if you requested 20 forecast starting with case number 101, then the first 101 observations for the new series will be copied from the original series, and then 20 forecasts (case 101 to 120) will be added.


ARIMA Results - Plots of Residuals

  Time Series Analysis ARIMA Results - Plots of Residuals

These plots allow you to review the distribution of the ARIMA residuals.  Note that the residuals are computed for the transformed and differenced series, and thus they may be different that those that can be computed via the Forecasting options above.  The ARIMA model assumes that the residuals (random shock component of the model: ε) are normally distributed.  Quick visual checks of the validity of this assumption can be performed via these plots.

Histogram.  This option will bring up a histogram for the residuals, with the normal distribution curve superimposed.

Normal, detrended normal, and half-normal probability plots.  These options will bring up the respective normal probability plot of the residuals.  The way the standard normal probability plot is constructed is as follows.  First the values are rank ordered.  From these ranks we can compute z values (i.e., standardized values of the normal distribution) based on the assumption that the data come from a normal distribution.  These z values are plotted on the Y-axis in the plot.  If the residuals (plotted on the X-axis) are normally distributed, then all points should fall onto a straight line in the plot.  If the residuals are not normally distributed, they will deviate from the line.  Outliers may also become evident in this plot.  The detrended normal probability plot is constructed in the same way as the standard normal probability plot, except that, before the plot is produced, the linear trend is removed.  This often "spreads out" the plot, thereby allowing the user to detect patterns of deviations more easily.  The half-normal probability plot is constructed in the same way as the standard normal probability plot, except that only the positive half of the normal curve is considered.  Consequently, only positive normal values will be plotted on the Y-axis.  This plot is basically used when one wants to ignore the sign of the residual, that is, when one is mostly interested in the distribution of absolute values, regardless of the sign.


ARIMA Results - Review and Plot Variables

  Time Series Analysis ARIMA Results - Review and Plot Variables

These options allow you to review or plot the original series, the transformed and differenced series, and the residuals (computed for the transformed and differenced series; thus those residuals may be different than those computed by the Forecasting options above).  The labeling of the individual observations (that is, of the respective points in time represented by the rows in Scrollsheets or the horizontal X-axis in plots) is determined by the selections in the Display/plot options dialog (click on the Options button below; these options are also available on the Transformations dialog).  For the plots, you can choose to Scale the X-axis in the plots manually.  This is often useful when the series consists of several regularly recurring time intervals, for example, if it is made up of 10 years with 12 (monthly) observations each.  Then it may be useful to scale the X-axis in the plot so that each major tickmark indicates one year.

Display/plot subset of cases only.  If this check box is set, then, before plotting or displaying a series, you will be prompted to select a range of observations to include in the plot or display.

Options (scaling, labels, etc.).  This option will bring up the Display/plot options dialog.  That dialog allows you to change the labeling of the observations (e.g., the X-axis in line plots can be labeled with case names, case numbers, dates from another variable, etc.) and the scaling of the X-axis in line plots (minimum, step size).

Review/Plot original series.  This button will bring up a Scrollsheet (or a plot) with the values for the original series (prior to transformations and differencing).

Review/Plot transformed series.  This button will bring up a Scrollsheet (or a plot) with the values for the transformed and differenced series.

Review/Plot residuals.  This button will bring up a Scrollsheet (or a plot) with the values for the residuals, computed from the transformed and differenced series.


ARIMA Results - Autocorrelations of Residuals

  Time Series Analysis ARIMA Results - Autocorrelations of Residuals

These options will compute the autocorrelation and partial autocorrelation for the residuals (computed for the transformed and differenced series); these statistics will be displayed in a Scrollsheet and drawn in a correlogram graph.  Refer to the Overview section for a brief description of how the pattern of (partial) autocorrelations aids in the determination of an appropriate ARIMA model.  In general, if the ARIMA model sufficiently reproduces the observed values in the series, then no (partial) autocorrelations should remain, that is, be present in the residuals.

Autocorrelations.  This option will bring up a Scrollsheet and plot of the autocorrelations for the residuals, for a lag of 1 through the number specified in the Number of lags edit field.  The Scrollsheet will report the autocorrelations, their standard errors, the so-called Box-Ljung statistic, and the significance level of that statistic.  In general, the autocorrelation is the correlation of the series with itself, lagged by a particular number of observations.  For details regarding the computations of those statistics refer to the autocorrelation section.

Alpha for highlighting.  Significant autocorrelations (significant Box-Ljung statistics) will be highlighted in the Scrollsheet.  This edit field allows you to specify the significance level that is used for highlighting.

White noise standard errors.  Under the assumption that the true moving average process in the series is of the order k-1, the approximate standard error of the autocorrelation rk is computed as:

                                2

StdErr(r ) = √{(1/N) * [1+2*Σ(r  )]}

        k                      i

(for i = 1 to k-1)

Here N is the number of observations in the series.  Under the assumption that the series is a white noise process, that is, that all autocorrelations are equal to zero, the standard error of rk is computed as:

StdErr(r ) = √{(1/N) * [(N-k)/(N+2)]}

        k

Check the White noise standard errors option to compute the standard errors in this manner.

Partial autocorrelations.  This option will bring up a Scrollsheet and plot of the partial autocorrelations of the residuals, for a lag of 1 through the number specified in the Number of lags edit field.  The Scrollsheet will report the partial autocorrelations and their standard errors.  In general, the partial autocorrelation is the partial correlation of a series with itself, lagged by a particular number of observations, and controlling for all correlations for lags of lower order.  For example, the partial autocorrelation for a lag of 2 represents the unique correlation of the series with itself at that lag, after controlling for the correlation at lag 1.  For details regarding the computations of the partial autocorrelation and its standard error refer to the partial autocorrelation section.  Partial autocorrelations that are larger than two times their respective standard errors will be highlighted in the Scrollsheet.

Number of lags.  This parameter determines the maximum number of lags for which the auto-, and partial autocorrelations will be computed.


  Time Series Analysis - ARIMA Parameter Estimation Options

The choices on this dialog pertain to some technical aspect of the parameter estimation procedure.  Usually, the default settings do not need to be changed, unless the model that you are trying to fit is "unusual" in some way, and those settings do not produce valid parameter estimates. In general, parameter estimation of ARIMA models is an iterative procedure.  In each iteration the program will compute the conditional sums of squares for the current parameter values (refer to the Overview section for a description of the approximate and exact maximum likelihood methods for estimating the conditional sums of squares, and to the Time Series Analysis - Index).  The goal of the estimation procedure is to find a set of parameters that will minimize the sums of squares.

The quasi-Newton method (see Fletcher & Powell, 1963; Fletcher, 1969) is used to minimize the Sums of Squares.  This method does not require explicit derivatives of the function to be minimized, but will approximate them via differencing.  Thus this is a very efficient general method.  Refer to the Nonlinear Estimation chapter for additional details concerning the estimation of non-linear models.  Iterations will continue until (1) the Maximum number of iterations have been exceeded (note that you can then request additional iterations and the procedure will continue where it left off; thus there is no point in requesting very many iterations in this dialog), or (2) the parameter accuracy is less than the Convergence criterion (see below for details).

Maximum number of iterations

Convergence criterion

Parameter Estimation Options dialog:

Start values for parameter estimates

Automatic

User-defined


ARIMA Parameter Estimation Options - Maximum Number of Iterations

  Time Series Analysis ARIMA Parameter Estimation Options - Maximum Number of Iterations

This parameter determines the maximum number of quasi-Newton iterations that will be performed.  When the maximum number of iterations is exceeded during estimation, you will be prompted and asked whether to perform additional iterations.


ARIMA Parameter Estimation Options - Convergence Criterion

  Time Series Analysis ARIMA Parameter Estimation Options - Convergence Criterion

This parameter determines the accuracy or precision with which the parameters will be estimated, or more specifically, the accuracy of the parameters with respect to the minimum of the conditional SS as computed by the respective approximate or exact maximum likelihood method (refer to the Overview section).  The estimation procedure will terminate when the changes in the ARIMA parameters over consecutive iterations are less than this value.  [For the ω (omega) parameters in an interrupted time series analysis, the convergence parameter is interpreted so that sufficient accuracy is defined as: .05*(convergence criterion)*Δω; where Δω stands for the change in the omega parameters from iteration to iteration.]


ARIMA Parameter Estimation Options - Start Values for Parameter Estimates

  Time Series Analysis ARIMA Parameter Estimation Options - Start Values for Parameter Estimates

The choice of radio button in this box determines how the parameter values will be computed prior to the estimation procedure, that is, with which values to start the iterations.


ARIMA Parameter Estimation Options - Automatic

  Time Series Analysis ARIMA Parameter Estimation Options - Automatic

If Automatic is chosen, then, for simple ARIMA models, all parameters are started with 0.1.  For interrupted time series ARIMA (refer also to the Overview section) (1) the ARIMA parameters are started at their previously estimated value if an identical ARIMA model (with respect to the number and types of parameters) was estimated just prior to the intervention analysis; otherwise they are started at 0.1; (2) the ω (omega) parameters for abrupt intervention types will be started as the difference between the values of the series prior to the intervention and after the intervention.


ARIMA Parameter Estimation Options - User-defined

  Time Series Analysis ARIMA Parameter Estimation Options - User-defined

If User-defined is chosen, then before beginning the parameter estimation (after clicking OK (Begin parameter estimation)) the ARIMA parameter start values dialog will be displayed, allowing you to manually specify start values for the parameter estimation.


  Time Series Analysis - ARIMA Parameter Start Values

The values specified in this dialog window will determine the parameter values used in the first iteration of the estimation procedure.  For details concerning the (interrupted time series) ARIMA model parameters and the estimation procedure refer to the Overview section.


  Time Series Analysis - Interrupted Time Series

This dialog allows you to specify an interrupted time series ARIMA analysis.  This technique has also been called impact analysis or intervention analysis.  In general, additional parameters (in addition to the autoregressive and moving average parameters) are estimated to account for one or more discrete events that either temporarily or permanently change the overall "level" or mean of the series.  The general logic of this type of analysis, and the different impact patterns are also discussed in the Overview section (see also, Time Series Analysis - Index).  An excellent brief and applications-oriented introduction to this method is provided by McDowall, McCleary, Meidinger, and Hay (1980).

The options for Specifying the ARIMA model. in this dialog are identical to those for the simple single series analysis (and are described there).  Described below are the options specific for interrupted time series analysis.

Interrupted Time Series ARIMA (Intervention Analysis) dialog:

Specify times and types of interventions

Impact Patterns

Review type of impact patterns


Interrupted Time Series - Specify Times and types of Interventions

  Time Series Analysis Interrupted Time Series - Specify Times and Types of Interventions

Up to 6 interventions can be specified.  To specify an intervention, first click on the respective check box and then enter the case number where the intervention occurred.  Note that the case number should reference the actual case number in the file, not the offset (plus 1) from the first valid case.  So for example, if the intervention occurs at case number 100 in the data file, but the first 20 cases of the series are missing, then you would still specify 100 as the time of intervention.  Then specify the desired Type of intervention.

McDowall et. al (1980) distinguish between three major types of impacts that are possible: (1) permanent abrupt, (2) permanent gradual, and (3) abrupt temporary.  These different impact patterns can also be reviewed (see the Impact patterns dialog).


Interrupted Time Series - Impact Patterns

  Time Series Analysis Interrupted Time Series - Impact Patterns

The following options are discussed in the Impact Patterns topic.

Abrupt Permanent Impact

Gradual Permanent Impact

Abrupt Temporary Impact


Interrupted Time Series - Review type of Impact Patterns

  Time Series Analysis Interrupted Time Series - Review Type of Impact Patterns

This option will bring up the Impact patterns dialog, allowing you to review the different types of impact patterns in graphs, and to try different values for the δ parameter.


  Time Series Analysis - Impact Patterns

These options allow you to visualize graphically the different impact patterns, and to review the effect of different δ (delta) parameters (see below).  First select the desired Type of intervention and then click OK.  (See also, Time Series Analysis - Index.)

Interrupted time series ARIMA

Abrupt permanent impact

Gradual permanent impact

Abrupt temporary impact


Impact Patterns - Interrupted Time Series ARIMA

  Time Series Analysis Impact Patterns - Interrupted Time Series ARIMA

A common research questions in time series analysis is whether an outside event affected subsequent observations.  For example, did the implementation of a new economic policy improve economic performance; did the a new anti-crime law affect subsequent crime rates; and so on.  In general, we would like to evaluate the impact of one or more discrete events on the values in the time series.  This type of interrupted time series analysis is described in detail in McDowall, McCleary, Meidinger, & Hay (1980).  McDowall et. al distinguish between three major types of impacts that are possible: (1) permanent abrupt, (2) permanent gradual, and (3) abrupt temporary.


Impact Patterns - Abrupt Permanent Impact

  Time Series Analysis Impact Patterns - Abrupt Permanent Impact

A permanent abrupt impact pattern simply implies that the overall mean of the times series shifted after the intervention; the overall shift is denoted by ω (omega).


Impact Patterns - Gradual Permanent Impact

  Time Series Analysis Impact Patterns - Gradual Permanent Impact

The gradual permanent impact pattern implies that the increase or decrease due to the intervention is gradual, and that the final permanent impact becomes evident only after some time.  This type of intervention can be summarized by the expression:

Impact  = δ*Impact   +ω

      t           t-1

(for all t  time of impact, else = 0).

Note that this impact pattern is defined by the two parameters δ (delta) and ω (omega).  If δ is near 0 (zero), then the final permanent amount of impact will be evident after only a few more observations; if δ is close to 1, then the final permanent amount of impact will only be evident after many more observations.  As long as the δ parameter is greater than 0 and less than 1 (the bounds of system stability), the impact will be gradual and result in an asymptotic change (shift) in the overall mean by the quantity:

Asymptotic change in level = ω/(1-δ)

The Time Series module will automatically compute the asymptotic change for gradual permanent impacts.  Note that, when evaluating a fitted model, it is important that both parameters are statistically significant; otherwise one could reach paradoxical conclusions.  For example, suppose the ω parameter is not statistically significant from 0 (zero) but the δ parameter is; this would mean that an intervention caused a significant gradual change, the final result of which was not significantly different from zero.


Impact Patterns - Abrupt Temporary Impact

  Time Series Analysis Impact Patterns - Abrupt Temporary Impact

The abrupt temporary impact pattern implies an initial abrupt increase or decrease due to the intervention which then slowly decays, without permanently changing the mean of the series.  This type of intervention can be summarized by the expressions:

Prior to intervention:	Impactt = 0

At time of intervention:	Impactt = ω

After intervention:	Impactt = δ*Impactt-1

Note that this impact pattern is again defined by the two parameters δ (delta) and ω (omega).  As long as the δ parameter is greater than 0 and less than 1 (the bounds of system stability), the initial abrupt impact will gradually decay.  If δ is near 0 (zero) then the decay will be very quick, and the impact will have entirely disappeared after only a few observations.  If δ is close to 1 then the decay will be slow, and the intervention will affect the series over many observations.  Note that, when evaluating a fitted model, it is again important that both parameters are statistically significant; otherwise one could reach paradoxical conclusions.  For example, suppose the ω parameter is not statistically significant from 0 (zero) but the δ parameter is; this would mean that an intervention did not cause an initial abrupt change, which then showed significant decay.


  Time Series Analysis - Distributed Lags Analysis

Select the dependent variable by highlighting the respective series in the active work area; select the independent variable with the Independent variable button.  After clicking OK, Scrollsheets will be computed (1) for the alpha weights (if Almon polynomial distributed lags was selected, see below), (2) with the analysis of variance table, and (3) with the regression weights.  For an overview over this method refer to the Distributed Lags Analysis section (see also, Time Series Analysis - Index).

Distributed Lags Analysis dialog

Independent variable

Lag length

Method

Review and plot variables

Autocorrelations

Histogram

Descriptive statistics

Normal, Detrended normal, and Half-normal probability plots

Other transformations and plots


Distributed Lags Analysis - Independent Variable

  Time Series Analysis Distributed Lags Analysis - Independent Variable

This option will bring up a standard variable selection window for selecting the independent (explanatory or exogenous) variable.


Distributed Lags Analysis - Lag Length

  Time Series Analysis Distributed Lags Analysis - Lag Length

This edit box specifies the maximum lag length to be used in the analysis; the default (and minimum value) is 1; the maximum lag is 48.  However, note that the maximum lag is also constrained by the number of cases in your data file.  Specifically, the valid number of cases in the data file must be larger than: 2 * lag length + 3.  Otherwise, reliable parameter estimates cannot be obtained.


Distributed Lags Analysis - Method

  Time Series Analysis Distributed Lags Analysis - Method

The Time Series module will estimate two types of distributed lags models:  The unconstrained lags model and the Almon polynomial distributed lag model (Almon, 1965; refer to the Distributed Lags Analysis overview section).

Polynomial order.  This edit box is only active if Almon distributed lags was selected.  You may specify the polynomial order for the parameter estimation (refer to the Distributed Lags Analysis overview section); this value must be smaller than the Lag length.


Distributed Lags Analysis - Review and Plot Variables

  Time Series Analysis Distributed Lags Analysis - Review and Plot Variables

These options allow you to review or plot the currently highlighted variable (together with other variables).  The labeling of the individual observations (that is, of the respective points in time represented by the rows in Scrollsheets or the horizontal X-axis in plots) is determined by the selections in the Display/plot options dialog (click on the Options button; these options are also available on the Transformations dialog).  For the plots, you can choose to Scale the X-axis in the plots manually.  This is often useful when the series consists of several regularly recurring time intervals, for example, if it is made up of 10 years with 12 (monthly) observations each.  Then it may be useful to scale the X-axis in the plot so that each major tickmark indicates one year.

Display/plot subset of cases only.  If this check box is set, then, before plotting or displaying one or more series, you will be prompted to select a range of observations to include in the plot or display.

Options (scaling, labels, etc.).  This option will bring up the Display/plot options dialog.  That dialog allows you to change the labeling of the observations (i.e., the rows in Scrollsheets and the X-axis in line plots can be labeled with case names, case numbers, dates from another variable, etc.) and the scaling of the X-axis in line plots (minimum, step size).

Review/Plot highlighted variable.  This button will bring up a Scrollsheet (or a plot) with the values for the currently highlighted variable.

Review/Plot multiple variables.  After clicking on this button, you will first be prompted to select a list of variables to be displayed or plotted.  When plotting multiple variables the vertical (Y) axis will have a common scale; thus, if the series that are plotted contain values of completely different magnitudes use option Plot two var lists with different scales (see below), instead.

Plot two var. lists with different scales.  This option allows you to plot two lists of variables using different scales for the vertical (Y) axes in the plot.  The first list will be plotted against the left Y-axis and the second list will be plotted against the right Y-axis.  For example, suppose you want to plot two variables (series) called S1 and S2, and that these variables contain values of different magnitudes: the values of S1 range from 1- 100 and the values of S2 range from 1000 to 10000.  If you plot S1 against the left Y-axis (scaled from 1-100) and S2 against the right Y-axis (scaled from 1000-10000) then both variables will be plotted with optimal resolution, and thus relationships between patterns across time (the X-axis) may become more clearly identifiable.


Distributed Lags Analysis - Autocorrelations

  Time Series Analysis Distributed Lags Analysis - Autocorrelations

These options will compute the autocorrelations and partial autocorrelations for the currently highlighted variable; these statistics will be displayed in a Scrollsheet and drawn in a correlogram graph.  Refer to the Overview section for a brief description of how the pattern of (partial) autocorrelations aids in the determination of an appropriate ARIMA model.

Autocorrelations.  This option will bring up a Scrollsheet and plot of the autocorrelations, for a lag of 1 through the number specified in the Number of lags edit field.  The Scrollsheet will report the autocorrelations, their standard errors, the so-called Box-Ljung statistic, and the significance level of that statistic.  In general, the autocorrelation is the correlation of the series with itself, lagged by a particular number of observations.  For details regarding the computations of those statistics refer to the autocorrelation section.

Alpha for highlighting.  Significant autocorrelations (significant Box-Ljung statistics) will be highlighted in the Scrollsheet.  This edit field allows you to specify the significance level that is used for highlighting.

White noise standard errors.  Under the assumption that the true moving average process in the series is of the order k-1, the approximate standard error of the autocorrelation rk is computed as:

                                2

StdErr(r ) = √{(1/N) * [1+2*Σ(r  )]}

        k                      i

(for i = 1 to k-1)

Here N is the number of observations in the series.  Under the assumption that the series is a white noise process, that is, that all autocorrelations are equal to zero, the standard error of rk is computed as:

StdErr(r ) = √{(1/N) * [(N-k)/(N+2)]}

        k

Check the White noise standard errors option to compute the standard errors in this manner.

Partial autocorrelations.  This option will bring up a Scrollsheet and plot of the partial autocorrelations, for a lag of 1 through the number specified in the Number of lags edit field.  The Scrollsheet will report the partial autocorrelations and their standard errors.  In general, the partial autocorrelation is the partial correlation of a series with itself, lagged by a particular number of observations, and controlling for all correlations for lags of lower order.  For example, the partial autocorrelation for a lag of 2 represents the unique correlation of the series with itself at that lag, after controlling for the correlation at lag 1.  For details regarding the computations of the partial autocorrelation and its standard error refer to the partial autocorrelation section.  Partial autocorrelations that are larger than two times their respective standard errors will be highlighted in the Scrollsheet.

Number of lags.  This parameter determines the maximum number of lags for which the autocorrelations and partial autocorrelations will be computed.


Distributed Lags Analysis - Histograms

  Time Series Analysis Distributed Lags Analysis - Histograms

This option will bring up a histogram of the currently highlighted variable.


Distributed Lags Analysis - Descriptive Statistics

  Time Series Analysis Distributed Lags Analysis - Descriptive Statistics

This option will bring up a Scrollsheet with descriptive statistics for all variables currently available in the active work area.


Distributed Lags Analysis - Normal, Detrended, Half-Normal Probability Plots

  Time Series Analysis Distributed Lags Analysis - Normal, Detrended, Half-Normal Probability Plots

These options will bring up the respective normal probability plot for the highlighted variable.  For more information on how these plots are constructed, see Normal Probability Plots, Half-Normal Probability Plots, and Detrended Normal Probability Plots.


Distributed Lags Analysis - Other Transformations and Plots

  Time Series Analysis Distributed Lags Analysis - Other Transformations and Plots

This option will bring up the General transformations dialog which allows you to perform a wide variety of transformations on the data.  The transformed series will be appended to the active work area.


  Time Series Analysis -Select Independent Variable for Distributed Lags Analysis

Select the independent variable for the Distributed Lags Analysis.  To select a variable, either double-click on the respective variable, or click once on the respective variable to highlight it and then click OK.


  Time Series Analysis - Exponential Smoothing

The options on this dialog allow you to perform exponential smoothing for time series with or without a seasonal component and trend (see also, Time Series Analysis - Index).  The implementation of these techniques in the STATISTICA Time Series module follows closely the comprehensive survey by Gardner, 1985; see the Exponential Smoothing overview section for details).  Click in the Variable or Long variable (series) name column to highlight the variable (series) in the active work area that is to be analyzed.  Then, select the appropriate exponential smoothing model from among the options in the Model box (see below).  For seasonal models, specify the seasonal lag (length of seasonal period) or accept the default lag of 12.  Click OK to begin the exponential smoothing process.  By default, 10 forecast values will be computed (past the last observed value in the series).  You can change the number of forecasts in the Forecast __ cases edit field of this dialog.

If the Add pred./errors to work area check box is set, then (on OK) the smoothed (forecast) values as well as residuals (observed minus smoothed values) will be appended to the active work area.  If you choose to append those series, make sure that there is sufficient "space" in the active work area for the respective variable, that is, that there are at least two (not locked) backups available.  You can increase the Number of backups parameter if necessary.  Also, be sure to Lock all important backups of the original variable (those that you want to retain); otherwise, those backups may be overwritten (refer to the section describing the memory management in the active work area).  To lock a backup, double-click in the Lock column on the respective variable.

Seasonal and Non-Seasonal Exponential Smoothing dialog:

Model

Make summary plot for each smooth

Add pred./errors to work area

Grid search

Automatic search for best parameters

Review and plot variables

Autocorrelations

Histogram

Descriptive statistics

Normal, detrended normal, and half-normal probability plots

Other transformations and plots


Exponential Smoothing - Model

  Time Series Analysis Exponential Smoothing - Model

The general ideas of exponential smoothing and forecasting are explained in the Exponential Smoothing overview section.  The exponential smoothing models available in this box are arranged in a two-way classification, as proposed by Gardner (1985): The time series may either contain no seasonal component, an additive component, or a multiplicative seasonal component.  In addition, there may be no upward or downward trend in the series, a linear trend, an exponential trend, or a damped trend.  The combination of these characteristics results in 12 different exponential smoothing models (which include the classical models developed by Winters, Holt, and Brown).  Refer to the Exponential Smoothing Models section for more detailed descriptions and examples of these models.

Seasonal lag.  This edit field is only available (active) when a seasonal model is chosen (see below).  This value will determine the assumed length of one seasonal cycle.  The default value is 12 (e.g., there are 12 months in each year).  When changed, this parameter will be retained (remembered) for other time series analyses involving a seasonal component (e.g., in ARIMA models or in Seasonal decomposition (Census I)).

Alpha (α).  This is the constant process smoothing parameter.  The α (alpha) parameter is necessary for all models.  If α is 0 (zero), then all smoothed values will be equal to the initial value (S0, see also User-defined initial value below).  If this parameter is 1, then each smoothed value (forecast) will be equal to the respective previous observation.  Values greater than 0 (zero) and less than 1 will produce a forecast that is a weighted average of the previous observations, with the weights decreasing exponentially the "older" the previous observation.  The closer the α parameter is to 0, the more slowly will the weights decrease (that is, the more slowly will the effect of prior observations disappear), the closer it is to 1, the faster will the weights decrease (and the greater will be the effect of immediately preceding or "younger" observations).  In plots of the series, small values of α will produce smooth fitted lines (forecasts) that only follow major trends or fluctuations spanning many observations; larger values of α (closer to 1) will produce more jagged lines that are greatly influenced by even minor disturbances in the series.

Delta (δ).  Parameter δ (delta) is the seasonal smoothing parameter, and only needs to be specified for seasonal models.  In general the one-step-ahead forecasts are computed as (for no trend models, for linear and exponential trend models a trend component is added to the model; see below):

Additive model:

Forecast  = S +I

        t    t  t-p

Multiplicative model:

Forecast  = S *I

        t    t  t-p

In this formula, St stands for the (simple) exponentially smoothed value of the series at time t, and It-p stands for the smoothed seasonal factor at time t minus p (the length of the season).  Thus, compared to simple exponential smoothing, the forecast is "enhanced" by adding or multiplying the simple smoothed value by the predicted seasonal component.  This seasonal component is derived analogous to the St value from simple exponential smoothing as:

Additive model:

I  = I   +d*(1-a)*e

 t    t-p          t

Multiplicative model:

I  = I   +d*(1-a)*e /S

 t    t-p          t  t

Put into words, the predicted seasonal component at time t is computed as the respective seasonal component in the last seasonal cycle plus a portion of the error (et; the observed minus the forecast value at time t).  Parameter δ can assume values between 0 and 1.  If it is zero, then the seasonal component for a particular point in time is predicted to be identical to the predicted seasonal component for the respective time during the previous seasonal cycle, which in turn is predicted to be identical to that from the previous cycle, and so on.  Thus, if δ is zero, a constant unchanging seasonal component is used to generate the one-step-ahead forecasts.  If the δ parameter is equal to 1, then the seasonal component is modified "maximally" at every step by the respective forecast error.  In most cases, when seasonality is present in the time series, the optimum δ parameter will fall somewhere between 0 (zero) and 1(one).

Gamma (γ) and phi (φ).  These are the trend smoothing parameters.  Parameter γ needs to be specified for linear and exponential trend models, and for damped trend models without seasonality.  Parameter φ must be specified for damped trend models.  Analogous to the seasonal component, when a trend component is included in the exponential smoothing process, an independent trend component is computed for each time, and modified as a function of the forecast error and the respective parameter.  If the γ parameter is 0 (zero), then the trend component is constant across all values of the time series (and for all forecasts).  If the parameter is 1, then the trend component is modified "maximally" at every step by the respective forecast error.  Parameter values that fall in-between, represent mixtures of those two extremes.  Parameter φ is a trend modification parameter, and affects how strongly changes in the trend will affect estimates of the trend for subsequent forecasts, that is, how quickly the trend will be "damped" or increased.

User-defined initial value.  If this check box is set, then the initial value of the smoothed series (S0, necessary in order to compute the forecast for the first observation) is taken from the edit field; otherwise S0 is computed from the data, depending on the model chosen.  Refer to the Exponential Smoothing Models section for details of how S0 is computed in that case.

User-defined initial trend value.  This option is only available if a model with trend is chosen.  In that case an initial estimate of the trend (T0) is necessary in order to compute the forecast for the first observation.  If this check box is set, then the initial value for the trend (T0) is taken from the edit field; otherwise it is computed from the data, depending on the model chosen.  Refer to the Exponential Smoothing Models section for details of how T0 is computed in that case.

Get seasonal factors from variable.  This option is only available if a model with a seasonal component is chosen.  In that case, in order to compute the forecasts for the values in the first seasonal cycle of the series, an initial estimate of the seasonal component is necessary.  If this check box is not set (default), then the initial seasonal factors will be computed from the data (following the procedures described in the Seasonal Decomposition (Census I) section).  If this check box is set, then you will be prompted to select a variable that contains the initial seasonal factors in the first p values in the file (where p is the length of the seasonal cycle).  Note that the program will always take the first p cases in the specified variable as the initial seasonal component, regardless of selection conditions that are in effect.  For additive seasonality, the initial values for the seasonal component must add to 0 (zero); for multiplicative seasonality, the initial values for the seasonal component must add to the length of the seasonal cycle (p).


Exponential Smoothing - Make Summary Plot for each Smooth

  Time Series Analysis Exponential Smoothing - Make Summary Plot for each Smooth

If this check box is set, then after each analysis (on OK) a summary plot is produced showing the values of the observed series, the smoothed series (forecasts), and the residuals (scaled against the right Y-axis).  This plot provides an immediate visual check of the adequacy of the forecasts, and the distribution of the errors (residuals) across the series.


Exponential Smoothing - Add Pred./Errors to Work Area

  Time Series Analysis Exponential Smoothing - Add Pred./Errors to Work Area

If this check box is set, then (on OK) the smoothed (forecast) values as well as residuals (observed minus smoothed values) will be appended to the active work area.  If you choose to append those series, make sure that there is sufficient "space" in the active work area for the respective variable, that is, that there are at least two (not locked) backups available.  Increase the Number of backups parameter if necessary.  Also, be sure to Lock all important backups of the original variable (those that you want to retain); otherwise, those backups may be overwritten (refer to the section describing the memory management in the active work area).  To lock a backup, double-click in the Lock column on the respective variable.


Exponential Smoothing - Grid Search

  Time Series Analysis Exponential Smoothing - Grid Search

This option will bring up a dialog for specifying a grid search of the parameter space (see Parameter Grid Search).  Strategies for identifying the optimum smoothing parameters are described in the Exponential smoothing overview section.  In general, this option allows you to systematically evaluate the goodness of fit for sets of parameters by starting each parameter at a particular value, and then increasing it by a small amount in consecutive steps.  You can view the results either for all steps, or only the 10 most successful combinations of parameter values (lack-of-fit indices are also described in the Exponential Smoothing overview section).


Exponential Smoothing - Automatic Search for Best Parameter

  Time Series Analysis Exponential Smoothing - Automatic Search for Best Parameter

As recommend by Gardner (1985), in order to obtain the best (most accurate) forecasts one should determine the best smoothing parameters from the data.  This option will allow you to perform an automatic search for the best set of parameters (given a user-defined lack-of-fit index; these are also described in the Exponential Smoothing overview section).  A quasi-Newton function minimization procedure (the same as in ARIMA, see also Automatic parameter search) is used to minimize either the mean squared error, mean absolute error, or mean absolute percentage error.  In most cases, this procedure is more efficient than the grid search, in particular, when more than one parameter must be determined.  Note that, by default, the parameter search is unconstrained, that is, parameter values outside the 0/1 boundaries may be estimated.  When clicking OK after the parameter search converged, invalid parameters will automatically be set to their respective minimum or maximum (e.g., α = -0.2 is set to α = 0; α = 1.2 is set to α = 1); and the a full set of results (like those produced by clicking OK on this dialog) will be displayed for the best parameters.


Exponential Smoothing - Review and Plot Variables

  Time Series Analysis Exponential Smoothing - Review and Plot Variables

These options allow you to review or plot the currently highlighted variable (together with other variables).  The labeling of the individual observations (that is, of the respective points in time represented by the rows in Scrollsheets or the horizontal X-axis in plots) is determined by the selections in the Display/plot options dialog (click on the Options button below; these options are also available on the Transformations dialog).  For the plots, you can choose to Scale the X-axis in the plots manually (select this option in the Display/plot options dialog).  This is often useful when the series consists of several regularly recurring time intervals, for example, if it is made up of 10 years with 12 (monthly) observations each.  Then it may be useful to scale the X-axis in the plot so that each major tickmark indicates one year.

Display/plot subset of cases only.  If this check box is set, then, before plotting or displaying one or more series, you will be prompted to select a range of observations to include in the plot or display.

Options (scaling, labels, etc.).  This option will bring up the Display/plot options dialog.  That dialog allows you to change the labeling of the observations (i.e., the rows in Scrollsheets and the X-axis in line plots can be labeled with case names, case numbers, dates from another variable, etc.) and the scaling of the X-axis in line plots (minimum, step size).

Review/Plot highlighted variable.  This button will bring up a Scrollsheet (or a plot) with the values for the currently highlighted variable.

Review/Plot multiple variables.  After clicking on this button, you will first be prompted to select a list of variables to be displayed or plotted.  When plotting multiple variables the vertical (Y) axis will have a common scale; thus, if the series that are plotted contain values of completely different magnitudes use option Plot two var lists with different scales (see below), instead.

Plot two var. lists with different scales.  This option allows you to plot two lists of variables using different scales for the vertical (Y) axes in the plot.  The first list will be plotted against the left Y-axis and the second list will be plotted against the right Y-axis.  For example, suppose you want to plot two variables (series) called S1 and S2, and that these variables contain values of different magnitudes: the values of S1 range from 1-100 and the values of S2 range from 1000 to 10000.  If you plot S1 against the left Y-axis (scaled from 1-100) and S2 against the right Y-axis (scaled from 1000-10000) then both variables will be plotted with optimal resolution, and thus relationships between patterns across time (the X-axis) may become more clearly identifiable.


Exponential Smoothing - Autocorrelations

  Time Series Analysis Exponential Smoothing - Autocorrelations

These options will compute the autocorrelations and partial autocorrelations for the currently highlighted variable; these statistics will be displayed in a Scrollsheet and drawn in a correlogram graph.  Refer to the Overview section for a brief description of how the pattern of (partial) autocorrelations aids in the determination of an appropriate ARIMA model.

Autocorrelations.  This option will bring up a Scrollsheet and plot of the autocorrelations, for a lag of 1 through the number specified in the Number of lags edit field.  The Scrollsheet will report the autocorrelations, their standard errors, the so-called Box-Ljung statistic, and the significance level of that statistic.  In general, the autocorrelation is the correlation of the series with itself, lagged by a particular number of observations.  For details regarding the computations of those statistics refer to the autocorrelation section.

Alpha for highlighting.  Significant autocorrelations (significant Box-Ljung statistics) will be highlighted in the Scrollsheet.  This edit field allows you to specify the significance level that is used for highlighting.

White noise standard errors.  Under the assumption that the true moving average process in the series is of the order k-1, the approximate standard error of the autocorrelation rk is computed as:

                                2

StdErr(r ) = √{(1/N) * [1+2*Σ(r  )]}

        k                      i

(for i = 1 to k-1)

Here N is the number of observations in the series.  Under the assumption that the series is a white noise process, that is, that all autocorrelations are equal to zero, the standard error of rk is computed as:

StdErr(r ) = √{(1/N) * [(N-k)/(N+2)]}

        k

Check the White noise standard errors option to compute the standard errors in this manner.

Partial autocorrelations.  This option will bring up a Scrollsheet and plot of the partial autocorrelations, for a lag of 1 through the number specified in the Number of lags edit field.  The Scrollsheet will report the partial autocorrelations and their standard errors.  In general, the partial autocorrelation is the partial correlation of a series with itself, lagged by a particular number of observations, and controlling for all correlations for lags of lower order.  For example, the partial autocorrelation for a lag of 2 represents the unique correlation of the series with itself at that lag, after controlling for the correlation at lag 1.  For details regarding the computations of the partial autocorrelation and its standard error refer to the partial autocorrelation section.  Partial autocorrelations that are larger than two times their respective standard errors will be highlighted in the Scrollsheet.

Number of lags.  This parameter determines the maximum number of lags for which the auto-, and partial autocorrelations will be computed.


Exponential Smoothing - Histogram

  Time Series Analysis Exponential Smoothing - Histogram

This option will bring up a histogram of the currently highlighted variable.


Exponential Smoothing - Descriptive Statistics

  Time Series Analysis Exponential Smoothing - Descriptive Statistics

This option will bring up a Scrollsheet with descriptive statistics for all variables currently available in the active work area.


Exponential Smoothing - Normal, Detrended, and Half-normal Probability Plots

  Time Series Analysis Exponential Smoothing - Normal, Detrended, and Half-normal Probability Plots

These options will bring up the respective normal probability plot for the highlighted variable.  For more information on how these plots are constructed, see Normal Probability Plots, Half-Normal Probability Plots, and Detrended Normal Probability Plots.


Exponential Smoothing - Other Transformations and Plots

  Time Series Analysis Exponential Smoothing - Other Transformations and Plots

This option will bring up the General transformations dialog which allows you to perform a wide variety of transformations on the data.  The transformed series will be appended to the active work area.


  Time Series Analysis - Exponential Smoothing Models

Shown below is a listing of available exponential smoothing models, as described in Gardner (1985).  The specific formulas for computing the one-step-ahead forecasts are also provided in that reference, and will not be repeated here.  Click on a model name in order to get more information on that model (see also, Time Series Analysis - Index).

  Nonseasonal, No Trend	  Nonseasonal, Exponential Trend

  Additive Season, No Trend	  Additive Season, Exponential Trend

  Multiplicative Season, No Trend	  Multiplicative Season, Exponential Trend

  Nonseasonal, Linear Trend	  Nonseasonal, Damped Trend

  Additive Season, Linear Trend	  Additive Season, Damped Trend

  Multiplicative Season, Linear Trend	  Multiplicative Season, Damped Trend


  Time Series Analysis - Parameter Grid Search

These options allow you to specify a grid search of the parameter space.  Strategies for identifying the optimum smoothing parameters are described in the Exponential Smoothing overview section.  In general, these options allow you to systematically evaluate the goodness of fit for sets of parameters by starting each parameter at a particular value (as specified in the Start parameter at column), and then increasing it by a small amount in consecutive steps (as specified in the Increment by column), all the way up the value specified in the Stop at column.  You can view the results either for all steps (i.e., for all combinations of parameter values), or only the 10 combinations of parameter values that resulted in the smallest mean squared error for the residuals (other lack-of-fit indices are also described in the Exponential Smoothing overview section).


  Time Series Analysis - Automatic Parameter Search

As recommend by Gardner (1985), in order to obtain the best (most accurate) forecasts one should determine the best smoothing parameters from the data.  This option will allow you to perform an automatic search for the best set of parameters (given a user-defined lack-of-fit index; these are also described in the Exponential Smoothing overview section; see also, Time Series Analysis - Index).  A quasi-Newton function minimization procedure (the same as in ARIMA) is used to minimize either the mean squared error, mean absolute error, or mean absolute percentage error.  In most cases, this procedure is more efficient than the grid search, in particular when more than one parameter must be determined.  Note that, by default, the parameter search is unconstrained, that is, parameter values outside the 0/1 boundaries may be estimated.  When clicking OK after the parameter search converged, invalid parameters will automatically be set to their respective minimum or maximum (e.g., α = -0.2 is set to α = 0; α = 1.2 is set to α = 1); and the a full set of results (like those produce by clicking OK on this dialog) will be displayed for the best parameters.

Automatic Search for Best Parameters dialog:

Max. number of iterations

Convergence criterion

Unconstrained parameter estimation

Lack-of-fit indicator

Parameter start values


Automatic Parameter Search - Max. Number of Iterations

  Time Series Analysis Automatic Parameter Search - Max. Number of Iterations

The value in this edit field determines the maximum number of quasi-Newton iterations that will be performed.  Note that if the maximum number of iterations is exceeded during the automatic parameter search, additional iterations can be requested at that point.  Thus, there is no need to specify an excessively large number in this field.


Automatic Parameter Search - Convergence Criterion

  Time Series Analysis Automatic Parameter Search - Convergence Criterion

This parameter determines the accuracy or precision with which the parameters will be estimated, or more specifically, the accuracy of the parameters with respect to the Lack of fit indicator that is selected (see below).  The estimation procedure will terminate when the changes in the parameters over consecutive iterations are less than this value.  Usually, the default value (.0001) is adequate to produce estimates for the best parameters with sufficient accuracy.


Automatic Parameter Search - Unconstrained Parameter Estimation

  Time Series Analysis Automatic Parameter Search - Unconstrained Parameter Estimation

By default (when this check box is set), the search algorithm will be unconstrained, that is, parameter estimates outside the 0/1 boundaries my be produced (if they minimize the respective Lack of fit indicator).  When clicking OK after the parameter search converged, invalid parameters will automatically be set to the respective minimum or maximum (e.g., α = -0.2 is set to α = 0; α = 1.2 is set to α = 1).  If this check box is not set, then a large (penalty) value will be assigned to the Lack of fit value during the iterative parameter estimation whenever an invalid parameter estimate results.  This will usually "entice" the search algorithm to move away from the respective minima and maxima of the parameters.  However, if, in fact, the best parameter values are near their minima or maxima (e.g., a constant slope, resulting in δ close to zero) then the parameter search may prematurely converge with less-than-optimal values for the other parameters.  Therefore, the unconstrained minimization procedure is the recommended default.


Automatic Parameter Search - Lack-of-Fit Indicator

  Time Series Analysis Automatic Parameter Search - Lack-of-Fit Indicator

These options determine which lack-of-fit indicator will be minimized during the parameter estimation process.  Various such indices have been proposed (see Makridakis, Wheelwright, and McGee, 1983), and they are described in the Exponential Smoothing overview section.

Mean squared error.  These values (MSE) are computed as the average of the squared error values.  This is the most commonly used lack-of-fit indicator in most statistical fitting procedures.

Mean absolute error.  The mean absolute error (MAE) value is computed as the average absolute error value.  If this value is 0 (zero), the fit (forecast) is perfect.  As compared to the mean squared error value, this measure of fit will "de-emphasize" outliers, that is, unique or rare large error values will affect the MAE less than the MSE value.

Mean absolute percentage error.  Another measure of relative overall fit is the mean absolute percentage error (MAPE).  Both the above measures rely on the actual error value.  It may seem reasonable to rather express the lack of fit in terms of the relative deviation of the one-step-ahead forecasts from the observed values, that is, relative to the magnitude of the observed values.  For example, when trying to predict monthly sales that may fluctuate widely (e.g., seasonally) from month to month, we may be satisfied if our prediction "hits the target" with about ±10% accuracy.  In other words, the absolute errors may be not so much of interest as are the relative errors in the forecasts.  To assess the relative error the so-called percentage error (PE) can be computed as:

PE  = 100*(X -F )/X

  t         t  t   t

where Xt is the observed value at time t, and Ft is the forecast (smoothed value).  The mean percentage error is the average of the PE values for the entire series.  This measure is often more meaningful than the mean squared error.  For example, knowing that the average forecast is "off" by ±5% is a useful and easily interpretable result, whereas a mean squared error of 30.8 is not immediately interpretable.


Automatic Parameter Search - Parameter Start Values

  Time Series Analysis Automatic Parameter Search - Parameter Start Values

These values will determine the initial value for the parameter search process.  The meaning of the parameters is explained in the context of the Exponential Smoothing dialog and in the Exponential Smoothing overview section.  In most cases, if the selected model is adequate for the data, the parameter values will converge at the same values, regardless of the parameter start values chosen.


  Time Series Analysis - Iterations

The parameter estimation procedure is iterative in nature, that is, parameter estimates are refined in successive iterations.  A quasi-Newton algorithm is used to minimize the chosen Lack of fit indicator (see the Automatic parameter search dialog).  The respective value of the indicator is listed in the Loss column in the window; the parameter values are listed to the right.

Note that, by default (when the respective option is checked on the Automatic parameter search dialog) the parameter search is unconstrained, that is, parameter values outside the 0/1 boundaries may be estimated.  When clicking OK after the parameter search converged, invalid parameters will automatically be set to the respective minimum or maximum (e.g., α = -0.2 is set to α = 0; α = 1.2 is set to α = 1); and the a full set of results (like those produce by clicking OK on the Exponential Smoothing dialog) will be displayed for the best parameters.


  Time Series Analysis - Seasonal Decomposition (Census I)

The options on this dialog allow you to perform classical seasonal decomposition, a technique also known as the Census I method (see Seasonal Decomposition (Census I) for details; see also, Time Series Analysis - Index).  Click in the Variable or Long variable (series) name column to highlight the variable (series) in the active work area that is to be analyzed.  Then, specify the seasonal lag (length of seasonal period) or accept the default value of 12 and click OK to begin the seasonal decomposition.

To append any or all of the components that are computed to the active work area, set the respective check boxes in the Append components to active work area box (see below).  If you choose to append components, make sure that there is sufficient "space" in the active work area for the respective variable, that is, that there are at least as many (not locked) backups available as there are components to be saved.  Increase the Number of backups parameter if necessary.  Also, be sure to Lock all important backups of the original variable (those which you want to retain); otherwise, those backups may be overwritten (refer to the section describing the memory management in the active work area).  To lock a backup, double-click in the Lock column on the respective variable.

In order to compute forecasts, use the Exponential smoothing facilities, which provide various options for computing forecasts based on additive or multiplicative seasonal models with or without trend.

Ratios-to-Moving Averages Classical Seasonal Decomposition
(Census Method I) dialog:

Seasonal model

On OK append components to active work area

Other transformations and plots

Histogram

Descriptive statistics

Normal, detrended normal, and half-normal probability plots

Review and plot variables

Autocorrelations


Seasonal Decomposition (Census I) - Seasonal Model

  Time Series Analysis Seasonal Decomposition (Census I) - Seasonal Model

The settings in this box determine the seasonal model.  In general, the seasonality in the series can be Additive or Multiplicative.  For example, when tracking the sales for a toy, it can be expected that during the December holiday season sales will increase; another seasonal increase could possible occur during the summer vacation months.

Additive/Multiplicative.  This seasonal fluctuations (e.g., the increase in sales during December) can be additive (e.g., on average, sales increase in December by about 1 million dollars over the year's average), or it can be multiplicative (on average, sales increase in December by 30%, that is, by a factor of 1.3).  In plots of a series, the distinguishing characteristic between these two types of seasonal components is that in the additive case, the series shows steady seasonal fluctuations, regardless of the overall level of the series; in the multiplicative case, the size of the seasonal fluctuations vary, depending on the overall level of the series.  Refer to the Seasonal decomposition (Census I) section for additional details.

Seasonal lag.  This value will determine the assumed length of one seasonal cycle.  The default value is 12 (e.g., there are 12 months in each year).  When changed, this parameter will be retained (remembered) for other time series analyses involving a seasonal component (e.g., in ARIMA models or in Exponential smoothing.

Centered moving averages.  As the first step in the decomposition, a moving average is computed for the series, with the moving average window width equal to the length of one season.  If the length of the season is even, then the user can choose to use either equal weights for the moving average or unequal weights can be used, where the first and last observation in the moving average window are averaged; this latter method is used when the Centered moving averages check box is set.  If the length of the season is odd, the setting of this check box will not affect the computations.


Seasonal Decomposition (Census I) - On OK Append to Active Work Area

  Time Series Analysis Seasonal Decomposition (Census I) - On OK Append to Active Work Area

The setting of these check boxes determine which components will be added to the  active work area.  If you choose to append components, make sure that there is sufficient "space" in the active work area for the respective variable, that is, that there are at least as many (not locked) backups available as there are components to be saved.  Increase the Number of backups parameter if necessary.  Also, be sure to Lock all important backups of the original variable (those that you want to retain); otherwise, those backups may be overwritten (refer to the section describing the memory management in the active work area).  To lock a backup, double-click in the Lock column on the respective variable.

Moving average.  First a moving average is computed for the series, with the moving average window width equal to the length of one season (as specified in the Seasonal lag edit field).  If the length of the season is even then the user can choose to use either equal weights for the moving average or unequal weights can be used, where the first and last observation in the moving average window are averaged (set the Centered moving averages check box; see above).

Ratios or differences.  In the moving average series (see above), all seasonal (within-season) variability will be eliminated; thus, the differences (in the additive model) or ratios (in the multiplicative model) of the observed and smoothed series will isolate the seasonal component (plus irregular component).  Specifically, the moving average is subtracted from the observed series (for the additive model) or the observed series is divided by the moving average values (for the multiplicative model).

Seasonal components.  The seasonal component is then computed as the average (for additive models) or medial average (for multiplicative models) for each point in the season.  (The medial average of a set of values is the mean after the smallest and largest values are excluded).  The resulting values represent the (average) seasonal component of the series.

Seasonally adjusted series.  The original series can be adjusted by subtracting from it (additive models) or dividing it by (multiplicative models) the seasonal component.  The resulting series is the seasonally adjusted series (i.e., the seasonal component will be removed).

Trend-cycle component.  The cyclical component is different from the seasonal component in that it is usually longer than one season, and different cycles can be of different lengths.  The combined trend and cyclical component can be approximated by applying to the seasonally adjusted series a 5 point (centered) weighed moving average smoothing transformation with the weights of 1, 2, 3, 2, 1.

Random or irregular component.  Finally, the random or irregular (error) component can be isolated by subtracting from the seasonally adjusted series (additive models) or dividing the adjusted series by (multiplicative models) the trend-cycle component.


Seasonal Decomposition (Census I) - Other Transformations and Plots

  Time Series Analysis Seasonal Decomposition (Census I) - Other Transformations and Plots

This option will bring up the General transformations dialog which allows you to perform a wide variety of transformations on the data.  The transformed series will be appended to the active work area.


Seasonal Decomposition (Census I) - Histograms

  Time Series Analysis Seasonal Decomposition (Census I) - Histograms

This option will bring up a histogram of the currently highlighted variable.


Seasonal Decomposition (Census I) - Descriptive Statistics

  Time Series Analysis Seasonal Decomposition (Census I) - Descriptive Statistics

This option will bring up a Scrollsheet with descriptive statistics for all variables currently available in the active work area.


Seasonal Decomposition (Census I) - Normal, Detrended Normal, and Half-Normal Probability Plots

  Time Series Analysis Seasonal Decomposition (Census I) - Normal, Detrended Normal, and Half-Normal Probability Plots

These options will bring up the respective normal probability plot for the highlighted variable.  For more information on how these plots are constructed, see Normal Probability Plots, Half-Normal Probability Plots, and Detrended Normal Probability Plots.


Seasonal Decomposition (Census I) - Review and Plot Variables

  Time Series Analysis Seasonal Decomposition (Census I) - Review and Plot Variables

These options allow you to review or plot the currently highlighted variable (together with other variables).  The labeling of the individual observations (that is, of the respective points in time represented by the rows in Scrollsheets or the horizontal X-axis in plots) is determined by the selections in the Display/plot options dialog (click on the Options button below; these options are also available on the Transformations dialog).  For the plots, you can choose to Scale the X-axis in the plots manually (select this option in the Display/plot options dialog).  This is often useful when the series consists of several regularly recurring time intervals, for example, if it is made up of 10 years with 12 (monthly) observations each.  Then it may be useful to scale the X-axis in the plot so that each major tickmark indicates one year.

Display/plot subset of cases only.  If this check box is set, then, before plotting or displaying one or more series, you will be prompted to select a range of observations to include in the plot or display.

Review/Plot highlighted variable.  This button will bring up a Scrollsheet (or a plot) with the values for the currently highlighted variable.

Review/Plot multiple variables.  After clicking on this button, you will first be prompted to select a list of variables to be displayed or plotted.  When plotting multiple variables the vertical (Y) axis will have a common scale; thus, if the series that are plotted contain values of completely different magnitudes use option Plot two var lists with different scales (see below), instead.

Options (scaling, labels, etc.).  This option will bring up the Display/plot options dialog.  This dialog allows you to change the labeling of the observations (i.e., the rows in Scrollsheets and the X-axis in line plots can be labeled with case names, case numbers, dates from another variable, etc.) and the scaling of the X-axis in line plots (minimum, step size).

Plot two var. lists with different scales.  This option allows you to plot two lists of variables using different scales for the vertical (Y) axes in the plot.  The first list will be plotted against the left Y-axis and the second list will be plotted against the right Y-axis.  For example, suppose you want to plot two variables (series) called S1 and S2, and that these variables contain values of different magnitudes: the values of S1 range from 1-100 and the values of S2 range from 1000 to 10000.  If you plot S1 against the left Y-axis (scaled from 1-100) and S2 against the right Y-axis (scaled from 1000-10000) then both variables will be plotted with optimal resolution, and thus relationships between patterns across time (the X-axis) may become more clearly identifiable.


Seasonal Decomposition (Census I) - Autocorrelations

  Time Series Analysis Seasonal Decomposition (Census I) - Autocorrelations

These options will compute the autocorrelations and partial autocorrelations for the currently highlighted variable; these statistics will be displayed in a Scrollsheet and drawn in a correlogram graph.  Refer to the Overview section for a brief description of how the pattern of (partial) autocorrelations aids in the determination of an appropriate ARIMA model.

Autocorrelations.  This option will bring up a Scrollsheet and plot of the autocorrelations, for a lag of 1 through the number specified in the Number of lags edit field.  The Scrollsheet will report the autocorrelations, their standard errors, the so-called Box-Ljung statistic, and the significance level of that statistic.  In general, the autocorrelation is the correlation of the series with itself, lagged by a particular number of observations.  For details regarding the computations of those statistics refer to the autocorrelation section.

Alpha for highlighting.  Significant autocorrelations (significant Box-Ljung statistics) will be highlighted in the Scrollsheet.  This edit field allows you to specify the significance level that is used for highlighting.

White noise standard errors.  Under the assumption that the true moving average process in the series is of the order k-1, the approximate standard error of the autocorrelation rk is computed as:

                                2

StdErr(r ) = √{(1/N) * [1+2*Σ(r  )]}

        k                      i

(for i = 1 to k-1)

Here, N is the number of observations in the series.  Under the assumption that the series is a white noise process, that is, that all autocorrelations are equal to zero, the standard error of rk is computed as:

StdErr(r ) = √{(1/N) * [(N-k)/(N+2)]}

        k

Check the White noise standard errors option to compute the standard errors in this manner.

Partial autocorrelations.  This option will bring up a Scrollsheet and plot of the partial autocorrelations, for a lag of 1 through the number specified in the Number of lags edit field.  The Scrollsheet will report the partial autocorrelations and their standard errors.  In general, the partial autocorrelation is the partial correlation of a series with itself, lagged by a particular number of observations, and controlling for all correlations for lags of lower order.  For example, the partial autocorrelation for a lag of 2 represents the unique correlation of the series with itself at that lag, after controlling for the correlation at lag 1.  For details regarding the computations of the partial autocorrelation and its standard error refer to the partial autocorrelation section.  Partial autocorrelations that are larger than two times their respective standard errors will be highlighted in the Scrollsheet.

Number of lags.  This parameter determines the maximum number of lags for which the auto-, and partial autocorrelations will be computed.


  Time Series Analysis - X-11 Seasonal Adjustment

The options on this dialog allow you to perform X-11 monthly seasonal decomposition, a technique also know as the Census II method (see X-11 Census Method II Seasonal Adjustment for details; see also, Time Series Analysis - Index).  The arrangement of options is specifically designed to closely follow the terminology and options of the X-11 procedure of the Bureau of the Census (Shiskin, Young, & Musgrave, 1967).

To select the variable (series) to be analyzed, click on the Variable or Long variable (series) name column to highlight the variable (series) in the active work area.  The successive observations in that series should contain data (e.g., sales, revenue figures, etc.) for consecutive months.  Next, specify the starting month of the series (either specify a date variable, or type the respective month and year into the From -- month/year edit fields), additional options if appropriate (or accept the defaults), and click OK to begin the seasonal decomposition.

After the last output table has been displayed (see X-11 Result Tables for a description of the tables produced by this method), the program will automatically append to the active work area the following series/components:

•  The final seasonal factors (table D 10),

•  The final seasonally adjusted series (D 11),

•  The final trend-cycle component (D 12), and

•  The final irregular series (random component; D 13).

Be sure to Lock all important backups of the original variable (those which you want to retain); otherwise, those backups may be overwritten (refer to the section describing the memory management in the active work area).  To lock a backup, double-click in the Lock column on the respective variable.  Note that if the display of consecutive results tables is interrupted, then none of these components will be appended to the active work area.

X-11 Monthly Seasonal Adjustment (Census II Method) dialog:

Number of backups per variable

Save variables

Delete

Other transf. & plots

Seasonal adjustment

Dates (start of series)

Summary measures (input is seasonally adjusted)

Printout tables (detail)

Charts

Batch print all tables/charts without interruption

Prior daily weights

Include a length of month allowance

Trading-day regression & adjustment of series

Prior monthly adjustment factors

Sigma limits for graduating extreme values

Moving averages for seasonal factor curves

Henderson curve moving average for variable trend-cycle

Adjust trend-cycle for strikes


X-11 Seasonal Adjustment - Number of Backups per Variable

  Time Series Analysis X-11 Seasonal Adjustment - Number of Backups per Variable

This parameter determines the maximum number of backups that is kept in the active work area for each variable.  When a new transformation is about to be appended and the maximum number of backups for the respective original variable has already been exceeded, then the "oldest" previous backup will be replaced.  You can lock a variable (prevent it from being overwritten) by double-clicking on the respective variable in the Lock column.  For more details, refer to the active work area section.


X-11 Seasonal Adjustment - Save Variables

  Time Series Analysis X-11 Seasonal Adjustment - Save Variables

This option allows you to save the variables (series) that are currently available in the active work area into a standard STATISTICA data file (which can be used as input for subsequent analyses).


X-11 Seasonal Adjustment - Delete

  Time Series Analysis X-11 Seasonal Adjustment - Delete

This option allows you to delete the currently highlighted variable.  To highlight a variable, click on it either in the Lock, Variable, or Long variable (series) name column.


X-11 Seasonal Adjustment - Other Transformations and Plots

  Time Series Analysis X-11 Seasonal Adjustment - Other Transformations and Plots

This option will bring up the General transformations dialog which allows you to perform a wide variety of transformations on the data.  The transformed series will be appended to the active work area.


X-11 Seasonal Adjustment - Seasonal Adjustment

  Time Series Analysis X-11 Seasonal Adjustment - Seasonal Adjustment

The setting of radio buttons in this box determines whether an Additive or Multiplicative seasonal adjustment will be performed (refer to the X-11 Census Method II Seasonal Adjustment overview for details).  In short, in the additive model the seasonal, trend-cycle, and irregular (random) components are assumed to combine in an additive fashion (e.g., the seasonal fluctuation adds $1,000,000 to the sales in the holiday month of December).  In the multiplicative model, they are thought to combine in a multiplicative fashion (e.g., due to the seasonal component, in December sales increase by 30%, i.e., 1.3 times the baseline).


X-11 Seasonal Adjustment - Dates (start of series)

  Time Series Analysis X-11 Seasonal Adjustment - Dates (Start of Series)

The setting in this box determines the start date of the series.  The start date will not only affect the labeling of the output tables, but can also substantially affect the computations.  The X-11 monthly adjustment procedure allows the user to adjust the series for fluctuations in the lengths of different months as well as the numbers of different days (i.e., Mondays, Tuesdays, etc.) in each month.  When you select the Variable option in this box, a variable selection dialog will open in which you can select the variable containing the starting date (i.e., the date stored in this variable in the first case of the respective series will be used as the start date of the series).  Selecting the From option will allow you to specify the specific month and year in which the series started.


X-11 Seasonal Adjustment - Summary Measure (Input is Seasonally Adjusted)

  Time Series Analysis X-11 Seasonal Adjustment - Summary Measures (Input is Seasonally Adjusted)

If this check box is set, then the program will assume that the input is already a seasonally adjusted series.  In that case, the X-11 procedure can be used to test for residual seasonality and trading-day variation by completing the standard steps in parts B and C of the computations (see X-11 Result Tables for details).  Note that part A and tables E 2, E 4, and E 6, are not applicable in that case; also, table D 11 (final seasonally adjusted series) will be identical to B 1 (the input series), and the final trend-cycle moving average is applied to table D 1.


X-11 Seasonal Adjustment - Printout Table

  Time Series Analysis X-11 Seasonal Adjustment - Printout Table

The setting of radio buttons in this box will determine the detail of results that will be reported after clicking OK.  The number of specific X-11 Result Tables that will be computed depends on the choices in this box.  Note that, if the Batch print all tables/charts without interruption check box is set (see below), then all selected tables will automatically be printed without interruption.  The X-11 Result Tables section describes which specific tables (Scrollsheets) are reported for the Standard, Long, or Full printout detail.

Standard:  When you select this radio button, 17 to 27 tables will be displayed.

Long:  When you select this radio button, 27 to 39 tables will be displayed.

Full:  When you select this radio button, 44 to 59 tables will be displayed.

Selected tables:  If you click on this radio button, the Select the X-11 tables and charts to be printed/displayed dialog will open in which the identifiers for all available tables are listed.  In this dialog, you can select the specific tables (Scrollsheets) that you want displayed and/or printed.  If no tables are selected (i.e., do not select any tables and click OK in this dialog), then only the final estimates of the seasonally adjusted series, the seasonal component, irregular component, and trend-cycle component will be appended to the active work area.


X-11 Seasonal Adjustment - Charts

  Time Series Analysis X-11 Seasonal Adjustment - Charts

The setting of radio buttons in this box will determine the detail of graphics results that will be reported after clicking OK in this dialog.  Note that, if the Batch print all tables/charts without interruption check box is set and Printer output is selected in the Page/Output Setup dialog, then the respective graphs will automatically be printed.  Refer also to the X-11 Result Tables section for description of the charts (line plots) computed by the procedure.

None.  If this radio button is set, then no plots will be produced.

Standard.  If this radio button is set, then charts G 1 (final seasonally adjusted series and final trend-cycle components; D 11 and D 12, respectively) and G 2 (final S-I differences or ratios with the extremes, the final S-I differences (ratios) without extremes, and the final seasonal factors; D 8, D 9, and D 10) will be computed.

All.  If this radio button is set, then all charts G 1 through G 4 will be displayed (see X-11 Result Tables for details).

Selected.  If this radio button is set, then the Select the X-11 tables and charts to be printed/displayed dialog will open in which all available output charts (and tables) are listed.  The user can then select the desired charts (line plots) to be computed.


X-11 Seasonal Adjustment - Batch Print all Tables/Charts without Interruption

  Time Series Analysis X-11 Seasonal Adjustment - Batch Print all Tables/Charts without Interruption

If this check box is set then all tables that are displayed will automatically be printed (to the printer, file, and/or Text/output Window, whichever is selected in the Page/Output Setup dialog) without requiring any additional user input.  If Printer output is selected, all graphs will also automatically be printed.


X-11 Seasonal Adjustment - Prior Daily Weights

  Time Series Analysis X-11 Seasonal Adjustment - Prior Daily Weights

This option is only available if Multiplicative adjustment was selected (see above).  Different months consist of different numbers of trading-days (i.e., Mondays, Tuesdays, etc.), which may greatly affect the monthly values (see X-11 Census Method II Seasonal Adjustment overview for details).  By specifying prior daily weights, the monthly observations can be adjusted so as to reflect the differences in the number of different days in each month (this adjustment can also be performed via least squares regression; see Trading-day regression & adjustment of series below).  For example, suppose the input series contains monthly revenues for an amusement park.  In this case, one may want to assign greater a priori weights to the Saturdays and Sundays (since most revenue is generated on those days) in order to adjust the monthly series prior to the seasonal decomposition.

When you set this check box, you will be able to enter the seven weights into the edit fields to the right.  Note that the program will automatically adjust the weights entered here so that they will sum to 7.


X-11 Seasonal Adjustment - Include a Length of Month Allowance

  Time Series Analysis X-11 Seasonal Adjustment - Include a Length of Month Allowance

This option is only available (meaningful) if Prior daily weights (see above) and/or Trading-day regression & adjustment are requested, and when Multiplicative adjustment is requested (see above).  When this check box is set, then the differences in the lengths of different months (30-day months, 31-day months, and Februarys) are not used to adjust the daily weights.  Consequently, the variability arising from differences in the lengths of months will be included in the trading-day factors.


X-11 Seasonal Adjustment - Trading Day Regression and Adjustment of Series

  Time Series Analysis X-11 Seasonal Adjustment - Trading Day Regression and Adjustment of Series

Different months consist of different numbers of trading-days (i.e., Mondays, Tuesdays, etc.), which may greatly affect the monthly values (see X-11 Census Method II Seasonal Adjustment overview for details).  The options in this box will determine whether and how a least-squares trading-day adjustment will be included in the analysis.

No adjustment.  If this radio button is set, then no automatic trading-day adjustment is performed.

Compute only.  If this radio button is set, then the trading-day weights are computed and reported; however, the series will not be adjusted by these weights.

Compute & adjust series.  If this radio button is set, then the trading-day weights are computed (starting with the year indicated, see below) and applied to adjust the input series (starting with the year indicated, see below).

Compute & adjust conditionally.  If this radio button is set, then the trading-day weights are computed (starting with year indicated, see below) and applied to adjust the input series (starting with the year indicated, see below).  However, in part C of the analysis (see X-11 Result Tables) the trading-day weights are only used if they explain statistically significant variation.

Start estimation, Adjust beginning.  These edit fields determine which years of the input series are used to compute the trading-day weights (by default all years), and to which years they are applied (by default to all years).

Sigma limit for excluding extreme values.  If trading-day regression is requested, then the value specified in this edit field determines how outliers in the irregular component are to be treated.  Specifically, all irregular values will be excluded from the computations if they deviate from 0 (additive model) or 1 (multiplicative model) by more than x * σ (where x is the value in the edit field and sigma is the estimate of the trading-day standard deviation).


X-11 Seasonal Adjustment - Prior Monthly Adjustment Factors

  Time Series Analysis X-11 Seasonal Adjustment - Prior Monthly Adjustment Factors

The user can specify a second series with prior monthly adjustment factors.  Prior to the analysis, this series will be subtracted from the input series (additive model) or divided into the input series (multiplicative model).  When setting this check box, the Currently Available Variables and Transformations dialog will open in which the user can select the second series with the prior adjustment factors (from among those in the active work area.


X-11 Seasonal Adjustment - Sigma Limits for Graduating Extreme Values

  Time Series Analysis X-11 Seasonal Adjustment - Sigma Limits for Graduating Extreme Values

One of the strengths of the X-11 method is in the treatment of outliers.  When estimating the seasonal and trend-cycle components, irregular values are assigned different weights depending on their deviation from 0 (zero; additive model) or 1 (multiplicative model).  See also X-11 Result Tables (table B 4) for details concerning this procedure.  The Full weight value determines the multiple of σ (sigma; the estimate of the trend-cycle standard deviation) below which a value will be assigned a full weight.  The Zero weight value determines the multiple of σ above which a zero weight will be assigned.  In-between these two cut-off values, linearly graduated weights are assigned.


X-11 Seasonal Adjustment - Moving Averages for Seasonal Factor Curves

  Time Series Analysis X-11 Seasonal Adjustment - Moving Averages for Seasonal Factor Curves

The radio buttons in this box determine the lengths of moving averages that are used to compute the seasonal factors (seasonal factor curve moving average).

Selected by program:  By default (Selected by program) the program will select a 3x3 moving average for the first estimate in each part (see X-11 Result Tables B 5, C 5, and D 5) and a 3x5 average for the second estimate (see X-11 Result Tables B 10, C 10, and D 10).  A 3x3 moving average is a 3-term moving average applied to a series previously smoothed by a 3-term moving average, which is equivalent to a 5-term weighted moving average; a 3x5 moving average is 3-term moving average applied to a series previously smoothed by a 5-term moving average, which is equivalent to a 7-term weighted moving average; for a discussion of different types of moving averages see Makridakis and Wheelwright (1983).

User-defined:  Clicking on the User-defined radio button will open the Moving Averages for Seasonal Factor Curves dialog in which you can select the length of moving average for each month (the same length will be used for both parts).


X-11 Seasonal Adjustment - Henderson Curve Moving Average for Trend-Cycle

  Time Series Analysis X-11 Seasonal Adjustment - Henderson Curve Moving Average for Trend-Cycle

The radio buttons in this box determine the choice of the moving average for the variable trend-cycle routine, which is used in the computation of the trend-cycle component from the seasonally adjusted series (e.g., see X-11 Result Tables B 7, C 7, and D 7).  In general, the Henderson curve moving average is a weighted moving average with the magnitudes of the weights following a bell-shaped curve (see, for example, Makridakis and Wheelwright, 1978, or Shiskin, Young, and Musgrave, 1967).  The choice of the appropriate length of the moving average is an important issue in the seasonal decomposition (i.e., the computation of the trend-cycle component).  The general idea is to choose a longer moving average when there is a lot of random fluctuation in the data relative to the trend-cycle component, and to choose a shorter moving average when there is only relative little random fluctuation.  The Automatic option below, implements this reasoning to choose the optimum length for the Henderson moving average.

Automatic.  If this radio button is set, then the program will select a moving average transformation automatically.  Specifically, first a preliminary 13-term Henderson (weighted) moving average of the seasonally adjusted series is computed (without extending to the ends of the series).  A preliminary estimate of the irregular component is then computed by subtracting this series from (additive model) or dividing it into (multiplicative model) the seasonally adjusted series.  Next, the average month-to-month difference (percent change) without regard to sign is computed for both the estimated irregular and trend-cycle components.  The ratio of the average month-to-month differences (percent changes) in the two series reflects the relative importance of the irregular variations relative to the movements in the trend-cycle component.  Depending on the value of this ratio, either a 9-term Henderson moving average is selected (if the ratio is between 0.0 and .99), a 13-term Henderson moving average is selected (if the ratio is between 1.0 and 3.49) or a 23-term Henderson moving average is selected (if the ratio is greater than 3.5).  Alternatively, the user can also specifically select one of those moving average transformations (see below).

9-term.  If this radio button is set, then a 9-term Henderson moving average will be selected to compute the trend-cycle component.

13-term.  If this radio button is set, then a 13-term Henderson moving average will be selected to compute the trend-cycle component.

23-term.  If this radio button is set, then a 23-term Henderson moving average will be selected to compute the trend-cycle component.


X-11 Seasonal Adjustment - Adjust Trend-Cycle for Strikes

  Time Series Analysis X-11 Seasonal Adjustment - Adjust Trend-Cycle for Strikes

An additional adjustment for strikes or other extreme outliers can be incorporated in the computation of the trend-cycle component (X-11 Result Tables B 7).  This adjustment for extremes may substantially reduce the effect of major prolonged strikes or similar irregular occurrences on the B 7 and subsequent trend-cycle estimates.  However, Shiskin, Young, and Musgrave (1967) caution that estimates near sharp business cycle peaks or troughs will also be affected by this adjustment.


Time series - X-11 Quarterly Adjustment

  Time Series Analysis - X-11 Quarterly Adjustment

The options on this dialog allow you to perform X-11 quarterly seasonal decomposition, a technique also know as the Census II method (see X-11 Census Method II Seasonal Adjustment for details; see also, Time Series Analysis - Index).  The arrangement of options is specifically designed to closely follow the terminology and options of the X-11 procedure of the Bureau of the Census (Shiskin, Young, & Musgrave, 1967).

To select the variable (series) that is to be analyzed, click on the Variable or Long variable (series) name column to highlight the variable (series) in the active work area.  The consecutive observations in that series should contain data (e.g., sales, revenue figures, etc.) for consecutive quarters.  Next, specify the starting quarter of the series (either specify a date variable, or type the respective quarter and year into the From -- quarter/year edit fields), additional options if appropriate (or accept the defaults), and then click OK to begin the seasonal decomposition.

After the last output table has been displayed (see X-11 Result Tables for a description of the result tables), the program will automatically append to the active work area, the following series/components:

•  The final seasonal factors (table D 10), the final seasonally adjusted series (D 11),

•  The final trend-cycle component (D 12), and

•  The final irregular series (random component; D 13).

Be sure to Lock all important backups of the original variable (those which you want to retain); otherwise, those backups may be overwritten (refer to the section describing the memory management in the active work area).  To lock a backup, double-click in the Lock column on the respective variable.  Note that if the display of consecutive results tables is interrupted, then none of these components will be appended to the active work area.

X-11 Quarterly Seasonal Adjustment (Census II Method) dialog:

Number of backups per variable

Save variables

Delete

Other transf. & plots

Seasonal adjustment

Dates (start of series)

Summary measures (input is seasonally adjusted)

Printout tables (detail)

Charts

Batch print all tables/charts without interruption

Sigma limits for graduating extreme values

Adjust trend-cycle for strikes (extremes)

Review and plot variables

Autocorrelations

Histogram

Descriptive statistics

Normal, detrended normal, and half-normal probability plots


Time series X-11 Quarterly Adjustment - Number of Backups per Variable

  Time Series Analysis X-11 Quarterly Adjustment - Number of Backups per Variable

This parameter determines the maximum number of backups that is kept in the active work area for each variable.  When a new transformation is about to be appended and the maximum number of backups for the respective original variable has already been exceeded, then the "oldest" previous backup will be replaced.  You can lock a variable (prevent it from being overwritten) by double-clicking on the respective variable in the Lock column.  For more details, refer to the active work area section.


Time series X-11 Quarterly Adjustment - Save Variables

  Time Series Analysis X-11 Quarterly Adjustment - Save Variables

This option allows you to save the variables (series) that are currently available in the active work area into a standard STATISTICA data file (which can be used as input for subsequent analyses).


Time series X-11 Quarterly Adjustment - Delete

  Time Series Analysis X-11 Quarterly Adjustment - Delete

This option allows you to delete the currently highlighted variable.  To highlight a variable, click on it either in the Lock, Variable, or Long variable (series) name column.


Time series X-11 Quarterly Adjustment - Other Transf. & Plots

  Time Series Analysis X-11 Quarterly Adjustment - Other Transf. & Plots

This option will bring up the General transformations dialog which allows you to perform a wide variety of transformations on the data.  The transformed series will be appended to the active work area.


Time series X-11 Quarterly Adjustment - Seasonal Adjustment

  Time Series Analysis X-11 Quarterly Adjustment - Seasonal Adjustment

The setting of radio buttons in this box determines whether an Additive or Multiplicative seasonal adjustment will be performed (refer to the X-11 Census Method II Seasonal Adjustment overview for details).  In short, in the additive model the seasonal, trend-cycle, and irregular (random) components are assumed to combine in an additive fashion (e.g., the seasonal fluctuation adds $1,000,000 to the sales in the holiday month of December).  In the multiplicative model, they are thought to combine in a multiplicative fashion (e.g., due to the seasonal component, in December sales increase by 30%, i.e., 1.3 times the baseline).


Time series X-11 Quarterly Adjustment - Dates (Start of Series)

  Time Series Analysis X-11 Quarterly Adjustment - Dates (Start of Series)

The setting in this box determines the start date of the series.  The start date will not only affect the labeling of the output tables, but can also substantially affect the computations.  When you select the Variable option in this box, a variable selection dialog will open in which you can select the variable containing the starting dates.  Selecting the From option will allow you to specify the specific quarter and year in which the series started.


Time series X-11 Quarterly Adjustment - Summary Measures (Input is Seasonally Adjusted)

  Time Series Analysis X-11 Quarterly Adjustment - Summary Measures (Input is Seasonally Adjusted)

If this check box is set, then the program will assume that the input is already a seasonally adjusted series.  In that case, the X-11 procedure can be used to test for residual seasonal variation by completing the standard steps in parts B and C of the computations (see X-11 Result Tables for details).


Time series X-11 Quarterly Adjustment - Summary Tables (Printout Details)

  Time Series Analysis X-11 Quarterly Adjustment - Summary Tables (Printout Details)

The setting of radio buttons in this box will determine the detail of results that will be reported after clicking OK.  The number of specific X-11 Result Tables that will be computed depends on the choices in this box.  Note that, if the Batch print all tables/charts without interruption check box is set (see below), then all tables will automatically be printed without interruption.  The X-11 Result Tables section describes which specific tables (Scrollsheets) are reported for the Standard, Long, or Full printout detail.

Standard:  When you select this radio button, 17 to 27 tables will be displayed.

Long:  When you select this radio button, 27 to 39 tables will be displayed.

Full:  When you select this radio button, 44 to 59 tables will be displayed.

Selected tables:  If you click on this radio button, the Select the X-11 tables and charts to be printed/displayed dialog will open in which the identifiers for all available tables are listed.  In this dialog, you can select the specific tables (Scrollsheets) that you want displayed and/or printed.  If no tables are selected (i.e., do not select any tables and click OK in this dialog), then only the final estimates of the seasonally adjusted series, the seasonal component, irregular component, and trend-cycle component will be appended to the active work area.


Time series X-11 Quarterly Adjustment - Charts

  Time Series Analysis X-11 Quarterly Adjustment - Charts

The setting of radio buttons in this box will determine the detail of graphics results that will be reported after clicking OK in this dialog.  Note that, if the Batch print all tables/charts without interruption check box is set and Printer output is selected in the Page/Output Setup dialog, then the respective graphs will automatically be printed.  Refer also to the X-11 Result Tables section for description of the charts (line plots) computed by the procedure.

None.  If this radio button is set, then no plots will be produced.

Standard.  If this radio button is set, then charts G 1 (final seasonally adjusted series and final trend-cycle components; D 11 and D 12, respectively) and G 2 (final S-I differences or ratios with the extremes, the final S-I differences (ratios) without extremes, and the final seasonal factors; D 8, D 9, and D 10) will be computed.

All.  If this radio button is set, then all charts G 1 through G 4 will be displayed (see X-11 Result Tables for details).

Selected.  If this radio button is set, then the Select the X-11 tables and charts to be printed/displayed dialog will open in which all available output charts (and tables) are listed.  The user can then select the desired charts (line plots) to be computed.


Time series X-11 Quarterly Adjustment - Batch Print all Tables/Charts without Interruption

  Time Series Analysis X-11 Quarterly Adjustment - Batch Print all Tables/Charts without Interruption

If this check box is set then all tables that are displayed will automatically be printed (to the printer, file, and/or Text/output Window, whichever is selected in the Page/Output Setup dialog) without requiring any additional user input.  If Printer output is selected, all graphs will also automatically be printed.


Time series X-11 Quarterly Adjustment - Sigma Limits for Graduating Extreme Values

  Time Series Analysis X-11 Quarterly Adjustment - Sigma Limits for Graduating Extreme Values

One of the strengths of the X-11 method is in the treatment of outliers.  When estimating the seasonal and trend-cycle components, irregular values are assigned different weights depending on their deviation from 0 (zero; additive model) or 1 (multiplicative model).  See also X-11 Result Tables (table B 4) for details concerning this procedure.  The Full weight value determines the multiple of σ (sigma; the estimate of the trend-cycle standard deviation) below which a value will be assigned a full weight.  The Zero weight value determines the multiple of σ above which a zero weight will be assigned.  In-between these two cut-off values, linearly graduated weights are assigned.


Time series X-11 Quarterly Adjustment - Adjust Trend-Cycle for Strikes (Extremes)

  Time Series Analysis X-11 Quarterly Adjustment - Adjust Trend-Cycle for Strikes (Extremes)

An additional adjustment for strikes or other extreme outliers can be incorporated in the computation of the trend-cycle component (X-11 Result Tables B 7).  This adjustment for extremes may substantially reduce the effect of major prolonged strikes or similar irregular occurrences on the B 7 and subsequent trend-cycle estimates.  However, Shiskin, Young, and Musgrave (1967) caution that estimates near sharp business cycle peaks or troughs will also be affected by this adjustment.


Time series X-11 Quarterly Adjustment - Review and Plot Variables

  Time Series Analysis X-11 Quarterly Adjustment - Review and Plot Variables

These options allow you to review or plot the currently highlighted variable (together with other variables).  The labeling of the individual observations (that is, of the respective points in time represented by the rows in Scrollsheets or the horizontal X-axis in plots) is determined by the selections in the Display/plot options dialog (click on the Options button; these options are also available on the Transformations dialog).  For the plots, you can choose to Scale the X-axis in the plots manually.  This is often useful when the series consists of several regularly recurring time intervals.  For example, if the series is made up of 10 years with 12 (monthly) observations each, then it may be useful to scale the X-axis in the plot so that each major tickmark indicates one year.

Display/plot subset of cases only.  If this check box is set, then, before plotting or displaying one or more series, you will be prompted to select a range of observations to include in the plot or display.

Options (scaling, labels, etc.).  Click on this button to bring up the Display/plot options dialog.  This dialog allows you to change the labeling of the observations (i.e., the rows in Scrollsheets and the X-axis in line plots can be labeled with case names, case numbers, dates from another variable, etc.) and the scaling of the X-axis in line plots (minimum, step size).

Review/Plot highlighted variable.  This button will bring up a Scrollsheet (or a plot) with the values for the currently highlighted variable.

Review/Plot multiple variables.  After clicking on this button, you will first be prompted to select a list of variables to be displayed or plotted.  When plotting multiple variables the vertical (Y) axis will have a common scale; thus, if the series that are plotted contain values of completely different magnitudes, use the option Plot two var lists with different scales (see below), instead.

Plot two var. lists with different scales.  This option allows you to plot two lists of variables using different scales for the vertical (Y) axes in the plot.  The first list will be plotted against the left Y-axis and the second list will be plotted against the right Y-axis.  For example, suppose you want to plot two variables (series) called S1 and S2, and that these variables contain values of different magnitudes: the values of S1 range from 1-100 and the values of S2 range from 1000 to 10000.  If you plot S1 against the left Y-axis (scaled from 1-100) and S2 against the right Y-axis (scaled from 1000-10000) then both variables will be plotted with optimal resolution, and thus relationships between patterns across time (the X-axis) may become more clearly identifiable.


Time series X-11 Quarterly Adjustment - Autocorrelations

  Time Series Analysis X-11 Quarterly Adjustment - Autocorrelations

These options will compute the autocorrelations and partial autocorrelations for the currently highlighted variable; these statistics will be displayed in a Scrollsheet and drawn in a correlogram graph.  Refer to the Overview section for a brief description of how the pattern of (partial) autocorrelations aids in the determination of an appropriate ARIMA model.

Autocorrelations.  This option will bring up a Scrollsheet and plot of the autocorrelations, for a lag of 1 through the number specified in the Number of lags edit field (see below).  The Scrollsheet will report the autocorrelations, their standard errors, the so-called Box-Ljung statistic, and the significance level of that statistic.  In general, the autocorrelation is the correlation of the series with itself, lagged by a particular number of observations.  For details regarding the computations of those statistics refer to the autocorrelation section.

Alpha for highlighting.  Significant autocorrelations (significant Box-Ljung statistics) will be highlighted in the Scrollsheet.  This edit field allows you to specify the significance level that is used for highlighting.

White noise standard errors.  Under the assumption that the true moving average process in the series is of the order k-1, the approximate standard error of the autocorrelation rk is computed as:

                                2

StdErr(r ) = √{(1/N) * [1+2*Σ(r  )]}

        k                      i

(for i = 1 to k-1)

Here, N is the number of observations in the series.  Under the assumption that the series is a white noise process, that is, that all autocorrelations are equal to zero, the standard error of rk is computed as:

StdErr(r  )= √{(1/N) * [(N-k)/(N+2)]}

        k

Check the White noise standard errors option to compute the standard errors in this manner.

Partial autocorrelations.  This option will bring up a Scrollsheet and plot of the partial autocorrelations, for a lag of 1 through the number specified in the Number of lags edit field.  The Scrollsheet will report the partial autocorrelations and their standard errors.  In general, the partial autocorrelation is the partial correlation of a series with itself, lagged by a particular number of observations, and controlling for all correlations for lags of lower order.  For example, the partial autocorrelation for a lag of 2 represents the unique correlation of the series with itself at that lag, after controlling for the correlation at lag 1.  For details regarding the computations of the partial autocorrelation and its standard error refer to the partial autocorrelation section.  Partial autocorrelations that are larger than two times their respective standard errors will be highlighted in the Scrollsheet.

Number of lags.  This parameter determines the maximum number of lags for which the auto- and partial autocorrelations will be computed.


Time series X-11 Quarterly Adjustment - Histograms

  Time Series Analysis X-11 Quarterly Adjustment - Histograms

This option will bring up a histogram of the currently highlighted variable.


Time series X-11 Quarterly Adjustment - Descriptive Statistics

  Time Series Analysis X-11 Quarterly Adjustment - Descriptive Statistics

This option will bring up a Scrollsheet with descriptive statistics for all variables currently available in the active work area.


Time series X-11 Quarterly Adjustment - Normal, Detrended, and Half-Normal Probability Plots

  Time Series Analysis X-11 Quarterly Adjustment - Normal, Detrended Normal, and Half-Normal Probability Plots

These options will bring up the respective normal probability plot for the highlighted variable.  For more information on how these plots are constructed, see Normal Probability Plots, Half-Normal Probability Plots, and Detrended Normal Probability Plots.


  Time Series Analysis - Moving Averages for Seasonal Factor Curves

The radio buttons in this dialog determine the lengths of moving averages that are used to compute the preliminary and final seasonal factors for each month in each part of the analysis (B, C, and D; see X-11 Census Method II Seasonal Adjustment; see also, Time Series Analysis - Index).

By default (Automatic) the program will select for each month a 3x3 moving average for the first estimate in each part (see X-11 Result Tables B 5, C 5, and D 5) and a 3x5 moving average for the second estimate (see X-11 Result Tables B 10, C 10, and D 10).  A 3x3 moving average is a 3-term moving average applied to a series previously smoothed by a 3-term moving average, which is equivalent to a 5-term weighted moving average; a 3x5 moving average is 3-term moving average applied to a series previously smoothed by a 5-term moving average, which is equivalent to a 7-term weighted moving average; for a discussion of different types of moving averages see Makridakis and Wheelwright (1983).

Alternatively, you can also choose a different type of moving average for each month.  In that case, the same type of moving average will be applied for both the preliminary (e.g., B 5) and final estimates (e.g., B 10) of the seasonal component in each part.  However, different moving averages can be applied to different months.


  Time Series Analysis - Selecting Monthly Adjustment Factors

To select the series containing the prior monthly adjustment factors in the Currently Available Variables and Transformations dialog, you can double-click on the respective series, or click once on the respective series to highlight it and then click OK.

The values in the selected series are used to adjust the input series prior to the seasonal decomposition/adjustment.  This is often useful when one wants to adjust for unusual holidays, strikes, or other events that affected the series of interest in a known (a priori) manner.  The factors specified here will be subtracted from the original series (additive model), or they will be used to divide the original series (if multiplicative seasonal adjustment was requested).  Thus, the values in this series must be unequal to zero in the latter case.  The original series adjusted by prior monthly adjustment factors will be displayed in the X-11 Result Table A 3.


  Time Series Analysis - Selecting Specific Output Tables and/or Charts

Select the desired output tables and/or charts (line plots G 1 through G 4, see below).  If no tables or charts are selected, then no Scrollsheets or line plots will be displayed; however, the final components D 10 through D 13 (see below) will still be appended to the active work area.

For details concerning the X-11 Census II method refer to the X-11 Census Method II Seasonal Adjustment overview section (see also, Time Series Analysis - Index).  See below for a more detailed description of the contents of the different results tables and charts. (Tables and charts marked by an asterisk [*] are not available for quarterly X-11 analysis.)

A	Prior adjustment (monthly seasonal adjustment only)

B	Preliminary estimation of trading-day variation (monthly X-11) and weights

C	Final estimation of trading-day variation (monthly X-11) and irregular weights

D	Final estimation of seasonal factors, trend-cycle, irregular, and seasonally adjusted series

E	Modified original, seasonally adjusted, and irregular series

F	Month (quarter) for cyclical dominance (MCD, QCD), moving average, and summary measures

G	Charts


Output Tables and/or Charts - A-Prior adjustment (monthly seasonal adjustment only)

  Output Tables and/or Charts - A-Prior Adjustment (Monthly Seasonal Adjustment

Note:  Tables and charts marked by an asterisk [*] are not available for quarterly X-11 analysis.

*A 1.  Original series

*A 2.  Prior monthly adjustment factors

*A 3.  Original series adjusted by prior monthly adjustment factors

*A 4. Prior trading-day adjustment factors


  Output Tables and/or Charts - B-Preliminary Estimation of Trading-Day Variation (Monthly X-11) and Weights

Note:  Tables and charts marked by an asterisk [*] are not available for quarterly X-11 analysis.

B 1. Prior adjusted series or original series

B 2. Trend-cycle (L)

B 3. Unmodified S-I differences or ratios

B 4. Replacement values for extreme S-I differences (ratios)

B 5. Seasonal factors

B 6. Seasonally adjusted series

B 7. Trend-cycle

B 8. Unmodified S-I differences (ratios)

B 9. Replacement values for extreme S-I differences (ratios)

B 10.  Seasonal factors

B 11. Seasonally adjusted series

B 12. (not used)

B 13. Irregular series

*B 14. Extreme irregular values excluded from trading-day regression

*B 15.  Preliminary trading-day regression

*B 16. Trading-day adjustment factors derived from regression coefficients

B 17. Preliminary weights for irregular component

*B 18. Trading-day factors derived from combined daily weights

*B 19. Original series adjusted for trading-day and prior variation


  Output Tables and/or Charts - C-Final Estimation of Trading-Day Variation (Monthly X-11) and Irregular Weights

Note:  Tables and charts marked by an asterisk [*] are not available for quarterly X-11 analysis.

C 1. Original series modified by preliminary weights and adjusted for trading-day and prior variation

C 2. Trend-cycle

C 3. (not used)

C 4. Modified S-I differences (ratios)

C 5. Seasonal factors

C 6. Seasonally adjusted series

C 7. Trend-cycle

C 8. (not used)

C 9. Modified S-I differences (ratios)

C 10. Seasonal factors

C 11. Seasonally adjusted series

C 12. (not used)

C 13. Irregular series

*C 14. Extreme irregular values excluded from trading-day regression

*C 15.  Final trading-day regression

*C 16. Final trading-day adjustment factors derived from regression coefficients

C 17. Final weights for irregular component

*C 18. Final trading-day factors derived from combined daily weights

*C 19. Original series adjusted for trading-day and prior variation


  Output Tables and/or Charts - D-Final Estimation of Seasonal Factors, Trend-Cycle, Irregular, and Seasonally Adjusted Series

D 1. Original series modified by final weights and adjusted for trading-day and prior variation

D 2. Trend-cycle

D 3. (not used)

D 4. Modified S-I differences (ratios)

D 5. Seasonal factors

D 6. Seasonally adjusted series.

D 7. Trend-cycle

D 8. Final unmodified S-I differences (ratios)

D 9. Final replacement values for extreme S-I differences (ratios)

D 10. Final seasonal factors

D 11. Final seasonally adjusted series

D 12. Final trend-cycle

D 13. Final irregular


  Output Tables and/or Charts - E-Modified Original, Seasonally Adjusted, and Irregular Series

E 1. Modified original series

E 2. Modified seasonally adjusted series

E 3. Modified irregular series

E 4. Differences (ratios) of annual totals

E 5. Differences (percent changes) in original series

E 6. Differences (percent changes) in final seasonally adjusted series


  Output Tables and/or Charts - F-Month (Quarter) for Cyclical Dominance (MCD, QCD), Moving Average, and Summary Measures

F 1. MCD (QCD) moving average

F 2. Summary measures


  Output Tables and/or Charts - G-Charts

G 1. Chart

G 2. Chart

G 3. Chart

G 4. Chart


  Time Series Analysis - Spectrum (Fourier) Analysis

The options on this dialog allow you to perform Spectrum (Fourier) Analysis for single variables as well as Cross-spectrum Analysis (see also, Time Series Analysis - Index).  Click in the Variable or Long variable (series) name column to highlight the variable (series) in the active work area that is to be analyzed.  For cross-spectrum analysis, that variable will be treated as the x or independent variable.  Then select the desired options (see below) and begin the analysis by clicking either on the Single series Fourier analysis or Two series Fourier analysis button.

Note that the input series should contain an even number of valid observations.  If this is not the case, then the last case of the series will automatically be ignored.

The components computed as the result of the analyses can later be appended to the active work area.  Thus, make sure that there is sufficient "space" in the active work area for the respective variable, that is, that there are at least as many (not locked) backups available as there are components that you want to save.  Increase the Number of backups parameter if necessary.  Also, be sure to Lock all important backups of the original variable (those which you want to retain); otherwise, those backups may be overwritten (refer to the section describing the memory management in the active work area).  To lock a backup, double-click in the Lock column on the respective variable.

Fourier Spectral Analysis dialog:

Single Series Fourier Analysis

Two Series Fourier Analysis

Transformation of Input Series

Padding of input series

Histogram

Descriptive statistics

Normal, detrended normal, and half-normal probability plots

Review and plot variables

Autocorrelations

Other transformations and plots


Spectrum (Fourier) Analysis - Single Series Fourier Analysis

  Time Series Analysis Spectrum (Fourier) Analysis - Single Series Fourier Analysis

This option will perform a spectrum analysis for the currently highlighted variable (series), and then bring up the Single Series Fourier (Spectral) Analysis Results dialog.  If selected, the transformations specified in the Transformation of input series box will be performed prior to the analysis.


Spectrum (Fourier) Analysis - Two Series Fourier Analysis

  Time Series Analysis Spectrum (Fourier) Analysis - Two Series Fourier Analysis

This option will perform a cross-spectrum analysis of the currently highlighted variable (series) and another variable.  The currently highlighted variable will be treated as the independent or x variable in the analyses.  After clicking on this button, a dialog will open, prompting the user to select the dependent variable for the analysis.


Spectrum (Fourier) Analysis - Transformation of Input Series

  Time Series Analysis Spectrum (Fourier) Analysis - Transformation of Input Series

The transformations available in this box will be performed on the series prior to the analysis.  The overview section (Single Spectrum (Fourier) Analysis) discusses the process of tapering, and the reasons for de-meaning/trending the data.

Taper.  The so-called process of split-cosine-bell tapering is a recommended transformation of the series prior to the spectrum analysis.  It usually leads to a reduction of leakage in the spectral density plots. (Leakage describes the condition when a strong periodicity at a particular frequency results in large spectral density estimates in several adjacent frequencies).  The rationale for this transformation is explained in detail in Bloomfield (1976, p. 80-94), see also Tapering

Subtract mean.  If this check box is set, then the overall mean will be subtracted from the series prior to the analysis.  Because the goal of spectrum analysis is to detect underlying periodicity, the overall mean is usually not of interest.  If the mean is not removed, then it will "show up" as the cosine coefficient at frequency 0 (zero; the mean can be thought of as a periodic cycle with a frequency of 0 per unit time).  Often, this will lead to an extremely large periodogram value at that frequency, which makes it hard to identify other spikes in the periodogram or spectral density plots.

Detrend.  If this check box is set, then the linear trend will be removed from the series prior to the analysis.  Like the mean, an overall trend is also not of interest when one wants to uncover periodicities in the series.  Therefore, it should be removed prior to the analysis.


Spectrum (Fourier) Analysis - Padding of Input Series

  Time Series Analysis Spectrum (Fourier) Analysis - Padding of Input Series

You may choose to pad the series prior to the analysis, that is, to add zeros to the end of the series.  Padding of the input series may be useful for two reasons:  First, in a sense, it allows you to apply a finer "frequency roster" to the series, checking for successive frequencies at smaller increments.  Second, for moderate to large size series (e.g., with more than 100,000 cases), choosing to pad (or truncate) the length of the series to a power of 2 may substantially reduce memory requirements and increase speed (for small series, you will not notice any difference).  Both of these issues are also discussed in the Single Spectrum (Fourier) Analysis overview section.  If extensive padding is used, we recommend that you also taper the series.

Do not pad series; use exact length.  If this radio button is set, then the series will not be padded, and the resulting periodogram will show values for N/2+1 distinct frequencies (where N is the even number of cases in the series).  As described in the overview section, the standard (and most efficient) FFT (fast Fourier transform) algorithm requires that the length of the input series is a power of 2.  If this is not the case, then additional computations have to be performed.  The Time Series module will use the simple explicit computational formulas as long as the input series is relatively small, and the number of computations can be performed in a relatively short amount of time.  For long time series, in order to still utilize the FFT algorithm, an implementation of the general approach described by Monro and Branch (1976) is used.  This method requires significantly more storage space, however, series of considerable length can still be analyzed very quickly, even if the number of observations is not equal to a power of 2.

Pad the end of the series with N zeros.  If this radio button is set, then N zeros will be added to the end of the input series (where N is the number of observations in the input series).  Note that the zeros will be added after the series has been de-meaned/trended (see above).

Truncate length to a power of 2.  If this radio button is set, then the length of the input series will be truncated so that the number of observations will be equal to a power of 2 (e.g., 8, 16, 32, 64, 128, ...).  When the length of the input series is a power of 2, then the so-called fast Fourier transform (FFT) algorithm (widely popularized by Cooley and Tukey, 1965; for various refinements and improvements see Monro,. 1975) can be used for the analysis.  This is the fastest method for computing the spectrum analysis (the processing time is proportional to N * log2(N)).

Pad length to a power of 2.  If this radio button is set, then the length of the input series will be padded with 0's (zeros) so that the number of observations will be equal to a power of 2 (e.g., 8, 16, 32, 64, 128, ...).  When the length of the input series is a power of 2, then the so-called fast Fourier transform algorithm (widely popularized by Cooley and Tukey, 1965; for various refinements and improvements, see Monro, 1975) can be used for the analysis.  This is the fastest method for computing the spectrum analysis (the processing time is proportional to N * log2(N)).


Spectrum (Fourier) Analysis - Histogram

  Time Series Analysis Spectrum (Fourier) Analysis - Histogram

This option will bring up a histogram of the currently highlighted variable.


Spectrum (Fourier) Analysis - Descriptive Statistics

  Time Series Analysis Spectrum (Fourier) Analysis - Descriptive Statistics

This option will bring up a Scrollsheet with descriptive statistics for all variables currently available in the active work area.


Spectrum (Fourier) Analysis - Normal, Detrended Normal, and Half-Normal Probability Plots

  Time Series Analysis Spectrum (Fourier) Analysis - Normal, Detrended Normal, and Half-Normal Probability Plots

These options will bring up the respective normal probability plot for the highlighted variable.  For more information on how these plots are constructed, see Normal Probability Plots, Half-Normal Probability Plots, and Detrended Normal Probability Plots.


Spectrum (Fourier) Analysis - Review and Plot Variables

  Time Series Analysis Spectrum (Fourier) Analysis - Review and Plot Variables

These options allow you to review or plot the currently highlighted variable (together with other variables).  The labeling of the individual observations (that is, of the respective points in time represented by the rows in Scrollsheets or the horizontal X-axis in plots) is determined by the selections in the Display/plot options dialog (click on the Options button; these options are also available on the Transformations dialog).  For the plots, you can choose to Scale the X-axis in the plots manually.  This is often useful when the series consists of several regularly recurring time intervals, for example, if it is made up of 10 years with 12 (monthly) observations each.  Then it may be useful to scale the X-axis in the plot so that each major tickmark indicates one year.

Display/plot subset of cases only.  If this check box is set, then, before plotting or displaying one or more series, you will be prompted to select a range of observations to include in the plot or display.

Options (scaling, labels, etc.).  This option will bring up the Display/plot options dialog.  That dialog allows you to change the labeling of the observations (i.e., the rows in Scrollsheets and the X-axis in line plots can be labeled with case names, case numbers, dates from another variable, etc.) and the scaling of the X-axis in line plots (minimum, step size).

Review/Plot highlighted variable.  This button will bring up a Scrollsheet (or a plot) with the values for the currently highlighted variable.

Review/Plot multiple variables.  After clicking on this button, you will first be prompted to select a list of variables to be displayed or plotted.  When plotting multiple variables the vertical (Y) axis will have a common scale; thus, if the series that are plotted contain values of completely different magnitudes use option Plot two var lists with different scales, instead.

Plot two var. lists with different scales.  This option allows you to plot two lists of variables using different scales for the vertical (Y) axes in the plot.  The first list will be plotted against the left Y-axis and the second list will be plotted against the right Y-axis.  For example, suppose you want to plot two variables (series) called S1 and S2, and that these variables contain values of different magnitudes: the values of S1 range from 1-100 and the values of S2 range from 1000 to 10000.  If you plot S1 against the left Y-axis (scaled from 1-100) and S2 against the right Y-axis (scaled from 1000-10000) then both variables will be plotted with optimal resolution, and thus relationships between patterns across time (the X-axis) may become more clearly identifiable.


Spectrum (Fourier) Analysis - Autocorrelations

  Time Series Analysis Spectrum (Fourier) Analysis - Autocorrelations

These options will compute the autocorrelations and partial autocorrelations for the currently highlighted variable; these statistics will be displayed in a Scrollsheet and drawn in a correlogram graph.  Refer to the Overview section for a brief description of how the pattern of (partial) autocorrelations aids in the determination of an appropriate ARIMA model.

Autocorrelations.  This option will bring up a Scrollsheet and plot of the autocorrelations, for a lag of 1 through the number specified in the Number of lags edit field.  The Scrollsheet will report the autocorrelations, their standard errors, the so-called Box-Ljung statistic, and the significance level of that statistic.  In general, the autocorrelation is the correlation of the series with itself, lagged by a particular number of observations.  For details regarding the computations of those statistics refer to the autocorrelation section.

Alpha for highlighting.  Significant autocorrelations (significant Box-Ljung statistics) will be highlighted in the Scrollsheet.  This edit field allows you to specify the significance level that is used for highlighting.

White noise standard errors.  Under the assumption that the true moving average process in the series is of the order k-1, the approximate standard error of the autocorrelation rk is computed as:

                                2

StdErr(r ) = √{(1/N) * [1+2*Σ(r  )]}

        k                      i

(for i = 1 to k-1)

Here N is the number of observations in the series.  Under the assumption that the series is a white noise process, that is, that all autocorrelations are equal to zero, the standard error of rk is computed as:

StdErr(r ) = √{(1/N) * [(N-k)/(N+2)]}

        k

Check the White noise standard errors option to compute the standard errors in this manner.

Partial autocorrelations.  This option will bring up a Scrollsheet and plot of the partial autocorrelations, for a lag of 1 through the number specified in the Number of lags edit field.  The Scrollsheet will report the partial autocorrelations and their standard errors.  In general, the partial autocorrelation is the partial correlation of a series with itself, lagged by a particular number of observations, and controlling for all correlations for lags of lower order.  For example, the partial autocorrelation for a lag of 2 represents the unique correlation of the series with itself at that lag, after controlling for the correlation at lag 1.  For details regarding the computations of the partial autocorrelation and its standard error refer to the partial autocorrelation section.  Partial autocorrelations that are larger than two times their respective standard errors will be highlighted in the Scrollsheet.

Number of lags.  This parameter determines the maximum number of lags for which the autocorrelations and partial autocorrelations will be computed.


Spectrum (Fourier) Analysis - Other Transformations and Plots

  Time Series Analysis Spectrum (Fourier) Analysis - Other Transformations and Plots

This option will bring up the General transformations dialog which allows you to perform a wide variety of transformations on the data.  The transformed series will be appended to the active work area.


Time Series Analysis - Selecting Dependent Variable for Cross-spectrum

  Time Series Analysis - Selecting a Dependent Variable for Cross-spectrum

Select the dependent (y) variable for the cross-spectrum analysis.  To select a variable, either double-click on the respective series, or click once on the variable to highlight it and then click OK.

For a discussion of cross-spectrum analysis refer to the Cross-spectrum analysis overview section.


Time Series Analysis - Single Spectrum Analysis Results

  Time Series Analysis - Single Variable Spectrum Analysis Results

This dialog provides options for computing all spectrum analysis results statistics.  The interpretation of the different statistics is also discussed in the Single Spectrum (Fourier) Analysis overview section (see also, Time Series Analysis - Index).  When reviewing the results from long series, you may use the Examine subset of periodogram check box.  When set, the results computed by the Summary option and all graph options (Periodogram, Spectral density, etc.) will be computed only for the range of cases specified in the edit boxes below the check box.  To append any of the computed statistics to the active work area, set the respective check boxes in the Append to work area on Exit box.  Note that if there are not enough unused or un-locked backups for the respective input variable available, then the program will automatically increase the Number of backups per variable parameter (see also the Spectrum (Fourier) Analysis Specifications dialog) by as much as possible.

Single Series Fourier (Spectral) Analysis Results dialog:

Info Box

Summary

Data windows for spectral density estimates

Examine subset of periodogram

N largest values

Append to work area on Exit

Periodogram and spectral density plots

Histogram of periodogram values

Spectral density


Single Spectrum Analysis Results - Info Box

  Time Series Analysis Single Variable Spectrum Analysis Results - Info Box

The info box reports the name of the series that was analyzed, the number of observations (before and after padding/truncating), and the 5 largest periodogram values and the frequencies where they occurred.


Single Spectrum Analysis Results - Summary

  Time Series Analysis Single Variable Spectrum Analysis Results - Summary

This button will produce a summary Scrollsheet with the frequencies, periods, cosine and sine coefficients, periodogram values, spectral density estimates (computed according to the selection in the Data windows box; see below), and the weights used to produce the spectral density estimates.  If the Highlight values larger than... check box is set, then all values in the periodogram and spectral density columns that are larger than the specified value will be highlighted.  Note that as the default graph for this Scrollsheet, you may select to plot the sine/cosine coefficients, the periodogram values (or log-periodogram), or the spectral density estimates (or the log-densities) against the frequencies or period.

Given a series (see Shumway, 1988, page 49):

x = a + (Σ{a *cos[2πf (t-1)]} + {b *sin[2πf (t-1)]})

 i   0   k  k        k            k         k

where the values are computed as follows:

Frequency (fk).  The frequency (fk) is defined as the number of cycles per unit time.  Since in the Time Series module, one observation is used as the time unit (i.e., frequency is expressed in terms of cycles per observation), the successive frequencies are computed as k/N (for k=0 to N/2) where N is the number observations in the series.  Thus, for example, a frequency of .0833 would mean that each observation completes .0833 of the full cycle, or that 12 observations complete one full cycle (.0833*12=1).  Thus, if the series contains monthly data collected over several years, the respective periodicity identifies an annual cycle.

Period (1/fk).  The period (1/fk) is computed as the inverse of the frequency.  Thus it can be interpreted as the number of observations that is necessary in order to complete one cycle at the respective frequency.

Cosine coefficients (ak).  The cosine coefficients (ak) can be interpreted as regression coefficients, that is, they tell us the degree to which the respective cosine functions are correlated with the data at the respective frequencies.

Sine coefficients (bk).  The sine coefficients (bk) can be interpreted analogous to the cosine coefficients (see previous paragraph).

Periodogram.  The periodogram values are computed as the sum of the squared sine and cosine coefficients at each frequency (times N/2).  The periodogram values can be interpreted in terms of variance (sums of squares) of the data at the respective frequency or period.

Spectral density estimates.  The spectral density estimates are computed by smoothing the periodogram values, using the specifications in the Data windows for spectral density estimates box.  By smoothing the periodogram one may identify the general frequency "regions" (or spectral densities) that significantly contribute to the cyclical behavior of the series.  Note that the weights used for the smoothing will always be standardized so that they add to 1.0.  Also, at the beginning and end of the series, the smoothing is done via reflection.

Weights.  This column will report the actual weights used in the smoothing window to produce the spectral density estimates (see above).  The different smoothing windows are described below (Data windows for spectral density estimates).  Note that the weights are standardized so that they will always sum to 1.


Single Spectrum Analysis Results - Data Window for Spectral Density Estimates

  Time Series Analysis Single Variable Spectrum Analysis Results - Data Windows for Spectral Density Estimates

As described in greater detail in the Single Spectrum (Fourier) Analysis overview section, the periodogram values themselves are subject to substantial random fluctuation.  A clearer picture of underlying periodicities often only emerges when examining the spectral densities, that is, the frequency regions, consisting of many adjacent frequencies, that contribute most to the overall periodic behavior of the series.  The spectral density estimates are computed by smoothing the periodogram values with a weighted moving average.  You can select the type of moving average smoothing via this option.  For more information on each window listed below, click on the window name.

Daniell (or equal weight) window

Tukey window

Hamming window

Parzen window

Bartlett window

User-defined window.

If the User-defined window radio button is selected, you will be prompted to enter the weights used for smoothing directly (a dialog box will come up prompting you to specify the weights).

Note that in all cases the Time Series module will standardize the weights so that they always sum to 1.  For example, if you entered 1 2 3 2 1 as the user-defined weights, they will be converted to: 1/9 2/9 3/9 2/9 1/9 (so that they add up to 1).  In many cases, all of the standard data windows will produce very similar results; but it is often useful to experiment with different windows of different widths, and to examine resulting density plots.


Single Spectrum Analysis Results - Examine Subset of Periodogram

  Time Series Analysis Single Variable Spectrum Analysis Results - Examine Subset of Periodogram

When reviewing the results for long time series, it is often useful to examine particular frequency ranges.  This can be accomplished by setting this check box, and then specifying the range of observations to review in the edit boxes below (From, To).  Note that the numbers specified here pertain to the numbers of rows in the Summary Scrollsheet, so for example, if you specify 100 and 200, then rows 100 to 200 of the Scrollsheet will be displayed (or plotted).  In addition to the Summary Scrollsheet option, the range selected here will also apply to all plots on this dialog.


Single Spectrum Analysis Results - N Largest Values

  Time Series Analysis Single Variable Spectrum Analysis Results - N Largest Values

This option will bring up a Scrollsheet with the same statistics as those computed by the Summary option; however, the results will only be shown for the N (as specified in the edit box to the right) largest periodogram or spectral density values, depending on the setting of the radio buttons to the right.


Single Spectrum Analysis Results - Append to Work Area on Exit

  Time Series Analysis Single Variable Spectrum Analysis Results - Append to Work Area on Exit

These check boxes will determine which of the results statistics will be appended to the active work area when exiting from this dialog.  The different statistics are described under the Summary option above.  If the currently available (unused and unlocked) number of backups in the active work area is less than the number of series that is to be appended, then the Number of backups per variable parameter (see also the Spectrum (Fourier) Analysis Specifications dialog) will be increased by as much as possible.


Single Spectrum Analysis Results - Periodogram and Spectral Density Plots

  Time Series Analysis Single Variable Spectrum Analysis Results - Periodogram and Spectral Density Plots

These options will produce line plots of the respective statistics; refer to the Summary option above for a description of the available results.  Note that all plots are produced either for the entire range of frequencies, or only for the range specified via the Examine subset of periodogram option.

Periodogram.  This option will bring up a line graph of the periodogram values, plotted either by frequency, period, or the log-period, depending on the setting of the radio buttons in the Plot by box.

Log periodogram.  This option will bring up a line graph of the log-periodogram values, plotted either by frequency, period, or the log-period, depending on the setting of the radio buttons in the Plot by box.

Spectral density.  This option will bring up a line graph of the spectral density values, plotted either by frequency, period, or the log-period, depending on the setting of the radio buttons in the Plot by box.

Log spectral density.  This option will bring up a line graph of the log-spectral density values, plotted either by frequency, period, or the log-period, depending on the setting of the radio buttons in the Plot by box.

Cosine coefficients.  This option will bring up a line graph of the cosine coefficient values, plotted either by frequency, period, or the log-period, depending on the setting of the radio buttons in the Plot by box.

Sine coefficients.  This option will bring up a line graph of the sine coefficient values, plotted either by frequency, period, or the log-period, depending on the setting of the radio buttons in the Plot by box.

Plot by.  The setting of the radio buttons in this box determines how the X (horizontal) axis in the line plots; the periodogram, spectral density, or sine/cosine coefficient values will be plotted (i.e., by Frequency, Period, or Log (period)).


Single Spectrum Analysis Results - Histogram of Periodogram Values

  Time Series Analysis Single Variable Spectrum Analysis Results - Histogram of Periodogram Values

If the observations in the time series are independent of each other (i.e., there is no periodicity), and they follow the normal distribution, such a time series is also referred to as a white noise series (like the white noise one hears on the radio when tuned in-between stations).  A white noise input series will result in periodogram values that follow an exponential distribution.  Thus, by testing the distribution of periodogram values against the exponential distribution, one may test whether the input series is different from a white noise series.  This option will produce a histogram of the periodogram values, and fit the exponential distribution to the histogram.  In addition, the user can also request to compute the Kolmogorov-Smirnov d statistic (see also Nonparametrics and Distributions for more details).  Note that, as with the line graphs, the histogram will be produced either for all frequencies, or for the range selected after setting the Examine subset of periodogram check box.  In this manner one can test whether the series is a white noise series over selected frequency ranges.


Single Spectrum Analysis Results - Spectral Density

  Time Series Analysis Single Variable Spectrum Analysis Results - Spectral Density

This option will bring up a histogram of the spectral density values.


  Time Series Analysis - Highlighting Periodogram Peaks

Enter here, the cut-off value that is to be used in the Scrollsheet for highlighting.


  Time Series Analysis - User-defined Spectral Window

Enter the user-defined weights to be used for the smoothing of the periodogram values.  To assign a common value to all weights, enter it in the respective edit box, click Apply, then click OK to accept the weights.  Note that the weights will always be standardized, so that they sum to 1.  For example, if you entered 1 2 3 2 1 as the user-defined weights, they will be converted to: 1/9 2/9 3/9 2/9 1/9 (so that they add up to 1).

As described in greater detail in the Single Spectrum (Fourier) Analysis overview section, the periodogram values themselves are subject to substantial random fluctuation.  A clearer picture of underlying periodicities often only emerges when examining the spectral densities, that is, the frequency regions, consisting of many adjacent frequencies, that contribute most to the overall periodic behavior of the series.  The spectral density estimates are computed by smoothing the periodogram values with a weighted moving average.  The standard weight functions assign the greatest weight to the observation in the center of the window, and (symmetrically) decreasing weights to the observation further away from the center (this also often helps to alleviate the problem of leakage; refer to the Single Spectrum (Fourier) Analysis overview section for details).


Time Series Analysis - Graphs for Single Spectrum Analysis from the Summary Scrollsheet

  Time Series Analysis - Graphs for Single Spectrum Analysis from the Summary Scrollsheets

Select the desired line plot.  The selected plot will be produced for the frequencies currently displayed in the Scrollsheet.  For a discussion of the interpretation of these plots refer to the Single Spectrum (Fourier) Analysis overview section (see also, Time Series Analysis - Index).

Periodogram.  This option will bring up a line graph of the periodogram values, plotted either by frequency, period, or the log-period, depending on the setting of the radio buttons in the Plot by box below.   The periodogram values are computed as the sum of the squared sine and cosine coefficients at each frequency (times N/2).  The periodogram values can be interpreted in terms of variance (sums of squares) of the data at the respective frequency or period.

Log periodogram.  This option will bring up a line graph of the log-periodogram values, plotted either by frequency, period, or the log-period, depending on the setting of the radio buttons in the Plot by box, below.

Spectral density.  This option will bring up a line graph of the spectral density values, plotted either by frequency, period, or the log-period, depending on the setting of the radio buttons in the Plot by box, below.  The spectral density estimates are computed by smoothing the periodogram values, using the specifications in the Data windows for spectral density estimates box on the Single Spectrum (Fourier) Analysis Results dialog.  By smoothing the periodogram one may identify the general frequency "regions" or (spectral densities) that significantly contribute to the cyclical behavior of the series.  Note that the weights used for the smoothing will always be standardized so that they add to 1.0.  Also, at the beginning and end of the series, the smoothing is done via reflection.

Log spectral density.  This option will bring up a line graph of the log-spectral density values, plotted either by frequency, period, or the log-period, depending on the setting of the radio buttons in the Plot by box, below.

Cosine coefficients.  This option will bring up a line graph of the cosine coefficient values, plotted either by frequency, period, or the log-period, depending on the setting of the radio buttons in the Plot by box below.  The cosine coefficients can be interpreted as regression coefficients, that is, they tell us the degree to which the respective cosine functions are correlated with the data at the respective frequencies.

Sine coefficients.  This option will bring up a line graph of the sine coefficient values, plotted either by frequency, period, or the log-period, depending on the setting of the radio buttons in the Plot by box below.  The sine coefficients can be interpreted analogous to the cosine coefficients (see previous paragraph).

Plot by.  The setting of the radio buttons in this box determines the X (horizontal) axis in the line plots; the periodogram, spectral density, or sine/cosine coefficient values can be plotted by Frequency, Period, or Log (period).


  Time Series Analysis - Cross-spectrum Analysis Results

This dialog provides options for computing all cross-spectrum analysis results statistics.  The interpretation of the different statistics is also discussed in the Cross-spectrum Analysis overview section (see also, Time Series Analysis - Index).  When reviewing the results from long series you may use the Examine subset of periodogram check box; when set, the results computed by the Summary option and all graphs will be computed only for the range of cases (frequencies) specified in the edit boxes below the check box.  To append any of the computed statistics to the active work area set the respective check boxes in the Append to work area on Exit box.  Note that if there are not enough unused or un-locked backups for the respective input variable available, then the program will increase the Number of backups per variable parameter (see also the Spectrum (Fourier) Analysis Specifications dialog) by as much as possible.

Bivariate Fourier (Cross-spectrum) Analysis Results dialog:

Info Box

Summary

Examine subset of periodogram

N largest values

Data windows for spectral density estimates

Append to work area on Exit

Periodogram and spectral density plots

Plot by


Cross-spectrum Analysis Results - Info Box

  Time Series Analysis Cross-spectrum Analysis Results - Info Box

The info box reports the names of the series that were analyzed and the number of observations (before and after padding/truncating).


Cross-spectrum Analysis Results - Summary

  Time Series Analysis Cross-spectrum Analysis Results - Summary

This button will produce a summary Scrollsheet with the frequencies, periods, cosine and sine coefficients, periodogram values, spectral density estimates (computed according to the selection in the Data windows box; see below), cross-periodogram values (real and imaginary), cospectral density and quadrature spectrum values (computed according to the selection in the Data windows box; see below), the cross amplitude values, coherency values, gain values, phase spectrum values, and the weights used to produce the spectral density estimates.  If the Highlight values larger than... check box is set, then all values in the periodogram and spectral density columns that are larger than the specified value will be highlighted.  The values in this Scrollsheet are computed as follows:

Frequency.  The frequency is defined as the number of cycles per unit time.  Since in the Time Series module, one observation is used as the time unit (i.e., frequency is expressed in terms of cycles per observation), the successive frequencies are computed as k/N (for k=0 to N/2) where N is the number observations in the series.  Thus, for example, a frequency of .0833 would mean that each observation completes .0833 of the full cycle, or that 12 observations complete one full cycle (.0833*12=1).  Thus, if the series contains monthly data collected over several years, the respective periodicity identifies an annual cycle.

Period.  The period is computed as the inverse of the frequency.  Thus it can be interpreted as the number of observations that is necessary in order to complete one cycle at the respective frequency.

Cosine coefficients.  The cosine coefficients can be interpreted as regression coefficients, that is, they tell us the degree to which the respective cosine functions are correlated with the data at the respective frequencies.  Cosine coefficients are computed for both the X and Y variable.

Sine coefficients.  The sine coefficients can be interpreted analogous to the cosine coefficients (see previous paragraph).  Sine coefficients are computed for both the X and Y variable.

Periodogram.  The periodogram values are computed as the sum of the squared sine and cosine coefficients at each frequency (times N/2).  The periodogram values can be interpreted in terms of variance (sums of squares) of the data at the respective frequency or period.  Periodogram values are computed for both the X and Y variable.

Spectral density estimates.  The spectral density estimates are computed by smoothing the periodogram values, using the specifications in the Data windows for spectral density estimates box.  By smoothing the periodogram one may identify the general frequency "regions" or (spectral densities) that significantly contribute to the cyclical behavior of the series.  Note that the weights used for the smoothing will always be standardized so that they add to 1.0.  Also, at the beginning and end of the series, the smoothing is done via reflection.

Cross-periodogram values.  Analogous to the results for the single variables, the Scrollsheet will also display periodogram values for the cross periodogram.  However, the cross-spectrum consists of complex numbers that can be divided into a real and an imaginary part.

Cospectral density.  The cospectral density is computed by smoothing the real part of the cross-periodogram values (using the specifications in the Data windows for spectral density estimates box).

Quadrature spectrum.  The quadrature spectrum values (quad density for short) are computed by smoothing the imaginary part of the cross-periodogram values (using the specifications in the Data windows for spectral density estimates box).

Cross amplitude.  The cross amplitude values are computed as the square root of the sum of the squared cross-density and quad-density values.  The cross-amplitude can be interpreted as a measure of covariance between the respective frequency components in the two series.

Coherency.  One can standardize the cross-amplitude values by squaring them and dividing by the product of the spectrum density estimates for each series.  The result is called the squared coherency, which can be interpreted similar to the squared correlation coefficient (see Correlations - Overview), that is, the coherency value is the squared correlation between the cyclical components in the two series at the respective frequency.  However, the coherency values should not be interpreted by themselves; for example, when the spectral density estimates in both series are very small, large coherency values may result (the divisor in the computation of the coherency values will be very small), even though there are no strong cyclical components in either series at the respective frequencies.

Gain.  The gain value is computed by dividing the cross-amplitude value by the spectrum density estimates for one of the two series in the analysis.  Consequently, two gain values are computed, which can be interpreted as the standard least squares regression coefficients for the respective frequencies

Phase spectrum.  The phase spectrum estimates are computed as tan**-1 of the ratio of the quad density estimates over the cross-density estimate.  The phase shift estimates (usually denoted by Greek letter ψ) are measures of the extent to which each frequency component of one series leads the other.

Weights.  This column will report the actual weights used in the smoothing window to produce the spectral density estimates (see above).  The different smoothing windows are described below (Data windows for spectral density estimates).  Note that the weights are standardized so that they will always sum to 1.


Cross-spectrum Analysis Results - Examine Subset of Periodogram

  Time Series Analysis Cross-spectrum Analysis Results - Examine Subset of Periodogram

When reviewing the results for long time series, it is often useful to examine particular frequency ranges.  This can be accomplished by setting this check box, and then specifying the range of observations to review in the edit boxes below (From, To).  Note that the numbers specified here pertain to the numbers of rows in the Summary Scrollsheet, so for example, if you specify 100 and 200, then rows 100 to 200 of the Scrollsheet will be displayed (or plotted).  In addition to the Summary Scrollsheet option, the range selected here will also apply to all plots on this dialog.


Cross-spectrum Analysis Results - N Largest Values

  Time Series Analysis Cross-spectrum Analysis Results - N Largest Values

This option will bring up a Scrollsheet with the same statistics as those computed by the Summary option; however, the results will only be shown for the N (as specified in the edit box to the right) largest real cross-periodogram or imaginary cross-periodogram values, depending on the setting of the radio buttons to the right.


Cross-spectrum Analysis Results - Data Windows for Spectral Density Estimates

  Time Series Analysis Cross-spectrum Analysis Results - Data Windows for Spectral Density Estimates

As described in greater detail in the Single Spectrum (Fourier) Analysis overview section, the periodogram (and cross-periodogram) values themselves are subject to substantial random fluctuation.  A clearer picture of underlying periodicities often only emerges when examining the spectral and cospectral densities, that is, the frequency regions, consisting of many adjacent frequencies, that contribute most to the overall periodic behavior of the series.  The spectral and cospectral density estimates are computed by smoothing the periodogram values with a weighted moving average.  Suppose the moving average window is of width m (which must be an odd number); the smoothers listed below are those which are most commonly cited in the literature (note: p = (m-1)/2).  For more information on each window listed below, click on the window name.

Daniell (or equal weight) window

Tukey window

Hamming window

Parzen window

Bartlett window

User-defined window.

If the User-defined window radio button is selected, you will be prompted to enter the weights used for smoothing directly (a dialog will open prompting you to specify the weights).

Note that in all cases the Time Series module will standardize the weights so that they always sum to 1.  For example, if you entered 1 2 3 2 1 as the user-defined weights, they will be converted to: 1/9 2/9 3/9 2/9 1/9 (so that they add up to 1).  In many cases, all of the standard data windows will produce very similar results; but it is often useful to experiment with different windows of different widths, and to examine resulting periodogram and density plots.


Cross-spectrum Analysis Results - Append to Work Area on Exit

  Time Series Analysis Cross-spectrum Analysis Results - Append to Work Area on Exit

These check boxes will determine which of the results statistics will be appended to the active work area when exiting from this dialog.  The different statistics are described under the Summary option above.  If the currently available (unused and unlocked) number of backups in the active work area is less than the number of series that is to be appended, then the Number of backups per variable parameter (see also the Spectrum (Fourier) Analysis Specifications dialog) will be increased by as much as possible.


Cross-spectrum Analysis Results - Periodogram and Spectral Density Plots

  Time Series Analysis Cross-spectrum Analysis Results - Periodogram and Spectral Density Plots

These options will produce line plots of the respective statistics; refer to the Summary option above for a description of the available results.  Note that all plots are produced either for the entire range of frequencies, or only for the range specified via the Examine subset of periodogram option (see above).

Plot results.  This option will produce line plots of the selected statistics in sequence.

Log.  This option will produce plots of the log-periodogram/densities; for other statistics the plots will be identical to those produced by the Plot results option.

Histogram.  This option will produce histograms showing the distributions of the statistics selected in the Results to plot box.  Note that the Single Spectrum (Fourier) Analysis Results dialog also contains options to fit an exponential distribution to the periodogram values, and to compute the Kolmogorov-Smirnov d statistic of goodness of fit (see also Nonparametric Statistics).  If the respective series is a white noise series, then the distribution of the periodogram values will follow the exponential distribution.


Cross-spectrum Analysis Results - Plot By

  Time Series Analysis Cross-spectrum Analysis Results - Plot By

The setting of the radio buttons in this box determines the X (horizontal) axis in the line plots; the selected statistics can be plotted by Frequency, Period, or Log (period).


  Megafile Manager

The Megafile Manager window displays the contents of the currently selected Megafile Manager file.

Megafile Manager Introductory Overview

Megafile Manager Toolbars

Megafile Manager Language (MML)

File Menu	Options Menu

Edit Menu	Window Menu

View Menu	Help Menu

MFM Analysis Menu


  Megafile Manager Window Toolbar Buttons

The following is a list of toolbar buttons for the Megafile Manager window.  For quick access to information about the Megafile Manager window, see Megafile Manager Introductory Overview.

For more information on specific dialogs or options, click on the [image] button in the upper-right corner of the dialog.

For more general information, see STATISTICA Index.

  Change Show Window

  STATISTICA Module Switcher

  Columns button

  Rows button

  Convert button

  Increase Column Width

  Decrease Column Width

  Megafile Manager Global Column Width

  Increase Decimal Tool

  Decrease Decimal Tool

  Open Megafile Manager File

  Save Megafile Manager File

  Print Megafile Manager File

  Cut

  Copy

  Paste

  Electronic Manual


Megafile Manager - Columns Toolbar Buttons

  Megafile Manager - Columns Toolbar Button

The following options are avaliable when you click on the Columns toolbar button in the Megafile Manager window

Column Specs

Add	Copy

Move	Delete


Megafile Manager - Rows Toolbar Buttons

  Megafile Manager - Rows Toolbar Button

The following options are avaliable when you click on the Rows toolbar button in the Megafile Manager window

Add	Copy

Move	Delete


Megafile Manager - Overview

  Megafile Manager - Introductory Overview

Megafile Manager is a specialized data base management system accessible from the Data Management module of STATISTICA.  Its unique feature is that it can manage and directly process types of data which need to be transformed, aggregated, extracted, or cleaned before they can be directly accessed by statistical or graphics procedures (e.g., data organized into extremely long records or data embedded inside very long text values).

Megafile Manager can process extremely large records of data (rows):  up to 32,000 columns with up to 255 characters each (up to 8 megabytes per row).  Data organized in such long records can, for example, be produced by some automated quality control measurement devices or other data acquisition or monitoring equipment.  Also, such files are sometimes useful in maintaining integrated, large archival data banks consisting of numerous merged or concatenated files.

Megafile Manager and other STATISTICA Facilities.  Most likely, the majority of common data processing needs can be easily addressed with the standard procedures available in every module of STATISTICA.  Therefore, Megafile Manager will typically be used only when there is a need for facilities to handle very unusual data importing, management, and pre-processing needs, for example, in order to maintain very large data bases, or perform pre-processing of imported long text values, etc.  Note that the standard procedures (offered in every module of STATISTICA) can also handle large size and very complex tasks; for example:

•	to compute descriptive statistics or correlation matrices for very many variables (e.g., over 1,000) in a single run, use the Quick Basic Stats facilities available in every module via the Analysis pull-down menu or the toolbar button [image].

•	to perform complex recoding and aggregation of data, extensive operations on text values, or complex cleaning and verification of data, use STATISTICA BASIC, available in every module of STATISTICA from the Analysis pull-down menu;

•	to import large files from other applications (e.g., Excel, Lotus, Quattro Pro, Paradox, etc.), use the Import options available from the pull-down menu File in every module of STATISTICA;

•	to perform sequential, hierarchical, or relational merging of files, use the Merge option from the Analysis pull-down menu in the Data Management module, or use the functions available in STATISTICA BASIC for accessing external files (and then use the available powerful STATISTICA BASIC functions to merge data via simple or complex user-defined algorithms).

Maintaining large, archival data banks; hierarchical relations between data bases.  Megafile Manager offers options for aggregating data sets from other applications and setting up very large (e.g., 8 megabytes per record), efficient archival data bases.  It also supports links between related (and hierarchically organized) data sets.  Subsets of columns from such archival data banks can be extracted and used with other applications (such as STATISTICA, Excel, or Paradox).

Preprocessing large records of raw data.  Another unique application of Megafile Manager is at the stage of analysis when raw data need to be aggregated or preprocessed before meaningful indices are obtained for use in data analysis.  Such raw data sets (e.g., from automated quality control measurement devices or other data acquisition equipment) may feature records that are too long to fit into any standard application (e.g., 32,000 measures per row).  Megafile Manager can be used to access such data sets, convert them into meaningful indices, and transfer to another application (such as STATISTICA or Excel) for further analysis.  Such raw data often need to be cleaned and verified before they can be preprocessed.  Custom-designed data verification (and interactive correction) can be performed in Megafile Manager using its integrated programming language which features specialized functions for interactive data editing and verification.

Data processing, analysis.  Thus, Megafile Manager not only offers facilities to aggregate, store, and maintain long-record files, but it can also efficiently process them.  Its integrated programming language (MML) features a variety of data analytic options and a library of functions.  Megafile Manager also includes basic statistics facilities that can process data regardless of the record size.  For example, it can tabulate data, compute descriptive statistics, or generate correlation matrices of practically unlimited size (the size of correlation matrices that could be generated by Megafile Manager exceeds the capacity of any existing storage device).

Long text values.  Another specific feature of Megafile Manager is its ability to process very long text values.  Also, its integrated programming language (MML) offers a comprehensive selection of functions to manipulate text data.

Exchanging data with STATISTICA data files.  Megafile Manager uses a specialized file format optimized for its specific applications (e.g., maintaining data types from a variety of programs).  However, easy to use and flexible facilities are provided in the Data Management module to move data in and out between STATISTICA data files and archival Megafile Manager data bases.  For more information about Megafile Manager, see:

•  Copy to the Clipboard	•  Import Megafile Manager File

•  Convert to STATISTICA	•  Export Megafile Manager File

•  Append STATISTICA File	•  Megafile Manager Language (MML)

See also Megafile Manager menus and toolbar.


  Megafile Manager - File Menu

These options are available from the Megafile Manager window File pull-down menu.

New MFM Data

Import

Open MFM Data

Open Other

New Data	Scrollsheet

Data File	Text/Output

Graph File	STATISTICA BASIC

Command Language (SCL)

Append STATISTICA File

Save

Save As

Export

Convert to STATISTICA

Print/Eject Current Pages

Print MFM Data

Page/Output Setup

Printer Setup

Exit


  Megafile Manager - Create New MFM Data

You can create new Megafile Manager files with the Create New File dialog (accessible from the New MFM Data option in the File pull-down menu or from the MFM: Create New Data option from the Analysis pull-down menu or the Data Management startup panel).

Megafile Manager: Create New File dialog:

New File Name	Column Name Prefix

Number of Columns	Format statement

Number of Rows	One-Line File Header

Example


  Create New MFM Data - New File Name

Click on this button to open the New Data:  Specify File Name dialog in which you can designate the file name for the new Megafile Manager file.


  Create New MFM Data - Number of Columns

Specify the number of columns to be included in the new data file.  Up to 32,000 columns may be created and maintained in Megafile Manager.


  Create New MFM Data - Number of Rows

Enter the number of rows to be included when creating the data file.  STATISTICA imposes practically no limit on the number of rows in one file (up to 2.14 billion rows may be specified).


  Create New MFM Data - Column Name Prefix

Specify the column name prefix here (all column names in this data file will have this prefix).  The column name prefix which is defined here will have a sequential number added to the end (e.g., COL1, COL2, COL3, etc.).


  Create New MFM Data - Format Statement

The (optional) format statement is a set of instructions for interpreting the structure of the new Megafile Manager file (optionally, you could double-click on a column title to open the Column Specs dialog in which you can specify the format for that particular column).  This option explicitly defines for STATISTICA the exact contents of the Megafile Manager file.  The format statement is entered as a list of formats in the form nXm, where n is an integer multiplier indicating the number of times the format is to be repeated (no multiplier = 1); X is the column type; m is the column width (e.g., 10A8 means 10 text value [alphanumeric] fields, each 8 characters long).

Column Type Specifiers:

A	Text (Alphanumeric)

F	Float (also R - Real, equivalent to Real 4B in the Column Specs dialog)

D	Double Float (also DR - Double Real, equivalent to Real 8B in the Column Specs dialog)

I	Integer (also NI - Normal Integer, equivalent to Int 2B in the Column Specs dialog)

S	Short Integer (also SI, equivalent to Int 1B in the Column Specs dialog)

LI	Long Integer (also J, equivalent to Int 4B in the Column Specs dialog)

L	Logical

For example, the format statement 2a15 i3 f5 defines four columns:  the first two columns contain text (symbol a), 15 characters in display width; the third column contains integer values (symbol i) of display width 3; the fourth float column (symbol f) contains values 5 characters in display width.  For more information on column types and widths in Megafile Manager, see Column Specs.

The following table describes all column types supported:

Type                    Range of Values    Examples      Bytes

----------------------  -----------------  ------------  -----

text                    any characters     John Brown    1-255

short integer (Int 1B)  ±127               -98             1

integer (Int 2B)        ±32767             9834            2

long integer (Int 4B)   ±2147483647        12345678        4

float (Real 4B)         ±3.4*10**+38       1234.5678       4

double float (Real 8B)  ±1.7*10**+308      123456.78974    8

logical                 yes/no/true/false  No              1

date                    from Jan.1, 1900   02/08/55        8


  Create New MFM Data - One Line File Header

Enter one line (up to 77 characters) of comment about the file here.


  Megafile Manager - Creating a New MFM Data

Follow the steps outlined below in order to create a new Megafile Manager data file.

Step 1:	Select the New MFM Data option from the File pull-down menu to open the Megafile Manager: Create New File dialog.

Step 2:	Specify in this dialog the new file name and path (click on the New File Name button), the file dimensions (number of rows and columns), and optionally the format (types and width of columns; by default columns of type Real will be created), as well as other information necessary to build the data file (each of the options are described below).  Note that all specifications of the file (entered in this dialog) can be modified after the file is created.

Step 3:	Click on the OK button to open a Megafile Manager spreadsheet in which you can enter data into the newly created file.


  Open Megafile Manager Data

Selecting this option will bring up the Open Megafile Manager File dialog from which you can select a Megafile Manager file (file with the extension *.mfm) to open.  Megafile Manager files contain data values and also labels and formats (see:  Column Specs), headers and notes (see:  Header) and other information.  In order to open a non-Megafile Manager format file (e.g., Excel, Lotus, Quattro, dBASE, ASCII, and others) use the Import option in the File pull-down menu.

Keyboard Shortcut:  Ctrl + O


  Save Megafile Manager File

Save a Megafile Manager data file with this option.  If the file has not been saved before, then the Save File As dialog will open in which you can specify the file name, and disk location for it to be saved.  Once the file name and location have been specified, whenever you select Save, the spreadsheet will automatically be saved, overwriting the previous copy of the file.  If you want to change the name or location of the file, select the Save As option.

Keyboard Shortcut:  Ctrl + S


  Save As Megafile Manager File

Every time you select this option, the Save File As dialog will open in which you can save the Megafile Manager file.  By default, the current file name and disk location will be displayed in this dialog.  You can save the Megafile Manager file under a new file name or edited default name, or specify a different disk location for the Megafile Manager file.

Keyboard Shortcut:  F12


  Megafile Manager - Importing Files

Importing data to Megafile Manager by converting foreign data files (e.g., worksheets or data bases) is one of several ways (offered in STATISTICA) of accessing data from other applications.  Other methods available in Megafile Manager include using the Clipboard (which in STATISTICA recognizes special Clipboard formatting conventions used by other Windows applications such as Excel or Lotus) and the Append STATISTICA File option from the Megafile Manager window File pull-down menu.

Import Data From dialog:

Each of the options below represents a group of formats (e.g., Lotus can import files from Lotus version 1A, 2, 3, Symphony, etc.).  When importing files, STATISTICA will use the column/field/variable names of the source file.  (If an imported name is longer than eight characters, the first eight characters will be used as the Megafile Manager column name.)

•  Import STATISTICA File	•  Import dBASE File

•  Import Excel File	•  Import SPSS File

•  Import Lotus File	•  Import ASCII Free

•  Import Quattro File	•  Import ASCII Fix

Options button:  Click on this button to open a dialog that will contain importing options specific to the import format that you choose.

Example


  Importing Files to Megafile Manager

Importing is a very simple operation; in the STATISTICA Megafile Manager window, select the Import option from the File pull-down menu (or the startup panel), then follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm or change the type of file to be imported in the Import Data From dialog.

Step 3:	Click the OK button in the latter dialog to import and store the data in the Megafile Manager file format.


  Megafile Manager - Import STATISTICA Data File

You can import data from a STATISTICA file format in the Megafile Manager window.  After you select STATISTICA from the Select File to Import dialog, the Import Data From dialog will open (by default, STATISTICA will be selected).  Click on the OK button in this dialog to import the STATISTICA data file that you select.

During import, STATISTICA variable long names (if they exist) become Megafile Manager column long names, and the STATISTICA one-line file header and comment are imported as the Megafile Manager one-line file header and comment.

STATISTICA Import Options dialog:

Case Names

Variables with Text Values

Example


  Import STATISTICA Data File - Case Names

When you select this option, the STATISTICA case names will be imported as standard Megafile Manager text values and placed in the first column of the Megafile Manager file.


  Import STATISTICA Data File - Variables with Text Values

STATISTICA's double notation of variables (text/numeric) may be expanded via these options to become up to three Megafile Manager columns with names related to the STATISTICA variable (representing the numeric values, text values, and value labels of the STATISTICA variable).  The settings of the following options will determine the creation of these columns:

Text Values.  When you select this option, a column containing the text values will be created.  If the STATISTICA variable name is shorter than 8 characters, then the Megafile Manager text column name will have a $ added to the end; if the name is 8 characters long, then the second character will be changed to a $.  This is done to avoid later conflicts regarding duplicated column names with the requirements of MML and other programs to which the data may be exported, and so that the automatic matching of text and numeric columns will be facilitated, if you later export the file to STATISTICA (or Convert to STATISTICA).

Numeric Values.  Select this option in order to create a column with the numeric equivalents to the text values.

Long Value Labels.  When you select this option, then a column with value labels will be created (if the STATISTICA variable name is shorter than 8 characters, then the Megafile Manager text column name will have a @ added to the end; if the name is 8 characters long, then the second character will be changed to a @).


  Importing STATISTICA Files to Megafile Manager

To import a STATISTICA data file, follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that STATISTICA has been selected as the type of file to be imported in the Import Data From dialog.

Step 3:	Click the OK button in the latter dialog to import and store the data in the Megafile Manager file format.


  Megafile Manager - Import Excel File

When importing an Excel file, column types are dynamically determined according to the Excel spreadsheet contents: if a spreadsheet column contains both labels and numeric values, then column type Text is used; if it contains both integer and real values, then a Float format will be used.

Please note that Megafile Manager will automatically convert the Excel spreadsheet into a "data base" at the point of import, therefore it is not necessary to save the Excel file as a "data base" before importing it.

Excel Import Options dialog:

Range

Column Names

Note that in addition to the file import operation, Excel data can be accessed by STATISTICA via the Clipboard (STATISTICA recognizes the Excel Clipboard format and will properly interpret "formatted" values such $100 or 2,000).

Example


  Import Excel File - Range

By default, the entire active area of the spreadsheet is imported.  This option permits selection of a specific range of rows and/or columns to be imported.

Columns:  Specify the range of columns to be imported (From which column, To which column, inclusive).

Rows:  Specify the range of rows to be imported (From which row, To which row, inclusive).


  Import Excel File - Column Names

This option specifies the source in Excel for Megafile Manager column names.

From spreadsheet:  When you select this option, Megafile Manager will use the Excel column designators (A, B, C, etc.) as Megafile Manager column names.

From First Row of Selected Range:  Select this option to use the labels from the first row of the specified import range (see above).  If any label is longer than eight characters, it will be truncated and only the first eight characters will be used as the Megafile Manager Column name.

Create (COL1, COL2, . . .):  This option will result in the use of a combination of the prefix COL and a sequential number (e.g., COL1, COL2, etc.) as column names in the imported file.


  Importing Excel Files to Megafile Manager

To import an Excel file, follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that Excel has been selected as the type of file to be imported in the Import Data From dialog.  You may click on the Options button to select the range of columns and rows to import as well as other importing options.

Step 3:	Click the OK button in the latter dialog to import and store the data in the Megafile Manager file (spreadsheet) format.


  Megafile Manager - Import Lotus File

Megafile Manager will import worksheets from Lotus 1-2-3 Release 1A (Lotus/1), Release 2.01/2.2 (Lotus/2), Release 3 (Lotus/3), and Lotus for Windows, as well as Symphony.  Due to their 3-dimensional structure, 1-2-3/3 and Lotus for Windows files are imported with each page placed in a successive set of columns in the Megafile Manager file.  Column types are dynamically determined according to the worksheet contents: if a spreadsheet column contains both labels and numeric values, then column type Text is used; if it contains both integer and real values, then a Float format will be used.

After you select a Lotus file from the Select File to Import dialog, the Import Data From dialog will open (by default, Lotus will be selected).  Now, in this dialog, click on the Options button to bring up the Lotus Import Options dialog (the same dialog is used for each version of Lotus that you are importing, see below).

Lotus Import Options dialog:

Range

Column Names

Note that in addition to the file import operation, Lotus data can be accessed by STATISTICA via Clipboard (STATISTICA recognizes the Lotus Clipboard format and will properly interpret "formatted" values such $100 or 2,000).

Example


  Import Lotus File - Range

By default, the entire active area of the worksheet is imported.  A portion of the worksheet can be selected by defining the range (see below).

Columns:  Specify the range of columns to be imported (From which column, To which column, inclusive).

Rows:  Specify the range of rows to be imported (From which row, To which row, inclusive).

Sheets:  This option is only available if a Lotus 1-2-3 Release 3 or Lotus/w file is being imported (otherwise the option is dimmed).  By default, all sheets are imported; however you can select specific sheets to be imported using this option (From which sheet, To which sheet, inclusive).

Review Ranges button:  Click on this button to open the Review Ranges window from which you can select a named range from a listing of all of the named ranges in the selected file.


  Import Lotus File - Column Names

This option specifies the source for names of columns.

From Spreadsheet:  Use Lotus 1-2-3 column designators (A, B, C, etc.) as Megafile Manager file column names (Lotus 1-2-3 Release 3 or Lotus/w uses names A:A, A:B, B:A, B:B, etc.; they will appear in Megafile Manager as A_A, A_B, B_A, B_B) when you select this option.  This option is especially useful in working with Release 3 or Lotus/w files which will eventually be exported once again (using Lotus' column designators will preserve the identification of columns originating in different sheets).

From First Row of Selected Range:  Megafile Manager will use labels from the first row of the specified range when you select this option.  If any label is longer than eight characters, only the first eight characters of the label will be used as the Megafile Manager column name.

Create (COL1, COL2, . . .):  This option will result in the use of a combination of the prefix COL and a sequential number (e.g., COL1, COL2, etc.) as column names in the imported file.


  Importing Lotus Files to Megafile Manager

To import a Lotus file, follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that Lotus has been selected as the type of file to be imported in the Import Data From dialog.  You may click on the Options button to select the range of columns and rows to import as well as other importing options.

Step 3:	Click the OK button in the latter dialog to import and store the data in the Megafile Manager file (spreadsheet) format.


  Megafile Manager - Import Lotus - Review Ranges

In Lotus, you can define "named ranges" of data in order to define distinctive sections of the worksheet.  Clicking the Review Ranges button in the Megafile Manager window Lotus Import Options dialog will bring up a list of defined ranges for the Lotus worksheet that you want to import.  Now, instead of importing the whole Lotus worksheet (which might include column headings and other text), you can import only a subset of data by selecting the named worksheet range (highlight the range name and click the OK button).


  Megafile Manager - Import Quattro File

Megafile Manager can import worksheets from Quattro Pro (the DOS and Windows versions; see the note about importing Quattro for Windows at the end of this section).

Quattro Import Options dialog:

Range

Column Names

Note that in addition to the file import operation, Quattro for Windows data can be accessed by STATISTICA via Clipboard (STATISTICA recognizes the Quattro for Windows Clipboard format and will properly interpret "formatted" values such $100 or 2,000).

Example


  Import Quattro File - Range

By default, the entire active area of the worksheet is imported.  A portion of the worksheet can be selected by defining the range (see below).

Columns:  Specify the range of columns to be imported (From which column, To which column, inclusive).

Rows:  Specify the range of rows to be imported (From which row, To which row, inclusive).


  Import Quattro File - Column Names

This option specifies the source for Megafile Manager column names.

From Spreadsheet:  Use Quattro column designators (A, B, C, etc.) as Megafile Manager column names.

From First Row of Selected Range:  Megafile Manager will use labels from the first row of the specified range when you select this option.  If any label is longer than eight characters, only the first eight characters of the label will be used as the Megafile Manager column name.

Create (COL1, COL2, . . .):  This option will result in the use of a combination of the prefix COL and a sequential number (e.g., COL1, COL2, etc.) as column names in the imported file.


  Importing Quattro Files to Megafile Manager

To import a Quattro file, follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that Quattro has been selected as the type of file to be imported in the Import Data From dialog.  You may click on the Options button to select the range of columns and rows to import as well as other importing options.

Step 3:	Click the OK button in the latter dialog to import and store the data in the Megafile Manager file (spreadsheet) format.


  Megafile Manager - Import SPSS File

Import SPSS Portable files, as well as all other files (e.g., exported from SAS) which follow the PFF (Portable File Format) convention with this option.  SPSS column names will become Megafile Manager column names, and SPSS variable long names (up to 80 characters long) will become Megafile Manager column long names.

SPSS Import Options dialog:

Import Value Labels:  When you select this option, Megafile Manager will import the SPSS value labels (up to 40 characters).  In the case of numeric SPSS columns, the program will also create text equivalents for the numeric values out of the first 8 characters of the value label.  If an SPSS value label contains illegal characters (e.g., " # & ' ( ) + , - . / ; : < = > [ ] ^ \ { } ~) then the text value assigned is an "_" (underscore character).

Note that missing data in SPSS columns may be defined in different ways:

•	If a single MD value has been assigned in a column, then that MD value will be used as the MD code in the STATISTICA variable.

•	If a range of values have been defined as MD for a column in SPSS, then Megafile Manager imports the actual data values (to maximize the information extracted from the source file), and assigns the first value from the list of MD values as the MD code in the Megafile Manager file.

Example


  Importing SPSS Files to Megafile Manager

To import an SPSS file, follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that SPSS has been selected as the type of file to be imported in the Import Data From dialog.  You may click on the Options button to bring up the SPSS Import Options dialog containing importing options specific to SPSS files.

Step 3:	Click the OK button in the latter dialog to import and store the data in the Megafile Manager file (spreadsheet) format.


  Megafile Manager - Import dBASE File

STATISTICA can import data files from dBASE versions III and IV.  dBASE files contain a flag within each record indicating whether the record is to be read or not; STATISTICA will ignore all records marked as having been deleted.  After you select a dBASE file from the Select File to Import dialog, the Import Data From dialog will open.  Now, in this dialog, click on the Options button to bring up the dBASE Import Options dialog (the same dialog is used for either version of dBASE that you are importing).

dBASE Import Options dialog:

Range:  By default, the entire active area of the data file is imported.  A portion of the data file can be selected by defining the range (see below).

Columns:  Specify the range of columns to be imported (From which column, To which column, inclusive).

Rows:  Specify the range of rows to be imported (From which row, To which row, inclusive).

Example


  Importing dBASE Files to Megafile Manager

To import a dBASE file, follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that dBASE has been selected as the type of file to be imported in the Import Data From dialog.  You may click on the Options button to select the range of columns and cases to import as well as other importing options.

Step 3:	Click the OK button in the latter dialog to import and store the data in the Megafile Manager file (spreadsheet) format.


  Megafile Manager - Import ASCII File

Megafile Manager can import both ASCII fixed (undelimited) and ASCII free (delimited) files.  Each type of ASCII file has its own dialog of options.  For more information on these options, click on the appropriate selection.

Import ASCII free file

Import ASCII fixed file


  Megafile Manager - Import ASCII Fixed File

After you select an ASCII fixed (fixed format) file from the Select File to Import dialog, the Import Data From dialog will open.  By default, ASCII will be selected and if the file name extension is *.fix, then Fixed will automatically be checked as the ASCII version.  If Megafile Manager is unable to recognize (from the file name extension) that the file is an ASCII Fixed file, then the Free ASCII version will be selected and you will need to change the type to Fixed.

ASCII Fixed Import Options dialog:

File Size

Format Statement

Example


  Import ASCII Fixed File - File Size

As in ASCII Free Format Files, in order for Megafile Manager to properly interpret the file, the number of columns and rows must be accurately specified.

Number of Columns:  Specify the number of columns (variables, fields) in the ASCII file here.

Number of Rows:  Specify the number of rows in the ASCII file here.  If you are uncertain about the exact number of rows, you may overestimate (Megafile Manager will detect the actual length of the file during import).  Note that each line in the ASCII source file may be up to 4000 characters in length.  This limit only applies to the individual line length and not the total length of a "row" of data:  Each imported row may be represented by many lines of data in the source file.


  Import ASCII Fixed File - Format Statement

This option explicitly defines for Megafile Manager the exact contents of the input ASCII file.  (This is an important distinction:  The format statement is a set of instructions for interpreting the structure of the input file, not a definition of the Megafile Manager columns to be created.)  The format statement is entered as a list of formats in the form nXm, where n is an integer multiplier indicating the number of times the format is to be repeated (no multiplier = 1); X is the column type; m is the column width (e.g., 10A8 means 10 text value [alphanumeric] fields, each 8 characters long).

Column Type Specifiers:

A	Text (Alphanumeric)

F	Float (also R - Real, equivalent to Real 4B in the Column Specs dialog)

D	Double Float (also DR - Double Real, equivalent to Real 8B in the Column Specs dialog)

I	Integer (also NI - Normal Integer, equivalent to Int 2B in the Column Specs dialog)

S	Short Integer (also SI, equivalent to Int 1B in the Column Specs dialog)

LI	Long Integer (also J, equivalent to Int 4B in the Column Specs dialog)

L	Logical

The format specified as logical is expected to contain text designators of true and false.  The following three conventions will be recognized by Megafile Manager when the data are imported:

TRUE or FALSE if the field length is 5 or more.

YES or NO if it is 3 or 4 characters long.

Y, N, or T, F respectively, if it is 1 character long.

Values of TRUE or YES will be imported as 1, FALSE or NO will be imported as 0.

The additional specifier Tx is available to instruct STATISTICA to jump to character number x in the current line in the input file (i.e., to skip to that position).  This may be used to jump over unwanted characters, or to return to an earlier character (if x specifies a character position which has already been read).

The slash character (/) may be used to indicate that the remainder of the line should be ignored (i.e., skip to the next line in the input file).  Example: 10I3 A8 T55 3I5 /  specifies the import of 14 values: ten 3-digit integers, followed by an 8-character text string, then skip to the 55th character in the record, import three 5-digit integers and ignore the rest of the record.  If the multiplier precedes a list of formats enclosed in parentheses, the list will be repeated as many times as specified in the multiplier (e.g., 10(2A3,I5)).


  Importing ASCII Fixed Files to Megafile Manager

To import an ASCII file, follow the steps outlined below.

Step 1:	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that ASCII has been selected as the type of file to be imported in the Import Data From dialog and the appropriate ASCII version is checked (Fixed).  Click on the Options button to open the ASCII Fixed Import Options dialog.

Step 3:	In this dialog, specify the number of rows and columns in the imported file as well as the file format (in order to identify the types of values, see below).

Step 4:	Click the OK button in the latter dialog to import and store the data in the Megafile Manager file format.


  Megafile Manager - Import ASCII Free File

After you select an ASCII Free file from the Select File to Import dialog, the Import Data From dialog will open (by default, ASCII Free will be selected).  Now, in this dialog, click on the Options button to bring up the ASCII Import Options dialog.

ASCII Free Import Options dialog:

File Size

Format Statement

Separators

Example


  Import ASCII Free File - File Size

As in ASCII Fixed Format Files, the number of columns must be accurately specified.

Number of Columns:  Specify the number of columns (variables, fields) in the ASCII file.

Number of Rows:  Specify the number of rows in the ASCII file.  If you are uncertain about the exact number of rows, you may overestimate (Megafile Manager will detect the actual length of the file during import).  Note that each line in the ASCII source file may be up to 4000 characters in length.  This limit only applies to the individual line length and not the total length of a "row" of data:  Each imported row may be represented by many lines of data in the source file.


  Import ASCII Free File - Format Statement

This option explicitly defines for Megafile Manager the exact contents of the input ASCII file.  (This is an important distinction:  The format statement is a set of instructions for interpreting the structure of the input file, not a definition of the Megafile Manager columns to be created.)  The format statement is entered as a list of formats in the form nX where n is an integer multiplier indicating the number of times the format is to be repeated (no multiplier = 1) and X is the column type (e.g., 40F means 40 fields containing numeric (here float) values).

Column Type Specifiers:

A	Text (Alphanumeric)

F	Float (also R - Real, equivalent to Real 4B in the Column Specs dialog)

D	Double Float (also DR - Double Real, equivalent to Real 8B in the Column Specs dialog)

I	Integer (also NI - Normal Integer, equivalent to Int 2B in the Column Specs dialog)

S	Short Integer (also SI, equivalent to Int 1B in the Column Specs dialog)

LI	Long Integer (also J, equivalent to Int 4B in the Column Specs dialog)

L	Logical

The format specified as logical is expected to contain text designators of true and false.  The following three conventions will be recognized by Megafile Manager when the data are imported:

TRUE or FALSE if the field length is 5 or more.

YES or NO if it is 3 or 4 characters long.

Y, N, or T, F respectively, if it is 1 character long.

Values of TRUE or YES will be imported as 1, FALSE or NO will be imported as 0.

Text fields (type A) must also include a length value from 1 to 255 immediately following the letter A, indicating the maximum possible length of text in this field.

The slash character (/) may be used to indicate that the remainder of the current line in the input file should be ignored (i.e., skip to the next line in the input file).  If the multiplier precedes a list of formats enclosed in parentheses, then the list of formats within the parentheses will be repeated the number of times specified by the multiplier.  Example:  2(2L a5) is equivalent to L L A5 L L A5  and specifies two Logical columns followed by a Text column that can hold up to five characters, then two more Logical columns and a final Text column (again up to five characters).


  Import ASCII Free File - Separators

Within this option, you will be able to define the characters used in the input file as delimiters.  (The final list of separators to be used will be the combination of the set of selected Basic and any Additional separators.)

Basic:  Select the type of delimiter used in the input file from four predefined sets of separators (CR stands for carriage return, LF stands for line feed, and FF stands for form feed).

Standard Set:  ,  ;  space  tab  CR\LF

Undefined:  do not use a predefined set (see Additional button, below)

Blank Characters:  space  tab  FF  LF  CR\LF

Non-Numeric:  (all but:  0 - 9  .  -  +)

Additional button:  Click on this button to bring up the ASCII Free Separators dialog from which you can select the delimiter(s).

Treat Multiple Separators as MD:  When you select this option, Megafile Manager will interpret each pair of adjacent separators as an occurrence of missing data (an absent value) and will place the default missing data value (-9999) in the position between the adjacent separators.  If this option is de-selected, then multiple separator characters are treated as one separator, and missing data must be explicitly coded into the ASCII file as a unique value (for instance -9999).  This option is particularly useful if, for instance, individual values in the data file are separated by spaces, with a variable number of spaces between values.  If spaces are used as separators, then each pair of spaces would be seen as an occurrence of missing data, and the resulting file would be full of missing values.

Use Quotation Marks as Text Boundaries:  Select this option if double (") or single (') quotation marks were used as text boundaries and the specified separator characters appear within the values of text columns in the input file (e.g., "John Jones, Ph.D.", uses the comma both as part of the text and as a separator after it).  In this case, when STATISTICA imports the data, the quotation marks will be recognized only as boundaries around the text values, keeping the text values and the embedded separator character together (the quotation marks will not be included as part of the imported text values).

Note that if a text string is to contain quotation marks as part of the string itself (e.g., as in the titles of books such as "Moby Dick"), then two methods may be used to import them:

•	Select this option and enclose the entire text string within the alternate quotation mark (opposite of the embedded one); e.g., 'William Shakespeare, "King Lear", Act 2, Scene 1' will be imported as William Shakespeare, "King Lear", Act 2, Scene 1.

•	Select this option and then double the quotation mark wherever it is to be preserved; e.g., "William Shakespeare's ""King Lear"", ""Macbeth"" and ""Hamlet"" will be imported as William Shakespeare's "King Lear", "Macbeth" and "Hamlet".

If this option is de-selected, then the character will be interpreted as a separator and not as a part of the text value, and the quotation marks will be imported as part of the text; e.g., .'William Shakespeare, "King Lear", Act 2, Scene 1' will be imported as 'William Shakespeare in one column, "King Lear" in another column, Act 2 in different column and Scene 1' in another column.


  Importing ASCII Free Files to Megafile Manager

To import an ASCII file, follow the steps outlined below.

Step 1	Select the file name in the Select File to Import dialog.

Step 2:	Confirm that ASCII has been selected as the type of file to be imported in the Import Data From dialog and the appropriate ASCII version is checked (Free).  Click on the Options button to open the ASCII Free Import Options dialog.

Step 3:	In this dialog, specify the number of rows and columns in the imported file as well as the file format (in order to identify the types of values, see below).

Step 4:	Click the OK button in the latter dialog to import and store the data in the Megafile Manager file (spreadsheet) format.


  Megafile Manager - Append STATISTICA File

When you select this option, the Select STATISTICA File to Append dialog will open in which you can select the file that will be appended to the Megafile Manager file.  The selected STATISTICA file will be appended to the current Megafile Manager file after the last column in the Megafile Manager file.  In order to adjust the order of columns or insert STATISTICA columns in a particular location in the Megafile Manager data set, use the Move Columns option after the STATISTICA data are appended.  If one file has fewer rows than the other file, then STATISTICA will fill the empty cells with missing values.  For example, consider the following files:

Megafile Manager file (2 rows):	STATISTICA data file (5 cases):

Col1   Col2   Col3	Var1   Var2

----   ----   ----	----   ----

  34     21    102	  78     90

  45     10     98	  64    125

  24     36

  36     12

When the STATISTICA file is appended to the Megafile Manager file, the resulting Megafile Manager file will appear as follows (where the empty cells in the first three columns contain missing data):

Col1   Col2   Col3   Var1    Var2

----   ----   ----  -----   -----

  34     21    102     78      90

  45     10     98     64     125

                       24      36

                       36      12


  Megafile Manager - Export Options

Megafile Manager files can easily be exported to other applications.  When you choose the Export option in Megafile Manager, the Export Data To dialog will open in which you can select the export program.  Note that because many applications cannot accommodate files as large as those that can be managed in Megafile Manager (32,000 columns, unlimited rows), it may be necessary to create a subset of the data file prior to exporting it.

Export Data To dialog:

The Megafile Manager file will be exported in the file format that you select here.  For more information on specific export options, click on the desired application name.

•  Lotus, Symphony, and 3D Lotus files

•  Excel	•  dBASE III and IV

•  Quattro	•  ASCII (free and fixed format)

•  STATISTICA	•  SPSS Portable File

See also Convert for a quick method to export an Megafile Manager file to STATISTICA.


  Megafile Manager - Export to STATISTICA Data File

The quickest method to convert Megafile Manager data (or its subset) to the STATISTICA format is using the Convert button on the Megafile Manager window toolbar.

Megafile Manager can create STATISTICA files containing up to 4092 "double variables" and the values of each of them can be labeled, thus potentially up to 12,277 Megafile Manager columns (including case names) can be exported to a single STATISTICA data file.  If the current Megafile Manager file is larger than this, use the Subset option on the Megafile Manager window Analysis pull-down menu to extract a smaller portion of the file for export.  Missing data codes from Megafile Manager columns will be used in creating the STATISTICA file.

STATISTICA files use a "double notation" format for variables:  Each variable may contain paired numeric and text (up to 8 characters) values.  Each numeric/text pair may also have a value label up to 40 characters in length.  When importing a STATISTICA data file (see Import STATISTICA file), "double variables" are automatically "split" (into two or three columns depending on whether they are labeled) to become sequential Megafile Manager columns, which can be automatically put together in the process of exporting them back to STATISTICA.  To create these "double variables" when exporting to the STATISTICA format, Megafile Manager columns are combined into pairs or triplets under the following conditions: A numeric column can be matched with one or two immediately-following text columns which will become the text values and value labels for the STATISTICA variable.  The first of the text columns may be up to 8 characters long and will become the text values for the STATISTICA variable; its column name must be the same as the numeric column name (with a $ added to the end if the numeric column name is less than 8 characters, or if the name is 8 characters long, the second character should be replaced by a $).  (NOTE: if the text values in this $ column is longer than 8 characters, then only the first 8 characters will be exported.)  The second of the text columns will become the value labels; its column name must be the same as the numeric column name with a @ added to the end (if the numeric column name is less than 8 characters - if the name is 8 characters, the second character should be replaced by @).  A one-to-one correspondence between the numeric and text values in these columns must exist: Each numeric value must be paired with only one unique text string in the text column(s).  This correspondence will be checked by Megafile Manager during the process of creating the STATISTICA file.  Megafile Manager also exports column long names as STATISTICA variable long names, case names (from a designated Megafile Manager column), and the one-line file header and the notes/comments (see Header).

STATISTICA Export Options dialog:

Export text columns

Export case names

Auto numeric/text match

Range

Example


  Export to STATISTICA Data File - Export Text Columns

When you select this option, Megafile Manager will export unpaired text columns (columns to which no numeric column has been matched) into STATISTICA "double variables" by assigning a numeric code (consecutive integer) for each text value.  If this option is de-selected, then no text variables will be created from the unpaired text columns.  If this option is de-selected and the Auto numeric/text match option is also de-selected, then all text columns will be excluded from the export file.


  Export to STATISTICA Data File - Export Case Names

Select this option in order to create STATISTICA case names from the first data column of the current Megafile Manager file.


  Export to STATISTICA Data File - Auto Numeric/Text Match

Selecting this option will match Megafile Manager columns to become STATISTICA "double variables" based on pairing a numeric column with one or two text columns with related names.  De-selecting this option will cause no pairing of columns.  If this option is de-selected and the Export text columns option is selected, then all text columns are automatically converted into new "double variables" with numeric (consecutive integers) and text values (up to 8 characters long).


  Export to STATISTICA Data File - Range

By default, the entire Megafile Manager file is exported.  A portion of the file can be selected by defining the range (see below).

Cols:  Specify the range of columns to be exported (From which column, To which column, inclusive).

Rows:  Specify the range of rows to be exported (From which row, To which row, inclusive).


  Exporting a Megafile Manager file to STATISTICA

To export a Megafile Manager file to STATISTICA, follow the steps outlined below.

Step 1:	Select the Export Data option from the File pull-down menu to open the Export Data To dialog.

Step 2:	Select STATISTICA as the type of file into which the data will be exported.  You may click on the Options button to select from several exporting options.

Step 3:	Click the OK button in the latter dialog to export and store (you will need to select a file name) the file in STATISTICA data file format.


  Megafile Manager - Export File to Excel

Excel files may contain up to 256 columns and 16384 rows.  If the current Megafile Manager file is larger than this, then you can create Subsets of the file and export each of those subsets separately.  When you select the Excel option from the Export dialog, click on the Options button to open the Excel Export Options dialog.

Excel Export Options dialog:

Export Column Names ...:  When this option is selected, STATISTICA will export the Megafile Manager column names into the first row of the Excel spreadsheet.  If this option is de-selected, then the column names will not be included in the Excel file.

Example


  Exporting a Megafile Manager file to Excel

To export a Megafile Manager file to Excel, follow the steps outlined below.

Step 1:	Select the Export Data option from the File pull-down menu to open the Export Data To dialog.

Step 2:	Select Excel as the type of file into which the data will be exported.  You may click on the Options button to select the exporting option.

Step 3:	Click the OK button in the latter dialog to export and store (you will need to select a file name) the file in Excel format.


  Megafile Manager - Export File to Lotus

Megafile Manager can export to Lotus 1-2-3 Release 1A, 2.01/2.2, Release 3, Lotus for Windows, and Symphony format files.  Lotus 1-2-3 Release 2.01/2.2, and Release 3 files may contain up to 256 columns and 8192 rows.  If the current Megafile Manager file is larger than this, then you can create Subsets of the file and export each of those subsets separately.

Lotus Export Options dialog:

Export Column Names ...:  When this option is selected, Megafile Manager will export the column names into the first row of the Lotus spreadsheet.  If this option is de-selected, then column names will not be included in the Lotus file.

Define Sheets:  These options are available only if the Lotus 1-2-3 Release 3 or Lotus for Windows format is selected from the Export Data To dialog.

How Many:  By default, all columns in the Megafile Manager file are exported as one worksheet.  If desired, Megafile Manager columns may be equally divided among a specified number of worksheets.  You can specify that number here.

By Names:  Alternately, the Megafile Manager columns may be assigned to specific worksheets by names: Columns named A_A through A_IV will be placed in worksheet A, columns B_A through B_IV in worksheet B, etc.  (This will be the case if the option From Spreadsheet was selected when originally importing column names from a Release 3 or Lotus for Windows worksheet.)

Example


  Exporting a Megafile Manager file to Lotus

To export a Megafile Manager file to Lotus, follow the steps outlined below.

Step 1:	Select the Export Data option from the File pull-down menu to open the Export Data To dialog.

Step 2:	Select Lotus as the type of file into which the data will be exported and then select the Lotus version (123/1, 123/2, 123/3, 123/w, and Symphony).  You may click on the Options button dialog to select from the exporting options.

Step 3:	Click the OK button in the latter dialog to export and store (you will need to select a file name) the file in Lotus format.


  Megafile Manager - Export File to Quattro

You may export Megafile Manager files to Quattro.  Quattro files may contain up to 256 columns and 8192 rows.  When you select the Quattro option from the Export Data To dialog, click on the Options button to open the Quattro Export Options dialog.

Quattro Export Options dialog:

Export Column Names ...:  When this option is selected, Megafile Manager will export the column names into the first row of the Quattro spreadsheet.  If this option is de-selected, then column names will not be included in the Quattro file.

Example


  Exporting a Megafile Manager file to Quattro

To export a Megafile Manager file to Quattro, follow the steps outlined below.

Step 1:	Select the Export Data option from the File pull-down menu to open the Export Data To dialog.

Step 2:	Select Quattro as the type of file into which the data will be exported.  You may click on the Options button to select the exporting option.

Step 3:	Click the OK button in the latter dialog to export and store (you will need to select a file name) the file in Quattro format.


  Megafile Manager - Export File to dBASE

Megafile Manager exports to dBASE III+ and dBASE IV file formats.  dBASE III+ files are limited to 128 fields and dBASE IV to 255 fields.  If the current Megafile Manager file is larger than this, then you can create Subsets of the file and export each of those subsets separately.  Field names in dBASE must begin with a letter A to Z, and may contain only uppercase letters (during export, lowercase letters in Megafile Manager column names are converted to uppercase), as well as numerals, and the underscore (_).  The Verify option from the Megafile Manager Analysis pull-down menu may be used to check Megafile Manager column names for agreement with these conventions, and to correct any which do not comply.

Example


  Exporting a Megafile Manager file to dBASE

To export a Megafile Manager file to dBASE, follow the steps outlined below.

Step 1:	Select the Export Data option from the File pull-down menu to open the Export Data To dialog.

Step 2:	Select dBASE as the type of file into which the data will be exported and then select the dBASE version (click on either III+ or IV).

Step 3:	Click the OK button in the latter dialog to export and store (you will need to select a file name) the file in dBASE format.


  Megafile Manager - Export File to SPSS

This Megafile Manager option exports to the SPSS Portable File Format.  When importing an SPSS Portable File, data values and value labels are automatically "split" to become sequential Megafile Manager columns, which can be automatically put together in the process of exporting them back to SPSS.  A numeric (or text column up to 8 characters long) may be paired with a long text column with a related name to become an SPSS Portable File column with value labels.  (If the name of the data column is less than 8 characters, the name of the related column has the same name with either an @ or a $ added to the end [in the same manner as data imported from STATISTICA]; if the name is 8 characters long, then the second character is replaced with an @ or $.)  Each numeric or text value in the data column must correspond to a unique text value in the matching text column.  Unpaired text columns will become text variables without value labels.  Megafile Manager files with up to 2000 columns may be exported to an SPSS Portable File, however, on some systems, SPSS imposes lower file size limits (check the SPSS manual for the particular system).  If the current Megafile Manager file is larger than 2000 columns, then you can create Subsets of the file and export each of those subsets separately.

SPSS column names may be up to 8 characters long, must begin either with an uppercase letter (A to Z; lowercase letters in Megafile Manager column names are automatically converted to uppercase during export), or the characters $ or @, and may also contain digits, periods, #, and underscore (_).  Certain names are reserved as keywords and may not be used as column names, including ALL, AND, BY, EQ, GE, GT, LE, LT, NE, NOT, OR, TO, and WITH.  The Verify option from the Megafile Manager Analysis pull-down menu may be used to check Megafile Manager columns names for agreement with these conventions, and to correct any which do not comply.

Example


  Exporting a Megafile Manager file to SPSS

To export a Megafile Manager file to SPSS, follow the steps outlined below.

Step 1:	Select the Export Data option from the File pull-down menu to open the Export Data To dialog.

Step 2:	Select SPSS as the type of file into which the data will be exported.

Step 3:	Click the OK button in the latter dialog to export and store (you will need to select a file name) the file in SPSS format.


  Megafile Manager - Export File to ASCII

Megafile Manager can export to both ASCII fixed (undelimited) and ASCII free (delimited) files.  Each type of ASCII file has its own dialog of options.  For more information on these options, click on the appropriate option below.

Export ASCII free file

Export ASCII fixed file


  Megafile Manager - Export File to ASCII Free Format

Megafile Manager can export to ASCII free format files.  If you choose instead to export to ASCII fixed format files, then values which are shorter than the format are padded with blanks so that the absolute position of each value is "fixed" within the line in the output file.  Free format (delimited) ASCII files are created without padding values to fill out column formats since user-specified characters are used to separate or delimit successive values.  When you select the ASCII Free option from the Export dialog, click on the Options button to open the ASCII Free Export Options dialog.

ASCII Free Export Options dialog:

Line Length:  The number of columns per line in the output file is determined by the specified line length.  Enter the length of the line in the ASCII file here (values can be from 80 to 4000).  If the specified line length is insufficient to contain all columns, then the line will be broken after the last complete column (i.e., a column will not be divided across lines).  If unbroken records are desired (i.e., each record occupies only one line in the output file), specify a line length long enough to accommodate the row length.

Separators:

Field Separator:  Click on this button to bring up the ASCII Free Separator dialog from which you can select a single character to be used to separate successive values in the output file (by default, a comma will be used as the field separator).

Row Separator:  The Row Separator serves to indicate the end of each of the original rows of data (one row of data may extend across several lines of the output file).  Click on this button to bring up the ASCII Free Separator dialog from which you can select a single character to be used to indicate the completion of each row of data in the output file (by default, a comma will be used as the row separator).  Note that if the length of the row in the Megafile Manager file is longer than the specified output Line Length (see above), then the row will extend across one or more lines in the output file.

Example


  Exporting a Megafile Manager file to ASCII Free

To export a Megafile Manager file to ASCII, follow the steps outlined below.

Step 1:	Select the Export Data option from the File pull-down menu to open the Export Data To dialog.

Step 2:	Select ASCII as the type of file into which the data will be exported and Free as the ASCII version.  You may click on the Options button to select the row and field separators as well as other exporting options.

Step 3:	Click the OK button in the latter dialog to export and store (you will need to select a file name) the file in ASCII Free format.


  Megafile Manager - Export File to ASCII Fixed Format

Unlike ASCII free format files, fixed format (undelimited) ASCII files will be created using the current column formats (values which are shorter than the format are padded with blanks so that the absolute position of each value is "fixed" within the line in the output file).  When you select the ASCII Fixed option from the Export dialog, click on the Options button to open the ASCII Fixed Export Options dialog.

ASCII Fixed Export Options dialog:

Line Length:  The number of columns per line in the output file is determined by the specified line length.  Enter the length of the line in the ASCII file here (values can be from 80 to 4000).  If the specified line length is insufficient to contain all columns, then the line will be broken after the last complete column (i.e., a column will not be divided across lines).  If unbroken records are desired (i.e., each record occupies only one line in the output file), specify a line length no less than the sum of all column formats.

Example


  Exporting a Megafile Manager file to ASCII Fixed

To export a Megafile Manager file to ASCII, follow the steps outlined below.

Step 1:	Select the Export Data option from the File pull-down menu to open the Export Data To dialog.

Step 2:	Select ASCII as the type of file into which the data will be exported and Fixed as the ASCII version.  You may click on the Options button to specify the line length.

Step 3:	Click the OK button in the latter dialog to export and store (you will need to select a file name) the file in ASCII Fixed format.


  Megafile Manager - Convert to a STATISTICA File

This option will allow you to quickly open the STATISTICA Export Options dialog in order to convert (i.e., export) a Megafile Manager file to a STATISTICA data file.  For more information on these export options, see STATISTICA Export Options.


  Megafile Manager - Print MFM Data

When you select this option the Megafile Manager: Print dialog will open in which you can choose from several printing options (described below).

Shortcut:  Click on the Print [image] Toolbar button, to bypass the Print dialog (i.e., the previously-selected settings or the default settings will be used) and print the Megafile Manager file.  Note that if a block is selected in the file, then that block will be printed, otherwise, the previously specified columns and rows will be printed.

Keyboard Shortcut:  Ctrl + P

Megafile Manager: Print dialog:

Columns

Rows

Print Data Values

Print Column Specifications

Print/Eject Pages after this Printout


  Print MFM Data - Columns

Click on this button to open the Megafile Manager: Select Columns dialog in which you can select the columns to be printed.


  Print MFM Data - Rows

Click on this button to open the Megafile Manager: Select Rows dialog in which you can select the rows to be printed.


  Print MFM Data - Print Data Values

Select this option to print the Megafile Manager file data values for the selected rows and columns.


  Print MFM Data - Print Column Specifications

Select this option to print the Megafile Manager file column specifications for the selected columns.


  Print MFM Data - Print/Eject Pages after this Printout

When selected, this option will cause the requested printout to automatically be sent to the printer or output file when you click OK in this dialog or when you press the Print [image] button on the toolbar (any other text previously left in the internal buffer will also be printed).  Thus, each requested printout (table) will start on a new page.  If this option is de-selected, then output will be stored in the internal buffer, and sent to the printer depending on the current setting of the check box Automatically Eject Each Filled Page (either whenever there is enough to fill one page or all at once later, e.g., when you exit the module or when you empty the buffer by using the option Print/Eject Current Pages).  Note that this option will only apply locally (temporarily) to the current STATISTICA module and the current session whereas, selecting the Print/Eject Pages after Each Printout option in the Page/Output Setup dialog, will apply globally (permanently).


  Megafile Manager - Edit Menu

The following options are available from the Megafile Manager Edit pull-down menu.

Edit Cell

Columns

Add	Delete

Move	Column Specs

Copy

Rows

Add	Copy

Move	Delete

Header	Clear

Cut	Find

Copy	Replace

Copy Raw	Transpose Block

Paste	Screen Catcher


  Megafile Manager - Add Columns

Add columns to the Megafile Manager file by designating the number of new columns to add, as well as where to add them (after which column) in the Add Columns dialog.  You can click on the column edit field in this dialog to bring up the list of columns in the current Megafile Manager file and select a column that the new column(s) will be placed after (see Megafile Manager: Select Column).

Megafile Manager: Add Columns dialog:

Number of Columns to Add

Insert After Column

Prefix

Type

Length

MD

Display format


  Megafile Manager Add Columns - Number of Columns to Add

Choose the desired number of columns to add to the current Megafile Manager file.  You may include up to 32,000 columns (with up to 255 characters per column) in Megafile Manager.


  Megafile Manager Add Columns - Insert After Column

Designate the location (column) in the Megafile Manager file that the new column(s) will be added after.  The new columns will be added to the right of the column specified here.

How to insert before column 1:  The easiest way to move and insert the values of a column or block of columns before column 1 is to use the Drag-and-Drop facilities in STATISTICA.  To do this, first hightlight the desired block.  Then, move the cursor to one of the corners of the block where it will change into an arrow.  Now, to move and insert the block, press SHIFT while dragging the block (see Move/Copy Block).  Next, position the insertion bar between the case name column and the first column and release the mouse-button to complete the insert.  Note that this method does not move the selected column(s) (i.e., their long value labels, formats, assignments of text/numerical values, etc.) but only the values of the selected block.

An alternative way to move and insert an entire variable or block of variables before column 1, first move the column(s) after column number 1and then move column number 1 to the right of the moved column(s) (you can also use the Copy Columns option to first copy the column(s) and then move them).


  Megafile Manager Add Columns - Prefix

You can specify the prefix for the new column names which will be followed by consecutive numbers (e.g., NEW1, NEW2, NEW3, ...).  In order to change the names of individual columns, double-click on the column name in the Megafile Manager spreadsheet to open the Column Specs dialog.


  Megafile Manager Add Columns - Type

Specify here the type of data values for the new columns.  Each type is described below:

Type                    Range of Values    Examples      Bytes

----------------------  -----------------  ------------  -----

text                    any characters     John Brown    1-255

short integer (Int 1B)  ±127               -98             1

integer (Int 2B)        ±32767             9834            2

long integer (Int 4B)   ±2147483647        12345678        4

float (Real 4B)         ±3.4*10**+38       1234.5678       4

double float (Real 8B)  ±1.7*10**+308      123456.78974    8

logical                 yes/no/true/false  Yes             1

date                    from Jan.1, 1900   02/08/55        8


  Megafile Manager Add Columns - Length

This option will become available when you select Text as the column type.  Enter here, the desired length (up to 255 characters) of the text values.


  Megafile Manager Add Columns - Missing Data

Enter a specific value for the missing data code (value of the column that indicates data points for which no data are available) or accept the default code of -9999 (the default MD code for all text, date, and logical values in Megafile Manager is fixed and cannot be changed).  Missing Data values are displayed as blanks in the cells of the Megafile Manager file (the value can be viewed in the Megafile Manager window toolbar Show Window when a blank cell is highlighted) and are ignored in all data analyses.


  Megafile Manager Add Columns - Display Format

The format determines the length of the field used to display (or print in reports) values from the respective column; the format does not affect the contents or precision of values stored in Megafile Manager data files and can be adjusted at any point.  For Real (4B or 8B) type columns, the format also determines the number of decimal places displayed; if a numeric value cannot fit in its format, Megafile Manager uses "compressed scientific notation" (e.g., a value of 30,000 will be displayed in a 3-character format as 3E5, i.e., 3*10**5); a string of asterisks (e.g., ***) is displayed when a value cannot be displayed even in compressed notation.  The formats that you specify here will be applied to each column added to the Megafile Manager file.  In order to change the format for an individual column, double-click on the column name in the Megafile Manager spreadsheet to open the Column Specs dialog.

Width:  Edit the width of the values of the columns to be added here.  The default format width is 8 characters.

Decimal:  Specify the number of decimal places for the added columns.  The default format is 3 decimal places.

Display as:  This option will become available when you select either Dates or Logical as the column type.  You can click on the combo box to select the desired Date or Logical display for those values.


  Megafile Manager - Move Columns

Move one or more columns in the Megafile Manager file by designating the range (inclusive) of columns to be moved and the location (column to insert after) in the Move Columns dialog.  You can easily replace one column name with another by clicking on the column edit field in the Move Columns dialog to bring up the list of columns in the current Megafile Manager file from which you can select the desired column.

Move Columns dialog:

From Column

To Column

Insert After


  Megafile Manager Move Columns - From Column

Designate the first column (inclusive) in the block of columns to be moved.  (Note that if you are moving only one column, then designate the same column in both the From Column and To Column lists.)


  Megafile Manager Move Columns - To Column

Designate the last column (inclusive) in the block of columns to be moved.


  Megafile Manager Move Columns - Insert After

Designate the location (column) in the Megafile Manager file that the column(s) will be moved after (you cannot insert a block of columns after a column that is included in the range of columns to be moved).  The block of columns will be "cut" from their current file location and moved to the right of the column specified here.

How to insert before column 1:  The easiest way to move and insert the values of a column or block of columns before column 1 is to use the Drag-and-Drop facilities in STATISTICA.  To do this, first hightlight the desired block.  Then, move the cursor to one of the corners of the block where it will change into an arrow.  Now, to move and insert the block, press SHIFT while dragging the block (see Move/Copy Block).  Next, position the insertion bar between the case name column and the first column and release the mouse-button to complete the insert.  Note that this method does not move the selected column(s) (i.e., their long value labels, formats, assignments of text/numerical values, etc.) but only the values of the selected block.

An alternative way to move and insert an entire variable or block of variables before column 1, first move the column(s) after column number 1and then move column number 1 to the right of the moved column(s) (you can also use the Copy Columns option to first copy the column(s) and then move them).


  Megafile Manager - Copy Columns

Place a copy of the specified column(s) at a designated location by specifying the range (inclusive) of columns to be copied and the Megafile Manager file location (insert after which column) in the Copy Columns dialog.  The copy will include not only the data but also the format, long name, display specifications, etc.  You can easily replace one column name with another by clicking on the column edit field in the Copy Columns dialog to bring up the list of columns in the current Megafile Manager file from which you can select the desired column.

Copy Columns dialog:

From Column:  Designate the first column (inclusive) in the block of columns to be copied.  (Note that if you are copying only one column, then designate the same column in both the From Column and To Column lists.)

To Column:  Designate the last column (inclusive) in the block of columns to be copied.

Insert After:  Designate the location (column) in the spreadsheet that the column(s) will be placed after copying (you cannot insert a block of columns after a column that is included in the range of columns to be copied).  The copied columns will be located to the right of the column specified here.

How to insert before column 1


  How to Insert Before Column 1

How to insert before column 1:  The easiest way to move and insert the values of a column or block of columns before column 1 is to use the Drag-and-Drop facilities in STATISTICA.  To do this, first hightlight the desired block.  Then, move the cursor to one of the corners of the block where it will change into an arrow.  Now, to move and insert the block, press SHIFT while dragging the block (see Move/Copy Block).  Next, position the insertion bar between the case name column and the first column and release the mouse-button to complete the insert.  Note that this method does not move the selected column(s) (i.e., their long value labels, formats, assignments of text/numerical values, etc.) but only the values of the selected block.

An alternative way to move and insert an entire variable or block of variables before column 1, first move the column(s) after column number 1and then move column number 1 to the right of the moved column(s) (you can also use the Copy Columns option to first copy the column(s) and then move them).


  Megafile Manager - Delete Columns

One or more columns can be deleted from the current Megafile Manager file when you designate the range (inclusive) of columns to be deleted in the Delete Columns dialog.  You can easily replace one column name with another by clicking on the column edit field in the Delete Columns dialog to bring up the list of columns in the current Megafile Manager file from which you can select the desired column.

Unlike deleting (clearing) the contents of a highlighted range or block of values in the Megafile Manager file, this option will remove both the contents of the column(s) and the column(s) itself, thus the subsequent columns will be moved to the left and the size of the file will decrease.

Delete Columns dialog:

From Columns:  Designate the first column (inclusive) in the block of columns to be deleted.  (Note that if you are deleting only one column, then designate the same column in both the From Column and To Column lists.)

To Columns:  Designate the last column (inclusive) in the block of columns to be deleted.


  Megafile Manager - Edit Column Specs

Specifications of the currently highlighted column (i.e., column name and format, missing data value, and label) can be edited in the Column Specs dialog.

Column Specs dialog:

Name

Type

Length

MD

Display format

Long Name

Values


  Megafile Manager Edit Column Specs - Name

Edit the column name here.  Column names can be up to 8 characters long and may contain all keyboard characters, including upper and lower case letters, numbers, spaces, punctuation, etc.).  In addition to their names, columns in Megafile Manager can also be referred to by their consecutive numbers, (e.g., in all cases where a column or a list of columns is to be entered).


  Megafile Manager Edit Column Specs - Type

Specify here the type of data values for the new columns.  The general type of data value (e.g., Integer for any integer type) that you choose here is displayed in the third line of the column header in the Megafile Manager spreadsheet.  Each type is described below:

Type                    Range of Values    Examples      Bytes

----------------------  -----------------  ------------  -----

text                    any characters     John Brown    1-255

short integer (Int 1B)  ±127               -98             1

integer (Int 2B)        ±32767             9834            2

long integer (Int 4B)   ±2147483647        12345678        4

float (Real 4B)         ±3.4*10**+38       1234.5678       4

double float (Real 8B)  ±1.7*10**+308      123456.78974    8

logical                 yes/no/true/false  No              1

date                    from Jan.1, 1900   02/08/55        8


  Megafile Manager Edit Column Specs - Length

This option will become available when you select Text as the column type.  Enter here, the desired length (up to 255 characters) of the text values.


  Megafile Manager Edit Column Specs - Missing Data

Enter a specific value for the missing data code (value of the column that indicates data points for which no data are available) or accept the default code of -9999 (the default MD code for all text, date, and logical values in Megafile Manager is fixed [set to a so-called "null character"] and cannot be changed).  Missing data values are displayed as blanks in the cells of the Megafile Manager file (the value can be viewed in the Megafile Manager window toolbar Show Window when a blank cell is highlighted) and are ignored in all data analyses.


  Megafile Manager Edit Column Specs - Display Format

The format determines the length of the field used to display (or print in reports) values from the respective column; the format does not affect the contents or precision of values stored in Megafile Manager data files and can be adjusted at any point.  For Real (4B or 8B) type columns, the format also determines the number of decimal places displayed; if a numeric value cannot fit in its format, Megafile Manager uses "compressed scientific notation" (e.g., a value of 30,000 will be displayed in a 3-character format as 3E5, i.e., 3*10**5); a string of asterisks (e.g., ***) is displayed when a value cannot be displayed even in compressed notation.

Width:  Edit the width of the values of the columns to be added here.  The default format width is 8 characters.

Decimal:  Specify the number of decimal places for the added columns.  The default format is 3 decimal places.

Display as:  This option will become available when you select either Dates or Logical as the column type (see above).  You can click on the combo box to select the desired Date or Logical display for those values.


  Megafile Manager Edit Column Specs - Long Name

For each column, you can assign a column long name up to 128 characters long.  The label can contain notes, including any printable characters.


  Megafile Manager Edit Column Specs - Values

Click on this button to open the Column Values Window in which you can view the values of the current column.


  Megafile Manager - Add Rows

Add rows to the Megafile Manager file by designating the number of new rows to add, as well as where to add them (after which row) in the Add Rows dialog.

Add Rows dialog:

Number of Rows to Add:  Choose the desired number of rows to add to the current Megafile Manager file.  The number of rows that you can add to a file is unlimited.

Insert After Row:  Designate the row number after which the new row(s) will be added.  The added rows will be located after the row specified here.

How to insert before row 1


  How to Insert Before Row 1

How to Insert (Move) Before Row 1:  The easiest way to move and insert the values of a row or block of rows before row 1 is to use the Drag-and-Drop facilities in STATISTICA.  To do this, first hightlight the desired block.  Then, move the cursor to one of the corners of the block where it will change into an arrow.  Now, to move and insert the block, press SHIFT while dragging the block (see Move/Copy Block).  Next, position the insertion bar between the variable names and the first row and release the mouse-button to complete the insert.

An alternative way to move and insert a row or block of rows before row 1, first add the row(s) after row number 1and then move row number 1 below the added row(s).


  Megafile Manager - Move Rows

Move one or more rows in the Megafile Manager file by designating the range (inclusive) of rows to be moved and the location (row to insert after) in the Move Rows dialog.

Move Rows dialog:

From Row:  Designate the first row (inclusive) in the block of row to be moved.  (Note that if you are moving only one row, then designate the same row in both the From Row and To Row lists.)

To Row:  Designate the last row (inclusive) in the block of rows to be moved.

Insert After:  Designate the location (row) in the Megafile Manager file that the row(s) will be moved after.  The moved rows will be located after the row specified here.

How to move before row 1


  How to Move Before Row 1

How to Insert (Move) Before Row 1:  The easiest way to move and insert the values of a row or block of rows before row 1 is to use the Drag-and-Drop facilities in STATISTICA.  To do this, first hightlight the desired block.  Then, move the cursor to one of the corners of the block where it will change into an arrow.  Now, to move and insert the block, press SHIFT while dragging the block (see Move/Copy Block).  Next, position the insertion bar between the variable names and the first row and release the mouse-button to complete the insert.

An alternative way to move and insert a row or block of rows before row 1, first move the row(s) after row number 1and then move row number 1 below the added row(s) (you can also use the Copy Rows option to first copy the rows and then move them).


  Megafile Manager - Copy Rows

Place a copy of the specified row(s) at a designated location by specifying the range (inclusive) of rows to be copied and the Megafile Manager file location (insert after which row) in the Copy Rows dialog.

Copy Rows dialog:

From Row:  Designate the first row (inclusive) in the block of rows to be copied.  (Note that if you are copying only one row, then designate the same row in both the From Row and To Row lists.)

To Row:  Designate the last row (inclusive) in the block of rows to be copied.

Insert After:  Designate the location (row) in the Megafile Manager file that the row(s) will be placed after copying.  The copied rows will be located after the row specified here.

How to copy before row 1


  How to Copy Before Row 1

How to Insert (Move) Before Row 1:  The easiest way to move and insert the values of a row or block of rows before row 1 is to use the Drag-and-Drop facilities in STATISTICA.  To do this, first hightlight the desired block.  Then, move the cursor to one of the corners of the block where it will change into an arrow.  Now, to move and insert the block, press SHIFT while dragging the block (see Move/Copy Block).  Next, position the insertion bar between the variable names and the first row and release the mouse-button to complete the insert.

An alternative way to move and insert a row or block of rows before row 1, first copy the row(s) after row number 1and then move row number 1 below the added row(s) (you can also use the Copy Rows option to first copy the rows and then move them).


  Megafile Manager - Delete Rows

One or more rows can be deleted from the current Megafile Manager file when you designate the range (inclusive) of rows to be deleted in the Delete Rows dialog.

Unlike deleting (clearing) the contents of a highlighted range or block of values in the Megafile Manager file, this option will remove both the contents of the row(s) and the row(s) itself, thus the subsequent rows will be moved up and the size of the file will decrease.

Delete Rows dialog:

From Row:  Designate the first row (inclusive) in the block of rows to be deleted.  (Note that if you are deleting only one row, then designate the same row in both the From Row and To Row lists.)

To Row:  Designate the last row (inclusive) in the block of rows to be deleted.


  Megafile Manager - File Header

Make notes or comments about the current Megafile Manager file in the Megafile Manager File Header and Info Page dialog.  You can include either a one line file header, several lines of notes, or both.

Megafile Manager File Header and Info Page dialog:

One Line Header:  Enter one line (up to 77 characters) of comment about the file here.  The One Line Header is saved as part of the file and is printed along with the data when the Print Column Specifications option is selected in the Print MFM Data dialog.

File Information/Notes:  Make a comment about the Megafile Manager file here.  These notes can be up to 1,970 characters in length and can include any printable characters.  The File Information/Notes are printed along with the data when the Print Column Specifications option is selected in the Megafile Manager: Print dialog.


  Megafile Manager - View Menu

The following options are available from the Megafile Manager View pull-down menu.

Font	Change Show

Colors	Status Bar

Titles	Auto Task Buttons

Toolbar


  Megafile Manager - Analysis Menu

The following options are available from the Megafile Manager Analysis pull-down menu.

  Merge	  Descriptives

  Subset	  Correlations

  Sort	  Frequencies

  Optimize Size	  Language (MML)

  Verify	  Other Statistics


  Megafile Manager - Merge Files

Merge operations combine data from two files, either by pasting files together (column and row merge), or by replacing data in a segment of the first file with data from a second file (overlay merge).  After selecting the type of merge and entering the name of the second Megafile Manager file (which will be merged to the current file), the respective merge dialog will open (see below).

Merge Files dialog

Merge:  Select one of three merging options.

•	Merge Columns

•	Merge Rows

•	Overlay

2nd File button:  Click on this button to open the Second File dialog from which you can select a file to merge with the current file.  Please note that you cannot merge a file to itself (i.e., you cannot enter the current file as the second file name).  If you wish to "double" the file, use the Save As option from the File pull-down menu to create a second copy of the file.


  Megafile Manager - Merge Columns

When you select the Merge Columns option from the Merge Files dialog, Megafile Manager will add the second file's columns after the columns of the first file.  The following options (available from the Merge Columns dialog) are used to align (match) the rows of the second file with those of the first.

Merge Columns dialog:

Mode

Relational Merge Options

Unmatched Cases

Example


  Megafile Manager Merge Columns - Mode

If the number and order of rows in the two Megafile Manager files are not precisely the same (i.e., if at least one row is missing in the second file or there is one row that has no equivalent in the first file), then all subsequent data would be merged with the wrong rows.  In order to avoid this problem, you will need to specify a mode of merging here.  When relationally merging rows from two files, you need to specify a key (row identifier) column in each file; then for each row, the program will check the values of this key in both files and merge the rows only if their respective keys match.

Not Relational:  Columns of the second file are simply added alongside those of the first when this mode is selected (this is the default mode).

Relational:  When you select this mode, the rows from the second file will be matched with those of the first file, based on the values of a specified key.

Relational hierarchical: This mode differs from the simple relational mode (see above) in the handling of multiple records with the same key value in either the primary or secondary file.  In the standard relational mode (see above), successive records with identical key values will be merged.  If there are uneven numbers of records with identical key values in the two files, missing data are added to "pad" the file with the lesser number of records.  In contrast, in the Relational hierarchical mode the file is padded with the values found in the last identical key record that was matched.  For example:

Standard Relational Merge, unmatched cases filled with missing data:

  File 1       File 2          Merged File

----------  ----------   -----------------------

Key1  Var1  Key2  Var2    Key1  Var1  Key2  Var2

----  ----  ----  ----   ----- ----- ----- -----

 1     1     1     1       1     1     1     1

 2     4     1     2     Miss  Miss    1     2

 2     5     1     3     Miss  Miss    1     3

 3     2     2     4       2     4     2     4

 3     3     2     5       2     5     2     5

                           3     2   Miss  Miss

                           3     3   Miss  Miss

Hierarchical Relational Merge, unmatched cases filled with missing data:

                               Merged File

                          ----------------------

                          Key1  Var1  Key2  Var2

                          ----  ---- ----- -----

                           1     1     1     1

                           1     1     1     2

                           1     1     1     3

                           2     4     2     4

                           2     5     2     5

                           3     2   Miss  Miss

                           3     3   Miss  Miss

Note that the sequence of rows is not changed during merging, therefore, each file should be sorted (see Sort Data) in order of its key column before merging.


  Megafile Manager Merge Columns - Relational Merge

When you choose either the Relational Merge or Relational Hierarchical Merge option, you will need to specify a key column for each file in order to merge the two files.  Megafile Manager will expect the two files to be sorted (see Sort Data) by their respective key column before a relational merge can be performed.

Key in File 1:  Enter here the number of the column to be used as the key in the first file.

Key in File 2:  Enter here the number of the column to be used as the key in the second file.


  Megafile Manager Merge Columns - Unmatched Cases

Select one of three ways of dealing with unmatched rows when the two files are merged.  Unmatched rows may result from unequal numbers of rows in the merged files, or because some of the rows do not meet the Relational merge criteria (see above).

Fill with MD:  Unfilled columns in unmatched rows are padded with missing data when you select this option.

Delete:  Rows from either file which cannot be matched will be removed from the merged file if you select this option.

Abort merge:  The presence of unmatched rows in either file will cause an error message to be displayed and the merge procedure to be abandoned.


  Megafile Manager - Merging Columns

Step 1:	Click on the Merge option from either the Analysis pull-down menu.

Step 2:	Select the Merge Columns option and click on the 2nd File button to select the file with the columns that will be added after the current file's columns.  Click OK to exit this dialog and open the Merge Columns dialog.

Step 3:	Select the Mode of merging the columns (see below) and the way that you want Megafile Manager to handle Unmatched Cases (see below).  Click OK to process the Merge.


  Megafile Manager - Merge Rows

Select this option from the Merge Files dialog when you want to merge rows from the second file after the rows of the first file.  (Note:  All column types in the second file must match those in the first file.)

Example


  Megafile Manager - Merging Rows

Step 1:	Click on the Merge option from either the Analysis pull-down menu.

Step 2:	Select the Merge Rows option and click on the 2nd File button to select the file with the rows that will be added after the current file's rows.  Click OK to exit this dialog and process the Merge.  Note that if the number of columns in the first two files are not the same, then the Merge may not be completed.


  Megafile Manager - Overlay Merge

This merging option will replace data in the first file with data from the second file starting in the user-defined file location (column/row).  When you select this option in the Merge Files dialog, the Overlay Merge dialog will open.

Overlay Merge dialog:

Update columns

Update rows


Megafile Manager - Update Columns

  Megafile Manager Overlay Merge - Update Columns

Start with column:  The column number that you specify here will determine the starting position in which the data from the second file will occupy within the first file by matching column numbers.

Based on names:  Alternatively, you can select this option in order to determine the starting position that the data from the second file will occupy within the first file by matching column names.  When you select this option, Megafile Manager will search for identical column names and will begin the overlay merge at the first identical column name that it encounters.


Megafile Manager - Update Rows

  Megafile Manager Overlay Merge - Update Rows

Start with row:  When you select this option, you can specify the starting row in the first file to receive data from the second file.

Based on keys (relational):  Rows from the second file will be matched to rows in the first file based on values of key columns (see below) when you select this option.  Megafile Manager will expect the two files to be sorted (see Sort) by their respective key column before an overlay merge can be performed.

Key in file I:  Specify the key column from the first file.

Key in file II:  Specify the key column from the second file.


  Megafile Manager - Subset

Use this Megafile Manager option to extract a section (subset) of the current file and store the subset under a new Megafile Manager name.  When you select this option from the Analysis pull-down menu, the Subset dialog will open.  After you have created this subset file, you will need to save it under a different file name using the Save As option from the File pull-down menu.

Subset dialog:

Columns:  Click on this button to bring up the Select Columns dialog from which you may select the columns to be included in the subsetted file.

Rows:  Click on this button to open the Select Rows dialog from which you may select a subset of rows to be included in the subsetted file.


  Megafile Manager - Sort Data

Megafile Manager performs hierarchical (nested) sorting on the basis of user-specified key columns (i.e., if two rows have identical values in a given key, the values of the next key are used to determine ranking).  When you select the Sort option from the Analysis pull-down menu, the Sort Options dialog will open.  You can choose up to three key columns by which to sort in this dialog (up to seven if you press the More Keys ... button).  Each key column has the same set of options (described below).

Sort Options dialog:

Column:  Type in the key column name or double-click on this window to open the Select Column dialog.  The Select Column dialog will display a list of columns from which you can select the key column.

Sorting Order:  Choose to use the Ascending or Descending sort order.

More Keys button:  When this dialog first opens, only three keys are displayed.  If you need to enter more keys than this, click on the More Keys button to increase the number of displayed keys to seven (the maximum).


  Megafile Manager - Optimize Size

Select this option in order to change both column type and format for best fit to the selected columns.  When you select this option, the Optimize Size dialog will open in which you can select the columns to be optimized.  This option is useful in reducing wasted space in files (e.g., a column type of Text-255 characters which contains less than 80 characters of data).  Some imported files (such as from the SPSS Portable File Format) may contain large amounts of wasted space, as all numeric columns are specified as Double Float (i.e., Real 8B); optimization compacts the column formats for the most efficient use of disk space.  For example, if data in a column specified as Double Float (Real 8B; format F16.6) are only 2 digit integers, optimization will change the column type to Short Integer (i.e., Int 1B), saving seven bytes per record (87.5% savings).

NOTE:  Values in Double Float columns which are within the range of normal Float values (±3.4*10**+38) will be converted to Float values during optimization, and will be rounded to 7 significant digits.  To preserve values with more than 7 significant digits, do not include them in the list of columns to be optimized.  Also note that MD codes are considered in the determination of optimal formats and they are preserved: for example, if an Integer column contains data values which fall within the range of Short Integers (±127), but contains a MD value which is outside this range (e.g., -9999), then the column will not be converted to Short Integer.


  Megafile Manager - Verify Column Names

This verification facility may be used to check for (and adjust) the "fit" of column Formats (see below) to the data, to check for duplicated column names, or to check their compliance with selected standards (e.g., STATISTICA, dBASE, SPSS).  When you select this option from the Analysis pull-down menu, the Verify dialog will open.

Verify dialog:

Column Names

Formats


  Megafile Manager Verify Column Names - Column Names

This option will check the correctness of the column names according to the requirements of STATISTICA, dBASE, or SPSS, or it will create standard names.  Select one of the options described below.  If an invalid or duplicated name is found, a Name Verification dialog will open allowing you to correct the name (either of the two names can be edited if a duplicate is found).

Do Not Verify:  Select this option if you are interested in only verifying column formats.

STATISTICA Correctness:  This option is used to check all column names for duplications, for compliance with the requirements of STATISTICA BASIC, MML, or prior to exporting the file.

dBASE Correctness:  When selected, this option checks for compliance with the requirements of dBASE.  All columns must have names which may contain the letters A-Z, a-z, the digits 0-9, and the underscore (_).  Each column name must begin with a letter, and all column names must be unique (which may be checked by using the STATISTICA Correctness option above).

SPSS Correctness:  When selected, this option checks for agreement with the requirements of SPSS.  All columns must have names which may contain the letters A-Z, a-z, the digits 0-9, underscore (_), period (.), @, #, and $.  Each column name must begin with either a letter, $, or @, and cannot be one of the reserved SPSS keywords (ALL, AND, BY, EQ, GE, GT, LE, LT, NE, NOT, OR, TO, and WITH).

Create Standard Names:  When selected, this option assigns "standard" names (a prefix plus a sequential number) to all columns through the following options.

•	Prefix:  Specify a five-letter prefix for standard column names.

•	Start Number:  Select the starting value for the numeric portion of the names (useful when you intend to merge the file with another Megafile Manager file).


  Megafile Manager Verify Column Names - Formats

When you select Yes, STATISTICA will examine all specified columns to determine whether the column formats are an appropriate "fit" to the data values.  For example, the value 1234.5 entered in a column whose format is 4.3 would result in the column format being expanded to 8.3 in order to accommodate the data (represented as 1234.500).  Also, if the format is longer than any of the values in the column (e.g., the value 12.34 in a column with a 15.7 format) the format length will be adjusted to the actual length of the longest value (however, the number of decimal places remains unchanged).


  Megafile Manager - Descriptive Statistics

Select this option in order to compute the mean, standard deviation, standard error, variance, skewness, and kurtosis for numeric and logical columns of data in Megafile Manager files.  The results of these analyses are saved as Megafile Manager files which may then be opened for further processing (e.g., editing, exporting, merging, etc.). Text variables are automatically excluded from the analysis.  The following options are available when you select Descriptives from the Analysis pull-down menu.

Descriptive Statistics dialog:

Columns

Rows

Descriptive Statistics

NOTE:  The descriptive statistics output is saved to a Megafile Manager file (you will be prompted to select the file name).  The first column of the output file always contains names of the descriptive statistics (mean, std.dev, etc.).  All other columns are Double Float and they store the values of the respective statistics with 15-digit precision.


  Megafile Manager Descriptive Statistics - Columns

Click on this button to open the Select Columns dialog in which you can select the columns for the analyses.


  Megafile Manager Descriptive Statistics - Rows

Click on this button to open the Select Rows dialog in which you can select the rows for the analyses.


  Megafile Manager Descriptive Statistics - Descriptive Statistics

Select the desired descriptive statistics here.

Mean:  Set this check box to compute the means of the selected columns.

Standard deviation:  Set this check box to compute the standard deviations.  The standard deviation is computed as the square root of the sum of squared deviations (from the mean) divided by n-1.

Valid n:  Set this check box to compute the number of valid rows for each selected column.

Standard error of the mean:  The standard error of the mean is computed as the standard deviation divided by the square root of n.

Variance:  Set this check box to compute the variances.  The variance of a column is computed as the sum of squared deviations (from the mean) divided by n-1.

Skewness:  The skewness is a measure of the symmetry of the distribution of values.  If the distribution is symmetrical, then the skewness is equal to zero.

Kurtosis:  The kurtosis is a measure of "peakedness" of the distribution of values.  If the distribution follows the standard normal distribution, then the value of the kurtosis is zero.


  Megafile Manager - Correlations

This option computes the Pearson product-moment correlations between selected columns.  The following options are used to select the range of data to be analyzed and the output format.

Correlations dialog:

Columns

Rows

Pairwise deletion of missing data

Display n

Display p-levels

NOTE:  The correlation matrix output is saved to a Megafile Manager file (you will be prompted to select the file name).  The format of the output varies according to the requested statistics.  The first column always contains the column names (and optionally the labels for the n's and p-levels).  If the Display n and/or Display p-levels options are selected, then all columns of the output file will be created as text columns (to permit the inclusion of text strings such as p<), and the correlation coefficients will be displayed with only six digits of precision.  If neither the Display n and/or Display p-levels options are selected, then the correlation matrix will be stored in double float columns (and the coefficients may be displayed with up to 15 digits of precision).  Therefore, if you are planning to process the output correlation matrix to STATISTICA (see Convert to STATISTICA and Export to STATISTICA) or another application (see Export), do not request to display the n's and p-levels.  Note also that in order to use the Megafile Manager correlation matrix as input for analyses in STATISTICA modules, (e.g., Multiple Regression, Canonical Correlation, Reliability and Item Analysis, Cluster Analysis, Multidimensional Scaling, Factor Analysis, etc.), you will need to add four rows to the end of the resulting STATISTICA file so that STATISTICA will recognize it as a matrix format file (see Matrix File Format for instructions as to the information that needs to be entered into those additional four rows).


  Megafile Manager Correlations - Columns

Click on this button to open the Select Columns dialog in which you can select the columns of the current Megafile Manager file to be included in the correlation analysis.


  Megafile Manager Correlations - Rows

Click on this button to open the Select Rows dialog in which you can select the rows of the current Megafile Manager file to be included in the correlation analysis.


  Megafile Manager Correlations - Pairwise Deletion of Missing Data

If this check box is set, then each correlation will be computed from all rows that have complete (valid) data for the respective pair of columns (i.e., pairwise deletion of missing data), possibly resulting in unequal n for different correlations.  If this check box is not set (i.e., casewise deletion of missing data), then only the rows that have complete (valid) data for all columns that are currently selected for the analysis will be included in the computation of the correlations.


  Megafile Manager Correlations - Display n

If this check box is set, then clicking OK in this dialog will produce an expanded format correlation matrix; each cell in the matrix will not only contain the respective correlation coefficient but also the valid n (if the Pairwise deletion of missing data check box is not set).


  Megafile Manager Correlations - Display p-levels

If this check box is set, then clicking OK in this dialog will produce an expanded format correlation matrix; each cell in the matrix will not only contain the respective correlation coefficient but also the p-level (if the Pairwise deletion of missing data check box is not set).


  Megafile Manager - Frequencies

This option allows you to compute frequency tables for the selected variables based on the specified mode of categorization (see below).  After clicking OK in this dialog, you will be requested to specify a file name under which the resulting frequencies can be saved.

Frequencies dialog:

Columns

Rows

Mode

Warning level

NOTE:  The frequency output is saved to a Megafile Manager file (you will be prompted to select the file name).  The first column of the output file contains the name of each tabulated column (repeated as many times as there are distinctive values or ranges for that column).  The second column (also text) contains the names of consecutive specific values or ranges.  The third column (labeled Freq_ncy) contains the actual frequency counts (stored in LongInteger format) for each value or range.  If desired, the output file may be reorganized by performing a hierarchical (nested) sort as follows:  select the first column (Name, i.e., the column names) as the first key, then select as the second key either the second column (Values, if each set of frequencies is to be sorted by values), or the third column (Freq_ncy, if each set of values is to be sorted by frequency).


  Megafile Manager Frequencies - Columns

Click on this button to open the Select Columns dialog in which you can select the columns for the analyses.


  Megafile Manager Frequencies - Rows

Click on this button to open the Select Rows dialog in which you can select the rows for the analyses.


  Megafile Manager Frequencies - Mode

The settings in this box will determine how the currently selected columns will be categorized or tabulated for the frequency tables.

Integer values:  If this radio button is set, then the frequency tables will be based on integer category (interval) boundaries and step sizes, starting with the smallest integer value found in the respective column.  All non-integer values will be rounded up or down to integer values in order to place them in integer categories.

Distinct values:  Select this option if you want the frequencies to be based on all of the distinct values for each of the selected columns.  They can be either numeric or text (or logical) values.

No of intervals:  If this radio button is set, then the entire range of values for each numeric column will be divided into the user-specified number of intervals.

Text values are always tabulated by Distinct values (see above).


  Megafile Manager Frequencies - Warning Level

Specify here, the limit on the number of categories for integer and distinct values tabulations.  If the limit is exceeded, then a warning message Specified number of distinct values exceeded.  Continue? (Yes/No/Cancel) will be issued, permitting the analysis to be completed or terminated.  This option is always used when tabulating text values, but has no effect when tabulating numeric values using the No. of intervals mode of categorization.


  Megafile Manager - Options Menu

The following options are available from the Megafile Manager Options pull-down menu.

General	Stats Graphs

Display	User Graphs

Print

Macro

Command Langage (SCL)	Keyboard Macro

STATISTICA BASIC	Recorded Show Macro

Quick Open File	Customize Auto Task Buttons


  Megafile Manager - Window Menu

The following options are available from the Megafile Manager Window pull-down menu.

Scrollsheet Manager	Tile Vertically

Graph Manager	Arrange Icons

Cascade	Close All

Tile Horizontally


  Megafile Manager - Help Menu

The following options are available from the Megafile Manager Help pull-down menu.

Index	Search Help On

Spreadsheet	Glossary

Scrollsheet	Keyboard

Graph	Advisor

Text/Output	About


  Megafile Manager - Select Columns

This dialog opens whenever you are requested to select columns from a single list.

Select Column dialog:

Selecting Columns

De-selecting Previously Selected Columns

Next >> and Previous << buttons

Select All

Spread/Shrink

Zoom


  Megafile Manager Select Columns - Selecting Columns

Select columns in this dialog either by highlighting them or entering the column numbers in the edit window (e.g., 1 25-50 56) and then clicking on the OK button.  If you choose to select the columns by highlighting them in the list, you can select a continuous block of columns by holding down the left-mouse-button and dragging the cursor over the columns that you want to highlight.  You can also highlight a continuous block of columns by clicking on the first column name that you want to select, and while holding down the SHIFT key, clicking on the last column name that you want to select.  This method will select (highlight) the first and last columns and all columns in-between.  You can select discontinuous blocks of columns by holding down the CTRL key and then clicking on each column that you want to select.


  Megafile Manager Select Columns - De-selecting Previously Selected Columns

You can de-select discontinuous or continuous blocks of previously selected columns by holding down the CTRL key and then clicking on each column that you want to de-select.  Alternatively, you can de-select columns by deleting the column number(s) from the list of columns in the edit window.


  Megafile Manager Select Columns - Next >> and Previous << Buttons

Up to 4000 columns can be displayed in the window (page) in this dialog.  If the Megafile Manager file contains more than 4000 columns, then the display of the columns in this window will be "broken down" into pages and Next and Previous buttons will appear allowing you to move forward or backward among the "pages" of column listings.  Selections made in one page of the column listings will be retained in the edit window while making selections in other pages.  In other words, highlighting column names in the window will affect only that part of the numeric list of columns in the edit box which apply to the current "page" of column names.


  Megafile Manager Select Columns - Select All

Click this button to automatically select all of the columns in the list.  Alternatively, you can enter an  *  (asterisk) in the edit window to select the entire list of columns.


  Megafile Manager Select Columns - Spread/Shrink

When you click on this button, any long names associated with each column will be displayed.  Click on this button again to remove the long names from the list.  Note that this option may not be available when the list of columns is very long.


  Megafile Manager Select Columns - Zoom

Clicking this button will open the Column Values Window for the first of the highlighted columns in which you can browse through a sorted list of the data values.


  Megafile Manager - Select a Single Column

This dialog opens whenever you are requested to select one column from a list of columns.

Select Column dialog:

Selecting Columns

Next >> and Previous << buttons

Spread/Shrink

Zoom


  Megafile Manager Select a Single Column - Selecting Columns

Select a column in this dialog either by double-clicking on the column name or by highlighting it (clicking once on the column name) and then clicking on the OK button.


  Megafile Manager Select a Single Column - Next >> and Previous << buttons

Up to 4000 columns can be displayed in the window (page) in this dialog.  If the Megafile Manager file contains more than 4000 columns, then the display of the columns in this window will be "broken down" into pages and Next and Previous buttons will appear allowing you to move forward or backward among the "pages" of column listings.


  Megafile Manager Select a Single Column - Spread/Shrink

When you click on this button, the long names (if there are any) associated with each column in the list will be displayed.  Click on this button again to remove the long names from the list.  Note that this option may not be available when the list of columns is very long.


  Megafile Manager Select a Single Column - Zoom

Clicking this button will open the Column Values Window in which you can browse through a scrollable, sorted list of the data values for the highlighted column.


  Megafile Manager - Select Rows

The Select Rows dialog opens whenever you are requested to specify a range of rows.  Enter either a continuous (e.g., 1-280) or discontinuous (e.g., 1 25-50 235-240) range of row numbers in this dialog.  Optionally, you can click on the Select All button in order to automatically select all rows in the current Megafile Manager file.


  Megafile Manager - View Column Values

This window allows you to examine the values of a column, as well as its name, missing data value, format and long name (if there is one).

Column Values:  The column values are presented in a scrollable, sorted list through which you can browse.  This window is accessed by pressing the Zoom button in a dialog and you can return to that dialog by clicking OK in this window, or by selecting the Column Values option from the right-mouse-button flying menu.


  Megafile Manager - Find Value

The Find dialog will enable you to search for a specific data value (text or numeric) in the currently highlighted column of the Megafile Manager file.

Find dialog:

Find What

Direction

Match whole word only

Match case

Find Next

Hint:  You can repeat the search by pressing CTRL+F.


  Megafile Manager Find Value - Find What

Specify here the column value (text or numeric) that you want to search for in the Megafile Manager file.


  Megafile Manager Find Value - Direction

Find will search either above (select the Up option button) or below (select the Down option button) the currently highlighted cell, but will stop the search when it reaches the top or bottom of the file.


  Megafile Manager Find Value - Match Whole Word Only

Select this option when you want to search for a whole word (e.g., male) and not places where the word may be a subset of a larger word (e.g., female).


  Megafile Manager Find Value - Match Case

Select this option when you want to match the uppercase and lowercase formatting of the word exactly (e.g., Females instead of females).


  Megafile Manager Find Value - Find Next

After you have specified the above options, click on this button to begin the search.  When there is more than one match, Find will pause so that you can either exit (Cancel button) the dialog, or click Find Next to search for the next match.


  Megafile Manager - Replace Value

The Replace dialog will enable you to search for a specific data value (text or numeric) in the currently highlighted column and replace it with a different value.

Replace dialog:

Find What

Replace With

Direction

Match whole word only

Match case

Find Next

Replace All


  Megafile Manager Replace Value - Find What

Specify the column value (text or numeric) that you want to search for and replace.


  Megafile Manager Replace Value - Replace With

Specify the value (text or numeric) here that will be used to replace the value or text that you are searching for.


  Megafile Manager Replace Value - Direction

Replace will search either above (select the Up option button) or below (select the Down option button) the currently highlighted cell or text, but will stop the search when it reaches the top or bottom of the file.


  Megafile Manager Replace Value - Match Whole Word Only

Select this option when you want to search for a whole word (e.g., male) and not places where the word may be a subset of a larger word (e.g., female).


  Megafile Manager Replace Value - Match Case

Select this option when you want to match the uppercase and lowercase formatting of the word exactly (e.g., Females instead of females).


  Megafile Manager Replace Value - Find Next

After you have specified the above options, click on this button to begin the search.  When Megafile Manager has found the specified text or value, you will be given the following choices to replace it:

Yes:  Click this button to replace the text or value with your specified replacement.

No:  Click this button to skip over this value (it will not be replaced).

Yes to All:  Click this button to replace all of the text or values that match without asking for confirmation.

Cancel:  Click this button to quit the search and leave the dialog.


  Megafile Manager Replace Value - Replace All

Click this button instead of the Find Next button to replace all values or text that match.  You will not be prompted to accept or reject each replacement.


  Megafile Manager - Global Width

The value entered in this dialog (minimum = 1, maximum = 63) determines the width of all selected columns (From column, To column) in the Megafile Manager file.  (This is a global operation, in that the value which you specify here will be applied to the specified range [inclusive] of columns in the file.)  Note that text values longer than 63 characters (up to 255 characters) can be reviewed by scrolling within their respective fields.


  Megafile Manager - Language (MML)

MML (Megafile Manager Language) is a specialized data base management and data transformation programming language integrated into the Megafile Manager window (accessible from the Data Management module).  MML is a simple but very powerful programming language, similar to Pascal in terms of its general syntax conventions.  MML offers extensions designed to aid transformations of data and statistical data base management.

Selecting this option will open an MML program window for the current Megafile Manager data file (i.e., the one which is active when MML is invoked).  Each MML program window is associated with the Megafile Manager data file window from which it was opened and the name of that data file is displayed in the caption bar of that MML program window.  In order to process a different Megafile Manager data file using a program that is already in a MML window not associated with that data file, open a new MML program window for that data set (i.e., select the Language (MML) option when that data set window is active) and copy the program to that window.

For more information about MML, select one of the following topics.

Index

Overview of MML	Syntax Reference

Quick Examples	Execution

Advanced Examples	Error Messages

Quick Syntax

Options

MML Options

Pause

Read


  Megafile Manager - Overview of MML (Megafile Manager Language)

Introduction

How MML Works

For more information, see the following topics:

Quick Examples	Syntax Reference

Advanced Examples	Execution

Quick Syntax	Error Messages


Megafile Manager Overview of MML - Introduction

  Megafile Manager Overview of MML (Megafile Manager Language) - Introduction

All transformations of Megafile Manager data, calculating values of new columns as a function of other columns, changing values of text columns, recoding data, as well as a variety of data base management and report file generation functions can be performed via MML (Megafile Manager Language), a simple but very powerful language (similar to Pascal) that is built into Megafile Manager.

Probably the most important advantage of MML is that it operates directly on your Megafile Manager data files and it recognizes their structure, column names, missing data, etc.  The user does not have to be concerned about input/output of data because it is handled automatically by MML:  all data from the current Megafile Manager data file are automatically available in the program and if you change their values, they will be automatically updated in the disk file.

MML was designed for users with different levels of computational needs and programming experience, from novices to advanced programmers.

MML for novices.  MML does not require any programming experience.  It can be used to write simple (formula oriented) statements to transform your data (e.g., place an average of columns 1 and 2 in column 3).  A number of small (several lines long) annotated example programs can be accessed in the Electronic Manual (accessible by pressisng one of the Help buttons on the MML toolbar) which perform typical operations (see Quick MML Examples).  Thus, even if you have never programmed before, you will be able to modify these sample programs easily to meet your specific needs.

MML for advanced users.  More experienced users will find MML comprehensive and powerful enough for the development of even large and sophisticated data analysis and data base management applications.  For example, programs written in MML support operations on relationally connected data files, and a variety of advanced functions that are useful in writing process simulation programs, Monte Carlo experiments, etc. (e.g., specialized functions are supported to generate random numbers following specific theoretical distributions, such as Normal or Poisson).  MML features an integrated compiler to speed up the execution of large programs.


Megafile Manager Overview of MML - How MML Works

  Megafile Manager Overview of MML (Megafile Manager Language) - How MML Works

All options and dialogs of MML are available from the MML window (which can be accessed by selecting the Language (MML) option from the MFM Analysis pull-down menu in the Megafile Manager window).

How to run an MML program.  The following steps are necessary in order to execute an MML program on your Megafile Manager data file:

•	You can write a new MML program in the MML window or open a previously-saved MML file using the Open Text option from the pull-down menu File of the MML window.  For example, a very simple program could look like this:

begin

  Write(' STATISTICA ')

end

•	After the program is written (or opened), press the Execute button on the MML window toolbar or select the Execute option in the MML window Analysis pull-down menu.  During compilation MML verifies the syntax of the program and also translates it into machine code which speeds up the execution.

•	During the execution of the program, the output (if any was requested) is displayed in the Text/output Window; the changes made in the Megafile Manager data file can be seen in the Megafile Manager spreadsheet in the background or can later be examined by clicking on the Megafile Manager file to bring it to the front.

Accessing data from Megafile Manager files.  MML processes the "current" Megafile Manager data file (i.e., the one for which the MML window was opened, see above).  Each MML program window is associated with the Megafile Manager data file from which is was opened and the name of that data file is displayed in the caption bar of that MML program window.  In order to process a different Megafile Manager data file using a program that is already in an MML window not associated with that data file, open a new MML program window for that data set (check the Language (MML) option when that data set window is active) and copy the program to that window.

Sequential processing of records of data.  MML programs are normally executed for each record of the currently open Megafile Manager data file (in a sequential manner, one record at a time).  However, a variety of facilities are supported in MML to select specific records for processing and/or to pass values of variables across records.

Test running the program.  There is an option to test run (i.e., "dry run") the program before it is finally executed on your Megafile Manager data file (see Test Run).  Test running allows you to inspect the calculated values and check for unexpected consequences of the data processing operations requested in the program (e.g., depending on the values encountered by the program in the data file, some data transformations may potentially lead to division by zero, illegal function calls, etc.).

Reversing the changes to data made in MML.  As in all other operations of Megafile Manager which involve modification of data, MML processes data in a temporary work file created by Megafile Manager.  Therefore, as long as you do not overwrite the original disk file (by saving the processed file over it - via Save from the Megafile Manager File pull-down menu) you can always return to the original.

Uppercase/lowercase conventions.  MML does not differentiate between lower and uppercase letters (in variable names, MML keywords, names of user-defined procedures, etc.), unless they are contents of string (i.e., text) values.  However, a set of conventions will be followed in the examples in order to increase readability:

•	names of columns in Megafile Manager data files are all uppercase (e.g., AGE, NAME, INCOME);

•	names of MML language keywords that are not "standard objects" (see below) are all lowercase (e.g., begin, if, recode);

•	names of MML "standard objects" (constants, reserved variables, standard functions and procedures, etc.) and user-declared objects are capitalized (e.g., Pi, CaseNo, Pause, MyVar).


  Megafile Manager - Quick MML Examples

Example Program 1:  Computing an Average of Two Columns

Example 2:  Using Conditional Statements (block if .. then .. else .. undefined) and Interactive Verification and Editing of Data

Example 3:  Using Loops and Passing Values of Variables between Records

Example 4:  Verification and Analysis of Data using the Recode Statement

Example 5:  Math Operations, Random Numbers

Example 6:  Operations on Strings (texts) and Dates, Printing Reports

Example 7:  Relational Operations on Two Data Files

See also, Introductory Overview.


  Megafile Manager - Quick Example MML Program 1

Example Program 1:  Computing an Average of Two Columns

This simple example demonstrates the basic elements of the syntax of all MML programs; we will illustrate how to calculate a value of one column based on values of other columns in a Megafile Manager data file.  The example data file EX1.MFM contains columns named INCOME1, INCOME2, and AV_INC, and the MML file EX1.MML contains the MML program for this example.

To run the MML program in this example, see How to run MML programs.

program Average;

{program name (optional)}

begin

{beginning of the main body of the program, this

 first word "begin" can be interpreted as: "for each

 row of the data file, do the following:"}

  AV_INC := (INCOME1+INCOME2)/2;

{compute the average of the values in columns

 INCOME1 and INCOME2 and place it in column

 AV_INC}

end

{end completes the program}

Once the program is completed, you can view the results by clicking on the Text/output Window in order to bring it to the front of the window.

NOTE:

•	You may optionally use a program name.

•	The program does not discriminate between uppercase and lowercase letters (e.g., Average = AVERAGE = AvErAgE ).

•	The main body of the program is enclosed between the words begin and end, and the statements enclosed in the main body are executed (i.e., "repeated") for each record of the current data file.  There can also be other blocks of statements (enclosed between separate begin and end statements) nested within the main body (as shown later).

•	The columns in the Megafile Manager data file can be referred to by their original names (they can also be referred to by their numbers as explained later).

•	Comments are enclosed in curly brackets: {comment}.

For more advanced examples, see:

Advanced Example 1:  Using Intrecode and Recode Constructions

Advanced Example 2:  Using User-defined Procedures; let...be...do Construction

Advanced Example 3:  Processing Data in Related files

Advanced Example 4:  Interactive Reprocessing of Data in Related Files


  Megafile Manager - How to run MML Programs

To run an example MML program, follow the steps outlined below.

Step 1:	In the Data Management or Megafile Manager window, click on the Open MFM Data option in the File pull-down menu and select the Megafile Manager file (e.g., EX1.MFM).

Step 2:	Select the option Language (MML) in the MFM Analysis pull-down menu to open the MML window.

Step 3:	Click on the Open Text option from the MML window File pull-down menu and select the appropriate program file (e.g., EX1.MML).

Step 4:	To run the program, click on the Execute button on the MML window toolbar.  To view the results of this program, click on the Megafile Manager file in order to bring it to the front.


  Megafile Manager - Quick Example MML Program 2

Using Conditional Statements (block if .. then .. else ..
undefined) and Interactive Verification and Editing of Data

For this example, use the Megafile Manager file EX2.MFM which contains data on patients of a hospital.  This example program (contained in the MML file EX2.MML) will illustrate how to verify one aspect of those data: We will test whether data in column PREGN (pregnancy data) are formally correct.  Specifically, we will test whether all patients who either were or currently are pregnant (i.e., with value of PREGN greater than 0) are females, and whether they are older than 15 years:

To run the MML program in this example, see How to run MML programs.

program VerPreg;

{program name (optional)}

begin

{beginning of the program}

  if (PREGN > 0) and

{if this patient was/is pregnant}

     ((AGE < 15) or

{and is either younger than 15 or}

     (GENDER = 'MALE')) then

{is a male, then}

    Pause

{let's pause to look at the data}

  else

{otherwise, the data are OK}

    Write(CaseNo,' row: Pregn. O.K.')

{and we will mark this fact in the Text/output
Window (see below), along with the current record
(i.e., "case") number}

  undefined

{however, if any of the values of columns used
in this "conditional statement" (i.e., PREGN,
AGE or GENDER) are undefined (i.e., equal
to MD), then}

    Write(CaseNo,' row: Pregn. = ??');

{let's mark it in the Text/output Window}

  Writeln

{advance the output to the next line}

end

{end of the program}

Once the program is completed, you can view the results of the verification by clicking on the Text/output Window in order to bring it to the front of the window.

NOTE:

•	The procedure called Pause is used to temporarily stop the program and review and/or edit values of all columns of the currently processed record of data.  The Write procedure is used to open and display the output in the Text/output Window (and/or send the printer, depending on the selection in the Page/Output Setup dialog).

•	The program uses the block if .. then .. else .. undefined statement to select:

(a)  records that meet the specified conditions (i.e., if .. then ..),

(b)  records that do not meet those conditions (.. else ..), and

(c)  records for which it cannot be determined whether the conditions are met or not because they have missing data in any of the columns specified in the conditions (.. undefined ..).

For more advanced examples, see:

Advanced Example 1:  Using Intrecode and Recode Constructions

Advanced Example 2:  Using User-defined Procedures; let...be...do Construction

Advanced Example 3:  Processing Data in Related files

Advanced Example 4:  Interactive Reprocessing of Data in Related Files


  Megafile Manager - Quick Example MML Program 3

Using Loops (for .. to .. do) and Passing Values of
Variables Between Records (using static variables)

The Megafile Manager file (EX3.MFM) used in this example contains data on sales in 8 stores of a chain, and the records represent consecutive weeks (see below).

WEEK      DATE     SHOP1 . SHOP10 WEEKINC TOTALINC

---- ------------- -----   ------ ------- --------

  2   7.01 - 13.01 304.1 . 909.66      MD       MD

  3  14.01 - 20.01 333.9 . 888.66      MD       MD

  4  ...

The columns WEEKINC and TOTALINC were reserved for weekly totals of all stores and the running total for the year, respectively.  These values will be computed in the following example program.  For each record, the total sales in each week (i.e., record) will be computed and then the running total will be updated by that amount.  File EX3.MML contains the MML program for this example.

To run the MML program in this example, see How to run MML programs.

program CountInc;

{program name (optional)}

  var i : integer;

{declaration of a "local" integer variable i
that will be used in the loop}

  static TotInc : real;

{declaration of a static variable TotInc
that will be used to pass the value of
the running total between consecutive records}

begin

{beginning of the program main body}

  WEEKINC := 0;

{at the beginning of processing each
record, set the value in data column
WEEKINC to 0 (originally it was MD)}

  for i := 3 to 10 do

{start the loop in which we will add up
sales in all 8 stores (columns 3 to 10)}

    WEEKINC := WEEKINC + V(i);

{this (single) statement inside the loop will
generate the total for all 8 stores; in this
example, we use an "indexed" way of referring
to columns: V(xxx), where xxx is the column
number}

  if WEEKINC then

{if the value of WEEKINC is not 0,}

    TotInc := TotInc + WEEKINC;

{add it to the "moving total" TotInc,}

  TOTALINC := TotInc;

{then place the value of TotInc in column
TOTALINC of the data file}

end

{end of the program}

To view the results of this program, click on the Megafile Manager file EX3.MFM in order to bring it to the front of the window.

The above program is an example of the use of "declaration of variables" (i.e., the part of the program between the program title and the word begin that starts the main body of the program).  Declaration is necessary whenever you need to use objects that are not "standard objects" of MML and that did not come from the data file (as did WEEKINC and TOTALINC).  In this example, a local variable i (to be used as a loop counter) and a global (static) variable TotInc are needed.  Remember that every MML program is executed ("repeated") for each consecutive record of the data file and values of all local variables of the program are reset to Missing data at the beginning of processing each record; however, static variables do not lose their values between records, and thus you can use them to collect data "across" records.

Another technique used in this example is the loop.  A loop causes a cycle of repetitions of operations (specified within the loop); each time the loop is executed the loop counter is incremented.  For example:

WEEKINC := 0;

for i := 5 to 10 do

   WEEKINC := WEEKINC + V(i);

is equivalent to:

WEEKINC := V(5)+V(6)+V(7)+V(8)+V(9)+V(10);

Another convention introduced in this example is the alternative way of referencing columns.  In MML programs, you can reference columns either by their original names (see Example 1), or you can use a reserved "indexed" variable V(xxx), where xxx is the consecutive number of the column in the data file.  For example, V(10) means: column number 10.  The obvious advantage of using this convention is that it allows you to use loops to perform operations on lists of consecutive columns (as in the current example).  In most other cases though, using actual names of columns is preferable (see the description of V(xxx)).

For more advanced examples, see:

Advanced Example 1:  Using Intrecode and Recode Constructions

Advanced Example 2:  Using User-defined Procedures; let...be...do Construction

Advanced Example 3:  Processing Data in Related files

Advanced Example 4:  Interactive Reprocessing of Data in Related Files


  Megafile Manager - Quick Example MML Program 4

Verification and Analysis of Data using the Recode Statement

File EX4.MFM contains data on sales offices of a large corporation (one record per office) and file EX4.MML contains the MML file for this example.  Each record contains data on one sales office and consists of a number of fields (e.g., NAME - name of the general manager, CITY - location of the office, PHONE - phone number, VALUE - monthly sales, etc.).  In the current example program, the names of cities will be verified and at the same time the total sales for groups of offices located in different regions of the world will be computed.  One way to do this is to define a recode function, which can transform one type of variable into another (e.g., text into numeric).  The recode function for this example will be specified such that it will "translate" the name of each recognized city into an integer code denoting a region of the world.

Before they can be used, all user-defined functions need to be declared (and defined).  In this example, the following function will be used:

recode Class(string[20]):integer;

{function declaration: name of the function is
Class, and it will transform string (i.e., text) values
up to 20 characters long into integer values, i.e.,
the function will return integers}

begin
{beginning of recodes}

  'New York','Dallas','Los Angeles','Detroit' = 1;
{USA}

  'Hamburg','London','Manchester','Paris' = 2;
{Western Europe}

  'Melbourne','Sydney','Canberra' = 3;
{Australia}

  'Moscow','Prague' = 4;
{Eastern Europe}

  Missing = -1
{Missing Data}

  else 0
{Error !}

end;
{end of the recoding function declaration}

Now, this function can be used to convert strings (names of cities) into integers 1 through 4.  The function will return -1 if the value for the string is Missing, or 0 if the string cannot be recognized (i.e., when it is not one of the cities defined in the function).  For example, if we use the statement x := Class(CITY); and if the value of CITY is Paris, then the value 2 will be returned (i.e., in this case, placed in variable x).

The recode function is very versatile and can be used for many purposes.  In the current example, it will be used to verify the names of cities in the data file and at the same time to calculate total sales for regions.

To run the MML program in this example, see How to run MML programs.

program Sales;

{program name (optional)}

static USA, WE, Aus, EE : real;

{declare static variables (for region totals)}

recode Class(string[20]):integer;

{declare/define the recode function}

begin

  'New York','Dallas','Los Angeles','Detroit' = 1;
{USA}

  'Hamburg','London','Manchester','Paris' = 2;
{WE  (Western Europe)}

  'Melbourne','Sydney','Canberra' = 3;
{Aus (Australia)}

  'Moscow','Prague' = 4;
{EE  (Eastern Europe)}

  Missing = -1

  else 0

end;

begin

  case Class(CITY) of

{beginning of the case block that will

check the region and update the

respective region total}

    1 : USA := USA + SALES;

{if USA (i.e., if Class(CITY) is equal

to 1), update the USA sales}

    2 : WE := WE + SALES;

{if Western Europe (i.e., if Class(CITY)

is equal to 2, update the WE sales}

    3 : Aus := Aus + SALES;

{if Australia (i.e., if Class(CITY)

is equal to 3), update the Aus sales}

    4 : EE := EE + SALES;

{if Eastern Europe (i.e., if Class(CITY)

is equal to 4), update the EE sales}

    0 : Pause;

{if value of Class(CITY) is 0, then it

means that CITY is not among

those defined in function Class, thus,

let's pause to examine/edit the data}

   -1 : Delete;

{if CITY is Missing, then delete this

record from the data file}

  end;

{end of the case block}

  Write(CaseNo,' USA:',USA,' WEST EUROPE:',WE, ' AUSTRALIA:',Aus,' EAST EUROPE:',EE);

{now, write updated values of sales to the screen}

  Writeln;

{advance the output to the next line}

end

{end of the program}

Once the program is completed, you can view the results by clicking on the Text/output Window in order to bring it to the front of the window.

NOTE:

•	The Pause procedure is called in this program in the event an error is encountered (i.e., when a city name is encountered that was not specified in the recode function Class).  Calling this procedure will open a dialog in which you can review and edit all values of the currently processed record of data.  The Write procedure is used to open and display the output in the Text/output Window (and/or to the printer, depending on the selection in the Page/Output Setup dialog).

•	This program uses the construction case which can be considered to be a more powerful version of the if .. then block.  The case block used in this example can be interpreted as follows: If the value of function Class of value CITY is equal to 1, then add the current value of SALES to variable USA, if it is equal to 2, then add SALES to WE, if 3, then add it to Aus, etc.

•	The program uses static variables, whose values are preserved from record to record (i.e., they are not reset automatically to missing data before the processing of each new record begins, as is the case with local variables).

•	All declarations (i.e., declarations of variables and of user defined functions - in this case, one recodefunction) are located at the beginning of the program, before the begin that starts the main body of the program.

•	The MML procedure Delete deletes the entire current record from the data file.

For more advanced examples, see:

Advanced Example 1:  Using Intrecode and Recode Constructions

Advanced Example 2:  Using User-defined Procedures; let...be...do Construction

Advanced Example 3:  Processing Data in Related files

Advanced Example 4:  Interactive Reprocessing of Data in Related Files


  Megafile Manager - Quick Example MML Program 5

Math Operations, Random Numbers

This example will illustrate some of the capabilities of the MML math library.  For this Megafile Manager data file (EX5.MFM), assume that values in column number 2 are expected to be a function of the sum of sines of values in columns number 3 and 4.  A random sample of records (approximately 10% of the total number of records) will be generated and the differences between the observed and expected values of the second column will be calculated.  A cumulative deviation of the observed values of that column from the expected values will also be calculated (i.e., calculate sin(VAR3) + sin(VAR4)).  The MML program for this example is contained in the file EX5.MML.

To run the MML program in this example, see How to run MML programs.

program Math;

{program name (optional)}

static Err : real;

{declare static variables Err (for error)}

       Obs : integer;

{and Obs (for the number of observations)}

begin

{beginning of the main body of the program}

  if Uniform(1) < 0.9 then

{draw a random number (following a uniform
distribution) from the range of [0,1] and
if it is less than 0.900, then}

    Exit;

{finish processing this record}

  Obs := Obs + 1;

{update the counter of observations (Obs)}

  Err := Err + abs(VAR2 - (sin(VAR3)+sin(VAR4)));

{update the value of accumulated error}

  Write('Error:',Err/Obs,'Obs:',Obs);

{write the number of observations and the
average error (Err/Obs) to the Text/output Window}

  Writeln;

{advance the output to the next line}

end

{end of the program}

Once the program is completed, you can view the results by clicking on the Text/output Window in order to bring it to the front of the window.

NOTE:

•	The Write procedure is used to open and display the output in the Text/output Window (and/or to the printer, depending on the selection in the Page/Output Setup dialog).

•	The program uses a Uniform(x) function to generate random numbers that follow the uniform distribution (from the range of 0 to x).

•	The procedure called Exit is used to finish processing the current record.

•	Static variables are used to compute the cumulative error and the total number of observations drawn by random (they are declared as real and integer, respectively).

For more advanced examples, see:

Advanced Example 1:  Using Intrecode and Recode Constructions

Advanced Example 2:  Using User-defined Procedures; let...be...do Construction

Advanced Example 3:  Processing Data in Related files

Advanced Example 4:  Interactive Reprocessing of Data in Related Files


  Megafile Manager - Quick Example MML Program 6

Operations on Strings (texts) and Dates, Printing Reports

This example data file (EX6.MFM) contains data on employees of a company and the MML program for this example is contained in the file EX6.MML.  The text column HIRED contains the dates (in the notation year/month/day) when each employee was hired.  In this example, employees that have been working for this company since before March 6, 1987 (i.e., records containing hiring dates that are earlier than March the 6th, 1987) will be selected, and all remaining records will be deleted from the data file.  A printed report containing the initial (i.e., the first letter of the first name) and the full last name of all employees that were hired after that date will also be created.

To run the MML program in this example, see How to run MML programs.

program TestDate;

{program name (optional)}

var YY,M,D : integer;

{"local" (not static) variables that will be
used to translate the date info into numbers}

begin

{begin the main body of the program}

  SDate( HIRED, YY, M, D );

{function SDate converts dates into numbers}

  if (YY > 1987) or

     ((YY = 1987) and ((M > 3) or

     ((M = 3) and (D > 6)))) then

{if the date is later than March 6, 1987, then}

    begin

{start a block}

      Write(CaseNo, Mid(FIRSTNAM,1,1) + '.' +

            LASTNAME, HIRED);

{display and print the data for this person}

      Delete;

{and delete this record}

    end;

{end of this block}

end

{end of the program}

Once the program is completed, you can view the results by clicking on the Text/output Window in order to bring it to the front of the window.

NOTE:

•	The Write procedure is used to open and display the output in the Text/output Window as well as to send the output to the printer, (depending on the selection in the Page/Output Setup dialog).

•	Function SDate converts a string (that follows any three-number date notation) into 3 numeric values representing the 3 components of the date.  The interpretation of those numbers is not limited to any particular order, thus dates in the US notation, European notation, as well as "computer notation" (yyyy/mm/dd) can be processed.

•	The specific list of values used in this program as an argument of the Write instruction illustrates

(a)  writing of variables and constants (string constants must be placed in quotation marks, e.g., '.');

(b)  so-called concatenation of strings (i.e., adding strings together using the + operator), and

(c)  the use of function Mid(a, x, y) which "extracts" from string a, a substring of y characters, starting at the x'th character of that string (in this case, this instruction was used to extract the first letter from the first name).

•	Procedure Delete is used to delete the current record from the data file.

For more advanced examples, see:

Advanced Example 1:  Using Intrecode and Recode Constructions

Advanced Example 2:  Using User-defined Procedures; let...be...do Construction

Advanced Example 3:  Processing Data in Related files

Advanced Example 4:  Interactive Reprocessing of Data in Related Files


  Megafile Manager - Quick Example MML Program 7

Relational Operations on Two Data Files

In this example we will illustrate the relational data base management capabilities of MML and its facilities to process hierarchically related records from two data files (when one record in one data file is related to a group of records in the second file).

In this example program, we will use the data file EX6.MFM (also used in the previous example) which contains names of employees of a company, and another (related) data file EX7.MFM that contains data on the children of those employees.  Some employees have more than one child, thus in some cases more than one record in the second data file is related to one record in the first data file.  For example:

       I file                     II file

---------------------     ----------------------

LASTNAME FIRSTNAM AGE     LNAME  CH_FNAME CH_GEN

-------- -------- ---     ------ -------- ------

Green    Stephen   39     Green  Teddy    Male

                          Green  Jimmy    Male

Hall     Mary      32     Hall   Andy     Male

Meyer    Doris     26

Rogers   Cathy     34     Rogers Debbie   Female

Smith    Jane      33     Smith  Robert   Male

                          Smith  Lacy     Female

                          Smith  David    Male

...                       ...

The purpose of this program is to add summary information to the first data file resulting from the analysis of data in the second data file.  Specifically, based on the second data file, the number of children and their gender for each employee will be determined, and this information will be written to the first data file.  Thus, you must first add two new columns to the first data file in order to store the data to be obtained from the second file; call these new columns MALE_CH and FEMA_CH.  You can do this easily in the Column Specifications dialog (via the pull-down menu Edit in the Megafile Manager window; both columns should be of type integer).

To run the MML program in this example, follow the steps outlined below.

Step 1:	In the Data Management or Megafile Manager window, click on the Open MFM Data option in the File pull-down menu and select the Megafile Manager file EX6.MFM.

Step 2:	Select the option Language (MML) in the MFM Analysis pull-down menu to open the MML window.

Step 3:	Before the data can be processed, you need to tell MML that a second data file will be used (in addition to the "first" or "main" data file that is currently open).  You can do this in the Megafile Manager: Options dialog.  Click on Options from the MML window Options pull-down menu to open the Megafile Manager: Options dialog.  Now, click on the Name button in this dialog and select file EX7.MFM as the second file.

Next, you need to instruct MML as to how to identify the specific records in the second data file (EX7.MFM) that are related to specific records in the first data file (EX6.MFM).  Specify column 1 in the edit fields next to the two options Key in main file and Key in relational file in the Megafile Manager: Options dialog.

The logic of this option (specifying a key column in each data file) is analogous to the one discussed in the context of relational merge options in Megafile Manager that are also based on matching values of key columns.  It allows you to "define a relation" between the two files by instructing MML which columns in the respective files correspond to each other (and thus where MML should look for values that will match).  In this example, the only way to identify related records in the data files is to look at the last names of employees (first file) and their children (second file).

Step 4:	Click on the Open Text option from the MML window File pull-down menu and select the program file EX7.MML.  This program is shown below.

program RelTest;

{name of the program (optional)}

var i : integer;

{declaration of a "local" variable i}

begin

{start of the main body of the program}

  MALE_CH := 0;

{initialize the number of male children to 0}

  FEMA_CH := 0;

{and female children to 0}

  for i:=1 to NofY do

{for each record in the 2nd data file that is related
to the current record of the main (i.e., 1st) data file}

  begin

{execute the following block of statements:}

    GetY(i);

{get the i'th related record}

    if CH_GEND = 'Male' then

{if it is a boy, then}

      MALE_CH := MALE_CH + 1

{update the number of boys}

    else

{otherwise (i.e., if it is a girl)}

      FEMA_CH := FEMA_CH + 1

{update the number of girls}

    undefined

{if MD encountered (errors in data?)}

      Write(CaseNo,': wrong record, no. ',i)

{write message (wrong record found in 2nd file)

  end;

{end of the block executed for the i'th record

(in the second file) related to the current

record (in the main data file)}

end

{end of the program}

Step 5: To run the program, click on the Execute button on the MML window toolbar.  Once the program is completed, you can view the results by clicking on the Text/output Window in order to bring it to the front of the window.

NOTE:

•	The Write procedure is used to open and display the output in the Text/output Window (and/or to the printer, depending on the selection in the Page/Output Setup dialog).

•	The columns of the second data file are referred to by their names (in the same way as columns of the main data file; they can also be referenced via a reserved indexed variable Y(xxx), where xxx is a column number).  The column names in the two files must not be duplicated.

•	The number of available records of the second data file that are related to the currently processed record (of the main data file) is stored in the reserved variable NofY ("Number of records Y").  MML updates the value of this variable for each consecutive record of the main data file (when it is open for processing), thus this information is always available.

•	Procedure GetY(i) ("Get record Y(i)") calls the i'th record of the second data file that is related to the current record of the main data file, and from this point on when you refer to columns in the second data file, values of this particular record will be returned.  The following loop illustrates the logic of accessing all consecutive records of the second data file that are related to the current record (of the main data file):

for i:=1 to NofY do

{for i equal to 1 through NofY (i.e., 1 through
the last "related" record)}

  begin

{execute the following instructions:}

    GetY(i);

{get the consecutive (i'th) related record}

    ...

{instructions that use data from that record}

    ...

{instructions ...}

  end;

{end of the loop}

For more advanced examples, see:

Advanced Example 1:  Using Intrecode and Recode Constructions

Advanced Example 2:  Using User-defined Procedures; let...be...do Construction

Advanced Example 3:  Processing Data in Related files

Advanced Example 4:  Interactive Reprocessing of Data in Related Files


  Megafile Manager - Advanced MML Examples

For more advanced examples, see:

Advanced Example 1:  Using Intrecode and Recode Constructions

Advanced Example 2:  Using User-defined Procedures; let...be...do Construction

Advanced Example 3:  Processing Data in Related files

Advanced Example 4:  Interactive Reprocessing of Data in Related Files


Megafile Manager - Advanced MML Examples (Using Intrecode and Recode Constructions)

  Megafile Manager - Advanced MML Example 1

Example 1:  Using Intrecode and Recode Constructions

This program illustrates the use of the intrecode and recode constructions.  The first four columns of Megafile Manager data file ANEX1.MFM contain information about tested persons (last name, first name, age and sex).  The next 20 columns contain their responses to the 20 questions of the test.  We will count the number of correct answers, compute the score (according to the weight of each question) and then categorize the final result of the test for each tested person.  The program will place the results in the last three columns of the data file (i.e., number of correct answers in NVALANS, final score in SCORE and final result in RESULT) which were originally empty (filled with missing data). The MML program is contained in the file ANEX1.MML.

To run the MML program in this example, see How to run MML programs.

program ExamRes;

{this program counts results of a test exam

containing 20 questions, each question having 5

 possible answers}

intrecode ValAns(1,20) = 1,4,3,2,5,2,4,4,2,1,4,1,3,5,2,4,5,2,2,3;

{ValAns defines numbers of correct answers for

 questions Q1, Q2,...,Q20, respectively}

intrecode QWeight(1,20) = 5,5,3,4,5,5,5,3,4,4,10,5,5,4,5,10,5,3,5,5;

{QWeight defines weights (measures of

 importance) for all questions: Q1, Q2,...,Q20}

recode PrntRes(integer) : string[10];

{PrntRes changes the result into text:}

begin

  0  .. 40  = 'VERY POOR';

  40 .. 50  = 'POOR';

  50 .. 67  = 'AVERAGE';

  67 .. 80  = 'GOOD';

  80 .. 90  = 'VERY GOOD';

  90 .. 100 = 'EXCELLENT'

end;

var i : integer;

{declare local variable}

begin

  SCORE := 0;

{initialize variable SCORE}

  NVALANS := 0;

{and the number of valid answers}

  for i := 1 to 20 do

    if Valid( V(4+i) ) then

{if the answer is not missing}

      if ValAns(i) = V(4+i) then

{and is correct }

      begin

        SCORE := SCORE + QWeight(i);

{then increment SCORE}

        NVALANS := NVALANS + 1;

{and the number of correct answers }

      end;

  RESULT := PrntRes( SCORE )

{categorize the result}

end

To run the program, click on the Execute button on the MML window toolbar.

See also:

Example 1:  Computing an Average of Two Columns

Example 2:  Using Conditional Statements (block if .. then .. else .. undefined) and Interactive Verification and Editing of Data

Example 3:  Using Loops and Passing Values of Variables between Records

Example 4:  Verification and Analysis of Data using the Recode Statement

Example 5:  Math Operations, Random Numbers

Example 6:  Operations on Strings (texts) and Dates, Printing Reports

Example 7:  Relational Operations on Two Data Files


Megafile Manager - Advanced MML Examples (Using User-defined Procedures; let..be..do Conventions)

  Megafile Manager - Advanced MML Examples

Example 2:  Using User-defined Procedures; let..be..do.. Conventions

This program illustrates the use of the let .. be .. do construction, a simple user-defined procedure.  The first three columns of the Megafile Manager data file ANEX2.MFM contain information (such as catalog number (NUMBER), technical symbol (SYMBOL) and the date when quality tests were last performed (LASTDATE)) about several products.  Columns 4 through 14 contain the results of tests obtained in various research laboratories: we assume that LAB1, RESLAB1, RESLAB2, RESLAB4, RESLAB5, LAB3DEP4, and LAB3DEP6 are results of tests performed on one particular feature (feature 1) of the products, and LAB2, RESLAB3, RESLAB6, and MAINLAB are results of testing another feature (feature 2; note the difference in results for the two groups).  We will find the maximum measurement for each feature (i.e., the maximum value in each group of columns), for each item listed in the data file.  The results will be placed in the last two columns MAX1 and MAX2 (for feature 1 and feature 2, respectively), which were originally empty (filled with missing data).  The MML program is in the file ANEX2.MML.

To run the MML program in this example, see How to run MML programs.

program Sort;

{program name (optional)}

var   TmpVar,

{declaration of local variables}

      Max : real8;

{this variable will store the current maximum}

procedure CompMax;

{this procedure updates the current maximum}

begin

  if TmpVar > Max then

{if the new value is greater than the current

maximum}

    Max := TmpVar

{assign new value to the maximum}

end;

begin

{find maximum of variables LAB1, RESLAB1,

RESLAB2, RESLAB4, RESLAB5, LAB3DEP4,

LAB3DEP6}

  Max := 0;

{initialize Max to 0 because all data > 0 }

  let TmpVar be [LAB1, RESLAB1, RESLAB2, RESLAB4,

                 RESLAB5, LAB3DEP4, LAB3DEP6] do

    CompMax;

{update Max via call to procedure CompMax}

  MAX1 := Max;

{store the result in the data file}

{computation of the first maximum is completed}

{find the maximum of LAB2, RESLAB3,

RESLAB6, and MAINLAB}

  Max := 0;

{initialize Max to 0 (again, all data > 0)}

  let TmpVar be [LAB2,RESLAB3,RESLAB6,MAINLAB] do

    CompMax;

{update Max via call to procedure CompMax}

  MAX2 := Max;

{store the result in the data file}

{computation of the second maximum is finished}

{now, prepare some simple output:}

  if CaseNo = 1 then

  begin

{write the output header}

    write(' NO     SYMBOL       DATE FIRSTMAX  SECONDMAX');

    writeln;

  end;

  write(NUMBER, SYMBOL, LASTDATE, MAX1, MAX2);

{the results are printed}

  writeln

{advance the output to the next line}

end

NOTE:

•	The let instruction allows you to repeat the same operation for a number of non-consecutive columns from the data file, which cannot be accomplished with an ordinary for loop (in this example we found the maximum values of two subsets of columns).  In this example, the let instruction was used in a somewhat unusual manner: it works in conjunction with the procedure CompMax, which receives its parameter in an indirect way via the variable TmpVar.

See also:

Example 1:  Computing an Average of Two Columns

Example 2:  Using Conditional Statements (block if .. then .. else .. undefined) and Interactive Verification and Editing of Data

Example 3:  Using Loops and Passing Values of Variables between Records

Example 4:  Verification and Analysis of Data using the Recode Statement

Example 5:  Math Operations, Random Numbers

Example 6:  Operations on Strings (texts) and Dates, Printing Reports

Example 7:  Relational Operations on Two Data Files


Megafile Manager - Advanced MML Examples (Processing Data in Related Files)

  Megafile Manager - Advanced MML Examples

Example 3:  Processing Data in Related Files

This program illustrates methods for handling two related files.  The main Megafile Manager data file ANEX3.MFM contains information (such as address, phone number, manager's name and quotes of expenses and sales) about several branch offices of a company.  Each office is identified by its number placed in the first column.  The related Megafile Manager data file ANEX3-R.MFM contains information about all employees who work for this company. This information includes name, age, date of hiring, and annual salary.  The number of the office for which a given person works is specified in the first column.  This program will count the average age, average sales, and average salary (per person) for each office of this company: such data can be helpful in assessing the efficiency of employees in comparison with their age and compensation.  The program will store the results in the last three columns of the main Megafile Manager file (i.e., AVAGE, AVSALES and AVSALARY) which were originally empty (filled with missing data).

To run the MML program in this example, follow the steps outlined below.

Step 1:	In the Data Management or Megafile Manager window, click on the Open MFM Data option in the File pull-down menu and select the Megafile Manager file ANEX3.MFM.

Step 2:	Select the option Language (MML) in the MFM Analysis pull-down menu to open the MML window.

Step 3:	Click on the Open Text option from the MML window File pull-down menu and select the program file ANEX3.MML.  This program is shown below.

program RelExam;

{program name (optional)}

var i,

{local variable used in the loop}

    TotAge, NbAge : integer;

{variables used for computing average age}

var TotSal : int4;

{variable used for computing average salary}

begin

  TotSal := 0;

{first, initialize the above variables:}

  TotAge := 0;

  NbAge := 0;

  for i := 1 to NofY do

{for each related record in the second file}

  begin

    GetY(i);

{load this record into memory}

    TotSal := TotSal + SALARY;

{increase total salary}

    TotAge := TotAge + Value(AGE);

{increase total age by value of AGE if the value

of AGE is not missing or otherwise 0}

    NbAge := NbAge + Valid(AGE);

{if AGE was not missing, increase NbAge}

  end;

  AvAge := TotAge div NbAge;

{compute average age using TotAge and NbAge}

  AvSales := SALES div NofY;

{compute sales per person}

  AvSalary := TotSal div NofY

{compute the average salary for this office}

end

Step 4:	Before the data can be processed, you need to tell MML that a second data file will be used (in addition to the "first" or "main" data file that is currently open).  You can do this in the Megafile Manager: Options dialog.  Click on Options from the MML window Options pull-down menu to open the Megafile Manager: Options dialog.  Now, click on the Name button in this dialog and select file ANEX3-R.MFM as the second file.

Next, you need to instruct MML as to how to identify the specific records in the second data file (ANEX3-R.MFM) that are related to specific records in the first data file (ANEX3.MFM).  Specify column 1 in the edit fields next to the two options Key in main file and Key in relational file in the Megafile Manager: Options dialog.

The logic of this option (specifying a key column in each data file) is analogous to the one discussed in the context of relational merge options in Megafile Manager that are also based on matching values of key columns.  It allows you to "define a relation" between the two files by instructing MML which columns in the respective files correspond to each other (and thus where MML should look for values that will match).  In this example, the only way to identify related records in the data files is to look at the number of the branch office (first file) and the employee's shop location number (second file).

Step 5:	To run the program, click on the Execute button on the MML window toolbar.

NOTE:  In this example, there is an important difference in the way we compute TotAge (total age) and TotSal (total salary): in the first case we use the functions Value and Valid, so that when missing data are encountered we can simply ignore it (we assume that information about employee's age is not essential).  In the case of salary we use simple addition: if missing data occurs the result will evaluate to Missing, which means that data are not complete (and should be checked).

See also:

Example 1:  Computing an Average of Two Columns

Example 2:  Using Conditional Statements (block if .. then .. else .. undefined) and Interactive Verification and Editing of Data

Example 3:  Using Loops and Passing Values of Variables between Records

Example 4:  Verification and Analysis of Data using the Recode Statement

Example 5:  Math Operations, Random Numbers

Example 6:  Operations on Strings (texts) and Dates, Printing Reports

Example 7:  Relational Operations on Two Data Files


Megafile Manager - Advanced MML Examples (Interactive Processing of Data in Related Files)

  Megafile Manager - Advanced MML Examples

Example 4:  Interactive Processing of Data in Related Files

This example illustrates further techniques for handling two related files, and simple methods of interactively aggregating data.  The main Megafile Manager data file ANEX4.MFM contains data on all positions in a company, such as maximum salary that will be offered, minimum aptitude test score, and minimum experience (in years).  Each position is identified by its number placed in the second column.  The related Megafile Manager data file ANEX4-R.MFM contains information (such as name, age, education, etc.) about candidates who applied for the job.  The position for which a given person applied is specified in the third column.  Our program will review all applicants for each position, select those who are qualified, and list their names and other information on the screen.  The user of the program can then interactively select the candidate that appears to be the best.  The names of selected applicants will be placed in the last two columns of the main file (LNAME, FNAME) which were originally empty (filled with missing data).

To run the MML program in this example, follow the steps outlined below.

Step 1:	In the Data Management or Megafile Manager window, click on the Open MFM Data option in the File pull-down menu and select the Megafile Manager file ANEX4.MFM.

Step 2:	Select the option Language (MML) in the MFM Analysis pull-down menu to open the MML window.

Step 3:	Click on the Open Text option from the MML window File pull-down menu and select the program file ANEX4.MML.  This program is shown below.

program GetJob;

{program name (optional)}

var i,nb : integer;

{temporary variables}

begin

  nb := 0;

  write(POSITION,'->');

  writeln;

  for i := 1 to NofY do

{for each related record in the second file}

  begin

    GetY(i);

{load this record into memory}

    if (MAXSALAR >= MINSAL) and

       (SCORE >= MINAPTIT) and

       (YEXP >= MINEXPER) then

{if the person qualifies}

      begin

        nb := nb + 1;

{increment the number of "good" candidates and

display information about this person on screen:}

        write(' NUMBER',i,'AGE',AGE,'SCORE',SCORE,

              'EXPERIENCE',YEXP,'years');

        write('EDUC:');

        if BACHEL then

          write('Bachelor')

        else

          if COLLYEAR >= 1 then

            write(COLLYEAR,'years of college');

       writeln;

       write('   References:',REFEREN);

       writeln;

      end;

  end;

  if nb = 0 then

{if no qualified applicants are found,}

{write a message on the screen: }

    write(' Sorry, no qualified applicants for

           this job ')

  else

{we have some good candidates: they are listed

on the screen; now it's time to review them...}

    begin

      write('Now you may select an applicant...');

      read(i);

{...and choose someone (type his/her number)}

      GetY(i);

{get information about the chosen applicant from

the respective record in the related file}

      LNAME := LASTNAME;

{and put his/her name in the main file}

      FNAME := FIRNAME;

      UpCase(FNAME);

{convert both first and last names to uppercase}

      UpCase(LNAME);

      writeln;

      write('  ...',FNAME,LNAME,'has been selected

             for the position.');

      writeln;

{write name of chosen applicant on the screen}

    end;

  writeln;

end

Step 4:	Before the data can be processed, you need to tell MML that a second data file will be used (in addition to the "first" or "main" data file that is currently open).  You can do this in the Megafile Manager: Options dialog.  Click on Options from the MML window Options pull-down menu to open the Megafile Manager: Options dialog.  Now, click on the Name button in this dialog and select file ANEX4-R.MFM as the second file.

Next, you need to instruct MML as to how to identify the specific records in the second data file (ANEX4-R.MFM) that are related to specific records in the first data file (ANEX4.MFM).  Specify column 2 in the edit field next to the option Key in main file and 3 in the edit field next to the option Key in relational file in the Megafile Manager: Options dialog.

The logic of this option (specifying a key column in each data file) is analogous to the one discussed in the context of relational merge options in Megafile Manager that are also based on matching values of key columns.  It allows you to "define a relation" between the two files by instructing MML which columns in the respective files correspond to each other (and thus where MML should look for values that will match).

Step 5:	To run the program, click on the Execute button on the MML window toolbar.

NOTE:  In the above example, the keys which are the basis for the relationship between the main and related data files are the second and third columns, from the main and related data files respectively.

See also:

Example 1:  Computing an Average of Two Columns

Example 2:  Using Conditional Statements (block if .. then .. else .. undefined) and Interactive Verification and Editing of Data

Example 3:  Using Loops and Passing Values of Variables between Records

Example 4:  Verification and Analysis of Data using the Recode Statement

Example 5:  Math Operations, Random Numbers

Example 6:  Operations on Strings (texts) and Dates, Printing Reports

Example 7:  Relational Operations on Two Data Files


  Megafile Manager - MML Quick Syntax Reference

In order to keep this Help window displayed (for quick reference) while you use the MML editor, click on the Always on Top option from the Help window Help pull-down menu.

The following is a list of MML keywords (and examples); for a more detailed description of the syntax, click on the respective topic.

Procedure	EXAMPLE

Abs(x)	X := Abs(ERROR);

ArcSin(x)	if ArcSin(VAL) < Pi/2 then

ArcCos(x)	X := ArcCos(VAL);

begin .. end	begin  temp:=M2;  M2:=M1;  M1:=temp  end;

Boolean	var small : Boolean;

Case .. of	case GENDER of 'MALE' : m:=m+1; 'FEMALE' : f:=f+1; ...

CaseNo	if CaseNo > 1000 then ...

Char	var Ch : Char;

Const	const Name = 'Rebel Without a Cause';

Cos(x)	R := Cos(VAL * Pi / 2);

CosH(x)	R := CosH(MEASUR7);

Count(x, a1, .., an)	C := Count(Missing, V(1), V(2), V(3);

Delete	if NOT Valid(TOTAL) then Delete;

Euler	ERROR := Euler - (1+1/N)^N;

Exit	if TOTAL > 300000 then Exit;

Exp(x)	U := Exp(v(8));

For..to..do	for i := 1 to 10 do v(i) := -1;

For..downto..do	for i := 200 downto 100 do SUM := SUM + v(i);

GetY(i)	if NofY >= 5 then begin GetY(3); v(1) := y(1) end;

Hi	recode A(int2):int2; begin 100 .. Hi = 10; ...

If..then..else..undefined	if COND then v(1):=1 else v(2):=1 undefined Pause;

IniAll	begin	IniAll; VAL8 := Uniform (10); ....

Integer, int1, int2, int4	var I : Integer;

Intrecode	intrecode Class (3,1) = 'First', 'Second', 'Third';

Len(a)	SLEN := Len(TITLE);

Let .. be .. do	let x be [v(1),v(2),v(3)] do x := 77;

Lo	case VAL5 of Lo .. 0 : Write ('less then 0'); ....

Log(x)	M := Log(A + B * C);

Log10(x)	NB := Log10(ERROR);

Log2(x)	QQ := Log2(BIGNUMB);

Log1	var ISBIG : Log1;

Math Library of MML	X := B * Sin(A) * Exp(A);

Metacommands	{$F:1000}{$N:300}

Mid(a, x, y)	S1 := Mid(TITLE, 10, 3);

Missing	v(i) := Missing;

NofY	if NofY > 0 then ...

Normal(x)	RNDVAL := Normal(Z+Q);

Pause	if ERROR then Pause;

Pi	if Sin (ALPHA * Pi) > .8 then ...

Poisson	QVAL := Poisson (10);

Procedure	Procedure A_half; begin v(2):=v(2)/2 end;

Program	Program Test; begin Pause end

Read(x)	if NOT Valid(U) then Read(U);

Real, Real4, Real8	var TINY : Real8;

Recode	recode Alpha (real):int2; begin Lo..-3 = -1; ...

Rnd(x)	VAL := Rnd(100);

Round(x)	VAL := Round(Uniform (20));

SDate(a, x, y, z)	SDate(TODAY, MM, DD, YY);

SDelete(a, x, y)	NEWSTR := SDelete(HEADER, POS, LEN);

SetMiss(x)	SetMiss (SCORE);

Sign(x)	if Sign(M1) = 1 then ...

Sin(x)	X := Sin(X);

SinH(x)	XH := SinH(XH);

SInsert(a, b, x)	NEWSTR := SInsert(SOURCE, INS, POS);

Sqrt(x)	R := Sqrt(A^2 + B^2);

Static	static TOTAL : Real8;

STime(a, x, y, z, q)	STime(CURRTIME, HH, MM, SS, HUNDR);

Stop	if MM1 > 100 then Stop;

Str(x, y, z)	NEWSTR := Str(VALUE, NBCHARS, NBDEC);

String[n]	var S : String[128];

String Library of MML	S := Str(TEXT, 10, 3) + SInsert(A, B, 5);

Tan(x)	t := Tan(alpha);

TanH(x)	tH := TanH(alphaH);

Trunc(x)	K := Trunc(A*B);

Uniform(x)	RNUMBER := Uniform(10) - 5;

UpCase(a)	UpCase(HEADER);

V(xxx)	X := V(10);

Val(a, x)	if Val(TEXT, NUMBER) then ...

Valid(x)	COND := Valid(v(99));

Value(x)	X := Valid(V(10));

Var	var i, j, k : integer;

Write	Write(TEXT, NUMBER);

Writeln	Write(A,B,C); Writeln;

Y(xxx)	GetY(K); V(7) := Y(10);

MML programs consist of declarations and instructions.  Following the Pascal convention, all objects used in the program must be either explicitly declared (e.g., var X, XX, XXX: integer), or be elements of MML syntax (e.g., begin, write).  The only exception are names of variables (i.e., columns) in the current and related Megafile Manager data files (e.g., MEASURE1, MEASURE2, AVDATA), which do not have to be declared; those variables can be used in MML programs like all other variables (and they preserve their types from the Megafile Manager file).

The title of the MML program (e.g., program Program1;) is optional.  There can be comments included in the text of the program; each comment must be enclosed in curly brackets (e.g., {comment}) or parentheses with asterisks (e.g., (* comment *) ).  Lowercase and uppercase letters are differentiated only inside string (i.e., text) values (e.g., 'abc' is different from 'ABC' but variable Abc can be referred to either as ABC or abC).

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

See also, Introductory Overview.


  Megafile Manager Language - Using Variables (fields) from Megafile Manager Data Files

MML programs can read from and write to fields (i.e., columns) of the current Megafile Manager data file.  These "data variables" (from the main data file) are referenced either by their original names or by a reserved indexed variable V(xxx) where the xxx index must be greater than, or equal to, 1 and must not exceed the number of columns in the current Megafile Manager file.  For example:

SALARY := 0;

if V(6) > -1 then V(7):=0;

V(2*i+1) := V(i) + 10*YEAR;

It is recommended to use the original column names in MML programs wherever possible because (a) this usually increases the clarity of the program and (b) it allows the compiler to create smaller and faster program execution code.  Additionally, if column names are used, (c) the MML compiler can perform more comprehensive error checking at the point of compilation and verify the correctness of expressions that use Megafile Manager column names against their actual types in the current data file (which helps to avoid potential run-time errors at the point of execution of the program).

The same syntax conventions apply to column names from the related data file (which can be referenced in the program if a related data file has been specified in the Options pull-down menu of MML).  The only difference is that in referencing columns from the related data file via the indexed variable convention, the name of the variable is Y(xxx) instead of V(xxx).  For example:

Y(3) := LASTNAME;

Y(i+1) := Y(i+1)/3;

SALARY := Y(1);

The column names in the main and related data files cannot be duplicated.

For more information on MML Syntax, see the following topics:

Syntax References

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)


Megafile Manager Language - Declarations, Recoding Functions, Procedures - Naming Conventions

  Megafile Manager Language - Declarations, Recoding Functions, Procedures

Declaring a new object in MML programs amounts to the assignment of an explicit type to a new symbol.  The types supported in MML are those introduced in the context of the general Megafile Manager data file structure (see Megafile Manager Overview):

Numeric variables may be defined as either integer or real:

Integer defines a 2-byte variable (as does int2).  Short integers (1 byte, equivalent to the Megafile Manager data column type ShortInteger) are defined as int1, long integers (4 bytes, equivalent to the Megafile Manager data column type LongInteger) as int4.

Real defines a 4-byte variable (as does real4).  Double precision (8-byte) variables are defined as real8.  Variable type real4 and real8 are equivalent to the Megafile Manager data column types Float and DoubleFloat, respectively.

Text values inside MML may be up to 200 characters long; thus if longer text values exist in the current Megafile Manager data file, the remainder (above 200 characters) will be ignored by the program.  Text variables are defined as string[n] where n is an integer value from 1 to 200.  In addition, char may be used to designate string variables of length 1.

Logical variables are defined as boolean or as log1.

The following objects can be declared in MML: constants, variables (local and global), recoding functions, and procedures.  For more information, see:

Naming conventions

Constants

Local Variables

Global (static) variables

Recoding functions

Procedures

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)


Declarations, Recoding Functions, Procedures - Naming Conventions

  MML Declarations, Recoding Functions, Procedures - Naming Conventions

Names of all user-defined objects (constants, variables, recoding functions, and procedures) in MML can be up to 8 characters long, and may contain any of the following characters: the letters A-Z and a-z, digits 0-9 (although not permitted as the first character), !, #, $, &, ?, @, \, ^, _, |, ~, and all extended ASCII characters from 128-254.  As in all other instances, MML does not differentiate between uppercase and lowercase letters (unless they are values of string variables).  These user-defined objects cannot be given names of any predefined objects of MML or any MML reserved words (otherwise a syntax error will occur).

See also:

Constants

Local Variables

Global (static) variables

Recoding functions

Procedures

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)


Declarations, Recoding Functions, Procedures - Constants

  MML Declarations, Recoding Functions, Procedures - Constants

Constants are declared using the following two conventions:

const name = value;

const name = [(+/-)]constant;

After the key word const (constant declaration), the left side of the equation states the name of the constant; the right side assigns a value to the constant, either directly or in terms of a previously declared constant.  For example:

const    TwoPi = 6.28;

const   ExText = 'California';

const  MinusPi = - Pi;

const Minus2Pi = - TwoPi;

See also:

Naming conventions

Local Variables

Global (static) variables

Recoding functions

Procedures

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)


Declarations, Recoding Functions, Procedures - Local Variables

  MML Declarations, Recoding Functions, Procedures - Local Variables

Local variables are those that are used "within" processing one record of data only, and they do not retain their values between processing of records (unlike static variables, see the below).  Values of local variables are initialized to Missing at the beginning of processing each record.  Local variables are declared using the standard declaration format starting with the word var (variable):

var Name1 [, ...] : type;

After the key word var (variable declaration), the left side of the colon contains a list of one or more variables to be declared; the right side defines their type.  For example:

var I, J, K : integer;

var Cond    : boolean;

var S       : string[40];

String variable declarations must include their length (in square brackets); however, later in the program, only their name is used to reference the variable, e.g., S := 'megafile';.  Specific characters in string variables cannot be referenced as elements of a table (e.g., S[5]:='M' is illegal); a library of string functions and procedures is included to allow for within-string character manipulations.

See also:

Naming conventions

Constants

Global (static) variables

Recoding functions

Procedures

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)


Declarations, Recoding Functions, Procedures - Global Variables

  MML Declarations, Recoding Functions, Procedures - Global (static) Variables

Global (static) variables are used when values need to be preserved in the program across individual records.  Unlike local variables (see the previous section) they retain their values between records.  Values of static variables are initialized only once, at the beginning of processing the first record (numeric variables are initialized to 0, string variables to an empty string, and logical variables to false).  Static variables are declared using the standard declaration format starting with the word static:

static Name1 [, ...] : type;

After the key word static, the list of variables is declared, followed by their type to the right side of the colon.  For example:

static      Sum : real;

static GlIncome : int4;

See also:

Naming conventions

Constants

Local Variables

Recoding functions

Procedures

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)


Declarations, Recoding Functions, Procedures - Recode

  MML Declarations, Recoding Functions, Procedures - Recoding Functions

Two types of recoding functions can be defined in MML: Intrecode and recode.  Both can be used to recode one type into another (e.g., Integer into String), or to categorize their values.

Intrecode.  The Intrecode; (Int(eger) recode) function is a special purpose version of the general recode function described below.  The function Intrecode name(i, j) = a1, .. aj transforms ranges of values between consecutive j integers starting with i, into the new values specified in the list on the right side of the equation.  The function is defined as follows:

Intrecode Name(i, j) = constant [, ...];

Both i and j must be integer constants, and the value for j must be in the range of 1 through 50 (i.e., no more than 50 values can be specified in a single Intrecode statement).  The right side of the equation contains a list of constants of any type (however, string constants cannot be mixed with other types).  There must be exactly j values specified in the list on the right side of the equation.

As a result, all numeric values in the range [i, i+1) will be transformed into the first constant in the list on the right side, all numeric values in the range [i+1, i+2) will be transformed into the second constant in the list on the right side, etc.  Values falling outside the specified range will be transformed into Missing data.

For example:

Intrecode Ex1(4, 3)=Pi, Missing, 0;

{declaration of function Ex1}

x := Ex1(0);

{0 is outside range, thus x becomes Missing}

x := Ex1(4);

{x will become Pi (first range)}

x := Ex1(6.675);

{x will become 0  (third range)}

x := Ex1(7);

{7 is outside range, x will become Missing}

Recode.  The recode function is a general data recoding and categorization facility and it can be used to transform values or ranges of values of any type into any other type.  The function is declared/defined as follows:

recode Fname( input_type ) : output_type;

begin

(constant/constant .. constant/Lo .. constant/constant .. Hi) [, ...] = (constant/Old)[;

...]

[else constant]

end;

The first line of the recode function begins with the keyword recode followed by a declaration of the function name (here: Fname) and the types of input and output values.  The keyword begin starts the recode definition, and the remaining lines contain the actual recoding statements.  The constants on the left side of each equation must be of input_type, whereas the constants on the right side must be of output_type.  In addition to lists of constants, ranges can also be used on the left sides of the recoding equations (e.g., 1 .. 10  or  Lo .. -1000  or  888 .. Hi, where Lo .. constant is a lower-unbounded interval, and constant .. Hi is an upper-unbounded interval).  Such ranges are always interpreted as excluding the upper endpoint of the range.  For example:  Lo to -10 = 1; -10 to 20 = 2;  20 to Hi = 3  would recode 0 as 2 (in the second range), but 20 would be recoded as 3 (not 2).  The word to can be used instead of two dots (e.g., Lo to -100 or 888 to Hi).

The right sides of the recoding equations can also contain the word Old which will cause the corresponding values from the left side to remain unchanged (this convention is allowed only if input_type and output_type of the function are compatible, i.e., if the right side can be assigned to the left side).  Here is an example of a recode function:

recode Ex1(integer) : integer;

{Ex1 will recode integers into integers}

begin

{begin recode definition}

  Lo to -10, 111 to 119 = 0;

{up to -10, and 111 to 119 will be recoded to 0}

  200 .. Hi = 1;

{200 and over will become 1}

  0, 1, 2, 10 .. 20 = Old;

{0, 1, 2 and 10 to 20 will not be changed}

  Missing = -2

{Missing values will become -2}

  else -1

{other values will become -1}

end;

x := Ex1(-50);

{x will be 0 because -50 ∈ (Lo .. -10)}

x := Ex1(1000);

{x will be 1 because 1000 ∈ [200 .. Hi)}

x := Ex1(2);

{x will be 2  because 2 was to remain Old}

x := Ex1(100);

{x will be -1 because 100 is outside defined range}

x := Ex1(Missing);

{x will be -2 because Missing was to become -2}

The maximum number of recoding equations in one recode function is 3000.  The specific constants listed on the left sides of the recoding equations cannot be duplicated in one recode function and the ranges cannot overlap.  The else segment of the recode definition is optional.  A recode function definition must contain at least one recoding equation.

NOTE: A semicolon should not precede either of the keywords end or else.

See also:

Naming conventions

Constants

Local Variables

Global (static) variables

Procedures

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)


Declarations, Recoding Functions, Procedures - Procedures

  MML Declarations, Recoding Functions, Procedures - Procedures

MML user-defined procedures are declared as follows:

procedure Name;

begin

instruction[;

...]

end;

Instructions included within a procedure may be assignments, conditional instructions, calling of other procedures, or compound instructions (see below)

User-defined procedures in MML can access all program variables and functions (and they do not have local variables), but, they cannot have parameters.  MML procedures cannot be nested.  Here is an example of a simple procedure:

procedure ExChange;

  begin

    Pom := X;

    X := Year;

    Year := Pom

  end;

NOTE:  User-defined procedures are the only part of the MML program where columns from Megafile Manager data files cannot be referenced by their names, but only by their number (using the V(xxx) or Y(xxx) indexed convention, where xxx is a column number; see Megafile Manager Introductory Overview).

See also:

Naming conventions

Constants

Local Variables

Global (static) variables

Recoding functions

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)


  Megafile Manager Language - Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

In general terms, every MML program must consist of a series of instructions; separated by semicolons ( ; ), which serve as "separators of instructions."  The following general types of instructions are used in the main body and procedures of MML programs: assignment, compound, conditional, and looping instructions, and procedure calls.  For more information on each, click on the topic name.

Assignment instructions (and MML expressions)

Compound instructions

Conditional blocks and case blocks

Conditional if .. then .. else .. undefined blocks

Case blocks

Looping instructions

Procedure instructions

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Predefined Objects and Special Conventions in MML (by category)


  MML Instructions - Assignment Instructions (and MML Expressions)

The general format of assignment instructions in MML is:

variable := expression;

The variable (on the left side of the assignment operator := ) can be a column name from the current Megafile Manager data file or a previously declared local or static variable.

The expression (on the right side of the assignment operator := ) must be of the same type as the variable on the left side.  For example, numeric values cannot be assigned to string variables, or real numbers cannot be assigned to integer variables (following the standard Pascal convention).  The expressions can consist of variables and constants (or functions of variables and constants) related by operators.

The operators supported in MML are presented in the following table (along with the types of variables with which they can be used).  The operators are listed in the order of their precedence (i.e., order of execution): from the lowest to the highest.

        |              |logi-|inte-|    |

operator|operation     | cal | ger |real|string

--------|--------------|-----|-----|----|------

=, <, >,|relational    |  +  |  +  |  + |   +

<>,<=,>=|operations    |  +  |  +  |  + |   +

        |              |     |     |    |

    +   |addition      |     |  +  |  + |   +

    -   |subtraction   |     |  +  |  + |

   or   |inclus. disj. |  +  |     |    |

        |              |     |     |    |

  *, /  |multip., div. |     |  +  |  + |

  div   |integer div.  |     |  +  |    |

  mod   |modulo div.   |     |  +  |    |

  and   |conjunction   |  +  |     |    |

        |              |     |     |    |

  **,^  |exponentiation|     |  +  |  + |

        |              |     |     |    |

  not   |negation      |  +  |     |    |

The precedence of execution can be modified via parentheses ( ) in the usual manner.  In the case of string values, addition means concatenation, and the results of relational operations are based on the ASCII order of characters in the strings being compared (e.g., 'abc' < 'bcd' is true, as is 'abc' > 'BCD').  The compiler checks the consistency of types of values and operators (a syntax error is issued when an inconsistency is detected).

Example:

var B : boolean;

    I : integer;

    X : real;

    S : string[40];

begin

  B := 23 > 99;

  I := 133 div 3 + ( 9 - 7 ) * 18;

  X := (sin( Pi / 8 ) + 1) ** 2;

  S := 'Megafile ' + 'means ' + '"huge file"';

end

See also:

Compound instructions

Conditional blocks and case blocks

Conditional if .. then .. else .. undefined blocks

Case blocks

Looping instructions

Procedure instructions

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Predefined Objects and Special Conventions in MML (by category)


  MML Instructions - Compound Instructions

Compound instructions in MML consist of a series of simple instructions separated by semicolons that are enclosed between begin and end, and that follow the standard Pascal conventions (a semicolon can be placed, but is not required, after the last instruction before the end).

begin

instruction[;

...]

end

See also:

Assignment instructions (and MML expressions)

Conditional blocks and case blocks

Conditional if .. then .. else .. undefined blocks

Case blocks

Looping instructions

Procedure instructions

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Predefined Objects and Special Conventions in MML (by category)


  MML Instructions - Conditional Blocks and Case Blocks

There are two types of conditional instructions supported in MML: conditional if .. then .. else .. undefined blocks and case block statements.

The if .. then .. else .. undefined blocks control the flow of the program in the most straightforward manner: if a condition is met then an instruction is executed, if it is (explicitly) not met (i.e., .. else ..) then another instruction is executed, and a third instruction can be specified which is executed if missing data are detected in any of the variables involved in the condition (i.e., when the condition is undefined).

The case blocks consist of a series of instructions assigned to specific values of a criterion expression and executed conditionally depending on the value of that expression.

See also:

Assignment instructions (and MML expressions)

Compound instructions

Conditional if .. then .. else .. undefined blocks

Case blocks

Looping instructions

Procedure instructions

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Predefined Objects and Special Conventions in MML (by category)


  MML Instructions - Conditional if .. then .. else .. undefined Blocks

The conditional if .. then .. else .. undefined block; in MML has the following format:

if expression then

   instruction

[else

   instruction]

[undefined

   instruction]

The expression does not have to be strictly of type logical, but can also be numeric (in which case 0 is interpreted as "not met" or "false").  It cannot be of type text.  The else and undefined segments of the block are optional.  The instructions inside the segments can be any valid MML instructions (e.g., they can be compound).  The execution of the block depends on the value of expression calculated by the program; if it is defined and not 0 or false, then the first instruction is executed, if it is 0 or false then the second instruction is executed; if the expression is undefined (i.e., it contains missing data) then the instruction specified after word undefined is executed.  For example:

if YEAR > 1980 then

{if YEAR is greater than 1980, then}

   SUM := SUM + INCOME

{add INCOME to SUM}

else

{otherwise }

   Write(YEAR)

{show the encountered value of YEAR}

undefined

{in case YEAR is undefined (i.e., MD)}

   Pause;

{Pause, to allow inspecting the data}

NOTE:  A common syntactic error is caused by inserting a semicolon (;) after individual instructions within the segments of the block (no semicolons are allowed before else and undefined in if .. then, case, and recode instructions).  Another common error is caused by omitting parentheses needed to adjust for the precedence of operators; for example, the expression:

x > 0 and x < 1

is incorrect (see the table of precedence of operators, above), and needs parentheses:

(x > 0) and (x < 1)

because relational operators (in this example, operators > and < ) have a lower precedence than conjunction (and).

See also:

Assignment instructions (and MML expressions)

Compound instructions

Conditional blocks and case blocks

Case blocks

Looping instructions

Procedure instructions

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Predefined Objects and Special Conventions in MML (by category)


  MML Instructions - Case Blocks

The conditional case .. of instruction in MML has the following general format (illustrated here with several possible formats of the individual "segment" specifications):

case expression of

(constant/constant .. constant/Lo ..

 constant/constant .. Hi) : instruction[;

...]

[else instruction]

end

NOTE:

The intervals specified on the left sides of the "segments" of the case block cannot overlap.

The keywords Lo and Hi may appear only once.

A semicolon should not precede either of the keywords end or else.

The expression must be numeric and the constants must be explicit constants.  If ranges are used on the left sides of the "segments" of the case block, they are interpreted as left-bound inclusive and they cannot overlap.  The words Hi and Lo (denoting respectively, a lower-unbounded interval and an upper-unbounded interval) can be used to specify ranges that are not limited on one side.  Note that the word to can be used in place of the two dots (e.g., Lo to -5).  The else segment is optional but if it is used, there should be no semicolon (;) preceding it.  Here is an example of a valid case block:

case x of

{in case the value of x is:}

  Lo .. -10 : Write(i);

{x < -10, display the value of i}

  2 : Delete;

{x = 2, delete this record }

  10 .. 20 : Delete;

{x >= 10 and x < 20, delete this record}

  100 .. Hi : begin

{x >= 100, do the following:}

     Write(i);

{(a) display the value of i}

     Pause

{(b) Pause to allow for data editing}

     end

{end of this "(a)+(b)" block}

  else Exit

{x is outside of the range, exit from this record}

end;

{end of this entire case block}

See also:

Assignment instructions (and MML expressions)

Compound instructions

Conditional blocks and case blocks

Conditional if .. then .. else .. undefined blocks

Looping instructions

Procedure instructions

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Predefined Objects and Special Conventions in MML (by category)


  MML Instructions - Looping Instructions

A looping instruction repeatedly executes a series of instructions specified in the body of the loop.  There are two types of looping instructions supported in MML: for .. to .. do loops and let loops.

For .. to .. do  loop.  The general format of the for .. to .. do loop is:

for variable := expression1 to expression2 do

instruction

The two expressions must be of integer type (i.e., integer, int1, int2, or int4).  The instruction (which can be any valid MML instruction, including compound, conditional, another loop, etc.) will be executed once for each integer greater than or equal to expression1 and less than or equal to expression2.  The variable serves as a loop counter and it assumes the values of consecutive integers from expression1 through expression2 at consecutive passes of the loop; the value of loop counter cannot be modified inside the loop.

The variable used as a loop counter must be declared as local (i.e., it cannot be a static variable or a Megafile Manager column name).

The for .. to .. do loop is based on the ascending loop counter and thus it will not be executed if expression1 is greater than expression2.  However, a descending loop can be requested in MML by replacing the word to by downto (i.e., for .. downto .. do).

For example:

for i:=(1+2) to 2*3 do

    V(i):=Missing;

is equivalent to:

    V(3):=Missing;

    V(4):=Missing;

    V(5):=Missing;

    V(6):=Missing;

whereas:

for j:=10 downto 8 do

    Write(j*1000);

is equivalent to:

    Write(10*1000);

    Write(9*1000);

    Write(8*1000);

Let .. be .. do looping construction.  The let .. be .. do loop is defined as follows:

let (variable be [varname [,...]]

/variable be [(constant/constant .. constant/ %constant*constant) [,...]])[;

...]  do

instruction;

and it causes the instruction (any valid MML instruction including compound, loops, conditional blocks, etc.) to be executed once for each of the values specified in the list (each list must consist of the same number of values).  At the i'th consecutive pass through the loop, variables (from each segment of the looping construction) are assigned the i'th consecutive values from their corresponding lists.

There can be up to 16 segments (i.e., variables and lists associated with them) specified in one let .. be .. do loop construction, with all but the last one ending in a semicolon (;).  The variables can be only local variables (i.e., declared via the var declaration statement).  The lists can consist of either variables or constants (but constants and variables cannot be mixed in one list).  If a list consists of constants, then it can also include the reserved constant Missing.

Lists of constants can contain the following two special conventions which save the typing multiple values:

[constant1 .. constant2] - means from constant1 to constant2

(e.g., [1 .. 3] or [1 to 3] means [1, 2, 3]);

[% constant1 * constant2] - means repeat constant2 constant1-times

(e.g., [%5*3] means [3,3,3,3,3]).

Here are several examples:

let i be [1 .. 3] do V(i) := 0;

and

let x be [V(1), V(2), V(3)] do x := 0;

are both equivalent to:

V(1) := 0;

V(2) := 0;

V(3) := 0;

The lists on the right side of be in each segment of the let construction are calculated before execution of the do instruction, thus the variable that identifies the list of the constants cannot be included in the following instruction on the right side of an assignment statement (or, for example, as an argument of the procedure Read).  Therefore, for example:

var i, j : integer;

begin

  i:=100;

  j:=200;

  let i be [1,2] ;

      j be [i,i] do

  begin

    write(i);

    write(j);

  end;

end

will produce: 1 100 2 100 (and not: 1 1 2 2) because before the instruction (the one after do) is executed, the [i,i] list is calculated (i.e., becomes a list of constants), thus it becomes [100,100] (as the value of i before let was 100).  Here is another example:

var a,b : integer;

begin

  a:=50;

  b:=100;

  let a be [1, 2, 3] ;

      b be [V(a), V(a+1), V(a-1)] do

        b:=a;

end

is equivalent to:

V(50):=1;

V(51):=2;

V(49):=3.

See also:

Assignment instructions (and MML expressions)

Compound instructions

Conditional blocks and case blocks

Conditional if .. then .. else .. undefined blocks

Case blocks

Procedure instructions

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Predefined Objects and Special Conventions in MML (by category)


  MML Instructions - Procedure Instructions

In addition to the user-defined procedures in MML, there are a number of predefined procedures in MML.  All procedures in MML are called by their names (in the case of user-defined procedures, the name must be declared in the definition of the procedure).

Some of the predefined MML procedures require that a list of arguments be specified; for example:

Write( 12.4, 'abc', INCOME, (10+2)*Pi );

{write this list of 4 elements on the screen}

Read( V(6) );

{prompt the user to enter a value for V(6)}

some others have no parameters; for example:

Pause;

{open the window for reviewing/editing

of values from the currently processed record}

Exit;

{stop processing this record of data

and move to the next record}

The specific procedures from these examples are discussed in more detail later.

See also:

Assignment instructions (and MML expressions)

Compound instructions

Conditional blocks and case blocks

Conditional if .. then .. else .. undefined blocks

Case blocks

Looping instructions

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Predefined Objects and Special Conventions in MML (by category)


  Megafile Manager Language - Predefined Objects, Functions, and Special Conventions in MML (by category)

MML offers a library of predefined objects (e.g., procedures and functions) which simplify writing programs.  However, the names of these procedures cannot be used to label columns in the current Megafile Manager data file or a syntax error will occur.  If any reserved MML words have been used as names in the current Megafile Manager file, they need to be changed before that file can be processed (use the Column Specifications dialog).

For more information on each of the predefined objects, click on the procedure or function name below:

Reserved Variable: CaseNo; Constant: Missing

Functions: Count, Valid, Value

Procedures

Math Library and Random Number Generators

Library of String Functions and Procedures (and Processing Time and Date)

Input and Output functions

Accessing Data from Megafile Manager "Related" Data File

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)


  Megafile Manager Language - Reserved Variable: CaseNo; Constant: Missing

CaseNo  a reserved variable that contains the number of the currently processed record (i.e., current "case").  CaseNo does not have to be declared, its type is always int4 (i.e., "long integer").

Missing    the value of the constant Missing is context-dependent; if it is assigned to a "data based" variable, it is equal to the specific missing data code for the respective data column.  Therefore, the type of the constant is always consistent with the type of the respective Megafile Manager column.  MML also supports a generic type of Missing value that can be assigned to any local or static variable and is interpreted as "undefined."  All MML expressions that contain missing data (or that contain other expressions which evaluate to missing data) evaluate to missing data.  Note that the assignment of specific values (e.g., -9999) which represent missing data codes in specific columns of the Megafile Manager data file is completed not "within" but "outside" the MML program (after the record is processed and before it is written to the disk).  Therefore, in order to allow the MML program to recognize a value as Missing, the constant Missing and not its specific value (e.g., -9999) should be assigned to the respective variable in the program.

For more information on each of the predefined objects, click on the procedure or function name below:

Functions: Count, Valid, Value

Procedures

Math Library and Random Number Generators

Library of String Functions and Procedures (and Processing Time and Date)

Input and Output functions

Accessing Data from Megafile Manager "Related" Data File

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)


  Megafile Manager Language - Functions: Count, Valid, Value

Count(x, a1[, ..., an])  a standard MML integer function that returns the number of times that the expression x (specified as the first argument of the function) occurs in the list of the following arguments (a1 through an).

Example:

begin

  V(6) := Count(Missing,V(1),V(2),V(3),V(4));

{count MD's in the list}

end

This program will count the number of missing values found among variables V(1) through V(4) and place this count in variable V(6).

Valid(x)    a standard MML logical function that is equal to true if the value of x is not Missing (i.e., when it is Valid).

Example:

begin

  if not Valid(INCOME) then

{if value of INCOME is Missing, then}

    Delete;

{delete this record from the data file}

end;

This program will delete all records in the data file for which the value of INCOME is Missing.

Value(x)   a standard MML function that is equal to 0 if the value of variable x is Missing; if the value of x is not Missing, however, the function returns the actual value of x (x must be numeric).  This function is particularly useful when calculating a sum, or if used in conjunction with function Count, an average of a list of values, adjusted for missing data.  (Normally, the result of the entire expression is set to missing data if the value of at least one element is Missing.)

Example:

begin

  MEAN := ( Value(V1) + Value(V2) + Value(V3) ) /

  ( 3 - Count(Missing, V1, V2, V3 ) );

end

This program calculates an average of V1, V2, and V3, adjusting for missing data.

For more information on each of the predefined objects, click on the procedure or function name below:

Reserved Variable: CaseNo; Constant: Missing

Procedures

Math Library and Random Number Generators

Library of String Functions and Procedures (and Processing Time and Date)

Input and Output functions

Accessing Data from Megafile Manager "Related" Data File

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)


  Megafile Manager Language - Procedures

Delete     a standard MML procedure that deletes the currently processed record from the data file.

Example:

begin

  if (GENDER = 'MALE') or (GENDER = 'FEMALE') then

    Write(' OK ')

  undefined

{if the value of GENDER is MD (undefined)}

    Delete

{delete the current record from the data file}

end

This program will write OK whenever it encounters a record with the value of GENDER equal to MALE or FEMALE, and it will delete records in which the value of GENDER is Missing (i.e., is "undefined").

Exit         a standard MML procedure which terminates processing of the current record (and proceeds to the next one).

Example:

begin

  if ( INCOME < 100 )

{if INCOME is less than 100}

    Exit;

{stop, and move to the next record}

  Write( CaseNo );

end

This program will list on the screen the numbers of records for which the value of INCOME is greater or equal to 100.

Pause      a standard MML procedure which temporarily stops the execution of the program and allows the user to review and edit values of all columns of the currently processed record and all MML program variables.  The procedure displays the number of the currently processed record in the resulting Megafile Manager: Pause dialog.

The user can also decide whether to continue processing this record (or the entire program).  This procedure is most useful in applications designed to verify and clean data based on criteria defined in the program (the procedure is called in such programs whenever an illegal value is detected).  Unlike in the data verification and cleaning facilities of Data Management which check only whether the verified values belong to specified lists or ranges of allowable values, the verification criteria used in MML programs may contain complex conditional relations between values in different fields of the same record.  For example, the number of pregnancies can be greater than 0 only if the person is older than 15, is not a male, or when his/her gender is not specified but he/she was pregnant before.  The procedure is also very helpful when debugging complex MML programs.

Example:

begin

  if not Valid(VALUE) then

{if value of VALUE is Missing, then}

    Pause;

{stop and show data from this record}

end;

This program will Pause whenever a missing value is encountered in column VALUE, so that data can be reviewed and edited.

SetMiss(x)  a standard MML procedure that assigns a missing data code to a local or static variable x.

Example:

var X : real;

begin

   SetMiss(X);

{set the value of X to Missing}

end

The statement SetMiss(x) is equivalent to x:=Missing.

Stop        a standard MML procedure that stops the execution of the program.

Example:

begin

 if CaseNo > 100 then

{if the number of record is greater than 100}

    Stop;

{stop the program (do not process new records)}

 Write( INCOME );

end

This program will be executed only for the first 100 records.

For more information on each of the predefined objects, click on the procedure or function name below:

Reserved Variable: CaseNo; Constant: Missing

Functions: Count, Valid, Value

Math Library and Random Number Generators

Library of String Functions and Procedures (and Processing Time and Date)

Input and Output functions

Accessing Data from Megafile Manager "Related" Data File

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)


  Megafile Manager Language - Math Library and Random Number Generators

Constants:

Euler       = 2.71828182845905

Pi          = 3.14159265358979

Functions:

Abs(x)      absolute value of x

ArcSin(x)   arc sine of x

ArcCos(x)   arc cosine of x

Cos(x)      cosine of x

CosH(x)     hyperbolic cosine of x

Exp(x)      exponential function (Euler to the power of x)

Log(x)      natural logarithm of x (base Euler)

Log10(x)    common logarithm of x (base 10)

Log2(x)     binary logarithm of x (base 2)

Round(x)    rounds x to an integer

Sign(x)     returns the sign of x (x<0 → -1;

              x=0 → 0; x>0 → 1)

Sin(x)      sine of x

SinH(x)     hyperbolic sine of x

Sqrt(x)     square root of x

Tan(x)      tangent of x

TanH(x)     hyperbolic tangent of x

Trunc(x)    truncates x to an integer

Functions which generate random numbers:

Normal(x) 	random real number from a normal distribution with the mean of 0 and the standard deviation of x

Poisson(x) 	random real number from a Poisson distribution with lambda equal to x (i.e., with a mean of x and the standard deviation of √x)

Uniform(x) 	random real number from a uniform distribution in the range of 0 to x

Rnd(x) 	same as Uniform(x)

Note that all random number generators in MML are initialized ("seeded") via procedure IniAll which is automatically called at the beginning of the execution of the program, but may also be called at any point from within an MML program.

For more information on each of the predefined objects, click on the procedure or function name below:

Reserved Variable: CaseNo; Constant: Missing

Functions: Count, Valid, Value

Procedures

Library of String Functions and Procedures (and Processing Time and Date)

Input and Output functions

Accessing Data from Megafile Manager "Related" Data File

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)


  Megafile Manager Language - Library of String Functions and Procedures (and Processing Time and Date)

Len(a)         this function returns the actual length of string a.

Example:

X := Len( 'abcdefg' );

will produce the same result as:

X := 7 ;

Mid(a, x, y)  starting with the x'th character of the string a, the function will return a substring of y subsequent characters.

Example:

T := Mid( 'Mary had a lamb', 6, 3 );

will produce the same result as:

T := 'had';

SDate(a, x, y, z)  interprets string a as date x/y/z.  The procedure allows for a variety of date formats, and it actually "searches" the entire string for a part interpretable as a date.  Specifically, input strings (interpretable by this procedure) may consist of the following (in sequence):  "any characters" + integer + separator + integer + separator + integer + "any characters."  If an interpretable substring is not found, then missing data are returned for each of the 3 numeric arguments.

For example statements:

SDate( '1987/03/16' , YY, MM, DD );

or:

SDate( 'Date: 03/16/1987' , MM, DD, YY );

will produce the same result as:

YY := 1987;  MM := 3;  DD := 16;

SDelete(a, x, y)  deletes from string a, a substring of y characters, starting at character number x.

Example:

T := SDelete( 'Mary had a lamb', 6, 3 );

will produce the same result as:

T := 'Mary  a lamb';

SInsert(a, b, x)  inserts string b into string a, starting at the x'th character position of string a.

Example:

T := SInsert('Mary a lamb' , 'had ' , 6);

will produce the same result as:

T := 'Mary had a lamb';

STime(a, x, y, z, q)  interprets string a as time x:y:z.q.  The procedure actually "searches" the entire string for a part interpretable as time.  Specifically, an input string (interpretable by this procedure) can consist of the following (in sequence):  "any characters" + integer + separator + integer + separator + integer + '.' (i.e., period) + integer + "any characters."  If an interpretable substring is not found, then missing data are returned for each of the 4 numeric arguments.

Example:

STime( '11:09:18.19', H, M, S, Hu );

will produce the same result as:

H := 11;  M := 9;  S:= 18;  Hu:=19;

Str(x, y, z)   returns a string of y characters, containing an image of value x, with z digits after the decimal point.

Example:

T := Str(123.456, 10, 5);

will produce the same result as:

T := ' 123.456  ';

UpCase(a)   converts all lower case letters in string a into upper case letters.

Example:

T := 'Mary had a lamb'; UpCase(T);

will produce the same result as:

T := 'MARY HAD A LAMB';

Val(a, x)      a logical function that returns, in x, a numeric interpretation of string a (up to the first character of the string that is interpretable as a separator); if string a does not contain a part interpretable as a number, then the value of function Val is false.

Example:

if Val('123.456',T) then

   Write(T)

else

   Write('Error');

This program will write:  123.456 .

For more information on each of the predefined objects, click on the procedure or function name below:

Reserved Variable: CaseNo; Constant: Missing

Functions: Count, Valid, Value

Procedures

Math Library and Random Number Generators

Input and Output functions

Accessing Data from Megafile Manager "Related" Data File

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)


  Megafile Manager Language - Input and Output Functions

Input/output to/from Megafile Manager files.  One of the most convenient features of MML is that it handles all disk input and output functions in a manner that is transparent to the user.  Consecutive records of the current main data file (i.e., the data file that is currently selected in the main menu of Megafile Manager) are processed automatically, and specific values are read from or written to the respective fields of disk files as an automatic consequence of "using" (or changing values of) respective variables in the program.

Pause and review and/or edit values of variables.  Because MML is a specialized programming language, it is assumed that in most cases the input and output will be conducted within selected Megafile Manager data files.  In addition to the previously mentioned "transparent" input/output operations (performed as a consequence of merely using "data variables" in MML programs), procedure Pause is provided to temporarily stop the execution of the program.  Pause will open an editing window which allows the user to review and interactively edit all values of the currently processed data record.

Other.  Finally, the common read and write procedures are supported, which allow for keyboard input and screen (or printer or disk file) output of data, respectively:

Read(x)       Read(x) stops execution of the program, opens a user-input window and prompts the user for input of a value.  The prompt contains a reminder of the expected type of the value to be input (depending on the type of the argument x of the Read(x) procedure).  A Missing value can be assigned to the input variable by pressing ESC in response to the prompt.

Write(x [, ...])  Write(x, ...) is used to display values from the list of arguments on the screen (default) or to send them to the printer or disk file, depending on the selection in the Page/Output Setup dialog.

Writeln        Writeln ("move to the next line") advances the output (screen, printer, or disk output file) to the next line.

For more information on each of the predefined objects, click on the procedure or function name below:

Reserved Variable: CaseNo; Constant: Missing

Functions: Count, Valid, Value

Procedures

Math Library and Random Number Generators

Library of String Functions and Procedures (and Processing Time and Date)

Accessing Data from Megafile Manager "Related" Data File

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)


  Megafile Manager Language - Accessing Data from Megafile Manager "Related" Data File

MML can process data from relationally connected data files and it can recognize their (optional) hierarchical structure, i.e., more than one record in the related data file can be related to each record of the main data file.  For example, each record in the main data file (i.e., the one that is currently selected) may contain fields describing one employee of a company, while records in the related data file may describe the children of each employee (thus there can be more than one "related" record corresponding to each "main" record).

An example of such data files and a simple illustration program that processes them is discussed in detail in Example program number 7.  That program explains the logic of relational (and hierarchical) data base management in MML.  Here, is a brief summary of the two specific facilities of MML which allow you to process related data files (refer to the reference section below for additional examples).

GetY(i)     ("Get record Y(i)") is a standard MML procedure that accesses the i'th record from the "second" (i.e., related) data file which is related to the currently processed record of the main data file.  After executing GetY(i), the consecutive fields of the i'th related record of data (in the related data file) became values of consecutive variables Y(xxx), which now can be used in the program.

NofY        ("Number of records Y") is a predefined MML variable that contains the total number of records in the related Megafile Manager data file (if one has been specified) which are related to the currently processed record in the main data file.

For more information on each of the predefined objects, click on the procedure or function name below:

Reserved Variable: CaseNo; Constant: Missing

Functions: Count, Valid, Value

Procedures

Math Library and Random Number Generators

Library of String Functions and Procedures (and Processing Time and Date)

Input and Output functions

For more information on MML Syntax, see the following topics:

Syntax References

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)


  Megafile Manager - MML Syntax Reference

The following topics contain the complete list of all words (i.e., procedures) of MML in alphabetical order.  For more information on each procedure, click on the procedure name.  Note that a syntax list is also available in Quick Syntax.

A	Abs(x)  ArcSine(x)  ArcCos(x)

B	begin .. end  Boolean

C	Case .. of  CaseNo  Char  Const  Cos(x)  CosH(x)  Count(x, a1, .., an)

D	Delete

E	Euler  Exit  Exp(x)

F	For..to/downto..do

G	GetY(i)

H	Hi

I	If..then..else..undefined  IniAll  Integer, int1, int2, int4  Intrecode

L	Len(a)  Let..be..do  Lo  Log(x)  Log10(x)  Log2(x)  Log1

M	Math Library of MML  Metacommands  Mid(a, x, y)  Missing

N	Nof(Y)  Normal(x)

P	Pause  Pi  Poisson  Procedure  Program ...

R	Read(x)  Real, Real4, Real8  Recode  Rnd(x)  Round(x)

S	SetMiss(x)  SDate(a, x, y, z)  SDelete(a, x, y)  Sign(x)  Sin(x)  SinH(x)  SInsert(a, b, x)  Sqrt(x)  Static  STime(a, x, y, z, q)  Stop  Str(x, y, z)  String[n]  String Library of MML

T	Tan(x)  TanH(x)  Trunc(x)

U	Uniform(x)  UpCase(a)

V	V(xxx)  Val(a, x)  Valid(x)  Value(x)  Var

W	Write(a)  Writeln

Y	Y(xxx)

For more information on MML Syntax, see the following topics:

Using Variables (fields) from Megafile Manager Data Files

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

See also, Introductory Overview.


  MML Syntax Reference - Abs(x)

Absolute value of x.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - ArcSin(x)

Arc sine of x.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - ArcCos(x)

Arc cosine of x.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - begin .. end

Category: MML keywords

"Syntactic parentheses" used to identify the beginning and end of the program, compound instruction, or body of a procedure or function.

Example:

program ExBegin;

begin ······························|

  if COUNT1 > 0 then         	|

  begin ····················|	|the

    Write( 'The value of' );|	|main

    Writeln;                |an inner	|body

    Write( 'COUNT1 is:' );  |inner	|of

    Writeln;                |program	|the

    Write( COUNT1 );        |loop	|program

    Writeln;                |	|

  end; ·····················|	|

end ································|

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Boolean

Category: variable type name

Used in variable declaration statements (see var and static) and other functions (recode, etc.) to specify a variable of type logical (the equivalent of Logical in the Megafile Manager window); synonymous with log1.

Example:

static Cond : boolean;

{declaration of a static Boolean variable}

begin

  Cond := Cond or (ALPHA > 0);

end

Variable Cond will be set to TRUE if a value in data column ALPHA is greater than zero in at least one record.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - case .. of

case expression of

(constant/constant .. constant/Lo .. constant/constant .. Hi) : instruction[;

...]

[else instruction]

end

Category: MML keyword

A "selection instruction" can be considered to be a more general version of the conditional construction if .. then ...  The expression  must be numeric, and the constants must be explicit constants.

The expression must be numeric and the constants must be explicit constants.  If ranges are used on the left sides of the "segments" of the case block, they are interpreted as left-bound inclusive and they cannot overlap.  The words Hi and Lo (denoting respectively, a lower-unbounded interval and an upper-unbounded interval) can be used to specify ranges that are not limited on one side.  Note that the word to can be used in place of the two dots (e.g., Lo to -5).  The else segment is optional but if it is used, there should be no semicolon (;) preceding it.

NOTE:

•	The intervals specified in the left sides of the "segments" of the case block cannot overlap.

•	The keywords Lo and Hi may appear only once.

•	The else segment is optional.

•	A semicolon should not precede either of the keywords end or else.

Example:

begin

  case GENDER of

    Lo .. 0 : Write('Unknown');

{if GENDER < 0, then write 'Unknown'}

    1       : Write('Female');

{if GENDER = 1, then write 'Female'}

    2       : Write('Male');

{if GENDER = 2, then 'Male' }

    4 .. 10 : Write('Other')

{if GENDER >= 4 and < 10, then write 'Other'}

    else Write(' ????? ')

{otherwise write ' ????? '}

  end;

{end of this case instruction}

end

{end of the program}

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - CaseNo

Category: predefined MML variable

Type: int4 (4-byte "long integer")

A reserved variable containing the number of the currently processed record (i.e., the current "case").  CaseNo does not have to be declared.

Example:

begin

  if ( CaseNo mod 10 ) = 1 then

{if CaseNo divided modulo by 10 is 1}

    Delete;

{delete the current record}

end

This example will delete records: 1, 11, 21, 31.. .

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - char

Category: variable type name

Used in variable declaration statements (var and static, see below) and other functions (recode, etc.) to specify a string variable of length equal to 1 (i.e., one character); char is synonymous with string[1].

Example:

var Letter : char;

{new variable Letter is declared as type char}

begin

    Letter := 'a';

end

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Const

const name = value;

const name = [(+/-)]constant;

Category: MML keyword

Used to declare a constant.

Example:

program MyProg;

const  TwoPi = 6.28;

{numeric constant}

       Name = 'George Washington';

{string (i.e., text) constant}

begin

  Write( TwoPi, Name );

  Writeln;

end

This example program will write 6.28 George Washington.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Cos(x)

Cosine of x.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - CosH(x)

Hyperbolic cosine of x.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Count(x, a1, .., an)

Category: standard function

Parameter types:

x - any type

a1 ... an - same type as x

Return value: integer

Returns the number of times that the expression x (specified as the first argument of the function) occurs in the list of arguments (a1 through an).

Example:

begin

  V(6) := Count(Missing,V(1),V(2),V(3));

{count MD's in the list}

end

This program will place the number of missing values found in variables V(1) through V(3) in variable V(6).

NOTE:  This function is useful for calculating indices based on frequencies of specific values, for counting missing data, etc.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Delete

Category: standard procedure

Deletes the currently processed record from the data file.

Example:

begin

  if (GENDER = 'MALE') or (GENDER = 'FEMALE') then

    Write(' OK ')

  undefined

{if the value of GENDER is MD (undefined)}

    Delete

{delete the current record from the data file}

end

This program will write OK whenever it encounters a record with the value of GENDER equal to MALE or FEMALE, and it will delete records in which the value of GENDER is Missing (i.e., "undefined").

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Euler

Euler (e) = 2.71828182845905

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Exit

Category: standard procedure

Terminates processing of the current record (and proceeds to the next record).

Example:

begin

  if ( INCOME < 100 )

{if INCOME is less than 100}

    Exit;

{stop, and move to the next record}

  Write( CaseNo );

end

This program will list in the Text/output Window the numbers of records for which the value of INCOME is greater than or equal to 100.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Exp(x)

Exponential function (Euler to the power of x)

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - for .. to .. do   and   for .. downto .. do

for variable := expression1 to expression2 do

instruction

for variable := expression1 downto expression2 do

instruction

Category: MML keywords

NOTE:

•	variable must be declared local (static and column names not allowed)

•	expression1, expression 2 may be integers (integer, int1, int2, int4)

These are looping instructions.  The instruction (which can be any valid MML instruction, including compound, conditional, another loop, etc.) will be executed once for each integer greater than or equal to expression1 and less than or equal to expression2 (or if for .. downto .. is used, for as many integers less than or equal to expression1 and greater than or equal to expression2).  The variable serves as a loop counter and it assumes the values of consecutive integers from expression1 through expression2 at consecutive passes of the loop; the value of variable cannot be modified inside the loop.

Example:

var i : integer;

begin

  for i := 1 to 3 do ··········| {first loop}

    Write(i); ·················| {(ascending counter)}

  Writeln;

  for i := 100 downto 97 do ···| {second loop}

    Write(i); ·················| {(descending counter)}

  Writeln;

end

This program will write the following (for each record):

  1 2 3

  100 99 98 97

For additional information, see Quick Example 3 (Using Loops and Passing Values of Variables Between Records); see also:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - GetY(i)

Category: standard procedure

Parameter types:

i - integer

("Get record Y(i)") is a standard MML procedure that accesses the i'th record from the "second" (i.e., related) data file which is related to the currently processed record of the main data file (this procedure is usually used with NofY ["Number of records Y"]).  After executing GetY(i), the consecutive fields of the i'th related record of data (in the related data file) assume the values of consecutive variables Y(xxx), which can now be used in the program.

Example:

var i:integer;

begin

  for i := 1 to NofY do

{"cycle" through all related records in the "2nd data file"}

    begin

       GetY(i);

{get the consecutive i'th related record}

       Write( CaseNo, R_NAME )

{write the "main record" number and R_NAME}

    end

end

This program will list values of column R_NAME in the related data file along with the numbers of records (see variable CaseNo) in the main data file to which they are related.

For additional information, see Quick Example 7 (Relational Operations on Two Data Files), Advanced Example 3 (Processing Data in Related Files, Advanced Example 4 (Interactive Processing of Data in Related Files; see also:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Hi

Category: MML keyword

Denotes an open upper limit of a range of values (as specified in recode or case statements).

Example:

recode AAA(integer): integer;

{declaration of a recode function}

begin

{beginning of the function}

  0 .. Hi = 99;

{recode values 0 and above into 99}

  else 1

{recode other valid values into 1}

end;

{end of the function definition}

begin

{beginning of a program using AAA}

  case GENDER of

{in case GENDER is:}

    3 .. Hi : Write(' Many ');

{in the range of 3 and above, write: Many}

    - 10    : Write(' Few  ');

{equal to -10, write: Few}

  end;

{end of the case block}

  Write( AAA( GENDER ) );

{write the value of function AAA of GENDER}

end

{end of the program}

If GENDER is 8; the program will write:  Many 99

NOTE:  The word to can be used instead of two dots; for example:
3 .. Hi : Write(' Many ');  is equivalent to:  3 to Hi : Write(' Many ');

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - if .. then .. else .. undefined

if expression then

instruction

[else

instruction]

[undefined

instruction]

Category: MML keywords

Conditional block construction.

NOTE:  The expression must be of numeric type.  The else and undefined components of the conditional block are optional; the simplest form of the construction is if expression then instruction.  Only one instruction per conditional block is permitted (unless begin .. end is used to enclose a compound instruction).

Example:

var Cond : boolean;

begin

  Cond := Missing;

  if Cond then ·····| { if Cond is true then do: }

    Write(' YES! ') |

  else ·············| { if Cond is false, do: }

    Write(' NO? ')  |

  undefined ········| { if Cond is missing (MD), do: }

    Write(' ! ') ···|

end

This program will write:  !

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - IniAll

Category: standard procedure

Initializes all MML generators of random numbers (Initialize All generators).

Example:

begin

  IniAll;

{initialize all MML random number generators}

  Write( Uniform(1) );

{write a random value from an

Uniform distribution}

end

This program will write the same number (in this case, produced by the generator of uniformly distributed random numbers from the range of 0 to 1) for each record.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Integer, Int1, Int2, Int4

Category: variable type names

Used in variable declaration statements (var and static) and other functions (recode, etc.) to declare integer variables in MML; they denote:  standard (2-byte), short (1-byte), standard (2-byte), and long (4-byte) integers, respectively.  These 4 terms correspond to types Integer, ShortInteger, Integer, and LongInteger, respectively, in the Megafile Manager window.  Note that integer is synonymous with int2.  If you are not familiar with the differences between these types, consult the section on types of data supported in Megafile Manager.

Example:

var    I : integer;

{I is declared as a standard integer}

   Big_i : int4;

{Big_i is declared as "long" integer}

begin

  I := 1000;

  Big_i := 50000;

{this would be outside the range of standard

integers, thus Big_i was declared as long integer}

end

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Intrecode

Intrecode Name(i, j) = constant [, ...];

Category: MML keyword

Declaration/definition of a "small" recoding function (Integer recode function) which transforms ranges of values between j consecutive integers starting with integer i, into new values specified as constants on the right side of the equation (note that there must be exactly j constants specified on the right side).

NOTE:

•	i, j must be integers, where j is a value from 1 to 50.

•	constants may be of any type (strings may not be mixed with other types).

Example:

Intrecode First_N(10,3)='John','Mary','Abraham';

{definition of First_N(x)}

begin

  Write ( First_N(10.5),'and',First_N(11) )

{show values of First_N(x)}

end

x  < 10	becomes Missing,

10  ≤ x < 11	becomes 'John',

11  ≤ x < 12	becomes 'Mary',

12  ≤ x < 13	becomes 'Abraham',

x  ≥ 13	becomes Missing,

therefore, the Write statement will produce:  John and Mary

For additional information, see Advanced Example 1 (Using the Intrecode and Recode Conventions); see also:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Len(a)

Category: standard function

Parameter type:

a - string

Return: integer

Returns the actual length of the string a.

Example:

x := Len( 'abcdefg' );

will produce the same result as:

x := 7 ;

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - let .. be .. do

let (variable be [varname [,...]]

/variable be [(constant/constant .. constant/ %constant*constant) [,...]])[;

...]  do

instruction;

Category: MML keywords

Multiple assignment looping construction which causes the instruction to be executed once for each value in the specified list.  At each pass through the loop, the variable in each segment is assigned the next value from its respective list.

NOTE:  A semicolon should not immediately precede do.

[constant1 .. constant2] - means from constant1 to constant2

(e.g., [1 .. 3] or [1 to 3] means [1, 2, 3]);

[% constant1 * constant2] - means repeat constant2 constant1-times

(e.g., [%5*3] means [3,3,3,3,3]).

Example:

var X, Z : real;

begin

  let X be [V(1), V(2), V(3)] ;

{for each argument in this list}

      Z be [1, 2, 3] do

{and each in this list, do the following:}

    X := Z;

{instruction "within" the loop}

end

This program will assign values 1, 2, and 3 to variables V(1), V(2), and V(3), respectively (for more details, see Looping Instructions).

For additional information, see Advanced Example 2 (Using User-defined Procedures; let..be..do Construction); see also:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Lo

Category: MML keyword

Denotes an open lower limit of a range of values (as specified in recode or case statements).

Example:

recode AAA(integer) : integer;

{declaration of the recode function}

begin

{beginning of the function}

  Lo .. -5 = -99;

{recode values up to -5 into 99}

  else 1

{recode other valid values into 1}

end;

{end of the function definition}

begin

{beginning of a program using AAA}

  case GENDER of

{in case GENDER is:}

    Lo .. 9 : Write('very small');

{in the range up to 9, write: very small}

    1000    : Write('very big  ');

{equal to 1000, write: very big}

  end;

{end of the case block}

  Write( AAA( GENDER ) );

{write the value of function AAA of GENDER}

end

{end of the program}

Let's assume that the value of GENDER is -8; then this program will write:

very small -99

NOTE:  The word to can be used instead of two dots; for example:

Lo to -5 = -99;  is equivalent to:  Lo .. -5 = -99;

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Log(x)

Natural logarithm of x (base Euler).

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Log10(x)

Common logarithm of x (base 10).

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Log2(x)

Binary logarithm of x (base 2).

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - log1

Category: variable type name

Used in variable declaration statements (see var and static, below) and other functions (recode, etc.) to specify a variable of type logical (the equivalent of Logical in the Megafile Manager window); synonymous with boolean).

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Math Library of MML

Math library of MML (numeric constants and math functions available in MML).

Parameter types:

Mathematical functions - any numeric type (i.e.: int1, int2, int4, real4, real8)

Return type:

Round, Sign, Trunc - integer

all other mathematical functions - real

Constants:

Euler 	= 2.71828182845905

Pi 	= 3.14159265358979

Functions:

Abs(x) 	absolute value of x

ArcSin(x) 	arc sine of x

ArcCos(x) 	arc cosine of x

Cos(x) 	cosine of x

CosH(x) 	hyperbolic cosine of x

Exp(x) 	exponential function (Euler to the power of x)

Log(x) 	natural logarithm of x (base Euler)

Log10(x) 	common logarithm of x (base 10)

Log2(x) 	binary logarithm of x (base 2)

Round(x) 	rounds x to an integer

Sign(x) 	returns the sign of x (x<0 → -1;
x=0 → 0; x>0 → 1)

Sin(x) 	sine of x

SinH(x) 	hyperbolic sine of x

Sqrt(x) 	square root of x

Tan(x) 	tangent of x

TanH(x) 	hyperbolic tangent of x

Trunc(x) 	truncates x to an integer

Functions which generate random numbers:

Normal(x) 	random real number from a normal distribution with the mean of 0 and the standard deviation of x

Poisson(x) 	random real number from a Poisson distribution with lambda equal to x (i.e., with a mean of x and the standard deviation of √x)

Uniform(x) 	random real number from a uniform distribution in the range of 0 to x

Rnd(x) 	same as Uniform(x)

NOTE:  All random number generators in MML are initialized ("seeded") via procedure IniAll which is called automatically at the beginning of the execution of the program, but may also be called at any point from within an MML program.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Metacommands

Metacommands are special commands of MML which control global aspects of the program, such as commands to instruct the program to redirect all output to the printer or disk file, or to select a subset of the data file to be processed.  In MML, metacommands are placed in curly brackets, and thus may look similar to comments, but they always begin with a dollar sign, e.g., {$P-}, or {$F:10}.  The following sections describe the MML metacommands.

Metacommands:  {$P+}, and  {$P-}

Category: metacommands

These MML output redirection metacommands control the output from all subsequent Write commands in the program (depending on the current setting of the output destination in the Page/Output Setup dialog).

Example:

begin

  {$P+}

{screen or printer output ON}

    Write(' Output is sent to the screen or printer ');

end

The text or values will appear in the Text/output Window and/or the printer (or in the disk file), depending on the setting in the Page/Output Setup dialog.

These metacommands are useful to temporarily disable (or enable) output from the program without removing the respective Write commands.

Metacommands:  {$F:xxx} and  {$N:yyy}

{$F:xxx} and  {$N:yyy}

Category: metacommands

Parameter type:

xxx, yyy - integer

The MML data subset metacommands.  Under normal circumstances, the entire record of the current Megafile Manager data file is available for processing with the MML program.  However, if records are very large (e.g., 8 megabytes each), the amount of processing space MML requires may exceed the memory of the computer and the data cannot be processed in the standard way (i.e., all columns simultaneously).  Then you will need to instruct MML which (continuous) subset of the entire set of columns will be used by the program.  The exact maximum number of columns that can be processed by MML without using the {$F:xxx} and {$N:yyy} metacommands depends on the width of the columns in the data file.  The {$F:xxx} ("first") metacommand instructs MML as to the position of the first column to be considered (where xxx is the consecutive number of that column in the current Megafile Manager data file), and the {$N:yyy} ("next") metacommand instructs MML that the next yyy columns (starting at the xxx'th column) will be used by the program.

Example:

{$F:101}

{process columns starting at column number 101}

{$N:250}

{process 250 consecutive columns}

begin

  INCOME := 0;

end

In this example, only columns number 101 through 350 will be used by the program.  The column INCOME must be among the selected columns, otherwise it will not be recognized.

NOTE:

•	If the columns which are to be processed do not form a continuous block (but are distributed across the entire large data file), reorder them first using the Megafile Manager options in the Megafile Manager Edit pull-down menu).

•	Unlike other MML metacommands, these two (if used) must be specified in the declaration section of the program, before the first word begin.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Mid(a, x, y)

Category: standard function

Parameter types:

a - string

x, y - integer

Return value: string

Starting at the x'th character of the string a, the function will return a substring of y subsequent characters.

Example:

T := Mid( 'Mary has a lamb', 6, 3 );

will produce the same result as:

T := 'has';

For additional information, see Quick Example 6 (Operations on Strings and Dates, Printing Reports); see also:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Missing

Category: predefined MML constant

Type: context sensitive

Denotes a missing value of the respective type of variable to which it is assigned (the specific value of Missing is context sensitive, i.e., it contains a missing data value for the variable to which it refers in the MML statement).

Example:

begin

  V(10) := Missing;

{set value in column 10 to its respective MD}

end

This program will assign the respective missing data value for column 10 to all records.  See the section on MML predefined variables for more information.

NOTE:  Because all expressions which contain Missing evaluate to Missing, the condition if x = Missing will always be undefined, thus the expression if not Valid(x) should be used instead to determine whether x is Missing.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - NofY

Category: predefined MML variable

Type: int4 (4-byte "long integer")

("Number of records Y") contains the total number of records in the related Megafile Manager data file (if one has been specified), which are related to the currently processed record in the main data file.  (NofY is usually used together with GetY(i) ["Get record Y(i)"] which accesses the i'th from among the total of NofY related records, see GetY(i).)

Example:

begin

  Write( CaseNo, NofY );

{ show the current (main) record number,

and the number of its "related" records }

  Writeln;

end

This program will show the sequential record number for each record of the main data file and the number of records related to it (in the related data file).

For additional information, see Quick Example 7 (Relational Operations on Two Data Files), Advanced Example 3 (Processing Data in Related Files), Advanced Example 4 (Interactive Processing of Data in Related Files); see also:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Normal(x)

Random real number from a normal distribution with the mean of 0 and the standard deviation of x.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Old

Category: keyword

Used in definitions of recoding functions (see Recode) to specify intervals which remain unchanged.

Example:

recode A;

  begin

    Lo .. 0, 10 = Old;

    3 = 10;

  end;

This recoding function (named A) will change 3 into 10, and the values that are either less than 0 or equal to 10 will remain unchanged (all other values will be set to missing data).

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Pause

Category: standard procedure

Temporarily stops the execution of the program and allows the user to review and edit values of all columns of the currently processed record and all variables used in the current MML program.  The procedure displays the  number of the currently processed record in the resulting Megafile Manager: Pause dialog.

When Pause is called, the user can also decide whether to continue processing this record (or the entire program).  This procedure is most useful in applications designed to verify and clean data based on criteria defined in the program (the procedure is called in such programs whenever an illegal value is detected).  Unlike in the data verification and cleaning facilities of Data Management which check only whether values belong to the specified lists or ranges of allowable values, the verification criteria used in MML programs may contain complex conditional relations between values in different fields of the same record.  The procedure is also very helpful for debugging complex MML programs.

Example:

begin

  if not Valid(VALUE) then

{when the value of VALUE is Missing, then}

    Pause;

{stop and show data from this record}

end;

This program will Pause whenever a missing value is encountered in column VALUE, so that data can be reviewed and edited (if desired).

For additional information, see Quick Example 2 (Using Conditional Statements and Interactive Verification and Editing of Data); see also:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Pi

Pi = 3.14159265358979

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

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MML Advanced Examples


MML Syntax Reference - Poisson

  MML Syntax Reference - Poisson(x)

Random real number from a Poisson distribution with lambda equal to x (i.e., with a mean of x and the standard deviation of √x).

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


MML Syntax Reference - Procedure

  MML Syntax Reference - Procedure ..

procedure Name;

begin

instruction[;

...]

end;

Category: MML keyword

Declaration of a user-defined procedure.

Example:

var i:integer;

{declaration of integer variable i}

procedure Results;

{declaration of name of the procedure (Results)}

begin

{beginning of the body of procedure Results}

  for i:=1 to 4 do

{... instruction of the procedure}

    Write(V(i));

  Writeln;

end;

{end of the procedure definition}

begin

{beginning of program using procedure Results}

  V(2):=V(2) + V(3);

  V(4):= V(2) / V(1);

  Results;

{call procedure Results here}

end

{ end of the program}

The procedure Results declared (and defined) at the beginning of the program is used to display values of four variables.  It is called in the program whenever new values of those variables are calculated.

NOTE:  Inside the user-defined procedures, columns in the Megafile Manager data file must be referred to by their numbers (using the V(xxx) convention) and not their names.  No variables need to be "passed" to user-defined procedures; the procedures can use all program variables.

For additional information, see Advanced Example 2 (Using User-defined Procedures; let..be..do Construction); see also:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


MML Syntax Reference - Program ...

  MML Syntax Reference - Program

program name;

Category: MML keyword

The (optional) name of the program.

Example:

program Example;

{the name of this program is Example}

begin

{beginning of the main body of the program}

  Pause;

{this program will Pause at each record}

end

{end of the program}

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Read(x)

Category: standard procedure

Parameter type:

x - variable of any type

Allows the user to interactively input a value for the variable specified in Read(x) during the execution of the program.

Read(x) stops execution of the program, opens the MML Read - Row Number ... dialog and prompts the user for input of a value in the edit field.  A Missing value can be assigned to the input variable x by pressing ESC in response to the prompt.

Example:

var X : real;

begin

  Read(X);

{stop and open the "user input"

window; expect a real value}

  V(7) := sin(X*Pi) + V(8) * cos(0.5*X*Pi);

end

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


MML Syntax Reference - real, real4, real8

  MML Syntax Reference - real, real4, and real8

Category: variable type names

Used in variable declaration statements (see var and static, below) and other functions (recode, etc.) to declare real (floating point) variables; real and real4 are alternative ways of referring to a standard (4-byte) real number, real8 denotes a long (8-byte) real number.  These three terms correspond to types Float and DoubleFloat, respectively, in the Megafile Manager window.  Note that real is synonymous with real4.  If you are not familiar with the differences between these types, see Megafile Manager Column Specs.

Example:

var    X : real;

{declare X as a standard real}

  Prec_x : real8;

{declare Prec_x as a "long" (8-byte) real}

begin

       X := 10.00001;

  Prec_x := 10.0001000010001;

end

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Recode

recode Fname( input_type ) : output_type;

begin

(constant/constant .. constant/Lo .. constant/constant .. Hi)
[, ...] = (constant/Old)[;

...]

[else constant]

end

Category: MML keyword

Declaration/definition of a function which recodes values and/or types of values.

NOTE:

•	The predefined MML variable Missing may be used as a constant only in the left side of the recoding equation.

•	The intervals specified on the left sides of the recoding equations cannot overlap.

•	The keywords Lo, Hi and Missing may appear only once.

•	Old may be used only if input_type and output_type of the function are compatible.

•	The maximum number of recoding equations in one recode function is 3000.

•	A semicolon should not precede either of the keywords end or else.

Example:

program ExRec;

recode AAA(integer):integer;

{declaration of integer recode function AAA(x)}

begin

{beginning of the function definition}

  Lo .. 0 = -1;

{recode all x≤0 as -1}

  1, 2, 3 = 1;

{recode 1, 2, and 3 as 1}

  Missing = 3

{recode Missing values as 3}

  else 2

{recode all other valid numbers become 2}

end;

{end of the function definition}

begin

{beginning of the program}

  Write( AAA(-5), AAA(3), AAA(Missing) );

{show AAA of the 3 values}

end

{end of the program}

This program will display:  -1  1  3  (for each record of the data file).

NOTE:

•	The word to can be used instead of two dots; for example:

Lo .. 0 = -1;  is equivalent to:  Lo to 0 = -1;

•	See the Example Program 4 on recode functions for more information.

For additional information, see Quick Example 4 (Verification and Analysis of Data using the Recode Statement), Advanced Example 1 (Using the Intrecode and Recode Conventions); see also:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Rnd(x)

Random real number from a uniform distribution in the range of 0 to x (same as Uniform(x)).

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Round(x)

Rounds x to an integer.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - SDate(a, x, y, z)

Category: standard procedure

Parameter types:

a - string

x, y, z - integer

Interprets string a as date x/y/z.  The procedure supports a variety of date formats, and it actually "searches" the entire string for a part interpretable as a date.  Specifically, an input string (interpretable by this procedure) can consist of the following (in a sequence): "any characters" + integer + separator + integer + separator + integer + "any characters."  If an interpretable substring is not found, then missing data are returned for each of the 3 numeric arguments.

For example statements:

SDate( '1987/03/16' , YY, MM, DD );

or:

SDate( 'Date: 1987/03/16' , YY, MM, DD );

will produce the same result as:

YY := 1987;  MM := 3;  DD := 16;

For additional information, see Quick Example 6 (Operations on Strings and Dates, Printing Reports); see also:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - SDelete(a, x, y)

Category: standard function

Parameter types:

a - string

x, y - integer

Return value:  string

Deletes (i.e., removes) a substring of y characters from string a, starting at character number x.

Example:

T := SDelete( 'Mary had a lamb', 6, 3 );

will produce the same result as:

T := 'Mary  a lamb';

See also, SInsert(a, b, x).

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - SetMiss(x)

Category: standard procedure

Parameter type:

x - variable of any type

Assigns a missing data code to a local or static variable x.

Example:

var X : real;

begin

  SetMiss(X);

{set the value of X to Missing}

end

The statement SetMiss(X) is equivalent to X:=Missing.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Sign(x)

Returns the sign of x (x<0 → -1; x=0 → 0; x>0 → 1).

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Sin(x)

Sine of x.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - SinH(x)

Hyperbolic sine of x.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - SInsert(a, b, x)

Category: standard function

Parameter types:

a, b - string

x - integer

Return value: string

Inserts string b into string a, starting at x'th character position of string a.

Example:

T := SInsert( 'Mary  a lamb', 'had', 6 );

will produce the same result as:

T := 'Mary had a lamb';

See also, SDelete(a, b, x).

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Sqrt(x)

Square root of x.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Static

static varname	: vartype;

[...   : ...;]

Category: MML keyword

Declares static (i.e., global) variables, i.e., program variables that retain their values across records (cases).  Static variables are initialized to false, 0 (zero), or empty string (text), depending on the variable type.  The initialization is performed only once at the beginning of the program (and not at the beginning of each record as is the case for local variables).

Example:

static Sum  : real;

{declare Sum as a static real variable}

       Sum1 : real8;

{declare Sum1 as a static real8 variable}

begin

    Sum := Sum + V(8);

    V(9) := Sum;

end

This program accumulates values of column number 8 across records, and places the cumulative sum in column number 9.

NOTE:  The keyword static does not have to be repeated in each consecutive line of declarations of static variables.

For additional information, see Quick Example 3 (Using Loops and Passing Values of Variables Between Records); see also:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - STime(a, x, y, z, q)

Category: standard procedure

Parameter types:

a - string

x, y, z, q - integer

Interprets string a as time x:y:z.q.  The procedure actually "searches" the entire string for a part interpretable as time.  Specifically, input strings (interpretable by this procedure) may consist of the following (in a sequence): "any characters" + integer + separator + integer + separator + integer + '.' (i.e., period) + integer + "any characters."  If an interpretable substring is not found, then missing data are returned for each of the 4 numeric arguments.

Example:

STime( '11:09:18.19', H, M, S, Hu );

will produce the same result as:

H := 11;  M := 9;  S:= 18;  Hu:=19;

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Stop

Category: standard procedure

Stops the execution of the program.

Example:

begin

 if CaseNo > 100 then

{if the number of record is greater than 100}

    Stop;

{stop the program (do not process any new records)}

 Write( INCOME );

end

This program will be executed only for the first 100 records.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Str(x, y, z)

Category: standard function

Parameter types:

x - any numeric type (int1, int2, int4, real4, real8)

y, z - integer

Return value: string

Returns a string of y characters, containing an image of value x, with z digits after the decimal point (i.e., this function "writes" number x to a string with the format specified by y and z).

Example:

T := Str(123.456, 10, 5);

will produce the same result as:

T := ' 123.456  ';

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - String[n]

Category: variable type name

Used (as part of the var or static variable declarations, and other functions such as recode, etc.) to declare a string (i.e., text) variable of length n characters (string[n] is equivalent to the type Text of length n in the Megafile Manager window).  The value of n may be from 1 to 200.  Note that square brackets are required.

Example:

var FullName: string[40];

{declare FullName as a 40-character string}

begin

{beginning of the program}

  FullName := F_NAME + L_NAME;

{calculate FullName as: F_NAME + L_NAME}

  Write( FullName );

{show the result}

end

{end of the program}

In this program, we are concatenating string (i.e., text) values of two columns from the current data file (F_NAME and L_NAME) and placing the resulting string in the newly declared local variable (FullName).  The library of MML functions for processing string values is listed later in this section (see the description of the MML string library).

NOTE:

•	String variables cannot be interpreted as "tables of characters;" thus, for example, the expression FullName[3] would not return the third character of the string variable in the above example (string functions should be used to access selected substrings of string values, as described in the following description).

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - String Library of MML

String library of MML (library of functions for performing operations on string values, including time and date values).

Len(a)	Actual length of string a.

Mid(a, x, y)	Substring of y characters of string a, starting at the x'th character.

SDate(a, x, y, z)	Interprets string a as date x/y/z.

SDelete(a, x, y)	Delete substring of y characters from string a, starting at the x'th character.

SInsert(a, b, x)	Insert string b into string a, starting at x'th character of string a.

STime(a, x, y, z, q)	Interprets string a as time x:y:z.q.

Str(x, y, z)	"Write" number x as a string with format specified by parameters y and z.

UpCase(a)	Converts all lower case letters in string a into upper case.

Val(a, x)	Returns in x a numeric interpretation of string a.  (If string a does not contain a part interpretable as a number, then the value of function Val is false.)

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Tan(x)

Tangent of x.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - TanH(x)

Hyperbolic tangent of x.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Trunc(x)

Truncates x to an integer.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Uniform(x)

Random real number from a uniform distribution in the range of 0 to x (same as Rnd(x)).

For additional information, see Quick Example 5 (Math Operations, Random Numbers); see also:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - UpCase(a)

Category: standard function

Parameter type:

a - string

Return value: string

Converts all lower case letters in string a into upper case letters.

Example:

T := 'Mary had a lamb'; UpCase(T);

will produce the same result as:

T := 'MARY HAD A LAMB';

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - V(xxx)

Category: predefined MML indexed variable

Parameter type:

xxx - integer

Reserved indexed variable used to reference variables (i.e., columns) from the main data file, where xxx is the consecutive column number in the data file.  Note that for the related data file (if one is specified), the analogous reserved variable which references columns is Y(xxx).

Example:

begin

  V(10) := 'ABC';

{assign value 'ABC' to column number 10}

  V(11) := 13;

{assign value 13 to column number 11}

  V( V(11) ) := 112;

{because V(11)=13, this statement will assign value

112 to column number 13}

end

It is generally recommended to refer to Megafile Manager data file columns by their actual names, because then an additional program error checking step can be performed by the compiler at compile time (and not just during execution).  For example, the compiler will detect potential variable type mismatches.  Also, if actual names are used (instead of indexed variables), MML will produce smaller and faster code.  However, in some circumstances, referencing column numbers via the indexed variable convention is more efficient (e.g., it allows looping across ranges of columns).  Also, it is the only permissible way of referring to data columns within user-defined procedures (see Procedures).

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Val(a, x)

Category: standard function

Parameter types:

a - string

x - real

Return value: boolean

Logical function which returns, in x, a numeric interpretation of string a (up to the first character of the string that is interpretable as a separator); if string a does not contain a part interpretable as a number, then the value of function Val is false.

Example:

if Val('123.456',T) then

   Write(T)

else

   Write('Error');

This program will write:  123.456 .

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Valid(x)

Category: standard function

Parameter type:

x - any type

Return value: boolean

Standard MML logical function which is equal to true if the value of expression x is not Missing (i.e., when it is valid).

Example:

begin

  if not Valid(INCOME) then

{if value of INCOME is Missing, then}

    Delete;

{delete this record from the data file}

end;

This program will delete all records in the data file in which the value of INCOME is Missing.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Value(x)

Category: standard function

Parameter type:

x - any numeric type (i.e.: int1, int2, int4, real4, real8)

Return value: same as parameter type

Standard MML function that is equal to 0 if the value of variable x is Missing; if the value of x is not Missing, however, the function returns the actual value of x (x must be numeric).  This function is particularly useful when calculating a sum, or if used in conjunction with function Count, calculating an average of a list of values, adjusted for missing data.  (Normally, the result of the entire expression is set to missing data if the value of at least one element is Missing).

Example:

begin

  MEAN := ( Value(V1) + Value(V2) + Value(V3) ) /

          ( 3 - Count(Missing, V1, V2, V3 ) );

end

This program calculates an average of V1, V2, and V3, adjusting for missing data.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Var

var Name1 [, ...] : type;

Category: MML keyword

Declares local (i.e., not static) variables, i.e., program variables which do not retain their values across records (cases).  Local variables are initialized to Missing at the beginning of each record.

Example:

var I : integer;

{local variable I is declared as integer}

    X : real;

{local variable X is declared as real}

begin

  for I:=1 to 5 do

    Write(10*i-3);

  let X be [V(1),V(2)] do

    X := Missing;

end

Note that the keyword var does not have to be repeated in each consecutive line of declarations of local variables.

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Write(a, ..)

Write(a1,...,an)

Category: standard procedure

Parameter type:

a1,...,an - any type

Used to display values from the list of arguments on the screen or to send them to the printer or disk file (depending on the metacommand used).

By default, the output is displayed in the Text/output Window.

Example:

begin

   Write(' John has',3,'horses');

{write the list of 3 values}

end

This program will write the string John has 3 horses for each record in the data file.  Note that MML automatically adds a leading blank before all numeric and string (i.e., text) values.

NOTE:  The output will be formatted according to specifications in the Print Setup dialog.

For additional information, see Quick Example 6 (Operations on Strings and Dates, Printing Reports); see also:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Writeln

Category: standard procedure

"Move to the next line" command.  This command causes the starting position of the next output from a Write(a, ..) command to advance to the next line (in the Text/output Window, printed output, or a disk output file; i.e. this command produces a "carriage return" and "line feed").

Example:

begin

    Write(CaseNo);

{write the value of CaseNo for this record}

    Writeln;

{move to the next line}

end

This program will list the numbers of all records one under another (each starting on a new line).

For additional information, see:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  MML Syntax Reference - Y(xxx)

Category: predefined MML indexed variable

Parameter type:

xxx - integer

Reserved indexed variable used to reference variables (i.e., columns) from the second (i.e., related, if one is specified) data file, where xxx is the consecutive column number in that data file.  (See also GetY(i) and NofY).  Note that there is an analogous reserved variable which references columns from the main data file: V(xxx).

Example:

begin

    GetY(1);

{access related record number 1}

    Write(Y(2));

{write the content of column number 2 in that record}

end

This program will assign a value of 26 to the second column of the data file (related to the main data file) in the first record related to the currently processed record of the main data file.  This Assignment is performed in the record that was "opened" by the GetY(1) command.

For additional information, see Quick Example 7 (Relational Operations on Two Data Files), Advanced Example 3 (Processing Data in Related Files, Advanced Example 4 (Interactive Processing of Data in Related Files); see also:

MML Quick Syntax

Declarations, Recoding Functions, Procedures

Instructions (Assignment, Conditional, Looping, Write, Read, etc.)

Predefined Objects and Special Conventions in MML (by category)

MML Quick Examples

MML Advanced Examples


  Megafile Manager - MML Execution

Click on the Execute toolbar button to process your MML program.  When you click this button, STATISTICA will check the syntax of the MML commands and give you a specific error message if the syntax is wrong (for more information on MML syntax, see Syntax References).  The MML Error Messages section contains an alphabetical list of MML compile-time and run-time error messages that are displayed if something is wrong.


  Megafile Manager - MML Error Messages

For more information on MML error messages, see the following topics:

MML Compiler Error Messages

MML Run-Time Error Messages


  MML Compiler Error Messages

',' expected.  The compiler didn't find a comma where one was expected.

'(' expected.  The compiler didn't find a left parenthesis where it expected one.

')'  expected.  The compiler didn't find a right parenthesis where one was expected.

'*' expected.  The compiler didn't find an asterisk where one was expected (e.g., in let statement).

'.' at the end of program expected.  The compiler didn't find a period at the end of the program.

'..' or 'to' expected.  The compiler didn't find .. (two dots) or to in the recode or case statement after Lo.

':' expected.  The compiler didn't find a colon ( : ) where one was expected.

':=' expected.  The compiler didn't find a colon followed by an equal sign, where one was expected (in an assignment statement).

';' expected.  The compiler didn't find a semicolon where one was expected.

';' or 'end' expected.  The compiler didn't find the end (i.e., semicolon or word end) of a statement, compound statement, or procedure.

'=' expected.  The compiler didn't find an equal sign where one was expected.

'[' expected.  The compiler didn't find a left bracket where one was expected.

']' expected.  The compiler didn't find a right bracket where one was expected.

'be' expected.  The compiler didn't find be in the let statement.

'begin' expected.  The compiler didn't find begin at the beginning of the program or recode statement.

'case' intervals overlap.  The intervals specified in a case statement overlap.

'do' expected.  The compiler didn't find do where it was expected (in the for or let loop statements).

'end' expected.  The compiler didn't find end at the end of the recode or case statement.

'of' expected.  The compiler didn't find of in the case statement.

'Old' is not permitted in this recode.  The compiler found the word Old in a recode which has incompatible types of input and output.

'recode' intervals overlap.  The intervals specified in the recode statement overlap.

'recode' too complicated.  You have defined a recode with a total of more than 3000 "left sides" (i.e., including intervals and individual numbers).

'then' expected.  The compiler didn't find then in the if statement.

'to' or 'downto' expected.  The compiler didn't find to or downto in a for statement.

Column name is MML keyword.  MML keywords (e.g., begin, if, procedure) are not permitted as column names in MML.  Use Verify Names from the Megafile Manager window Analysis pull-down menu to correct the problem.

Compiler memory overflow.  The MML compiler has run out of dynamic memory space.  This usually means that your program contains many symbols and/or complex expressions.

Constant and variable mismatch.  You have attempted to use variables and constants in a single let list (e.g., let x be [a, b, 20, 30]).

Constant expected.  The compiler didn't find a constant where it expected one.  It may occur in constant declarations, or in lists used in the if statement.

Different lengths of lists in 'let.'  All lists in the let statement must be of the same length.

Duplicated 'Hi' in 'case' or 'recode.'  You have attempted to use Hi twice in the case or recode statement.

Duplicated 'Lo' in 'case' or 'recode.'  You have attempted to use Lo twice in the case or recode construction.

Duplicated 'Missing'.  You have attempted to use Missing twice in the case or recode construction.

Duplicated identifier.  The compiler found an identifier that is declared more than once or is also used in the current data file as one of column names.  This error may also occur if the name of a standard constant, variable, function or procedure is used as column name in the data file (or in a declaration).

Duplicated Missing definition.  You have attempted to define a constant as Missing.  The predefined MML constant Missing is exclusively reserved to denote missing data in MML.

Duplicated names in disk file.  The compiler found a duplicated column (field) name in the data file.

Duplicated or illegal 'F' option.  Metacommand {$F:xxx} (the first column number in the specified subset) appeared twice or the specified integer constant xxx is invalid.

Duplicated or illegal 'N' option.  Metacommand {$N:xxx} (the number of columns in the specified subset) appeared twice or the specified integer constant xxx is invalid (greater than the number of columns in the data file or less than 1).

Error in 'if' statement.  Syntax error was found in the conditional if statement.  For example, a semicolon may have been placed before the word else or undefined.

Error in expression.  Invalid or empty expression was found.  This error may occur if one of the arguments of an operator is missing, or as the result of another syntax error.

Error in list of 'let' statement.  An invalid symbol was found in the list of the let loop.

Error in string type definition.  There is an error in the string type declaration.  The correct format is as follows: var (or static) Name : string[xxx]; , where Name is a user-selected string name and xxx is the string length (greater than 0 and less than 201).

Identifier expected.  The compiler didn't find an identifier where one was expected.  This error may occur in declarations (e.g., const, var, static, recode) and in statements (e.g., for, let).

Identifier not declared.  The compiler found an undefined (or misspelled) identifier.

Identifier too long.  Declared identifier (variable, function, constant or procedure name) is longer than 8 characters.

Illegal operator.  You have attempted to use an operator other than:  **, ^, =, <, >, <>, <=, >=, +, -, or, *, /, div, mod, and, not.

Incompatible types in add. expr.  An addition argument (+, -, or) was encountered within a string argument.

Integer constant expected.  The compiler didn't find an integer where one was expected (e.g., in let statement such as let x be [3.5 .. 10]).

Integer constant out of range.  The compiler found a type Int4 constant with an absolute value greater than 2,147,483,647.

Internal MML Compiler error.  An unusual combination of circumstances (data structure and the structure of the program) has caused the failure of an internal consistency check within MML.  Please contact StatSoft Technical Support.

Invalid character in column name.  This message is issued whenever an invalid character is used in a column name.  Column names can be up to 8 characters long and may contain all keyboard characters, including upper and lower case letters, numbers, spaces, punctuation, etc.  You can use the Verify Names option from the Megafile Manager window Analysis pull-down menu to correct the names.

Invalid interval in 'case.'  The left limit of an interval in the case construction is greater than the right limit.

Invalid interval in 'recode.'  The left limit of an interval in the recode construction is greater than the right limit.

Invalid real numeric constant.  There is a recode error in a real constant.  Number may be too large, or contain invalid characters.

Local variable expected.  Variables used as loop counters must be declared as local (i.e., via the var declaration).

MML: external disk error.  An input/output error has occurred when MML was accessing the current Megafile Manager data files (e.g., drive door not closed, no diskette in drive, diskette bad).

Multiplier after '%' out of range.  A multiplier used in the let list (in the %xxx convention) must be less than or equal to 500.

Number expected.  The compiler didn't find a number where one was expected (e.g., var CODE1: string[Able]; or Intrecode First[A,B] = 1, 2;).

Number inside the interval.  In a Recode function, you have specified a number which is inside one of the intervals specified in another equation of the same function.

Numeric expression expected.  Expression in the case statement must be of type integer.

Procedure identifier in expression.  You have attempted to use a procedure in an expression (or the expression is invalid).

Text expression in 'if.'  String expression was used instead of a logical or numeric expression in the if statement.

Too few intervals in 'Intrecode.'  The second parameter in Intrecode is less than 1.

Too large interval in 'let' list.  The compiler found an interval in the let list which is larger than 500.

Too many 'Intrecodes.'  You have defined more than 16 Intrecode statements.

Too many 'recodes.'  You have defined more than 16 recode statements.

Too many intervals in 'Intrecode.'  The second parameter in Intrecode is greater than 50.

Type expected.  The compiler didn't find a type name where one was expected.  Probably the type name is missing or misspelled in the declaration (var, static, recode) statement.

Unexpected ';'.  The compiler found a semicolon before else or undefined in either the if .. then or case statement.

Unexpected character.  While scanning, the compiler found an unexpected special character which is not part of a string constant (&, @, etc.).

Unexpected constant.  The compiler found a constant in an unexpected place.  For example, it may occur if you used a constant on the left side of an assignment statement.

Unexpected end of file.  While scanning, the compiler found an unexpected end of file mark in a comment, metacommand or other illegal location.  Probably the result of a missing curly bracket } in a comment or a closing end in a compound statement (e.g., begin...end).

Unexpected function.  There is a function name in an unexpected place.  This error may also occur if a function was used as a procedure.

Unknown identifier or syntax error.  The compiler found an undefined (or misspelled) identifier or other syntax error.

V, Y are MML reserved words.  The compiler found declaration of an item with name V or Y.  These words are reserved and used to reference fields (columns) in the input files.  Use another name (e.g., VV or YY).

Variable identifier expected.  You have attempted to use a constant, procedure, or function identifier in an assignment statement or as a parameter, where a variable is expected (e.g., in the Read procedure).

Variable is of illegal type.  You have attempted to use a variable of illegal type as a parameter in a procedure or function (e.g., integer variable in the UpCase procedure).

Wrong argument of 'div' or 'mod' oper.  A non-integer argument is used with the operator div or mod.

Wrong argument of 'or' operator.  A non-logical argument is used with the or operator.

Wrong argument of 'and' operator.  A non-logical argument is used with the conjuction operator (and).

Wrong argument of mult. operator.  A multiplication operator (*, /, div, mod, and) is used with a string argument.

Wrong argument of the '*' or '/' operator.  An illegal operator (*, /) is used with a logical argument.

Wrong first character in column name.  This message is issued whenever an invalid first character is detected in a column name (e.g., when a number is used as the first character).  You can use the Verify Names option from the Megafile Manager window Analysis pull-down menu to correct the problem.

Wrong string constant.  The line ended before the closing quotation mark, or in a constant definition a minus or plus (- or +) sign was found before a string constant.

Wrong type in 'let' list.  The compiler found a type of item in the let list which does not match the let control variable.

Wrong type.  You have attempted to use incompatible types in an assignment statement, expression, or as a procedure/function parameter.

You cannot assign values to Y.  You have attempted to use a Y-variable (Y(xxx)) on the left side of an assignment statement.  This is not permitted (values of the related data file cannot be changed).

See also, MML Run-Time Error Messages


  MML Run-time Error Messages

Argument out of domain.  An attempt has been made to apply to a math function an argument which is out of the function's domain (e.g.,  x := ArcSin(z) where z is out of the range from -1 to +1)

Argument singularity.  An attempt has been made to apply an argument to a math function which is the function's singular point (e.g.,  x := Log(0) ).

Cannot read from disk.  A disk input error occurred when reading from main or related Megafile Manager data file (may result from breaking execution of the program).

Cannot write record to disk.  A disk output error occurred when writing to the current Megafile Manager data file (may result from breaking execution of the program).

Division by zero.  A attempt to perform division by zero has been detected.

Executer memory overflow.  The MML executer has run out of dynamic memory space.  This usually means that your program contains many symbols and/or complex expressions.

Floating-point error.  A floating-point error in computation has been detected.

Index of variable V out of range.  The number of column xxx (in the Megafile Manager data file) used as index of the V(xxx) variable is less than 1 or greater than the total number of columns in the current data file.

Index of variable Y out of range.  The number of column xxx (in the Megafile Manager data file) used as index of the Y(xxx) variable is less than 1 or greater than the total number of columns in the relational data file.

Internal MML run-time error.  An unusual combination of circumstances (data structure and the structure of the program) has caused the failure of an internal consistency check within MML.  Please contact StatSoft Technical Support.

Invalid argument of string function.  A wrong value (or a wrong number of arguments) is used as parameters of a string function (SDate, STime, Mid, SInsert, SDelete, Str and Val).

Invalid integer operator argument.  An argument of the div or mod operator was incorrect.

Invalid operation.  Program contains an instruction which is not valid (usually involving an operation on a non-numeric or infinitely large value).

Limit of Missing data exceeded.  Number of missing data assignments specified by user before execution as acceptable (see Options) has been exceeded.

Missing as a parameter in GetY.  Argument i of the GetY(i) procedure was evaluated to Missing.

No related records for this row.  You have attempted to access a column from the related file, but for the currently processed record there are no related records in the second data file.

Numeric argument required.  An attempt has been made to apply a math function to a non-numeric (string or boolean) argument.

Range overflow.  During the computation process an invalid (out of range) number appeared (e.g., an operation such as  x := 1e200 * 1e200 ).

Second file not specified.  An attempt to access data from the related file has been made without previously specifying the second file to be used.

Wrong parameter in GetY.  You have called the GetY(i) procedure with an argument i which is either less than 1 or greater than the number of related records.

Wrong reference to field.  In V(xxx) or Y(xxx) the expression xxx was evaluated to a string or to Missing.

Wrong STRING value assignment.  You have attempted to assign to a string variable a value which is longer than the declared length of that string variable.

Wrong type.  You have attempted to use incompatible types of values in an assignment statement or in a procedure or function.  This error may occur when you refer to data columns (in Megafile Manager data files) via the V(xxx) convention (otherwise such errors are detected at compile time).

Wrong value assigned to INT1 variable.  You have attempted to assign a value greater than 127 or less than -127 to an INT1 variable.

Wrong value assigned to INT2 variable.  You have attempted to assign a value greater than 32,767 or less than -32,767 to an INT2 (INTEGER) variable.

Wrong value assigned to INT4 variable.  You have attempted to assign a value greater than 2,147,483,647 or less than -2,147,483,647 to an INT4 variable.

Wrong value assigned to REAL variable.  You have attempted to assign a value greater than 3.4E38 or less than -3.4E38 to a REAL variable.

Wrong value assigned to REAL8 variable.  You have attempted to assign a value greater than 1.7E308 or less than -1.7E308 to a REAL8 variable.

Wrong value is set to LOG1 variable.  You have attempted to assign a value different than Missing, true or false to a logical variable.

See also, MML Compiler Error Messages


  Megafile Manager - MML Options

The Megafile Manager: Options dialog is accessible by clicking on MML Options from the MML window Options pull-down menu or by clicking on the [image] button on the toolbar.

Megafile Manager: Options dialog:

MD Assignments

Relational file


  Megafile Manager MML Options - MD Assignments

During the execution of the MML program, it may be necessary to assign the missing data value to one or more of the Megafile Manager columns (all MML expressions which contain missing data, or contain other expressions which evaluate to missing data, are themselves evaluated to missing data).  Once the limit specified in the Less than edit box is exceeded, an error message will be displayed and the execution of the program will stop.  You can use this option as an additional verification process (in addition to MML's syntax verification) in order to verify that the program is being executed as expected.  Note that selecting the Unlimited option essentially "turns off" the display of this error message.


  Megafile Manager MML Options - Relational File

These options permit the selection of a second Megafile Manager file related to the currently open file.  See Quick Example 7: Relational Operations on Two Data Files, Advanced Example 3: Processing Data in Related Files, Advanced Example 4: Interactive Processing of Data in Related Files.'

Name button:  Click on this button to select the second Megafile Manager file from the MML - Select Relational File dialog.

Key in main file/Key in relational file:  Specify the key columns in the main and relational files, respectively.

Note:  the two key columns must be of the same type, and each file should be sorted according to its key before processing with MML.


  Megafile Manager - Pause

This Megafile Manager procedure temporarily stops the execution of the program and allows the user to review and edit values of all columns of the currently processed record and all MML program variables.  The procedure displays the number of the currently processed record in the MML: Pause dialog (see the caption bar of the dialog) in which you can review and edit the values for the respective variables.

When Pause is called, the user can also decide whether to continue processing this record (or the entire program).  This procedure is most useful in applications designed to verify and clean data based on criteria defined in the program (the procedure can be called in such programs whenever an illegal value is detected).  Unlike in the data verification and cleaning facilities of Data Management which check only whether values belong to the specified lists or ranges of allowable values, the verification criteria used in MML programs may contain complex conditional relations between values in different fields of the same record.  The procedure is also very helpful for debugging complex MML programs.

Example: (see also Example Program 4)

begin

  if not Valid(VALUE) then

{when the value of VALUE is Missing, then}

    Pause;

{stop and show data from this record}

end;

This program will Pause whenever a missing value is encountered in column VALUE, so that the data can be reviewed and edited (if desired).

Megafile Manager Pause dialog:

Variable

Value

Get

Put

Continue

Restart Row

Next Row

Stop Program

Review Columns


  Megafile Manager Pause - Variable

Enter here the Megafile Manager data column name or MML program variable name whose value you want to review or edit for the row specified in the title of this dialog. (Note that you can click on the Review Columns button, below, to view a list of the column names for the current Megafile Manager file.)


  Megafile Manager Pause - Value

Enter or edit here, the value of the previously specified data column or program variable.  You can use the Get button to place here the current value of this variable for editing.


  Megafile Manager Pause - Get

Click on this button to place the current value of the previously specified data column or program variable in the Value edit field.


  Megafile Manager Pause - Put

When you have edited the value of the previously-selected data column or program variable, you can click on this button to "put" that value back into the program variable or the Megafile Manager data file.  Note that this is done automatically when you click on the Continue button, however, if you want to edit more than 8 variables at a time for one row, you will need to "reuse" the edit fields.  Therefore, you can use the Put button to make the changes for a respective variable, clear those edit fields and then edit the values for another variable without leaving the current row of data.


  Megafile Manager Pause - Continue

Click on this button to continue the MML program and accept all of the current changes made to the selected variable values.  The Pause dialog will re-open for another case (if necessary) preserving the currently specified selection of variables or data columns or when Pause is next encountered in the program.


  Megafile Manager Pause - Restart Row

Click on this button to re-evaluate the currently specified row (shown in the title of the Pause dialog).


  Megafile Manager Pause - Next Row

Unlike the Continue button which will open the Pause dialog when it is called next in the program (not necessarily for the next row), clicking on this button will bring up the Pause dialog for the next consecutive row.


  Megafile Manager Pause - Stop Program

Click on this button to "break" the execution of the MML program and return to the MML window.


  Megafile Manager Pause - Review Columns

Click on this button to open the Megafile Manager: Review Columns dialog in order to view a listing of the column names for the current Megafile Manager data file.


  Megafile Manager - Read - Row Number...

This procedure is more convenient than Pause, when review and/or editing of only specified MML program variables or Megafile Manager data column values is necessary.  It allows the user to interactively input a value for the variable specified in Read(x) during the execution of the program.  The Read(x) procedure stops execution of the program, opens the MML Read - Row Number ... dialog and prompts the user for input of a value in the edit field; the prompt contains a reminder of the expected type of the value to be input (depending on the type of the argument x of the Read(x) procedure).  A Missing value can be assigned to the input variable x by pressing ESC in response to the prompt.

Example:

var X : real;

begin

  Read(X);

{stop and open the "user input"

window; expect a real value}

  V(7) := sin(X*Pi) + V(8) * cos(0.5*X*Pi);

end


  Megafile Manager - Verify

Click on this option from the MML window Analysis pull-down menu in order to verify the syntax of the MML program.  If a syntax error occurs an error message will be displayed (see MML Error Messages).

Note that you can also "test run" the program for other errors (e.g., math errors) via the Test Run option from the Analysis pull-down menu.


  Megafile Manager - Test Run

This option (accessible from the MML window Analysis pull-down menu) allows you to test the MML program for correct operation without actually changing the data.  Test running may uncover unexpected consequences of the operations performed by the program (e.g., division by zero, logarithms of negative values, etc.) which can be caused by particular characteristics of the data, and cannot be anticipated during compilation.  If an error occurs, an error message will be displayed (see MML Error Messages).

Note that you can also verify the syntax of the program via the Verify option from the Analysis pull-down menu.


  STATISTICA BASIC Overview

STATISTICA BASIC is a simple to use but powerful programming language which can be used for a variety of types of applications ranging from simple data transformations (e.g., whenever you need to do more than can be done using the spreadsheet formulas, e.g., loops, recoding functions) to building custom, complex, permanent extensions to computational, graphics, and data management procedures of STATISTICA.

For more information, see:

General Conventions of STATISTICA BASIC

Using STATISTICA BASIC

Integration with STATISTICA and direct access to the STATISTICA system data files

Alphabetical list of all Commands and Functions

Specialized statistical functions and procedures

Data Management Operations

Graphics

Matrix Language

Interactive user-input, custom dialogs

Output:  data files, text files, Scrollsheets, graphics, reports

Scrollsheets, follow-up analysis

Accessibility, multiple program windows

Quick Access to your custom STATISTICA BASIC applications (custom extensions of STATISTICA and developing your own "new modules")

Capacity

Support for external DLLs (an ultimate application-integration tool)


Accessibility, Multiple Program Windows

  STATISTICA BASIC Overview - Accessibility, Multiple Program Windows

STATISTICA BASIC is accessible in every module (from the pull-down menu Analysis or the floating Auto Task Buttons toolbar) and you can open multiple STATISTICA BASIC programs in one module (or in different modules).  For example, you may have 5 or more different programs opened in their separate windows and cut and paste the code between the programs or execute them in arbitrary sequences.


Using STATISTICA BASIC

  STATISTICA BASIC Overview - Using STATISTICA BASIC

The BASIC is accessible at any point in your analysis; it comes with an integrated environment that allows you to write, edit, verify, debug (i.e., "dry run"), and execute your programs.  STATISTICA BASIC is very easy to use; however, it is a specialized language that offers numerous unique advantages over general-purpose programming languages (refer to the remaining topics in the Overview for more information).


Integration with STATISTICA and Direct Access to STATISTICA System Data Files

  STATISTICA BASIC Overview - Integration with STATISTICA and Direct Access to STATISTICA System Data Files

STATISTICA BASIC operates directly on STATISTICA system data files, thus, the user does not have to be concerned about file handling, input, output, etc.  It supports two flexible modes of accessing data from STATISTICA system files:

•	spreadsheet-like RandomAccess Mode, where all data are referenced in a predefined array Data(case, variable), and

•	data-base-like Sequential Mode, where data records are read sequentially, one at a time (although this can be changed with a Jump command) and the entire program is automatically executed (repeated) for each record (case).

STATISTICA BASIC is fully integrated into the STATISTICA system; for example, it offers direct access to the currently specified system case selection conditions, variable names, missing data codes, text values, case names, long value labels, variable comments/formulas, etc.  Programs written in STATISTICA BASIC can be run as part of a STATISTICA macro, or an SCL (STATISTICA Command Language) program.  New procedures written in STATISTICA BASIC can be made easily accessible and integrated with STATISTICA by assigning them to buttons on the Auto Task Buttons floating toolbars, so that they become your custom-designed extensions of the STATISTICA system.


Capacity

  STATISTICA BASIC Overview - Capacity

STATISTICA BASIC is a powerful programming language that is well suited to handle large computational problems:  It supports local data arrays with up to 8 dimensions and there is no limit to the size of the arrays (all memory available in your system can be addressed), so custom procedures involving operations on large multidimensional matrices can be developed (a comprehensive selection of matrix operations are also supported).


Output from STATISTICA BASIC

  STATISTICA BASIC Overview - Output from STATISTICA BASIC

(1):  Data files, text/graphics reports, external files.  The output from STATISTICA BASIC can be handled in a variety of ways.  First of all, the values (numeric or text) can be written directly to the current STATISTICA data file (e.g., when you need to perform data transformations or cleaning).  It can also be directed to the printer, disk files, or the report window (where it can combine graphs with text or tables in a single document).  Also, graphs of practically unlimited complexity can be created (see Graphics Library of STATISTICA BASIC) and text or tabular output can be sent to new Scrollsheets.

(2):  Scrollsheets.  In addition to the various report, external file, or data file output options (see above), you can create new Scrollsheets or "cascades" of Scrollsheets (directly from within your BASIC program) and display your tabular or text results in a way that is most efficient to review.  Creating a simple output Scrollsheet takes just one line of code, and as a result, you get a "tool" to review tables and values that is incomparably more efficient and user-friendly than traditional text-output editors.  For example, the value display format, column width, etc., can be interactively customized by the user of your STATISTICA BASIC program, edited (including Drag-and-Drop, AutoFill, etc.), printed as tables with high-resolution grid lines, selectively copied, exported, etc.; the values can also be interactively visualized in graphs of any type supported in STATISTICA.  Moreover, if you need to create specific, highly customized Scrollsheets that look like those created by STATISTICA (with titles, custom formatting, etc.), a comprehensive set of functions is provided and can be used in your BASIC program.  As all other functions in STATISTICA BASIC, these functions are easy to use because they can be inserted with a help of a Wizard.  For a complete list of all Scrollsheet functions, see Scrollsheet Functions in STATISTICA BASIC

For a complete list of the input/output functions, see STATISTICA BASIC Syntax Reference - User Input/output Function.

See also Advanced Examples.


Interactive User-Input, Custom Dialogs

  STATISTICA BASIC Overview - Interactive User-Input, Custom Dialogs

Simple to use and flexible facilities can be called using STATISTICA BASIC with a single function call to accept the user input.  For example, a statement as simple as Read(A) will display a dialog box and prompt the user of your BASIC program to enter a value for variable A; the statement PauseAndEdit will display an interactively customizable dialog where you can display and/or edit (in run time) current values of any variable in the program (an invaluable aid for debugging your programs, but also a perfect tool to be incorporated in your custom BASIC applications).

A selection of most commonly used types of dialogs for displaying messages, warnings, Yes/No/Cancel prompts, etc., as well as more complex custom-input dialogs (e.g., a series of edit boxes or buttons) are available in a "mini-resource" library built into STATISTICA BASIC.  Their main advantage is that they are extremely easy to set up (each can be called with a simple function - and even that is aided by the Wizard).  Also, the selection of those standard Windows resources callable from the BASIC is quite comprehensive and sufficient in most standard applications.  However, if you have the need for more specialized or customized dialogs, floating toolbars, palettes, etc., you can define them using standard Windows development tools and call them from your STATISTICA BASIC program as an external DLL function (STATISTICA BASIC supports external DLLs).

The supported functions include:

•	dialogs with messages, warnings, Yes/No/Cancel prompts, issue alerting beeps, etc.;

•	interactively customizable dialogs where the user can select from listed options;

•	dialogs enabling the user to edit (in run time) current values of any variable in the program (an invaluable aid for debugging your programs, but also a perfect tool to be incorporated in your custom BASIC applications);

•	variable selection dialogs enabling the user to select up to four lists of variables, each with its own limitations on the maximum number of permissible variables;

•	standard Windows file selection dialogs (for files of a specified type);

•	define more specialized or customized dialogs, such as floating toolbars, palettes, etc., can be defined using standard Windows development tools and can be called from your STATISTICA BASIC program as an external DLL function (STATISTICA BASIC supports external DLLs).

See also, Calling STATISTICA BASIC from within SCL

Example 1:

This program will display a list of three items (the first item will be highlighted by default), then display the user's selection in a message box.

RandomAccess;

x := DisplayListBox('Select One', 'Item A|Item B|Item C', 1);

GetDelimitedString('Item A|Item B|Item C', x, select$);

DisplayMessageBox(MB_OK, 'You Have Selected', select$);

Example 2:

This program will create a dialog box with two buttons; the user can then choose to print the current Scrollsheet or graph.

RandomAccess;

button := DisplayButtonBox('Select Output', 'Print Report|Print Graph');

if button = 1 then

   PrintScrollsheet(GetScrollsheet(0));

if button = 2 then

   PrintGraph(GetGraph(0));

Advanced Examples

For a list of advanced examples of STATISTICA BASIC programs using graphics procedures, refer to Advanced Examples of STATISTICA BASIC Programs.

For a complete list of user input/output functions, see User Input/Output Functions in STATISTICA BASIC


Support for External DLLs

  STATISTICA BASIC Overview - Support for External DLLs

Your STATISTICA BASIC applications can also be further extended by calling procedures written in other programming languages.  STATISTICA BASIC can call external programs via a flexible interface to external DLLs (Dynamic Link Libraries; see Calling Functions or Subroutines Defined in External DLL Files), thus your STATISTICA BASIC programs can serve as an interface between existing applications written in other programming languages (e.g., commercial or public domain procedures) and your STATISTICA data files, graphs, and reports.  Also, STATISTICA BASIC can be used to develop STATISTICA-compatible front ends for other applications.


Quick Access to Custom STATISTICA BASIC Applications

  STATISTICA BASIC Overview - Quick Access to Custom STATISTICA BASIC Applications

Custom extensions of STATISTICA and developing your own "new modules."  Your STATISTICA BASIC applications, such as custom data transformations, other computational procedures, interfaces to other programs, or new, user-designed graphs can be permanently added to your STATISTICA system and made easily accessible by assigning them to the Auto Task Buttons on the floating toolbars.  Libraries of your programs can be easily organized using local or global floating Auto Task Buttons toolbars.  STATISTICA BASIC can also be used to develop your own custom-designed "STATISTICA modules" or "STATISTICA applications" based on the STATISTICA File Server foundation (included in the package).

Advanced Examples.  For a list of advanced examples of STATISTICA BASIC programs using graphics procedures, refer to Advanced Examples of STATISTICA BASIC Programs.


  STATISTICA BASIC Language

STATISTICA BASIC is a specialized data transformation and graphics programming language integrated into every module of STATISTICA.  The language is similar to BASIC in terms of its general syntax conventions (e.g., variables do not have to be declared).  However, it offers numerous specialized extensions designed to aid transformations of data and statistical data base management.  STATISTICA BASIC can also be used to produce customized graphs and diagrams.  For more information, see:

Overview of STATISTICA BASIC

General Conventions of STATISTICA BASIC

Using STATISTICA BASIC

Integration with STATISTICA and direct access to the STATISTICA system data files

Alphabetical list of all Commands and Functions

Specialized statistical functions and procedures

Data Management Operations

Graphics

Matrix Language

Interactive user-input, custom dialogs

Output:  data files, text files, Scrollsheets, graphics, reports

Scrollsheets, follow-up analysis

Accessibility, multiple program windows

Quick Access to your custom STATISTICA BASIC applications (custom extensions of STATISTICA and developing your own "new modules")

Capacity

Support for external DLLs (an ultimate application-integration tool)

Quick Reference

Quick Examples

Quick Syntax

Reference

General Conventions

Sequential vs. RandomAccess Mode

Alphabetical list of all Commands and Functions

Execution

Specific Categories

Program Flow	Distributions	Recodes

General	Graphics	Scrollsheets

Operators	Math & Trig	Statistical

Data Management	Matrix Operations	Text

User Input/Output	User-defined Functions

Options

Default Processing Mode

Interrupt after: (specified number of) errors

Size of MEMORY Array

On Math Error

Display All Warnings and Error Messages

Expandability of STATISTICA BASIC

Examples

Quick Examples

Annotated Examples

Advanced Examples

Error Messages

Compile-Time Error Messages

Run-time Error Messages

General

STATISTICA Spreadsheet Formulas vs. STATISTICA BASIC

Advantages of STATISTICA BASIC

How to use/define variables in STATISTICA BASIC

How to use arrays in STATISTICA BASIC Functions

How to use strings in STATISTICA BASIC Functions

How to set (or leave unchanged) default values of function parameters

How to pass lists of strings to STATISTICA BASIC Functions

How to retrieve lists of strings using STATISTICA BASIC Functions

Including Source Code Files


  STATISTICA BASIC Random Number Generator

Using the uniform random number generator and the inverse distribution functions available in STATISTICA BASIC or the spreadsheet formulas (see Spreadsheet Edit Specs), you can generate random numbers that follow various distributions (see Distribution Functions, their Integrals and Inverse Distribution Functions).  For example, the spreadsheet formula:

= vweibul(rnd(1), 1, 2, 0)

will produce random numbers that follow the Weibull distribution with scale parameter 1, shape parameter 2, and location parameter 0.  For additional details, see Evans, Hastings, and Peacock (1993, pages 23-24; see References).

To seed the random number generator in STATISTICA BASIC you can either use function IniAll (which will use the computer-time as the seed), or you can use function SetSeed to use a specific seed-number (so you can replicate series of random numbers).

For information on filling blocks with random values from a Uniform distribution, see Spreadsheet/Scrollsheet Fill Random Values.


  STATISTICA BASIC Introductory Overview - STATISTICA Spreadsheet Formulas vs. STATISTICA BASIC

The STATISTICA spreadsheet formulas are sufficient for performing most simple data transformation, recoding, and verification tasks (see Spreadsheet Edit Specs and Data Verification).  However, many statistical data management tasks require performing operations that cannot be defined via individual formulas, such as transformations with nested logical conditions, loops, complex recoding functions, iterative processing of cases, or accessing random cases in the data file.  Performing such operations require a "true" programming language, and they can be accomplished most efficiently using STATISTICA BASIC.

Also, STATISTICA BASIC offers access to graphics, Scrollsheets, matrix operations, statistical functions, text values, more flexibility in specification of formulas, and calls to external DLLs (Dynamic Link Libraries).


  STATISTICA BASIC Introductory Overview - Advantages of STATISTICA BASIC

STATISTICA BASIC is a specialized programming language that offers many advantages over general purpose languages.

•	First of all, STATISTICA BASIC can operate directly on STATISTICA data files, thus the user does not have to be concerned about file handling, input, output, etc.  STATISTICA BASIC recognizes and takes advantage of the STATISTICA system data file structure; its programs can reference variables by names, recognize STATISTICA system missing data, delete or aggregate cases in STATISTICA data files, etc.

•	STATISTICA BASIC works in an environment that is integrated into every module, and it can use for input not only the data from the current data file, but also from Scrollsheets and graphs (as well as relevant disk files). The programs can be executed as part of the STATISTICA SCL (command language) programs and Macros within all modules to perform operations that use the various facilities of the respective module.

•	STATISTICA BASIC includes large libraries of specialized procedures and functions (not found in general purpose programming languages) that are particularly useful for statistical data analysis, graphics, and data base management.  For example, STATISTICA BASIC supports designated data recoding statements, conditional deletion of cases, functions that create random numbers following specific theoretical distributions, functions that calculate indices while automatically adjusting counters for missing data, and random access to cases in the data file.

•	STATISTICA BASIC provides specialized statistical and matrix functions which may be performed on values in STATISTICA data files, Scrollsheets, text files, or any derived or computed values, in any combination (see Matrix Library of STATISTICA BASIC and Statistical Functions in STATISTICA BASIC).  Also, a large selection of distribution functions, their inverses and integrals are included.

•	STATISTICA BASIC provides access to STATISTICA graphics procedures (see Graphics Library of STATISTICA BASIC), allowing you to create custom graphical applications, retrieve and modify previously created graphs, design custom graph customization options (that can be assigned to Auto Task Buttons), automate routine sets of modifications of existing graphs, and more.

•	STATISTICA BASIC includes a mini-library of custom controls (dialog boxes, message boxes, etc.; see User Input/Output Functions), thus its programs may interact with the user to obtain input, display informational or warning messages, interactively edit values of variables (or values from the STATISTICA data file) during program execution and control program flow (for example, allowing the user to select actions or pausing to allow the user to review output).

•	Numerical results can be displayed in Scrollsheets created as part of STATISTICA BASIC programs, with control over all aspects of the contents and appearance of the Scrollsheet, including titles, color, formats, fonts, etc. (see Scrollsheet Library of STATISTICA BASIC - Overview).

•	The capabilities of STATISTICA BASIC can be extended by calling functions and/or subroutines from external DLLs (Dynamic Link Library) files.

•	Finally, STATISTICA BASIC programs can accept input from multiple sources: directly from the user, from STATISTICA system data files, Scrollsheets, and ASCII (text) files.  Output can be written to STATISTICA system data files, Scrollsheets, text/graphic reports, text files, or displayed on-screen.


  STATISTICA BASIC - Calling Functions or Subroutines Defined in External DLL Files

STATISTICA BASIC can be used to call functions and/or subroutines from external DLL (Dynamic Link Library) files (you can also write user-defined functions and subroutines in the STATISTICA BASIC language).  In order to do this, you must first DECLARE the subroutine (SUB) or function (FUNCTION) at the beginning of the STATISTICA BASIC programs (before any instructions are executed) and then later in the program, you can call the function or subroutine.

Declaration of Function/Subroutine

The declaration statement syntax is as follows:

For subroutines:

DECLARE SUB SubrName LIB "DLL_Name" (types_of_parameters);

For functions

DECLARE FUNCTION FunctName LIB "DLL_Name" (types_of_parameters) AS type_of_result;

where

SubrName 	is the name of the subroutine in the external DLL

FunctName	is the name of the function in the external DLL

DLL_Name	is the name of the external DLL file

types_of_parameters and type_of_result depend on the specific function/subroutine.

The syntax for defining these is described below..

The type_of_parameters which can be declared are described below.  (The pointer to ... specifier enables the external functions to change the values of variables.)

char,    pointer to char      (signed 1 byte values ± 127)

byte,    pointer to byte      (unsigned 1 byte values from 0 to 255)

integer, pointer to integer   (signed 2 byte values ± 32,767)

word,    pointer to word      (unsigned 2 byte values from 0 to 65,534)

long,    pointer to long      (signed 4 byte values ± 2,147,483,647)

dword,   pointer to dword     (unsigned 4 byte values from 0 to 4,294,967,294)

float,   pointer to float     (4 byte floating point number)

double,  pointer to double    (8 byte floating point number)

string,  pointer to string    (string of characters)

The type_of_results which can be declared are described below.  This parameter should describe the returned value of the function and consequently, the type of variable to which the returned value will be assigned.

char,    (signed 1 byte values ± 127)

byte,    (unsigned 1 byte values from 0 to 255)

integer, (signed 2 byte values ± 32,767)

word,    (unsigned 2 byte values from 0 to 65,534)

long,    (signed 4 byte values ± 2,147,483,647)

dword,   (unsigned 4 byte values from 0 to 4,294,967,294)

float,   (4 byte floating point number)

double,  (8 byte floating point number)

string,  (string of characters)

Using Functions/Subroutines

To use external functions/subroutines, call them like built-in routines.  For example:

1.	Subroutines:

DECLARE SUB MessageBeep LIB "c:\windows\user.exe" (integer);

MessageBeep(0);

2.	Functions:

DECLARE FUNCTION RunTest LIB "d:\run.dll" (integer, pointer to integer) AS integer;

v1 := RunTest(v2, v3);

The first statement above, declares the name of the function (RunTest) contained in the external DLL file run.dll.

3.	Even if you declare a routine as a function, you can disregard the result if it is convenient to do so (results of functions are not required to be assigned to variables).

Writing External Functions/Subroutines

Programmers interested in creating their own external DLLs should consult the Microsoft Windows SDK for more information.

Example

The following statement declares the function FindWindow from standard Windows DLLs.

DECLARE FUNCTION FindWindow LIB "c:\windows\user.exe" (string, string);

window := FindWindow("", "My Scrollsheet");

scr := GetScrollsheet(window);

PrintScrollsheet(scr);

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Expressions

Operators

Compound Instructions (Begin..End)

Conditional Constructions

Loops

GOTO Statements

User-defined Functions and Subroutines

Recoding Statements

Missing data

Transferring Values Between Cases

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


  STATISTICA BASIC Examples

Following are six examples of STATISTICA BASIC programs.  For examples with more detailed descriptions, see Annotated Examples and Advanced Examples; see also STATISTICA BASIC Introductory Overview.

EXAMPLE PROGRAM 1:  Loop, if...then

Sequential;                   {specifies Sequential mode; the program will be executed once for each case}

v1:=(v2+v3)/2;                {simple assignment statement (calculate values of variable 1)}

for i:=11 to 21 do            {beginning of loop: FOR..TO..DO..}

   v(i):=v(i)/1000;           {body (one instruction) and end (;) of loop}

if v4<0 then v4:=0;           {a simple (one-line) IF..THEN instruction}

if Valid(v6) then begin       {IF with a block (BEGIN..END) of instructions}

   v7:=0; v8:=1; v9:=2; end;  {end of the BEGIN..END block}

EXAMPLE PROGRAM 2:  Nested loop, Write

RandomAccess;                        {specifies RandomAccess mode; this statement is not required unless you change the default BASIC settings}

sum := 0;                            {initializes temporary variable sum}

  for i := 1 to NCases do            {beginning of first loop: FOR..TO..DO..}

    for j := 1 to NVars do           {beginning of second loop: FOR..TO..DO..}

      sum := sum + Value(Data(i,j)); {body (one instruction) and end (;) of loop}

WriteLn('sum=',sum);                 {Write sum to selected output device (WriteLn)}

EXAMPLE PROGRAM 3:  Creating a simple graph

RandomAccess;                        {specifies RandomAccess mode; this statement is not required unless you change the default BASIC settings}

x$ := VarName(1);                    {places 1st variable name in string variable x$}

y$ := VarName(2);                    {places 2nd variable name in string variable y$}

NewGraph(SCATTERPlot, 'Scatterplot', {creates new 2D scatterplot}

         x$, y$, NCases, v1, v2);    {using all values of 1st and 2nd variables}

EXAMPLE PROGRAM 4:  Arrays, Correlations, Text Values, Scrollsheets

RandomAccess;                        {specifies RandomAccess mode; this statement is not required unless you change the default BASIC settings}

ReDim corr(NVars, NVars);            {declares square array corr of size equal to number}

                                     {of variables in current data file}

MatrixCorrelations(Data, 1, corr);   {computes correlations from data and places results}

                                     {in the array corr }

name$ := VarName(1);                 {places 1st variable name in string variable name$}

for i := 2 to NVars do               {beginning of loop: FOR..TO..DO..}

  name$ := name$ + '|' + VarName(i); {builds delimited string containing variable names}

scr := NewScrollsheet(NVars, NVars,  {displays correlation matrix in a new Scrollsheet}

        corr, 'Correlations', name$, name$);

PrintScrollsheet(scr);               {Prints the Scrollsheet to the printer}

EXAMPLE PROGRAM 5:  Goto, DisplayMessageBox

run:=1;                                       {initializes variable run, to be used as a run counter}

start:                                        {label denoting place to goto}

  WriteLn ('This is run number: ',run);       {prints run number}

  run:=run+1;                                 {increases the run counter}

  answer:=DisplayMessageBox (MB_YESNO,

          'Question','Repeat one more time?');{asks if the user wants to continue}

if answer = IDYES then goto start;            {if yes, then go to to the label start}

EXAMPLE PROGRAM 6:  Functions and Subroutines

Function factorial(x)                      {declares function}

begin                                      {beginning of block defining the function}

  Factorial:=1;                            {initializes the function return value to 1}

  For i:=1 to X do Factorial:=Factorial*i; {computes the factorial function X!=1*2*..*X}

end;                                       {end of function}

Sub Noverr(n,r, byref X)                   {declares subroutine, X is passed by reference}

begin                                      {beginning of  block defining the subroutine}

  X:=Factorial(n)/(Factorial(r)*Factorial(n-r));{computes X as N-over-r}

end;                                       {end of subroutine}

noverr(5,3,x);                             {main program: call subroutine noverr}

WriteLn('Number of ways to select 3 objects from 5 objects:',X);


  Annotated STATISTICA BASIC Examples

Following are examples of STATISTICA BASIC programs with detailed descriptions.

Example 1:  Loop, if, block, CaseNo

Example 2:  Adjusting for Missing Data

Example 3:  Transferring Values Between Cases, Jump

Example 4:  Calling a Function Defined in an External DLL File (Calling the Windows Message Box)

Example 5:  User-defined Functions and Subroutines

For a list of short, simple examples (loops, if...then, graphs, Scrollsheets), see Quick Examples.

For a comprehensive list of advanced example programs, see Advanced Examples of STATISTICA BASIC Programs.


  Annotated STATISTICA BASIC Examples - Loop, if, block, CaseNo

In the following simple example we illustrate several elementary features of the STATISTICA BASIC Syntax.

Sequential;                    {specifies Sequential mode}

v1:=(v2+v3)/2;                 {EXAMPLE PROGRAM 1}

for i:=11 to 21 do             {beginning of loop}

   v(i):=v(i)/1000;            {body and end (;) of loop}

if v4<0 then v4:=0;            {if v4<0 then set it to 0}

if Valid (v6) then begin        {if v6 is not missing}

   v7:=0; v8:=1; v9:=2; end;   {end of begin..end}

if (CaseNo=6) and (v7>0) then  {if case number is 6 and v7>0, then}

   Jump(20)                    {Jump to case number 20}

The first line of this program specifies a Sequential processing mode.  In the second line, a new value for variable v1 is calculated (as the mean of v2 and v3).  In the second and third line a loop is executed in which variables v11 through v21 are processed (each of those variables is divided by 1000).  In the next line a simple conditional statement is executed in which the value of v4 is set to 0 if it was less than 0.  The next if..then statement contains a compound instruction (i.e., a begin..end block of instructions) consisting of three simple assignment statements.  This compound instruction is executed only if the current value of variable v6 is valid (i.e., when it is not missing).  Finally, in the last two lines the program checks whether the current case number (CaseNo) is 6 and if variable number 7 is greater than 0; if this condition is met, the program will jump to case number 20.


  Annotated STATISTICA BASIC Examples - Adjusting for Missing Data

In the following example we will compute a sum of squares of variables v3 through v10 while skipping missing data (variables with missing data will be assigned -1).  The resulting sum of squares will be stored in variable SQSUM.

Sequential;                 {specifies Sequential mode}

begin                       {BEGINing of program (optional)}

  sqsum:=0;                 {initialize variable sqsum}

  for i:=3 to 10 do         {for variables 3 to 10}

    if Valid(v(i)) then     {if not missing data}

      sqsum:=sqsum+v(i)**2  {update sqsum}

    else                    {if value is missing}

      v(i) := -1;           {set it to -1}

end;                        {END of program (optional)}

Note that the word end at the end of the program is optional but it is required if the program starts with begin (begin and end are always symmetrical).


  Annotated STATISTICA BASIC Examples - Transferring Values Between Cases, Jump

In the following programs, we will map all values in variable v1 into the range from -1 through 1.  These two examples will illustrate differences between the Sequential and RandomAccess mode of STATISTICA BASIC.

Sequential mode:  In Sequential mode, the program will read the data file twice (sequentially, one case at a time).  In the first pass through the data file, the program will find the maximum absolute value of v1.  After reaching case number 100, the program will return (Jump) to case number 1 and (in the second pass) all values will be divided by that maximum value (found in the first pass).  Note that variable Mem(1) is used to flag the second pass of the program (otherwise the program would execute an endless loop).  Variable Mem(2) is used to store the maximum absolute value.

Sequential;          {specifies Sequential mode}

if Mem(1) = 0 then   {if this is the first pass}

   begin

     if abs(v1) > Mem(2) then Mem(2) := abs(v1);

     if CaseNo > 100 then

        begin

           Mem(1) := 1;

           Jump(1);

        end;

   end

else                 {if this is the second pass}

   begin

     v1 := v1 / Mem(2);

     if CaseNo > 100 then Stop;

   end;

RandomAccess mode:  In RandomAccess mode, all cases of the data file are accessible to the STATISTICA BASIC program in the predefined data array Data(i,j).  The program will find the maximum absolute value of variable 1 for cases 1-100 and that value will be held in the variable MAXVAL.  Then, for cases 1-100, the values of variable 1 will be divided by that maximum value.

RandomAccess;                   {specifies RandomAccess mode}

maxval := -9999;

  for i := 1 to 100 do

    if abs(Data(i,1)) > maxval then

      maxval := abs(Data(i,1));

  for i := 1 to 100 do

    Data(i,1) := Data(i,1)/maxval;

NOTE:  When comparing these two examples, you can see that it is much simpler to perform this particular analysis in RandomAccess mode than in Sequential mode; also, the RandomAccess mode will be executed much faster.


  Annotated STATISTICA BASIC Examples - Calling a Function Defined in an External DLL File (Calling the Windows Message Box)

The following STATISTICA BASIC program is an example of calling a function which is defined in an external DLL file (for more information on functions and subroutines in external DLLs, see Calling Functions or Subroutines Defined in External DLL Files).  Upon execution of this program, you will be given the option to set missing data in variable v10 to zero, and to set data in variable v9 that is less than 15 to 15.  The program uses a function from the MS Windows User.exe file called MessageBox.  This function requires four parameters and returns an integer.

SEQUENTIAL;

DECLARE FUNCTION MessageBox LIB "user.exe" (integer,string, string, integer) as integer;

v10 := v1 + v2 + v3 + v4 + v5;	{if any of these values are missing then v10 will also be missing}

if Mem(1) = 0 then

begin

   if not valid(v10) then

   begin

      i := MessageBox (0,'Missing Data. Set to 0?','Missing Data',35);

      if i = 2 then Mem(1) :=1;

      if i = 6 {yes} then v10 := 0;

   end;

end;

valsum(v,6,2,v9);

if Mem(2) = 0 then

begin

  if (v9 < -15) then

    begin

      i := MessageBox (0,'Data Out of Range. Set to -15?', 'Out of Range', 51);

      if i = 6 {yes} then v9 := -15;

    end;

end;

As the program encounters each instance of missing data or a value less than -15, the user is given the opportunity to choose whether action is taken or the value is not changed (you will also be able to Cancel the operation of each message box).


  Annotated STATISTICA BASIC Examples - User-defined Functions and Subroutines

In the following simple example we illustrate user-defined functions and subroutines in the STATISTICA BASIC Syntax.

RandomAccess;                   {specifies RandomAccess mode}

Function Factorial(x)                      {declares function}

begin                                      {beginning of block defining the function}

  Factorial:=1;                            {initializes the function return value to 1}

  For i:=1 to x do Factorial:=Factorial*i; {computes factorial function x!=1*2*..*x}

end;                                       {end of function}

Sub NoverR(X,n, byref total)               {declares subroutine}

begin                                      {beginning of block defining the subroutine}

 dim x(n);                                 {declares array X}

 total:=0;                                 {initializes variable total}

 for i:=1 to n do begin                    {beginning of loop}

  x(i):=Factorial(n)/(Factorial(i)*Factorial(n-i));{computes X as N-over-i}

  total:=total+x(i);                       {updates variable total}

 end;                                      {end of loop}

end;                                       {end of subroutine}

dim x(5);

noverr(x,5, total);                        {main program: call subroutine noverr}

MatrixDisplay (x, 'Total='+str(total,3,0));{display results}

The first line of this program specifies the Randomaccess processing mode.  Next, function Factorial is defined, which computes the factorial function x!  = 1*2* .. *x.  Then subroutine NoverR is declared.  Argument X in the subroutine is an array, argument n is passed by value, and argument total is passed by reference.  Thus, the value of variable total can be changed in the subroutine, and the updated value will be returned to the main program that calls the routine.  Finally, the main program calls subroutine NoverR and then displays the results in a Scrollsheet.


  STATISTICA BASIC - General Conventions of STATISTICA BASIC

The following topics provide summary overviews of the STATISTICA BASIC conventions.  Note that in all value assignments, STATISTICA BASIC uses the BASIC " : = " convention (instead of the " = " used in spreadsheet transformations).  In STATISTICA BASIC, the simple equal sign is used only in logical expressions.  For more information on a General Convention topic, click on that topic name.

General Operation:  Sequential vs. RandomAccess Mode

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Expressions

Operators

Compound Instructions (Begin..End)

Conditional Constructions

Loops

GOTO Statements

Recoding Statements

User-defined Functions and Subroutines

Missing data

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


  General Conventions of STATISTICA BASIC - Sequential vs. RandomAccess Mode

STATISTICA BASIC can operate in one of two modes:  Sequential [i.e., data-base style, one record (case) is read in and processed at a time] or RandomAccess (i.e., spreadsheet style, all cases are loaded into a data array before the processing begins).  The mode can be specified either at the beginning of a STATISTICA BASIC program (by including one of the two keywords) or via the STATISTICA BASIC Options dialog.

Sequential Mode

When you specify Sequential mode, the STATISTICA BASIC programs are executed separately for each case in the data file.  In other words, all variables are initialized and the program is "run repeatedly" for consecutive cases.  STATISTICA variables used in the programs represent data values of the currently processed case.  For example:

Income := Revenue - Cost;

will calculate the difference between the values of variables Revenue and Cost (and assign the result to variable Income) in all cases in the data file.

Unless you request otherwise, cases in the file are processed in consecutive order, execution of each case is independent, and no values are transferred between cases.  This can be changed by using the Jump(x) command that instructs the program to "jump" to case number x.  You can also transfer values between cases by using (i.e., writing to and reading from) the reserved Memory array.

In Sequential mode, referencing a particular cell in a data file (as in the RandomAccess mode, e.g., Data(1,2)) will produce an error message.  Therefore, the following methods of referencing variables are NOT valid when Sequential is specified (for more information on these methods, see below):

Data(i,j)

V(i,j)

Vj(i)

VARNAME(i)

Applications, Advantages of Sequential Mode

RandomAccess Mode

In the default RandomAccess mode, the STATISTICA BASIC program is executed only once (and not once for each case as in Sequential mode).  Data cells may be accessed by referencing both the variable and case numbers.  For example, the following STATISTICA BASIC statement:

Income(1) := Revenue(5) - Cost(5);

will calculate the difference between the values of variables Revenue and Cost for case number 5 and write the result into the first case of variable Income.

Because both the variable number and case number must be specified in RandomAccess mode, referencing a variable using the convention Vj (as in Sequential mode, e.g., v3 := v2 + v1) will produce an error message.  Therefore, in RandomAccess mode, data cells within variables may be referenced in the following manner:

Data(i,j)	where i is the case number and j is the variable number (e.g., Data(1,3) := REVENUE(5) - COST(5);)

V(i,j)	equivalent to Data(i,j)

Vj(i)	where j (the variable number) is explictly specified and i is the case number (e.g., v3(1) := v4(5) - v5(5);)

VARNAME(i)	where VARNAME is the variable name and i is the case number (e.g., INCOME(1) := v4(5) - v5(5);)

The following instructions are NOT valid in RandomAccess mode:

CaseNo

Delete

Jump

and the following instruction must have an extra parameter (cn) representing the case number:

CaseName(cn)

Applications, Advantages of RandomAccess Mode

For other General Conventions topics, see:

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Expressions

Operators

Compound Instructions (Begin..End)

Conditional Constructions

Loops

GOTO Statements

Recoding Statements

User-defined Functions and Subroutines

Missing data

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


General Conventions of STATISTICA BASIC - Applications, Advantages of Sequential Mode in STATISTICA BASIC

  Applications, Advantages of Sequential Mode in STATISTICA BASIC

The main advantage of this simple mode is that the user does not have to be concerned with writing code to access each consecutive case.  A Sequential mode program can consist of a simple formula (e.g., v1:=v2+v3;) and STATISTICA BASIC will automatically execute it for each case (record) in the data file.  To achieve the same result, a STATISTICA BASIC program written for RandomAccess execution, would need to include more code - a specification of a loop that would "cycle" through all cases in the data file.  The Sequential mode is less convenient, however, for applications where there is a need to access specific cases in the data file and calculate (or plot) results of operations that involve values of more than one case at a time.  These types of operations can be executed in the Sequential mode only by using the slower (and often less convenient to use) Jump(x) command (to "jump" to specific cases) and by storing the results of intermediate calculations in the Memory(xxx) array to prevent them from being lost (because in the Sequential mode, all program variables except for Memory(xxx) are initialized to 0 for each case).

See also Applications, Advantages of RandomAccess Mode, Sequential vs. RandomAccess Mode.


General Conventions of STATISTICA BASIC - Applications, Advantages of RandomAccess Mode in STATISTICA BASIC

  Applications, Advantages of RandomAccess Mode in STATISTICA BASIC

This (default) mode is convenient to use when the STATISTICA BASIC program is designed to produce results (calculations, graphs) based on combinations of values from different cases in the data file (and not merely process each case, one at a time, and produce a result based on values of one case at a time, only).  In the RandomAccess mode, the entire data file is loaded into a predefined data array Data(i,j) (or equivalently, V(i,j)), and all its values are accessible for processing by referencing them using the spreadsheet-like conventions (i = row/case number, j = column/variable number).  A relative disadvantage of this mode is when operations need to be performed for each case in the data file; this is done automatically in the Sequential mode, whereas in RandomAccess mode, it requires specifying a loop that would "cycle" through all cases.

See also Applications, Advantages of Sequential Mode, Sequential vs. RandomAccess Mode.


  General Conventions of STATISTICA BASIC - Variables and Values of Variables

Variables

There are two types of variables in STATISTICA BASIC:  standard STATISTICA variables (which exist in the current data file) and temporary variables.  Each of these will be discussed below.

1.  STATISTICA Variables

There are several methods of referencing standard STATISTICA data file variables in STATISTICA BASIC programs (depending on which operation mode you are using).  Those methods are described below.

Sequential mode:  In Sequential mode, case numbers are not used, because all operations are applied to all cases.  You refer only to variables, either by specifying the variable number or variable name, as described below:

•	You can use the standard STATISTICA "v-notation" (e.g., v1, v5, v300) used in STATISTICA Case Selection Conditions, Spreadsheet Formulas and other STATISTICA applications.  This method requires less typing than any other method; for example:

Sequential;

v4 := ( v1 + v2 ) / 2

•	You can use the modified "indexed" notation (e.g., v(1), v(5), v(300)), that is useful for performing operations on STATISTICA variables in loops, and in instances when the index (number) of the variable is computed in the program; for example:

Sequential;

v(4) := ( v(1) + v(2) + v(3) ) / 3;

for i:=1 to 10 do v(i):=v(i)/100;

v(12) := v(12+k)

Equivalently, you can use Data(i) to reference the variable.

•	STATISTICA variables can be referenced by their original names as specified in the STATISTICA data file; for example:

Mean := ( Score1 + Score2 + Score3 ) / 3

Note that variable names can be entered in either upper or lower case letters (e.g., MEAN, Mean, or mean).

When using the first two conventions, variables are accessed based on their sequential numbers in the STATISTICA data file.  When using the third convention, variables are accessed in a position-independent manner, that is, even if variables were reordered in the file, they will still be identified correctly based on their unique names.

RandomAccess mode:  In RandomAccess mode, both the variable number and case number must be specified.

•	You can use the predefined data array Data(i,j) (where i is the case number and j is the variable number) to access any data cell in the current data file.  For example, the following program will compute the average of the values of 3 variables for case 1 and place the resulting value in variable 1, case 10.

Data(10,1) := ( v2(1) + v3(1) + v4(1) ) / 3;

This method is very flexible in that both parameters i and j may be expressions that are evaluated during execution of the program.  For example, the following program will compute the sum of values for all variables in the current data file.

RandomAccess;

sum := 0;

  for i := 1 to NCases do

    for j := 1 to NVars do

      sum := Sum + Value(Data(i,j));

WriteLn('SUM=',sum);

Equivalently, you can use V(i,j) to reference the case and variable numbers, respectively.

•	Another method of specifying the variable and case in RandomAccess mode is to use Vj(i) where j (the variable number) is explicitly specified and i is the case number.  For example:

v5(2) := Hypot(v6(3),v6(8));

•	You can also specify the variable name using the NAME(i) convention where NAME is the variable name and i is the case number.  For example:

Profit(1) := Sales(5) - Cost(5);

2.  Temporary Variables

Temporary variables can be either numeric or text (text variables must be designated as such by placing a $ at the end of the name, e.g., temp$).  Temporary variables can be used to hold values or text strings.  In the example below, both average_value and text$ are temporary variables:

average_value := ValSum(array,1,10)/ValCount(array,1,10)

text$ := GetText(Group, 3);

WriteLn('Group being evaluated:  ', text$)

Unlike the names of STATISTICA variables which are limited to 8 characters, names of temporary STATISTICA BASIC variables, can be up to 32 characters long (and the values of temporary text variables can be up to 255 characters long).

Note that the names of temporary variables may not be the same as the name of any variable from the current data file, unless the function NoDataFileVariableNames is specified.

Values of Variables from the Data File

You can specify the values of variables in STATISTICA BASIC by using the text values (e.g., v1:='MALE';) or their numeric equivalents (e.g., v1:=1;); for more information about text values in STATISTICA data files, see Double Notation (Numeric/Text) of Values.  Text values must be enclosed in single or double quotation marks.  By default, numeric values are represented as floating point real numbers (stored in double precision).

The following functions can be used with text values of STATISTICA variables:

AddTextValue(vn,tv,nv) for variable vn, creates a new text value tv, with numerical equivalent nv;

GetText(vn,nv) - for variable vn, returns the text value which is equivalent to the numeric value nv.

GetNumber(vn,tv) - for variable vn, returns the numeric value which is equivalent to the text value tv.

See also, Text Values Manager.

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Elementary Instructions (Assignments)

Expressions

Operators

Compound Instructions (Begin..End)

Conditional Constructions

Loops

GOTO Statements

Recoding Statements

User-defined Functions and Subroutines

Missing data

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


  General Syntax Conventions (Instructions, Line Length, Separators, Uppercase/lowercase, Comments in Programs)

STATISTICA BASIC programs consist of executable instructions.  The most elementary instruction is the assignment statement in which the expression on the right side of the equation is evaluated and the result is assigned to the variable on the left side; for example:

v1 := v2 + v3;             {in Sequential mode}

or

v1(14) := v2(14) + v3(14); {in RandomAccess mode}

Other common instructions are conditional statements (if..then) and loops (for..to..do); there are also other direct instructions that perform specific operations [such as stop the program -- stop, delete case -- delete (for Sequential mode), etc., see STATISTICA BASIC Syntax Reference].

The length of each program line can extend to many lines of text and is practically unlimited.  Thus, the physical end of line (ENTER) does not end a STATISTICA BASIC instruction (unless it is the last instruction of the program).  Instructions in the program are separated by semicolons (;).  There can be many instructions in one physical line of the program; for example:

v1:=0; v2:=3; v3:=5; v4:=7; v5:=9; v6:=11; v7:=12;

The semicolon ends (separates) instructions, thus it is used at the end of the loop statement; for example:

for a := 1 to 10 do

     v(a) := a + 10;

STATISTICA BASIC does not differentiate between the lower- and uppercase letters (in variable names, keywords, names of user-defined recoding functions, etc.).  However, it does recognize upper- and lowercase letters in text values and constants.  For example, the text value 'MALE' is not the same as 'male'.

There can be comments included in the text of STATISTICA BASIC programs.  Each comment must be enclosed in curly brackets; for example:

v1 := v1**2;  {this is my comment}

For other General Conventions topics, see:

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Expressions

Operators

Compound Instructions (Begin..End)

Conditional Constructions

Loops

GOTO Statements

Recoding Statements

User-defined Functions and Subroutines

Missing data

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


  General Conventions of STATISTICA BASIC - Elementary Instructions (Assignments)

STATISTICA BASIC is a data transformation language and its elementary (and probably the most often used) structure is the assignment statement in which the expression on the right side of the : = (assignment) sign is evaluated and its value is assigned to the variable on the left side.  STATISTICA BASIC programs can be as simple as a single assignment statement (formula).  For example, the following is a correct complete STATISTICA BASIC program:

v1(1) := 0

This particular program will assign 0 to variable number 1 in case number 1 in the current data file.

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Expressions

Operators

Compound Instructions (Begin..End)

Conditional Constructions

Loops

GOTO Statements

Recoding Statements

User-defined Functions and Subroutines

Missing data

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


  General Conventions of STATISTICA BASIC - Expressions

STATISTICA BASIC supports numeric and logical expressions; they consist of variables, constants, functions, and operators and they evaluate to numeric values (for example, (v1>0),  (v1=v2)/2,  ((v1>0) and (v1<1)), etc.).  Logical expressions evaluate to 1 if they are true and 0 if they are false.

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Operators

Compound Instructions (Begin..End)

Conditional Constructions

Loops

GOTO Statements

Recoding Statements

User-defined Functions and Subroutines

Missing data

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


  General Conventions of STATISTICA BASIC - Operators Summary

The numerical and string operators that can be used in STATISTICA BASIC expressions are listed below in the order of their precedence (i.e., order of execution), from the lowest to the highest.

Numerical Operators Summary:  The following operators can be used in numerical expressions.

•  Relational operators:  =,  <,  >,  <>,  <=,  >=

•  Addition:  +

•  Subtraction:  -

•  Inclusive disjunction:  OR  (the value of inclusive disjunction is 0 only if both arguments are 0; for example (v1 or v2) is 0 if both v1 and v2 are 0)

•  Multiplication:  *

•  Division:  /

•  Integer Division:  DIV  (when performing integer (div) division, the arguments are first truncated to integers and then the result is truncated to an integer)

•  Modulo division:  MOD  (when performing modulo (mod) division, the arguments are first truncated to integers and the operation returns the remainder from the division).  For example, the STATISTICA BASIC program

begin

v3:=50 mod 7

end;

will return the value 1 (i.e., 7 goes into 50 seven times with a remainder of 1).

•  Conjunction:  AND  (the value of conjunction is 0 if at least one of the arguments is 0; for example (v1 and v2) is 0 if either v1 or v2 is 0)

Note:  A common error is caused by omitting parentheses needed to adjust for the precedence of operators; for example, the expression x > 0 and x < 1 is incorrect and needs parentheses: (x > 0) and (x < 1) because relational operators (here, > and <) have a lower precedence than the conjuction (and).

•  Exponentiation:  **, ^

•  Negation:  NOT  (the value of negation is 1 if the argument is 0; for example (not x) is 1 if x is 0)

String Operators Summary:The following operators can be used in string expressions.

•  Concatenation:  +

•  Comparisons (logical operators):  =,  <,  >,  <=,  >=

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Expressions

Compound Instructions (Begin..End)

Conditional Constructions

Loops

GOTO Statements

Recoding Statements

User-defined Functions and Subroutines

Missing data

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


  General Conventions of STATISTICA BASIC - Compound Instructions (Begin..End)

Compound instructions consist of a set of simple instructions placed between the words begin..end (the begin..end serves as "syntactic parentheses"); for example, see the set of four instructions (between the words begin..end) below:

for a:=1 to 100 do

     begin  ·························|

          v(a):=v(a)*10;             |

          if v(a)<-1 then v(a):=-1;  | compound

          if v(a)=0 then v(a):=-99;  | instruction

          if v(a)>1 then v(a):=1;    |

     end;   ·························|

Compound instructions can be nested and they are most typically used in conditional if..then..else statements and loops.  The entire program can be considered, in a sense, one "compound instruction" and placed within the begin..end words (e.g., to maintain compatibility with MML or other languages).

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Expressions

Operators

Conditional Constructions

Loops

GOTO Statements

Recoding Statements

User-defined Functions and Subroutines

Missing data

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


  General Conventions of STATISTICA BASIC - Conditional Constructions

The assignment and other instructions can be executed conditionally.  For example:

if (v2>1) and (v2<2) then v1:=0 else v1:=5;

The word undefined can be used in conditional constructions to identify conditions in which the expression evaluates to a missing value (in the above example, when v2 is missing).  For example:

if (v2>1) then

          v1:=0

     else

          v1:=1

     undefined

          v1:=2;

In this example, the value 2 will be assigned to variable v1 in cases where the value of v2 is missing (i.e., undefined).  Note that a semicolon (;) is not (and should not be) placed at the end of instructions preceding the words else or undefined, as this would end the conditional statement (consequently, the word else or undefined following the semicolon (;) would be interpreted as the beginning of a new instruction, causing a STATISTICA BASIC Syntax error).  Conditional constructions in STATISTICA BASIC can contain compound instructions (i.e., groups of statements enclosed inside the begin..end blocks); for example:

if (v2>1) then

          begin

               v1:=0;

               v3:=1;

               v4:=2;

          end

     else

          begin

               v1:=10;

               v3:=11;

               v4:=12;

          end;

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Expressions

Operators

Compound Instructions (Begin..End)

Loops

GOTO Statements

Recoding Statements

User-defined Functions and Subroutines

Missing data

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


  General Conventions of STATISTICA BASIC - Loops

Looping instructions for..to..do (or for..downto..do) can be used to execute one or more STATISTICA BASIC instructions included in the body of the loop.  For example, the following loop:

Sequential;                   {specifies Sequential mode}

for i:=1 to 10 do v(i):=1000;

will repeat the v(i):=1000 assignment statement 10 times, for values of i (called the loop counter) equal to 1, 2, 3, .. 10.  Thus, in this example, values of the first 10 variables of each case of the current data file will be set to 1000.

If the body of the loop consists of only one statement (as in the example above), the looping construction ends with a semicolon (;) as in any other statement.  Loops can also contain groups of statements enclosed inside the begin..end blocks.  For example, in the following program:

Sequential;                   {specifies Sequential mode}

for i:=1 to 20 do

     begin

          v(i):=v(i)+1000;

          v(i+20):=v(i+20)+2000;

          if v(i)<v(i+20) then v(i):=v(i+20);

     end;

the two assignment statements and one conditional statement will be executed 20 times for values of the loop counter (i) equal to 1, 2, 3, .. 20.

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Expressions

Operators

Compound Instructions (Begin..End)

Conditional Constructions

GOTO Statements

Recoding Statements

User-defined Functions and Subroutines

Missing data

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


  General Conventions of STATISTICA BASIC - GOTO Statements

GOTO statements can be used to branch unconditionally to a specified label within a STATISTICA BASIC program.  For example, the following program shows how to implement loops using GOTO statements.  This program:

RandomAccess;                     {specifies RandomAccess mode}

const DESIRED_SUM = 200;

i:=1;

sum:=0;

loop:

     if sum + v1(i) >= DESIRED_SUM then goto done;

     sum:=sum+v1(i);

     i:=i+1;

     if i > NCases then

  begin

     DisplayMessageBox (MB_OK, 'Error',

                       'Total sum does not add up to '+

                       Str (DESIRED_SUM, 10, 3)+'.');

     Exit;

  end;

goto loop;

done:

writeln ('We need ',i,' cases to reach a sum greater than ',DESIRED_SUM);

will count the number of cases that is necessary to add in order to obtain a sum greater than the number DESIRED_SUM which equals 200.  If the running sum is greater than 200, then goto done instructs STATISTICA to print the message 'We need 'i' cases to reach a sum greater than 200'.  If the running sum is not greater than 200, the looping process continues.

You can also use GOTO statements to branch outside a loop.  For example, in the following program

RandomAccess;                   {specifies RandomAccess mode}

const LIMIT = -1;

sum := 0;

for i:=1 to NCases do

    for j:=1 to Nvars do

    begin

       if data (i, j) < LIMIT then goto ErrorExit;

       sum := sum + data (i, j);

    end;

writeln ('Sum of all values: ',sum);

Exit;

ErrorExit:

writeln ('Error, some values are invalid');

the sum of all values in the current data file will be calculated and displayed unless any value is less than -1, in which case the error message is displayed.

While GOTO statements can be used to branch to a label from within a loop (as in the example above), it is not allowed to jump (or branch) to a label that is within a loop, unless the GOTO statement is also within the loop.  Also, you cannot branch from one program, function, or subroutine into the body of another function or subroutine (see User-defined functions and subroutines for additional details).

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Expressions

Operators

Compound Instructions (Begin..End)

Conditional Constructions

Loops

Recoding Statements

User-defined Functions and Subroutines

Missing data

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


  General Conventions of STATISTICA BASIC - Recoding Statements

Custom recoding functions can be defined in STATISTICA BASIC and used repeatedly like any other function to change values of variables.  The definitions of all recoding functions should be placed at the beginning of the program.  Each definition consists of the word recode followed by a name (up to 32 characters long) of the function and a list of recoding statements enclosed inside the begin..end block.  For example, the following function called New1:

recode New1;

     begin

          0 = 1;

          1 to 5 = 2;

          6 to Hi = 3;

          else -9999;

     end;

will convert 0 into 1, 1 through 5 (excluding 5 which will be set to missing) into 2, 6 through Hi (highest) into 3, and all other values (else) into -9999 (missing data value; these missing values will be displayed as blank cells).

The next example recoding function (New2) is identical to the previous one, except that all other values (else) will not change (i.e., they will remain Old):

recode New2;

     begin

          0 = 1;

          1 to 5 = 2;

          6 to Hi = 3;

          else Old;

     end;

After a function is defined, it can be used in the STATISTICA BASIC program like any other mathematical function.  For example, the statement:

v1 := New2(v1);

will recode values of variable 1 according to the above definition of New2 (e.g., if it was 0, then it will become 1; if it was 6, it will become 3; etc.).

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Expressions

Operators

Compound Instructions (Begin..End)

Conditional Constructions

Loops

GOTO Statements

User-defined Functions and Subroutines

Missing data

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


  General Conventions of STATISTICA BASIC - Missing Data

STATISTICA BASIC recognizes missing data values as defined (assigned to specific variables) in the current STATISTICA data file.  It supports the context-dependent constant Missing which can be assigned to STATISTICA variables in the program; for example:

v1 := Missing;

The actual value assigned to variable v1 in this example will be equal to the missing data code as currently defined for v1 in the current data file.

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Expressions

Operators

Compound Instructions (Begin..End)

Conditional Constructions

Loops

GOTO Statements

Recoding Statements

User-defined Functions and Subroutines

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


  General Conventions of STATISTICA BASIC - Transferring Values Between Cases (in Sequential Mode)

In Sequential mode, numeric values can be transferred between cases (or accumulated across cases) by using the predefined data array (i.e., subscripted variable) Memory(yyy), alternatively referred to as Mem(yyy).

By default, the number of data values that can be stored in this array is equal to 8,000.  However, if necessary, its size parameter yyy can be set to a different value if such a large array is not needed (the size of this array can be adjusted in the Options window of the STATISTICA BASIC menu).

The array Memory can also be used in RandomAccess mode (for temporary storage), although in RandomAccess mode, the STATISTICA BASIC program is executed only once (and variables are not initialized for each case) and thus in RandomAccess mode, there is no need to use any particular method to transfer values between cases.

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Expressions

Operators

Compound Instructions (Begin..End)

Conditional Constructions

Loops

GOTO Statements

Recoding Statements

User-defined Functions and Subroutines

Missing data

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


  General Conventions of STATISTICA BASIC - Reversing the Changes to Data Made in STATISTICA BASIC

When modifying data, STATISTICA BASIC processes the data in a temporary work file created upon opening the data file.  Therefore, as long as you do not overwrite the original disk file (by Saving the processed file over it) you can always return to the original.

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Expressions

Operators

Compound Instructions (Begin..End)

Conditional Constructions

Loops

GOTO Statements

Recoding Statements

User-defined Functions and Subroutines

Missing data

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


  General Conventions of STATISTICA BASIC - Format of STATISTICA BASIC Source Code Files

The source code of STATISTICA BASIC files (program files with extension *.STB) is stored by default in Rich Text Format (RTF) files, which preserves all formating information and allows the file to be read and interpreted by other RTF-compatible applications (e.g., MS Word).  (STATISTICA BASIC files may also be saved as standard text (ASCII) format files by setting the Save As Text option in the Save File As dialog.  If you save the code As Text, then you can use not only word processors but any editors (e.g., Windows Notepad) to edit those files.)  However, using the built-in STATISTICA BASIC program editor is preferable in most cases because that editor is integrated into every module of STATISTICA, features the language syntax help window, variable name review windows, etc.  If you edit those files with your word processor, be sure to save them as Rich Text Format (RTF) or as text only (or unformatted; the term depends on the word processor).  Otherwise, the text will include embedded specific formatting characters used by the particular word processor which will not be recognized by STATISTICA BASIC.

For information on the syntax of the metacommand for specifying include files see Metacommand {$I:'FileName'}.

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Expressions

Operators

Compound Instructions (Begin..End)

Conditional Constructions

Loops

GOTO Statements

Recoding Statements

User-defined Functions and Subroutines

Missing data

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

STATISTICA BASIC Compiler (Technical Note)


  General Conventions of STATISTICA BASIC - STATISTICA BASIC Compiler (Technical Note)

STATISTICA BASIC does not produce stand-alone applications that can be executed outside of the STATISTICA system.  However, in order to achieve fast execution speed, it internally works as a compiler.  Specifically, at the point of verifying the syntax of the program (after you select the Execute option from the Analysis pull-down menu, or click on the Execute Toolbar button), STATISTICA BASIC also compiles the source code into its own internal object code.

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Expressions

Operators

Compound Instructions (Begin..End)

Conditional Constructions

Loops

GOTO Statements

Recoding Statements

User-defined Functions and Subroutines

Missing data

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files


  STATISTICA BASIC - Quick Syntax Reference

NOTE:  STATISTICA BASIC can operate in Sequential or RandomAccess mode.  See also STATISTICA BASIC Introductory Overview.

Categories:

Operators	Data Management	Distributions

Graphics	Math & Trig 	Matrix Operations

Recodes	Scrollsheet	Statistical

Text	User Input/Output	User-defined Functions

Program Flow:

word               Example and {comment}

Abort	if v1<0 then ABORT;

{ABORTs execution of program; undoes changes.}

Begin	begin v1:=v2; v2:=sin(v3) end;

{Marks BEGINning of block.}

Delete	if Income <= 0 then Delete;

{DELETEs current case from file (Sequential mode only).}

End	begin v1:=0; v2:=1; v3:=2 end;

{Marks END of block.}

Exit	if v10 >= 10000 then Exit;

{EXITs to the next case; in RandomAccess mode, EXITs the program}

For	for i:=4 to 10 do v(i):=1;

{FOR..TO..DO.. starts a loop.}

Function	Function aplusb(a,b) begin aplusb:=a+b;end;

{Defines a user-defined function aplusb.}

Goto	if x < y then goto ErrorExit;

{Branches unconditionally to a specific label.}

If	if (x>1) and (x<2) then x:=1 else x:=2 undefined x:=3;

{"IF..THEN"; the part after UNDEFINED executes if condition evaluates to missing.}

Jump(x)	if v1 >= 100 then Jump(10);

{JUMPs to case number 10 (Sequential mode only).}

Pause	scroll:=OpenScrollsheet("c:\new.scr");  Pause;  DeleteScrollsheet(scroll);

{Pause temporarily stops execution of the program.}

PauseAndEdit	OpenScrollsheet("c:\new.scr");  PauseAndEdit;

{Allows you to review and edit values of the scrollsheet.}

RandomAccess	RandomAccess; Data(5,1) := ( v2(1) + v3(1) ) / 2;

{Specifies RandomAccess mode (rather than Sequential) of data processing for the program; all data are loaded into Data(i,j) array and are referenced in a spreadsheet-like manner.}

Read	Read(Gender,Advert,Measur2);

{Stops execution of the program, opens a user-input window and prompts the user for the input of a value for the specified variables.}

SelectionConditions	If SelectionConditions(4) then Beep;

{Beeps if specified case meets the current selection conditions.}

SelectionConditionsGet	If SelectionConditionsGet (inc, str$) then writeln ('Selection Conditions',str$);

{Returns status of current selection conditions.}

Sequential	Sequential; v(1) := ( v2 + v3 ) / 2;

{Specifies the Sequential mode (as opposed to RandomAccess) of data processing for the program which is executed for each case.}

Stop	if v(1)=-1 then Stop;

{STOPs execution of the program.}

Sub	Sub aplusb(a,b) begin writeln(a+b);end;

{Defines a user-defined subroutine aplusb.}

General:

word               Example and {comment}

CaseNo	if CaseNo > 9 then Exit;

{CaseNo=current case number=v(0)=v0 (Sequential mode only).}

Data(i,j)	Data(1,4) := v1(3) + v5(9);

{In RandomAccess mode, accesses any Data cell (i=case number, j=variable number) in the current data file.}

Dim	Dim array1(10, 10);

{Declares a two-dimensional matrix named array1.}

Memory(x)	Mem(4):=v6;

{A static array (Mem or Memory) where numeric values can be stored}

Missing	v1:=Missing;

{Assigns MISSING data to variable v1.}

NCases	for i := 1 to NCases do v1(i) := rnd(5);

{The number of cases in the current data file.}

NVars	for i := 1 to NVars do v(i) := rnd(5);

{The number of variables in the current data file.}

NoDataFileVariableNames	NoDataFileVariableNames;

{Suppresses the use (i.e., the recognition)of data file variable names in program.}

RandomAccess	RandomAccess; Data(5,1) := ( v2(1) + v3(1) ) / 2;

{Specifies RandomAccess mode (as opposed to Sequential) of data processing for the program; all data are loaded into the Data(i,j) array and are referenced in a spreadsheet-like manner.}

ReDim	ReDim array1(i+1, j+1);

{Resizes the two-dimensional matrix named array1.}

SelectionConditions	If SelectionConditions(4) then Beep;

{Beeps if specified case meets the current selection conditions.}

SelectionConditionsGet	If SelectionConditionsGet (inc, str$) then writeln ('Selection Conditions',str$);

{Returns status of current selection conditions.}

{Returns status of current selection conditions.}

Sequential	Sequential; v(1) := ( v2 + v3 ) / 2;

{Specifies the Sequential mode (as opposed to RandomAccess) of data processing for the program which is executed for each case.}

V(xxx)	v(3):=Missing; v(v(3)+2):=0;

{In Sequential mode, V(xxx) = STATISTICA data file variable xxx.}

Vxxx	v3:=Missing; v234:=0;

{In Sequential mode, Vxxx = STATISTICA data file variable xxx.  STATISTICA variables can also be referenced by name; e.g: Age, Test1,....}

Vxxx(i)	v3(59):=Missing; v234(3):=0;

{In RandomAccess mode, Vxxx(i) = STATISTICA data file variable xxx for a specific case number i, STATISTICA variables can also be referenced by name; e.g: Age(i), Test1(i),....}

Write(a,...)	Write(CaseName, ' : ', Age);

{Prints the case names, a colon, and the values of Age for each case in the file.  To start a new line, use WriteLn.}

WriteLn(a,...)	WriteLn(CaseName, ' : ', Age);

{Prints the case names, a colon, and the values of Age for each case in the file.  A new line will start for each WriteLn statement.}

Metacommand:

{$I:'FileName'}	{I:'c:\stat\library.stb'}

{Includes the file Library.stb during compilation.}


  STATISTICA BASIC Data Management Functions - Overview

A variety of data management operations can be performed using STATISTICA BASIC (many of them can be performed by using the general Matrix Language functions of STATISTICA BASIC and applying them to the current data file).

In general, any matrix function which accepts an array as a parameter can reference the currently connected data file using the predefined array Data.  For example,

MatrixDisplay(Data, 'Contents of Data File');

will display the contents of the current data file in a Scrollsheet.

The Matrix Language functions and other functions of STATISTICA BASIC make it possible to perform operations on data files, such as:

•	copying, renaming, and deleting files.

•	modifying values in individual cells of the spreadsheet (in RandomAccess mode, values in the currently connected data file may be referenced as Data(row, column) or V(row, column);

•	transforming variables from the data file; specific columns (column vectors) in the data file can be referenced in matrix functions operating on vectors as Data(1, column); specific columns can also be referenced using the Vxxx notation, where xxx refers to the specific variable number in the data file, e.g., v1, v2, or by the variable name, e.g., Work_1, Age, etc.;

•	accessing text values, assigning new text/numeric equivalents;

•	using case names and variable names from the data file;

•	modifying variable names in specified data files;

•	sorting and ranking specific variables without rearranging the entire data file;

•	retrieving the currently specified STATISTICA Case Selection Conditions, testing if specified cases meet the conditions;

•	converting Scrollsheets and STATISTICA BASIC matrices to STATISTICA system data files and vice versa.

For example, the following program will sort only the values of variable 3, leaving values of all other variables in their original order:

RandomAccess;

VectorSort(v3, SORT_ASCENDING);

The following program will add 10 to every value in the current data file:

RandomAccess;

MatrixElemAdd(Data, 10, Data);

Advanced Examples

For a list of advanced examples of STATISTICA BASIC programs using graphics procedures, refer to Advanced Examples of STATISTICA BASIC Programs.

For a complete listing of data management functions in STATISTICA BASIC, see Data Management Function in STATISTICA BASIC.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


  STATISTICA BASIC Quick Syntax Reference - Data Management Functions

These functions are useful for performing specific data management operations on the current data file or specified matrix.

Overview

Function	Example and {Comment}

AddTextValue	AddTextValue(Gender,'Male',1);

{Adds the text value "Male" with the numeric equivalent 1 to the variable Gender.}

CaseName(cn)	WriteLn(CaseName(3));

{In RandomAccess mode, "prints" the name of the third case.}

CaseName	WriteLn(CaseName);

{In Sequential mode, "prints" the case name of the current case.}

CopyFile	CopyFile ('D:\STAT\report.txt', 'D:\PROJECT\project.new');

{Copies the file D:\STAT\report.txt to D:\PROJECT\project.new.}

DeleteFile	DeleteFile ('g:\junk\old.dat');

{Deletes the file g:\junk\old.dat.}

GetNumber	response := GetNumber(Item1,'YES');

{Assigns the numeric equivalent of "YES" from variable Item1 to the local variable response.}

GetScrollsheet	DuplicateScrollsheet(GetScrollsheet(0));

{Makes a copy of the Scrollsheet displayed on top.}

GetText	label$ := GetText(Item1,3);

{Assigns the text value associated with the value 3 from variable Item1 to the local variable label$.}

MatrixCopy	MatrixCopy(Data, 3, 1, 0, Data, 3, 5);

{Copies values from variable 1, 3rd through last case, to variable 5 starting at 3rd case.}

MatrixDisplay	MatrixDisplay(Data,'Contents of Data File');

{Displays the contents of the current data file in a Scrollsheet with the specified title.}

MatrixDuplicate(Data, array)	MatrixDuplicate(Data, array1);

{Copies the contents of the current data file to the matrix array1.}

MatrixDuplicate(var, array)	MatrixDuplicate(Var1, array1);

{Copies the contents of the variable 1 to the matrix array1.}

MatrixElemAdd	MatrixElemAdd(Data, 10, Data);

{Adds 10 to every value in the current data file.}

MatrixElemDivide	MatrixElemDivide(Data, 10, Data);

{Divides every value in the current data file by 10.}

MatrixElemMultiply	MatrixElemMultiply(Data, 10, Data);

{Multiplies every value in the current data file by 10.}

MatrixElemSubtract	MatrixElemSubtract(Data, 10, Data);

{Subtracts 10 from every value in the current data file.}

MatrixExtract	MatrixExtract(Data, 1, 2, 5, 10, array1);

{Extracts values of 5 cases, 10 variables, from the current data file and places them in array1, beginning in the first case of the second variable.}

MatrixFill	MatrixFill(3.14, Data, 1, 3, 5, 5);

{Fills a 5x5 block, beginning in case 1, variable 3 with the value 3.14.}

MatrixRead	MatrixRead('c:\mat1.txt', Data);

{Reads tab-delimited values from the specified text file and places them into the current data file.}

MatrixReadFromDataFile	MatrixReadFromDataFile('c:\data.sta', 0, 0, 0, 0, array);

{Reads values from the specified data file and places them into the specified matrix.}

MatrixSaveAsData	MatrixSaveAsData(DATA,'c:\stat\data.sta')

{Saves the specified matrix as the specifed data file.}

MatrixSetToZero	MatrixSetToZero(Data);

{Sets all values of the current data file to zero.}

RenameFile	RenameFile ('c:\data.sta', 'c:\report.sta');

{Renames c:\data.sta as c:\report.sta.}

SaveScrollsheetAsDataFile	SaveScrollsheetAsDataFile(GetScrollsheet(0), 'c:\new.sta');

{Saves the top Scrollsheet as a data file under the specified name.}

SelectionConditions	If SelectionConditions(4) then Beep;

{Beeps if case 4 meets the current selection conditions.}

SelectionConditionsGet	If SelectionConditionsGet (inc, str$) then writeln ('Selection Conditions',str$);

{Returns status of current selection conditions.}

SetVarName	SetVarName ('c:\data\new.sta',2,'SAMPLE')

{Sets the name of the second variable in the specified data set to SAMPLE.}

VarLongName	WriteLn(VarLongName(3));

{"Prints" the long variable name of variable 3.}

VarName	WriteLn(VarName(3));

{"Prints" the name of variable 3.}

VectorDualSort	VectorDualSort(v3, v4, SORT_ASCENDING);

{Sorts variable 3 in ascending order, keeping values of variable 4 paired with them.}

VectorRank	VectorRank(v2, SORT_ASCENDING, RANK_MEAN);

{Ranks variable 2 in ascending order, assigning mean rank to tied values.}

VectorSort	VectorSort(v2, SORT_ASCENDING);

{Sorts variable 2 in ascending order.}


  STATISTICA BASIC Overview - Statistical Functions

STATISTICA BASIC offers numerous specialized procedures that are particularly useful for statistical data analysis and statistical data base management.  For example, supported procedures include correlations, crossproducts, eigenvalues, eigenvectors, a wide selection of descriptive statistics functions, custom data recoding functions, random sampling of cases, functions that create random variables that follow theoretical distributions (see Math Library), a wide selection of distribution functions, their inverses and integrals, specialized functions that automatically adjust for missing data, conditional deletion of cases, and many others.

A variety of statistical procedures are available in the Matrix Library of STATISTICA may be applied to the current data file or to specific variables in the current data file.

Notes

•	You should use the RandomAccess (default) mode of operation when executing statistical functions.

•	Functions which accept arrays as parameters may refer to the entire current data file by using the reserved name Data as the specified array.

•	Functions which accept vectors as parameters may refer to specific variables from the current data file by name (Age, Measure1, etc.), by using the Vxxx convention, where xxx refers to the specific variable number in the current data file (e.g., v1, v2, etc.).  Specific columns (column vectors) in the data file can be referenced as Data(1, column).

Example 1

This example will compute the means for all variables in the current data file and display them in a Scrollsheet.

RandomAccess;

ReDim means(NVars);

for i := 1 to NVars do

   ValMean(Data(1,i), 1, NCases, means(i));

MatrixDisplay(means, 'Means');

Example 2

This program will compute correlations between variables in the current data file and display them in a Scrollsheet with the title Correlations, then compute the eigenvalues from the correlation matrix and display them in a Scrollsheet with the title Eigenvalues.

RandomAccess;

ReDim corr(NVars, NVars);

ReDim eigenval(NVars);

MatrixCorrelations(Data, 1, corr);

MatrixDisplay(corr, 'Correlations');

MatrixEigenvalues(corr, eigenval, numeigen);

MatrixDisplay(eigenval, 'Eigenvalues');

Advanced Examples

For a list of advanced examples of STATISTICA BASIC programs using graphics procedures, refer to Advanced Examples of STATISTICA BASIC Programs.

For a complete list of statistical functions, see Statistical Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


  STATISTICA BASIC Quick Syntax Reference - Statistical Functions

These functions are useful for performing specific statistical operations on the current data file or specified matrix.

Overview

Function	Example and {Comment}

MatrixCorrelations	MatrixCorrelations(array1, 1, corrs);

{Computes correlations between columns of array1 and places coefficients in square matrix corrs.}

MatrixCrossProductOfDev	MatrixCrossProductOfDev(array1, 1, cross1);

{Computes squared deviations and crossproducts of deviations for matrix array1 and places results in square matrix cross1.}

MatrixEigenvalues	MatrixEigenvalues(array1, eigenval, numeign);

{Places eigenvalues computed for matrix array1 into vector eigenval and places number of positive eigenvalues computed into variable numeigen.}

MatrixEigenvectors	MatrixEigenvectors(array1, eigenval, eigenvec, numeign);

{Places eigenvectors computed for matrix array1 into the matrix eigenvec, eigenvalues into vector eigenval, and places number of positive eigenvalues computed in variable numeigen.}

MatrixMeans	MatrixMeans(array1, vectmean);

{Computes means of columns of array1 and places results in vector vectmean.}

ValCount	valid_n := ValCount(v3, 1, 10);

{Computes the number of non-missing values of variable 3 for the first 10 cases and puts the value in the variable valid_n.}

ValMax	ValMax(v3, 1, 10, max);

{Computes the maximum of non-missing values of variable 3 for the first 10 cases and puts the value in the variable max.}

ValMean	ValMean(v3, 1, 10, mean);

{Computes the mean of non-missing values of variable 3 for the first 10 cases and puts the value in the variable mean.}

ValMedian	ValMedian(v3, 1, 10, median);

{Computes the median of non-missing values of variable 3 for the first 10 cases and puts the value in the variable median.}

ValMin	ValMin(v3, 1, 10, min);

{Computes the minimum of non-missing values of variable 3 for the first 10 cases and puts the value in the variable min.}

ValMode	ValMode(v3, 1, 10, mode);

{Computes the mode of non-missing values of variable 3 for the first 10 cases and puts the value in the variable mode.}

ValPercentile	ValPercentile(v3, 17, 10, centile);

{Computes the 17th percentile of non-missing values of variable 3 for the first 10 cases and puts the value in the variable centile.}

ValQuartiles	ValQuartiles(v3, 1, 10, quartiles);

{Computes the quartiles of non-missing values of variable 3 for the first 10 cases and puts the values in the array quartiles.}

ValStDeviation	ValStDeviation(v3, 1, 10, StDev);

{Computes the standard deviation of non-missing values of variable 3 for the first 10 cases and puts the value in the variable stdev.}

ValStError	ValStError(v3, 1, 10, StErr);

{Computes the standard error of non-missing values of variable 3 for the first 10 cases and puts the value in the variable sterr.}

ValSum	ValSum(v3, 1, 10, result);

{Computes the sum of the non-missing values of variable 3 for the first 10 cases and puts the value in the variable result.}

Value	v1 := Value(v2) + Value(v4);

{Computes variable 1 as the sum of non-missing values of variables 2 and 4.}

ValVariance	ValVariance(v3, 1, 10, varnc);

{Computes the variance of non-missing values of variable 3 for the first 10 cases and puts the value in the variable varnc.}


  STATISTICA BASIC Quick Syntax Reference - Recode Functions

Overview

The word recode starts the definition of a recoding function (that can be used repeatedly like any other function to change values of variables).  The definitions of all recoding functions should be placed at the beginning of the program.

The following keywords are used in recoding functions

Function	Example and {Comment}

Begin	recode My_recod  begin 1, 3, 5 = 0;...

{Marks the BEGINning of the list of recode statements for recoding function My_recod.}

Else	recode ... else 99; ...

{Otherwise unspecified values will become 99 (note that an equal sign is not used).}

End	recode ... 0 to Hi = 1; end;

{Marks the END of the list of recode statements.}

Hi	recode ...; 9 to Hi = 0; ...

{From 9 to HIghest will become 0}

Lo	recode ... ; Lo to 0 = 1; ...

{In recoding, from LOwest to 0 will become 1.}

Old	recode ...; O to 1 = Old; ...

{In recoding, from 0 to 1 will not be changed.}

Recode	recode Tr;   begin 6,8=1;   10 to Hi = Old;   else 7   end;

{User defined RECODing function Tr: 6 and 8 will become 1; 10 to highest value will remain unchanged, all other values become 7.}

Each definition consists of the word recode followed by a name (up to 8 characters long) of the function and a list of recoding statements enclosed inside the begin..end block.  For example, the following function called My_recod:

recode My_recod;

     begin

          0 = 1;

          1 to 5 = 2;

          6 to Hi = 3;

          else -9999;

     end;

will convert 0 into 1, 1 through 5 (excluding 5) into 2, 6 through Hi (highest) into 3, and all other values (else) into 9999.

After a function is defined, it can be used in the STATISTICA BASIC program like any other function.  For example, the statement:

v1 := My_recod(v1);

will convert values of variable v1 according to the recoding specifications of function My_recod.

For more information, see Recode.

The If..then..else..undefined conditional block construction can also be used to recode values of variables.


  STATISTICA BASIC Quick Syntax Reference - Operators

The following operators are available in STATISTICA BASIC:

Relational:	=   <   >   <>   <=   >=

Arithmetic:	+   -  *   /   div   mod   **   ^

Logical:	and   not   or

Operators are listed below in order of their precedence (order of execution) from lowest to highest (parentheses may be used to change the order of operation).

Relational:	=   <   >   <>   <=   >=

Addition:	+   -   or

Multiplication:	*   /   div   mod   and

Exponentiation:	**   ^

Negation:	not

Note:  A common error is caused by omitting parentheses needed to adjust for the precedence of operators; for example, the expression x > 0 and x < 1 is incorrect and needs parentheses: (x > 0) and (x < 1) because relational operators (here, > and <) have a lower precedence than the conjuction (and).

Concatenation of String Values:

In order to concatenate two or more strings, use +.

For more information, see STATISTICA BASIC Library of String Functions and Operators - Concatenation

Comparisons of String Values:

Logical operators (=, <, <=, >, >=) can be used to compare two or more strings.

For more information, see STATISTICA BASIC Library of String Functions and Operators - Comparisons


STATISTICA BASIC - Complete Syntax Reference - A

  STATISTICA BASIC - Complete Syntax Reference

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Abort

Abs(x)

AddTextValue

ArcSin(x)

ArcCos(x)

ArcTan(x)

AddTextValue


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  STATISTICA BASIC - Complete Syntax Reference

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Beep

Begin

Beta(x,ν,ω) [iBeta(x,ν,ω), vBeta(x,ν,ω)]

Binom(x,p,n) [iBinom(x,p,n)]


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  STATISTICA BASIC - Complete Syntax Reference

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CaseName

CaseName(cn)

CaseNo

Cauchy(x,η,θ) [iCauchy(x,η,θ), vCauchy(x,η,θ)]

Chi2(x,ν) [iChi2(x,ν), vChi2(x,ν)]

ColorRGB

Const

CopyFile

Cos(x)

CosH(x)


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  STATISTICA BASIC - Complete Syntax Reference

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Data(i,j)

Data(xxx)

Data Management Functions in STATISTICA BASIC

Delete

DeleteFile

DeleteGraph

DeleteScrollsheet

Dim

DisplayButtonBox

DisplayGraph

DisplayInputBox

DisplayLastError

DisplayListBox

DisplayMessageBox

DisplayNumericInputBox

DisplaySelectionBox

Distribution Functions, their Integrals and Inverse Distribution Functions

dNormal(x,μ,σ) [iNormal(x,μ,σ), vNormal(x,μ,σ)]

dPoisson(x,λ) [iPoisson(x,λ)]

DuplicateGraph

DuplicateScrollsheet


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End

Euler

Exit

Expon(x,λ) [iExpon(x,λ), vExpon(x,λ)]

Exp(x)

Extreme(x,a,b) [iExtreme(x,a,b)]


STATISTICA BASIC - Complete Syntax Reference - F

  STATISTICA BASIC - Complete Syntax Reference

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FDistr(x,ν,ω) [iFDistr(x,ν,ω), vF(x,ν,ω)]

For..to..do.., for..downto..do

Function


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  STATISTICA BASIC - Complete Syntax Reference

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Gamma(x,c) [iGamma(x,c), vGamma(x,c)]

Geom(x,p) [iGeom(x,p)]

GetDelimitedString

GetGraph

GetNumber(vn,tv)

GetScrollsheet

GetText(vn,nv)

GOTO Statements

GraphAddBWPlot

GraphAddMinMaxPlot

GraphAddPlot

GraphAddPlotXYZ

GraphAddRangePlot

GraphChangeMappingBase

GraphCopyToClipboard

GraphDrawArrow

GraphDrawArrow3D

GraphDrawArrowTernary

GraphDrawPolyline

GraphDrawShape

GraphDrawShape3D

GraphDrawShapeTernary

GraphDrawText

GraphDrawText3D

GraphDrawTextParam

GraphDrawTextParam3D

GraphDrawTextParamTernary

GraphDrawTextTernary

GraphEmbedGraph

GraphEmbedGraph3D

GraphEmbedGraphTernary

GraphGetHwnd

GraphInsertFile

GraphInsertFile3D

GraphInsertFileTernary

GraphSetBWPlot2DLayout

GraphSetDataPointLabel

GraphSetDataPointLabels

GraphSetDefaultFont

GraphSetEyePosition

GraphSetGridlines

GraphSetLegend

GraphSetMappingArea

GraphSetMatrixHistograms

GraphSetObjectAreaStyle

GraphSetObjectLineStyle

GraphSetObjectPatternStyle

GraphSetPieLayout

GraphSetPieStyle

GraphSetPlot2DLayout

GraphSetPlotAreaStyle

GraphSetPlotBarLineStyle

GraphSetPlotConfidBands

GraphSetPlotEllipse

GraphSetPlotFitLineStyle

GraphSetPlotFitting

GraphSetPlotFittingFunction

GraphSetPlotFittingParam

GraphSetPlotLineStyle

GraphSetPlotName

GraphSetPlotPointStyle

GraphSetProportion

GraphSetRangePlot2DLayout

GraphSetScaleParam

GraphSetScaleTextLabel

GraphSetScaleTextLabels

GraphSetScaleTickmarks

GraphSetScaleValuesStyle

GraphSetScaling

GraphSetTitle

GraphSetXYZFittingFunction

GraphSetXYZFittingParam

GraphSetXYZLayout


STATISTICA BASIC - Complete Syntax Reference - H

  STATISTICA BASIC - Complete Syntax Reference

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Hi

Hypot(x,y)


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  STATISTICA BASIC - Complete Syntax Reference

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iBeta(x,ν,ω)

iBinom(x,p,n)

iCauchy(x,η,θ)

iChi2(x,ν)

iExpon(x,λ)

iExtreme(x,a,b)

If..then..else..undefined

iFDistr(x,ν,ω)

iGamma(x,c)

iGeom(x,p)

iLaplace(x,a,b)

iLogis(x,a,b)

iLognorm(x,μ,σ)

Include File ({$I:'FileName'})

IniAll

iNormal(x,μ,σ)

iPareto(x,c)

iPoisson(x,λ)

iRayleigh(x,b)

iStudent(x,n)

iWeibull(x,b,c,θ)


STATISTICA BASIC - Complete Syntax Reference - J

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Jump(x)


  STATISTICA BASIC - Complete Syntax Reference - K

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This topic intentionally left blank


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Laplace(x,a,b) [iLaplace(x,a,b), vLaplace(x,a,b)]

Len(a)

Library of String Functions

Lo

Logis(x,a,b) [iLogis(x,a,b), vLogis(x,a,b)]

Lognorm(x,μ,σ) [iLognorm(x,μ,σ), vLognorm(x,μ,σ)]

Log(x)

Log10(x)

Log2(x)


STATISTICA BASIC - Complete Syntax Reference - M

  STATISTICA BASIC - Complete Syntax Reference

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Math Library of STATISTICA BASIC

Matrix Library of STATISTICA BASIC

MatrixAdd

MatrixAllNonZero

MatrixAnyNonZero

MatrixCholeskyDecomposition

MatrixCombineHoriz

MatrixCombineVert

MatrixCopy

MatrixCorrelations

MatrixCrossProductOfDev

MatrixDet

MatrixDisplay

MatrixDuplicate

MatrixEigenvalues

MatrixEigenvectors

MatrixElemAdd

MatrixElemDivide

MatrixElemMultiply

MatrixElemSubtract

MatrixExtract

MatrixFill

MatrixGeneralPseudoInverse

MatrixGetColumn

MatrixGetDiagonal

MatrixGetRow

MatrixGramschmidtOrt

Matrixidentity

MatrixInverse

MatrixIsEqual

MatrixIsGreater

MatrixIsGreaterEqual

MatrixIsLess

MatrixIsLessEqual

MatrixIsNotEqual

MatrixKroneckerMultiply

MatrixLogicalAnd

MatrixLogicalNot

MatrixLogicalOr

MatrixMeans

MatrixMultiply

MatrixRank

MatrixRead

MatrixReadFromDataFile

MatrixSaveAsDataFile

MatrixSetColumn

MatrixSetDiagonal

MatrixSetRow

MatrixSetToZero

MatrixSingularValues

MatrixSingularValuesDecomp

MatrixSolve

MatrixSubtract

MatrixSumOfSquares

MatrixSweep

MatrixTrace

MatrixTranspose

MatrixWrite

Max(x,y)

Memory(yyy), Mem(yyy)

Mid(a,x,y)

Min(x,y)

Missing


STATISTICA BASIC - Complete Syntax Reference - N

  STATISTICA BASIC - Complete Syntax Reference

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NCases

NewContour

NewGraph

NewGraph3DHistogram

NewGraph3DSequential

NewGraphXYZ

NewIconGraph

NewMatrix

NewRectMatrix

NewScrollsheet

NewSurface

NewTernary

NoDataFileVariableNames

Normal(x)

Normal Distribution Function (dNormal)

NVars


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  STATISTICA BASIC - Complete Syntax Reference

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Old

OpenGraph

OpenScrollsheet


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  STATISTICA BASIC - Complete Syntax Reference

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Pareto(x,c) [iPareto(x,c), vPareto(x,c)]

Pause

PauseAndEdit

Pi

Poisson(x)

Poisson Distribution Function

PrinterSetOrientation

PrintGraph

PrintGraphToOutputWindow

PrintScrollsheet

PrintScrollsheetToOutputWindow


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  STATISTICA BASIC - Complete Syntax Reference

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Quick Syntax Reference


STATISTICA BASIC - Complete Syntax Reference - R

  STATISTICA BASIC - Complete Syntax Reference

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RandomAccess mode

Rayleigh(x,b) [iRayleigh(x,b), vRayleigh(x,b)]

Read

Recode

ReDim

RenameFile

Rnd(x)

Round(x)


STATISTICA BASIC - Complete Syntax Reference - S

  STATISTICA BASIC - Complete Syntax Reference

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SaveGraph

SaveScrollsheet

SaveScrollsheetAsDataFile

Scrollsheet Library of STATISTICA BASIC

ScrollsheetAppendColumns

ScrollsheetAppendRows

ScrollsheetGetColName

ScrollsheetGetHwnd

ScrollsheetGetMatrix

ScrollsheetGetNbCols

ScrollsheetGetNbRows

ScrollsheetGetRowName

ScrollsheetGetTextValue

ScrollsheetGetTitle

ScrollsheetGetValue

ScrollsheetSetColumnFormat

ScrollsheetSetColumnName

ScrollsheetSetCoumnNameColor

ScrollsheetSetColumnWidth

ScrollsheetSetDataColor

ScrollsheetSetFont

ScrollsheetSetHeaderColor

ScrollsheetSetHilite

ScrollsheetSetHiliteColor

ScrollsheetInforColor

ScrollsheetSetMatrix

ScrollsheetSetRowName

ScrollsheetSetRowNameColor

ScrollsheetSetRowNameWidth

ScrollsheetSetTextValue

ScrollsheetSetTitle

ScrollsheetSetValue

SDelete(a,x,y)

SelectionConditions

SelectionConditionsGet

SelectSaveFileName

SelectOpenFileName

SelectVariables1

SelectVariables2

SelectVariables3

SelectVariables4

Sequential mode

SetDrawingMatrixCoordinates

SetSeed

SetVarName

Sign(x)

Sin(x)

SinH(x)

SInsert(a,x,y)

Sqrt(x)

Statistical Functions in STATISTICA BASIC

Stop

Str(x,y,z)

String Library of STATISTICA BASIC

Student(x,n) [iStudent(x,n), vStudent(x,n)]

Sub


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  STATISTICA BASIC - Complete Syntax Reference

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Tan(x)

TanH(x)

Trunc(x)


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  STATISTICA BASIC - Complete Syntax Reference

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Uniform(x)

Upcase(a)


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  STATISTICA BASIC - Complete Syntax Reference

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V(i,j)

V(xxx)

Vxxx

Val(a)

ValCount

Valid(x)

ValMax

ValMean

ValMedian

ValMin

ValMode

ValPercentile

ValQuartiles

ValStDeviation

ValStError

ValSum

Value(x)

ValVariance

VarLongName(vn)

VarName(vn)

vBeta(x,ν,ω)

vCauchy(x,η,θ)

vChi2(x,ν)

VectorDualSort

VectorRank

VectorSort

vExpon(x,λ)

vF(x,ν,ω)

vGamma(x,c)

vLaplace(x,a,b)

vLogis(x,a,b)

vLognorm(x,μ,σ)

vNormal(x,μ,σ)

vPareto(x,c)

vRayleigh(x,b)

vStudent(x,n)

vWeibull(x,b,c,θ)


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Weibull(x,b,c,θ) [iWeibull(x,b,c,θ), vWeibull(x,b,c,θ)]

Write

WriteLn


  STATISTICA BASIC Syntax Reference - Distribution Functions, their Integrals and Inverse Distribution Functions

STATISTICA BASIC provides a wide range of distributions, their integrals and inverse distribution functions.  They can be used as all other functions in STATISTICA BASIC.  The meaning of the parameters, as well as the number of parameters, depends on the respective distribution function.  Below, is a listing of all available functions.

NOTE:  The distribution names shown below are the same as those used in Spreadsheet formulas and User-defined Functions in graphs, with the exception of  Normal, Poisson, and if.  These names are already used in STATISTICA BASIC.  Therefore, the names for the Normal and Poisson distributions and for the integral of the F distribution have been modified slightly [dnormal(x,μ,σ), dpoisson(x,λ), and iFDistr(x,ν,ω), respectively].

Density or	Inverse

Probability	Distribution	Distribution

Distribution	Function	Function	Function

Beta Distribution	beta(x,ν,ω)	ibeta(x,ν,ω)	vbeta(x,ν,ω)

Binomial Distribution	binom(x,p,n)	ibinom(x,p,n)

Cauchy Distribution	cauchy(x,η,θ)	icauchy(x,η,θ)	vcauchy(x,η,θ)

Chi-square Distribution	chi2(x,ν)	ichi2(x,ν)	vchi2(x,ν)

Exponential Distribution	expon(x,λ)	iexpon(x,λ)	vexpon(x,λ)

Extreme Distribution	extreme(x,a,b)	iextreme(x,a,b)

F Distribution	FDistr(x,ν,ω)	iFDistr(x,ν,ω)	vF (x,ν,ω)

Gamma Distribution	gamma(x,c)	igamma(x,c)	vgamma(x,c)

Geometric Distribution	geom(x,p)	igeom(x,p)

Laplace Distribution	laplace(x,a,b)	ilaplace(x,a,b)	vlaplace(x,a,b)

Logistic Distribution	logis(x,a,b)	ilogis(x,a,b)	vlogis(x,a,b)

Lognormal Distribution	lognorm(x,μ,σ)	ilognorm(x,μ,σ)	vlognorm(x,μ,σ)

Normal Distribution	dnormal(x,μ,σ)	inormal(x,μ,σ)	vnormal(x,μ,σ)

Pareto Distribution	pareto(x,c)	ipareto(x,c)	vpareto(x,c)

Poisson Distribution	dpoisson(x,λ)	ipoisson(x,λ)

Rayleigh Distribution	rayleigh(x,b)	irayleigh(x,b)	vrayleigh(x,b)

Student's t Distribution 	student(x,df)	istudent(x,df)	vstudent(x,df)

Weibull Distribution	weibull(x,b,c,θ)	iweibull(x,b,c,θ)	vweibull(x,b,c,θ)


  STATISTICA BASIC Syntax Reference - NoDataFileVariableNames

Including this statement at the beginning of the STATISTICA BASIC program will suppress the use of names of variables from the data file within the program.  This permits the creation of programs which use temporary variable names that would otherwise conflict with the names of variables in the current STATISTICA data file.

Example:

RandomAccess;

NoDataFileVariableNames;

for i := 1 to NCases do

  for j := 1 to NVars do

    Data(i,j) := Rnd(10);

This program will set all values of the current data file to random numbers between 0 and 10.  If the file contains variables named I or J, the program would not compile without specifying NoDataFileVariableNames.


  STATISTICA BASIC Syntax Reference - Abort

Stops execution of the program without preserving any changes made to the data.  Note that the procedure Stop also halts the program, but it preserves the changes made to the data up to the point that Stop was executed.

Example:

v1 := 0;

if v2 <= 0 then Abort;

This program will assign 0 to the first variable only if values of the second variable are positive (in all cases).  If the program encounters a negative value for v2, then the processing is aborted and the results of all previous assignments (i.e., instruction v1:=0) will not be preserved.


  STATISTICA BASIC Syntax Reference - Abs(x)

Abs(x) - Computes the absolute value of x

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - ArcSin(x)

ArcSin(x) - Computes the arc sine of x

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - ArcCos(x)

ArcCos(x) - Computes the arc cosine of x

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - ArcTan(x)

ArcTan(x) - Computes the arc tangent of x

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - AddTextValue(vn,tv,nv)

Parameters:	vn - variable name

tv - text value (may be represented by a string constant (e.g., 'MALE') or a string variable (e.g., LABEL$)

nv - numeric value

This function will add a specified text value tv to the desired STATISTICA data file variable vn and assign that text value the specified numeric equivalent nv.  If the numeric value already has a text equivalent or the text value exists with a different numeric equivalent, then the old text-numeric pair(s) will be replaced by the new assignment.

Example:  The following program can be used to give meaningful names to the values of a variable representing gender.

RandomAccess;	{specifies RandomAccess mode}

AddTextValue(Gender, 'Male',1);

AddTextValue(Gender, 'Female',2);

AddTextValue(Gender, 'Unknown',0);

Related topics: Text Values Manager, Library of String Functions and Operators


  STATISTICA BASIC Syntax Reference - begin..end

"Syntactic parentheses" used to identify the beginning and end of blocks of instructions (i.e., compound instructions), recode functions, user-defined functions and subroutines, or (optionally) the entire program.

Example:

begin······························· |

  if Profit > 0 then                 | the

  begin··················| a block      | main

    Pr_Sum := Pr_Sum +   | of condi-  | body

              Profit;    | tionally    | of

    NB := NB + 1;        | executed   | the

    if Profit > 100 then | instruct-      | program

      OK := 1;           | ions      | (optio-

  end;···················|           | nal)

end; ······························· |

Note that the word end at the end of the program is optional but it is required if the program starts with begin (begin and end are symmetrical, i.e., there must be one end for each begin in the program).


STATISTICA BASIC Syntax Reference - CaseName[(cn)]

  STATISTICA BASIC Syntax Reference - CaseName or CaseName(cn)

Parameters (for RandomAccess mode only):  cn is the desired case number

Return value:  In RandomAccess mode, the case name for case number cn will be returned.  In Sequential mode, the case name for the currently processed case will be returned.

Example 1:

RandomAccess;	{specifies RandomAccess mode}

WriteLn(CaseName(3));	{WriteLn "prints" the name of the third case}

This command will write (to the previously selected output device, see Page/Output Setup) the name of case number 3 in the current file.

Example 2:

Sequential;	{specifies Sequential mode}

WriteLn(CaseName)	{WriteLn "prints" the case names};

This command will write (to the previously selected output device, see Page/Output Setup) the names of all cases in the file.

Note that if no case names are used in the file, then CaseName(cn) will return a text representation of the case number.

Note that CaseName cannot be the used on the left side of an assignment statement.


  STATISTICA BASIC Syntax Reference - CaseNo

In Sequential mode, CaseNo is a reserved variable containing the number of the currently processed case.  Following the standard STATISTICA convention, the case number is stored in variable number 0, and instead of CaseNo you can use v0 or v(0).

Example:

if CaseNo>100 then  {if case number is greater than 100}

   Delete;          {delete the current case}

This example program will leave only the first 100 cases in the data file.

Note:  This instruction is not valid in RandomAccess mode because there is no "current" case in this mode.


  STATISTICA BASIC Syntax Reference - Const

Const - declares the value of a numeric or string constant.  Once defined, the value of the constant cannot be changed within the STATISTICA BASIC program.

Example:

Const Pie = 3.14;                 {declares value of numeric constant Pie}

Const Cake$ = 'A small pie';      {declares value of string constant Cake$}


  STATISTICA BASIC Syntax Reference - Cos(x)

Cos(x) - Computes the cosine of x

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - CosH(x)

CosH(x) - Computes the hyperbolic cosine of x

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - Data(i,j)

In RandomAccess mode, you can use the predefined array Data(i,j) (or equivalently, you can use V(i,j), where i is the case number and j is the variable number) to access any data cell in the current data file.  For example, the following program will compute the average of the values of 3 variables for case 1 and place the resulting value in variable 1, case 10.

Data(10,1) := ( v2(1) + v3(1) + v4(1) ) / 3;

This method is very flexible in that both parameters i and j may be expressions that are evaluated during execution of the program.  For example, the following program will compute the sum of values for all variables in the current data file.

RandomAccess;

Sum := 0;

  for i := 1 to NCases do

    for j := 1 to NVars do

      Sum := Sum + Value(Data(i,j));

WriteLn('SUM=',Sum);

For other methods of referencing data in RandomAccess mode (Vj(i) and VARNAME(i)), see Referencing STATISTICA Variables.


  STATISTICA BASIC Syntax Reference - Delete

In Sequential mode, this instruction deletes the currently processed record from the data file.

Example:

if (Gender=1) or (Gender=2) then

    OK := 1

  else

    OK := 0

  undefined  {if the value of GENDER is missing}

    Delete   {delete current case from data file}

This program will delete records in which the value of GENDER is Missing (i.e., undefined).

Note:  This instruction is not valid in RandomAccess mode because there is no "current" case in this mode.


  STATISTICA BASIC Syntax Reference - Euler

Euler = 2.71828182845905

Euler is a predefined constant.

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - Exit

In Sequential mode, this instruction terminates processing of the current case (and proceeds to the next case).

Example:

Sequential;         {specifies Sequential mode}

if (v1 < 100) then  {if v1 is less than 100}

    Exit;           {stop, and move to the next record}

v1 := Income - High_Tax * Income;

This program will compute a new value for variable v1 if the current value of v1 is greater than or equal to 100.


  STATISTICA BASIC Syntax Reference - Exp(x)

Exp(x) - Exponential function (computes Euler to the power of x)

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - for..to..do.., for..downto..do

The looping construction is used to repeatedly perform one or more instructions; the general format of STATISTICA BASIC loops is:

for iii:=expression1 to expression2 do instruction

Variable iii cannot be a current STATISTICA data file variable; it also cannot be a STATISTICA BASIC reserved word.  The instruction (which can be any valid STATISTICA BASIC instruction, including compound, conditional, another loop, etc.) will be executed a number of times depending on values of expression1 and expression2.  Variable iii serves as a loop counter and it assumes the values of consecutive integers from expression1 up (or down if downto is used) to expression2 at consecutive passes of the loop.  Values of expression1 and expression2 do not have to be integers.

Example 1:

Sequential;                {specifies Sequential mode}

for i:=1 to 10 do v(i):=0;

In the above example, a constant (0) will be assigned to the first 10 variables in the data file; the semicolon marks the end of the loop.

Example 2:

Sequential;                {specifies Sequential mode}

for i:=0.5 to 4.5 do

     v(2*i) := i;

In this example, v1 will be set to 0.5, v3 will be set to 1.5, v5 will be set to 2.5, etc.

Example 3:

Sequential;                {specifies Sequential mode}

for i:=1 to 20 do

   begin

      v(i):=v(i)**2;

      if v(i)<.001 then v(i):=0;

      if v(i)>1000 then v(i):=-9999;

   end;

In this example, a block of three instructions (enclosed between the words begin..end) will be executed (in Sequential mode) for the first 20 variables.  The word end marks the end of the loop.

Example 4:

RandomAccess;              {specifies RandomAccess mode}

for i:= 1 to NCases do

  for j := 1 to 20 do

   begin

      Data(i,j) := (Data(i,j))**2;

      if Data(i,j)<.001 then Data(i,j):=0;

      if Data(i,j)>1000 then Data(i,j):=-9999;

   end;

In this example, a block of three instructions (enclosed between the words begin..end) will be executed (in RandomAccess mode) for the first 20 variables.  The word end marks the end of the loop.


  STATISTICA BASIC Syntax Reference - GetText(vn,nv)

Parameters:	vn - variable name

nv - numeric value

This function will return the text value associated with the specified numeric value nv for variable vn.

Example:  For this example, let State be a variable in a STATISTICA file holding values 1-50 (which represent the U.S. states) and let each numeric value have a text assignment (e.g., 'Alabama', 'Alaska', ...).  Then, the following program will print (to the previously selected output device, see Page/Output Setup) the numeric-text assignments for the variable STATE.

RandomAccess;	{specifies RandomAccess mode}

for i := 1 to 50 do

  WriteLn (i, ' : ', GetText(State, i));	{WriteLn "prints" returned values};

Related topics: Text Values Manager, Library of String Functions and Operators


  STATISTICA BASIC Syntax Reference - GetNumber(vn,tv)

Parameters:	vn - variable name

tv - text value

This function will return the numeric equivalent associated with the specified text value tv for variable vn.

Example 1:

Response := GetNumber(Item1, 'YES');

This instruction will assign to variable Response, the numeric equivalent of the text value 'YES' (from variable Item1).

Example 2 (changing an existing text value):

AddTextValue(Gender, 'FEMALE', GetNumber(Gender, 'F'));

This instruction will assign the text value 'FEMALE' to the number previously associated with the text value 'F' (i.e., replace 'F' with 'FEMALE').

See also, Library of String Functions and Operators.


  STATISTICA BASIC Syntax Reference - Hi

Denotes an open upper limit of a range of values in definitions of recoding functions (see Recode).  The ranges of values specified with Hi are always inclusive.

Example:

Sequential;       {specifies Sequential mode}

recode Rec1;

  begin

    0, 1, 2, 3 = 0;

    10 to Hi = 1;

  end;

  v2 := Rec1(v1);

This recoding function (Rec1) will transform values 0, 1, 2, and 3 into 0, and values equal to or greater than 10 into 1 (all other values will become MD).


  STATISTICA BASIC Syntax Reference - Hypot

Hypot(x,y) - Computes the hypotenuse [=square root(x**2 + y**2)].

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - if..then..else..undefined

Conditional block instruction of the general format:

if expression then

   instruction

[else                {optional}

  instruction]

[undefined           {optional}

  instruction]

The expression does not have to be strictly logical (e.g., v0<100); it can also be numeric (e.g., v1*v2 where 0 is interpreted as "not met" or "false").  The else and undefined segments of the block are optional.

Only one instruction per conditional block is permitted unless begin..end is used to enclose a compound instruction.  The execution of the block depends on the value of the expression calculated by the program; if it is defined and not 0 or false, then the first instruction is executed, if it is 0 or false then the second instruction (specified after the word else) is executed; if the expression is undefined (i.e., it contains missing data) then the instruction specified after the word undefined is executed.

Example:

Sequential;       {specifies Sequential mode}

if v5 > 100 then

  v5 := 1         {note: no semicolon before ELSE}

else

begin

  v6 := v5;

  v5 := v5 / 100;

end               {note: no semicolon before UNDEFINED}

undefined

  v5 := 0;

In this example the program will change the value of variable v5.  If it is greater than 100, then it will be set to 1; if v5 is missing then it will be set to 0, otherwise the value of v5 is stored in v6, and v5 is divided by 100.

NOTE:  A common syntactic error is caused by inserting a semicolon (;) after individual instructions within the segments of the block (no semicolons are allowed before else and undefined in if..then..else instructions).  Another common error is caused by omitting parentheses needed to adjust for the precedence of operators; for example, the expression:

  x > 0 and x < 1

is incorrect and needs parentheses:

  (x > 0) and (x < 1)

because relational operators (here, > and <) have a lower precedence than the conjunction (and).

Note:  The world else is also used in definitions of recode functions (see the topic on recodes for specific syntax conventions).


  STATISTICA BASIC Syntax Reference - IniAll

Initializes all STATISTICA BASIC generators of random numbers (Initialize All generators).

Example:

IniAll;  {initialize all random number generators}

v16 := rnd(1);

This program will assign to variable v16 the same number in each case (in this instance, produced by the generator of uniformly distributed random numbers from the range of 0 to 1).

Note that all random number functions in STATISTICA BASIC are based on a common uniform random number generator.  IniAll will initialize (seed) this random number generator with a number based on the respective current computer time.  Use function SetSeed(x) to use a specific seed value X, for example, in order to replicate identical series of random numbers.


  STATISTICA BASIC Syntax Reference - Jump(x)

In Sequential mode, procedure Jump(x) can be used to "jump" to case number x.  The argument x can be any expression (the expression evaluates to the target case number).

Example:

if (CaseNo >100) and (CaseNo<201) then Jump(201);

This instruction will skip cases number 101 through 200; the same effect could be achieved by the following instruction:

if CaseNo =101 then Jump(201);

Note:  This instruction is not valid in RandomAccess mode because there is no "current" case in this mode.


  STATISTICA BASIC Syntax Reference - Len(a)

Parameters:  a - string

Return value:  integer

Returns the length of the string a.

Example:

x := Len( 'abcdefg' );

will produce the same result as:

x := 7 ;

(i.e., the value of x will be 7)

See also, Library of String Functions and Operators.


  STATISTICA BASIC Library of String Functions and Operators - Overview

STATISTICA BASIC supports the use of text values called strings.  Strings can be used either directly or by using string variables; when used directly, strings are enclosed in 'single' or "double" quotes.  String variables are designated by adding a "$" character to the end of the variable name (for example, text$, name$).

The STATISTICA BASIC String Library includes functions to manage string values of local variables (designated by adding a "$" character to the end of the variable name, as mentioned above), and text values of variables (see Double Notation of Values).

Example 1

This example will convert to uppercase the text value assigned to numeric value 1 for the first variable in the file.

RandomAccess;

text$ := GetText(v1, 1);

text$ := UpCase(text$);

AddTextValue(v1, text$, 1);

Example 2

This example will display the mean of variable 2.  The title of the scrollsheet is defined as the value of the string variable name$

RandomAccess;

name$ := 'Mean of ' + VarName(2);

ValMean(v2, 1, NCases, mean);

MatrixDisplay(mean, name$);

For general information about strings see How to Use Strings in STATISTICA BASIC.

For a complete library of string operations see STATISTICA BASIC String Library.

See also, Passing Lists of Strings to STATISTICA BASIC Functions and Retrieving Lists of Strings in STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - Library of String Functions and Operators

Overview

Operators:  Concatenation and Comparisons.

Functions	Example and {Comment}

AddTextValue(vn,tv,nv)	AddTextValue(Area, 'Midwest',3);

{Creates the text value Midwest with the numeric equivalent 3 for the variable Area.}

CaseName	WriteLn('Case ', CaseNo, ': ', CaseName);

{In Sequential mode, prints the case number and case name for each case in the file on a separate line.}

CaseName(cn)	WriteLn('Case 3: ', CaseName(3));

{In RandomAccess mode, prints the case number and case name for each case in the file on a separate line.}

GetDelimitedString	GetDelimitedString(input$, 1, output$);

{Returns as output$ the first string from the delimited string of values input$.}

GetNumber(vn,tv)	GetNumber(Area, 'Midwest');

{Returns the numeric value associated with the text value 'Midwest'.}

GetText(vn,nv)	GetText(Area, 3);

{Returns the text value associated with value 3 for variable Area.}

Len(a)	strlen := Len( 'abcdefghijkl' );

{Returns the length of the specified text string.}

Mid(a,x,y)	text$ := Mid( 'Mary had a lamb', 6, 3 );

{Starting with character 6, returns a substring of 3 characters.}

SDelete(a,x,y)	text$ := SDelete( 'Mary had a lamb', 6, 3 );

{Starting with character 6, deletes a substring of 3 characters.}

SInsert(a,b,y)	text$ := SInsert('Mary a lamb' , 'had ' , 6);

{Starting at the 6th character in string 'Mary a lamb', inserts the string 'had '.}

Str(x,y,z)	text$ := Str(1234.25693287, 10, 5);

{Returns a 10 character image of 1234.25693287 with 5 places after the decimal.}

UpCase(a)	text$ := 'Mary had a lamb'; UpCase(text$);

{Makes the text string 'Mary had a lamb' upper case.}

Val(a)	new := Val('$10.99');

{Returns the numeric value 10.99 from the string '$10.99'.}

VarLongName	name$ := VarName(i) +': '+ VarLongName(i);

{Assigns text string, including current short and long variable name, to local string variable name$.}

VarName	name$ := 'Analysis of ' + VarName(i);

{Assigns text string, including current variable name, to local string variable name$.}

Write(a, ...)	Write(CaseName, ' : ', Age);

{In Sequential mode, prints the case names, a colon, and the values of Age for each case in the file.  To start a new line, use WriteLn.}

WriteLn(a, ...)	WriteLn(CaseName, ' : ', Age);

{In Sequential mode, prints the case names, a colon, and the values of Age for each case in the file.  A new line will start for each WriteLn statement.}


Library of String Functions and Operators - Concatenation
  STATISTICA BASIC Library of String Functions and Operators - Concatenation

In order to concatenate two or more strings, use +.  For example, the following program will concatenate two text strings.

RandomAccess;	{specifies RandomAccess mode}

a$ := 'Means of ' + VarName(1);

   WriteLn(a$);	{WriteLn "prints" the value of a$}

This program will add the name of variable 1 (see VarName(vn)) to the text string 'Means of' (e.g., Means of Measur1) and send it to the previously specified ouptut device (see WriteLn).


Library of String Functions and Operators - Comparisons
  STATISTICA BASIC Library of String Functions and Operators - Comparisons

Logical operators (=, <, <=, >, >=) can be used to compare two or more strings.  For example, the following program will compare the text string being concatenated with the specified text string.

Sequential;	{specifies Sequential mode}

name$ := UpCase(GetText(F_Name,F_Name) + ' ' + GetText(L_Name,L_Name));

if name$ = 'JOHN SMITH' then

   WriteLn('JOHN SMITH found in case ', CaseNo);

For each case in the data file, the program will get the text value of variable F_Name and concatenate it with the text value for variable L_Name (with a space in the middle).  If the resulting text string is equal to 'JOHN SMITH' then the case number in which that text string occurs will be written next to it.


Library of String Functions and Operators - AddTextValue(vn,tv,nv)
  STATISTICA BASIC Library of String Functions and Operators - AddTextValue(vn,tv,nv)

The AddTextValue(vn,tv,nv) function will add a specified text value tv to the text values existing in variable vn and assign that text value the specified numeric equivalent nv.

Example:

AddTextValue(Area, 'Midwest',3);

This program will assign the text value 'Midwest' to the numeric value 3 for the variable Area.

See also Text Values Manager.


Library of String Functions and Operators - GetText(vn,nv)
  STATISTICA BASIC Library of String Functions and Operators - GetText(vn,nv)

The GetText(vn,nv) function will return the text value associated in variable vn with the specified numeric equivalent nv.

Example 1:

WriteLn(GetText(Area, 3));

This program will print to the previously selected output device, the text value associated with value 3 for variable Area.

Example 2:

Sequential;                   {specifies Sequential mode}

   WriteLn(GetText(Area, Area));

This program will print to the previously selected output device (see WriteLn), the text values corresponding to consecutive numeric values of variable AREA (i.e., first argument "Area" indicates the variable, the second argument "Area" indicates the value of that variable in the currently processed case).

The equivalent operation in RandomAccess mode would look like this:

RandomAccess;

for i := 1 to NCases do

   WriteLn(GetText(Area, Area(i)));

See also Text Values Manager.


Library of String Functions and Operators - GetNumber(vn,tv)
  STATISTICA BASIC Library of String Functions and Operators - GetNumber(vn,tv)

The GetNumber(vn,tv) function will return the numeric value associated in variable vn with the specified text value tv.

Example:

WriteLn(GetNumber(Area, 'Midwest'));

This program will print to the previously selected output device, the numeric value associated with the text value 'Midwest'.

See also Text Values Manager.


Library of String Functions and Operators - Len(a)
  STATISTICA BASIC Library of String Functions and Operators - Len(a)

The Len(a) function returns the length of string a.

Example:

x := Len( 'abcdefghijkl' );

will produce the same result as:

x := 12 ;


Library of String Functions and Operators - Mid(a,x,y)
  STATISTICA BASIC Library of String Functions and Operators - Mid(a,x,y)

Starting with the x'th character of the string a, the Mid(a, x, y) function will return a substring of y subsequent characters.

Example:

t$ := Mid( 'Mary had a lamb', 6, 3 );

will produce the same result as:

t$ := 'had';


Library of String Functions and Operators - SDelete(a,x,y)
  STATISTICA BASIC Library of String Functions and Operators - SDelete(a,x,y)

Starting at character number x, the SDelete(a, x, y) function deletes from string a, a substring of y characters.

Example:

t$ := SDelete( 'Mary had a lamb', 6, 3 );

will produce the same result as:

t$ := 'Mary  a lamb';


Library of String Functions and Operators - SInsert(a,b,y)
  STATISTICA BASIC Library of String Functions and Operators - SInsert(a,b,y)

Starting at the y'th character position of string a, the SInsert(a, b, y) function inserts string b into string a.

Example:

t$ := SInsert('Mary a lamb' , 'had ' , 6);

will produce the same result as:

t$ := 'Mary had a lamb';


Library of String Functions and Operators - Str(x,y,z)
  STATISTICA BASIC Library of String Functions and Operators - Str(x,y,z)

The Str(x, y, z) function returns a string of y characters, containing an image of value x, with z digits after the decimal point.

Example:

t$ := Str(1234.25693287, 10, 5);

will produce the same result as:

t$ := '1234.25693';


Library of String Functions and Operators - UpCase(a)
  STATISTICA BASIC Library of String Functions and Operators - UpCase(a)

The UpCase(a) function converts all lower case letters in string a into upper case letters.

Example:

t$ := 'Mary had a lamb';

UpCase(t$);

will produce the same result as:

t$ := 'MARY HAD A LAMB';


Library of String Functions and Operators - Val(a)
  STATISTICA BASIC Library of String Functions and Operators - Val(a)

The Val(a) function returns a numeric interpretation of string a (up to the first character of the string that is not interpretable as a part of a number); if string a does not contain a number, then the value of function Val is 0.

Example:

RandomAccess;    {specifies RandomAccess mode}

New := Val('$10.99');

The program will assign the value of 10.99 to variable New.


  STATISTICA BASIC Syntax Reference - Lo

Denotes an open lower limit of a range of values in recode definitions (see Recode).  The ranges of values specified with Lo are always exclusive.

Example:

recode Rec2;

  begin

    Lo to 0 = -1;

    10, 20, 30 = 0;

  end;

  v2 := Rec2(v1);

This recoding function (Rec2) will transform values 10, 20, and 30 into 0, values less than 0 into 1 (all other values will become missing data).


  STATISTICA BASIC Syntax Reference - Log(x)

Log(x) - Computes the natural logarithm of x (base Euler)

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - Log10(x)

Log10(x) - Computes the common logarithm of x (base 10)

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - Log2(x)

Log2(x) - Computes the binary logarithm of x (base 2)

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - Math Library of STATISTICA BASIC

The math library of STATISTICA BASIC consists of numeric constants, math functions, and several random number generators which can be used to generate random numbers following a variety of distributions.

Constants:

Euler  = 2.71828182845905

Pi     = 3.14159265358979

Functions:

Abs(x)     - absolute value of x

ArcCos(x)  - arc cosine of x

ArcSin(x)  - arc sine of x

ArcTan(x)  - arc tangent of x

Cos(x)     - cosine of x

CosH(x)    - hyperbolic cosine of x

Exp(x)     - exponential function (Euler to the power of x)

Hypot(x,y) - hypotenuse of x,y [square root(x**2 + y**2)]

Log(x)     - natural logarithm of x (base Euler)

Log10(x)   - common logarithm of x (base 10)

Log2(x)    - binary logarithm of x (base 2)

Max(x,y)   - returns the greater value of x and y

Min(x,y)   - returns the lesser value of x and y

Round(x)   - rounds x to an integer

Sign(x)    - returns the sign of x (x<0 → -1; x=0 → 0;  x>0 → 1)

Sin(x)     - sine of x

SinH(x)    - hyperbolic sine of x

Sqrt(x)    - square root of x

Tan(x)     - tangent of x

TanH(x)    - hyperbolic tangent of x

Trunc(x)   - truncates x to an integer

Random number generators:

Normal(x)   - random number from a normal distribution with a mean of 0 and a standard deviation of x;

Poisson(x)  - random number from a Poisson distribution with lambda equal to x (i.e., with a mean of x and a standard deviation of  √x);

Uniform(x)  - random number from a uniform distribution in the range of 0 to x (same as Rnd(x));

Rnd(x)      - random number from a uniform distribution in the range of 0 to x (same as Uniform(x)).

All random number generators are based on a common uniform random number generator.  A wide variety of other random number generators can be built in STATISTICA BASIC using the basic functions and the Distribution functions.

Random number generator initialization (seed):

IniAll      - initializes the common uniform random number generator based on the respective current computer time;

SetSeed(x)  - initializes the common uniform random number generator with the value of X.

The random number generator in STATISTICA BASIC is initialized (i.e., seeded) via procedure IniAll which is called automatically at the beginning of the execution of the program, but may also be called at any point from within STATISTICA BASIC programs.  Procedure IniAll will initialize the uniform random number generator based on the respective current computer time.  Use function SetSeed(x) to use a specific seed value X, for example, in order to replicate identical series of random numbers.

Distribution functions:

For a complete list of distribution functions (and their integrals) supported in STATISTICA BASIC, see Distribution functions.


  STATISTICA BASIC Syntax Reference - Max(x,y)

Max(x,y) - Returns the greater value of x and y.

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - Memory(yyy), Mem(yyy)

Memory (shortcut: Mem) is a predefined data array that can be used to transfer values between cases (or accumulate values across cases) in Sequential mode.  Note that in Sequential mode processing, values of all other variables are initialized at the beginning of each case.

The array Memory can also be used in RandomAccess mode (for temporary storage), although in RandomAccess mode, the STATISTICA BASIC program is executed only once (and variables are not initialized for each case) and thus in RandomAccess mode, there is no need to use any particular method to transfer values between cases.

By default, the number of data values that can be stored in this array is equal to 8,000.  However, if necessary, its size can be set to a different value if such a large array is not needed (the size of this array can be adjusted in the Options window of the STATISTICA BASIC menu).  The values in the array are initialized to 0 before the execution of the program.

Example:

Sequential;          {specifies Sequential mode}

if CaseNo = 11 then

begin

  for i := 1 to 20 do

    v(i) := Mem(i);

  Stop;

end;

for i := 1 to 20 do

  if v(i) > Mem(i) then

    Mem(i) := v(i);

The above program finds the maximum value of the first 20 variables in the first 10 cases; the value that is found is then assigned to the first 20 variables in case number 11.


  STATISTICA BASIC Syntax Reference - Mid(a, x, y)

Parameters:	a - string

x, y - integer

Return value: string

Starting at the x'th character of the string a, the function will return a substring of y subsequent characters.

Example:

x$ := Mid( 'Quick Basic Statistics', 7, 10 );

will produce the same result as:

x$ := 'Basic Stat';

See also, Library of String Functions and Operators.


  STATISTICA BASIC Syntax Reference - Min(x,y)

Min(x,y) - Returns the lesser value of x and y.

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - Missing

Denotes a missing value of the respective variable to which it is assigned (the specific value of Missing is context sensitive, i.e., it contains a missing data value for the variable to which it refers in the STATISTICA BASIC statement).

Example:

v(10) := Missing;

This program will assign the respective missing data value to variable 10 in all cases.

Note.  Because all expressions which contain Missing values evaluate to Missing, the condition if x=Missing will always be undefined; thus the expression if not Valid(x) should be used instead to determine whether x is Missing.


  STATISTICA BASIC Syntax Reference - NCases

Returns the number of cases in the current data file.

Example:

RandomAccess;	{specifies RandomAccess mode}

for i :=1 to NCases do

  data(i,1) := 0;

This program will set the value of variable 1 to 0 for all cases (NCases).


  STATISTICA BASIC Syntax Reference - Normal(x)

Normal(x) - Random real number from a normal distribution with a mean of 0 and a standard deviation of x

Example:

for i := 1 to NVars do

  v(i) := Abs(Normal(5));

This program will compute positive random numbers (following the normal distribution) for variables 1 through the number of variables in the file (NVars).

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - NVars

Returns the number of variables in the current data file.

Example:

Sequential;	{specifies Sequential mode}

for i := 1 to NVars do

  V(i) := Abs(Normal(5));

This program will fill the data file with absolute values of random numbers from the Normal distribution.


  STATISTICA BASIC Syntax Reference - Old

Used in definitions of recoding functions to specify intervals which remain unchanged.

Example:

recode A;

  begin

    Lo .. 0, 10 = Old;

    3 = 10;

  end;

This recoding function (A) will change 3 into 10, and the values that are either less than 0 or equal to 10 will remain unchanged (all other values will be set to missing data).


  STATISTICA BASIC Syntax Reference - Pi

Pi = 3.14159265358979

Pi is a predefined constant.


  STATISTICA BASIC Syntax Reference - Poisson(x)

Poisson(x) - Random real number from a Poisson distribution with lambda equal to x (i.e., with a mean of x and a standard deviation of  √x)

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - RandomAccess

See RandomAccess vs. Sequential mode.

By stating RandomAccess at the beginning of a STATISTICA BASIC program, STATISTICA will process data in cases (records) of the current data file in a random access mode.  As opposed to sequential mode, in RandomAccess mode, the program is executed once and any data cell may be accessed by referencing both the variable and case numbers.

For more information, see Sequential vs. RandomAccess mode; see also Applications, Advantages of RandomAccess Mode.

Example:

RandomAccess;

WriteLn(CaseName(20));

The above program will write the case name for case number 20 to the previously specified ouptut device (see WriteLn).

NOTES:

•	Instead of specifying the mode (Sequential or RandomAccess) at the beginning of a program, you can select it as a global option in the STATISTICA BASIC Options dialog.

•	Because both the variable number and case number must be specified in RandomAccess mode, referencing a variable using the convention Vj (e.g., v3 := v2 + v1) will produce an error message.  Therefore, in RandomAccess mode, data cells within variables may be referenced using one of the following methods:

Data(i,j)	where i is the case number and j is the variable number (e.g., Data(3,1) := 0); both variable and case numbers can be specified as any numerical expression.

V(i,j)	this is equivalent to Data(i,j), described above

Vj(i)	where j (the variable number) is explicitly specified and i is the case number (e.g., V1(3) := 0); case numbers can be specified as any numerical expression.

VARNAME(i)	where VARNAME is the variable name and i is the case number (e.g., NEWVAR(3) := 0); case numbers can be specified as any numerical expression.

•	The following instructions are not valid in RandomAccess mode because there is no "current" case in this mode:

CASENO	("current" case number in the Sequential mode)

DELETE	(deletes the "current" case number in the Sequential mode)

JUMP(x)	(go to case number x in the Sequential mode)

and the following instructions must have an extra parameter (cn) representing the case number:

CASENAME(cn)


  STATISTICA BASIC Syntax Reference - Recode

The word recode starts the definition of a recoding function (that can be used repeatedly like any other function to change values of variables).  The definitions of all recoding functions should be placed at the beginning of the program.  Each definition consists of the word recode followed by a name (up to 8 characters long) of the function and a list of recoding statements enclosed inside the begin..end block.  For example, the following function called My_recod:

recode My_recod;

     begin

          0 = 1;

          1 to 5 = 2;

          6 to Hi = 3;

          else -9999;

     end;

will convert 0 into 1, 1 through 5 (excluding 5) into 2, 6 through Hi (highest) into 3, and all other values (else) into 9999.

After a function is defined, it can be used in the STATISTICA BASIC program like any other mathematical function.  For example, the statement:

v1 := My_recod(v1);

will convert values of variable v1 according to the recoding specifications of function My_recod.

Note that in addition to lists of constants, ranges can also be used on the left sides of the recoding equations (e.g., 1 .. 10  or  Lo .. -1000  or  888 .. Hi, where Lo .. "constant" is a lower-unbounded interval, and "constant" .. Hi is an upper-unbounded interval).  Such ranges are always interpreted as excluding the upper endpoint of the range.  For example:

Lo to -10 = 1; -10 to 20 = 2;  20 to Hi = 3

would recode 0 as 2 (in the second range), but 20 would be recoded as 3 (in the third range).

The right sides of the recoding equations can also contain the word Old which will cause the corresponding values from the left side to remain unchanged.

recode New1;

     begin

          0 = 1;

          Missing = 2;

          6 to Hi = Old;

     end;

No equal sign is used after else; for example:

recode New2;

     begin

          0 = 1;

          1 to 5 = 2;

          6 to Hi = 3;

          else Old;

     end;

Values not specified on the left sides of recoding statements are recoded either to MD or to the value specified by the else part (if one exists).

The specific constants listed on the left sides of the recoding equations cannot be duplicated in one recoding function, and the ranges cannot overlap. The keywords Lo, Hi and Missing may appear on the left side only once.

The else segment of the recode definition is optional.  A recode function definition must contain at least one recoding equation.  The word to can be used instead of two dots (..); for example:

Lo .. 0 = -1;    is equivalent to:    Lo to 0 = -1;

Example:

Sequential;                  {specifies Sequential mode}

recode Ex1;

begin                        {begin recode definition}

  Lo to -10, 111 to 119 = 0; {values up to -10, and 111 to 119 will be recoded to 0}

  200 .. Hi = 1;             {200 and over will become 1}

  0, 1, 2, 10 .. 20 = Old;   {0, 1, 2 and 10 to 20 (excluding 20) will not be changed}

  Missing = -2               {Missinghqml_syn_missing>main values will become -2}

  else -1                    {all other values will become -1}

end;

v2:=Ex1(v1);


  STATISTICA BASIC Syntax Reference - Else

In recode functions, Else denotes values which are otherwise unspecified on the left sides of recoding statments.  For example:

recode New2;

     begin

          0 to Hi = 3;

          else -1;

     end;

In this recoding function, values less than 0 (values not in the range from 0 to Hi) will become -1.  Note that an equal sign is not used after else.

In If..then..else conditional block constructions, Else denotes the alternative condition when the first condition (between if and then is not satisifed).  For example

if v5 > 100 then

  v5 := 1

else

  v5 := 2;

In this conditional construction, variable 5 is assigned the value of 2 if the condition v5 > 100 is not satisfied.  Note that a semicolon is not used before else.


  STATISTICA BASIC Syntax Reference - Rnd(x)

Rnd(x) - Random real number from a uniform distribution in the range of 0 to x (same as Uniform(x))

See also, SetSeed(x), Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - Round(x)

Round(x) - Rounds x to an integer ("away from zero"; i.e., Abs(Round(x))  Abs(x) )

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - SDelete(a, x, y)

Parameters:	a - string

x, y - integer

Return value:  string

Deletes (i.e., removes) a substring of y characters from string a, starting at character number x.

Example:

a$ := SDelete( 'Results of Analysis for Variables 1-14', 8, 12 );

will produce the same result as:

a$ := 'Results for Variables 1-14';

See also, SInsert(a, b, x)

Library of String Functions and Operators


  STATISTICA BASIC Syntax Reference - SetSeed(x)

SetSeed(x) will set the seed for the uniform random number generator.  Given a particular seed number X, the random number generator will produce a particular series of random numbers.  Thus, you can replicate series of successive random numbers by seeding the random number generator with the same value in each replication.  The valid range for the seed is from 0 to 32,000.

Note that the normal random number generator (function normal(x)) and Poisson random number generator (function Poisson(x)) are based on the uniform random number generator, and the values generated by those functions will also be affected by the seed value.

Use function IniAll to seed the random number generator with a constant that is dependent on the respective computer-time.

See also rnd(x), uniform(x), normal(x), and Poisson(x).


  STATISTICA BASIC Syntax Reference - Sequential

See Sequential vs. RandomAccess mode.

By stating Sequential at the beginning of a STATISTICA BASIC program, STATISTICA will process data in cases (records) of the current data file in a sequential mode.  As opposed to RandomAccess mode, in Sequential mode, the program is executed for each case in the data file.

For more information, see Sequential vs. RandomAccess mode; see also Applications, Advantages of Sequential Mode.

Example:

Sequential;

WriteLn(CaseName);

The above program will write the case names for the current data file to the previously specified ouptut device (see WriteLn).

NOTES:

•	The default mode is RandomAccess (Sequential needs to be requested).

•	Instead of specifying the mode (Sequential or RandomAccess) at the beginning of a program, you can select this global option in the STATISTICA BASIC Options dialog.

•	The following methods of referencing data are not valid when Sequential is specified (for more information on these methods, see RandomAccess):

Data(i,j)

V(i,j)

Vj(i)

VARNAME(i)

In Sequential mode, referencing a particular cell in a variable will produce an error message.

•	The following instructions are valid only in Sequential mode:

CASENO	("current" case number in the Sequential mode)

DELETE	(deletes the "current" case number in the Sequential mode)

JUMP(x)	(go to case number x in the Sequential mode)

and for the following instructions, you cannot use the case number parameter (cn; as is used in RandomAccess mode):

CASENAME


  STATISTICA BASIC Syntax Reference - Sign(x)

Sign(x) - Returns the sign of x (x<0 → -1; x=0 → 0;  x>0 → 1)

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - Sin(x)

Sin(x) - Computes the sine of x

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - SinH(x)

SinH(x) - Computes the hyperbolic sine of x

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - SInsert(a, b, y)

Parameters:	a, b - string

y - integer

Return value: string

Inserts string b into string a, starting at y'th character position of string a.

Example:

t$ := SInsert( 'Results for Variables 1-14', 'of Analysis ', 9 );

will produce the same result as:

t$ := 'Results of Analysis for Variables 1-14';

See also, SDelete(a, b, x)

Library of String Functions and Operators


  STATISTICA BASIC Syntax Reference - Sqrt(x)

Sqrt(x) - Computes the square root of x (equivalent to  x**.5  and  x^.5)

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - Stop

Stops the execution of the program; all changes made to the data file before Stop was executed are preserved.  Note that this procedure is similar to Abort, but Abort does not preserve any changes made to the data.

Example:

sequential;                   {specifies sequential mode; the program will be executed once for each case}

if CaseNo>100 then            {if the case number is greater than 100}

    Stop;                     {stop the program (do not process any new records)}

Income := Inc1 + Inc2 + Inc7; {otherwise..}

This assignment Income:=... will be executed only for the first 100 cases.


  STATISTICA BASIC Syntax Reference - Str(x, y, z)

Parameters:	x - numeric

y, z - integer

Return value:  string

Returns a string of y characters, containing an image of value x, with z digits after the decimal point (i.e., this function writes number x to a string with the format specified by y and z).

Example:

x$ := Str(12.613081, 6, 3);

will produce the same result as:

x$ := '12.613';

See also, Library of String Functions and Operators.


  STATISTICA BASIC Syntax Reference - Tan(x)

Tan(x) - Computes the tangent of x

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - TanH(x)

TanH(x) - Computes the hyperbolic tangent of x

See also, Math Library of STATISTICA BASIC.


STATISTICA BASIC Syntax Reference - trunc

  STATISTICA BASIC Syntax Reference - Trunc(x)

Trunc(x) - Truncates x to an integer ("towards zero"; i.e., Abs(Trunc(x)) ≤ Abs(x) )

See also, Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - Uniform(x)

Uniform(x) - Random real number from a uniform distribution in the range of 0 to x (same as Rnd(x))

See also, SetSeed(x), normal(x), Poisson(x), and Math Library of STATISTICA BASIC.


  STATISTICA BASIC Syntax Reference - UpCase(a)

Parameter:  a - string

Return value:  string

Converts all lower case letters in string a into upper case letters.

Example:

t$ := UpCase('Correlations between v1 and v2');

will produce the same result as:

t$ := '	CORRELATIONS BETWEEN V1 AND V2';

See also, Library of String Functions and Operators.


STATISTICA BASIC Syntax Reference - Vxxx(i)

  STATISTICA BASIC Syntax Reference - Vxxx, Vxxx(i)

Parameter (in RandomAccess mode only):  i - the case number

Sequential mode:

Vxxx (where xxx is a sequential variable number in the current STATISTICA data file) represents one of the three alternative ways of referencing STATISTICA data set variables in Sequential mode in STATISTICA BASIC programs.  The other two methods are:  indexed method (e.g., v(iii) where iii is either a constant, variable, or expression) or by name (e.g., INCOME1, INCOME2, etc.).

Example:

v2 := v10 + v20;

v3 := v10 * v20;

v1 := v3 / (10 - v2);

Referencing STATISTICA variables by their names is the preferred method because it allows STATISTICA BASIC to produce smaller and faster internal (compiled) code before the execution begins.

RandomAccess mode:

Vxxx(i) (where xxx is a sequential variable number in the current STATISTICA data file and i is the case number) represents one of the three alternative ways of referencing STATISTICA data set variables in RandomAccess mode in STATISTICA BASIC programs.  The other two methods are: Data(i,j) method (where j is the variable number and i is the case number) or by name (e.g., INCOME1(i), INCOME2(i), etc., where i is the case number).

Example:

v2(1) := v10(5) + v20(5);

v3(15) := v10(1) * v20(1);

v1(i) := v3(i) / (10 - v2(i));


  STATISTICA BASIC Syntax Reference - V(xxx)

V(xxx) (where xxx is a constant, variable, or expression that evaluates to the sequential variable number in the current STATISTICA data file) represents one of three alternative ways of referencing STATISTICA data set variables in Sequential mode in STATISTICA BASIC programs.  The other two methods are: standard STATISTICA method (e.g., Viii where iii is a variable number) or by name (e.g., INCOME1, INCOME2, etc.).

Example:

for i:=1 to 10 do v(2*i+1):=-1;

v(v10):=0;

Alternatively, you can use Data(i) to reference the desired variable.

Referencing STATISTICA variables by their names is the preferred method because it allows STATISTICA BASIC to produce smaller and faster internal (compiled) code before the execution begins.

When referencing variables in RandomAccess mode, use the following conventions:

Data(i,j)	where i is the case number and j is the variable number (e.g., Data(3,1) := 0); both variable and case numbers can be specified as any numerical expression.

V(i,j)	where i is the case number and j is the variable number (equivalent to Data(I,j)).

Vj(i)	where j (the variable number) is explicitly specified and i is the case number (e.g., V1(3) := 0); case numbers can be specified as any numerical expression.

VARNAME(i)	where VARNAME is the variable name and i is the case number (e.g., NEWVAR(3) := 0); case numbers can be specified as any numerical expression.

For more information, see Sequential vs.RandomAccess mode.


  STATISTICA BASIC Syntax Reference - Val(a)

Parameter:  a - string

Return value:  numeric

This function returns a numeric interpretation of string a (up to the first character of the string that is not interpretable as part of a number); if string a does not contain a number, then the value of function Val is 0.

Example:

temp := Val(GetText(v2,100));

WriteLn (temp);   {"prints" the value of temp}

If the text value of variable 2 associated with the numeric equivalent 100 is $12.45, then this program will write:  12.45.  (See also GetText.)

See also, Library of String Functions and Operators.


STATISTICA BASIC Syntax Reference - ValCount

  STATISTICA BASIC Syntax Reference - ValCount(Array, Start, ?HowMany)

Parameters:

Array	array name

Start	start with element number

?HowMany	how many sequential elements in which to count the number of non-missing values

The ValCount function returns the number of non-missing values among the specified number of array elements beginning with the specified element.  Note that you can specify a variable name, array name or the current data file (using Data as the array name) for the parameter Array.

Example 1:

RandomAccess;

count := ValCount(v3, 1, NCases);

WriteLn('n = ', count);

The above example will return the number of non-missing values in variable 3 for all cases in the data file.

The syntax for the ValCount function has been improved from previous versions of STATISTICA.  The function has been generalized to accept any array rather than only accepting an array from the data file.  Note that as with previous versions of STATISTICA, it is possible to calculate the number of non-missing values of variables for each case.  The following example shows the correct syntax for doing this.

Example 2:

Sequential;

v10 := ValCount(v,3,6);

This example places the number of non-missing values of variables v3-v8 (for each case) in v10.

Related topics: ValMax, ValMean, ValMedian, ValMin, ValMode, ValPercentile, ValQuartiles, ValStDeviation, ValStError, ValSum, and ValVariance

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Statistical functions, see STATISTICA BASIC Quick Syntax Reference.


STATISTICA BASIC Syntax Reference - ValMax

  STATISTICA BASIC Syntax Reference - ValMax (Array, Start, ?HowMany, Result)

Parameters:

Array	array name

Start	start with element number

?HowMany	how many sequential elements in which to find maximum value

Result	return value

The ValMax function computes the maximum of the non-missing values from among the specified number of array elements beginning with the specified element.  Note that you can specify a variable name, array name or the current data file (using Data as the array name) for the parameter Array.

Example 1:

RandomAccess;

ValMax(v3, 1, Ncases, x);

WriteLn('Maximum = ', x);

The above example will return the maximum value in variable 3 for all cases in the data file.

Note that the ValMax function can also be used in Sequential mode.  For example, it is possible to determine the maximum value of the non-missing values of variables for each case.  The following example shows the correct syntax for doing this.

Example 2:

Sequential;

ValMax(v,3,6,v11);

This example places the maximum value of non-missing values of variables v3-v8 (for each case) in v11.

Related topics: ValCount, ValMean, ValMedian, ValMin, ValMode, ValPercentile, ValQuartiles, ValStDeviation, ValStError, ValSum, and ValVariance

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Statistical functions, see STATISTICA BASIC Quick Syntax Reference.


STATISTICA BASIC Syntax Reference - ValMean

  STATISTICA BASIC Syntax Reference - ValMean (Array, Start, ?HowMany, Result)

Parameters:

Array	array name

Start	start with element number

?HowMany	how many sequential elements in which to compute mean value

Result	return value

The ValMean function computes the mean of the non-missing values from among the specified number of array elements beginning with the specified element.  Note that you can specify a variable name, array name or the current data file (using Data as the array name) for the parameter Array.

Example 1:

RandomAccess;

ValMean(v3, 1, Ncases, mean);

WriteLn('Mean = ', mean);

The above example will return the mean of variable 3 for all cases in the data file.

Note that the ValMean function can also be used in Sequential mode.  For example, it is possible to calculate the mean of the non-missing values of variables for each case.  The following example shows the correct syntax for doing this.

Example 2:

Sequential;

ValMean(v,3,6,v11);

This example places the mean of non-missing values of variables v3-v8 (for each case) in v11.

Related topics: ValCount, ValMax, ValMedian, ValMin, ValMode, ValPercentile, ValQuartiles, ValStDeviation, ValStError, ValSum, and ValVariance

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Statistical functions, see STATISTICA BASIC Quick Syntax Reference.


STATISTICA BASIC Syntax Reference - ValMedian

  STATISTICA BASIC Syntax Reference - ValMedian (Array, Start, ?HowMany, Result)

Parameters:

Array	array name

Start	start with element number

?HowMany	how many sequential elements in which to compute the median value

Result	return value

The ValMedian function computes the median of the non-missing values from among the specified number of array elements beginning with the specified element.  Note that you can specify a variable name, array name or the current data file (using Data as the array name) for the parameter Array.

Example 1:

RandomAccess;

ValMedian(v3, 1, Ncases, median);

WriteLn('Median = ', median);

The above example will return the median value of variable 3 for all cases in the data file.

Note that the ValMedian function can also be used in Sequential mode.  For example, it is possible to calculate the median of the non-missing values of variables for each case.  The following example shows the correct syntax for doing this.

Example 2:

Sequential;

ValMedian(v,3,6,v11);

This example places the median of non-missing values of variables v3-v8 (for each case) in v11.

Related topics: ValCount, ValMax, ValMean, ValMin, ValMode, ValPercentile, ValQuartiles, ValStDeviation, ValStError, ValSum, and ValVariance

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Statistical functions, see STATISTICA BASIC Quick Syntax Reference.


STATISTICA BASIC Syntax Reference - ValMin

  STATISTICA BASIC Syntax Reference - ValMin (Array, Start, ?HowMany, Result)

Parameters:

Array	array name

Start	start with element number

?HowMany	how many sequential elements in which to find the minimum value

Result	return value

The ValMin function returns the minimum of the non-missing values from among the specified number of array elements beginning with the specified element.  Note that you can specify a variable name, array name or the current data file (using Data as the array name) for the parameter Array.

Example 1:

RandomAccess;

ValMin(v3, 1, Ncases, x);

WriteLn('Minimum = ', x);

The above example will return the minimum value in variable 3 for all cases in the data file.

Note that the ValMin function can also be used in Sequential mode.  For example, it is possible to determine the minimum value of the non-missing values of variables for each case.  The following example shows the correct syntax for doing this.

Example 2:

Sequential;

ValMin(v,3,6,v11);

This example places the minimum value of the non-missing values of variables v3-v8 (for each case) in v11.

Related topics: ValCount, ValMax, ValMean, ValMedian, ValMode, ValPercentile, ValQuartiles, ValStDeviation, ValStError, ValSum, and ValVariance.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Statistical functions, see STATISTICA BASIC Quick Syntax Reference.


STATISTICA BASIC Syntax Reference - ValMode

  STATISTICA BASIC Syntax Reference - ValMode (Array, Start, ?HowMany, Result)

Parameters:

Array	array name

Start	start with element number

?HowMany	how many sequential elements in which to find the mode

Result	return value

The ValMode function returns the mode (most common value) of the non-missing values from among the specified number of array elements beginning with the specified element.  If more than one mode exists, no value for Result is returned.  Note that you can specify a variable name, array name or the current data file (using Data as the array name) for the parameter Array.

Example 1:

RandomAccess;

ValMode(v3, 1, Ncases, mode);

WriteLn('Mode = ', mode);

The above example will return the mode of variable 3 for all cases in the data file.

Note that the ValMode function can also be used in Sequential mode.  For example, it is possible to calculate the mode of the non-missing values of variables for each case.  The following example shows the correct syntax for doing this.

Example 2:

Sequential;

ValMode(v,3,6,v11);

This example places the mode of non-missing values of variables v3-v8 (for each case) in v11.

Related topics: ValCount, ValMax, ValMean, ValMedian, ValMin, ValPercentile, ValQuartiles, ValStDeviation, ValStError, ValSum, and ValVariance

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Statistical functions, see STATISTICA BASIC Quick Syntax Reference.


STATISTICA BASIC Syntax Reference - ValPercentile

  STATISTICA BASIC Syntax Reference - ValPercentile (Array, Start, ?HowMany, Percentile, Result)

Parameters:

Array	array name

Start	start with element number

?HowMany	how many sequential elements in which to find the percentile

Percentile	percentile to be computed

Result	return value

The ValPercentile function returns the specified percentile of the non-missing values from among the specified number of array elements beginning with the specified element.  Note that you can specify a variable name, array name or the current data file (using Data as the array name) for the parameter Array.

Example 1:

RandomAccess;

ValPercentile(v3, 1, Ncases, 10, centile);

WriteLn('Mode = ', centile);

The above example will return the tenth percentile value for variable 3 for all cases in the data file.

Note that the ValPercentile function can also be used in Sequential mode.  For example, it is possible to calculate a specific percentile of the non-missing values of variables for each case.  The following example shows the correct syntax for doing this.

Example 2:

Sequential;

ValPercentile(v,3,6,15,v11);

This example places the 15th percentile of non-missing values of variables v3-v8 (for each case) in v11.

Related topics: ValCount, ValMax, ValMean, ValMedian, ValMin, ValMode, ValQuartiles, ValStDeviation, ValStError, ValSum, and ValVariance

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Statistical functions, see STATISTICA BASIC Quick Syntax Reference.


STATISTICA BASIC Syntax Reference - ValQuartiles

  STATISTICA BASIC Syntax Reference - ValQuartiles (Array, Start, ?HowMany, Quart)

Parameters:

Array	array name

Start	start with element number

?HowMany	how many sequential elements in which to compute quartile values

Quart	vector of return values

The ValQuartiles function returns the quartiles of the non-missing values from among the specified number of array elements beginning with the specified element.  The return vector Quart must contain at least three elements; the first three elements will contain the 25th, 50th, and 75th quartiles, respectively.  Note that you can specify a variable name, array name or the current data file (using Data as the array name) for the parameter Array.

Example 1:

RandomAccess;

Dim Quart(3);

ValQuartiles(v3, 1, Ncases, Quart);

WriteLn('25th % = ', Quart(1), '50th % = ', Quart(2), '75th % = ', Quart(3));

The above example will return the 25th, 50th, and 75th quartile values in variable 3 for all cases in the data file.

Note that the ValQuartiles function can also be used in Sequential mode.  For example, it is possible to calculate the quartiles of the non-missing values of variables for each case.  The following example shows the correct syntax for doing this.

Example 2:

Sequential;

Dim Quart(3);

ValQuartiles(v,3,8,Quart);

v11:= Quart(1);

v12:= Quart(2);

v13:= Quart(3);

This example places the 25th, 50th, and 75th quartiles of non-missing values of variables v3-v10 (for each case) in v11,v12 and v13, respectively.

Related topics: ValCount, ValMax, ValMean, ValMedian, ValMin, ValMode, ValPercentile, ValStDeviation, ValStError, ValSum, and ValVariance

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Statistical functions, see STATISTICA BASIC Quick Syntax Reference.


STATISTICA BASIC Syntax Reference - ValStDeviation

  STATISTICA BASIC Syntax Reference - ValStDeviation (Array, Start, ?HowMany, Result)

Parameters:

Array	array name

Start	start with element number

?HowMany	how many sequential elements in which to compute the standard deviation

Result	return value

The ValStDeviation function returns the standard deviation of the non-missing values from among the specified number of array elements beginning with the specified element.  Note that you can specify a variable name, array name or the current data file (using Data as the array name) for the parameter Array.

Example 1:

RandomAccess;

ValStDeviation(v3, 1, Ncases, stdev);

WriteLn('Std.Dev. = ', stdev);

The above example will return the standard deviation of variable 3 for all cases in the data file.

Note that the ValStDeviation function can also be used in Sequential mode.  For example, it is possible to calculate the standard deviation of the non-missing values of variables for each case.  The following example shows the correct syntax for doing this.

Example 2:

Sequential;

ValStDeviation(v,3,6,v11);

This example places the standard deviation of non-missing values of variables v3-v8 (for each case) in v11.

Related topics: ValCount, ValMax, ValMean, ValMedian, ValMin, ValMode, ValPercentile, ValQuartiles, ValStError, ValSum, and ValVariance.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Statistical functions, see STATISTICA BASIC Quick Syntax Reference.


STATISTICA BASIC Syntax Reference - ValStError

  STATISTICA BASIC Syntax Reference - ValStError (Array, Start, ?HowMany, Result)

Parameters:

Array	array name

Start	start with element number

?HowMany	how many sequential elements in which to compute the standard error

Result	return value

The ValStError function returns the standard error of the non-missing values from among the specified number of array elements beginning with the specified element.  Note that you can specify a variable name, array name or the current data file (using Data as the array name) for the parameter Array.

Example 1:

RandomAccess;

ValStError(v3, 1, Ncases, StErr);

WriteLn('Std.Err. = ', StErr);

The above example will return the standard error of variable 3 for all cases in the data file.

Note that the ValStError function can also be used in Sequential mode.  For example, it is possible to calculate the standard error of the non-missing values of variables for each case.  The following example shows the correct syntax for doing this.

Example 2:

Sequential;

ValStError(v,3,6,v11);

This example places the standard error of non-missing values of variables v3-v8 (for each case) in v11.

Related topics: ValCount, ValMax, ValMean, ValMedian, ValMin, ValMode, ValPercentile, ValQuartiles, ValStDeviation, ValSum, and ValVariance.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Statistical functions, see STATISTICA BASIC Quick Syntax Reference.


STATISTICA BASIC Syntax Reference - ValVariance

  STATISTICA BASIC Syntax Reference - ValVariance (Array, Start, ?HowMany, Result)

Parameters:

Array	array name

Start	start with element number

?HowMany	how many sequential elements in which to compute the variance

Result	return value

The ValVariance function returns the variance of the non-missing values from among the specified number of array elements beginning with the specified element.  Note that you can specify a variable name, array name or the current data file (using Data as the array name) for the parameter Array.

Example 1:

RandomAccess;

ValVariance(v3, 1, Ncases, Varn);

WriteLn('Variance = ', Varn);

The above example will return the variance of variable 3 for all cases in the data file.

Note that the ValVariance function can also be used in Sequential mode.  For example, it is possible to calculate the variance of the non-missing values of variables for each case.  The following example shows the correct syntax for doing this.

Example 2:

Sequential;

ValVariance(v,3,6,v11);

This example places the variance of non-missing values of variables v3-v8 (for each case) in v11.

Related topics: ValCount, ValMax, ValMean, ValMedian, ValMin, ValMode, ValPercentile, ValQuartiles, ValStDeviation, ValStError, and ValSum.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Statistical functions, see STATISTICA BASIC Quick Syntax Reference.


  STATISTICA BASIC Syntax Reference - Valid(x)

Parameters: x - any expression

Return value: true (1) if x is not missing (i.e., not MD) or false (0) if x is missing

The logical function Valid(x) returns true (1) if the value of expression x does not evaluate to the missing value (i.e., when it is valid) or false (0) when it evaluates to the missing value.

Example:

if not Valid(Income) then      {if value of Income is Missing, then}

    Delete;                    {delete this record from the data file}

This program will delete all records in the data file in which the value of Income is Missing.


STATISTICA BASIC Syntax Reference - ValSum

  STATISTICA BASIC Syntax Reference - ValSum(Array, Start, ?HowMany, Result)

Parameters:

Array	array name

Start	start with element number

?HowMany	how many sequential elements in which to sum the non-missing values

Result	destination variable.

The ValSum function sums up the non-missing values from among the specified number of array elements beginning with the specified element and stores the value in the specified variable (see parameter Result).  Note that you can specify a variable name, array name or the current data file (using Data as the array name) for the parameter Array.

Example 1:

RandomAccess;

ValSum(v3, 1, Ncases, sum);

WriteLn('Sum of Non-missing Values = ', sum);

The above example will return the sum of the of non-missing values in variable 3 for all cases in the data file.

The syntax for the ValSum function has been improved from previous versions of STATISTICA.  The function has been generalized to accept any array rather than only accepting an array from the data file.  Note that as with previous versions of STATISTICA, it is possible to calculate the sum of non-missing values of variables for each case.  The following example shows the correct syntax for doing this.

Example 2:

Sequential;

ValSum(v,3,6,v10);

This example places the sum of non-missing values of variables v3-v8 (for each case) in v10.

Related topics: ValCount, ValMax, ValMean, ValMedian, ValMin, ValMode, ValPercentile, ValQuartiles, ValStDeviation, ValStError, and ValVariance

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Statistical functions, see STATISTICA BASIC Quick Syntax Reference.


  STATISTICA BASIC Syntax Reference - Value(x)

Parameters: x - any expression

This function returns zero (0) if the value of expression x is Missing; if the value of x is not Missing, however, the function returns the actual value of x.  This function is particularly useful when calculating a sum adjusted for missing data.  Note that normally, the result of the entire expression is set to missing data if the value of at least one element is Missing.

Example:

Gross := Value(v1) + Value(v2) + Value(v10);

This program calculates the sum of variables v1, v2, and v10, adjusting for missing data; in other words, even if data in one or two of those variables are missing, the resulting value of Gross will not be set to missing but will amount to whatever is the sum of the non-missing values of v1, v2, and v10.


  STATISTICA BASIC Syntax Reference - VarLongName(vn)

Parameters:  vn is the variable number

Return value:  Returns the long name (or Spreadsheet Formula) of the specified variable from the current file

Example:

RandomAccess;	{specifies RandomAccess mode}

WriteLn(VarLongName(3));    {"Prints" the long variable name}

This command will write (to the previously selected output device; see Page/Output Setup) the long name of variable 3 in the current file.

Note that VarLongName cannot be the used on the left side of an assignment statement.


  STATISTICA BASIC Syntax Reference - VarName(vn)

Parameters:  vn is the variable number

Return value:  Returns the name of the specified variable from the current file

Example:

RandomAccess;	{specifies RandomAccess mode}

WriteLn(VarName(3));    {"Prints" the variable name}

This command will write (to the previously selected output device; see Page/Output Setup) the name of variable 3 in the current file.

Note that VarName cannot be the used on the left side of an assignment statement.


STATISTICA BASIC Syntax Reference - Write(a, ..)

  STATISTICA BASIC Syntax Reference - Write(a, ...)

Write(a1,...,an)

Parameters:  a1,...,an - any type

Used to send values from the list of arguments to the printer, disk file, or Text/output Window (depending on the current settings in the Page/Output Setup dialog).

Example:

Sequential;	{specifies Sequential mode}

Write('v3 = ', v3);

This program will write the value of v3 for all cases to the currently selected output device (see Page/Output Setup dialog).  After filling one line, the output will continue on the next line.

NOTES:

If you want each list of values (a1, ..., an) to be written in a spearate line, use WriteLn (for example, WriteLn('v3=', v3, 'v4=', v4);)

If no output device is selected (in the Page/Output Setup dialog) and the STATISTICA BASIC program included Write or WriteLn statements, then upon execution, STATISTICA will automatically open the Text/Output Window and send the output to that window.

For a complete list of Input/output functions, see User Input/output Functions.


STATISTICA BASIC Syntax Reference - Writeln(a, ..)

  STATISTICA BASIC Syntax Reference - WriteLn(a, ...)

WriteLn(a1,...,an)

Parameters:  a1,...,an - any type

Used to send values from the list of arguments to the printer, disk file, or Text/output Window (depending on the current settings in the Page/Output Setup dialog).  A new line will start after execution of each WriteLn procedure (see also Write).

Example:

Sequential;	{specifies Sequential mode}

WriteLn('v3 = ', v3);

This program will write the value of v3 for all cases to the currently selected output device (see Page/Output Setup dialog).  Each value will be written in a separate line.

NOTES:

This procedure can also be used to insert a blank line in the output (when you do not include any arguments and no parentheses).

If you want the output to be written continuously (i.e., only after filling one line, the output will continue on the next line), use Write.

If no output device is selected (in the Page/Output Setup dialog) and the STATISTICA BASIC program included WriteLn or Write statements, then upon execution, STATISTICA will automatically open the Text/Output Window.

For a complete list of Input/output functions, see User Input/output Functions.


  STATISTICA BASIC Execution

Click on the [image] toolbar button to process your STATISTICA BASIC program.  When you click this button, STATISTICA will check the syntax of the STATISTICA BASIC commands and give you a specific error message if the syntax is wrong (for more information on STATISTICA BASIC syntax, see Syntax References).

The STATISTICA BASIC Error Messages section contains an alphabetical list of STATISTICA BASIC compile-time error messages that are displayed if the syntax is wrong as well as an alphabetical list of run-time error messages.


  STATISTICA BASIC Compile-Time Error Messages

".." or "TO" after "LO" expected.  Ranges in recode functions are defined either as LO .. x or LO TO x, not as LO x (where x is a number).

".." or "TO" after "MISSING.  The constructions MISSING TO x or MISSING .. x are not allowed (Missing must stand alone, and not as part of a range).

";" before ELSE or UNDEFINED.  A semicolon should not precede either of the keywords ELSE or UNDEFINED (in an IF...THEN...ELSE...UNDEFINED statement).

'(' expected.  STATISTICA BASIC did not find a left parenthesis where one was expected.

')'  expected.  STATISTICA BASIC did not find a right parenthesis where one was expected.

',' expected.  STATISTICA BASIC did not find a comma (,) where one was expected.

':=' expected.  STATISTICA BASIC did not find a colon followed by an equal sign where one was expected (in an assignment statement).

';' expected.  STATISTICA BASIC did not find a semicolon where one was expected (i.e. in an assignment or recode statement).

';' or 'end' expected.  STATISTICA BASIC did not find the end (i.e., semicolon or word END) of a statement, compound statement, or procedure.

'=' expected.  STATISTICA BASIC did not find an equal sign where one was expected (e.g., in a recode definition).

Array name expected:  The name which was passed was not the name of an array, but an array name was expected.  See also, Specifying Arrays.

BEGIN expected.  The keyword BEGIN is expected at the start of recode definitions.

Cannot modify loop counter.  The value of the loop counter (in a For...To...Do loop construction) should not be changed within the loop.

Cannot use constant in this context:  You cannot use a constant in a context where the value of the constant might be changed.

Declare recodes at beginning.  Recode definitions must precede the body of the program.

Dimension specification expected:  STATISTICA BASIC expected to find a dimension specification.  See also, Specifying Arrays.

DO expected.  STATISTICA BASIC did not find DO where it was expected (in a For...To...Do loop statement).  See also, Loops.

Duplicate label definition:  You have used the same label more than once (e.g., you specified GOTO error; and error:; is defined in more than one place).

Duplicate left side "MISSING" in recode.  The keyword MISSING appears more than once in the recode definition.  See also, Recode.

Duplicate LO in recode.  You have attempted to use LO twice in the recode construction.  See also, Recode.

Duplicated name.  The same identifier has been used twice in the program (e.g., as a recode function name and as a loop counter).

END at the end of recode expected.  Recode definitions must finish with the word END.  See also, Recode.

Identifier too long.  Identifier (loop counter, function, or constant name) is longer than 8 characters.

Illegal expression (may be empty).  Invalid or empty expression was found.  This error may occur if one of the arguments or an operator is missing, or as the result of some other syntax error.

Illegal Operator:  The operator you have used cannot be used with strings.

Illegal subroutine call:  You have called a subroutine which cannot be used at this time.  Most likely you are trying to use it as a function rather than as a subroutine.

Incompatible types:  The argument types which you have specified do not match.  For example, you might have tried to add a text value to a numeric value.

Incorrect CONST statement:  You have not correctly defined the constant which you are trying to create.  See also, Const.

Incorrect DECLARE statement:  You have not correctly used the DECLARE statement.  See also, External Subroutines.

Incorrect DIM statement:  You have not correctly specified the dimension of this array.  See also, Specifying Arrays.

Incorrect number of dimensions specified in REDIM statement:  You have either specifed too many or too few dimensions in the REDIM statement.  See also, Specifying Arrays.

Internal STATISTICA BASIC error.  An unusual combination of circumstances (data structure and the structure of the program) has caused the failure of an internal consistency check within STATISTICA BASIC.  Please contact StatSoft Technical Support.

Invalid number  An absolute value larger than 1.7E308 is present in the program.

Invalid right side of assignment.  An unknown or misspelled identifier is present after the equal sign in a recode definition.  See also, Elementary Instructions.

Invalid right side of interval.  An unknown or misspelled identifier is present in a range in a recode definition (e.g., LO .. @#$!$ or 14 TO %&*#!$).

Invalid scientific format number specified:  You have incompletly specified a number in scientific format.

Invalid type of argument:  You have either passed a number to a function that expects a string, or you have passed a string to a function that expects a number.

Invalid type of operand:  The operand you have used cannot be used in a string (for example, - ^,  or / cannot be used in a string).

Invalid value of ELSE.  In recode functions, ELSE must assign a constant, MISSING or OLD.

Label expected:  You have used a GOTO statement without defining a label.

Limit of local variables exceeded:  You have used more than 100 local variables in this program.

LO and HI in one definition.  The statement LO TO HI (or LO .. HI) is not permitted.  See also, Recode.

Loop variable cannot be from file.  Variables used as loop counters must not be variables from the data file.

Loop variable expected.  The loop counter variable is missing in FOR..TO..DO (e.g., FOR 1 TO 10 DO instead of FOR i := 1 TO 10 DO).

Names must be unique - Names must be unique - this name is already used by an array:  The name you have used is already being used by an array.

Names must be unique - this is a variable name and cannot be redefined:  You have tried to rename or redefine a variable name.

Names must be unique - this is an internal name and cannot be redefined:  You have tried to rename an internal STATISTICA BASIC name.

Names must be unique - this name is already used by a constant:  The name you have used is already being used by a constant.

Names must be unique - this name is already used by a local variable:  The name you have used is already being used by a local variable.

Names must be unique - this name is already used by a recode:  The name you have used is already being used by a recode.

Names must be unique - this name is already used by an external function/subroutine:  The name you have used is already being used by an external function or a subroutine.

No errors detected.  STATISTICA BASIC has successfully finished checking and compiling your program (normal conditions).

No work space for new recodes.  STATISTICA BASIC has run out of dynamic memory space.  Split the task and create two separate programs.

NoDataFileVariableNames mode can be specified only once:  You have tried to specify NoDataFileVariableNames mode more than one time.

Nothing to do - program empty:  Your program does not include any executable instructions.

Number expected.  The minus sign ( - ) is present without being followed by a number (e.g., VAR1).

Overlapping intervals.  Ranges in recode definitions must be exclusive.  See also, Recode.

Recode must have unique name.  The name of a recode function should not be the same as any variable or STATISTICA BASIC reserved keyword.  See also, Recode.

Recode name expected.  STATISTICA BASIC expects to find the name of the recode function following the keyword RECODE.  See also, Recode.

Sequential and RandomAccess mode can be specified only once:  You have tried to specify Sequential or RandomAccess mode more than one time and they can only be specified once.

Specified identifier cannot be a label:  The identifier you have chosen cannot be used as a label in a GOTO statement.

STATISTICA BASIC memory overflow.  STATISTICA BASIC has run out of dynamic memory space.  This usually means that your program contains many symbols and/or complex expressions.

String constant too long:  Your string constant has more than 256 characters.

THEN expected - wrong condition.  The sequence should be IF ... THEN ... ELSE ... UNDEFINED (note that ELSE and UNDEFINED are optional).  See also, If..Then...

TO or DOWNTO expected.  STATISTICA BASIC did not find TO or DOWNTO in a FOR..TO..DO or  FOR..DOWNTO..DO statement.  See also, For..To..Do...

Too many 'recodes.'  You have defined more than 16 recode statements.

Too many arguments in READ:  You have used more than eight (8) arguments in READ.

Too many constants defined:  You have defined more than 6,553 constants.

Too many dimensions specified:  You have specified more than 8 dimensions in an array.

Too many external declarations:  You have more than 256 external declarations.

Too many items in recode.  You have defined a recode with a total of more than 500 "left sides" (i.e., including intervals and individual numbers).

Too many labels used in the program:  You cannot use more that 256 labels in one program.

Too many nested loops.  Loops cannot be nested more than 16 levels deep.

Too many parameters in external function/subroutine declaration:  You have used more than 32 parameters in an external function or subroutine declaration.

Too many string constants used in the program:  You have used more than 256 string constants in the program.

Unexpected end of file.  While scanning, STATISTICA BASIC found an unexpected end of file mark in a comment or other illegal location.  Probably the result of a missing curly bracket } or closing END.

Unexpected function.  A statement is present which is not part of an assignment (e.g., sin(x); instead of v1 := sin(x);).

Unknown function or procedure specified:  STATISTICA BASIC does not recognize the function or procedure which you have specified.

Unknown identifier.  STATISTICA BASIC found an undefined (or misspelled) identifier or other syntax error.  For example, this error will occur when a local (new) variable is used in an expression (or as a function argument) before it is initialized (by assigning a value to that variable).

Unrecognized symbol.  STATISTICA BASIC found an undefined (or misspelled) identifier (a variable or recode name).

Unresolved GOTO statement:  You have used a GOTO statement without defining a label (e.g., you have said GOTO error; and error:; is not defined in your program).

Variable expected:  STATISTICA BASIC expected a variable in the procedure you are using and it did not find one.  For example, you may have used a constant in a READ statement (READ (5)).

See also, Run-Time Error Messages.


  STATISTICA BASIC Run-Time Error Messages

A matrix that is supposed to be a vector has more than one column.  You have specified a matrix with more than one column in an operation that requires a vector.

A matrix that is supposed to be a vector has more than one row.  You have specified a matrix with more than one row in an operation that requires a vector.

Argument out of domain.  An attempt has been made to apply to a math function an argument which is out of the function's domain (e.g., x := arcsin(z), where z is out of the range from -1 to +1).

Argument singularity.  An attempt has been made to apply an argument to a math function which is the function's singular point (e.g., x := log(0);).

At least one matrix does not have the right number of dimensions.  One (or more) of the matrices in your computation does not have the number of dimensions required for the requested operation.

Bad input in matrix.  The designated matrix has incorrect dimensions.

Cannot compute.  STATISTICA cannot compute the operation(s) which you have requested.

Cannot duplicate Scrollsheet.  STATISTICA BASIC was not able to duplicate the specified Scrollsheet.

Cannot find external function:  STATISTICA BASIC could not locate the external function which you requested.  Perhaps the name has not been correctly specified.  See also, External Functions.

Cannot load DLL:  STATISTICA BASIC could not load the DLL which you specified.  Perhaps the path has not been correctly specified.  See also, Calling DLL files.

Cannot open the specified file.  STATISTICA BASIC cannot open the file which has been specified.  Most likely the specified file does not have the required format (e.g, you need to open a data set, but the file you have given is a graph file).

Cannot write to specified file.  STATISTICA BASIC cannot write to the file which has been specified.  There are several scenarios which could cause this problem.  It could be the file is a read-only file, the file is in use by someone else or you are out of disk space.

Case index out of range:  The case index you have used exceeds the number of cases in your data set.  For example, you might have requested case number 24 when you data set only has 20 cases.

Determinant overflowed.  An overflow occurred during the calculation of the determinant which means the matrix is ill-conditioned.

Divide by zero requested.  To perfrom the requested operation, STATISTICA would need to divide by zero and this is not possible.

Division by zero.  An attempt to perform division by zero has been detected.

Error in Scrollsheet operation.  An error has occurred in one (or more) of the requested Scrollsheet operations.

Error while deleting Scrollsheet.  An error occurred while STATISTICA BASIC was deleting the specified Scrollsheet.

Error while setting Scrollsheet title.  An error occurred while STATISTICA BASIC was setting the specified Scrollsheet title.

Floating-point error.  A floating-point error in computation has been detected.

Graph embedding failed.  STATISTICA BASIC was not able to embed the specified graph.

Incorrect file name specified.  The file name you have specified is not correct.  You should verify the name of the data file you wish to use.

Incorrect number of columns in a matrix.  Either the input matrix or destination matrix needs more (or fewer) columns in order to complete this operation.

Incorrect number of rows in a matrix.  Either the input matrix or destination matrix needs more (or fewer) rows in order to complete this operation.

Index of MEMORY out of range.  The specified index to the MEMORY array exceeds the currently declared size of the array (use the STATISTICA BASIC Options menu to increase the size of the array).

Index of variable out of range.  The number xxx used as an index of the V(xxx) variable is less than 1 or greater than the total number of variables in the current data file.

Internal STATISTICA BASIC run-time error.  An unusual combination of circumstances (data structure and the structure of the program) has caused the  failure of an internal consistency check within STATISTICA BASIC.  Please contact StatSoft Technical Support.

Invalid array argument:  The array argument you have used is not valid.  For example, you cannot access element 20 in an array that only has 10 elements.

Invalid coordinates specified for this graph.  The coordinates you have specified for this graph do not exist or are not valid coordinates.

Invalid file structure.  The specified file was not in the form expected.

Invalid graph type for this operation.  The graph type you have selected is not appropriate for this operation.

Invalid input to a STATISTICA BASIC function.  This is a parameter error which occurs when you give inconsistent input for the desired function.  For example, if you passed a negative value to STATISTICA BASIC while using the ValPercentile function, you would receive this message.

Invalid jump inside the loop:  The label you have specified is inside a loop, and you cannot use a GOTO statement to branch to a label that is inside a loop unless the GOTO statement is also inside the loop.

Invalid operation.  The program contains an instruction which is not valid (usually involving an operation on a non-numeric or infinitely large value).

Invalid Scrollsheet column width.  The Scrollsheet column width which you have requested exceeds the allowable Scrollsheet column width.

Invalid Scrollsheet margin width.  The Scrollsheet margin width which you have requested exceeds the allowable Scrollsheet margin width.

Invalid Scrollsheet row name width.  The Scrollsheet row name width which you have requested exceeds the allowable Scrollsheet row name width.

Invalid Scrollsheet title number.  The Scrollsheet title number which you have specified is not valid (e.g., you have specified Scrollsheet title number 4 when the Scrollsheet only has three titles).

Invalid shape parameter specified.  A parameter error has occurred because the specified shape parameter is not a valid shape parameter.

JUMP to nonexistent case.  The JUMP command makes reference to a case not in the file (this may happen if DELETE has been used and the file is now shorter; the remaining cases are renumbered each time DELETE is used).

Limit of MD assignments exceeded.  The number of missing data assignments currently specified as acceptable has been exceeded (use the STATISTICA BASIC Options menu to increase the limit).

Limit of text values exceeded:  STATISTICA BASIC has run out of memory.

Matrices which need to be equal size are not.  To perform the requested operation, the  dimensions of the two designated matrices need to be equal and they are not equal.

Matrix has no variance.  Either the input matrix or destination matrix needs to have variance in order to complete this operation.

Matrix is not of full rank.  Either the input matrix or destination matrix needs to be of full rank in order to complete this operation.

Matrix is not square.  The designated matrix for this operation must be square, but it is not square.

Matrix is singular.  The function you have requested requires that the matrix be non-singular.  Generally, this message occurs when you request the determinant of a singular matrix or if the requested function requires the determinant of a matrix.

One or more matricies are not the expected size.  The input matrix (and/or the destination matrix) is not the size needed in order to complete this operation.

Out of memory.  STATISTICA BASIC was unable to complete the desired operation because more memory was requested than was available.

Range overflow.  During the computation process an invalid (out of range) number occurred (e.g., an operation such as x := 1e200 * 1e200 ).

Specified argument is not an array.  A parameter error has occurred because the specified argument was not an array.

Specified graph handle is invalid.  The handle (identifier) which has been given to STATISTICA BASIC is not a valid graph handle.

STATISTICA BASIC executer memory overflow.  The STATISTICA BASIC executer has run out of dynamic memory space.  This usually means that your program contains many symbols and/or complex expressions.

Text value not found for this variable:  You have specified a text value which does not exist for this variable.  Perhaps the text value has been typed incorrectly.

Text value too long:  The text value has more than 256 characters.

The column dimensions of two matricies which need to be equal are not.  To perform the requested operation, the column dimensions of the two designated matrices need to be equal and they are not equal.

The passed handle was not a valid Scrollsheet handle.  The handle (identifier) which has been given to STATISTICA BASIC is not a valid Scrollsheet handle.

The passed value is not a vector.  The operation you have specified requires a vector; however, the passed value is not a vector.

The row dimensions of two matricies which need to be equal are not.  To perform the requested operation, the row dimensions of the two designated matrices need to be equal and they are not equal.

The SetDrawingMatrixCoordinates function must be called before using Dynamic coordinates in matrix plots.  Before using Dynamic coordinates in a matrix plot, you must first call SetDrawingMatrix Coordinates.

The specified column does not exist.  You have specified a column which does not exist (e.g., you have specified column 10 and the matrix only has 9 columns).

The specified file is not a valid STATISTICA data file.  The designated file is not a valid STATISTICA data file.  You should verify the name of the data file you wish to use.

The specified row does not exist.  You have specified a row which does not exist (e.g., you have specified row 10 and the matrix only has 9 rows).

The specified Scrollsheet column does not exist.  The Scrollsheet column which you have specified does not exist (e.g., you have specified Scrollsheet column number 4 when the Scrollsheet only has two columns).

The specified Scrollsheet row does not exist.  The Scrollsheet row which you have specified does not exist (e.g., you have specified Scrollsheet row number 4 when the Scrollsheet only has two rows).

See also, Compile-Time Error Messages


  STATISTICA BASIC Options

The options available from the STATISTICA BASIC Options pull-down menu or button are:  Mode: (displaying the current processing mode), Error Level (the number of allowable missing data assignments before the execution stops), Memory Size (the size of the designated "inter-record" memory data array), and On Math Error (what action to take if an invalid math operation occurs).  When you select any of these four options from the pull-down menu, the STATISTICA BASIC Options dialog will open.

STATISTICA BASIC Options dialog

Default processing mode:  Select either Sequential or RandomAccess processing mode here.  If you select Sequential, then the STATISTICA BASIC instructions are executed for each case in the data file.  RandomAccess mode executes the program only once.  (For more information and examples, see Sequential and RandomAccess.)

Interrupt after: ____ errors (or MD assignments):  The number specified in this option represents the acceptable number of missing data assignments that can occur during execution of the STATISTICA BASIC program.  Once this limit is exceeded, an error message will be displayed and the execution of the program will stop.  You can use this option as an additional verification process (in addition to STATISTICA's syntax verification) in order to verify that the program is being executed as expected, or that the data lend themselves to the requested transformations (e.g., the statement v1 : = v2+v3+v4+v5 executed on a data set with many missing values may result in assigning MD to variable 1 in almost all cases; in this case, the Valsum option may be more appropriate).

Size of the (inter-record) MEMORY Array:  Specifies the size of the predefined indexed array called MEMORY(xxx) (or MEM(xxx), where xxx is an integer value) which in Sequential mode is not initalized for each case being processed and thus can be used to transfer values "across" cases (records of data).  By default, the size of this array is 8000 elements.

On Math Error:  Define the action to take if an invalid math operation occurs.

Set the Result to MD:  When you select this option, the program will assign missing data if an invalid math operation (such as division by zero) occurs during program execution.

Stop Execution of the BASIC Program:  If you select this option, then STATISTICA BASIC will display an error message and terminate execution.  This option is usually preferable while developing and debugging programs.

Display All Warnings and Error Messages:  Setting this option will cause all warnings and error messages to be displayed.  Whenever a warning or error message occurs, it will halt execution of the STATISTICA BASIC program.  Deselecting this option will suppress the display of non-fatal warnings and error messages during program execution, without interrupting program execution.  Advanced users may wish to incorporate their own methods of error handling within their STATISTICA BASIC programs, and use the DisplayLastError function if it is necessary to display a program error message to the user.


 Applications of the Graphics Procedures in STATISTICA BASIC

Creating even complex graphs with STATISTICA BASIC is surprisingly easy.  For example, only one line of code is all that is necessary to create a graph (e.g., from a particular combination of values in the data file or any data computed in your program).  The applications of the graphics functions of the BASIC language range from simple line graphs (e.g., created for every case in a data file and overlaid in one display) to new, complex types of specialized graphs, technical drawings, and diagrams linked to your data.  The BASIC language can also be used to automate routine sets of modifications or customizations of existing graphs (e.g., you can design a library of your own, menu-driven graph customization procedures).  A Wizard-style tool is provided to speed up entry of the graphics functions.

STATISTICA BASIC can create complex compound graphics documents with OLE links (including nested documents), diagrams related to data (that can be updated/redrawn by pressing a button), and many other types of displays.  The graphics output can be combined with numeric or text output and sent to the report editor (see Text/output Window) to produce customized reports.  The graphs can also be saved or printed directly.  Your new, custom-designed graphics procedures can be added to the STATISTICA system by assigning them to buttons on the floating Auto Task Buttons toolbars.  Simple to use, predefined dialogs can be set up (with simple function calls) to produce customized "front ends" for these new procedures (e.g., prompting the user to enter the necessary parameters, text of titles, select specific options, or any other type of input).

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


 Graphics Library of STATISTICA BASIC - Overview

STATISTICA BASIC is a powerful graphics development tool, offering access to virtually all of the STATISTICA graphics procedures (see Applications of the Graphics Procedures in STATISTICA BASIC).

There are three basic ways in which you can operate on graphs in STATISTICA BASIC. You can:

(1)	open a previously saved STATISTICA graph file (*.stg) and then make modifications or customizations to the graph or print or save this graph (see Example 1 below),

(2)	create a new graph and then make modifications or customizations to this graph or print or save the graph (see Example 2 below), or

(3)	make modifications or customizations to a currently displayed graph or print or save the graph (see Example 3 below).

Notes

•	You should use the RandomAccess (default) mode of operation when executing graphic functions unless you intend to repeat all graphs specified in the program for each case of the current data set (see Sequential mode).

•	The graph handle (a unique value for each graph which is assigned to a temporary variable) can be obtained by using the OpenGraph, GetGraph, or NewGraph family of functions.  You can use GetGraph(0) in order to obtain the handle of the top-most graph.

Example 1

This example will first open a previously saved graph and then modify the third top title before printing it.

RandomAccess;

graph := OpenGraph('c:\bwplot.stg');

GraphSetTitle(graph, Title_Top3, 'This is the New Title Text');

PrintGraph(graph);

Example 2

This example will create a 2D scatterplot with linear fit and then save it.

RandomAccess;

Const Size = 100;

Dim X(size), Y(size);

for i := 1 to size do begin

  X(i) := rnd(10);

  Y(i) := rnd(1);

end;

graph := NewGraph(SCATTERPLOT, 'This is my Scatterplot', 'Y-axis', 'X-axis', Size, X, Y);

GraphSetPlotFitting( graph, 1, FIT_LINEAR);

SaveGraph(graph, 'c:\scatt.stg');

Example 3

This example will add a linear fit to the top-most graph and then print the modified graph.

RandomAccess;

graph := GetGraph(0);

GraphSetScaling(graph, AX_Y, SCALING_MANUAL_0, 0, 30, 5);

PrintGraph(graph);

Advanced Examples

For a list of advanced examples of STATISTICA BASIC programs using graphics procedures, refer to Advanced Examples of STATISTICA BASIC Programs.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


How to Specify Arrays in STATISTICA BASIC Functions

 STATISTICA BASIC - How to Specify Arrays in STATISTICA BASIC Functions

STATISTICA BASIC supports the use of arrays (collections of related values) to organize your data.  You can declare an array of up to 8 dimensions (at the beginning of the program) by using the Dim (or ReDim) statement.  The most common kinds of arrays are the 1 and 2 dimensional arrays.

One dimensional arrays.  The 1 dimensional array is also known as a vector.  You can define a vector using the Dim (or ReDim) statement as follows:

Dim A(5);

The above definition creates an array named A which has 5 values.  Each value in an array is called an element, and these elements are referenced by a numeric index.  In the above example, the individual elements of array A can be referenced by the following convention:  A(i) where the subscript i represents the element number (e.g., A(1) references the first element while A(5) references the fifth element in the array).  For example, you can assign a value of 6 to element number 3 in the array A with the following statement:

A(3) := 6;

STATISTICA BASIC provides a pre-defined variable vector Vxxx (where xxx is the variable number).  This vector refers to an entire column in the current data file, that is, all cases for a specified variable.  For example:

v5(3) := 8;      { sets case 3 of variable 5 to 8 }

You can use this pre-defined array in any STATISTICA BASIC function that accepts arrays.  For example, the following sequence will copy all of variable 3 into variable 7:

MatrixDuplicate(v3, v7);

In Sequential mode, if you wish to refer to the currently processed row (a row vector) from the data file, use the predefined V vector.  For example:

Sequential;

v51 := ValSum(v, 1, 50);

This program will compute the valid sum of the first 50 variables in the each case, and place the resulting value in variable 51 of the respective case.

Two dimensional arrays.  A two dimensional array is referred to as a matrix.  You can easily create a two dimensional array using either the Dim (or ReDim) or Data statements.  For example:

Dim B(3,2);

The resulting array is 3 rows by 2 columns.  The elements in B are referenced with two subscripts B(i,j).  Here, i represents the row element and j represents the column element. The following program segment shows how you might reference the elements of a two dimensional array in order to assign specific values to them:

Dim B(3,2);

B(1,1) := 10;     You can visualize	Column 1  Column 2

B(2,1) := 20;      this array as a table:	Row 1      10        40

B(3,1) := 30;     -------------->	Row 2      20        50

B(1,2) := 40;	Row 3      30        60

B(2,2) := 50;

B(3,2) := 60;

Although you can read the values of the current data file into an array created using the Dim statement, a pre-defined two dimensional array Data(i,j) is provided to easily reference the currently open data file.   For example:

Data(2,3) := 5;    {sets case 2, variable number 3 to the value 5 }

Multi-dimensional arrays.  STATISTICA BASIC allows you to create tables of up to 8 dimensions using the Dim or ReDim statements.  For example:

Dim A(2,2,2,3,2,2,3,2);  { This array has 2*2*2*3*2*2*3*2 = 576 elements }

Though it is difficult to visualize what an array of this size looks like, they are useful in some types of statistical analyses.

Resizing arrays.  STATISTICA BASIC allows you to dynamically resize a previously defined array using the ReDim statement (the number of dimensions must remain the same, e.g., a 2-dimensional array cannot be re-dimensioned to be a 3-dimensional array).  For example:

ReDim B(NVars);

{This one dimensional array has as many elements as the number of cases in the current data file}

The ReDim statment can also be used to create new arrays.


How to Set (or Leave Unchanged) Default Values of Function Parameters

 STATISTICA BASIC - How to Set (or Leave Unchanged) Default Values of Function Parameters

Many functions in STATISTICA BASIC have multiple parameters; to simplify programming, STATISTICA BASIC allows you to ignore those parameters which are not absolutely necessary.  You can do this in one of two ways:

(1)	Instead of specifying the value of a parameter, place a "?" before any word in place of the parameter (for text parameters, a "$" must be used at the end of the word).  Note that if you insert the function from the Function Wizard dialog, this is how the parameter keywords will appear until you change them to the desired values.  (These can even be abbreviated as "?" for numeric parameters or "?$" for text parameters.)

For example, the following program will leave the titles in the resulting scatterplot unchanged and place the default arrow type, style, size, and angle in the specified position on the graph.

RandomAccess;

my_graph := NewGraph(SCATTERPLOT, ?Top_Title$, ?Left_Title$, ?Left_Title$,
            NCases, v5, v10);

GraphDrawArrow(my_graph, ?ArrowType, ?Size, ?Angle, ?Style, 43, 55, 66, 59);

(2)	Instead of specifying the value of a parameter, use the keyword UNUSED (or UNUSED$ for text parameters) if you do not want to change the parameter and accept the default settings.  For example, the above program could be written as:

RandomAccess;

my_graph := NewGraph(SCATTERPLOT, UNUSED$, UNUSED$, UNUSED$, NCases,
            v5, v10);

GraphDrawArrow(my_graph, UNUSED, UNUSED, UNUSED, UNUSED, 43, 55, 66, 59);

in order to achieve the same results.


How to Use Strings in STATISTICA BASIC

 STATISTICA BASIC - How to use Strings in STATISTICA BASIC

STATISTICA BASIC supports the use of text values called strings.  Strings can be used either directly or by using string variables.  When strings are used directly, they need to be enclosed in single or double quotes.  For example:

DisplayMessageBox (MB_OK, 'Warning',"N is <= 0");

String variables are designated as such by adding a "$" character at the end.  For example, text$ is a string variable in the program below:

text$ := 'N is <= 0';

This string variable can then be used anywhere strings are expected.  For example:

DisplayMessageBox (MB_OK, 'Warning', text$);

Many STATISTICA BASIC operations and functions are defined using strings.  For example:

•	Concatenation:

a$ := 'Summary for current ';

b$ := 'month';

c$ := 'quarter';

text1$ := a$ + b$; {text1$ becomes 'Summary for current month'}

text2$ := a$ + c$; {text1$ becomes 'Summary for current quarter'}

•	Comparisons:

if text1$ > text2$ then

WriteLn(text1$)

else

WriteLn(text2$);

•	Functions retrieving variable names (VarName (i), VarLongName (i)), case name (CaseName (i));

•	Functions which manage strings, for example:

Mid (returns substring of text)

SInsert (inserts one string into another)

SDelete (deletes text)

UpCase (upper-cases text)

GetText (returns specified text value)

For a complete library of string operations see STATISTICA BASIC String Library.

You can also declare string constants which later can be used in your program:

const  companyname$ = 'StatSoft, Inc.';

and then later in the program, you could specify:

WriteLn (companyname$);

Related topics:

Passing lists of strings to STATISTICA BASIC functions

Retrieving lists of strings in STATISTICA BASIC

For a complete list of string functions, see Library of String Functions and Operators.


Passing Lists of Strings to STATISTICA BASIC Functions

  STATISTICA BASIC - Passing Lists of Strings to STATISTICA BASIC Functions

In some STATISTICA BASIC functions, it is neccessary to pass collections (lists) of strings, (e.g. a list of case names for a plot, names of entry/edit fields in a list box, etc.).  In this cases you must use delimited text strings (i.e. text separated by a tab or the character "|").  Some examples of such strings are:

names$ := "Anna|Carolyn|Diane|Francis";

DisplayInputBox("Enter name", "First Name:|LastName:", edit$);

                   {the second parameter is a list of delimited strings}

The following program excerpt shows how to make such a delimited string of text from the names of all variables in the current data file:

name$ := VarName(1);

for i := 2 to NVars do

   name$ := name$ + '|' + VarName(i);

The individual entries within the delimited string can be retrieved by using the function GetDelimitedString (see Retrieving Lists of Strings in STATISTICA BASIC).

For general information about strings see How to Use Strings in STATISTICA BASIC.

For a complete library of string operations see STATISTICA BASIC String Library.


Retrieving Lists of Strings in STATISTICA BASIC

  STATISTICA BASIC - Retrieving Lists of Strings in STATISTICA BASIC

In certain STATISTICA BASIC functions, lists of strings are returned.  These lists are delimited lists of text with either a tab or the character '|' as the delimiter. In order to use such lists, the function GetDelimitedString should be used. For example:

DisplayInputBox("Enter name", "Title:|Author:", edit$);

GetDelimitedString(edit$, 1, title$);

GetDelimitedString(edit$, 2, author$);

Whenever the DisplayInputBox function is executed, the user is prompted to enter one or more individual values in entry fields; these entries are returned by the function as a delimited string containg the user's entries.  Then, the function GetDelimitedString is used to copy parts of edit$ (containing the entered text) into title$ and author$.

For general information about strings see How to Use Strings in STATISTICA BASIC.

For a complete library of string operations see STATISTICA BASIC String Library.

See also, Passing Lists of Strings to STATISTICA BASIC Functions.


Graphics Library of STATISTICA BASIC

  STATISTICA BASIC Syntax Reference - Graphics Library of STATISTICA BASIC

Overview

Functions	Example and {Comment}

ColorRGB	light_pink := ColorRGB(251, 206, 243);

{Defines the specified color.}

DeleteGraph	DeleteGraph(dup_plot);

{Closes the specified graph.}

DisplayGraph	DisplayGraph(mygraph);

{Forces an update of the contents of the specified graph window.}

DuplicateGraph	dup_graph := DuplicateGraph(graph);

{Makes a duplicate of the graph associated with the graph handle graph and assigns its handle to the variable dup_graph.}

GetGraph	graph := GetGraph(0);

{Assigns the graph handle of the top-most graph to variable graph.}

GraphAddBWPlot	newplot := GraphAddBWPlot(mygraph, 'Mean', 'Std Error', 'Std Dev.', NCases, v5, v3, v4, v7, v8, v9);

{This function will add a new box-whisker plot to the specified graph.}

GraphAddMinMaxPlot	newplot := GraphAddMinMaxPlot(mygraph, MinMax_X, 'New Values', NCases, v3, v4);

{This function will add a new Min-Max X plot to the specified graph.}

GraphAddPlot	newplot := GraphAddPlot(graph, PIECHART, 'New Values', NCases, v3, v4);

{This function will add a new pie plot to the specified graph.}

GraphAddPlotXYZ	newplot := GraphAddPlotXYZ(graph, SCATTERPLOT, 'New Values', NCases, v3, v4, v5);

{This function will add a new scatterplot to the specified 3D graph.}

GraphAddRangePlot	newplot := GraphAddRangePlot(mygraph, 'Midpoints', 'Range', NCases, v5, v3, v4, v7);

{This function will add a new range plot to the specified graph.}

GraphChangeMappingBase	GraphChangeMappingBase(mygraph, -32);

{Proportionally increases (+) or decreases (-) all fonts, line thicknesses, etc. in the graph.}

GraphCopyToClipboard	GraphCopyToClipboard(mygraph);

{Copies the specified graph to the Clipboard.}

GraphDrawArrow	newarrow := GraphDrawArrow(mygraph, Head_Fancy_Filled, 5, 6, 10, 43, 55, 66, 59);

{Inserts an arrow in fixed coordinates into the graph.}

GraphDrawArrow3D	newarrow := GraphDrawArrow3D(mygraph, Head_Fancy_Filled, 5, 6, 10, 41, 125, 66, 59, 140, 88);

{Inserts an arrow in dynamic, 3D coordinates into the graph.}

GraphDrawArrowTernary	newarrow := GraphDrawArrowTernary(mygraph, Head_Fancy_Filled, 5, 6, 10, 0.3, 0.2, 0.5, 11, 0.4, 0.25, 0.35, 18);

{Inserts an arrow in dynamic, triangular coordinates into the graph.}

GraphDrawPolyline	polyline := GraphDrawPolyline(mygraph, 5, polyarray);

{Draws a polyline in the graph.}

GraphDrawShape	arc := GraphDrawShape(mygraph, Shape_arc, 27, 76, 85, 36);

{Draws the specified shape at the specified fixed coordinates in the graph.}

GraphDrawShape3D	arc := GraphDrawShape3D(mygraph, Shape_arc, 41, 125, 66, 59, 140, 88);

{Draws the specified shape at the specified dynamic 3D coordinates in the graph.}

GraphDrawShapeTernary	arc := GraphDrawShapeTernary(mygraph, Shape_arc, 0.3, 0.2, 0.5, 11, 0.4, 0.25, 0.35, 18);

{Draws the specified shape at the specified dynamic triangular coordinates in the graph.}

GraphDrawText	newtext := GraphDrawText(mygraph, 'Include this text in the graph', 78, 65);

{Inserts custom text in the graph.}

GraphDrawText3D	newtext := GraphDrawText3D(mygraph, 'Include this text in the graph', 41, 125, 66);

{Inserts custom text in dynamic, 3D coordinates into the graph.}

GraphDrawTextParam	newtext := GraphDrawTextParam(mygraph, 'This is the text to be drawn', 78, 65, 'Arial', 14, Green, 45, Al_Center, Al_Center, On, Fill_White);

{Inserts custom text and specifies specific parameters for this text.}

GraphDrawTextParam3D	newtext := GraphDrawTextParam3D(mygraph, 'This is the text to be drawn', 78, 65, 93, 'Arial', 14, Green, 45, Al_Center, Al_Center, On, Fill_White);

{Inserts custom text in dynamic, 3D coordinates, and specifies specific parameters for this text.}

GraphDrawTextParamTernary	newtext := GraphDrawTextParamTernary(mygraph, 'This is the text to be drawn', 0.4, 0.25, 0.35, 18, 'Arial', 14, Green, 45, Al_Center, Al_Center, On, Fill_White);

{Inserts custom text in dynamic, triangular coordinates, and specifies specific parameters for this text.}

GraphDrawTextTernary	newtext := GraphDrawTextTernary(mygraph, 'Include this text in the graph', 0.4, 0.25, 0.35, 18);

{Inserts custom text in dynamic, triangular coordinates into the graph.}

GraphEmbedGraph	Object := GraphEmbedGraph(mygraph, scatgraph, MAPPING_ANISOTROPIC, True, False, 0 , 50 , 100, 50, TRUE);

{Embeds the graph with the graph handle scatgraph into the graph with graph handle mygraph.}

GraphEmbedGraph3D	Object := GraphEmbedGraph3D(mygraph, scatgraph, TRUE, FALSE, MAPPING_FIXEDSIZE, 20, 80, 38, 40, 30, 85);

{Embeds the graph with the graph handle scatgraph into the 3D graph with graph handle mygraph.}

GraphEmbedGraphTernary	Object := GraphEmbedGraphTernary(mygraph, scatgraph, TRUE, FALSE, MAPPING_ISOTROPIC, 0.2, 0.3, 0.5, 15, 0.3, 0.4, 0.3, 20);

{Embeds the graph with the graph handle scatgraph into the ternary graph with graph handle mygraph.}

GraphGetHwnd	win_handle := GraphGetHwnd(mygraph);

{Retrieves the Graph handle of the specified graph and assigns its handle to the variable win_handle.}

GraphInsertFile	GraphInsertFile(mygraph, 'c:\car.bmp', TRUE, FALSE, 7, 3, 10, 5, TRUE);

{Inserts contents of the specified bitmap file into graph.}

GraphInsertFile3D	GraphInsertFile3D(mygraph, 'c:\car.bmp', TRUE, FALSE, 17, 13, 10, 25, 20, 30);

{Inserts contents of the specified bitmap file into the 3D graph.}

GraphInsertFileTernary	GraphInsertFileTernary(mygraph, 'c:\car.bmp', TRUE, FALSE, 0.3, 0.3, 0.4, 11, 0.2, 0.5, 0.3, 17);

{Inserts contents of the specified bitmap file into the ternary graph.}

GraphSetBWPlot2DLayout	GraphSetBWPlot2DLayout(mygraph, plot, ?DataLabels, 0, ?OutsideBarStyle, .5, ?OutsideBarWidth, ?IsRightAxis);

{Sets specific plot layout options for box-whisker plots.}

GraphSetDataPointLabel	GraphSetDataPointLabel(scatter_graph, 1, 17, 'Case Number 17');

{Assigns the designated data point label to the 17th data point in the specified plot.}

GraphSetDataPointLabels	GraphSetDataPointLabels(scatter_graph, 2, 4, 'Work_1|Work_2|Work_3|Work_4');

{Assigns the designated data point labels to consecutive points in the specified plot.}

GraphSetDefaultFont	GraphSetDefaultFont(mygraph, 'Courier New', 8, BLUE);

{Sets the font style, size, and color.}

GraphSetEyePosition	GraphSetEyePosition(mygraph, 11, -14, 3);

{Sets the viewpoint for the specified graph.}

GraphSetGridlines	GraphSetGridlines(mygraph, GRIDLINES_XY);

{Sets X and Y gridlines in the graph.}

GraphSetLegend	GraphSetLegend(mygraph, On, Off);

{Places a fixed graph legend in the graph.}

GraphSetMappingArea	GraphSetMappingArea(mygraph, -1, 1445, 1250, -1);

{Sets the graph area to the specified dimensions.}

GraphSetMatrixHistograms	GraphSetMatrixHistograms(mygraph, Matrix_Hist_Common, 5);

{Sets specific layout options for the histograms in Matrix plots.}

GraphSetObjectAreaStyle	GraphSetObjectAreaStyle(mygraph, newobject, On, A_Dots, BLUE);

{Edits the specified object's area fill pattern.}

GraphSetObjectLineStyle	GraphSetObjectLineStyle(mygraph, newobject, On, L_Dotted, 4, Cyan);

{Edits the specified object's line style.}

GraphSetObjectPatternStyle	GraphSetObjectPatternStyle(mygraph, newobject, TRUE, TrUE);

{Sets the specified object's area or line patern transparancy.}

GraphSetPieLayout	GraphSetPieLayout(mygraph, plot, Pie_3D, Pie_Ellipse, 0, 0, 25, 25, 0, PieLabels_Perc, 1);

{Sets specific plot layout options for pie charts.}

GraphSetPieStyle	GraphSetPieStyle(mygraph, plot, Pie_3D, Pie_Ellipse, PieLabels_Perc, 1);

{Sets specific style options for pie charts.}

GraphSetPlot2DLayout	GraphSetPlot2DLayout(mygraph, plot, StepPlot, DataLabels_Off, ?BarStyle, ?BarWidth, ?DevLevel, False);

{Sets specific plot layout options for 2D graphs.}

GraphSetPlotAreaStyle	GraphSetPlotAreaStyle(mygraph, plot, On, A_Forward_Diagonal, Yellow);

{Sets the area size, pattern, and color for the specified plot.}

GraphSetPlotBarLineStyle	GraphSetPlotBarLineStyle(mygraph, plot, On, L_Dotted, 1, PURPLE);

{Sets the bar line size, pattern, and color for the specified plot.}

GraphSetPlotConfidBands	GraphSetConfidBands(scatgraph, 4, On, .90);

{Sets confidence bands about the specified fitting line (see above) for the specified plot.}

GraphSetPlotEllipse	GraphSetPlotEllipse(scatgraph, 1, Ellipse_Conf, .99);

{Sets a confidence ellipse about the specified fitting line (see above) for the specified plot.}

GraphSetPlotFitLineStyle	GraphSetPlotFitLineStyle(mygraph, plot, On, L_Long_Dash, 5, Gray);

{Sets the fitting line size, pattern, and color for the specified plot.}

GraphSetPlotFitting	GraphSetPlotFitting(scatgraph, 1, Fit_Spline);

{Specifies a spline fit for the specified plot in the graph.}

GraphSetPlotFittingFunction	GraphSetPlotFittingFunction(scatter_graph, 2, 'y=normal(x, 50,12)');

{Specifies a custom function to fit to the data in the specified graph.}

GraphSetPlotFittingParam	GraphSetPlotFittingParam(scatter_graph, 3, ?PolyOrder, TRUE);

{Specifies the order of polynomial fit and logarithmic fit base for the specified plot.}

GraphSetPlotLineStyle	GraphSetPlotLineStyle(mygraph, plot, On, L_Solid, 3, Blue);

{Sets the line size, pattern, and color for the specified plot.}

GraphSetPlotName	GraphSetPlotName(mygraph, 1, 'Median', 'Income');

{Changes the plot name (legend) of the specified plot.}

GraphSetPlotPointStyle	GraphSetPlotPointStyle(mygraph, plot, On, P_Star, 5, PURPLE);

{Sets the point size, pattern, and color for the specified plot.}

GraphSetProportion	GraphSetProportion(mygraph, PROP_PRINTER);

{Sets the graph proportion to printer or screen proportion, or custom-defined proportion.}

GraphSetRangePlot2DLayout	GraphSetRangePlot2DLayout(mygraph, plot, DataLabels_Off, 0, .5, ?IsRightAxis);

{Sets specific plot layout options for range plots.}

GraphSetScaleParam	GraphSetScaleParam(line_graph, AX_X, Scaling_Linear, Scaling_Layout_Auto, ?ShiftScale, Off, False);

{Specifies scaling type, layout, etc.}

GraphSetScaleTextLabel	GraphSetScaleTextLabel(line_graph, AX_X, 100, 'Scale Position: 100');

{Creates a text label for the scale value 100 on the X-axis.}

GraphSetScaleTextLabels	GraphSetScaleTextLabels(line_graph, AX_X, 5, Values, 'Baseline|+10 units|+20 units');

{Creates text labels for the scale values on the X-axis.}

GraphSetScaleTickmarks	GraphSetScaleTickmarks(line_graph, AX_X, Tickmarks_Outside, 5, Tickmarks_Inside, 3, 4);

{Changes the major and minor tickmarks for the X-axis.}

GraphSetScaleValuesStyle	GraphSetScaleValuesStyle(line_graph, AX_X, ScaleValues_Numeric, 5, 2, ?DateType, ?SkippedLabels);

{Specifies the type, width, etc. of scale values.}

GraphSetScaling	GraphSetScaling(line_graph, AX_X, Scaling_Manual, -10, 30, 10)

{Changes the graph scaling for the X-axis to Manual with a step size of 10.}

GraphSetTitle	GraphSetTitle(surface_plot, Title_Top1, 'Change to this Title');

{Changes the designated title to the specified text.}

GraphSetXYZFittingFunction	GraphSetXYZFittingFunction(mygraph, 'z = x^3 + sqrt(y)');

{Specifies a custom function to fit to the 3D XYZ graph.}

GraphSetXYZFittingParam	GraphSetXYZFittingParam(mygraph, 15, 20, Off, On, CONTOUR_Lines, 5, 10);

{Sets specific layout options for 3D XYZ graphs.}

GraphSetXYZLayout	GraphSetXYZLayout(mygraph, DataLabels_X, On, 0, 5);

{Sets specific layout options for 3D XYZ graphs charts.}

NewContour	contour_plot := NewContour(Contour_Areas, Fit_Quadratic_3D, ?FunctionName$, 'Area Contour Plot with Quadratic Fit', 'X-axis', 'Y-axis', 'Z-axis', 100, v3, v4, v5);

{Creates an area contour plot with a quadratic fit and assigns its handle to the variable contour_plot.}

NewGraph	line_plot := NewGraph(LinePlot, 'Line Plot of two Measurement Variables', 'Measur1', 'Measur2', 25, v3, v4);

{Creates a 2D line plot and assigns its handle to the variable line_plot.}

NewGraph3DHistogram	biv_histogram := NewGraph3DHistogram(Hist3D_Boxes, '3D Histogram-Boxes', 'v1', 'v2', 'v3', 3, 5, Array, 'v1|v2|v3', 'case1|case2|case3|case4|case5');

{Creates a 3D bivariate histogram.}

NewGraph3DSequential	seq_graph := NewGraph3DSequential(Seq3D_Boxes, '3D Sequential Box Plot', 'V1', 'V2', 'V3', 3, 5, Data, 'v1|v2|v3', 'case1|case2|case3|case4|case5');

{Creates a 3D sequential box plot.}

NewGraphXYZ	space_plot := NewGraphXYZ(SpacePlotXYZ, '3D XYZ Space Plot', 'X-axis', 'Y-axis', 'Z-axis', 100, v3, v4, v5);

{Creates a 3D XYZ space plot and assigns its handle to the variable space_plot.}

NewIconGraph	iconplot := NewIconGraph(Icon_Stars, 'Stars Icon Plot', Unused$, Unused$, 5, 2, Data, ?IconNames$, 'v1|v2|v3|v4');

{Creates an Icon plot of star icons.}

NewMatrix	sq_matrix_graph := NewMatrix(Matrix_Scatterplot, 'Square Scatterplot Matrix', ?Left_Title$, ?Bottom_Title$, 5, 30, Array, 'v1|v2|v3|v4|v5');

{Creates a square scatterplot matrix.}

NewRectMatrix	rectmatrix := NewRectMatrix(Matrix_Scatterplot, 'Rectangular Scatterplot Matrix', ?Left_Title$, ?Bottom_Title$, 2, 3, 100, Array, 'v1|v2|v3|v4|v5|v6');

{Creates a rectangular scatterplot matrix.}

NewSurface	surface_plot := NewSurface(Fit_Quadratic_3D, ?FunctionName$, 'Surface Plot with Quadratic Fit', 'X-axis', 'Y-axis', 'Z-axis', NCases, v3, v4, v5);

{Creates a 3D surface plot with a quadratic fit and assigns its handle to the variable surface_plot.}

NewTernary	ternary_plot := NewTernary(Ternary_Scatterplot, Fit_Tern_Linear, ?FunctionName$, ?ContourType, 'Ternary (Trilinear) Scatterplot with Linear Fit', 'X-axis', 'Y-axis', 'Z-axis', 'V-axis', NCases, v3, v4, v5, v6);

{Creates a 3D ternary scatterplot with a linear fit.}

OpenGraph	graph := OpenGraph('d:\gra1.stg');

{Opens a previously saved graph.}

PrinterSetOrientation	PrinterSetOrientation(ORIENT_LANDSCAPE);

{Sets printer orientation in all applications.}

PrintGraph	PrintGraph(graph);

{Prints the specified graph to the printer.}

PrintGraphToOutputWindow	PrintGraphToOutputWindow(graph);

{Prints the specified graph to the Text/output window.}

SaveGraph	SaveGraph(my_graph, 'd:\my_gra.stg');

{Saves the graph associated with the graph handle my_graph to the specified file.}

SetDrawingMatrixCoordinates	SetDrawingMatrixCoordinates(my_graph, 2, 3, FALSE);

{Drawing in dynamic mode will be placed in specified row and column of matrix plot.}


STATISTICA BASIC - OpenGraph

  STATISTICA BASIC Library of Graph Functions - OpenGraph (Filename$)

Parameter:

FileName$	string with path and file name of graph to be opened (see Strings in Functions)

Return value:  graph handle

The OpenGraph function opens a previously saved graph.

Example:

RandomAccess;

graph := OpenGraph('d:\mygraph.stg');

This program will open the graph mygraph.stg and assign a graph handle to the temporary variable Graph.  The resulting graph can then be printed, modified, updated, etc.

Related topics: SaveGraph, GetGraph, SaveGraph, GetGraph, DeleteGraph, GraphCopyToClipboard, and NewGraph.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - PrintGraph

  STATISTICA BASIC Library of Graph Functions - PrintGraph (Graph)

Parameter:

Graph	graph handle of graph to be printed.

The PrintGraph function prints the specified graph.

Example:

RandomAccess;

Const Size=25;

Dim X(Size), Y(Size);

for i:=1 to Size do begin

  X(i):=rnd(25);

  Y(i):=rnd(10);

end;

scat2d := NewGraph (SCATTERPlot, '2D Scatterplot', 'Random1', 'Random2', Size, X, Y);

PrintGraph(scat2d);

This program will first create a 2D scatterplot (assigning its graph handle to the variable Scat2d) and then print the graph to the printer (regardless of the currently specified output channel).

Related topics: PrintGraphToOutputWindow, GraphCopyToClipboard, SaveGraph, OpenGraph, GetGraph, DeleteGraph, and NewGraph.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - PrinterSetOrientation

  STATISTICA BASIC Library of Graph Functions - PrinterSetOrientation (Orient)

Parameter:

Orient	printer orientation (ORIENT_PORTRAIT or ORIENT_LANDSCAPE).

The PrinterSetOrientation function sets the printer orientation to portrait or landscape.  Note that this function will affect not only STATISTICA, but all other Windows applications.

Example:

RandomAccess;

mygraph := OpenGraph('c:\stat\graph1.stg');

PrinterSetOrientation(ORIENT_LANDSCAPE);

PrintGraph(mygraph);

This program will open an existing graph, set the printer orientation to landscape, then print the graph to the printer.

Related topics:  PrintGraph, PrintGraphToOutputWindow, GraphCopyToClipboard, SaveGraph, OpenGraph, GetGraph, DeleteGraph, and NewGraph.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - PrintGraphToOutputWindow

  STATISTICA BASIC Library of Graph Functions - PrintGraphToOutputWindow (Graph)

Parameter:

Graph	graph handle of graph to be printed.

The PrintGraphToOutputWindow function prints the specified graph to the Text/output Window.

Example:

RandomAccess;

Const Size=25;

Dim X(Size), Y(Size);

for i:=1 to Size do begin

  X(i):=rnd(25);

  Y(i):=rnd(10);

end;

scat2d := NewGraph (SCATTERPlot, '2D Scatterplot', 'Random1', 'Random2', Size, X, Y);

PrintGraphToOutputWindow(scat2d);

This program will first create a 2D scatterplot (assigning its graph handle to the variable Scat2d) and then print the graph to the Text/output Window.

Related topics:  PrintGraph, GraphCopyToClipboard, SaveGraph, OpenGraph, GetGraph, DeleteGraph, and NewGraph.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - SaveGraph

  STATISTICA BASIC Library of Graph Functions - SaveGraph (Graph, Filename$)

Parameters:

Graph	graph handle of graph to be saved.

Filename$	string with path and file name (see, Strings in Functions).

The SaveGraph function saves the specified graph to the designated path and file name.

Example:

RandomAccess;

if DisplayInputBox('Enter File Name', 'File Name:', name$) then

   SaveGraph(GetGraph(0), name$);

This program will bring up a dialog prompting you to enter the path and file name for the desired graph and then the SaveGraph function will use that file name under which to save the top-most graph.

Related topics: OpenGraph, PrintGraph, GraphCopyToClipboard, GetGraph, DeleteGraph, and NewGraph.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - DuplicateGraph

  STATISTICA BASIC Library of Graph Functions - DuplicateGraph (Graph)

Parameter:

Graph	graph handle of graph to be duplicated.

Return value:	graph handle for the copy of the graph.

The DuplicateGraph function makes a copy of the specified graph.

Example:

RandomAccess;

mygraph := OpenGraph('c:\stat\graph1.stg);

new_graph := DuplicateGraph(mygraph);

GraphSetTitle(new_graph, TITLE_TOP2, 'Data from Project 7');

PrintGraph(new_graph);

DeleteGraph(new_graph);

This program will open an existing graph, then make a copy it and assign the graph handle of this copy to the temporary variable new_graph.  After changing one of the graph titles in the copy, the copy is printed and then removed from the screen.

Related topics:  OpenGraph, GraphCopyToClipboard, and NewGraph.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GetGraph

  STATISTICA BASIC Library of Graph Functions - GetGraph (?Window)

Parameter:

?Window	window handle

Return value:	graph handle

The GetGraph function returns the graph handle for the specified window.  If the value of Window equals zero (i.e., GetGraph(0)), the function returns the graph handle for the top-most graph window.

Example:

RandomAccess;

PrintGraph(GetGraph(0));

This program will print the top-most graph (as indicated by the parameter value 0 for GetGraph).

Related topics:  OpenGraph, GraphCopyToClipboard, DeleteGraph, SaveGraph, and NewGraph.

Note:  For increased speed of execution, the newly created graph is not displayed until the end of the STATISTICA BASIC program, and therefore, its graph handle should be accessed by assigning it to a variable whenever a new graph is opened or created.  For example, the following program will not execute properly:

RandomAccess;

NewGraph(BarPlot, '2D Bar Plot', 'This is the Y Axis', 'This is the X Axis', 50, v3, v4);

gr_handle := GetGraph(0);   {graph is not displayed at this point!}

PrintGraph(gr_handle);   {gr_handle is not defined - printing fails}

Instead, you should retrieve the graph handle when the graph is first created:

RandomAccess;

gr_handle := NewGraph(BarPlot, '2D Bar Plot', 'This is the Y Axis',

                     'This is the X Axis', 50, v3, v4);

PrintGraph(gr_handle);

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - DeleteGraph

  STATISTICA BASIC Library of Graph Functions - DeleteGraph (Graph)

Parameter:

Graph	graph handle of graph to be closed

The DeleteGraph function will close the specified graph.

Example:

RandomAccess;

graphname$ := 'c:\stat\examples\working.stg';

a_graph := OpenGraph(graphname$);

GraphCopyToClipboard(a_graph);

DeleteGraph(a_graph);

This program will open a previously saved graph, copy it to the Clipboard, and then close it.

Related topics: PrintGraph, GetGraph, SaveGraph, GraphCopyToClipboard, and NewGraph.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphCopyToClipboard

  STATISTICA BASIC Library of Graph Functions - GraphCopyToClipboard (Graph)

Parameter:

Graph	graph handle

The GraphCopyToClipboard function will copy the specified graph to the Clipboard.

Example:

RandomAccess;

graphname$ := 'c:\working.stg';

a_graph := OpenGraph(graphname$);

GraphCopyToClipboard(a_graph);

DeleteGraph(a_graph);

This program will open a previously saved graph, copy it to the clipboard, and then close it.

Related topics:  PrintGraph, GetGraph, SaveGraph, OpenGraph, DeleteGraph and NewGraph.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - NewGraph

  STATISTICA BASIC Library of Graph Functions - NewGraph (GraphType, ?Top_Title$, ?Left_Title$, ?Bottom_Title$, NumberOfPoints, XValues, YValues)

Parameters:

GraphType	graph type:  SCATTERPLOT, LINEPLOT, STEPPLOT, BARPLOT, BARLEFTPLOT, BARRIGHTPLOT, BARTOPPLOT, PIECHART, MULTIPATTERNBAR, VORONOIPLOT, or IGNOREDPLOT

?Top_Title$	string for top title (see, Strings in Functions)

?Left_Title$	string for left title (see, Strings in Functions)

?Bottom_Title$	string for bottom title (see, Strings in Functions)

NumberOfPoints	number of points to be plotted

XValues	array of values for X coordinates (see also Arrays in Functions)

YValues	array of values for Y coordinates (see also Arrays in Functions)

Return value:	graph handle

The NewGraph function will create the specified 2D graph.

Example:

RandomAccess;

new_plot := NewGraph(BarPlot, '2D Bar Plot', 'This is the Y Axis',

                    'This is the X Axis', 50, v3, v4);

GraphSetPlot2DLayout(new_plot, 0, BARPLOT, DATALABELS_OFF, BAR_COLUMNS,

                    .5, ?DevLevel, ?IsRightAxis);

This program will create a 2D column bar plot from variables 3 and 4 of the current data file and assign its graph handle to the temporary variable New_plot.

Related topics:  NewContour, NewGraph3DHistogram, NewGraph3DSequential, NewGraphXYZ, NewIconGraph, NewMatrix, NewRectMatrix, NewSurface, NewTernary, GraphAddPlot, GraphAddBWPlot, GraphAddMinMaxPlot, and GraphAddRangePlot.

Note:  For increased speed of execution, the newly created graph is not displayed until the end of the STATISTICA BASIC program, and therefore, its graph handle should be accessed by assigning it to a variable in all NewGraph program instructions.  For example, the following program will not execute properly (i.e., function GetGraph will get the handle of the currently "displayed-on-top" graph, not the handle of the graph to be created by the NewGraph function, which is not yet displayed):

RandomAccess;

NewGraph(BarPlot, '2D Bar Plot', 'This is the Y Axis', 'This is the X Axis', 50, v3, v4);

gr_handle := GetGraph(0);

PrintGraph(gr_handle);

Instead, you should retrieve the graph handle when the graph is first created:

RandomAccess;

gr_handle := NewGraph(BarPlot, '2D Bar Plot', 'This is the Y Axis',

                     'This is the X Axis', 50, v3, v4);

PrintGraph(gr_handle);

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - NewGraphXYZ

  STATISTICA BASIC Library of Graph Functions - NewGraphXYZ (GraphType, ?Top_Title$, ?X_Title$, ?Y_Title$, ?Z_Title$, NumberOfPoints, XValues, YValues, ZValues)

Parameters:

GraphType	graph type:  SCATTERPLOTXYZ, SPACEPLOTXYZ, SPECTRALPLOTXYZ, DEVIATIONPLOTXYZ, or TRACEPLOTXYZ

?Top_Title$	string for top title (see, Strings in Functions)

?X_Title$	string for X-axis title (see, Strings in Functions)

?Y_Title$	string for Y-axis title (see, Strings in Functions)

?Z_Title$	string for Z-axis title (see, Strings in Functions)

NumberOfPoints	number of points to be plotted

XValues	array of values for X coordinates (see also Arrays in Functions)

YValues	array of values for Y coordinates (see also Arrays in Functions)

ZValues	array of values for Z coordinates (see also Arrays in Functions)

Return value:	graph handle

The NewGraphXYZ function will create the specified 3D graph.

Example:

RandomAccess;

xyzscat := NewGraphXYZ(ScatterplotXYZ, 'Stats Graph 3D XYZ Scatterplot',

                      'X-axis', 'Y-axis', 'Z-axis', NCases, v15, v4, v25);

PrintGraph(xyzscat);

This program will create a 3D scatterplot from variables 15, 4, and 25 of the current data file. Next, the graph will be printed instead of displayed.

Related topics:  NewGraph, NewContour, NewGraph3DHistogram, NewGraph3DSequential, NewIconGraph, NewMatrix, NewRectMatrix, NewSurface, NewTernary, and GraphSetXYZLayout.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - NewSurface

  STATISTICA BASIC Library of Graph Functions - NewSurface (FittingType, ?FunctionName$, ?Top_Title$, ?X_Title$, ?Y_Title$, ?Z_Title$, NumberOfPoints, XValues, YValues, ZValues)

Parameters:

FittingType	fit type:  FIT_LINEAR_3D, FIT_QUADRATIC_3D, FIT_LEASTSQUARES_3D, FIT_NEGEXP_3D, FIT_SPLINE_3D, or FIT_USERDEFINED_3D

?FunctionName$	user-defined function if FIT_USERDEFINED_3D is specified (otherwise, use ?FunctionName$ or UNUSED$ as the entry for this parameter; see Strings in Functions)

?Top_Title$	string for top title (see, Strings in Functions)

?X_Title$	string for X-axis title (see, Strings in Functions)

?Y_Title$	string for Y-axis title (see, Strings in Functions)

?Z_Title$	string for Z-axis title (see, Strings in Functions)

NumberOfPoints	number of points to be plotted

XValues	array of values for X coordinates (see also Arrays in Functions)

YValues	array of values for Y coordinates (see also Arrays in Functions)

ZValues	array of values for Z coordinates (see also Arrays in Functions)

Return value:	graph handle

The NewSurface function will create the specified 3D surface graph.

Example:

RandomAccess;

spline := NewSurface(Fit_Spline_3D, ?FunctionName$, 'Surface Plot with Spline Fit',

                    'X-axis', 'Y-axis', 'Z-axis', NCases, v13, v24, v5);

PrintGraph(spline);

Creates a 3D surface plot with a spline fit and assigns its graph handle to the temporary variable Spline.

Related topics:  NewGraph, NewContour, NewGraph3DHistogram, NewGraph3DSequential, NewGraphXYZ, NewIconGraph, NewMatrix, NewRectMatrix, NewTernary, and GraphSetXYZFittingFunction.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - NewContour

  STATISTICA BASIC Library of Graph Functions - NewContour (ContourType, ?FittingType, ?FunctionName$, ?Top_Title$, ?X_Title$, ?Y_Title$, ?Z_Title$, NoOfPoints, XValues, YValues, ZValues)

Parameters:

ContourType	contour type:  CONTOUR_LINES or CONTOUR_AREAS

FittingType	fit type:  FIT_LINEAR_3D, FIT_QUADRATIC_3D, FIT_LEASTSQUARES_3D, FIT_NEGEXP_3D, FIT_SPLINE_3D, or FIT_USERDEFINED_3D

?FunctionName$	user-defined function if FIT_3D_USERDEFINED is specified (otherwise, use ?FunctionName$ or UNUSED$ as the entry for this parameter; see Strings in Functions)

?Top_Title$	string for top title (see, Strings in Functions)

?X_Title$	string for X-axis title (see, Strings in Functions)

?Y_Title$	string for Y-axis title (see, Strings in Functions)

?Z_Title$	string for Z-axis title (see, Strings in Functions)

NumberOfPoints	number of points to be plotted

XValues	array of values for X coordinates (see also Arrays in Functions)

YValues	array of values for Y coordinates (see also Arrays in Functions)

ZValues	array of values for Z coordinates (see also Arrays in Functions)

Return value:	graph handle

The NewContour function will create the specified 3D contour plot.

Example:

RandomAccess;

contour := NewContour(Contour_Areas, Fit_Quadratic_3D, ?FunctionName$,

                     'Area Contour Plot with Quadratic Fit', 'X-axis',

                     'Y-axis', 'Z-axis', NCases, v3, v4, v5);

PrintGraph(contour);

This program creates an area contour plot for the specified variables in the current data file.

Related topics:  NewGraph, NewGraph3DHistogram, NewGraph3DSequential, NewGraphXYZ, NewIconGraph, NewMatrix, NewRectMatrix, NewSurface, NewTernary, and GraphSetXYZFittingFunction.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - NewTernary

  STATISTICA BASIC Library of Graph Functions - NewTernary (GraphType, ?FittingType, ?FunctionName$, ?ContourType, ?Top_Title$, ?X_Title$, ?Y_Title$, ?Z_Title$, ?V_Title$, NumberOfPoints, XValues, YValues, ZValues, VValues)

Parameters:

GraphType	type of ternary graph:  TERNARY_2D, TERNARY_SCATTERPLOT, TERNARY_SPACEPLOT, TERNARY_DEVIATIONPLOT, TERNARY_TRACEPLOT, TERNARY_SURFACE, or TERNARY_CONTOUR

?FittingType	fit type:  FIT_TERN_LINEAR, FIT_TERN_QUADRATIC, FIT_TERN_FULLCUBIC, FIT_TERN_SPECCUBIC, or FIT_TERN_USERDEFINED

?FunctionName$	user-defined function if FIT_TERN_USERDEFINED is specified (otherwise, use ?FunctionName$ or UNUSED$ as the entry for this parameter; see Strings in Functions)

?ContourType	contour type if TERNARY_CONTOUR is specified:  CONTOUR_LINES or CONTOUR_AREAS

?Top_Title$	string for top title (see, Strings in Functions)

?X_Title$	string for X-axis title (see, Strings in Functions)

?Y_Title$	string for Y-axis title (see, Strings in Functions)

?Z_Title$	string for Z-axis title (see, Strings in Functions)

?V_Title$	string for V-axis title (see, Strings in Functions)

NumberOfPoints	number of points to be plotted

XValues	array of values for X coordinates (see also Arrays in Functions)

YValues	array of values for Y coordinates (see also Arrays in Functions)

ZValues	array of values for Z coordinates (see also Arrays in Functions)

VValues	array of values for V coordinates (see also Arrays in Functions)

Return value:	graph handle

The NewTernary function will create the specified ternary (trilinear) graph.

Example:

RandomAccess;

ternary := NewTernary(Ternary_SURFACE, Fit_Tern_FULLCUBIC, ?FunctionName$,

                     ?ContourType, 'Ternary Surface Plot', 'X-axis', 'Y-axis',

                     'Z-axis', 'V-axis', NCases, v3, v4, v5, v7);

PrintGraph(ternary);

This program creates a ternary surface plot from values of the specified variables in the current data file.

Related topics:  NewGraph, NewContour, NewGraph3DHistogram, NewGraph3DSequential, NewGraphXYZ, NewIconGraph, NewMatrix, NewRectMatrix, NewSurface and GraphSetXYZFittingFunction.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - NewGraph3DSequential

  STATISTICA BASIC Library of Graph Functions - NewGraph3DSequential (Type, ?Top_Title$, ?X_Title$, ?Y_Title$, ?Z_Title$, NumberColumns, NumberRows, Values, ?ColumnNames$, ?RowNames$)

Parameters:

Type	graph type:  SEQ3D_BOXES, SEQ3D_BLOCKS, SEQ3D_RIBBONS, SEQ3D_LINES, SEQ3D_SPIKES, SEQ3D_CONTOUR_DISCRETE, SEQ3D_SURFACE, SEQ3D_CONTOUR

?Top_Title$	string for top title (see, Strings in Functions)

?X_Title$	string for X-axis title (see, Strings in Functions)

?Y_Title$	string for Y-axis title (see, Strings in Functions)

?Z_Title$	string for Z-axis title (see, Strings in Functions)

NumberColumns	number of columns in the graph

NumberRows	number of rows in the graph

Values	data array, size = NumberRows x NumberColumns (see Arrays in Functions)

?ColumnNames$	delimited string of column names (see Lists of Strings in Functions)

?RowNames$	delimited string of row names (see Lists of Strings in Functions)

Return value:	graph handle

The NewGraph3DSequential function will create the specified 3D sequential graph.

Example:

RandomAccess;

seq := NewGraph3DSequential(Seq3D_RIBBONS, '3D Sequential Ribbon Plot',

                           'v1', 'v2', 'v3', 3, 20, Data, 'v1|v2|v3',

                           'c1|c2|c3|c4|c5|c6|c7|c8|c9|c10|c11|c12|c13|

                            c14|c15|c16|c17|c18|c19|c20');

This program will create a 3D sequential ribbon plot for the first 3 variables in the data file.

Related topics:  NewGraph, NewContour, NewGraph3DHistogram, NewGraphXYZ, NewIconGraph, NewMatrix, NewRectMatrix, NewSurface, and NewTernary.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - NewGraph3DHistogram

  STATISTICA BASIC Library of Graph Functions - NewGraph3DHistogram (Type, ?Top_Title$, ?X_Title$, ?Y_Title$, ?Z_Title$, NumberY, NumberX, Values, ?Y_Names$, ?X_Names$)

Parameters:

Type	graph type:  HIST3D_BOXES, HIST3D_SPIKES, HIST3D_CONTOUR_DISCRETE, HIST3D_SURFACE, or HIST3D_CONTOUR

?Top_Title$	string for top title (see, Strings in Functions)

?X_Title$	string for X-axis title (see, Strings in Functions)

?Y_Title$	string for Y-axis title (see, Strings in Functions)

?Z_Title$	string for Z-axis title (see, Strings in Functions)

NumberY	number of columns in the graph

NumberX	number of rows in the graph

Values	data array, size = NumberX x NumberY (see Arrays in Functions)

?Y_Names$	delimited string of column names (see Lists of Strings in Functions)

?X_Names$	delimited string of row names (see Lists of Strings in Functions)

Return value:	graph handle

The NewGraph3DHistogram function will create the specified 3D bivariate histogram.

Example:

RandomAccess;

histo := NewGraph3DHistogram(Hist3D_Boxes, '3D Histogram-Boxes', 'v1', 'v2', 'v3',

                            3, 5, Data, 'test1|test2|test3', 'patient1|patient2|

                            patient3|patient4|patient5');

The above program will create a 3D Bivariate Histogram with a box-style display.

Related topics:  NewGraph, NewContour, NewGraph3DSequential, NewGraphXYZ, NewIconGraph, NewMatrix, NewRectMatrix, NewSurface, and NewTernary.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - NewMatrix

  STATISTICA BASIC Library of Graph Functions - NewMatrix (Type, ?Top_Title$, ?Left_Title$, ?Bottom_Title$, NumberColumns, NumberRows, Values, ?ColumnNames$)

Parameters:

Type	graph type:  MATRIX_SCATTERPLOT, MATRIX_LINES, or MATRIX_COLUMNS

?Top_Title$	string for top title (see, Strings in Functions)

?Left_Title$	string for left title (see, Strings in Functions)

?Bottom_Title$	string for bottom title (see, Strings in Functions)

NumberColumns	number of matrix plot variables in the graph

NumberRows	number of points to be plotted

Values	data array, size = NumberColumns x NumberOfPoints (see Arrays in Functions)

?ColumnNames$	delimited string of the names of matrix variables to be placed on the respective histogram (see Lists of Strings in Functions)

Return value:	graph handle

The NewMatrix function will create the specified square matrix graph.

Example:

RandomAccess;

sq_matrix := NewMatrix(Matrix_SCATTERPLOT, 'Square Lines Matrix', 'Rows',

                      'Columns', 5, NCases, Data, 'Hist. Var1|Hist. Var2|

                      Hist. Var3|Hist. Var4|Hist. Var5');

The above program will create a 5x5 square scatterplot matrix graph for the values of the current data file.

Related topics:  NewGraph, NewContour, NewGraph3DHistogram, NewGraph3DSequential, NewGraphXYZ, NewIconGraph, NewRectMatrix, NewSurface, NewTernary, and GraphSetMatrixHistograms.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - NewRectMatrix

  STATISTICA BASIC Library of Graph Functions - NewRectMatrix (Type, ?Top_Title$, ?Left_Title$, ?Bottom_Title$, MatrixCols, MatrixRows, NumberOfPoints, Values, ?ColumnNames$)

Parameters:

Type	graph type:  MATRIX_SCATTERPLOT, MATRIX_LINES, or MATRIX_COLUMNS

?Top_Title$	string for top title (see, Strings in Functions)

?Left_Title$	string for left title (see, Strings in Functions)

?Bottom_Title$	string for bottom title (see, Strings in Functions)

MatrixCols	number of column variables in the matrix plot

MatrixRows	number of row variables in the matrix plot

NumberOfPoints	number of points to be plotted

Values	data array, size = NumberOfPoints * (MatrixRows + MatrixColumns) (see Arrays in Functions)

?ColumnNames$	delimited string of the names of matrix variables for both axes (list the column variables first, followed by the row variables) to be placed on the respective histogram (see Lists of Strings in Functions)

Return value:	graph handle

The NewRectMatrix function will create the specified rectangular matrix graph.  The Values matrix should contain as many rows as the specified NumberOfPoints, and one column for each of the specified MatrixColumns variables, followed by one column for each of the specified MatrixRows variables..

Example:

RandomAccess;

rect_matrx := NewRectMatrix(Matrix_SCATTERPLOT, 'Rectangular Lines Matrix', 'Rows',

                           'Columns', 5,  3, NCases, Data, 'Hist. Var1|Hist.

                            Var2|Hist. Var3|Hist. Var4|Hist. Var5|Hist. Var6|Hist.

                            Var7|Hist. Var8');

The above program will create a 3x5 rectangular scatterplot matrix graph with the first 5 variables in the data file as the matrix column variables and the next 3 variables as the matrix row variables.  All cases from the data file will be plotted.

Related topics:  NewGraph, NewContour, NewGraph3DHistogram, NewGraph3DSequential, NewGraphXYZ, NewIconGraph, NewMatrix, NewSurface, NewTernary, and GraphSetMatrixHistograms.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - NewIconGraph

  STATISTICA BASIC Library of Graph Functions - NewIconGraph (Type, ?Top_Title$, ?Left_Title$, ?Bottom_Title$, NumberColumns, NumberRows, Values, ?IconNames$, ?VarNames$)

Parameters:

Type	graph type:  ICON_FACES, ICON_STARS, ICON_SUNRAYS, ICON_POLYGONS, ICON_PIES, ICON_COLUMNS, ICON_LINES, or ICON_PROFILES

?Top_Title$	string for top title (see, Strings in Functions)

?Left_Title$	string for left title (see, Strings in Functions)

?Bottom_Title$	string for bottom title (see, Strings in Functions)

NumberColumns	number of columns in the graph (representing the icon characteristics)

NumberRows	number of rows in the graph (representing the number of cases; one icon per case)

Values	data array, size = NumberRows x NumberColumns (see Arrays in Functions)

?IconNames$	delimited string of the names (labels) of icons (see Lists of Strings in Functions)

?VarNames$	delimited string of the names of icon variables (see Lists of Strings in Functions)

Return value:	graph handle

The NewIconGraph function will create the specified icon plot with the specified number of columns (cases) and rows.

Example:

RandomAccess;

iconplot := NewIconGraph(Icon_PIES, 'Pie Chart Icon Plot', ?Left_Title$,

                        ?Bottom_Title$, 5, 10, Data, ?IconNames$,

                        'Measur1|Measur2|Measur3|Measur4|Measur5');

This program will create a pie icon chart where the values of the first five variables in the current data file will be represented as slices of the pie and each pie will represent a specific case (the first 10 cases in the data file).

Related topics:  NewGraph, NewContour, NewGraph3DHistogram, NewGraph3DSequential, NewGraphXYZ, NewMatrix, NewRectMatrix, NewSurface, and NewTernary.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetTitle

  STATISTICA BASIC Library of Graph Functions - GraphSetTitle (Graph, TitleNumber, Name$)

Parameters:

Graph	graph handle

TitleNumber	title number to be changed:  TITLE_TOP1, TITLE_TOP2, TITLE_TOP3, TITLE_TOP4, TITLE_TOP5, TITLE_BOTTOM1, TITLE_BOTTOM2, TITLE_LEFT1, TITLE_LEFT2, TITLE_RIGHT1, TITLE_RIGHT2, TITLE_X1, TITLE_X2, TITLE_Y1, TITLE_Y2, TITLE_Z1, TITLE_Z2, TITLE_V1, or TITLE_V2

Name$	string for title (see Strings in Functions)

The GraphSetTitle function will add or change the specified title.  To delete a title, pass an empty string ('') with nothing between a pair of single quotes.  (For more information about titles in graphs, see Titles.)

The following titles are applicable to specific types of graphs:
all graphs:	TITLE_TOP1-5
2D graphs: 	TITLE_BOTTOM1-2, TITLE_LEFT1-2, TITLE_RIGHT1-2.
3D graphs: 	TITLE_X1-2, TITLE_Y1-2, TITLE_Z1-2.
ternary (trilinear) graphs:	TITLE_X1-2, TITLE_Y-2, TITLE_Z1-2, TITLE_V1-2.

Example:

RandomAccess;

GraphSetTitle(NewGraph (BarPlot, 'Stats Graph', 'Y Axis', 'X Axis', 50, v3, v4),

             TITLE_TOP2, '2D Bar Column Plot');

This program will create a 2D column bar plot from variables 3 and 4 of the current data file.  The GraphSetTitle function will then add a second title at the top of the graph.

Related topics:  GraphSetDefaultFont, GraphSetLegend, GraphSetDataPointLabel, and GraphSetDataPointLabels.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetScaling

  STATISTICA BASIC Library of Graph Functions - GraphSetScaling (Graph, Scale, ScaleType, ?Min, ?Max, ?Step)

Parameters:

Graph	graph handle

Scale	scale to be changed:  AX_X, AX_Y, AX_RY, AX_TOP, AX_Z, or AX_V

ScaleType	scale type:  SCALING_AUTO_0, SCALING_AUTO, SCALING_MANUAL_0, or SCALING_MANUAL

?Min	minimum scale value (used whenever SCALING_MANUAL_0 or SCALING_MANUAL is specified)

?Max	maximum scale value (used whenever SCALING_MANUAL_0 or SCALING_MANUAL is specified)

?Step	step size (used whenever SCALING_MANUAL_0 or SCALING_MANUAL is specified)

The GraphSetScaling function allows you to specify the desired scale type (for more information, see Scale Options).

The following scales are applicable to specific types of graphs:
2D graphs:	AX_X, AX_Y, AX_RY, and AX_TOP
3D graphs:	AX_X, AX_Y, and AX_Z
ternary (trilinear) graphs:	AX_X, AX_Y, AX_Z, and AX_V.

Example:

RandomAccess;

mygraph := OpenGraph('c:\my_graph.stg');

GraphSetScaling(mygraph, AX_X, Scaling_Manual, -10, 30, 10);

SaveGraph(mygraph, 'c:\new_graf.stg');

This program will first open the specified graph, then it will change the scaling on the X-axis to Manual with a minimum value of -10, a maximum value of 30, and a step size of 10.  Next, the edited graph will be saved under a new file name.

Related topics:  GraphSetScaleParam, GraphSetScaleTextLabel, GraphSetScaleTextLabels, GraphSetScaleTickmarks, GraphSetScaleValuesStyle, and GraphSetGridlines.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetScaleTickmarks

  STATISTICA BASIC Library of Graph Functions - GraphSetScaleTickmarks (Graph, Scale, ?MajorType, ?MajorSize, ?MinorType, ?MinorSize, ?MinorCount)

Parameters:

Graph	graph handle

Scale	scale to be changed:  AX_X, AX_Y, AX_RY, AX_TOP, AX_Z, or AX_V

?MajorType	type of major tickmarks:  TICKMARKS_OFF, TICKMARKS_OUTSIDE, TICKMARKS_INSIDE, or TICKMARKS_CROSSED

?MajorSize	major tickmarks size (in points)

?MinorType	type of minor tickmarks:  TICKMARKS_OFF, TICKMARKS_OUTSIDE, TICKMARKS_INSIDE, or TICKMARKS_CROSSED

?MinorSize	minor tickmarks size (in points)

?MinorCount	number of minor tickmarks (between major tickmarks)

The GraphSetScaleTickmarks function allows you to specify the major and minor tickmarks for the specified axis in the graph (for more information, see Scale Options).

The following scales are applicable to specific types of graphs:
2D graphs:	AX_X, AX_Y, AX_RY, and AX_TOP
3D graphs:	AX_X, AX_Y, and AX_Z
ternary (trilinear) graphs:	AX_X, AX_Y, AX_Z, and AX_V.

Example:

RandomAccess;

mygraph := NewGraph(SCATTERPLOT, 'Predictors of Poverty', 'Percent Poor in County',

                   'Population Change in County', NCases, v3, v4);

GraphSetScaleTickmarks(mygraph, AX_X, Tickmarks_CROSSED, 5, Tickmarks_OUTside, 3, 4);

This program will first create a 2D scatterplot and then customize the tickmarks on the X-axis.

Related topics: GraphSetScaling, GraphSetScaleParam, GraphSetScaleTextLabel, GraphSetScaleTextLabels, GraphSetScaleValuesStyle, and GraphSetGridlines.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetScaleTextLabel

  STATISTICA BASIC Library of Graph Functions - GraphSetScaleTextLabel (Graph, Scale, TextLabelValue, TextLabel$)

Parameters:

Graph	graph handle

Scale	scale to be changed:  AX_X, AX_Y, AX_RY, AX_TOP, AX_Z, or AX_V

TextLabelValue	scale value for which the text label is to be created

TextLabel$	text label (see Strings in Functions)

The GraphSetScaleTextLabel function allows you to specify a text label for a specific scale value on the respective axis (for more information, see Scale Options).

The following scales are applicable to specific types of graphs:
2D graphs:	AX_X, AX_Y, AX_RY, and AX_TOP
3D graphs:	AX_X, AX_Y, and AX_Z
ternary (trilinear) graphs:	AX_X, AX_Y, AX_Z, and AX_V.

Example:

RandomAccess;

mygraph := NewGraph(SCATTERPLOT, 'Predictors of Poverty', 'Percent Poor in County',

                   'Population Change in County', NCases, v3, v4);

GraphSetScaleTextLabel(mygraph, AX_Y, .5, '50% Poverty');

This program will create a 2D scatterplot and then change the label for scale value 0.5 along the Y-axis.

Related topics: GraphSetScaleParam, GraphSetScaling, GraphSetScaleTickmarks, GraphSetScaleValuesStyle, GraphSetGridlines, and GraphSetScaleTextLabels.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetScaleTextLabels

  STATISTICA BASIC Library of Graph Functions - GraphSetScaleTextLabels (Graph, Scale, NumberOfLabels, TextLabelValues, TextLabels$)

Parameters:

Graph	graph handle

Scale	scale to be changed:  AX_X, AX_Y, AX_RY, AX_TOP, AX_Z, or AX_V

NumberOfLabels	number of scale labels

TextLabelValues	name of array containing scale values for which text labels are to be created

TextLabels$	delimited string of text labels (in order, corresponding to TextLabelValues; see Lists of Strings in Functions)

The GraphSetScaleTextLabels function allows you to specify text labels for the specified scale values on the specified axis (for more information, see Scale Options).

The following scales are applicable to specific types of graphs:
2D graphs:	AX_X, AX_Y, AX_RY, and AX_TOP
3D graphs:	AX_X, AX_Y, and AX_Z
ternary (trilinear) graphs:	AX_X, AX_Y, AX_Z, and AX_V.

Example:

RandomAccess;

Dim Labels(4);

Labels(1) := 0;

Labels(2) := 10;

Labels(3) := 20;

Labels(4) := 30;

mygraph := NewGraph(SCATTERPLOT, 'Predictors of Poverty', 'Percent Poor in County',

                   'Population Change in County', NCases, v3, v4);

GraphSetScaleTextLabels(mygraph, AX_X, 4, Labels, 'zero|ten|twenty|thirty');

This program will create a 2D scatterplot and then change the labels along the X-axis.

Related topics: GraphSetScaleParam, GraphSetScaling, GraphSetScaleTextLabel, GraphSetScaleTickmarks, GraphSetScaleValuesStyle, and GraphSetGridlines.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetScaleValuesStyle

  STATISTICA BASIC Library of Graph Functions - GraphSetScaleValuesStyle (Graph, Scale, ?Style, ?NumWidth, ?NumDec, ?DateType, ?SkippedLabels)

Parameters:

Graph	graph handle

Scale	scale to be changed:  AX_X, AX_Y, AX_RY, AX_TOP, AX_Z, or AX_V

?Style	scale value style:  SCALEVALUES_OFF, SCALEVALUES_NUMERIC, SCALEVALUES_TEXT, or SCALEVALUES_DATES

?NumWidth	width of field used for numerical scale values

?NumDec	number of decimals for numerical scale values

?DateType	format of date for date scale values

?SkippedLabels	specify number of labels to skip on axes

The GraphSetScaleValuesStyle function allows you to specify several scale characteristics (for more information, see Scale Options).

The following scales are applicable to specific types of graphs:
2D graphs:	AX_X, AX_Y, AX_RY, and AX_TOP
3D graphs:	AX_X, AX_Y, and AX_Z
ternary (trilinear) graphs:	AX_X, AX_Y, AX_Z, and AX_V.

Example:

RandomAccess;

mygraph := NewGraph(SCATTERPLOT, 'Predictors of Poverty', 'Percent Poor in County',

                   'Population Change in County', NCases, Pop_chng, Pt_poor);

GraphSetScaleValuesStyle(mygraph, AX_X, ScaleValues_Numeric, 2, 0, ?DateType,

                        ?SkippedLabels);

This program will first create a 2D scatterplot and then customize the scale values on the X-axis.

Related topics:  GraphSetScaling, GraphSetScaleParam, GraphSetScaleTextLabel, GraphSetScaleTextLabels, and GraphSetScaleTickmarks, GraphSetGridlines.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetScaleParam

  STATISTICA BASIC Library of Graph Functions - GraphSetScaleParam (Graph, Scale, ?ScalingType, ?ValueLayout, ?ShiftScale, ?ScaleBreak, ?ScaleReversed)

Parameters:

Graph	graph handle

Scale	scale to be changed:  AX_X, AX_Y, AX_RY, AX_TOP, AX_Z, or AX_V

?ScalingType	scale type:  SCALING_LINEAR, SCALING_LOG, or SCALING_LOGDECIMAL

?ValueLayout	layout of scale values on axis:  SCALING_LAYOUT_AUTO, SCALING_LAYOUT_PARALLEL, SCALING_LAYOUT_NORMAL, or SCALING_LAYOUT_ALTERNATE

?ShiftScale	shift scale by specified number of points

?ScaleBreak	place scale break on axis:  ON or OFF

?ScaleReversed	reverse sequence of specified scale values:  TRUE or FALSE

The GraphSetScaleParam function allows you to set several scale characteristics (for more information, see Scale Options).

The following scales are applicable to specific types of graphs:
2D graphs:	AX_X, AX_Y, AX_RY, and AX_TOP
3D graphs:	AX_X, AX_Y, and AX_Z
ternary (trilinear) graphs:	AX_X, AX_Y, AX_Z, and AX_V.

Note that the scaling types SCALING_LOG and SCALING_LOGDECIMAL are not applicable to the X and Y axes in 3D graphs.

Example:

RandomAccess;

mygraph := NewGraph(SCATTERPLOT, 'Predictors of Poverty', 'Percent Poor in County',

                   'Population Change in County', NCases, v3, v4);

GraphSetScaleValuesStyle(Mygraph, AX_X, ScaleValues_Numeric, 2, 0, ?DateType,

                        ?SkippedLabels);

GraphSetScaleParam(mygraph, AX_X, SCALING_LINEAR, SCALING_LAYOUT_ALTERNATE, ?ShiftScale,

                  ?ScaleBreak, ?ScaleReversed);

This program will first create a 2D scatterplot and then customize the scale values on the X-axis.

Related topics: GraphSetScaling, GraphSetScaleTextLabel, GraphSetScaleTextLabels, GraphSetScaleTickmarks, and GraphSetGridlines.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetPlotFitting

  STATISTICA BASIC Library of Graph Functions - GraphSetPlotFitting (Graph, PlotNumber, FitType)

Parameters:

Graph	graph handle

PlotNumber	plot number

FitType	fit type for 2D graph:  FIT_LINEAR, FIT_LOG, FIT_EXP, FIT_SPLINE, FIT_POLYNOMIAL, FIT_LEASTSQUARES, or FIT_NEGEXP

The GraphSetPlotFitting function allows you to fit the specified function to the data in a 2D graph.  In order to fit a custom function to the data, use GraphSetPlotFittingFunction.

RandomAccess;

mygraph := NewGraph(SCATTERPLOT, 'Predictors of Poverty', 'Percent Poor in County',

                   'Population Change in County', NCases, v3, v4);

GraphSetPlotFitting(mygraph, 1, Fit_LEASTSQUARES);

This program will first create a 2D scatterplot and then a curve is fitted to the XY coordinate data according to the distance-weighted least squares smoothing procedure.

Related topics:  GraphSetPlotConfidBands, GraphSetPlotEllipse, GraphSetPlotFitLineStyle, GraphSetPlotFittingFunction, and GraphSetPlotFittingParam.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetPlotFittingFunction

  STATISTICA BASIC Library of Graph Functions - GraphSetPlotFittingFunction (Graph, PlotNumber, Function)

Parameters:

Graph	graph handle

PlotNumber	plot number

Function	custom 2D function to be plotted

The GraphSetPlotFittingFunction function allows you to fit a user-defined function to the data in a 2D graph.  In order to fit a pre-defined function to the data, use GraphSetPlotFitting.

RandomAccess;

mygraph := NewGraph(SCATTERPLOT, 'Predictors of Poverty', 'Percent Poor in County',

                   'Population Change in County', NCases, v3, v4);

GraphSetPlotFittingFunction(mygraph, 1, 'y=x^2');

This program will first create a 2D scatterplot and then fit the specified function to the data.

Related topics:  GraphSetPlotConfidBands, GraphSetPlotEllipse, GraphSetPlotFitLineStyle, GraphSetPlotFitting, and GraphSetPlotFittingParam.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetPlotFittingParam

  STATISTICA BASIC Library of Graph Functions - GraphSetPlotFittingParam (Graph, PlotNumber, ?PolyOrder, ?LogBase10)

Parameters:

Graph	graph handle

PlotNumber	plot number

?PolyOrder	order of polynomial

?LogBase10	base 10 logarithm:  TRUE or FALSE (if FALSE, base Euler is used)

The GraphSetPlotFittingParam function allows you to set the order of polynomial (for a polynomial fit) or the base for logarithmic fitting.  To set either of these fits, see GraphSetPlotFitting.

RandomAccess;

mygraph := NewGraph(SCATTERPLOT, 'Predictors of Poverty', 'Percent Poor in County',

                   'Population Change in County', NCases, v3, v4);

GraphSetPlotFitting(mygraph, 1, Fit_POLYNOMIAL);

GraphSetPlotFittingParam(mygraph, 1, 5, TRUE);

This program will first create a 2D scatterplot and then fit a fifth order polynomial to the data.

Related topics:  GraphSetPlotConfidBands, GraphSetPlotEllipse, GraphSetPlotFitLineStyle, GraphSetPlotFitting, and GraphSetPlotFittingFunction.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetPlotConfidBands

  STATISTICA BASIC Library of Graph Functions - GraphSetPlotConfidBands (Graph, PlotNumber, BandsType, Coeff)

Parameters:

Graph	graph handle

PlotNumber	plot number

ConfidBands	confidence bands:  ON or OFF

Coeff	probability level which represents the probability that the "true" fitted line falls between the bands

The GraphSetPlotConfidBands function allows you to place confidence bands around the linear or polynomial fit.  To set either of these fits, see GraphSetPlotFitting.

RandomAccess;

mygraph := NewGraph(SCATTERPLOT, 'Predictors of Poverty', 'Percent Poor in County',

                   'Population Change in County', NCases, v3, v4);

GraphSetPlotFitting(mygraph, 1, Fit_POLYNOMIAL);

GraphSetPlotFittingParam(mygraph, 1, 5, ?LogBase);

GraphSetPlotConfidBands(mygraph, 1, On, .90);

This program will first create a 2D scatterplot, fit a fifth order polynomial to the data, and then place 90% confidence bands around the fitting line.

Related topics:  GraphSetPlotEllipse, GraphSetPlotFitLineStyle, GraphSetPlotFitting, GraphSetPlotFittingFunction, and GraphSetPlotFittingParam.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetPlotEllipse

  STATISTICA BASIC Library of Graph Functions - GraphSetPlotEllipse (Graph, PlotNumber, EllipseType, Coeff)

Parameters:

Graph	graph handle

PlotNumber	plot number

EllipseType	ellipse type:  ELLIPSE_OFF, ELLIPSE_CONF, ELLIPSE_RANGE

Coeff	probability level which represents the probability that the values will fall within the area marked by the ellipse

The GraphSetPlotEllipse function allows you to place a confidence ellipse around the previously specified fit (see GraphSetPlotFitting).

RandomAccess;

mygraph := NewGraph(SCATTERPLOT, 'Predictors of Poverty', 'Percent Poor in County',

                   'Population Change in County', NCases, v3, v4);

GraphSetPlotFitting(mygraph, 1, Fit_POLYNOMIAL);

GraphSetPlotFittingParam (mygraph, 1, 5, ?LogBase);

GraphSetPlotEllipse(mygraph, 1, ELLIPSE_CONF, .90);

This program will first create a 2D scatterplot, fit a fifth order polynomial to the data, and then place a 90% confidence ellipse around the fitting line.

Related topics:  GraphSetPlotConfidBands, GraphSetPlotFitLineStyle, GraphSetPlotFitting, GraphSetPlotFittingFunction, and GraphSetPlotFittingParam.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetDataPointLabel

  STATISTICA BASIC Library of Graph Functions - GraphSetDataPointLabel (Graph, PlotNumber, LabelNumber, Label$)

Parameters:

Graph	graph handle

PlotNumber	plot number

LabelNumber	number of of the data point to be labeled

Label$	delimited string (label; see Strings in Functions)

The GraphSetDataPointLabel function allows you to label individual (selected) data points in the graph.

RandomAccess;

mygraph := NewGraph(SCATTERPLOT, 'Success in the Workplace', 'Males', 'Females',

                   NCases, v3, v4);

GraphSetDataPointLabel(mygraph, 1, 17, 'Case Number 17');

This program will first create a 2D scatterplot and then label the 17th data point point with the specified label.

Related topics:  GraphSetPlot2DLayout, GraphSetLegend, GraphSetTitle, GraphSetDataPointLabels, and GraphSetDefaultFont.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetDataPointLabels

  STATISTICA BASIC Library of Graph Functions - GraphSetDataPointLabels (Graph, PlotNumber, NumberOfLabels, Labels$)

Parameters:

Graph	graph handle

PlotNumber	plot number

NumberOfLabels	number of labels

Labels$	delimited string of labels (see Lists of Strings in Functions)

The GraphSetDataPointLabels function allows you to label data points in the graph.

RandomAccess;

mygraph := NewGraph(SCATTERPLOT, 'Success in the Workplace', 'Males', 'Females',

                   NCases, v3, v4);

GraphSetDataPointLabels(mygraph, 1, 4, 'Nurse|Teacher|Accountant|Programmer');

This program will first create a 2D scatterplot and then label the first four points with the specified labels.

Related topics:  GraphSetPlot2DLayout, GraphSetLegend, GraphSetTitle, GraphSetDefaultFont, and GraphSetDataPointLabel

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetGridlines

  STATISTICA BASIC Library of Graph Functions - GraphSetGridlines (Graph, GridType)

Parameters:

Graph	graph handle

GridType	gridlines type:  GRIDLINES_NONE, GRIDLINES_X, GRIDLINES_Y, GRIDLINES_XY, GRIDLINES_Z, GRIDLINES_XZ, GRIDLINES_YZ, GRIDLINES_XYZ

The GraphSetGridlines function allows you to set the display of gridlines in the specified graph.

RandomAccess;

xyzscat := NewGraphXYZ(ScatterplotXYZ, 'Stats Graph 3D XYZ Scatterplot',

                      'X-axis', 'Y-axis', 'Z-axis', NCases, v15, v4, v25);

GraphSetGridlines(xyzscat, GRIDLINES_XY);

PrintGraph(xyzscat);

This program will create a 3D scatterplot and turn on the display of the XY gridlines.

Related topics: GraphSetScaleTickmarks.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetLegend

  STATISTICA BASIC Library of Graph Functions - GraphSetLegend (Graph, ?FixedLegend, ?ContourLegend)

Parameters:

Graph	graph handle

?FixedLegend	fixed legend in graph:  ON or OFF

?ContourLegend	contour legend in graph:  ON or OFF

The GraphSetLegend function allows you to turn on/off legends in graphs.

RandomAccess;

contourplot := NewContour(Contour_Areas, Fit_Quadratic_3D, ?FunctionName$,

                         'Area Contour Plot with Quadratic Fit', 'X-axis',

                         'Y-axis', 'Z-axis', NCases, v3, v4, v2);

GraphSetLegend(contourplot, ?FixedLegend, OFF);

This program will create an area contour plot without the contour legend.

Related topics: GraphSetXYZLayout, GraphSetTitle, and GraphSetDefaultFont.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphAddPlot

  STATISTICA BASIC Library of Graph Functions - GraphAddPlot (Graph, PlotType, ?Name$, NoOfPoints, XValues, YValues)

Parameters:

Graph	graph handle

PlotType	type of plot to add:  SCATTERPLOT, LINEPLOT, STEPPLOT, BARPLOT, BARLEFTPLOT, BARRIGHTPLOT, BARTOPPLOT, PIECHART, MULTIPATTERNBAR, VORONOIPLOT, or IGNOREDPLOT

?Name$	string with legend name (see Strings in Functions)

NoOfPoints	number of points

XValues	array of values for X coordinates (see also Arrays in Functions)

YValues	array of values for Y coordinates (see also Arrays in Functions)

The GraphAddPlot function allows you to add the specified plot to the graph.

RandomAccess;

mygraph := NewGraph(SCATTERPLOT, 'Success in the Workplace', 'Low Income', 'Mid Income',

                   NCases, v1, v2);

lplot := GraphAddPlot(mygraph, LINEPLOT, 'High Income', NCases, v3, v4);

GraphSetPlot2DLayout(mygraph, lplot, LINEPLOT, DATALABELS_Y, ?BarStyle, ?BarWidth,

                    ?DevLevel, ?IsRightAxis);

GraphSetPlotLineStyle(mygraph, lplot, ON, L_LONG_DASH, 2, NAVY);

This program will create a 2D scatterplot and then add a new line plot to the graph and further modify the new line plot.

Related topics:  GraphAddBWPlot, GraphAddMinMaxPlot, GraphAddRangePlot, GraphSetPlot2DLayout, GraphSetPlotLineStyle, GraphSetPlotBarLineStyle, and GraphSetPlotAreaStyle.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphAddPlotXYZ

  STATISTICA BASIC Library of Graph Functions - GraphAddPlotXYZ (Graph, ?Name$, NoOfPoints, XValues, YValues, ZValues)

Parameters:

Graph	graph handle

?Name$	string with legend name (see Strings in Functions)

NoOfPoints	number of points

XValues	array of values for X coordinates (see also Arrays in Functions)

YValues	array of values for Y coordinates (see also Arrays in Functions)

ZValues	array of values for Z coordinates (see also Arrays in Functions)

The GraphAddPlotXYZ function allows you to add the specified 3D plot to the graph.

RandomAccess;

mygraph := OpenGraph('c:\stat\xyzplot.stg');

GraphAddPlotXYZ(mygraph, 'High Income', NCases, v3, v4, v5);

GraphSetXYZLayout(mygraph, DataLabels_Z, On, 0, 0);

This program will open a previously saved graph and then add a 3D scatterplot to the graph and further modify the new scatterplot.

Related topics:  GraphSetXYZLayout.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphAddMinMaxPlot

  STATISTICA BASIC Library of Graph Functions - GraphAddMinMaxPlot (Graph, PlotType, ?Name$, NoOfPoints, XValues, TopValues, BottomValues)

Parameters:

Graph	graph handle

PlotType	type of plot to add:  MINMAX_X or MINMAX_Y

?Name$	string with legend name (see Strings in Functions)

NoOfPoints	number of points

XValues	array containing values for X coordinates (see also Arrays in Functions)

TopValues	array containing the maximum values (see also Arrays in Functions)

BottomValues	array containing the minimum values (see Arrays in Functions)

The GraphAddMinMaxPlot function allows you to add the specified min-max plot to an existing graph.  Note that if you wish to create a new min-max plot, it is first necessary to define a new graph (using the NewGraph function; set the plot type to IGNOREDPLOT), then use the GraphAddMinMaxPlot function to add the desired min-max plot to this graph.

RandomAccess;

mygraph := NewGraph(IGNOREDPLOT, 'Success in the Workplace', 'Low Income', 'Mid Income',

                   1, v1, v2);

minmax := GraphAddMinMaxPlot(mygraph, MinMax_X, ?name$, NCases, v3, v4, v5);

GraphSetPlot2DLayout(mygraph, minmax, MINMAX_X, ?DataLabels, BAR_WHISKERS, 0.8,

                    ?DevLevel, ?IsRightAxis);

This program will create a new graph, add a new Min-Max X plot to the graph, and then modify the new min-max plot.

Related topics:  GraphAddPlot, GraphAddBWPlot, and GraphAddRangePlot.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphAddRangePlot

  STATISTICA BASIC Library of Graph Functions - GraphAddRangePlot (Graph, ?MidPointName$, ?RangeName$, NoOfPoints, XValues, MidValues, TopValues, BottomValues)

Parameters:

Graph	graph handle

?MidPointNames$	string with legend name of midpoint (see Strings in Functions)

?RangeName$	string with legend name of ranges (see Strings in Functions)

NoOfPoints	number of points

XValues	array containing values for X coordinates (see also Arrays in Functions)

MidValues	array containing the midpoint values (see Arrays in Functions)

TopValues	array containing the upper-range values (see Arrays in Functions)

BottomValues	array containing the lower-range values (see Arrays in Functions)

The GraphAddRangePlot function allows you to add a 2D range plot to the graph.

RandomAccess;

graph := OpenGraph('c:\graph4.stg');

plot := GraphAddRangePlot(graph, 'Midpoints', 'Range', NCases, v5, v3, v4, v7);

GraphSetRangePlot2DLayout(graph, plot, DataLabels_Off, 1, .5, ?IsRightAxis);

GraphSetPlotPointStyle(graph, plot, ON, P_SQUARE, 5, RED);

This program will open a previously saved graph and then add a new range plot to the graph.  Note that the added range plot is actually added in two plots -- the first plot for the range (variable plot-1) and next plot for the midpoints (variable plot).  You can modify the midpoints via the functions GraphSetPlot2DLayout or GraphSetPlotPointStyle, and the ranges via the GraphSetRangePlot2DLayout function (see the example above).

Related topics:  GraphAddPlot, GraphAddBWPlot, GraphAddMinMaxPlot, GraphSetPlotPointStyle, GraphSetPlot2DLayout, and GraphSetRangePlot2DLayout.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphAddBWPlot

  STATISTICA BASIC Library of Graph Functions - GraphAddBWPlot (Graph, ?MidPointName$, ?BWInsideName$, ?BWOutsideName$, NoOfPoints, XValues, MidValues, InsideTopValues, InsideBottomValues, OutsideTopValues, OutsideBottomValues)

Parameters:

Graph	graph handle

?MidPointNames$	string with legend name of midpoints (see Strings in Functions)

?BWInsideName$	string with legend name of box (see Strings in Functions)

?BWOutsideName$	string with legend name of whiskers (see Strings in Functions)

NoOfPoints	number of points

XValues	array containing values for X coordinates (see also Arrays in Functions)

MidValues	array containing the midpoint values (see Arrays in Functions)

InsideTopValues	array containing the upper-box values (see Arrays in Functions)

InsideBottomValues	array containing the lower-box values (see Arrays in Functions)

OutsideTopValues	array containing the upper-whisker values (see Arrays in Functions)

OutsideBottomValues	array containing the lower-whisker values (see Arrays in Functions)

The GraphAddBWPlot function allows you to add a 2D box-whisker plot to the graph.

RandomAccess;

mygraph := OpenGraph('c:\graph4.stg');

newplot := GraphAddBWPlot(mygraph, 'Mean', 'Standard Error', 'Standard Deviation', 10, v5,

                         v3, v4, v7, v8, v9);

GraphSetBWPlot2DLayout(mygraph, newplot, ?DataLabels, BAR_COLUMNS, BAR_WHISKERS, .5,

                        .6, ?IsRightAxis);

GraphSetPlotPointStyle(mygraph, newplot, ON, P_STAR, 5, RED); {this statement modifies

                                                                 the midpoint in the box-

                                                                 whisker plot}

This program will open a previously saved graph and then add a new box-whisker plot to the graph.  Note that the added box-whisker plot is actually added in three plots -- the first plot for the box (variable newplot-2), the second plot for the whiskers (variable newplot-1), and third plot for the midpoints (variable newplot).  You can modify the midpoints via the GraphSetPlot2DLayout or GraphSetPlotPointStyle functions, and the box and whiskers via the GraphSetBWPlot2DLayout function (see the above example).

Related topics:  GraphAddPlot, GraphAddMinMaxPlot, GraphAddRangePlot, GraphSetPlotPointStyle, GraphSetPlot2DLayout, and GraphSetBWPlot2DLayout.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetEyePosition

  STATISTICA BASIC Library of Graph Functions - GraphSetEyePosition (Graph, X, Y, Z)

Parameters:

Graph	graph handle

X	X-axis position

Y	Y-axis position

Z	Z-axis position

The GraphSetEyePosition function allows you to specify the viewpoint for the 3D graph. This option allows you to expose specific aspects of the 3D display for analytic purposes and also to create special presentation effects by changing the perspective of the graph.  The GraphSetEyePosition function parameters determine the location of the "view point" of the graph separately for each of the three axes X, Y, and Z.  The absolute value of each parameter determines the distance between the eye and the respective axis (i.e., the degree of the perspective transformation for the respective plane).  The sign of the parameter determines the side from which the axis is viewed (i.e., a value of 0 represents the "facing position" and no perspective transformation; negative and positive values represent left and right or up and down shifts of the viewpoint, respectively).

RandomAccess;

surf_plot := NewSurface(Fit_Quadratic_3D, ?FunctionName$, 'Surface Plot',

                       'X-axis', 'Y-axis', 'Z-axis', NCases, v3, v4, v5);

GraphSetXYZFittingFunction(surf_plot, 'z = x^3 + y^2');

GraphSetEyePosition(surf_plot, -2.5, -3, 3);

This program will create a 3D surface plot with a specified user-defined function fitted to the data.  A custom viewpoint is then selected from which to view the graph.

Related topics: GraphSetMappingArea, GraphChangeMappingBase.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetPlot2DLayout

  STATISTICA BASIC Library of Graph Functions - GraphSetPlot2DLayout (Graph, PlotNumber, PlotType, ?DataLabels, ?BarStyle, ?BarWidth, ?DevLevel, ?IsRightAxis)

Parameters:

Graph	graph handle

PlotNumber	number of plot to be changed or edited

PlotType	plot type:  SCATTERPLOT, LINEPLOT, STEPPLOT, MINMAX_X, MINMAX_Y, BARPLOT, BARLEFTPLOT, BARRIGHTPLOT, BARTOPPLOT, PIECHART, MULTIPATTERNBAR, VORONOIPLOT, or IGNOREDPLOT

?DataLabels	data labels:  DATALABELS_OFF, DATALABELS_TEXT, DATALABELS_X, DATALABELS_Y, or DATALABELS_X_Y

?BarStyle	bar style:  BAR_COLUMNS, BAR_LINES, BAR_WHISKERS, or BAR_RECTANGLES

?BarWidth	width of bar (in units of the respective axis)

?DevLevel	deviation level for deviation plots

?IsRightAxis	scale plot along right axis:  TRUE or FALSE

The GraphSetPlot2DLayout function allows you to modify the specified components of plots in 2D graphs.

RandomAccess;

mygraph := NewGraph(STEPPLOT, 'Success in the Workplace', 'Low Income', 'Mid Income',

                   NCases, v1, v2);

GraphSetPlot2DLayout(mygraph, 1, StepPlot, DataLabels_X_Y, ?BarStyle, ?BarWidth, ?DevLevel,

                    False);

This program will create a 2D step plot and then modify the graph by turning on display of data point labels (XY coordinates).

Other functions used in this example:  RandomAccess and  NewGraph.

Related topics:  GraphAddPlot, GraphSetBWPlot2DLayout, GraphSetRangePlot2DLayout, GraphSetPieLayout, and GraphSetXYZLayout.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetPieLayout

  STATISTICA BASIC Library of Graph Functions - GraphSetPieLayout (graph, PlotNumber, ?Style, ?Shape, CenterX, CenterY, RadiusX, RadiusY, StartAngle, ?LabelsType, ?ExplodedSlice)

Parameters:

Graph	graph handle

PlotNumber	plot number to be changed or edited

?Style	pie style:  PIE_2D or PIE_3D

?Shape	pie shape:  PIE_CIRCLE or PIE_ELLIPSE

CenterX	x coordinate of the center of the pie

CenterY 	y coordinate of the center of the pie

RadiusX	x radius of the pie

RadiusY 	y radius of the pie

StartAngle	angle of starting slice

?LabelsType	pie labels:  PIE_LABELS_OFF, PIE_LABELS_PERC, PIE_LABELS_VALUES, PIE_LABELS_TEXT, PIE_LABELS_TEXT_PERC, or PIE_LABELS_TEXT_VALUES

?ExplodedSlice	number of slice to eplode

The GraphSetPieLayout function allows you to specify several pie chart characteristics.

Example:

RandomAccess;

new_graph := NewGraph(PIECHART, 'PieChart', ?Left_Title$, ?Bottom_Title$, NCases, v1, v2);

GraphSetPieLayout(new_graph, 1, Pie_3D, Pie_Ellipse, 0, 0, 25, 25, 0, Pie_Labels_Perc, 1);

This program will first create a pie chart and then modify that chart.

Related topics: GraphSetPieStyle, GraphAddPlot, GraphSetPlot2DLayout, GraphSetBWPlot2DLayout, GraphSetRangePlot2DLayout, and GraphSetXYZLayout.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetPieStyle

  STATISTICA BASIC Library of Graph Functions - GraphSetPieStyle (graph, PlotNumber, ?Style, ?Shape, ?LabelsType, ?ExplodedSlice)

Parameters:

Graph	graph handle

PlotNumber	plot number to be changed or edited

?Style	pie style:  PIE_2D or PIE_3D

?Shape	pie shape:  PIE_CIRCLE or PIE_ELLIPSE

?LabelsType	pie labels:  PIE_LABELS_OFF, PIE_LABELS_PERC, PIE_LABELS_VALUES, PIE_LABELS_TEXT, PIE_LABELS_TEXT_PERC, or PIE_LABELS_TEXT_VALUES

?ExplodedSlice	number of slice to eplode

The GraphSetPieStyle function allows you to specify several pie chart characteristics.

Example:

RandomAccess;

new_graph := NewGraph(PIECHART, 'PieChart', ?Left_Title$, ?Bottom_Title$, NCases, v1, v2);

GraphSetPieStyle(new_graph, 1, Pie_2D, Pie_CIRCLE, Pie_Labels_Perc, 1);

This program will first create a pie chart and then modify that chart.

Related topics: GraphSetPieLayout, GraphSetPlotAreaStyle, GraphSetPlotBarLineStyle, GraphSetPlotFitLineStyle, GraphSetPlotLineStyle, and GraphSetPlotPointStyle.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetRangePlot2DLayout

  STATISTICA BASIC Library of Graph Functions - GraphSetRangePlot2DLayout (Graph, PlotNumber, ?DataLabels, ?BarStyle, ?BarWidth, ?IsRightAxis)

Parameters:

Graph	graph handle

PlotNumber	plot number to be changed or edited

?DataLabels	data labels:  DATALABELS_OFF, DATALABELS_TEXT, DATALABELS_X, DATALABELS_Y, or DATALABELS_X_Y

?BarStyle	bar style:  BAR_COLUMNS, BAR_LINES, BAR_WHISKERS, or BAR_RECTANGLES

?BarWidth	width of bar (in points)

?IsRightAxis	scale plot along right axis:  TRUE or FALSE

The GraphSetRangePlot2DLayout function allows you to modify a 2D range plot.

RandomAccess;

graph:=OpenGraph('c:\graph4.stg');

plot := GraphAddRangePlot(graph, 'Midpoints', 'Range', NCases, v5, v3, v4, v7);

GraphSetRangePlot2DLayout(graph, plot, DataLabels_Off, BAR_COLUMNS, .5, ?IsRightAxis);

This program will open a previously saved graph and then add a new range plot to the graph.  Note that the range plot is actually added in two plots -- one plot for the range and one plot for the midpoints.  The GraphSetRangePlot2DLayout function allows you to modify the ranges (see the example above) while the midpoints can be modified via the GraphSetPlot2DLayout function.

Related topics: GraphAddRangePlot, GraphSetBWPlot2DLayout, GraphSetPieLayout, GraphSetPlot2DLayout, and GraphSetXYZLayout.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetBWPlot2DLayout

  STATISTICA BASIC Library of Graph Functions - GraphSetBWPlot2DLayout (Graph, PlotNumber, ?DataLabels, ?InsideBarStyle, ?OutsideBarStyle, ?InsideBarWidth, ?OutsideBarWidth, ?IsRightAxis)

Parameters:

Graph	graph handle

PlotNumber	plot number to be changed or edited

?DataLabels	data labels:  DATALABELS_OFF, DATALABELS_TEXT, DATALABELS_X, DATALABELS_Y, or DATALABELS_X_Y

?InsideBarStyle	bar style of box:  BAR_COLUMNS, BAR_LINES, BAR_WHISKERS, or BAR_RECTANGLES

?OutsideBarStyle	bar style of whiskers:  BAR_COLUMNS, BAR_LINES, BAR_WHISKERS, or BAR_RECTANGLES

?InsideBarWidth	width of bar style in box (in points)

?OutsideBarWidth	width of bar style in whiskers (in points)

?IsRightAxis	scale plot along right axis:  TRUE or FALSE

The GraphSetBWPlot2DLayout function allows you to modify a 2D box-whisker plot.

RandomAccess;

graph:=OpenGraph('c:\graph4.stg');

plot := GraphAddBWPlot(graph, 'Mean', 'Standard Error', 'Standard Deviation', 10, v5,

                      v3, v4, v7, v8, v9);

GraphSetBWPlot2DLayout(graph, plot, ?DataLabels, BAR_COLUMNS, BAR_WHISKERS, .5,

                      .6, ?IsRightAxis);

This program will open a previously saved graph and then add a new box-whisker plot to the graph.  Note that the box-whisker plot is actually added in three plots -- one plot for the box (which could be referenced in a program as plot-2), one plot for the whiskers (plot-1), and one plot for the midpoints (plot).  The box and whiskers can be modified using the GraphSetBWPlot2DLayout function (see the above example), while the midpoints can be modified via the GraphSetPlot2DLayout function.

Related topics:  GraphSetPieLayout, GraphSetBWPlot2DLayout, GraphSetPlot2DLayout, GraphSetRangePlot2DLayout, and GraphSetXYZLayout.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetXYZLayout

  STATISTICA BASIC Library of Graph Functions - GraphSetXYZLayout (Graph, ?DataLabels, ?IsSpike, ?DevLevel, ?NumberSpectralPlanes)

Parameters:

Graph	graph handle

?DataLabels	data labels:  DATALABELS_OFF, DATALABELS_TEXT, DATALABELS_X, DATALABELS_Y, DATALABELS_X_Y, DATALABELS_Z, DATALABELS_X_Z, DATALABELS_Y_Z, or DATALABELS_X_Y_Z

?IsSpike	draw spike lines:  ON or OFF

?DevLevel	deviation level

NumberSpectralPlanes	number of spectral planes

The GraphSetXYZLayout function will modify the layout of the specified 3D XYZ graph.

Example:

RandomAccess;

graph := NewGraphXYZ(SPECTRALPLOTXYZ, 'Stats Graph 3D XYZ Spectral Plot',

                    'X-axis', 'Y-axis', 'Z-axis', NCases, v15, v4, v25);

GraphSetXYZLayout(graph, DataLabels_X, On, 0, 5);

This program will create a 3D spectral plot and then modify that graph.

Related topics:  NewGraphXYZ, GraphSetBWPlot2DLayout, GraphSetPieLayout, GraphSetPlot2DLayout, GraphSetRangePlot2DLayout, GraphSetXYZFittingFunction, and GraphSetXYZFittingParam.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetXYZFittingFunction

  STATISTICA BASIC Library of Graph Functions - GraphSetXYZFittingFunction (Graph, Function$)

Parameters:

Graph	graph handle

?Function	user-defined fitting function

The GraphSetXYZLayout function will fit a user-defined function to the specified 3D XYZ graph.

Example:

RandomAccess;

surf_plot := NewSurface(Fit_Quadratic_3D, ?FunctionName$, 'Surface Plot',

                       'X-axis', 'Y-axis', 'Z-axis', NCases, v3, v4, v5);

GraphSetXYZFittingFunction(surf_plot, 'z = x^3 + sqrt(y)');

This program will create a 3D surface plot and then fit the specified user-defined function to the data.

Related topics:  GraphSetXYZFittingParam, GraphSetXYZLayout, NewGraphXYZ.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetXYZFittingParam

  STATISTICA BASIC Library of Graph Functions - GraphSetXYZFittingParam (Graph, ?NumberCutsX, ?NumberCutsY, ?Spikes, ?SurfaceContour, ?SurfaceContourType, ?PolyOrder, ?LogBase10)

Parameters:

Graph	graph handle

?NumberCutsX	number of cuts on X-axis

?NumberCutsY	number of cuts on Y-axis

?Spikes	draw spikes to raw data points:  TRUE, FALSE or ON, OFF

?SurfaceContour	draw contour for surface plot:  TRUE, FALSE or ON, OFF

?SurfaceContourType	surface contour type:CONTOUR_LINES or CONTOUR_AREAS

?PolyOrder	order of polynomial

?LogBase10	use base 10 logarithm:  (TRUE = base 10, FALSE = base Euler)

The GraphSetXYZFittingParam function will modify the specified 3D XYZ graph.

Example:

RandomAccess;

surf_plot := NewSurface(Fit_Quadratic_3D, ?FunctionName$, 'Surface Plot',

                       'X-axis', 'Y-axis', 'Z-axis', NCases, v3, v4, v5);

GraphSetXYZFittingParam(surf_plot, 15, 20, Off, On, CONTOUR_Lines, 5, 10);

This program will create a 3D surface plot and then modify the graph.

Related topics: , GraphSetXYZLayout, NewGraphXYZ, GraphSetPlotFitting, GraphSetPlotFittingFunction, GraphSetPlotFittingParam, and GraphSetXYZFittingFunction.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetMatrixHistograms

  STATISTICA BASIC Library of Graph Functions - GraphSetMatrixHistograms (Graph, ?ScalingType, ?NumberOfBins)

Parameters:

Graph	graph handle

?ScalingType	scaling for matrix histograms:  MATRIX_HIST_OFF, MATRIX_HIST_COMMON, or MATRIX_HIST_INDEPENDENT

?NumberOfBins	number of bins for matrix histograms

The GraphSetMatrixHistograms function will modify the histograms in matrix graphs.

Example:

RandomAccess;

rect_matrix := NewRectMatrix(MATRIX_SCATTERPLOT, 'Rectangular Scatterplot Matrix', 'Rows',

                            'Columns', 5,  3, NCases, Data, 'Hist. Var1|Hist.

                             Var2|Hist. Var3|Hist. Var4|Hist. Var5|Hist.

                             Var6|Hist. Var7|Hist. Var8');

GraphSetMatrixHistograms(rect_matrix, MATRIX_HIST_COMMON, 8);

The above program will create a 3x5 rectangular scatterplot matrix graph with the first 3 variables in the data file as the matrix column variables and the next 5 variables as the matrix row variables.  Next, the histograms in the matrix graph will be modified.

Related topics:  NewMatrix, NewRectMatrix, and GraphSetPlot2DLayout.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - SetDrawingMatrixCoordinates

  STATISTICA BASIC Library of Graph Functions - SetDrawingMatrixCoordinates (Graph, XVar, YVar, ?IsHisto)

Parameters:

Graph	graph handle

XVar	column variable in matrix plot in which to place drawing

YVar	row variable in matrix plot in which to place drawing (if drawing is placed in histogram, this parameter is ignored)

?IsHisto	place drawing in histogram: TRUE or FALSE

The SetDrawingMatrixCoordinates function will select the row and column variables (or optionally, the histogram), as listed in the Graph Data Editor, in a matrix graph in which to place a drawing created using dynamic coordinates.

Example:

RandomAccess;

rect_matrix := NewRectMatrix(Matrix_SCATTERPLOT, 'Rectangular Scatterplot Matrix', 'Rows',

                            'Columns', 5,  3, NCases, Data, 'Hist. Var1|Hist.

                            Var2|Hist. Var3|Hist. Var4|Hist. Var5|Hist.

                            Var6|Hist. Var7|Hist. Var8');

SetDrawingMatrixCoordinates(rect_matrix, 2, 6, FALSE);

GraphDrawText(rect_matrix, 'Var2 x Var6', 85, 125);

The above program will create a 3x5 rectangular scatterplot matrix graph with the first 3 variables in the data file as the matrix column variables and the next 5 variables as the matrix row variables (for a total of 3+5=8 variables, which are placed in consecutive columns of the the Graph Data Editor).  Next, custom text is added to the scatterplot of the second by sixth variables at the specified, dynamic coordinates of that graph; specifically, the variable pair (individual scatterplot in the matrix plot) that is referenced (2, 6) is the second variable by the sixth variable.

Note that any text, drawing, arrows, etc. placed in this manner in the matrix scatterplot will be dynamically attached to the plot for that specific pair of variables (in the case of scatterplots).  Thus, if you later rearrange the order of variables in the plot (option Var. Order on the General Layout and Plot Layout - Matrix Graphs dialog; see Volume II), or the layout of the plot (e.g., change the number of rows and columns), the respective text will be moved to the same dynamic location in the plot for the same variables as before.

Related topics:  NewMatrix, NewRectMatrix, GraphSetPlot2DLayout, GraphDrawArrow, GraphDrawPolyline, GraphDrawShape, GraphDrawText, and GraphDrawTextParam.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetPlotPointStyle

  STATISTICA BASIC Library of Graph Functions - GraphSetPlotPointStyle (Graph, PlotNumber, ?Display, ?Pattern, ?Size, ?Color)

Parameters:

Graph	graph handle

PlotNumber	number of plot to be edited or changed

?Display	display points in graph:  ON or OFF

?Pattern	point marker pattern:  P_CROSS, P_STAR, P_FILLED_DIAMOND, P_FILLED_TRIANGLE, P_FILLED_SQUARE, P_FILLED_CIRCLE, P_DIAMOND, P_TRIANGLE, P_SQUARE, P_CIRCLE, or P_HORIZONTAL_LINE

?Size	size in points

?Color	color of points:  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

The GraphSetPlotPointStyle function allows you to customize point patterns, styles, etc. in the graph.

Example:

RandomAccess;

mynewgraph := NewGraph(SCATTERPLOT, 'Success in the Workplace', 'Low Income',

                      'Mid Income', NCases, v1, v2);

GraphSetPlotPointStyle(mynewgraph, 1, On, P_Star, 5, MAROON);

This program will create a 2D scatterplot and then customize the points in the graph.

Related topics:  GraphSetPlotLineStyle, GraphSetPlotAreaStyle, GraphSetPlotBarLineStyle, and ColorRGB.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetPlotLineStyle

  STATISTICA BASIC Library of Graph Functions - GraphSetPlotLineStyle (Graph, PlotNumber, ?Display, ?Pattern, ?Size, ?Color)

Parameters:

Graph	graph handle

PlotNumber	number of plot to be changed or edited

?Display	display line in graph:  ON or OFF

?Pattern	line pattern:  L_SOLID, L_LONG_DASH, L_SHORT_DASH, L_LONG_SHORT_DASH, L_LONG_SHORT_SHORT_DASH, L_DOTTED, or L_DENSE_DOTTED

?Size	size in points

?Color	color of line:  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

The GraphSetPlotLineStyle function allows you to customize line patterns, styles, etc. in the graph.

Example:

RandomAccess;

mynewgraph := NewGraph(LINEPLOT, 'Success in the Workplace', 'Low Income', 'Mid Income',

                      NCases, v1, v2);

GraphSetPlotLineStyle(mynewgraph, 1, On, L_Solid, 3, TEAL);

This program will create a 2D line plot  and then customize the lines in the graph.

Related topics:  GraphSetPlotPointStyle, GraphSetPlotAreaStyle, GraphSetPlotBarLineStyle, and ColorRGB.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetPlotAreaStyle

  STATISTICA BASIC Library of Graph Functions - GraphSetPlotAreaStyle (Graph, PlotNumber, ?Display, ?Pattern, ?Color)

Parameters:

Graph	graph handle

PlotNumber	number of plot

?Display	display area in graph:  ON or OFF

?Pattern	area pattern:	A_SOLID,  A_EMPTY,  A_HORIZONTAL_HATCH,  A_VERTICAL_HATCH,  A_FORWARD_DIAGONAL,  A_BACKWARD_DIAGONAL,  A_CROSS,  A_DIAGONAL_CROSS,  A_HORIZONTAL_HATCH_DENSE,  A_VERTICAL_HATCH_DENSE,  A_FORWARD_DIAGONAL_DENSE,  A_BACKWARD_DIAGONAL_DENSE,  A_HORIZONTAL_HATCH_H,  A_VERTICAL_HATCH_H,  A_FORWARD_DIAGONAL_H,  A_BACKWARD_DIAGONAL_H,  A_CROSS_H,  A_DIAGONAL_CROSS_H,  A_DOTS,  A_DENSE,  A_GENERIC,  A_CHESS,  A_BRICK,  or A_BALLS

?Color	color of pattern:  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

The GraphSetPlotAreaStyle function allows you to customize areas (e.g., columns, backgrounds, etc.) in the graph.

Example:

RandomAccess;

mygraph:=OpenGraph('c:\graph4.stg');

plot := GraphAddBWPlot(mygraph, 'Mean', 'Standard Error', 'Standard Deviation', 10, v5,

                      v3, v4, v7, v8, v9);

GraphSetBWPlot2DLayout(mygraph, plot, ?DataLabels, BAR_COLUMNS, ?OutsideBarStyle, .5,

                      ?OutsideBarWidth, ?IsRightAxis);

GraphSetPlotAreaStyle(mygraph, plot-1, On, A_Forward_Diagonal, Yellow);

This program will open a previously saved graph and add a new box-whisker plot to the graph.  Then, the area pattern and color of the boxes in the plot will be customized.

Related topics:  GraphSetPlotLineStyle, GraphSetPlotPointStyle, GraphSetPlotBarLineStyle, and ColorRGB.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetPlotName

  STATISTICA BASIC Library of Graph Functions - GraphSetPlotName (Graph, PlotNumber, ?Name1$, ?Name2$)

Parameters:

Graph	graph handle

PlotNumber	number of plot to be changed

?Name1$	string for first line of legend (see Strings in Functions)

?Name2$	string for second line of legend (see Strings in Functions)

The GraphSetPlotName function allows you to customize the plot names (legends) of the specified plot in the graph.

Example:

RandomAccess;

mygraph:=OpenGraph('c:\graph4.stg');

newplot:=GraphAddPlot(mygraph, SCATTERPLOT, 'Income', NCases, v3, v4);

GraphSetPlotName(mygraph, newplot, 'Median', 'Income');

This program will open a previously saved graph and add a new scatterplot to the graph, then customize the legend names of the new plot.

Related topics:  GraphSetPlotAreaStyle, GraphSetPlotLineStyle, GraphSetPlotPointStyle, GraphSetPlotBarLineStyle, and ColorRGB.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetPlotBarLineStyle

  STATISTICA BASIC Library of Graph Functions - GraphSetPlotBarLineStyle (Graph, PlotNumber, ?Display, ?Pattern, ?Size, ?Color)

Parameters:

Graph	graph handle

PlotNumber	number of plot to be changed or edited

?Display	display bar in graph:  ON or OFF

?Pattern	bar line pattern:  L_SOLID, L_LONG_DASH, L_SHORT_DASH, L_LONG_SHORT_DASH, L_LONG_SHORT_SHORT_DASH, L_DOTTED, or L_DENSE_DOTTED

?Size	size in points

?Color	color of line:  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

The GraphSetPlotBarLineStyle function allows you to customize the bar line pattern, color, and size in the graph.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph5.stg');

plot := GraphAddPlot(mygraph, BARPLOT, 'High Income', NCases, v3, v4);

GraphSetPlot2DLayout(mygraph, plot, BARPLOT, DataLabels_Off, BAR_COLUMNS, 1, ?DevLevel,

                    ?IsRightAxis);

GraphSetPlotBarLineStyle(mygraph, plot, On, L_Dotted, 1, Green);

This program will open a previously saved graph and add a bar plot to the graph.  Then, the pattern and color of the bars in the plot will be customized.

Related topics: GraphSetPlotAreaStyle, GraphSetPlotLineStyle, GraphSetPlotPointStyle, GraphSetPlot2DLayout, GraphSetPlotFitLineStyle, and ColorRGB.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetPlotFitLineStyle

  STATISTICA BASIC Library of Graph Functions - GraphSetPlotFitLineStyle (graph, PlotNumber, ?Display, ?Pattern, ?Size, ?Color)

Parameters:

Graph	graph handle

PlotNumber	number of plot to be edited or changed

?Display	display bar in graph:  ON or OFF

?Pattern	bar line pattern:  L_SOLID, L_LONG_DASH, L_SHORT_DASH, L_LONG_SHORT_DASH, L_LONG_SHORT_SHORT_DASH, L_DOTTED, or L_DENSE_DOTTED

?Size	size in points

?Color	color of line:  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

The GraphSetPlotFitLineStyle function allows you to customize the fitting line pattern, color, and size in the graph.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph5.stg');

GraphSetPlotFitting(mygraph, 1, Fit_POLYNOMIAL);

GraphSetPlotFitLineStyle(mygraph, 1, On, L_LONG_DASH, 1, LIME);

This program will open a previously saved graph and fit a polynomial function to the data.  Then, the pattern and color of this fitting line will be customized.

Related topics: GraphSetPlotAreaStyle, GraphSetPlotBarLineStyle, GraphSetPlotLineStyle, GraphSetPlotPointStyle, GraphSetPlot2DLayout, and ColorRGB.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphEmbedGraph

  STATISTICA BASIC Library of Graph Functions - GraphEmbedGraph (Graph, EmbededGraph, ?OrigProportion, ?Frame, ?MappingMode, Left, Top, Right, Bottom, ?Dynamic)

Parameters:

Graph	graph handle in which to embed graph object

EmbededGraph	graph handle handle of graph object to be embedded

?OrigProportion	retain original proportion of the embedded object:  TRUE or FALSE

?Frame	place frame around embedded graph:  TRUE or FALSE

?MappingMode	graph mapping mode:  MAPPING_FIXEDSIZE, MAPPING_ISOTROPIC, MAPPING_ANISOTROPIC (default = MAPPING_ISOTROPIC)

Left	upper-left X coordinate of the object (in fixed coordinates)

Top	upper-left Y coordinate of the object (in fixed coordinates)

Right	lower-right X coordinate of the object (in fixed coordinates)

Bottom	lower-right Y coordinate of the object (in fixed coordinates)

?Dynamic	use dynamic graph coordinates:  TRUE or FALSE (default = FALSE)

The GraphEmbedGraph function allows you to embed a specified STATISTICA graph into another specified graph.  After embedding, the embedded graph's handle is no longer accessible, because it has become an embedded object (and is no longer displayed in a separate window).  If you wish to maintain access to that graph, use the DuplicateGraph function.

Example:

RandomAccess;

graph1 := OpenGraph('c:\graph1.stg');

graph2 := OpenGraph('c:\graph4.stg');

GraphEmbedGraph(graph1, graph2, TRUE, FALSE, MAPPING_ANISOTROPIC, 80, 22, 120, 2, TRUE);

This program will open two previously saved graphs and embed graph2 into graph1.

Related topics:  DuplicateGraph.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphEmbedGraph3D

  STATISTICA BASIC Library of Graph Functions - GraphEmbedGraph3D (Graph, EmbededGraph, ?OrigProportion, ?Frame, ?MappingMode, X1, Y1, Z1, X2, Y2, Z2)

Parameters:

Graph	graph handle in which to embed graph object

EmbededGraph	graph handle handle of graph object to be embedded

?OrigProportion	retain original proportion of the embedded object:  TRUE or FALSE

?Frame	place frame around embedded graph:  TRUE or FALSE

?MappingMode	graph mapping mode:  MAPPING_FIXEDSIZE, MAPPING_ISOTROPIC, MAPPING_ANISOTROPIC (default = MAPPING_ISOTROPIC)

X1	dynamic X coordinate of the upper left corner of the object

Y1	dynamic Y coordinate of the upper left corner of the object

Z1	dynamic Z coordinate of the upper left corner of the object

X2	dynamic X coordinate of the lower right corner of the object

Y2	dynamic Y coordinate of the lower right corner of the object

Z2	dynamic Z coordinate of the lower right corner of the object

The GraphEmbedGraph3D function allows you to embed a specified STATISTICA graph into another specified 3D graph.  After embedding, the embedded graph's handle is no longer accessible, because it has become an embedded object (and is no longer displayed in a separate window).  If you wish to maintain access to that graph, use the DuplicateGraph function.

Example:

RandomAccess;

graph1 := OpenGraph('c:\graph1.stg');

graph2 := OpenGraph('c:\graph4.stg');

GraphEmbedGraph3D(graph1, graph2, TRUE, FALSE, MAPPING_FIXEDSIZE, 20, 80, 38, 40, 30, 85);

This program will open two previously saved graphs and embed graph2 into graph1.

Related topics:  DuplicateGraph.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphEmbedGraphTernary
  STATISTICA BASIC Library of Graph Functions - GraphEmbedGraphTernary (Graph, EmbededGraph, ?OrigProportion, ?Frame, ?MappingMode, X1, Y1, Z1, V1, X2, Y2, Z2, V2)

Parameters:

Graph	graph handle in which to embed graph object

EmbededGraph	graph handle handle of graph object to be embedded

?OrigProportion	retain original proportion of the embedded object:  TRUE or FALSE

?Frame	place frame around embedded graph:  TRUE or FALSE

?MappingMode	graph mapping mode:  MAPPING_FIXEDSIZE, MAPPING_ISOTROPIC, MAPPING_ANISOTROPIC (default = MAPPING_ISOTROPIC)

X1	dynamic X-axis coordinate of the upper left corner of the object

Y1	dynamic Y-axis coordinate of the upper left corner of the object

Z1	dynamic Z-axis coordinate of the upper left corner of the object

V1	dynamic vertical coordinate of the upper left corner of the object

X2	dynamic X-axis coordinate of the lower right corner of the object

Y2	dynamic Y-axis coordinate of the lower right corner of the object

Z2	dynamic Z-axis coordinate of the lower right corner of the object

V1	dynamic vertical coordinate of the lower right corner of the object

The GraphEmbedGraphTernary function allows you to embed a specified STATISTICA graph into another specified ternary (trilinear) graph.  After embedding, the embedded graph's handle is no longer accessible, because it has become an embedded object (and is no longer displayed in a separate window).  If you wish to maintain access to that graph, use the DuplicateGraph function.

Example:

RandomAccess;

graph1 := OpenGraph('c:\graph1.stg');

graph2 := OpenGraph('c:\graph4.stg');

GraphEmbedGraphTernary(graph1, graph2, TRUE, FALSE, MAPPING_ISOTROPIC, 0.2, 0.3, 0.5, 15,

                       0.3, 0.4, 0.3, 20);

This program will open two previously saved graphs and embed graph2 into graph1.

Related topics:  DuplicateGraph.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphInsertFile

  STATISTICA BASIC Library of Graph Functions - GraphInsertFile (graph, FileName$, ?OrigProportion, ?Frame, Left, Top, Right, Bottom, ?Dynamic)

Parameters:

Graph	graph handle in which to embed graph object

FileName$	string containing name of object to be embedded (see Strings in Functions)

?OrigProportion	retain original proportion of the embedded object:  TRUE or FALSE

?Frame	place frame around embedded object:  TRUE or FALSE

Left	upper-left X coordinate of the object

Top	upper-left Y coordinate of the object

Right	lower-right X coordinate of the object

Bottom	lower-right Y coordinate of the object

?Dynamic	use dynamic graph coordinates:  TRUE or FALSE (default = FALSE)

The GraphInsertFile function allows you to embed an object from a file (e.g., a metafile, bitmap, or other OLE-compliant object) into the specified graph.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph1.stg');

GraphInsertFile (mygraph, 'c:\car.bmp', TRUE, FALSE, 7, 3, 10, 5, TRUE);

This program will open a previously saved graph and embed the specified bitmap at the specified dynamic graph coordinates.

Related topics:  GraphInsertFile3D, GraphInsertFileTernary, GraphEmbedGraph.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphInsertFile3D

  STATISTICA BASIC Library of Graph Functions - GraphInsertFile3D (graph, FileName$, ?OrigProportion, ?Frame, X1, Y1, Z1, X2, Y2, Z2)

Parameters:

Graph	graph handle in which to embed graph object

FileName$	string containing name of object to be embedded (see Strings in Functions)

?OrigProportion	retain original proportion of the embedded object:  TRUE or FALSE

?Frame	place frame around embedded object:  TRUE or FALSE

X1	dynamic X coordinate of the upper left corner of the object

Y1	dynamic Y coordinate of the upper left corner of the object

Z1	dynamic Z coordinate of the upper left corner of the object

X2	dynamic X coordinate of the lower right corner of the object

Y2	dynamic Y coordinate of the lower right corner of the object

Z2	dynamic Z coordinate of the lower right corner of the object

The GraphInsertFile3D function allows you to embed an object from a file (e.g., a metafile, bitmap, or other OLE-compliant object) into the specified 3D graph at the specified, dynamic axis coordinates.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph1.stg');

GraphInsertFile3D(mygraph, 'c:\car.bmp', TRUE, FALSE, 17, 13, 10, 25, 20, 30);

This program will open a previously saved 3D graph and embed the specified bitmap at the specified dynamic graph coordinates.

Related topics:  GraphInsertFile, GraphInsertFileTernary, GraphEmbedGraph.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphInsertFileTernary

  STATISTICA BASIC Library of Graph Functions - GraphInsertFileTernary (graph, FileName$, ?OrigProportion, ?Frame, X1, Y1, Z1, V1, X2, Y2, Z2, V2)

Parameters:

Graph	graph handle in which to embed graph object

FileName$	string containing name of object to be embedded (see Strings in Functions)

?OrigProportion	retain original proportion of the embedded object:  TRUE or FALSE

?Frame	place frame around embedded object:  TRUE or FALSE

X1	dynamic X-axis coordinate of the upper left corner of the object

Y1	dynamic Y-axis coordinate of the upper left corner of the object

Z1	dynamic Z-axis coordinate of the upper left corner of the object

V1	dynamic vertical coordinate of the upper left corner of the object

X2	dynamic X-axis coordinate of the lower right corner of the object

Y2	dynamic Y-axis coordinate of the lower right corner of the object

Z2	dynamic Z-axis coordinate of the lower right corner of the object

V1	dynamic vertical coordinate of the lower right corner of the object

The GraphInsertFile3D function allows you to embed an object from a file (e.g., a metafile, bitmap, or other OLE-compliant object) into the specified ternary (trilinear) graph at the specified, dynamic axis coordinates.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph1.stg');

GraphInsertFileTernary(mygraph, 'c:\car.bmp', TRUE, FALSE, 0.3, 0.3, 0.4, 11,

                       0.2, 0.5, 0.3, 17);

This program will open a previously saved ternary (trilinear) graph and embed the specified bitmap at the specified dynamic graph coordinates.

Related topics:  GraphInsertFile, GraphInsertFile3D, GraphEmbedGraph.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphGetHwnd

  STATISTICA BASIC Library of Graph Functions - GraphGetHwnd (Graph)

Parameters:

Graph	graph handle

The GraphGetHwnd function returns the window handle of the graph with the specified graph handle.

Example:

RandomAccess;

OpenGraph('c:\new.stg');

graph1 := GraphGetHwnd(GetGraph(0));

This program will open a previously saved graph and place the window handle value in the variable graph1.

Related topics: OpenGraph, GetGraph.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphDrawText

  STATISTICA BASIC Library of Graph Functions - GraphDrawText (Graph, Text$, Xpos, Ypos, ?Dynamic)

Parameters:

Graph	graph handle

Text$	string to be "drawn" in the graph (see Strings in Functions)

Xpos	fixed X-axis coordinate of upper-left corner of the text (positon of anchor point)

Ypos	fixed Y-axis coordinate of upper-left corner of the text (positon of anchor point)

?Dynamic	use dynamic graph coordinates:  TRUE or FALSE (default = FALSE)

The GraphDrawText function allows you to place added text into the specified graph.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph5.stg');

GraphDrawText(mygraph, 'This is some text to be added to the graph', 15, 90, ?DYNAMIC);

This program will open a previously saved graph and place the specified text at the specified position in the graph.

Related topics: GraphDrawArrow, GraphDrawPolyline, GraphDrawShape, GraphDrawTextParam, GraphEmbedGraph, GraphSetDefaultFont, GraphSetObjectAreaStyle, and GraphSetObjectLineStyle.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphDrawText3D

  STATISTICA BASIC Library of Graph Functions - GraphDrawText3D (Graph, Text$, X, Y, Z)

Parameters:

Graph	graph handle

Text$	string to be "drawn" in the graph (see Strings in Functions)

X	dynamic X-axis coordinate of upper-left corner of the text (positon of anchor point)

Y	dynamic Y-axis coordinate of upper-left corner of the text (positon of anchor point)

Z	dynamic Z-axis coordinate of upper-left corner of the text (positon of anchor point)

The GraphDrawText3D function allows you to place added text into the specified 3D graph at the specifed dynamic graph axis coordinates.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph5.stg');

GraphDrawText3D(mygraph, 'This is some text to be added to the graph', 15, 90, 45);

This program will open a previously saved 3D graph and place the specified text at the specified, dynamic 3D coordinates in the graph.

Related topics: GraphDrawArrow3D, GraphDrawShape3D, GraphDrawTextParam3D, and NewGraphXYZ.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphDrawTextTernary

  STATISTICA BASIC Library of Graph Functions - GraphDrawTextTernary (Graph, Text$, X, Y, Z, V)

Parameters:

Graph	graph handle

Text$	string to be "drawn" in the graph (see Strings in Functions)

X	dynamic X-axis coordinate of upper-left corner of the text (positon of anchor point)

Y	dynamic Y-axis coordinate of upper-left corner of the text (positon of anchor point)

Z	dynamic Z-axis coordinate of upper-left corner of the text (positon of anchor point)

V	dynamic V-axis coordinate of upper-left corner of the text (positon of anchor point)

The GraphDrawTextTernary function allows you to place added text into the specified ternary (trilinear) graph at the specifed, dynamic graph axis coordinates.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph5.stg');

GraphDrawTextTernary(mygraph, 'This is some text to be added to the graph', 0.3, 0.2, 0.5 15);

This program will open a previously saved ternary (trilinear) graph and place the specified text at the specified dynamic triangular coordinates in the graph.

Related topics: GraphDrawArrowTernary, GraphDrawShapeTernary, GraphDrawTextParamTernary, and NewTernary.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphDrawTextParam

  STATISTICA BASIC Library of Graph Functions - GraphDrawTextParam (Graph, Text$, ?FontName$, ?FontSize, ?Color, ?Orientation, ?HorizAlignment, ?VertAlignment, ?Border, ?Fill, X, Y, ?Dynamic)

Parameters:

Graph	graph handle

Text$	string to be "drawn" in the graph (see Strings in Functions)

?FontName$	name of font

?FontSize	size of font (in points)

?Color	color of font:  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

?Orientation	text angle:  specify angle between 0 and 360 or use O_HORIZONTAL, O_VERTICAL_LEFT, O_VERTICAL_RIGHT

?HorizAlignment	horizontal alignment of text:  AL_LEFT, AL_CENTER, or AL_RIGHT

?VertAlignment	vertical alignment of text:  AL_TOP, AL_CENTER, or AL_BOTTOM

?Border	place border around text:  ON or OFF

?Fill	fill text area:  FILL_TRANSPARENT, FILL_WHITE, FILL_OUTSIDE_BACKGROUND, or FILL_INSIDE_BACKGROUND

X	fixed X-axis coordinate of upper-left corner of the text (positon of anchor point)

Y	fixed Y-axis coordinate of upper-left corner of the text (positon of anchor point)

?Dynamic	use dynamic graph coordinates:  TRUE or FALSE (default = FALSE)

The GraphDrawTextParam function allows you to place customized text in the specified graph.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph5.stg');

GraphDrawTextParam(mygraph, 'This is some text to be added to the graph', 'Arial',

      12, BLUE, O_VERTICAL_LEFT, Al_LEFT, Al_TOP, On, Fill_TRANSPARENT, 58, 65, ?DYNAMIC);

for i := 1 to 5 do

   GraphDrawTextParam(mygraph, 'Sample Text', 'Times New Roman' 16, RED, (I-1)*30,

       0, 0, ON, FILL_WHITE, 50, 50, ?DYNAMIC);

This program will open a previously saved graph and place the specified text at the specified position, alignment, orientation, etc. in the graph.

Related topics: GraphDrawArrow, GraphDrawPolyline, GraphDrawShape, GraphDrawText, GraphEmbedGraph, GraphSetDefaultFont, GraphSetObjectAreaStyle, and GraphSetObjectLineStyle.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphDrawTextParam3D

  STATISTICA BASIC Library of Graph Functions - GraphDrawTextParam3D (Graph, Text$, ?FontName$, ?FontSize, ?Color, ?Orientation, ?HorizAlignment, ?VertAlignment, ?Border, ?Fill, X, Y, Z)

Parameters:

Graph	graph handle

Text$	string to be "drawn" in the graph (see Strings in Functions)

?FontName$	name of font

?FontSize	size of font (in points)

?Color	color of font:  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

?Orientation	text angle:  specify angle between 0 and 360 or use O_HORIZONTAL, O_VERTICAL_LEFT, O_VERTICAL_RIGHT

?HorizAlignment	horizontal alignment of text:  AL_LEFT, AL_CENTER, or AL_RIGHT

?VertAlignment	vertical alignment of text:  AL_TOP, AL_CENTER, or AL_BOTTOM

?Border	place border around text:  ON or OFF

?Fill	fill text area:  FILL_TRANSPARENT, FILL_WHITE, FILL_OUTSIDE_BACKGROUND, or FILL_INSIDE_BACKGROUND

X	dynamic X-axis coordinate of upper-left corner of the text (positon of anchor point)

Y	dynamic Y-axis coordinate of upper-left corner of the text (positon of anchor point)

Z	dynamic Z-axis coordinate of upper-left corner of the text (positon of anchor point)

The GraphDrawTextParam3D function allows you to place customized text in the specified 3D graph at specific, dynamic axis coordinates.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph5.stg');

GraphDrawTextParam(mygraph, 'Some text to be added to the graph', 'Arial', 12, BLUE,

                  O_VERTICAL_LEFT, Al_LEFT, Al_TOP, On, Fill_TRANSPARENT, 58, 65, 87);

for i := 1 to 5 do

   GraphDrawTextParam(mygraph, 'Sample Text','Times New Roman' 16,

                     RED, (i-1)*30, 0, 0, ON, FILL_WHITE, 50, 50, 74);

This program will open a previously saved 3D graph and place the specified text at the specified dynamic 3D axis position, alignment, orientation, etc. in the graph.

Related topics: GraphDrawArrow3D, GraphDrawShape3D, GraphDrawText3D, GraphEmbedGraph, and NewGraphXYZ.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphDrawTextParamTernary

  STATISTICA BASIC Library of Graph Functions - GraphDrawTextParamTernary (Graph, Text$, ?FontName$, ?FontSize, ?Color, ?Orientation, ?HorizAlignment, ?VertAlignment, ?Border, ?Fill, X, Y, Z, V)

Parameters:

Graph	graph handle

Text$	string to be "drawn" in the graph (see Strings in Functions)

?FontName$	name of font

?FontSize	size of font (in points)

?Color	color of font:  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

?Orientation	text angle:  specify angle between 0 and 360 or use O_HORIZONTAL, O_VERTICAL_LEFT, O_VERTICAL_RIGHT

?HorizAlignment	horizontal alignment of text:  AL_LEFT, AL_CENTER, or AL_RIGHT

?VertAlignment	vertical alignment of text:  AL_TOP, AL_CENTER, or AL_BOTTOM

?Border	place border around text:  ON or OFF

?Fill	fill text area:  FILL_TRANSPARENT, FILL_WHITE, FILL_OUTSIDE_BACKGROUND, or FILL_INSIDE_BACKGROUND

X	dynamic ternary X-axis coordinate of upper-left corner of the text (positon of anchor point)

Y	dynamic ternary Y-axis coordinate of upper-left corner of the text (positon of anchor point)

Z	dynamic ternary Z-axis coordinate of upper-left corner of the text (positon of anchor point)

V	dynamic ternary V-axis coordinate of upper-left corner of the text (positon of anchor point)

The GraphDrawTextParamTernary function allows you to place customized text in the specified ternary (trilinear) graph at the specified, dynamic ternary axis coordinates.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph5.stg');

GraphDrawTextParamTernary(mygraph, 'This is some text to be added to the graph',

                         'Arial', 12, BLUE, O_VERTICAL_LEFT, Al_LEFT, Al_TOP, On,

                         Fill_TRANSPARENT, 0.4, 0.3, 0.3. 12);

This program will open a previously saved ternary (trilinear) graph and place the specified text at the specified, dynamic ternary axis coordinates, alignment, orientation, etc. in the graph.

Related topics: GraphDrawArrowTernary, GraphDrawShapeTernary, GraphDrawTextTernary, and NewTernary.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphDrawShape

  STATISTICA BASIC Library of Graph Functions - GraphDrawShape (Graph, ShapeType, Left, Top, Right, Bottom, ?Dynamic)

Parameters:

Graph	graph handle

ShapeType	shape type:  SHAPE_RECTANGLE, SHAPE_ROUNDEDRECTANGE, SHAPE_ELLIPSE, or SHAPE_ARC

Left	fixed left side coordinate of the shape

Top	fixed upper coordinate of the shape

Right	fixed right side coordinate of the shape

Bottom	fixed lower coordinate of the shape

?Dynamic	use dynamic graph coordinates:  TRUE or FALSE (default = FALSE)

The GraphDrawShape function allows you to add the specified shape to the specified graph.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph5.stg');

ellipse := GraphDrawShape(mygraph, Shape_ellipse, 32, 90, 48, 80, ?DYNAMIC);

GraphSetObjectLineStyle(mygraph, ellipse, ON, L_SOLID,

                       1.5, RED);

This program will open a previously saved graph and place an ellipse at the specified position in the graph.

Related topics: GraphDrawArrow, GraphDrawPolyline, GraphDrawText, GraphDrawTextParam, GraphEmbedGraph, GraphSetObjectAreaStyle, and GraphSetObjectLineStyle.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphDrawShape3D

  STATISTICA BASIC Library of Graph Functions - GraphDrawShape3D (Graph, ShapeType, X1, Y1, Z1, X2, Y2, Z2)

Parameters:

Graph	graph handle

ShapeType	shape type:  SHAPE_RECTANGLE, SHAPE_ROUNDEDRECTANGE, SHAPE_ELLIPSE, or SHAPE_ARC

X1	X coordinate of the upper left corner of the shape

Y1	Y coordinate of the upper left corner of the shape

Z1	Z coordinate of the upper left corner of the shape

X2	X coordinate of the lower right corner of the shape

Y2	Y coordinate of the lower right corner of the shape

Z2	Z coordinate of the lower right corner of the shape

The GraphDrawShape3D function allows you to add the specified shape to a 3D graph in dynamic coordinates.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph5.stg');

ellipse := GraphDrawShape3D(mygraph, Shape_ellipse, 77, 90, 115, 48, 80, 95);

GraphSetObjectLineStyle(mygraph, ellipse, ON, L_SOLID,

                       1.5, RED);

This program will open a previously saved 3D graph and place an ellipse at the specified, dynamic coordinates in the graph.

Related topics: GraphDrawArrow3D, GraphDrawText3D, and GraphDrawTextParam3D.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphDrawShapeTernary

  STATISTICA BASIC Library of Graph Functions - GraphDrawShapeTernary (Graph, ShapeType, X1, Y1, Z1, V1, X2, Y2, Z2, V2)

Parameters:

Graph	graph handle

ShapeType	shape type:  SHAPE_RECTANGLE, SHAPE_ROUNDEDRECTANGE, SHAPE_ELLIPSE, or SHAPE_ARC

X1	X coordinate of the upper left corner of the shape

Y1	Y coordinate of the upper left corner of the shape

Z1	Z coordinate of the upper left corner of the shape

V1	V coordinate of the upper left corner of the shape

X2	X coordinate of the lower right corner of the shape

Y2	Y coordinate of the lower right corner of the shape

Z2	Z coordinate of the lower right corner of the shape

V2	V coordinate of the lower right corner of the shape

The GraphDrawShapeTernary function allows you to add the specified shape to a ternary (trilinear) graph at the specified, dynamic coordinates.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph5.stg');

ellipse := GraphDrawShapeTernary(mygraph, Shape_ellipse, 77, 90, 115, 100, 48, 80, 95, 78);

GraphSetObjectLineStyle(mygraph, ellipse, ON, L_SOLID, 1.5, RED);

This program will open a previously saved ternary (trilinear) graph and place an ellipse at the specified, dynamic coordinates in the graph.

Related topics: GraphDrawArrow3D, GraphDrawText3D, and GraphDrawTextParam3D.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphDrawPolyline

  STATISTICA BASIC Library of Graph Functions - GraphDrawPolyline (Graph, NoOfPoints, Points, ?Dynamic)

Parameters:

Graph	graph handle

NoOfPoints	number of points in the polyline

Points	matrix of polyline point coordinates; the X and Y coordinates must be respectively the first and second dimensions of a 2-dimensional matrix (see Arrays in Functions); if drawing in a 3-dimensional graph and dynamic coordinates are specified, the X, Y, and Z coordinates must be respectively the first, second and third dimensions of a 3-dimensional matrix.

?Dynamic	use dynamic graph coordinates:  TRUE or FALSE (default = FALSE)

The GraphDrawPolyline function allows you to add a polyline to the specified graph.

Example:

RandomAccess;

Dim P1(7,2);

P1(1,1):=12;   P1(1,2):=90;

P1(2,1):=12;   P1(2,2):=80;

P1(3,1):=40;   P1(3,2):=80;

P1(4,1):=45;   P1(4,2):=30;

P1(5,1):=95;   P1(5,2):=30;

P1(6,1):=95;   P1(6,2):=90;

P1(7,1):=12;   P1(7,2):=90;

graph := GetGraph(0);

poly:=GraphDrawPolyline(graph, 7, P1, ?DYNAMIC);

GraphSetObjectLineStyle(graph, poly, ON, L_DOTTED, 1, RED);

GraphSetObjectAreaStyle(graph, poly, ON, A_BRICK, RED);

GraphDrawTextParam(graph, "OK!", "Times New Roman", 18, RED, UNUSED,

                  AL_CENTER, 0, UNUSED, FILL_WHITE, 69, 62, ?DYNAMIC);

This program will draw a polyline in the currently displayed graph according to the coordinates in the array P1.

Related topics: GraphDrawArrow, GraphDrawShape, GraphDrawText, GraphDrawTextParam, GraphEmbedGraph, GraphSetObjectAreaStyle, and GraphSetObjectLineStyle.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphDrawArrow

  STATISTICA BASIC Library of Graph Functions - GraphDrawArrow (Graph, ?ArrowType, ?Size, ?Angle, ?Style, Left, Top, Right, Bottom, ?Dynamic)

Parameters:

Graph	graph handle

?ArrowType	type of arrow:  HEAD_FANCY_FILLED, HEAD_FANCY_EMPTY, HEAD_TRIANGULAR_FILLED, HEAD_TRIANGULAR_EMPTY, HEAD_REGULAR_EMPTY, or HEAD_ERROR_BAR

?Size	size of arrow head (1 - 15)

?Angle	angle of arrow head (1 - 15)

?Style	style of arrow head (1 - 15)

Left	left side coordinate of the arrow

Top	upper coordinate of the arrow

Right	right side coordinate of the arrow

Bottom	lower coordinate of the arrow

?Dynamic	use dynamic graph coordinates:  TRUE or FALSE (default = TRUE)

Return value:	object handle

The GraphDrawArrow function allows you to add an arrow to the specified graph.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph5.stg');

obj_arrow := GraphDrawArrow(mygraph, Head_Fancy_EMPTY, 5, 10, 10, 43, 55, 66, 59, ?DYNAMIC);

GraphSetObjectLineStyle(mygraph, obj_arrow, On, L_DENSE_DOTTED, 4, NAVY);

This program will open a previously saved graph and draw the specified arrow in the specified position on the graph.

Related topics:  GraphDrawPolyline, GraphDrawShape, GraphDrawText, GraphDrawTextParam, GraphEmbedGraph, GraphSetObjectAreaStyle, and GraphSetObjectLineStyle.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphDrawArrow3D

  STATISTICA BASIC Library of Graph Functions - GraphDrawArrow3D (Graph, ?ArrowType, ?Size, ?Angle, ?Style, X1, Y1, Z1, X2, Y2, Z2)

Parameters:

Graph	graph handle

?ArrowType	type of arrow:  HEAD_FANCY_FILLED, HEAD_FANCY_EMPTY, HEAD_TRIANGULAR_FILLED, HEAD_TRIANGULAR_EMPTY, HEAD_REGULAR_EMPTY, or HEAD_ERROR_BAR

?Size	size of arrow head (1 - 15)

?Angle	angle of arrow head (1 - 15)

?Style	style of arrow head (1 - 15)

X1	dynamic X coordinate of the upper left corner of the arrow

Y1	dynamic Y coordinate of the upper left corner of the arrow

Z1	dynamic Z coordinate of the upper left corner of the arrow

X2	dynamic X coordinate of the lower right corner of the arrow

Y2	dynamic Y coordinate of the lower right corner of the arrow

Z2	dynamic Z coordinate of the lower right corner of the arrow

The GraphDrawArrow3D function allows you to add an arrow to the specified graph.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph5.stg');

obj_arrow := GraphDrawArrow3D(mygraph, Head_Fancy_EMPTY, 5, 10, 10, 4, 5, 7, 16, 19, 20);

GraphSetObjectLineStyle(mygraph, obj_arrow, On, L_DENSE_DOTTED, 4, NAVY);

This program will open a previously saved 3D graph and draw an arrow at the specified, dynamic coordinates in the graph.

Related topics:  GraphDrawPolyline, GraphDrawShape, GraphDrawText, GraphDrawTextParam, GraphEmbedGraph, GraphSetObjectAreaStyle, and GraphSetObjectLineStyle.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphDrawArrowTernary

  STATISTICA BASIC Library of Graph Functions - GraphDrawArrowTernary (Graph, ?ArrowType, ?Size, ?Angle, ?Style, X1, Y1, Z1, V1, X2, Y2, Z2, V2)

Parameters:

Graph	graph handle

?ArrowType	type of arrow:  HEAD_FANCY_FILLED, HEAD_FANCY_EMPTY, HEAD_TRIANGULAR_FILLED, HEAD_TRIANGULAR_EMPTY, HEAD_REGULAR_EMPTY, or HEAD_ERROR_BAR

?Size	size of arrow head (1 - 15)

?Angle	angle of arrow head (1 - 15)

?Style	style of arrow head (1 - 15)

X1	dynamic X coordinate of the upper left corner of the arrow

Y1	dynamic Y coordinate of the upper left corner of the arrow

Z1	dynamic Z coordinate of the upper left corner of the arrow

V1	dynamic V coordinate of the upper left corner of the arrow

X2	dynamic X coordinate of the lower right corner of the arrow

Y2	dynamic Y coordinate of the lower right corner of the arrow

Z2	dynamic Z coordinate of the lower right corner of the arrow

V2	dynamic V coordinate of the lower right corner of the arrow

The GraphDrawArrowTernary function allows you to add an arrow to the specified ternary (trilinear) graph at the specified, dynamic triangular axis coordinates.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph5.stg');

obj_arrow := GraphDrawArrowTernary(mygraph, Head_Fancy_EMPTY, 5, 10, 10, 0.3, 0.5, 0.2,

                                   59, 0.4, 0.3, 0.3, 65);

GraphSetObjectLineStyle(mygraph, obj_arrow, On, L_DENSE_DOTTED, 4, NAVY);

This program will open a previously saved ternary (trilinear) graph and draw the specified arrow at the specified, dynamic coordinates in the graph.

Related topics: GraphDrawShapeTernary, GraphDrawTextTernary, GraphDrawTextParamTernary, GraphSetObjectAreaStyle, and GraphSetObjectLineStyle.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetObjectLineStyle

  STATISTICA BASIC Library of Graph Functions - GraphSetObjectLineStyle (Graph, Object, ?Display, ?Pattern, ?Size, ?Color)

Parameters:

Graph	graph handle

Object	object handle (returned by function which created object)

?Display	display object:  ON or OFF

?Pattern	line pattern:   L_SOLID, L_LONG_DASH, L_SHORT_DASH, L_LONG_SHORT_DASH, L_LONG_SHORT_SHORT_DASH, L_DOTTED, or L_DENSE_DOTTED

?Size	size in points

?Color	color of line:  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

The GraphSetObjectLineStyle function allows you to customize the specified object in the specified graph.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph5.stg');

new_object := GraphDrawArrow(mygraph, Head_Fancy_EMPTY, 5, 60, 10, 43, 55, 66, 59, ?DYNAMIC);

GraphSetObjectLineStyle(mygraph, new_object, On, L_DENSE_DOTTED, 4, NAVY);

This program will open a previously saved graph, add an arrow, and then modify the arrow.

Related topics:  GraphSetObjectPatternStyle, GraphDrawArrow, GraphDrawPolyline, GraphDrawShape, GraphDrawText, GraphDrawTextParam, GraphEmbedGraph, and GraphSetObjectAreaStyle.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetObjectAreaStyle

  STATISTICA BASIC Library of Graph Functions - GraphSetObjectAreaStyle (Graph, Object, ?Display, ?Pattern, ?Color)

Parameters:

Graph	graph handle

Object	object handle (returned by function which created object)

?Display	display object:  ON or OFF

?Pattern	area pattern:	A_SOLID,  A_EMPTY,  A_HORIZONTAL_HATCH,  A_VERTICAL_HATCH,  A_FORWARD_DIAGONAL,  A_BACKWARD_DIAGONAL,  A_CROSS,  A_DIAGONAL_CROSS,  A_HORIZONTAL_HATCH_DENSE,  A_VERTICAL_HATCH_DENSE,  A_FORWARD_DIAGONAL_DENSE,  A_BACKWARD_DIAGONAL_DENSE,  A_HORIZONTAL_HATCH_H,  A_VERTICAL_HATCH_H,  A_FORWARD_DIAGONAL_H,  A_BACKWARD_DIAGONAL_H,  A_CROSS_H,  A_DIAGONAL_CROSS_H,  A_DOTS,  A_DENSE,  A_GENERIC,  A_CHESS,  A_BRICK,  or A_BALLS

?Color	color of area line:  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

The GraphSetObjectAreaStyle function allows you to customize the specified object in the specified graph.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph5.stg');

new_object := GraphDrawShape(mygraph, Shape_ellipse, 32, 90, 48, 80,?DYNAMIC);

GraphSetObjectAreaStyle(mygraph, new_object, On, A_Dots, SILVER);

This program will open a previously saved graph, add an ellipse, and then modify the area within the ellipse.

Related topics: GraphSetObjectPatternStyle, GraphDrawArrow, GraphDrawPolyline, GraphDrawShape, GraphDrawText, GraphDrawTextParam, GraphEmbedGraph, and GraphSetObjectLineStyle.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetObjectPatternStyle

  STATISTICA BASIC Library of Graph Functions - GraphSetObjectPatternStyle (Graph, Object, ?IsArea, ?IsTransp)

Parameters:

Graph	graph handle

Object	object handle (returned by function which created object)

?IsArea	change object area pattern:  TRUE (change area) or FALSE (change line pattern)

?IsTransp	set object pattern to transparent:  TRUE or FALSE

The GraphSetObjectPatternStyle function allows you to set transparent or opaque patterns for areas or lines of the specified object in the specified graph.  Note that only non-solid line patterns (see GraphSetObjectLineStyle) and the six area patterns denoted with a final "_H" (A_HORIZONTAL_HATCH_H,  A_VERTICAL_HATCH_H,  A_FORWARD_DIAGONAL_H,  A_BACKWARD_DIAGONAL_H,  A_CROSS_H,  A_DIAGONAL_CROSS_H) in the pattern name (see GraphSetObjectAreaStyle) may be made transparent.

Example:

RandomAccess;

mygraph := OpenGraph('c:\graph5.stg');

new_object := GraphDrawShape(mygraph, Shape_ellipse, 32, 90, 48, 80, ?DYNAMIC);

GraphSetObjectAreaStyle(mygraph, new_object, On, A_CROSS_H, RED);

GraphSetObjectPatternStyle(mygraph, new_object, TRUE, TRUE);

This program will open a previously saved graph, add an ellipse, and then modify the area within the ellipse by selecting the area pattern and setting it to transparent.

Related topics: GraphDrawArrow, GraphDrawPolyline, GraphDrawShape, GraphDrawText, GraphDrawTextParam, GraphEmbedGraph, GraphSetObjectAreaStyle, and GraphSetObjectLineStyle.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - ColorRGB

  STATISTICA BASIC Library of Graph Functions - ColorRGB (Red, Green, Blue)

Parameters:

Red	proportion of red (from 0 to 255)

Green	proportion of green (from 0 to 255)

Blue	proportion of blue (from 0 to 255)

The ColorRGB function allows you to define a custom color from red, green, and blue components for use within a function requiring a color parameter, or assign the resulting color number to a variable name (which can then be used in functions with color parameters).

Example:

RandomAccess;

DARK_ORANGE := ColorRGB(94,60,2);

mygraph := OpenGraph('c:\graph5.stg');

new_object := GraphDrawShape(mygraph, Shape_ellipse, 32, 90, 48, 80, ?DYNAMIC);

GraphSetObjectLineStyle(mygraph, new_object, On, A_Dots, 3, ColorRGB(100, 100, 100));

GraphSetObjectAreaStyle(mygraph, new_object, On, A_Dots, DARK_ORANGE);

This program will open a previously saved graph, add an ellipse, and then modify the ellipse by changing the line and area background colors to custom colors created via ColorRGB.

Colors specified via the ColorRGB function from the intensities of Red, Green, and Blue components are defined by a color number.  The color number is calculated as:

                                       2

color number = (RED) + 256*(BLUE) + 256  *(GREEN)

Some of the most commonly used colors are pre-defined and are listed below.

                                      Color

Color     RED     GREEN     BLUE     Number

BLACK       0         0        0          0

MAROON    128         0        0        128

GREEN       0       128        0      32768

OLIVE     128       128        0      32896

NAVY        0         0      128    8388608

PURPLE    128         0      128    8388736

TEAL        0       128      128    8421376

GRAY      128       128      128    8421504

SILVER    192       192      192   12632256

RED       255         0        0        255

LIME        0       255        0      65280

YELLOW    255       255        0      65535

BLUE        0         0      255   16711680

FUSCHIA   255         0      255   16711935

AQUA        0       255      255   16776960

WHITE     255       255      255   16777215

Related topics:  GraphDrawArrow, GraphDrawPolyline, GraphDrawShape, GraphDrawText, GraphDrawTextParam, GraphEmbedGraph, GraphSetObjectAreaStyle, and GraphSetObjectLineStyle.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetDefaultFont

  STATISTICA BASIC Library of Graph Functions - GraphSetDefaultFont (Graph, ?FontName$, ?FontSize, ?Color)

Parameters:

Graph	graph handle

?FontName$	name of font

?FontSize	size of font (in points)

?Color	font color:  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

The GraphSetDefaultFont function allows you to set the default font style, size, and color for the graph.  This font affects all graph components.

Example:

RandomAccess;

mygraph := NewGraph(LINEPLOT, 'Success in the Workplace', 'Low Income', 'Mid Income',

                   NCases, v1, v2);

GraphSetDefaultFont(mygraph, 'Times New Roman', 14, PURPLE);

This program will create a line plot in which the default font for the graph (e.g., for the titles, scale values, etc.) will be Times New Roman, 14 point, purple.

Related topics:  GraphDrawText, GraphDrawTextParam, GraphSetLegend.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetProportion

  STATISTICA BASIC Library of Graph Functions - GraphSetProportion (Graph, Proportion)

Parameters:

Graph	graph handle

Proportion	graph proportion:  value from 0.125 to 8.0 or PROP_SCREEN or PROP_PRINTER

The GraphSetProportion function allows you to set the graph window proportion (see Graph Window Proportion).

Example:

RandomAccess;

mygraph := NewGraph(LINEPLOT, 'Success in the Workplace', 'Low Income', 'Mid Income',

                   NCases, v1, v2);

GraphSetProportion(mygraph, PROP_PRINTER);

This program will create a line plot and set the graph window proportions to the same as the printer page definition.

Related topics:  GraphChangeMappingBase, NewGraph, OpenGraph, PrintGraph.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphSetMappingArea

  STATISTICA BASIC Library of Graph Functions - GraphSetMappingArea (Graph, Left, Top, Right, Bottom)

Parameters:

Graph	graph handle

Left	left coordinate value

Top	top coordinate value

Right	right coordinate value

Bottom	bottom coordinate value

The GraphSetMappingArea function option allows you to position the graph within the window by specifying the coordinates for the graph viewing area (within a logical coordinate system of -4000 to +4000 by -4000 to +4000).  For more information, see Graph Mapping Options.

Example:

RandomAccess;

mygraph:=OpenGraph('c:\bas_cor1.stg');

GraphSetMappingArea(mygraph, -200, 1200, 1200, -200);

This program will open a previously saved graph, then redefine the graph viewing area to increase the margins around all sides of the graph.

Related topics:  GraphChangeMappingBase.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - GraphChangeMappingBase

  STATISTICA BASIC Library of Graph Functions - GraphChangeMappingBase (Graph, Modifier)

Parameters:

Graph	graph handle

Modifier	amount by which the fonts will be modified (e.g., +16 to increase the fonts, etc., or -16 to decrease the fonts, etc., proportionately)

The GraphChangeMappingBase function will proportionately increase or decrease all fonts, line thicknesses, etc used in the graph by changing the graph Mapping Base.  (See also, Graphics Increase, Decrease All Font by 16% (Ctrl - 4%) Toolbar Buttons).

Example:

RandomAccess;

mygraph := OpenGraph('c:\bas_cor1.stg');

GraphChangeMappingBase(mygraph, -16);

This program will first open a previously saved graph, then proportionately decrease the size of all fonts, points, lines, etc. in the specified graph.

Related topics:  GraphSetMappingArea.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


STATISTICA BASIC - DisplayGraph

  STATISTICA BASIC Library of Graph Functions - DisplayGraph  (graph)

Parameters:

Graph	graph handle

The DisplayGraph function will force the redrawing of the specified graph at a particular point within the STATISTICA BASIC program, displaying all changes made to that point.

Example:

RandomAccess;

Mygraph := OpenGraph('c:\ bas_cor1.stg');

GraphSetDefaultFont(Mygraph, 'Times New Roman', 14, NAVY);

DisplayGraph(Mygraph);

reply := DisplayMessageBox(MB_YESNO+MB_ICONQUESTION, 'STATISTICA: Graphics',

                          'Print Graph?');

if reply = IDYES then

   PrintGraph(Mygraph);

This program will open a previously saved graph, change the default font, display the updated graph, then ask the user whether to print the modified graph.

For increased speed of execution, the displayed graph is not updated following each STATISTICA BASIC graphics operation.  By including the DisplayGraph function at a specific point in your program, you will allow the display to be updated at that point.

Related topics:  DuplicateGraph, GraphCopyToClipboard, PrintGraph.

For a complete list of graphics functions, see Graphics Library of STATISTICA BASIC.


  Scrollsheet Library of STATISTICA BASIC - Overview

The STATISTICA BASIC Scrollsheet Library allows you to create and customize output tables of results of procedures developed in STATISTICA BASIC.  Scrollsheets may be saved, printed (to the printer or Text/output Window), copied to the Clipboard, and saved as STATISTICA system data files.

The Scrollsheet functions in STATISTICA BASIC can be used to:

(1)	open a previously saved STATISTICA Scrollsheet file (*.scr) and then make modifications or customizations to the contents or print or save this Scrollsheet (see Example 1 below),

(2)	create a new Scrollsheet and then make modifications or customizations to this Scrollsheet or print or save the Scrollsheet (see Example 2 below), or

(3)	make modifications or customizations to a currently displayed Scrollsheet or print or save the Scrollsheet (see Example 3 below).

Notes

•	You should use the RandomAccess (default) mode of operation when executing Scrollsheet functions unless you intend to repeat all Scrollsheets specified in the program for each case of the current data set (see Sequential mode).

•	The Scrollsheet handle can be obtained by using the OpenScrollsheet, GetScrollsheet, or NewScrollsheet family of functions.  You can use GetScrollsheet(0) in order to obtain the handle of the top-most Scrollsheet window.

•	Many Scrollsheet functions can pass several text values in a single string (such as setting titles, row names and column names in the NewScrollsheet function).  These are "delimited" strings, where the different text values are separated by either the "|" character or by tabs.  For instance, the string "AA|BB|CC" contains three different text values, "AA", "BB", and "CC".  For more information, see Strings in Functions, Passing Lists of Strings in STATISTICA BASIC Functions, and Retrieving Lists of Strings in STATISTICA BASIC Functions.

Example 1

This example will first open a previously saved Scrollsheet and then modify its title before printing it.

RandomAccess;

scrollsheet := OpenScrollsheet('c:\results.scr');

ScrollsheetSetTitle(scrollsheet, TopTitle, 'This is the New Title Text');

PrintScrollsheet(scrollsheet);

Example 2

This example will create a new Scrollsheet from an array and then save it.

RandomAccess;

Dim NewArray(10,2);

MatrixCopy(Data, 1, 1, 10, 2, NewArray, 1, 1);

scrollsheet := NewScrollsheet(10, 2, NewArray, 'Title of Scrollsheet', ?RowNames$,

                             ?ColumnNames$);

SaveScrollsheet(scrollsheet, 'e:\array.scr');

Example 3

This example will add a new column to the top-most Scrollsheet (note the use of the function GetScrollsheet) and then print the modified Scrollsheet.

RandomAccess;

scrollsheet1 := GetScrollsheet(0);

ScrollsheetAppendColumns(scrollsheet1, 1, 10, v3);

PrintScrollsheet(scrollsheet1);

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


Scrollsheet Library of STATISTICA BASIC

  STATISTICA BASIC Syntax Reference - Scrollsheet Library of STATISTICA BASIC

Overview

Functions	Example and Comment

DeleteScrollsheet	DeleteScrollsheet(scroll);

{Closes the specified Scrollsheet.}

DuplicateScrollsheet	DuplicateScrollsheet(scroll);

{Duplicates the specified Scrollsheet.}

GetScrollsheet	my_scroll := GetScrollsheet(0);

{Returns the Scrollsheet handle for the specified Scrollsheet and assigns its handle to the variable my_scroll.}

MatrixDisplay	MatrixDisplay(array, 'Matrix Array');

{Displays the contents of matrix array as a Scrollsheet.}

NewScrollsheet	NewScrollsheet(2, 3, array, "New Scrollsheet", "Row 1|Row 2", "Col A|Col B|Col C");

{Creates a new 2 row by 3 column Scrollsheet from the contents of matrix array and names the row and columns.}

OpenScrollsheet	OpenScrollsheet("c:\ new.scr");

{Opens a previously saved Scrollsheet file.}

PrintScrollsheet	PrintScrollsheet(scroll);

{Prints the specified Scrollsheet to the printer.}

PrintScrollsheetToOutputWindow	PrintScrollsheetToOutputWindow(scroll);

{Prints the specified Scrollsheet to the Text/output Window.}

SaveScrollsheet	SaveScrollsheet(scroll, "c:\new.scr");

{Saves the specified Scrollsheet to disk as a Scrollsheet file.}

SaveScrollsheetAsDataFile	SaveScrollsheetAsDataFile(scroll, "c:\new.sta");

{Saves the specified Scrollsheet to disk as a STATISTICA data file.}

ScrollsheetAppendColumns	ScrollsheetAppendColumns(scroll, 4);

{Appends four columns to the specified Scrollsheet.}

ScrollsheetAppendRows	ScrollsheetAppendRows(scroll, 3);

{Appends three rows to the specified Scrollsheet.}

ScrollsheetGetColName	ScrollsheetGetColName(scroll, 3, name1$, name2$);

{Retrieves the column names from the specified column in the specified Scrollsheet.}

ScrollsheetGetHwnd	win_handle := ScrollsheetGetHwnd(scroll);

{Retrieves the Scrollsheet handle of the specified Scrollsheet and assigns its handle to the variable win_handle.}

ScrollsheetGetMatrix	ScrollsheetGetMatrix(scroll, 1, 2, array);

{Extracts values from the specified Scrollsheet beginning at row 1, column 2 and assigns the values to the matrix array.}

ScrollsheetGetNbCols	number_cols := ScrollsheetGetNbCols(scroll);

{Returns the number of columns in the specified Scrollsheet and assigns that value to the variable number_cols.}

ScrollsheetGetNbRows	number_rows := ScrollsheetGetNbRows(scroll);

{Returns the number of rows in the specified Scrollsheet and assigns that value to the variable number_rows.}

ScrollsheetGetRowName	ScrollsheetGetRowName(scrolls, 3, Name$);

{Retrieves the row name from the specified row in the specified Scrollsheet.}

ScrollsheetGetTextValue	ScrollsheetGetTextValue(scroll, 1, 3, text$);

{Returns the text value in the first row, third column of the specified Scrollsheet and assigns that text value to the variable text$.}

ScrollsheetGetTitle	ScrollsheetGetTitle(scroll, 1, title$);   {Returns the first title of the specified Scrollsheet and assigns that text value to the variable title$.}

ScrollsheetGetValue	ScrollsheetGetValue(scroll, 1, 3, cell_value);

{Returns the value in the first row, third column of the specified Scrollsheet and assigns that value to the variable cell_value.}

ScrollsheetSetColumnFormat	ScrollsheetSetColumnFormat(scroll, 1, SCF_DECIMAL, 6);

{Sets the format of the first column of the specified Scrollsheet to six Decimal places.}

ScrollsheetSetColumnName	ScrollsheetSetColumnName(scroll, 2, 'Name 1', 'Name 2');

{Sets the contents for the first and second column names of the second column of the specified Scrollsheet.}

ScrollsheetSetColumnNameColor	ScrollsheetSetColumnNameColor(scroll, SILVER, GREEN);

{Sets the color of the column names of the specified Scrollsheet to Green text on a Silver background.}

ScrollsheetSetColumnWidth	ScrollsheetSetColumnNameWidth(scroll, 2, 7, 1);

{Sets the width to 7 and the margin wdth to 1 for the second column of the specified Scrollsheet.}

ScrollsheetSetDataColor	ScrollsheetSetDataColor(scroll, SILVER, NAVY);

{Sets the color of the data area of the specified Scrollsheet to Navy text on a Silver background.}

ScrollsheetSetFont	ScrollsheetSetFont(scroll, 'Times New Roman', 12);

{Sets the font of the specified Scrollsheet to Times New Roman, 12 point.}

ScrollsheetSetHeaderColor	ScrollsheetSetHeaderColor(scroll, TEAL, BLACK);

{Sets the color of the header area of the specified Scrollsheet to Black text on a Teal background.}

ScrollsheetSetHilite	ScrollsheetSetHiliteColor(scroll, 2, 3, 1);

{Highlights the specified cell in the Scrollsheet.}

ScrollsheetSetHiliteColor	ScrollsheetSetHiliteColor(scroll, RED);

{Sets the highlight color of the specified Scrollsheet to Red text.}

ScrollsheetSetInfoColor	ScrollsheetSetInfoColor(scroll, AQUA, GREEN);

{Sets the color of the 'Info' area of the specified Scrollsheet to Green text on an Aqua background.}

ScrollsheetSetMatrix	ScrollsheetSetMatrix(scroll, 2, 4, Array);

{Places the contents of the matrix Array into the specified Scrollsheet beginning at row 2, column 4.}

ScrollsheetSetRowName	ScrollsheetSetRowName(scroll, 2, 'Row Number 2');

{Sets the content of the row name of the second row in the specified Scrollsheet.}

ScrollsheetSetRowNameColor	ScrollsheetSetRowNameColor(scroll, YELLOW, MAROON);

{Sets the color of the row names in the specified Scrollsheet to Maroon text on a Yellow background.}

ScrollsheetSetRowNameWidth	ScrollsheetSetRowNameWidth(scroll, 12);

{Sets the width of the row names in the specified Scrollsheet to 12.}

ScrollsheetSetTextValue	ScrollsheetSetTextValue(scroll, 1, 2, 'ABCDE');

{Sets the contents of the first row, second column in the specified Scrollsheet to ABCDE.}

ScrollsheetSetTitle	ScrollsheetSetTitle(scroll, 1, 'New Scrollsheet');

{Sets the first title of the specified Scrollsheet to New Scrollsheet.}

ScrollsheetSetValue	ScrollsheetSetValue(scroll, 2, 3, 3.1416);

{Sets the contents of the second row, third column in the specified Scrollsheet to 3.1416.}


STATISTICA BASIC - DeleteScrollsheet

  STATISTICA BASIC Library of Scrollsheet Functions - DeleteScrollsheet (Handle)

Parameter:

Handle	Scrollsheet handle

The DeleteScrollsheet function will close the specified Scrollsheet.

Example:

RandomAccess;

newscrol := NewScrollsheet(3, 5, Data, 'My Scrollsheet', 'Row 1|Row 2|Row3',

                          'Col 1|Col 2|Col 3|Col 4|Col 5');

Pause;

DeleteScrollsheet(newscrol);

This program will create a new Scrollsheet and assigns its Scrollsheet handle to the variable newscrol.  After pausing for the user to click OK, the Scrollsheet will be closed.

Related topics:  NewScrollsheet, OpenScrollsheet, SaveScrollsheet, GetScrollsheet.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - DuplicateScrollsheet

  STATISTICA BASIC Library of Scrollsheet Functions - DuplicateScrollsheet (Handle)

Parameter:

Handle	Scrollsheet handle

Return value:	Scrollsheet handle for duplicated Scrollsheet

The Duplicate Scrollsheet function will create a copy of the specified Scrollsheet.

Example:

RandomAccess;

scrollsheet := GetScrollsheet(0);

copyscroll := DuplicateScrollsheet(scrollsheet);

ScrollsheetSetTitle(copyscroll, TOPTITLE, 'This is a copy');

PrintScrollsheet(copyscroll);

DeleteScrollsheet(copyscroll);

This program will create a copy of the current Scrollsheet and the copy's Scrollsheet handle will be assigned to the variable copyscroll.  The duplicate Scrollsheet's title is changed, it is printed, and then closed.

Related topics:  NewScrollsheet, OpenScrollsheet, SaveScrollsheet, GetScrollsheet, DeleteScrollsheet.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - GetScrollsheet

  STATISTICA BASIC Library of Scrollsheet Functions - GetScrollsheet (Window)

Parameter:

Window	window handle

Return value:	Scrollsheet handle

The GetScrollsheet function returns the Scrollsheet handle of the specified Scrollsheet window.  If used as GetScrollsheet(0), then the handle of the active Scrollsheet (on top) is returned.

Example:

RandomAccess;

scroll := GetScrollsheet(0);

ScrollsheetSetTitle(scroll, TOPTITLE, 'New Title');

reply := DisplayMessageBox(MB_YESNO, 'Print', 'Print Scrollsheet?');

if reply = IDYES then

   PrintScrollsheet(scroll);

This program will use the GetScrollsheet function to assign the Scrollsheet handle of the top Scrollsheet window to the variable scroll.  The Scrollsheet handle is used in subsequent functions to change the title of the Scrollsheet and optionally print it.

Related topics:  SaveScrollsheetAsDataFile, SaveScrollsheet, PrintScrollsheet, NewScrollsheet, DeleteScrollsheet, DuplicateScrollsheet.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - NewScrollsheet

  STATISTICA BASIC Library of Scrollsheet Functions - NewScrollsheet (?NoOfRows, ?NoOfColumns, Array, ?Title$, ?RowNames$, ?ColumnNames)

Parameters:

?NoOfRows	number of rows in the new Scrollsheet.  Can be 0 (or -1) to use the number of rows in 'Array'.

?NoOfColumns	number of columns in the new Scrollsheet.  Can be 0 (or -1) to use the number of columns in 'Array'.

Array	variable or array with values to place in the new Scrollsheet (see also Arrays in Functions).

?Title$	string for title(s) of the Scrollsheet.  Up to three titles can be specified by a delimited string (see, Lists of Strings in Functions).

?RowNames$	delimited string containing the row names (see, Lists of Strings in Functions).

?ColumnNames$	delimited string containing the column names (see, Lists of Strings in Functions).

Return value:	Scrollsheet handle

The NewScrollsheet function will create a Scrollsheet with the specified contents.

Example:

RandomAccess;

Dim array(2,3);

for i := 1 to 2 do

   for j := 1 to 3 do

      array(i,j) := i*10+j;

NewScrollsheet(2, 3, array, 'Title1', 'Row 1|Row 2',

              'Column1|Column2|Column3');

This program will create a new Scrollsheet with two rows and three columns, containing values from the matrix array.

Related topics:  OpenScrollsheet, SaveScrollsheet, PrintScrollsheet, GetScrollsheet, ScrollsheetSetMatrix.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.  See also, Passing Lists of Strings to Functions in STATISTICA BASIC.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - OpenScrollsheet

  STATISTICA BASIC Library of Scrollsheet Functions - OpenScrollsheet (FileName$)

Parameters:

FileName$	string containing the name of the Scrollsheet file to be displayed (see, Strings in Functions).

Return value:	Scrollsheet handle

The OpenScrollsheet function will open a previously saved Scrollsheet file.

Example 1:

RandomAccess;

OpenScrollsheet('c:\new.scr');

This program will open the Scrollsheet previously saved to the disk as C:\New.scr.

Example 2:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

PrintScrollsheet(scroll);

This program will open a previously saved Scrollsheet and print it to the printer (note that the value scroll returned by the function OpenScrollsheet is a Scrollsheet handle).

Related topics:  NewScrollsheet,  SaveScrollsheet, PrintScrollsheet, GetScrollsheet, DeleteScrollsheet.

For more information on specifying strings, see Strings in Functions.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - PrintScrollsheet

  STATISTICA BASIC Library of Scrollsheet Functions - PrintScrollsheet (Handle)

Parameters:

Handle	Scrollsheet handle

The PrintScrollsheet function will print the Scrollsheet with the specified Scrollsheet handle to the printer.

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

PrintScrollsheet(scroll);

This program will open a previously saved Scrollsheet and print it to the printer (note that the value scroll returned by the function OpenScrollsheet is a Scrollsheet handle).

Related topics:  PrintScrollsheetToOutputWindow, NewScrollsheet,  SaveScrollsheet, OpenScrollsheet, GetScrollsheet, DeleteScrollsheet.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - PrintScrollsheetToOutputWindow

  STATISTICA BASIC Library of Scrollsheet Functions - PrintScrollsheetToOutputWindow (Handle)

Parameters:

Handle	Scrollsheet handle

The PrintScrollsheetToOutputWindow function will print the Scrollsheet with the specified Scrollsheet handle to the Text/output Window.

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

PrintScrollsheetToOutputWindow(scroll);

This program will open a previously saved Scrollsheet and print it to the Text/output Window.

Related topics:  PrintScrollsheet, NewScrollsheet,  SaveScrollsheet, OpenScrollsheet, GetScrollsheet, DeleteScrollsheet.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - SaveScrollsheet

  STATISTICA BASIC Library of Scrollsheet Functions - SaveScrollsheet (Handle, FileName$)

Parameters:

Handle	Scrollsheet handle

FileName$	string containing the name of the file under which the Scrollsheet will be saved (see, Strings in Functions).

The SaveScrollsheet function will save the Scrollsheet with the specified Scrollsheet handle to disk using the specified file name.

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\old.scr');

ScrollsheetSetTitle(scroll, TOPTITLE, 'New Title';

SaveScrollsheet(scroll, 'c:\new.scr');

This program will open an existing Scrollsheet, change its first title and save it to the disk as C:\New.scr.

Related topics:  NewScrollsheet,  PrintScrollsheet, OpenScrollsheet, GetScrollsheet, DeleteScrollsheet.

For more information on specifying strings, see Strings in Functions and Passing Lists of Strings to Functions in STATISTICA BASIC.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - SaveScrollsheetAsDataFile

  STATISTICA BASIC Library of Scrollsheet Functions - SaveScrollsheetAsDataFile (Handle, FileName$)

Parameters:

Handle	Scrollsheet handle

FileName$	string containing the name of the STATISTICA data file under which the Scrollsheet will be saved (see, Strings in Functions)

The SaveScrollsheetAsDataFile function will save the Scrollsheet with the specified Scrollsheet handle to disk as a STATISTICA data file using the specified file name.

Example:

RandomAccess;

ReDim means(NVars);

MatrixMeans (Data, means);

name$ := VarName(1);

for i := 2 to NVars do

   name$:=name$ + '|' + VarName(i);

newscrl:=NewScrollsheet(NVars, 1, means, 'Means', name$, 'Mean');

SaveScrollsheetAsDataFile(newscrl, 'c:\means.sta');

This program will create a new Scrollsheet and save it to the disk as the STATISTICA data file C:\Means.sta.

Related topics:  SaveScrollsheet, OpenScrollsheet, and NewScrollsheet, GetScrollsheet, DeleteScrollsheet, .

For more information on specifying strings, see Strings in Functions and Passing Lists of Strings to Functions in STATISTICA BASIC.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetAppendColumns

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetAppendColumns (Handle, NoOfColumns)

Parameters:

Handle	Scrollsheet handle

NoOfColumns	number of new columns to append to the Scrollsheet.

The ScrollsheetAppendColumns function will add the specified number of columns to the right side (after the last current column) of the specified Scrollsheet.

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetAppendColumns(scroll, 10);

ScrollsheetSetMatrix(scroll, 1, ScrollsheetGetNbCols(scroll)-9, Data);

This program will open a previously saved Scrollsheet and append to it 10 new columns, filling them with values from the current data file.

Related topics:  ScrollsheetAppendRows, GetScrollsheet, ScrollsheetSetValue, ScrollsheetSetColumnName, ScrollsheetSetRowName.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetAppendRows

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetAppendRows (Handle, NoOfRows)

Parameters:

Handle	Scrollsheet handle

NoOfRows	number of new rows to append to the Scrollsheet.

The ScrollsheetAppendRows function will add the specified number of rows to the bottom (after the last current row) of the specified Scrollsheet.

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetAppendRows(scroll, 10);

ScrollsheetSetMatrix(scroll, ScrollsheetGetNbRows(scroll)-9, 1, Data);

This program will open a previously saved Scrollsheet and append to it nine new rows, filling them with values from the current data file.

Related topics:  ScrollsheetAppendColumns, GetScrollsheet, ScrollsheetSetValue, ScrollsheetSetColumnName, ScrollsheetSetRowName.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetGetColName

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetGetColName (Handle, Column, Name1$, Name2$)

Parameters:

Handle	Scrollsheet handle

Column	column number from which to retrieve names.

Name1$	string variable which will contain the top column name of the specified column (see Strings in Functions)

Name2$	string variable which will contain the bottom column name of the specified column (see Strings in Functions)

The ScrollsheetGetColName function will retrieve the names of the specified column of the specified Scrollsheet and place the names in the specified string variables (see the parameters Name1$ and Name2$).

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetGetColName(scroll, 2, col2nam1$, col2nam2$);

WriteLn(col2nam1$, ' ', col2nam2$);

This program will open a previously saved Scrollsheet, place the names of the second column into the string variables col2nam1$ and col2nam2$, respectively, and write the names to the current output channel.

Related topics:  ScrollsheetGetRowName, ScrollsheetSetColumnName, ScrollsheetSetRowName.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetGetHwnd

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetGetHwnd (Handle)

Parameters:

Handle	Scrollsheet handle

The ScrollsheetGetHwnd function returns the window handle of the Scrollsheet with the specified Scrollsheet handle.

Example:

RandomAccess;

OpenScrollsheet('c:\new.scr');

scroll:= ScrollsheetGetHwnd(GetScrollsheet(0));

This program will open a previously saved Scrollsheet and place the window handle value in the variable scroll.

Related topics:  GetScrollsheet.

Experienced users may refer to the Microsoft Windows SDK for more information about window handles.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetGetMatrix

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetGetMatrix (Handle, Row, Column, Matrix)

Parameters:

Handle	Scrollsheet handle

Row	starting row number in the Scrollsheet

Column	starting column number in the Scrollsheet

Matrix	array which will contain the retrieved values (see Arrays in Functions)

The ScrollsheetGetMatrix function extracts a matrix from the Scrollsheet with the specified Scrollsheet handle, starting at the specified Scrollsheet row and column.  If there are more data than can fit in the destination array, then the data will be truncated.

Example:

RandomAccess;

Dim array(2,3);

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetGetMatrix(scroll, 1, 2, array);

This program will open a previously saved Scrollsheet, assigning its Scrollsheet handle to the variable Scroll.  Then, values from the Scrollsheet, beginning with the first row, second column, will be placed in the matrix array (see also, Arrays in Functions).

Related topics:  ScrollsheetSetMatrix, ScrollsheetGetValue, ScrollsheetSetValue.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetGetNbCols

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetGetNbCols (Handle)

Parameters:

Handle	Scrollsheet handle

The ScrollsheetGetNbCols function returns the number of columns in the Scrollsheet with the specified Scrollsheet handle.

Example:

RandomAccess;

Dim array(10);

scroll := OpenScrollsheet('c:\new.scr');

ncols := ScrollsheetGetNbCols(scroll);

ScrollsheetGetMatrix(scroll, 1, ncols, array);

This program will open a previously saved Scrollsheet and place the number of columns in the Scrollsheet in the temporary variable ncols.  This value is then used to place the first 10 values of the last column of the Scrollsheet into the matrix array.

Related topics:  ScrollsheetGetNbRows, ScrollsheetAppendColumns, ScrollsheetAppendRows.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetGetNbRows

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetGetNbRows (Handle)

Parameters:

Handle	Scrollsheet handle

The ScrollsheetGetNbRows function returns the number of rows in the Scrollsheet with the specified Scrollsheet handle.

Example:

RandomAccess;

Dim array(5);

scroll := OpenScrollsheet('c:\new.scr');

nrows := ScrollsheetGetNbRows(scroll);

ScrollsheetGetMatrix(scroll, nrows, 1, array);

This program will open a previously saved Scrollsheet and place the number of rows in the Scrollsheet in the variable Rownums. This value is then used to place the first 5 values of the last row in the Scrollsheet into the matrix array.

Related topics:  ScrollsheetGetNbCols, ScrollsheetAppendColumns, ScrollsheetAppendRows.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetGetRowName

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetGetRowName (Handle, Row, Name$)

Parameters:

Handle	Scrollsheet handle

Row	row number from which to retrieve names.

Name$	string variable which will contain the row name of the specified row (see Strings in Functions).

The ScrollsheetGetRowName function will retrieve the name of the specified row of the Scrollsheet with the specified Scrollsheet handle and place the name in the specified string variable (see parameter Name$).

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetGetRowName(scroll, 2, row2name$);

WriteLn(row2name$);

This program will open a previously saved Scrollsheet, retrieve the name of the second row into the string variable row2name$, and print it to the current output channel.

Related topics:  ScrollsheetGetColName, ScrollsheetSetColumnName, ScrollsheetSetRowName.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetGetTextValue

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetGetTextValue (Handle, Row, Column, Text$)

Parameters:

Handle	Scrollsheet handle

Row	row number from which to retrieve the text value.

Column	column number from which to retrieve the text value.

Text$	string variable which will contain the text value from the specified row and column of the Scrollsheet (see Strings in Functions).

The ScrollsheetGetTextValue function will retrieve the text value in the specified row and column of the Scrollsheet with the specified Scrollsheet handle and place the text value in the specified string variable (see parameter Text$).

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetGetTextValue(scroll , 2, 3, txtval$);

DisplayMessageBox(MB_OK, 'Scrollsheet Value', txtval$);

This program will open a previously saved Scrollsheet and retrieve the text value from the second row, third column into the string variable txtval$, displaying the value in a message box.

Related topics:  ScrollsheetSetTextValue, ScrollsheetGetTitle, ScrollsheetGetValue.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetGetTitle

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetGetTitle (Handle, TitleNo, String$)

Parameters:

Handle	Scrollsheet handle

TitleNo	row number from which to retrieve names.

String$	string variable which will contain the row name of the specified row (see Strings in Functions).

The ScrollsheetGetTitle function will retrieve the specified title of the Scrollsheet with the specified Scrollsheet handle and place the name in the specified string variable (see parameter String$).

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetGetTitle(scroll, 1, title$);

DisplayMessageBox(MB_OK, 'Scrollsheet Title', title$);

This program will open a previously saved Scrollsheet and retrieve the Scrollsheet name (title 1) into the string variable title$.

Related topics:  ScrollsheetSetTitle, ScrollsheetGetTextValue, ScrollsheetGetValue.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetGetValue

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetGetValue (Handle, Row, Column, Value)

Parameters:

Handle	Scrollsheet handle

Row	row number from which to retrieve text value.

Column	column number from which to retrieve text value.

Value	variable which will contain the numeric value from the specified row and column of the Scrollsheet.

The ScrollsheetGetValue function will retrieve the numeric value in the specified row and column of the Scrollsheet with the specified Scrollsheet handle and place the value in the specified variable (see parameter Value).

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetGetValue(scroll, 2, 3, cellvalue);

Writeln('Scrollsheet value = ', cellvalue);

This program will open a previously saved Scrollsheet, retrieve the numeric value from the second row of the third column, place it into the temporary variable cellvalue, then print the value.

Related topics:  ScrollsheetSetValue, ScrollsheetGetTextValue, ScrollsheetSetTextValue.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetSetColumnFormat

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetSetColumnFormat (Handle, Column, Format, FmtParam)

Parameters:

Handle	Scrollsheet handle

Column	column number for which to set format.

Format	format contstants: SCF_AUTOMATIC (automatic format), SCF_OPTIMAL (optimal format), SCF_DECIMAL (decimal format), or SCF_INTEGER (integer format).

FmtParam	format width for SCF_DECIMAL and SCF_INTEGER formats

The ScrollsheetSetColumnFormat function sets the format of the specified column of the Scrollsheet with the specified Scrollsheet handle.

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetSetColumnFormat(scroll, 1, SCF_DECIMAL, 3);

PrintScrollsheet(scroll);

This program will open a previously saved Scrollsheet and set the format of the third column to three decimal places prior to printing it.

Related topics:  ScrollsheetSetColumnWidth.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetSetColumnName

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetSetColumnName (Handle, Column, Name1$, Name2$)

Parameters:

Handle	Scrollsheet handle

Column	column number in which to set names.

Name1$	string text or variable containing the top column name for the specified column (see Strings in Functions).

Name2$	string text or variable containing the bottom column name for the specified column (see Strings in Functions).

The ScrollsheetSetColumnName function will set the names of the specified column of the Scrollsheet with the specified Scrollsheet handle to the specified string text or variables (see parameters Name1$ and Name2$).

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetAppendColumns(scroll, 1);

ncols := ScrollsheetGetNbCols(scroll);

ScrollsheetSetColumnName(scroll, ncols, 'New', 'Column');

SaveScrollsheet(scroll, 'c:\new_scr.scr');

This program will open a previously saved Scrollsheet, append a new column, and set the top and bottom names of the new column to the strings 'New' and 'Column', respectively.

Related topics:  ScrollsheetGetColName, ScrollsheetGetNbCols.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetSetColumnNameColor

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetSetColumnNameColor (Handle, ?BackgroundColor, ?TextColor)

Parameters:

Handle	Scrollsheet handle

?BackgroundColor	background color (use -1 to leave unchanged):  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

?TextColor	text color (use -1 to leave unchanged):  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

The ScrollsheetSetColumnNameColor function will set the colors of the column names for the Scrollsheet with the specified Scrollsheet handle.  Colors may be specified by predefined names or color numbers (see ColorRGB).

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetSetColumnNameColor(scroll, SILVER, GREEN);

SaveScrollsheet(scroll, 'c:\new_scr.scr');

This program will open a previously saved Scrollsheet and set the colors of the column names to Green text on a Silver background.

Related topics: ScrollsheetSetDataColor, ScrollsheetSetHeaderColor, ScrollsheetSetHiliteColor, ScrollsheetSetInfoColor, ScrollsheetSetRowNameColor, ScrollsheetSetFont, ColorRGB.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetSetColumnWidth

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetSetColumnWidth (Handle, ?ColumnWidth, ?MarginWidth)

Parameters:

Handle	Scrollsheet handle

?ColumnWidth	new column width (use -1 to leave unchanged).

?MarginWidth	new margin width (use -1 to leave unchanged).

The ScrollsheetSetColumnWidth function will set the column and margin width of the Scrollsheet with the specified Scrollsheet handle.

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetSetColumnWidth(scroll, 10, 2);

PrintScrollsheet(scroll);

This program will open a previously saved Scrollsheet and set the column width to 10 and the margin width to 2.

Related topics:  ScrollsheetSetColumnFormat, ScrollsheetSetRowName, ScrollsheetSetRowNameWidth.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetSetDataColor

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetSetDataColor (Handle, ?BackgroundColor, ?TextColor)

Parameters:

Handle	Scrollsheet handle

?BackgroundColor	background color (use -1 to leave unchanged):  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

?TextColor	text color (use -1 to leave unchanged):  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

The ScrollsheetSetDataColor function will set the colors of the data area for the Scrollsheet with the specified Scrollsheet handle.  Colors may be specified by predefined names or color numbers (see also, ColorRGB).

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetSetDataColor(scroll, AQUA, -1);

This program will open a previously saved Scrollsheet and set the colors of the data area to an Aqua background and leaves the text color unchanged.

Related topics:  ScrollsheetSetColumnNameColor, ScrollsheetSetHeaderColor, ScrollsheetSetHiliteColor, ScrollsheetSetInfoColor, ScrollsheetSetRowNameColor, ScrollsheetSetFont, ColorRGB.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetSetFont

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetSetFont (Handle, FontName$, FontSize)

Parameters:

Handle	Scrollsheet handle

FontName$	name of the font typeface.

FontSize	font size in points.

The ScrollsheetSetFont function will set the font and font size for the specified Scrollsheet.

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetSetFont(scroll, 'Helvetica', 14);

SaveScrollsheet(scroll, 'c:\new_scr.scr');

This program will open a previously saved Scrollsheet and set the font to 14 point Helvetica.

Related topics:  ScrollsheetSetColumnNameColor, ScrollsheetSetDataColor, ScrollsheetSetHeaderColor, ScrollsheetSetHiliteColor, ScrollsheetSetInfoColor, ScrollsheetSetRowNameColor, ScrollsheetSetColumnWidth, ScrollsheetSetColumnFormat.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetSetHeaderColor

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetSetHeaderColor (Handle, ?BackgroundColor, ?TextColor)

Parameters:

Handle	Scrollsheet handle

?BackgroundColor	background color (use -1 to leave unchanged):  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

?TextColor	text color (use -1 to leave unchanged):  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

The ScrollsheetSetHeaderColor function will set the colors of the header area for the Scrollsheet with the specified Scrollsheet handle.  Colors may be specified by predefined names or color numbers (see also, ColorRGB).

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetSetHeaderColor(scroll, FUSCHIA, BLACK);

This program will open a previously saved Scrollsheet and set the colors of the header area to Black text on a Fuschia background.

Related topics:  ScrollsheetSetColumnNameColor, ScrollsheetSetDataColor, ScrollsheetSetHiliteColor, ScrollsheetSetInfoColor, ScrollsheetSetRowNameColor, ScrollsheetSetFont, ColorRGB.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetSetHilite

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetSetHilite (Handle, Row, Column, State)

Parameters:

Handle	Scrollsheet handle

Row	row number of cell to be highlighted

Column	column number of cell to be highlighted

State	1 = highlight, 0 = de-highlight

The ScrollsheetSetHilite function will change the highlight state of the specified cell in the Scrollsheet with the specified Scrollsheet handle.

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetSetHilite (scroll, 2, 3, 1);

This program will open a previously saved Scrollsheet and highlight the value in the second row, third column.

Related topics:  ScrollsheetSetHiliteColor, ScrollsheetGetValue, ScrollsheetSetValue, ScrollsheetSetTextValue.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetSetHiliteColor

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetSetHiliteColor (Handle, ?TextColor)

Parameters:

Handle	Scrollsheet handle

?TextColor	text color (use -1 to leave unchanged):  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

The ScrollsheetSetHiliteColor function will set the color of highlighted text for the specified Scrollsheet.  Colors may be specified by predefined names or color numbers (see also, ColorRGB).

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetSetHiliteColor(scroll, MAROON);

ScrollsheetSetHilite(scroll, 2, 3, 1);

This program will open a previously saved Scrollsheet and set the color of the highlighted text to Maroon.  The program then highlights the value in the second row, third column.

Related topics:  ScrollsheetSetHilite, ScrollsheetSetColumnNameColor, ScrollsheetSetDataColor, ScrollsheetSetHeaderColor, ScrollsheetSetInfoColor, ScrollsheetSetRowNameColor, ScrollsheetSetFont.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetSetInfoColor

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetSetInfoColor (Handle, ?BackgroundColor, ?TextColor)

Parameters:

Handle	Scrollsheet handle

?BackgroundColor	background color (use -1 to leave unchanged):  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

?TextColor	text color (use -1 to leave unchanged):  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

The ScrollsheetSetInfoColor function will set the colors of the 'Info' area (the upper-left corner) of the Scrollsheet with the specified Scrollsheet handle.  Colors may be specified by predefined names or color numbers (see also, ColorRGB).

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetSetInfoColor(scroll, YELLOW, BLUE);

This program will open a previously saved Scrollsheet and set the colors of the info area to Blue text on a Yellow background.

Related topics:  ScrollsheetSetColumnNameColor, ScrollsheetSetDataColor, ScrollsheetSetHeaderColor, ScrollsheetSetHiliteColor, ScrollsheetSetRowNameColor, ScrollsheetSetFont, ColorRGB.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetSetMatrix

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetSetMatrix (Handle, Row, Column, Matrix)

Parameters:

Handle	Scrollsheet handle

Row	starting row number in the Scrollsheet

Column	starting column number in the Scrollsheet

Matrix	name of matrix containing values to be set in the Scrollsheet (see Arrays in Functions)

The ScrollsheetGetMatrix function places values from a matrix into the Scrollsheet with the specified Scrollsheet handle, starting at the specified Scrollsheet row and column.  If there are the matrix contains more data than can fit in the Scrollsheet at the specified location, the data will be truncated.

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\scroll.scr');

ScrollsheetSetMatrix(scroll, 1, 2, Data);

This program will open a previously saved Scrollsheet, and place the values from the the Data matrix into the Scrollsheet, beginning with the first row, second column (see also, Arrays in Functions).

Related topics:  ScrollsheetGetMatrix, ScrollsheetGetValue, ScrollsheetSetValue.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetSetRowName

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetSetRowName (Handle, Row, Name$)

Parameters:

Handle	Scrollsheet handle

Row	column number in which to set names.

Name$	string text or variable containing the top column name for the specified column (see Strings in Functions).

The ScrollsheetSetRowName function will set the name of the specified row of the specified Scrollsheet to the string text or variable (see the parameter Name$).

Example:

RandomAccess;

scroll:= NewScrollsheet(Ncases, Nvars, Data, ?Title$, ?RowNames$, ?ColumnNames$);

ScrollsheetSetRowNameWidth(scroll, 10);

for i := 1 to Ncases do

   ScrollsheetSetRowName(scroll, i, CaseName(i));

This program will create a Scrollsheet from the current data file, and set the row names to be the case names from the data file.

Related topics:  ScrollsheetSetRowNameWidth, ScrollsheetSetColumnName.

For more information on using string variables, see Strings in Functions.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetSetRowNameColor

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetSetRowNameColor (Handle, ?BackgroundColor, ?TextColor)

Parameters:

Handle	Scrollsheet handle

?BackgroundColor	background color (use -1 to leave unchanged):  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

?TextColor	text color (use -1 to leave unchanged):  BLACK, MAROON, GREEN, OLIVE, NAVY, PURPLE, TEAL, GRAY, SILVER, RED, LIME, YELLOW, BLUE, FUSCHIA, AQUA, WHITE, or a user-defined color (see ColorRGB)

The ScrollsheetSetRowNameColor function will set the colors of the row names for the Scrollsheet with the specified Scrollsheet handle.  Colors may be specified by predefined names or color numbers (see also, ColorRGB).

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetSetRowNameColor(scroll, -1, NAVY);

This program will open a previously saved Scrollsheet, set the text color of the row names to Navy and leave the background color unchanged.

Related topics:  ScrollsheetSetColumnNameColor, ScrollsheetSetDataColor, ScrollsheetSetHeaderColor, ScrollsheetSetHiliteColor, ScrollsheetSetInfoColor, ScrollsheetSetFont, ColorRGB.

For more information on specifiying default parameters, see How to set (or leave unchanged) default values of function parameters.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetSetRowNameWidth

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetSetRowNameWidth (Handle, Width)

Parameters:

Handle	Scrollsheet handle

Width	new width of row names.

The ScrollsheetSetRowNameWidth function will set the width of the row names of the Scrollsheet with the specified Scrollsheet handle.

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetSetRowNameWidth(scroll, 16);

PrintScrollsheet(scroll);

This program will open a previously saved Scrollsheet and set the width of the row names to 16.

Related topics:  ScrollsheetSetColumnWidth, ScrollsheetSetRowName,

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetSetTextValue

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetSetTextValue (Handle, Row, Column, Text$)

Parameters:

Handle	Scrollsheet handle

Row	row number in which to place the text value.

Column	column number in which to place the text value.

Text$	text string or string variable containing the text value (see Strings in Functions)

The ScrollsheetSetTextValue function will place the text string in the specified row and column of the Scrollsheet with the specified Scrollsheet handle.

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ncols := ScrollsheetGetNbCols(scroll);

nrows := ScrollsheetGetNbRows (scroll);

for i := 1 to nrows do

  for j := 1 to ncols do begin

    ScrollsheetGetValue(scroll , i, j, x);

    if x > 1000 then

      ScrollsheetSetTextValue(scroll, i, j, 'HIGH');

  end;

This program will open a previously saved Scrollsheet and place the text value HIGH in each cell of the Scrollsheet which has a value greater than 1000.

Related topics:  ScrollsheetGetTextValue, ScrollsheetSetValue, ScrollsheetGetValue.

For more information on using string variables, see Strings in Functions.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetSetTitle

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetSetTitle (Handle, TitleNo, 'Text$')

Parameters:

Handle	Scrollsheet handle

TitleNo	number of title to be changed:  use 1, 2, or 3 or TOPTITLE, SECONDTITLE, or THIRDTITLE.

Text$	text string or string variable containing new text of the title (set to an empty string to delete a title; see Strings in Functions).

The ScrollsheetSetTitle function will set the specified title of the specified Scrollsheet with the specified string (see parameter Text$).

Example:

RandomAccess;

scroll:= OpenScrollsheet('c:\scrollsh.scr');

ScrollsheetSetTitle(scroll), TOPTITLE, 'Data From Spreadsheet');

ScrollsheetSetTitle(scroll), SECONDTITLE, 'Analysis Results');

PrintScrollsheet(scroll);

This program will open an existing Scrollsheet and set the top two Scrollsheet names to Data From Spreadhseet and Analysis Results, respectively.

For more information on using string variables, see Strings in Functions.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC - ScrollsheetSetValue

  STATISTICA BASIC Library of Scrollsheet Functions - ScrollsheetSetValue (Handle, Row, Column, Value)

Parameters:

Handle	Scrollsheet handle

Row	row number in which to set the value.

Column	column number in which to set the value.

Value	value or variable containing the value to be set

The ScrollsheetSetValue function will set the specified value in the specified row and column of the specified Scrollsheet.

Example:

RandomAccess;

scroll := OpenScrollsheet('c:\new.scr');

ScrollsheetSetValue(scroll, 2, 3, 49.52);

This program will open a previously saved Scrollsheet and set the text value of the second row, third column to 49.52.

Related topics:  ScrollsheetSetTextValue, ScrollsheetGetValue, ScrollsheetGetTextValue, ScrollsheetSetMatrix, ScrollsheetGetMatrix.

For a complete list of Scrollsheet functions, see Scrollsheet Library of STATISTICA BASIC.


STATISTICA BASIC Syntax Reference - User Input/Output

  STATISTICA BASIC Syntax Reference - User Input/Output Functions

The following functions enable the user to perform a variety of input/output operations in STATISTICA BASIC.

Overview

Functions	Example and Comment

Beep	if not Valid(x) then Beep;

{Sounds a warning beep.}

CopyFile	CopyFile ('D:\STAT\report.txt', 'D:\PROJECT\project.new');

{Copies the file D:\STAT\report.txt to D:\PROJECT\project.new.}

DeleteFile	DeleteFile ('g:\junk\old.dat');

{Deletes the file g:\junk\old.dat.}

DisplayButtonBox	button := DisplayButtonBox('This is my dialog', 'Button1|Button2|Button3');

{Opens a dialog containing 3 buttons and returns the chosen button in the variable button.}

DisplayInputBox	DisplayInputBox('This is my dialog', 'Field1|Field2|Field3', output$);

{Opens a dialog containing 3 labeled edit fields; user entries in these fields will be returned in the variable output$; use GetDelimitedString function to retrieve the output from variable output$.}

DisplayLastError	DisplayLastError('Unable to Complete Execution');

{Opens a message box with the specified title containing the last error message.}

DisplayListBox	DisplayListBox('This is my dialog', 'Item1|Item2|Item3', 2);

{Creates a dialog box with a single-selection list box and OK/Cancel buttons.}

DisplayMessageBox	DisplayMessageBox(MB_OK, 'Message Box', 'This is my message text');

{Creates a message/warning box with the specified text.}

DisplayNumericInputBox	DisplayNumericInpuptBox('This is my dialog', 'Field 1:|Field 2:' array);

{Creates a dialog box with labeled numeric entry/edit fields; user entries are returned in the array.}

DisplaySelectionBox	DisplaySelectionBox('Selection Dialog', 'A|B|C|D|E', array, 3);

{Creates a dialog box with a multiple-selection list box (allows maximum of 3 items to be selected).}

GetDelimitedString	GetDelimitedString(input$, 1, output$);

{Returns as output$ the first string from the delimited string of values input$.}

MatrixRead	MatrixRead('c:\mat.txt', array);

{Reads the contents of text file "c:\mat.txt" into matrix array.}

MatrixSaveAsData	MatrixSaveAsData(DATA,'c:\stat\data.sta')

{Saves the specified matrix as the specifed data file.}

MatrixWrite	MatrixWrite('c:\mat.txt', array);

{Writes the contents of matrix array into text file "c:\mat.txt".}

OpenScrollsheet	scroll := OpenScrollsheet("c:\new.scr");

{Opens a previously saved Scrollsheet file.}

PauseAndEdit	if not Valid(x) then PauseAndEdit;

{Allows you to review and edit values of the scrollsheet.}

Pause	NewScrollsheet(2, 1, Data, 'Title1', 'Row 1|Row 2', 'Column 1'); Pause;

{Pause temporarily stops execution of the program.}

PrinterSetOrientation	PrinterSetOrientation(ORIENT_PORTRAIT);

{Sets the printer orientation in all applications.}

Read	Read(v1, text$, array(10));

{Stops execution of the program, opens a user-input window and prompts for input of values for the specified variables v1, text$ and array(10).}

RenameFile	RenameFile ('c:\data.sta', 'c:\report.sta');

{Renames c:\data.sta as c:\report.sta.}

SaveScrollsheetAsDataFile	SaveScrollsheetAsDataFile(newscroll, "c:\new.sta");

{Saves the specified Scrollsheet to disk as a STATISTICA data file.}

SaveScrollsheet	SaveScrollsheet(newscroll, "c:\examples\new.scr");

{Saves the specified Scrollsheet to disk as a Scrollsheet file.}

SelectOpenFileName	SelectOpenFileName('Select a Scrollsheet file', fname$, 'SCR');

{Displays a standard file open dialog and selects file name to be opened.}

SelectSaveFileName	SelectSaveFileName('Choose Graph file name', fname$, 'STG');

{Displays a standard file save dialog and selects the file name to be saved.}

SelectVariables1	SelectVariables1('Select Variables', 1, NVars, sellist, numlist, 'Variables for graph');

{Displays a single variable selection dialog.}

SelectVariables2	SelectVariables1('Select Variables', 1, NVars, sellist1, numlist1, 'Variables for graph', 0, 1, sellist2, numlist2, 'grouping by...');

{Displays a two variable list selection dialog.}

SelectVariables3	SelectVariables1('Select Variables', 1, NVars, sellist1, numlist1, 'List 1', , 0, NVars, sellist2, numlist2, 'List 2', 0, 1, sellist3, numlist3, 'grouping by...');

{Displays a three variable list selection dialog.}

SelectVariables4	SelectVariables1('Select Variables', 1, NVars, sellist1, numlist1, 'List 1', 0, Nvars, sellist2, numlist2, 'List 2', 0, NVars, sellist3, numlist3, 'List 3, 0, 1, sellist4, numlist4, 'grouping by...');

{Displays a four variable list selection dialog.}

Write(a, ...)	Write(CaseName, ' : ', Age);

{In Sequential mode, prints the case names, a colon, and the values of Age for each case in the file.  To start a new line, use WriteLn.}

WriteLn(a, ...)	WriteLn(CaseName, ' : ', Age);

{In Sequential mode, prints the case names, a colon, and the values of Age for each case in the file.  A new line will start for each WriteLn statement.}


STATISTICA BASIC - Read(x)

  STATISTICA BASIC Syntax Reference - Read(Variable, ...)

Parameters:

Variable	variable(s) for which value will be entered

The Read function will call the STATISTICA BASIC Read dialog with values of the specified variables.  This dialog allows the user to interactively input a value for the specified variables during the execution of the program.  The variables may be from the current data file, temporary variables, or array elements.

Examples:

Sequential;

Read(Gender, Advert);

In sequential mode, the Read function will open the STATISTICA BASIC Read dialog and prompt the user to enter values for the specified variables for each case in the data file.

RandomAccess;

for i := 1 to NCases do

  Read(Gender(i), Advert(i));

In RandomAccess mode, the Read function will open the STATISTICA BASIC Read dialog and prompt the user to enter values for the specified variables, for each specified case.

For more information about the Read dialog, see PauseAndEdit, Read Dialogs.

Related topics:  DisplayInputBox, DisplayNumericInputBox, PauseAndEdit

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - Pause

  STATISTICA BASIC Syntax Reference - Pause

Pause temporarily stops the execution of the program.  Click OK in the resulting dialog to continue with the STATISTICA BASIC program.

Example:

RandomAccess;

NewScrollsheet(2, 3, Data, 'Scrollsheet 1', 'Row 1|Row 2', 'Column 1|Column 2|Column 3');

Pause;

NewScrollsheet(3, 2, Data, 'Scrollsheet 2', 'Row 1|Row 2|Row 3', 'Column 1|Column 2');

Pause;

This program will create a two new Scrollsheets, temporarily pausing after creating each one.

Related topics:  PauseAndEdit.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - PauseAndEdit

  STATISTICA BASIC Syntax Reference - PauseAndEdit

PauseAndEdit temporarily stops the execution of the program and allows the user to review and edit the values of all variables of the currently processed case and all temporary variables used in the current STATISTICA BASIC program.  This procedure is most useful in applications designed to verify and clean data based on criteria defined in the program (the procedure is called in such programs whenever an illegal value is detected), and for debugging programs.

Example:

Sequential;

v1:=(v2+v3)/2;

if v1 < 0 then

   PauseAndEdit;

This program will transform the values of v1 and then verify the values using the PauseAndEdit function.  If a value falls below 0, then the STATISTICA BASIC Pause dialog will open.  You will then be able to edit those values as well as the values of other variables in the current data file for the respective case.

Pauseandedit in User-Defined Functions and Subroutines

When the pauseandedit statement is used inside of user-defined functions and subroutines, only the values of global variables and arguments are visible, i.e., can be reviewed and changed.  Variables and arrays that are local to the respective function and subroutine cannot be accessed.

For more information about the PauseAndEdit dialog, see PauseAndEdit, Read Dialogs.

Related topics:  DisplayInputBox, DisplayNumericInputBox, Read.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - DisplayButtonBox

  STATISTICA BASIC Syntax Reference - DisplayButtonBox (Title$, Text$)

Parameters:

Title$	title of dialog box (see Strings in Functions)

Text$	delimited button text (see Passing Lists of Strings in STATISTICA BASIC)

The DisplayButtonBox function allows you to create your own dialog box with up to 10 user-specified buttons (plus the Cancel button).  The number of the button pressed is returned by this function.

Example:

RandomAccess;

button := DisplayButtonBox('Select Output', 'Print Report|Print Graph');

if button = 1 then

   PrintScrollsheet(GetScrollsheet(0));

if button = 2 then

   PrintGraph(GetGraph(0));

This program will create a dialog box with two buttons; the user can then choose to print the current Scrollsheet or graph.

Related topics:  DisplayInputBox, DisplayListBox, Display MessageBox, DisplayNumericInputBox, DisplaySelectionBox, PauseAndEdit, Read.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - DisplayInputBox

  STATISTICA BASIC Syntax Reference - DisplayInputBox (Title$, Text$, Edit$)

Parameters:

Title$	title of dialog box (see Strings in Functions)

Text$	items to be displayed for the edit fields, passed as a delimited string (see Passing Lists of Strings in STATISTICA BASIC)

Edit$	variable in which to place the entered values or text (see Retrieving lists of strings in STATISTICA BASIC).  As input, may pass initial values (see Passing Lists of Strings in STATISTICA BASIC).

The DisplayInputBox function allows you to define a dialog box in which the user can enter text and/or numeric values and store those values in a text variable (see parameter Edit$).  The function will return a value of 1 if the user presses OK.  It will return a value of 0 if the user presses Cancel.  If you want to enter only numeric values, use the function DisplayNumericInputBox.

Example:

RandomAccess;

DisplayInputBox('An Example of an Input Dialog Box', 'City of Residence|

                  State of Residence', out$);

GetDelimitedString(out$,1,city$);

GetDelimitedString(out$,2,state$);

This program will create a dialog box with two edit fields -- one in which you can enter the city and one in which you can enter the state.  The function GetDelimitedString will allow you to retreive the inputted values.

Related topics:  DisplayButtonBox, DisplayListBox, Display MessageBox, DisplayNumericInputBox, DisplaySelectionBox, PauseAndEdit, Read.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - DisplayLastError

  STATISTICA BASIC Syntax Reference - DisplayLastError (Title$)

Parameters:

Title$	title of dialog box (see Strings in Functions)

The DisplayLastError function allows you to create a dialog in which the last program error will be displayed.  For a complete list of error messages, see Run-Time Errors and Compile-Time Errors.

Example:

RandomAccess;

dim scroll(5);	{declaration of an array for Scrollsheet handles}

scroll(1):=OpenScrollsheet('d:\corr1.scr');

scroll(2):=OpenScrollsheet('d:\corr2.scr');

scroll(3):=OpenScrollsheet('d:\corr3.scr');

scroll(4):=OpenScrollsheet('d:\corr4.scr');

scroll(5):=OpenScrollsheet('d:\corr5.scr');

if MatrixAllNonZero(scroll) = 0 then

  DisplayLastError('Unable to open one or more files');

If the option Display all Warnings and Error Messages is deselected in the STATISTICA BASIC Options dialog, (accessible by selecting Mode from the Options pull-down menu), this program will open all files which exist.  If the Display all Warnings and Error Messages option is selected, the program will stop at the first file which does not exist.

By default, STATISTICA BASIC will display all error messages and warnings which occur and halt execution of the program.  However, this display may be supressed (see the option Display all Warnings and Error Messages in the STATISTICA BASIC Options dialog), and program execution will not be interrupted.  Advanced users may wish to incorporate their own methods of error handling within their STATISTICA BASIC programs, and use the DisplayLastError function if it is necessary to display a program error message to the user.

Related topics:  DisplayMessageBox.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - DisplayListBox

  STATISTICA BASIC Syntax Reference - DisplayListBox (Title$, Text$, DefaultItem)

Parameters:

Title$	title of dialog box (see Strings in Functions)

Text$	delimited list text (see Passing Lists of Strings in STATISTICA BASIC)

DefaultItem	number of the default item in the list

The DisplayListBox function allows you to create a dialog in which the user can select a value from a pre-defined list of values.  The number of the selected item is returned by the function.  In order to select multiple items from a list, use DisplaySelectionBox.

Example:

RandomAccess;

nbitem := DisplayListBox('Select an Item to be set to 0', 'Item1|Item2|Item3', 1);

if nbitem > 0 then

   Gender(nbitem) := 0;

This program will open a dialog containing the specified list of values.  Value number 1 (Item1) will be highlighted in the list.  The selected item from the list is returned in the variable nbitem.

Related topics:  DisplayButtonBox, DisplayInputBox, Display MessageBox, DisplayNumericInputBox, DisplaySelectionBox.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - DisplayMessageBox

  STATISTICA BASIC Syntax Reference - DisplayMessageBox (Type, Title$, Text$)

Parameters:

Type	type of message box:  MB_OK, MB_OKCANCEL, MB_RETRYCANCEL, MB_YESNO, MB_YESNOCANCEL

Title$	title of dialog box (see Strings in Functions)

Text$	text of message (see Strings in Functions)

Return value:	a code indicating which button was pressed (see below).

The DisplayMessageBox function allows you to create a dialog with a user-specified message.  By specifiying the Type, you can choose the buttons to be included in the box (e.g., OK or Yes, No, and Cancel).  The function returns the code of the button that was pressed; the following predefined button code values are supported:  IDYES, IDNO, IDOK, IDCANCEL, IDABORT, IDRETRY, IDIGNORE.

The message dialog may be further customized by selecting an icon from among the following types: MB_ICONSTOP, MB_ICONQUESTION, MB_ICONEXCLAMATION, MB_ICONINFORMATION.  To include the respective icon, add its value to the basic Type specified for the dialog (e.g., MB_OK+MB_ICONSTOP).

Example:

Sequential;

if v2 = 0 then

   if DisplayMessageBox(MB_OK+MB_ICONQUESTION, 'Zero Value Detected',

                        'Continue?') = IDNO then

      Stop;

This program will open a message box which will allow the user to respond to the message 'Do You Want to Continue?'

Related topics:  DisplayButtonBox, DisplayInputBox, DisplayListBox, DisplayNumericInputBox, DisplaySelectionBox.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - DisplayNumericInputBox

  STATISTICA BASIC Syntax Reference - DisplayNumericInputBox (Title$, Text$, Values)

Parameters:

Title$	title of dialog box (see Strings in Functions)

Text$	delimited text containing labels for input fields (see Passing Lists of Strings in STATISTICA BASIC)

Values	array in which to place the entered values (see Arrays in Functions).  On input, may contain initial values of entry fields.

The DisplayNumericInputBox function allows you to define a dialog box in which the user can enter numeric values and store those values in an array (see parameter Values).  The function will return a value of 1 if the user presses OK.  It will return a value of 0 if the user presses Cancel.  If you want to enter text and numeric values, use the function DisplayInputBox.

Example:

RandomAccess;

Dim Param(2);

DisplayNumericInputBox ('An Example of an Input Dialog Box', 'Value 1|Value 2', Param);

for i := 1 to NCases do

  v2 := Param(1) + Param(2)*v1;

This program will create a dialog box with two edit fields.  The values that are input here will be placed in the vector Param and used to compute new values for the second variable in the current data file.

Related topics:  DisplayButtonBox, DisplayInputBox, DisplayListBox, Display MessageBox, DisplaySelectionBox.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - DisplaySelectionBox

  STATISTICA BASIC Syntax Reference - DisplaySelectionBox (Title$, Text$, SelectedItems, ?MaxItems)

Parameters:

Title$	title of dialog box (see Strings in Functions)

Text$	items to be displayed in the list box, passed as a delimited string (see Passing Lists of Strings in STATISTICA BASIC)

SelectedItems	array to which the output will be sent (see Arrays in Functions)

MaxItems	maximum number of items which can be selected from list

The DisplaySelectionBox function allows you to create a dialog in which the user can select one or more values from a pre-defined list of values.  The function will return the number of items selected.  The numbers of the selected items will be placed in the array Selected Items (see Arrays in Functions).  In order to select single items from a list, use DisplayListBox.

Example:

RandomAccess;

Dim Out(4);

nbsel := DisplaySelectionBox('Select Item', 'Scatterplot|Lineplot|Stepplot|Scrollsheet',

                             Out, 4);

for i := 1 to nbsel do begin

  sel := Out(i);

  if sel = 1 then

     NewGraph(SCATTERPLOT, 'Scatterplot', VarName(3), VarName(4), NCases, v3, v4);

  if sel = 2 then

     NewGraph(LINEPLOT, 'Line plot', VarName(3), VarName(4), NCases, v3, v4);

  if sel = 3 then

     NewGraph(STEPPLOT, 'Step plot', VarName(3), VarName(4), NCases, v3, v4);

  if sel = 4 then

     NewScrollsheet(NCases, Nvars, Data, 'Data from Spreadsheet', ?RowNames$, ?ColNames$);

  end;

This program will open a dialog containing the specified list of items.  After selecting one or more items from this list, the the number of items selected will be returned in the variable nbsel and the list of selected items will be sent to the array Out.  The program will then produce the requested output.

Related topics:  DisplayButtonBox, DisplayInputBox, DisplayListBox, Display MessageBox, DisplayNumericInputBox.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - GetDelimitedString

  STATISTICA BASIC Syntax Reference - GetDelimitedString (Text$, Nb, String$)

Parameters:

Text$	delimited string (see Lists of Strings in STATISTICA BASIC)

Nb	number of the text item from delimited string to retrieve

String$	string variable (see Strings in Functions) to which the specified text will be outputted

The GetDelimitedString function allows you to retrieve delimited text (for example, output from the DisplayInputBox function).

Example:

RandomAccess;

DisplayInputBox('College Graduates', 'Name|Degree|Year Graduated|School', candidate$);

GetDelimitedString (candidate$, 1, name$);

GetDelimitedString (candidate$, 2, degree$);

GetDelimitedString (candidate$, 3, year$);

GetDelimitedString (candidate$, 4, school$);

WriteLn(name$, ' received a ', degree$, ' from ', school$, ' on ', year$);

This program will open a dialog in which you can enter the requested values (see DisplayInputBox).  After selecting one or more values from this list, the output will be sent to the string variable candidate$.  The function WriteLn will write the retrieved values to the printer, file, or Text/output Window (whichever is selected in the Page/Output Setup dialog).

Related topics:  DisplayButtonBox, DisplayInputBox, DisplayListBox, Display MessageBox, DisplayNumericInputBox, DisplaySelectionBox.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - SelectOpenFileName

  STATISTICA BASIC Syntax Reference - SelectOpenFileName (?Title$, FileName$, ?Extension$)

Parameters:

?Title$	title of the dialog box (see Strings in Functions)

FileName$	string variable containing name of file to be opened (see Strings in Functions)

?Extension$	string containing file extension to search for (see Strings in Functions):  may be STG, STA, SCR, TXT or other user-specified extension (if the default ? is used, All Files will be specified).  If a user-specified extension is given, the generic description Specified Files is given as a title.

Return value:	0 - Cancel, 1 - OK

The SelectOpenFileName function displays a standard file open dialog.  The file name selected is returned in the variable specified as FileName$.

Example:

RandomAccess;

SelectOpenFileName ('Select Scrollsheet file', fname$, 'SCR');

OpenScrollsheet(fname$);

This program will display a standard file open dialog and prompt for the selection of a Scrollsheet file name to be opened.  The selected Scrollsheet file is then displayed.

Related topics:  OpenScrollsheet, OpenGraph.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - SelectSaveFileName

  STATISTICA BASIC Syntax Reference - SelectSaveFileName (?Title$, FileName$, ?Extension$)

Parameters:

?Title$	title of the dialog box (see Strings in Functions)

FileName$	string variable containing name of file to be saved (see Strings in Functions)

?Extension$	string containing file extension to search for (see Strings in Functions):  may be STG, STA, SCR, TXT or other user-specified extension (if the default ? is used, All Files will be specified).  If a user-specified extension is given, the generic description Specified Files is given as a title.

Return value:	0 - Cancel, 1 - OK

The SelectSaveFileName function displays a standard file save dialog.  The file name selected is returned in the variable specified as FileName$.

Example:

RandomAccess;

SelectSaveFileName('Specify Scrollsheet file name', fname$, 'SCR');

SaveScrollsheet(GetScrollsheet(0), fname$);

This program will display a standard file save dialog and prompt for the entry of the name of a Scrollsheet file to be saved.  The current Scrollsheet file is then saved as this name.

Related topics:  SaveScrollsheet, SaveGraph.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - SelectVariables1

  STATISTICA BASIC Syntax Reference - SelectVariables1 (?Title$, ?MinVars1, ?MaxVars1, VarList1, Count1, ?Text1$)

Parameters:

?Title$	title of the dialog box (see Strings in Functions)

?MinVars1	minimum number of variables to be selected

?MaxVars1	maximum number of variables to be selected

VarList1	vector (see Arrays in Functions) containing the list of selected variable numbers

Count1	number of variables selected

?Text1$	text of prompt in the dialog box

Return value:	0 - Cancel, 1 - OK

The SelectVariables1 function displays a standard one variable list selection dialog.  The numbers of the variables selected are returned as elements in the vector VarList1.

Example:

RandomAccess;

Dim case(50);

SelectVariables1('Select Variables', 1, 1, yvar, count, 'Variables to be plotted');

for j := 1 to NCases do case(j) := j;

graph := NewGraph(LINEPLOT, 'Line Plot', VarName(yvar), 'Case Number', NCases,

                    case, Data(1,yvar));

DisplayGraph(graph);

if DisplayMessageBox(MB_YESNO, 'Print', 'Print Graph?') = IDYES then

   PrintGraph(graph);

DeleteGraph(graph);

This program will prompt for the selection of a variable from the list of all variables in the current data file, then produce a line plot of the selected variable.

Related topics:  SelectVariables2, SelectVariables3, SelectVariables4.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - SelectVariables2

  STATISTICA BASIC Syntax Reference - SelectVariables2 (?Title$, ?MinVars1, ?MaxVars1, VarList1, Count1, ?Text1$, ?MinVars2, ?MaxVars2, VarList2, Count2, ?Text2$)

Parameters:

?Title$	title of the dialog box (see Strings in Functions)

?MinVars1	minimum number of variables to be selected in first list

?MaxVars1	maximum number of variables to be selected in first list

VarList1	vector (see Arrays in Functions) containing the first list of selected variable numbers

Count1	number of variables selected in first list

?Text1$	text of prompt for first list in the dialog box

?MinVars2	minimum number of variables to be selected in second list

?MaxVars2	maximum number of variables to be selected in second list

VarList2	vector (see Arrays in Functions) containing the second list of selected variable numbers

Count2	number of variables selected in second list

?Text2$	text of prompt for second list in the dialog box

Return value:	0 - Cancel, 1 - OK

The SelectVariables2 function displays a standard two variable list selection dialog.  The numbers of the selected variables from each list are returned as elements in the vectors VarList1 and VarList2, respectively.

Example:

RandomAccess;

ReDim yvar(NVars);

SelectVariables2('Select Variables', 1, 1, xvar, count1, 'Select one X variable',

                 1, NVars, yvar, count2, 'Select Y variable(s)');

for i := 1 to count2 do

   NewGraph(SCATTERPLOT, 'Scatterplot', VarName(yvar(i)), VarName(xvar), NCases,

            Data(1,Xvar), Data(1,Yvar(i)));

This program will prompt for the selection of one X and one or more Y variables, then produce a scatterplot of the selected variables.

Related topics:  SelectVariables1, SelectVariables3, SelectVariables4.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - SelectVariables3

  STATISTICA BASIC Syntax Reference - SelectVariables3 (?Title$, ?MinVars1, ?MaxVars1, VarList1, Count1, ?Text1$, ?MinVars2, ?MaxVars2, VarList2, Count2, ?Text2$, ?MinVars3, ?MaxVars3, VarList3, Count3, ?Text3$)

Parameters:

?Title$	title of the dialog box (see Strings in Functions)

?MinVars1	minimum number of variables to be selected in first list

?MaxVars1	maximum number of variables to be selected in first list

VarList1	vector (see Arrays in Functions) containing the first list of selected variable numbers

Count1	number of variables selected in first list

?Text1$	text of prompt for first list in the dialog box

?MinVars2	minimum number of variables to be selected in second list

?MaxVars2	maximum number of variables to be selected in second list

VarList2	vector (see Arrays in Functions) containing the second list of selected variable numbers

Count2	number of variables selected in second list

?Text2$	text of prompt for second list in the dialog box

?MinVars3	minimum number of variables to be selected in third list

?MaxVars3	maximum number of variables to be selected in third list

VarList3	vector (see Arrays in Functions) containing the third list of selected variable numbers

Count3	number of variables selected in third list

?Text3$	text of prompt for third list in the dialog box

Return value:	0 - Cancel, 1 - OK

The SelectVariables3 function displays a standard three variable list selection dialog.  The numbers of the variables selected from each list are returned as elements in the vectors VarList1, VarList2, and VarList3, respectively.

Example:

RandomAccess;

SelectVariables3('Select Variables', 1, 1, x, count1, 'Select X variable', 1, 1, y,

                 count2, 'Select Y variable', 1, 1, z, count3, 'Select Z variable');

NewSurface(FIT_QUADRATIC_3D, ?UNUSED$, '3D Surface Plot@A@F', VarName(x),

           VarName(y), VarName(z), NCases, Data(1,x), Data(1,y), Data(1,z));

This program will prompt for the selection of three variables, then produce a 3D surface plot of the selected variables.

Related topics:  SelectVariables1, SelectVariables2, SelectVariables4.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - CopyFile

  STATISTICA BASIC Syntax Reference - CopyFile (Sourcename$, Destname$)

Parameters:

Sourcename$	name of file to be copied

Destname$	destination of file to be copied

Return value:	0 - Failure, 1 - Success

The CopyFile function copies the source file to the destination file.

Example 1:

CopyFile('d:\stat\data1.sta', 'd:\help\data2.sta');

This program will copy the file data1.sta to a the destination file data2.sta.

This procedure returns the value 1 if the file is copied successfully and the value 0 if the file is not copied.  Possible reasons for failure include incorrect path name and insufficient disk space.

Example 2:

completed:= CopyFile ('c:\temp\file1.txt','d:\project\file2.txt');

if (completed = 1) then writeln ('Operation Completed')

else writeln ('Operation Failed');

This program assigns the value 1 to the variable completed if file1.txt is successfully copied to file2.txt, then it writes Operation Completed in the currently selected output device (see Page/Output Setup dialog).  Otherwise the program writes Operation Failed in the currently selected output device.

Note:  This command is not limited to STATISTICA file formats, and it can be used with any type of file.

Related topics:  DeleteFile, RenameFile.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - DeleteFile

  STATISTICA BASIC Syntax Reference - DeleteFile (Filename$)

Parameter:

Filename$	name of file to be deleted

Return value:	0 - Failure, 1 - Success

The DeleteFile function deletes the specified file.

Example 1:

DeleteFile('d:\stat\junk.rtf');

This program will delete the program d:\stat\junk.rtf

This procedure returns the value 1 if the file is deleted successfully and the value 0 if the file is not deleted.  Possible reasons for failure include incorrect path name and file in use by another user.

Example 2:

completed:= DeleteFile ('d:\temp\old.txt');

if (completed = 1) then writeln ('Operation Completed')

else writeln ('Operation Failed');

This program assigns the value 1 to the variable completed if old.txt is successfully deleted, then it writes Operation Completed in the currently selected output device (see Page/Output Setup dialog).  Otherwise the program writes Operation Failed in the currently selected output device.

Note:  This command is not limited to STATISTICA file formats, and it can be used with any type of file.

Related topics:  CopyFile, RenameFile.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - RenameFile

  STATISTICA BASIC Syntax Reference - RenameFile (Sourcename$, Destname$)

Parameters:

Sourcename$	name of file to be renamed

Destname$	destination of file to be renamed

Return value:	0 - Failure, 1 - Success

The RenameFile function renames the source file with the destination filename.

Example 1:

RenameFile('d:\stat\noname.sta', 'd:\data\newdata.sta');

This program will rename the file d:\stat\noname.sta with the name d:\data\newdata.sta.

This procedure returns the value 1 if the file is copied successfully and the value 0 if the file is not copied.  Possible reasons for failure include incorrect path name and insufficient disk space.

Example 2:

completed:= RenameFile ('c:\report\file1.txt','c:\report\file2.txt');

if (completed = 1) then writeln ('Operation Completed')

else writeln ('Operation Failed');

This program assigns the value 1 to the variable completed if file1.txt is successfully renamed as file2.txt, then it writes Operation Completed in the currently selected output device (see Page/Output Setup dialog).  Otherwise the program writes Operation Failed in the currently selected output device.

Note:  This command is not limited to STATISTICA file formats, and it can be used with any type of file.

Related topics:  CopyFile, DeleteFile.

For a complete list of Input/Output functions, see User Input/Output Functions.


STATISTICA BASIC - SelectVariables4

  STATISTICA BASIC Syntax Reference - SelectVariables4 (?Title$, ?MinVars1, ?MaxVars1, VarList1, Count1, ?Text1$, ?MinVars2, ?MaxVars2, VarList2, Count2, ?Text2$, ?MinVars3, ?MaxVars3, VarList3, Count3, ?Text3$, ?MinVars4, ?MaxVars4, VarList4, Count4, ?Text4$)

Parameters:

?Title$	title of the dialog box (see Strings in Functions)

?MinVars1	minimum number of variables to be selected in first list

?MaxVars1	maximum number of variables to be selected in first list

VarList1	vector (see Arrays in Functions) containing the first list of selected variable numbers

Count1	number of variables selected in first list

?Text1$	text of prompt for first list in the dialog box

?MinVars2	minimum number of variables to be selected in second list

?MaxVars2	maximum number of variables to be selected in second list

VarList2	vector (see Arrays in Functions) containing the second list of selected variable numbers

Count2	number of variables selected in second list

?Text2$	text of prompt for second list in the dialog box

?MinVars3	minimum number of variables to be selected in third list

?MaxVars3	maximum number of variables to be selected in third list

VarList3	vector (see Arrays in Functions) containing the third list of selected variable numbers

Count3	number of variables selected in third list

?Text3$	text of prompt for third list in the dialog box

?MinVars4	minimum number of variables to be selected in fourth list

?MaxVars4	maximum number of variables to be selected in fourth list

VarList4	vector (see Arrays in Functions) containing the fourth list of selected variable numbers

Count4	number of variables selected in fourth list

?Text4$	text of prompt for fourth list in the dialog box

Return value:	0 - Cancel, 1 - OK

The SelectVariables4 function displays a standard four variable list selection dialog.  The numbers of the variables selected from each list are returned as elements in the vectors VarList1, VarList2, VarList3 and VarList4, respectively.

Example:

RandomAccess;

SelectVariables4('Select Variables', 1, 1, x, count1, 'Select X variable', 1, 1, y,

                 count2, 'Select Y variable', 1, 1, z, count3, 'Select Z variable',

                 1, 1, va, count4, 'Select V variable');

NewTernary(TERNARY_SURFACE, FIT_TERN_QUADRATIC, ?UNUSED$, ?UNUSED, 'Ternary Plot@A@F',

           VarName(x), VarName(y), VarName(z), VarName(va), NCases, Data(1,x), Data(1,y),

           Data(1,z), Data(1,va));

This program will prompt for the selection of four variables, then produce a ternary (trilinear) plot of the selected variables.

Related topics:  SelectVariables1, SelectVariables2, SelectVariables3.

For a complete list of Input/Output functions, see User Input/Output Functions.


  STATISTICA BASIC - PauseAndEdit, Read Dialogs

This STATISTICA BASIC procedure temporarily stops the execution of the program and allows the user to review and edit values of the currently processed data file and all STATISTICA BASIC program variables.  The procedure displays the STATISTICA BASIC PauseAndEdit or Read dialog (depending on which function was used) in which you can review and edit the values for the respective variables.

When this dialog is called, the user can also decide whether to continue executing the STATISTICA BASIC program.  This procedure is most useful in applications designed to verify and clean data based on criteria defined in the program (the procedure can be called in such programs whenever an illegal value is detected).  Unlike in the data verification and cleaning facilities of Data Management which check only whether values belong to the specified lists or ranges of allowable values, the verification criteria used in STATISTICA BASIC programs may contain complex conditional relations between values in the data file.  The procedure is also very helpful for debugging complex STATISTICA BASIC programs.

Example:

Sequential;

  if not Valid(varx) or (v1 + v2 > 3) then {when the value of varx is Missing or the

                                             sum of v1 and v2 greater than 3, then}

    PauseAndEdit;                          {stop and show data from this record}

This program will pause whenever a missing value is encountered in variable varx or the sum of variables 1 and 2 is greater than 3, so that the data can be reviewed and edited (if desired).

Pause dialog:

Variable

Value

Get

Put

Continue

Cancel

Stop Program

Review Variables


STATISTICA BASIC Pause and Edit, Read Dialogs - Variable

  STATISTICA BASIC Pause, Read Dialogs - Variable

In this edit field, the name of the variable for which to retrieve (Get) or write (Put) the respective value may be entered or changed.  The variable may be from the current data file (referenced by name or by Vx, where x is the variable number), a temporary variable from the STATISTICA BASIC program, or an array element (see Arrays in Functions.  Subscripted variables are used to refer to specific elements of arrays (e.g, v1(3), GENDER(10), Array(5), etc.).


STATISTICA BASIC Pause and Edit, Read Dialogs - Value

  STATISTICA BASIC Pause, Read Dialogs - Value

In this edit field, the value of the respective variable may be entered or changed.  The current value of the variable may be placed in this field by pressing the Get button; the updated value may be written back to the variable by pressing the Put button.  Pressing Continue will write all values to the respective variables and close the dialog.


STATISTICA BASIC Pause and Edit, Read Dialogs - Get

  STATISTICA BASIC Pause, Read Dialogs - Get

Press this button to read the current value of the respective Variable into the Value field.


STATISTICA BASIC Pause and Edit, Read Dialogs - Put

  STATISTICA BASIC Pause, Read Dialogs - Put

Press this button to write the value in the Value field to the respective Variable.


STATISTICA BASIC Pause and Edit, Read Dialogs - Continue

  STATISTICA BASIC - Pause, Read Dialogs - Continue

Press this button to return to the execution of the current STATISTICA BASIC program.  All current Values will be written to the respective Variables.


STATISTICA BASIC Pause and Edit, Read Dialogs - Cancel

  STATISTICA BASIC - Pause, Read Dialogs - Cancel

Press this button to return to the execution of the current STATISTICA BASIC program without writing values to the respective variables.  (Note: if Put is pressed, the respective Value is immediately written to the respective Variable.)


STATISTICA BASIC Pause and Edit, Read Dialogs - Stop

  STATISTICA BASIC - Pause, Read Dialogs - Stop Program

Press this button to halt execution of the current STATISTICA BASIC program.


STATISTICA BASIC Pause and Edit, Read Dialogs - Review Variables

  STATISTICA BASIC Pause, Read Dialogs - Review Variables

Pressing this button will open the Reviewing Variables dialog in which you can review the names of variables from the current STATISTICA data file, as well as other variable attributes.


STATISTICA BASIC - Beep

  STATISTICA BASIC Syntax Reference - Beep

This STATISTICA BASIC procedure sounds a beep.

Example:

Sequential;

  if not Valid(v1) then   {when the value of v1 is Missing, then}

    begin

      Beep;   {sound a warning}

      PauseAndEdit;   {stop and show data from this record}

    end;

This program will sound a warning and PauseAndEdit whenever a missing value is encountered in variable 1, so that the data can be reviewed and edited (if desired).


Matrix Library of STATISTICA BASIC - Overview

 Matrix Library of STATISTICA BASIC - Conventions and Overview

STATISTICA BASIC includes an integrated, powerful Matrix Language allowing you to develop your own statistical and other computational programs by writing compact code referencing a comprehensive library of highly optimized matrix procedures.  The supported Matrix Language operations include a complete matrix algebra language and a comprehensive selection of specialized procedures that are particularly useful in the development of custom statistical applications:

•	functions for computing the determinant, inverse, eigenvalues, eigenvectors, sweeping, GramSchmidt orthonormalization, Cholesky decomposition, singular values, singular value decomposition, matrix rank, solutions to linear equations, general pseudo-inverse;

•	functions for computing correlations and covariances (with or without the intercept);

•	functions for extracting specific columns, rows, submatrices, a diagonal, transposing, and combining matrices;

•	addition, subtraction, multiplication, division by scalar (for each element of the matrix);

•	addition, subtraction, multiplication of matrices;

•	elementwise relational operators (<, <=, >, >=, =, not =);

•	elementwise logical operators (not, and, or);

•	tests for all elements  0, any element  0;

•	options to read matrices from STATISTICA data files or ASCII text files, and save them as STATISTICA data files or ASCII text files.

The Matrix Language procedures of STATISTICA BASIC make the programming of even sophisticated statistical procedures quick, easy, and extremely efficient.  For example, developing a customized multiple regression procedure takes just a few lines of code.  Also, the output from your custom procedures can be easily handled in a most "professional" and efficient manner (see Output from STATISTICA BASIC), so that your custom procedures will look like "a part of STATISTICA."

Matrix Language procedures may be applied to the current data file to perform many common data management procedures (see Data Management Functions).

Processing Mode

The matrix functions in STATISTICA BASIC are most useful if the current mode is RandomAccess (the default mode), unless you intend to repeat all matrix operations specified in the program for each case of the current data set (see Sequential vs. RandomAccess Mode).

Matrices and Vectors

Arrays, other than those representing the data file (array Data or array V), are declared using either the Dim or ReDim statement.  The Dim statement (which must appear at the beginning of the program) declares an array with specific dimensions, e.g.:

Dim array1(4,6);

In this example, array1 is a two-dimensional array (matrix) with 4 rows and 6 columns.  Matrices may have up to 8 dimensions, but most useful matrix functions will operate on one-dimensional arrays or vectors, or two-dimensional matrices.

The ReDim statement may be used to declare new arrays or change the size of previously-declared arrays (the number of dimensions must remain the same; e.g., you cannot re-dimension a two-dimensional array as a three-dimensional array).  The array dimensions specified using ReDim may be dynamic, computed at the time of execution of the program, e.g.:

ReDim array2(NCases, NVars);

In this example, array2 is a two-dimensional array (matrix) with as many rows and columns as the respective number of cases and variables in the current data file.

For more information on using arrays, see Arrays in Functions.

Sizes of Matrices and Vectors

All matrix functions can handle huge arrays, that is, arrays that are as large as your system permits; STATISTICA will allocate as much memory as possible given your system configuration.  Thus, you can write programs for performing operations on extremely large matrices.

Columns and Rows

The program follows the standard convention for referencing the elements in two-dimensional matrices as Matrix(row,column).  For example, the array declared as:

Dim array1(10,6);

has 10 rows and 6 columns.

Referencing the Input Data File

The values in the currently connected data file may be referenced as Data(row, column); this reserved matrix name (Data) cannot be used in any other way.  Specific columns (column vectors) in the data file can be referenced as Data(1,column).  For example:

MatrixCopy (Data(1,1), 1, 1, 0, 0, Data(1,2), 1, 1);

This statement will copy the first column of the data file (data (1,1)) to the second column of the data file (data(1,2)); for additional details concerning the syntax of this command, refer to MatrixCopy.

Matrix Functions

Like all other functions in STATISTICA BASIC, all matrix functions are accessible via the Function Wizard.  Because the program will automatically "remember" the dimensions of matrices, they do not have to be passed as arguments to the matrix functions, greatly simplifying the task of writing programs.  For example:

Dim corr (8,8);

MatrixCorrelations (Data, 1, corr);

MatrixDisplay (corr, 'Correlation Matrix');

This program will compute a correlation matrix (8 by 8) for a data file with 8 variables, and display it in a Scrollsheet.

For a complete list of matrix functions, see STATISTICA BASIC Library of Matrix Functions.

Memory Arrangement of Arrays

Matrices are stored internally in memory by columns.


Matrix Library of STATISTICA BASIC

  STATISTICA BASIC Syntax Reference - Matrix Library of STATISTICA BASIC

STATISTICA BASIC allows you to perform a variety of matrix operations (listed below).  For a description of using arrays in STATISTICA BASIC, see How to Specify Arrays in STATISTICA BASIC Functions.

Overview

Functions	Example and Comment

Dim	Dim array(10, 10);

{Declares a two-dimensional matrix named array.}

MatrixAdd	MatrixAdd(array1, array2, resultar);

{Adds each element of array1 to corresponding element of array2 and places result in matrix resultar.}

MatrixAllNonZero	result := MatrixAllNonZero(array);

{Assigns 1 to variable result if each element of array is non-zero, otherwise result is set to 0.}

MatrixAnyNonZero	result := MatrixAnyNonZero(array);

{Assigns 1 to variable result if any element of array is non-zero, otherwise result is set to 0.}

MatrixCholeskyDecomposition	MatrixCholeskyDecomposition(array1, array2);

{Performs Cholesky Decomposition of matrix array1 and stores results in array2.}

MatrixCombineHoriz	MatrixCombineHoriz(array1, array2, resultar);

{Places values of array2 to the right of array1 in result matrix resultar.}

MatrixCombineVert	MatrixCombineVert(array1, array2, resultar);

{Places values of array2 below array1 in result matrix resultar.}

MatrixCopy	MatrixCopy(array1, 1, 1, 4, 5, array2, 1, 2);

{Copies 4 rows, 5 columns from array1 beginning at first row and first column, and places copied values in array2 beginning at first row, second column.}

MatrixCorrelations	MatrixCorrelations(array, 1, corrs);

{Computes correlations between columns of array and places coefficients in square matrix corrs.}

MatrixCrossProductOfDev	MatrixCrossProductOfDev(array, 1, cross);

{Computes squared deviations and crossproducts of deviations for matrix array and places results in square matrix cross.}

MatrixDet	MatrixDet(array, det);

{Computes determinant of square matrix array and places resulting determinant in variable det.}

MatrixDisplay	MatrixDisplay(array, 'Matrix Array');

{Displays values of matrix array in a Scrollsheet titled Matrix Array.}

MatrixDuplicate	MatrixDuplicate(array, dupl);

{Duplicates matrix array into matrix dupl.}

MatrixEigenValues	MatrixEigenValues(array, eigenval, numeign);

{Places eigenvalues computed for matrix array into vector eigenval and places number of positive eigenvalues computed into variable numeigen.}

MatrixEigenVectors	MatrixEigenVectors(array, eigenval, eigenvec, numeign);

{Places eigenvectors computed for matrix array into the matrix eigenvec, eigenvalues into vector eigenval, and places number of positive eigenvalues computed in variable numeigen.}

MatrixElemAdd	MatrixElemAdd(array, scalar, resultar);

{Adds value of constant scalar to each element of matrix array and places result in matrix resultar.}

MatrixElemDivide	MatrixElemDivide(array, scalar, resultar);

{Divides each element of matrix array by value of constant scalar and places result in matrix resultar.}

MatrixElemMultiply	MatrixElemMultiply(array, scalar, resultar);

{Multiplies each element of matrix array by value of constant scalar and places result in matrix resultar.}

MatrixElemSubtract	MatrixElemSubtract(array, scalar, resultar);

{Subtracts value of constant scalar from each element of matrix array and places result in matrix resultar.}

MatrixExtract	MatrixExtract(array, 1, 2, 4, 5, submatrx);

{Extracts 4 rows, 5 columns of values from matrix array, beginning with row 1, column 2, and places extracted values in matrix submatrx.}

MatrixFill	MatrixFill(2.71828, array, 2, 1, 1, 0);

{Fills entire second column of matrix array with the value 2.71828.}

MatrixGeneralPseudoInverse	MatrixGeneralPseudoInverse(array, resultar);

{Computes the generalized inverse of the matrix array and places it in the matrix resultar.}

MatrixGetColumn	MatrixGetColumn(array, 3, vect);

{Extracts the third column from the matrix array and places it in the vector vect.}

MatrixGetDiagonal	MatrixGetDiagonal(array, vect);

{Extracts the main diagonal from the matrix array and places it in the vector vect.}

MatrixGetRow	MatrixGetRow(array, 2, vect);

{Extracts the second row from the matrix array and places it in the vector vect.}

MatrixGramSchmidtOrt	MatrixGramSchmidtOrt(array, resultar);

{Performs Gram-Schmidt orthonormalization of the matrix array and places results in the matrix resultar.}

MatrixIdentity	MatrixIdentity(array);

{Sets the values of matrix Array to the identity matrix (1 along main diagonal, 0 elsewhere).}

MatrixInverse	MatrixInverse(array, resultar);

{Computes the inverse of the matrix array and places it in the matrix resultar.}

MatrixIsEqual	MatrixIsEqual(array1, array2, resultar);

{Compares each element of array1 to the corresponding element of array2 and if equal, places a 1 in the corresponding element of matrix resultar.}

MatrixIsGreater	MatrixIsGreater(array1, array2, resultar);

{Compares each element of array1 to the corresponding element of array2 and if value of array1 is greater, places a 1 in the corresponding element of matrix resultar.}

MatrixIsGreaterEqual	MatrixIsGreaterEqual(array1, array2, resultar);

{Compares each element of array1 to the corresponding element of array2 and if value of array1 is equal or greater, places a 1 in the corresponding element of matrix resultar.}

MatrixIsLess	MatrixIsLess(array1, array2, resultar);

{Compares each element of array1 to the corresponding element of array2 and if value of array1 is less, places a 1 in the corresponding element of matrix resultar.}

MatrixIsLessEqual	MatrixIsLessEqual(array1, array2, resultar);

{Compares each element of array1 to the corresponding element of array2 and if value of array1 is equal or less, places a 1 in the corresponding element of matrix resultar.}

MatrixIsNotEqual	MatrixIsNotEqual(array1, array2, resultar);

{Compares each element of array1 to the corresponding element of array2 and if not equal, places a 1 in the corresponding element of matrix resultar.}

MatrixKroneckerMultiply	MatrixKroneckerMultiply(array1, array2, resultar);

{Computes the Kronecker product of the matrices array1 and array2 and places results in the matrix resultar.}

MatrixLogicalAnd	MatrixLogicalAnd(array1, array2, resultar);

{Performs a logical comparison of each element of array1 with the corresponding element of array2 and if both are true (values > 0), places a 1 in the corresponding element of matrix resultar.}

MatrixLogicalNot	MatrixLogicalNot(array, resultar);

{Performs a logical negation of each element of array (where true = values > 0), places result in the corresponding element of matrix resultar.}

MatrixLogicalOr	MatrixLogicalOr(array1, array2, resultar);

{Performs a logical comparison of each element of array1 with the corresponding element of array2 and if either is true (values > 0), places a 1 in the corresponding element of matrix resultar.}

MatrixMeans	MatrixMeans(array, vectmean);

{Computes means of columns of array and places results in vector vectmean.}

MatrixMultiply	MatrixMultiply(array1, array2, result);

{Multiplies the matrices array1 by array2 and places results in result (may be a matrix, vector, or single value).}

MatrixRank	MatrixRank(array, result);

{Computes the rank of matrix array and places result in variable result.}

MatrixRead	MatrixRead('c:\mat.txt', array);

{Reads the contents of text file "c:\mat.txt" into matrix array.}

MatrixReadFromDataFile	MatrixReadFromDataFile('c:\data.sta', 1, 1 0, 0, array);

{Reads the contents of data file "c:\data.sta" into matrix array.}

MatrixSetColumn	MatrixSetColumn(array, 2, vect);

{Places the contents of vector vect into the second column of matrix array.}

MatrixSetDiagonal	MatrixSetDiagonal(array, 2, vect);

{Places the contents of vector vect into the main diagonal of matrix array.}

MatrixSetRow	MatrixSetRow(array, 3, vect);

{Places the contents of vector vect into the third row of matrix array.}

MatrixSetToZero	MatrixSetToZero(array);

{Sets all values of matrix array to zero.}

MatrixSingularValues	MatrixSingularValues(array, vect);

{Computes singular values of matrix array and places them into vector vect.}

MatrixSingularValuesDecomp	MatrixSingularValuesDecomp(array, resultarrayb, resultvectorc, resultarrayd);

{Performs singular value decomposition of matrix array and places resultant values into matrix resultarrayb, vector resultvectorc, and matrix resultarrayd.}

MatrixSolve	MatrixSolve(array1, arrayb, arrayx);

{For each column vector in arrayx and arrayb, solves the linear equations array1 * vectorx = vectorb and places the results in the respective columns of arrayx.}

MatrixSubtract	MatrixSubtract(array1, array2, result);

{Subtracts each element of array2 from corresponding element of array1 and places result in matrix result.}

MatrixSumOfSquares	MatrixSumOfSquares(array, result);

{Computes sum of squares of each element of array and places result in variable result.}

MatrixSweep	MatrixSweep(array, 1, 10, -1);

{Performs backward sweep of array from column 1 to 10.}

MatrixTrace	MatrixTrace(array, result);

{Computes trace of matrix array and places result in variable result.}

MatrixTranspose	MatrixTranspose(array, result);

{Transposes matrix array and places result in matrix result.}

MatrixWrite	MatrixWrite('c:\mat.txt', array);

{Writes the contents of matrix array into text file "c:\mat.txt".}

NewScrollsheet	NewScrollsheet(2, 3, array, 'New Scrollsheet', 'Row 1|Row 2', 'Col A|Col B|Col C');

{Creates a new 2 row by 3 column Scrollsheet from the contents of matrix array and names the rows and columns.}

ReDim	ReDim array(i+3, NVars);

{Dynamically changes the size of array; if array was previously defined, the number of dimensions must be the same, but expressions can be used for the dimensions themselves.}

ScrollsheetGetMatrix	ScrollsheetGetMatrix(scroll1, 1, 2, array);

{Extracts values from the specified Scrollsheet beginning at row 1, column 2 and assigns the values to the matrix array.}

ScrollsheetSetMatrix	ScrollsheetSetMatrix(scroll1, 2, 4, array);

{Places the contents of the matrix array into the specified Scrollsheet beginning at row 2, column 4.}

VectorDualSort	VectorDualSort(vector, indexvector, SORT_ASCENDING);

{Sorts the elements of vector into ascending order; the elements of indexvector are rearranged, so that the pairs of values vector(i) and indexvector(i) remain the same.}

VectorRank	VectorRank(vector, SORT_ASCENDING, RANK_MEAN);

{Ranks the elements of vector in ascending order, assigning mean ranks to tied values.}

VectorSort	VectorSort(vector, SORT_DESCENDING);

{ Sorts the elements of vector in descending order.}


User-defined Functions and Subroutines

  STATISTICA BASIC Syntax Reference - User-defined Functions and Subroutines

STATISTICA BASIC supports user-defined subroutines and functions, allowing the user to build large structured programs.  Libraries of subroutines and functions can be saved in separate files, and included in programs via the Include metacommand ({$I:'FileName'}).

Declaration of Functions

The general format of function definitions is:

Function Name [(Arguments)] ;

begin

  [Declarations]

  { [Instruction] | [Name := Expression] | [Exit Function]

    [;[Instruction] | [Name := Expression] | [Exit Function], ...] }

end [Function];

The components of the function definition are:

Name	name of the function; the name also determines the function type; if the function name ends with a dollar character ($) then the function will return a string; otherwise it will return a number

Arguments	list of variables representing arguments that are passed to the function when it is called; multiple variables are separated by commas; arguments that are to be changed when returning to the calling program have to be passed by reference, and declared using the keyword byref (see User-defined Functions and Subroutines (Arguments))

begin ... end	block denoting the body of the function

Declarations	contains declarations of any array arguments and other local variables

Instruction	instructions to be executed inside the body of the function

Name := Expression	instruction assigning a return value of the function

Exit Function	instruction causing an immediate exit from the function; several Exit Function instructions can appear anywhere in a function

Declaration of Subroutines

The general format of subroutine definitions is very similar to that of functions, except that no return value can be specified:

SUB Name [(Arguments)] ;

begin

  [Declarations]

  { [Instruction] | [Exit SUB]

    [;[Instruction] | [Exit SUB], ...] }

end [Subroutine];

For more information on User-defined Functions and Subroutines, see User-defined Functions and Subroutines.


User-defined Functions and Subroutines (Arguments)

  STATISTICA BASIC Syntax Reference - User-defined Functions and Subroutines (Arguments)

The general syntax for arguments in a function or subroutine declaration is:

[Sub | Function] Name ( [BYREF | BYVAL] ArgName [,[BYREF | BYVAL] ArgName, ...] )

•	Arguments are optional.

•	BYREF indicates that an argument is passed by reference (see also Passing Arguments by Reference, in User-defined Functions and Subroutines).  When an argument is passed by reference, the function or subroutine has access to the actual variable.  As a result, the variable's value can be changed by the procedure to which it is passed, and the changed value will be passed back to the calling program, function, or subroutine.

•	BYVAL indicates that an argument is passed by value (this is the default).  When an argument is passed by value, the function or subroutine only has access to a "copy" of the variable.  As a result, the variable's value in the calling program cannot be changed by the procedure to which it is passed.

•	ArgName is the name of a variable representing the argument.  Strings are denoted by argument names with a dollar sign ($) at the end.  Arrays are defined in the function or subroutine body, as usual, via the Dim statement.  Multiple arguments are separated by comma.

Note that more information on passing arguments is available in User-defined Functions and Subroutines.


STATISTICA BASIC - Dim

  STATISTICA BASIC Library of Matrix Functions - Dim Array_Name (XDim, ...)

Parameters:

Array_Name	name of data array (see Arrays in Functions).

Xdim	number of elements in specified dimension of matrix (see Arrays in Functions).

The Dim function serves two purposes:

•	to declare an array (see Arrays in Functions) of the specified dimensions.

•	to declare global variables or arrays in Userdefined Functions and Subroutines.

Specifying Arrays

Arrays may be one, two, or multidimensional (up to 8 dimensions).  Multi-dimensional arrays may be defined by listing the number of elements in each dimension.  The array name is used to refer to the array in all matrix functions.  All array declarations using Dim must occur at the beginning of the STATISTICA BASIC program.  (Array declarations and redefinitions using ReDim may occur at any point within the STATISTICA BASIC program.)

Example:

RandomAccess;

Dim newarray(4,6);

MatrixDisplay(newarray, 'This is a new Array');

This program will define a new 2-dimensional data matrix (see Arrays in Functions) named newarray with 4 rows and 6 columns and display the matrix in a Scrollsheet with the title This is a new Array.

Specifying Global Variables and Arrays

The Dim statement can also be used before user-specfied functions and subroutines, in order to declare global variables and arrays.

Example:

Dim x(10);

Dim n;

Sub FILLARRAY(Y)

begin

 for I:=1 TO N do x(I):=y/I;

end;

n:=10;

FILLARRAY(2);

This program will call the subroutine fillarray to fill the elements of array x with successive values of 2/i.  Note that both the array x(10) and the variable n are globally "visible" to the following subroutines, after they are declared by the dim statement.

Related topics:  ReDim.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - ReDim

  STATISTICA BASIC Library of Matrix Functions - ReDim Array_Name (XDim, ...)

Parameters:

Array_Name	name of data array (see Arrays in Functions).

Xdim	number of elements in specified dimension of matrix (see Arrays in Functions).

The ReDim function will dynamically change the size of the specified array (see Arrays in Functions).  ReDim may be used to initially define an array, or to change the size of an existing array (the number of dimensions must remain the same, e.g., a 2-dimensional array cannot be re-dimensioned to be a 3-dimensional array).  Arrays may be one, two, or multidimensional (up to 8 dimensions).  Multi-dimensional arrays may be defined by listing the number of elements in each dimension.  The array name is used to refer to the array in all matrix functions.  Array declarations and redefinitions using ReDim may occur at any point within the STATISTICA BASIC program.  (All array declarations using Dim must occur at the beginning of the STATISTICA BASIC program.)

Example:

RandomAccess;

ReDim means(NVars);

MatrixMeans(Data, means);

MatrixDisplay(means, 'Means from current data file');

This program will define a new 1-dimensional data vector (see Arrays in Functions) named means with as many elements as the number of variables in the current data file.  The means for each variable are placed in the vector means, and the matrix is displayed in a Scrollsheet with the title Means from current data file.

Related topics:  Dim.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixAdd

  STATISTICA BASIC Library of Matrix Functions - MatrixAdd (Matrix1, Matrix2, MatrixResult)

Parameters:

Matrix1	name of first data array (see Arrays in Functions).

Matrix2	name of second data array (see Arrays in Functions).

MatrixResult	destination matrix (see Arrays in Functions); may be the same as Matrix1 or Matrix2, if desired.

The MatrixAdd function will add each element of the two specified matrices (see Arrays in Functions) and place the resulting values in the specified matrix (see the parameter MatrixResult; the result matrix may be the same as either Matrix1 or Matrix2 if you wish to overwrite the original values of that array).  All matrices must be of the same size (rows x columns).

Example:

RandomAccess;

Dim array1(4,6),  array2(4,6);

MatrixRead('c:\mat1.txt', array1);

MatrixRead('c:\mat2.txt', array2);

MatrixAdd(array1, array2, array2);

MatrixDisplay(array2, 'Array1 + Array2');

This program will read two data matrices from text files, add their elements together, and display the results in a Scrollsheet with the title Array1 + Array2.

Related topics:  MatrixRead, MatrixSubtract, MatrixMultiply.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixAllNonZero

  STATISTICA BASIC Library of Matrix Functions - MatrixAllNonZero (Matrix)

Parameters:

Matrix	name of data array (see Arrays in Functions).

The MatrixAllNonZero function will return a value of 1 if each element in the specified matrix (see Arrays in Functions) is non-zero, otherwise, the function returns a value of 0.

Example:

RandomAccess;

Dim array(4,6);

MatrixRead('c:\mat1.txt', array);

result := MatrixAllNonZero(array);

This program will read a data matrix from a text file, check whether all values in the matrix are non-zero and assign the result code to the STATISTICA BASIC variable Result.

Related topics: MatrixAnyNonZero.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixAnyNonZero

  STATISTICA BASIC Library of Matrix Functions - MatrixAnyNonZero (Matrix)

Parameters:

Matrix	name of data array (see Arrays in Functions).

The MatrixAnyNonZero function will return a value of 1 if any element in the specified matrix (see Arrays in Functions) is non-zero (otherwise, the function returns a value of 0).

Example:

RandomAccess;

Dim array(4,6);

MatrixRead('c:\mat1.txt', array);

result := MatrixAnyNonZero(array);

This program will read a data matrix from a text file, check whether all values in the matrix are non-zero and assign the result code to the temporary variable result.

Related topics:  MatrixAllNonZero.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixCholeskyDecomposition

  STATISTICA BASIC Library of Matrix Functions - MatrixCholeskyDecomposition (Matrix, MatrixResult)

Parameters:

Matrix	name of square, symmetric, positive-definite matrix to decompose (see Arrays in Functions).

MatrixResult	name of result data matrix (see Arrays in Functions).

The MatrixCholeskyDecomposition function will compute the so-called triangular (or Cholesky) decomposition of the symmetric, non-singular Matrix.

For the symmetric input matrix A, the function will compute the (triangular) matrix B, so that B' * B = A, where B' stands for the transpose of matrix B.

Example:

RandomAccess;

Dim array(4,4);

MatrixRead('c:\mat1.txt', array);

MatrixCholeskyDecomposition(array, array);

MatrixDisplay(array, 'Cholesky Decomposition');

This program will read a data matrix from a text file, compute the triangular decomposition, and display the results in a Scrollsheet with the title Cholesky Decomposition.

Related topics: MatrixInverse, MatrixGeneralPseudoInverse, MatrixSweep, MatrixSingularValuesDecomp, .

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixCombineHoriz

  STATISTICA BASIC Library of Matrix Functions - MatrixCombineHoriz (Matrix1, Matrix2, MatrixResult)

Parameters:

Matrix1	name of first data matrix (see Arrays in Functions); will be on the left in MatrixResult.

Matrix2	name of second data matrix (see Arrays in Functions); will be on the right in MatrixResult.

MatrixResult	destination matrix (see Arrays in Functions).

The MatrixCombineHoriz  function will combine the elements of the two specified matrices (see Arrays in Functions), placing the resulting values in the specified array (see parameter MatrixResult).  Matrix1 and Matrix2 must have the same number of rows, and the number of columns in MatrixResult will be equal to the sum of the number of columns in Matrix1 and Matrix2.

Example:

RandomAccess;

Dim array1(4,6),  array2(4,6),  arrayresult(4,12);

MatrixRead('c:\mat1.txt', array1);

MatrixRead('c:\mat2.txt', array2);

MatrixCombineHoriz(array1, array2, arrayresult);

MatrixDisplay(arrayresult, 'Combined Array1 & Array2');

This program will read two data matrices from text files, append the columns of array2 to array1, and display the resulting matrix arrayresult in a Scrollsheet with the title Combined Array1 & Array2.

Related topics: MatrixCombineVert, MatrixRead, MatrixDisplay.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixCombineVert

  STATISTICA BASIC Library of Matrix Functions - MatrixCombineVert (Matrix1, Matrix2, MatrixResult)

Parameters:

Matrix1	name of first data matrix (see Arrays in Functions); will be on top in MatrixResult.

Matrix2	name of second data matrix (see Arrays in Functions); will be on the bottom in MatrixResult.

MatrixResult	destination matrix (see Arrays in Functions).

The MatrixCombineVert function will combine the elements of the two specified matrices (see Arrays in Functions), placing the resulting values in the specified array (see parameter MatrixResult).  Matrix1 and Matrix2 must have the same number of columns, and the number of rows in MatrixResult will be equal to the sum of the number of rows in Matrix1 and Matrix2.

Example:

RandomAccess;

Dim array1(4,6),  array2(4,6),  arrayresult(8,6);

MatrixRead('c:\mat1.txt', array1);

MatrixRead('c:\mat2.txt', array2);

MatrixCombineVert(array1, array2, arrayresult);

MatrixDisplay(arrayresult, 'Combined Array1 & Array2');

This program will read two data matrices from text files, append the rows of array2 to array1, and display the resulting matrix arrayresult in a Scrollsheet with the title Combined Array1 & Array2.

Related topics: MatrixCombineHoriz, MatrixRead, MatrixDisplay.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixCopy

  STATISTICA BASIC Library of Matrix Functions - MatrixCopy (SrcMatrix, SrcRow, SrcCol, ?NoOfRows, ?NoOfCols, DestMatrix, DestRow, DestCol)

Parameters:

ScrMatrix	name of source data matrix (see Arrays in Functions).

ScrRow	number of first row from which to begin the copy.

ScrCol	number of first column from which to begin the copy.

?NoOfRows	number of rows to be copied (0 = all remaining rows in source or destination matrix, whichever is smaller).

?NoOfCols	number of columns to be copied (0 = all remaining columns in source or destination matrix, whichever is smaller).

DestMatrix	name of destination data matrix (see Arrays in Functions); may be same as source matrix.

DestRow	number of first row into which values will be copied.

DestCol	number of first column into which values will be copied.

The MatrixCopy function will copy the specified number of rows and columns beginning at the specified location (see parameters ScrRow and ScrCol) from the source matrix (see parameter ScrMatrix) and place the resulting values in the specified location (see parameters DestRow and DestCol) of the destination matrix (see parameter DestMatrix).  Note that the destination matrix may be the same as the source matrix if you wish to overwrite the original values of the source matrix.

Example:

RandomAccess;

Dim array(4,6);

MatrixRead('c:\mat1.txt', array);

MatrixCopy(array, 1, 1, 0, 1, array, 1, 4);

MatrixDisplay(array, 'Array');

This program will read a data matrix from a text file, copy the values from the first column into the fourth column of the same matrix, and display the results in a Scrollsheet with the title Array.

Related topics:  MatrixDuplicate, MatrixRead, MatrixDisplay, MatrixExtract, MatrixGetColumn, MatrixGetRow.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixCopy

  STATISTICA BASIC Library of Data Management Functions - MatrixCopy (Data, SrcRow, SrcCol, ?NoOfRows, ?NoOfCols, Data, DestRow, DestCol)

This application of the general matrix function MatrixCopy allows the user to perform data managment operations on the current data file.

Parameters:

Data	current data file.

ScrRow	number of first row from which to begin the copy.

ScrCol	number of first column from which to begin the copy.

?NoOfRows	number of rows to be copied (0 = all remaining rows in source or destination matrix, whichever is smaller).

?NoOfCols	number of columns to be copied (0 = all remaining columns in source or destination matrix, whichever is smaller).

Data	current data file.

DestRow	number of first row into which values will be copied.

DestCol	number of first column into which values will be copied.

The MatrixCopy function will copy the specified number of rows and columns beginning at the specified location (see parameters ScrRow and ScrCol) from the current data file and place the resulting values in the specified location (see parameters DestRow and DestCol) of the current data file.

Example:

RandomAccess;

MatrixCopy(Data, 3, 1, 0, Data, 3, 5);;

This program will copy values of the first variable, beginning in the third case, into the fifth variable, also beginning with the third case.

Related topics:  MatrixDuplicate, MatrixRead, MatrixDisplay, MatrixExtract, MatrixGetColumn, MatrixGetRow.

For more information on using arrays, see Arrays in Functions.

For a complete listing of data management functions, see STATISTICA BASIC Library of Data Management Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixCorrelations

  STATISTICA BASIC Library of Matrix Functions - MatrixCorrelations (Matrix, Intercept, MatrixResult)

Parameters:

Matrix	name of data matrix (see Arrays in Functions).

Intercept	if 1, correlations computed with intercept; if 0, correlations computed without intercept.

MatrixResult	square destination matrix (see Arrays in Functions; number of rows and columns equals number of columns in the source data matrix).

The MatrixCorrelations function will compute the correlations between values in the columns of the specified source Matrix and place the resulting values in the specified array (see parameter MatrixResult).  The correlations may be computed with or without the intercept (see parameter Intercept).  If Intercept is set to 1 (i.e., with intercept), then MatrixResult will contain the regular Pearson product-moment correlation coefficients; if Intercept is set to 0 (i.e., without intercept), then MatrixResult will contain the standardized matrix of sums of squared crossproducts of deviations from 0 (zero); the diagonal elements of MatrixResult will always be equal to 1.

Example:

RandomAccess;

ReDim corr(NVars, NVars);

MatrixCorrelations(Data, 1, corr);

MatrixDisplay(corr, 'Correlations (with intercept)');

This program will compute the correlations between the variables of the current data file, writing the correlation coefficients into the matrix corr, and display the results in a Scrollsheet with the title Correlations (with intercept).

Related topics: ReDim, MatrixCrossProductOfDev, MatrixMeans, MatrixDisplay.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixCrossProductOfDev

  STATISTICA BASIC Library of Matrix Functions - MatrixCrossProductOfDev (Matrix1, Intercept, MatrixResult)

Parameters:

Matrix1	name of source data matrix (see Arrays in Functions).

Intercept	if 1, crossproducts are computed with intercept; if 0, crossproducts are computed without intercept.

MatrixResult	square destination matrix  (see Arrays in Functions; number of rows and columns equals number of columns in the source data matrix).

The MatrixCrossProductOfDev function will compute a matrix of squared deviations and crossproducts of deviations for the specified Matrix (see also, Arrays in Functions).  The resulting values will be placed in the square matrix MatrixResult.  If the parameter Intercept is set to 1, then MatrixResult will contain the sums of squared deviations from the means in the diagonal elements and the crossproducts of deviations from the means in the off-diagonal elements of the matrix.  If the parameter Intercept is set to 0, then MatrixResult will contain sums of the squared deviations from 0 (zero) in the diagonal, and crossproducts of deviations from 0 (zero) in the off-diagonal elements.

Note that you can divide each element in the crossproduct matrix by either N or (N-1) to obtain the covariance matrix [use MatrixElemDivide to divide the elements in the matrix by the scalar N or (N-1)].

Example:

RandomAccess;

ReDim crossprod(NVars, NVars);

ReDim covar(NVars, NVars);

MatrixCrossProductofDev(Data, 1, crossprod);

MatrixDisplay(crossprod, 'Crossproducts (with intercept)');

MatrixDuplicate(crossprod, covar);

MatrixElemDivide(covar, NCases, covar);

MatrixDisplay(covar, 'Covariance Matrix');

This program will read compute the matrix of squared deviations, and crossproducts of deviations from the means for all variables in the current data file, and display the results in a Scrollsheet with the title Crossproducts (with intercept).  The elements of the crossproduct matrix are then divided by the number of cases in the current data file, and the resulting matrix of covariances is displayed in a Scrollsheet with the title Covariance Matrix.

Related topics: MatrixElemDivide, MatrixCorrelations, MatrixRead, MatrixDisplay, ReDim.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixDet

  STATISTICA BASIC Library of Matrix Functions - MatrixDet (Matrix, Result)

Parameters:

Matrix	name of data matrix (see Arrays in Functions).

Result	destination variable.

The MatrixDet function will compute the determinant of the specified square Matrix (see Arrays in Functions) and place the resulting value in the STATISTICA BASIC variable specified as Result).  Note that the determinant for a singular square matrix (where at least one column or row is a linear function of one or more other columns or rows) is equal to zero.

Example:

RandomAccess;

Dim datarray(4,4);

MatrixRead('c:\mat1.txt', datarray);

MatrixDet(datarray, det);

This program will read a data matrix from a text file, compute the determinant of the matrix, and assign the result to the STATISTICA BASIC variable det.

Related topics:  MatrixRank, MatrixTrace, MatrixRead.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixDisplay

  STATISTICA BASIC Library of Matrix Functions - MatrixDisplay (Matrix, ?Title$)

Parameters:

Matrix	name of data matrix (see Arrays in Functions) to be displayed in a Scrollsheet.

?Title$	title of Scrollsheet (see Strings in Functions).

Return value:	Scrollsheet handle

The MatrixDisplay function will place the contents of the specified Matrix (see Arrays in Functions) in a Scrollsheet with the given Title$ text as the Scrollsheet title, using default column and row names.

Example:

RandomAccess;

Dim newarray(4,6);

MatrixCopy(Data, 1, 1, 0, 0, newarray, 1, 1);

MatrixDisplay(newarray, 'This is a new Array');

This program will define a 2-dimensional data matrix (see Arrays in Functions) named newarray with 4 rows and 6 columns, copy into it values from the current data file, and display the matrix in a Scrollsheet with the title This is a new Array.

Related topics:  MatrixWrite, ScrollsheetSetColumnName, ScrollsheetSetRowName, DeleteScrollsheet.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixDisplay

  STATISTICA BASIC Library of Data Management Functions - MatrixDisplay (Data, ?Title$)

This application of the general matrix function MatrixDisplay allows the user to perform data managment operations on the current data file.

Parameters:

Data	current data file to be displayed in a Scrollsheet.

?Title$	title of Scrollsheet (see Strings in Functions).

The MatrixDisplay function will display the current data file contents in a Scrollsheet with the given Title$ text as the Scrollsheet title, using default column and row names.

Example:

RandomAccess;

MatrixDisplay(Data, 'Data from current file');

This program will display the contents of the current data file in a Scrollsheet with the title Data from current file.

Related topics:  MatrixWrite, ScrollsheetSetColumnName, ScrollsheetSetRowName, DeleteScrollsheet.

For more information on using arrays, see Arrays in Functions.

For a complete listing of data management functions, see STATISTICA BASIC Library of Data Management Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixSaveAsDataFile

  STATISTICA BASIC Library of Data Management Functions - MatrixSaveAsDataFile (Matrix, Filename$)

Parameters:

Matrix	name of source data matrix (see Arrays in Functions).

Filename$	name of destination data file.

Return value:	0 - Failure, 1 - Success

The MatrixSaveAsDataFile function will save the specified Matrix (see Arrays in Functions) as a STATISTICA data file.  Variable names in the new data file will have the prefix Var followed by the variable number (the names can later be changed using the SetVarName function, as illustrated below).  A value of one will be returned if the function is successful; otherwise a value of zero will be returned.  Reasons for possible failure include incorrect path or insufficient disk space.

Example:

ReDim Subset (10,1);

MatrixCopy (Data, 1, 1, 10, 1, Subset, 1,1);

MatrixSaveAsDataFile (Subset, 'd:\stat\tech_dat\subset.sta');

SetVarName ('d:\stat\tech_dat\subset.sta', 1, 'Gender');

This program will create a matrix which is a subset of the current data set and save that matrix as a STATISTICA data file.  It then will assign a new  name (Gender) to variable number one.

Related topic:  SetVarName.

For more information on using arrays, see Arrays in Functions.

For a complete listing of data management functions, see STATISTICA BASIC Library of Data Management Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - SetVarName

  STATISTICA BASIC Library of Data Management Functions - SetVarName (Filename$, Varno, Varname$)

Parameters:

Filename$	name of the data file to be manipulated.

Varno	variable number to which the new name will be assigned.

Varname$	name which will be assigned to the specified variable

Return value:	0 - Failure, 1 - Success

The SetVarName function will assign a new name to a specified variable in the specified data set.  A value of one will be returned if the function is successful; otherwise a value of zero will be returned.  Reasons for possible failure include incorrect path or variable number.

ReDim Subset (10,1);

MatrixCopy (Data, 1, 1, 10, 1, Subset, 1,1);

MatrixSaveAsDataFile (Subset, 'd:\stat\tech_dat\subset.sta');

SetVarName ('d:\stat\tech_dat\subset.sta', 1, 'Gender');

This program will create a matrix which is a subset of the current data set and save that matrix as a STATISTICA data file.  It then will assign a new  name (Gender) to variable number one.

Related topic:  MatrixSaveAsDataFile.

For more information on using arrays, see Arrays in Functions.

For a complete listing of data management functions, see STATISTICA BASIC Library of Data Management Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - SelectionConditions

  STATISTICA BASIC Library of Data Management Functions - SelectionConditions (Casenumber)

Parameter:

Casenumber	number of the case for which the current case selection conditions will be verified.

Return value:	0 - Selection Conditions are not met, 1 - Selection Conditions are met

The SelectionConditions function will verify whether the specified case meets the current selection conditions.  It will return a value of one is the specified case meets the current selection conditions.  Otherwise it returns a value of zero.

Example:

selon := SelectionConditionsGet (include, seltext$);

if selon then

begin

  Write ('Selection Conditions:');

  if include then

     Write ('Include if ')

  else

     Write ('Exclude if ');

  WriteLn (seltext$);

  for i := 1 to ncases do

     if SelectionConditions (i) then

      WriteLn ('Case ',i,' meets selection conditions');

end

else

  WriteLn ('Selection conditions are not specified');

This program first uses the function SelectionConditionsGet to determine the current status of the STATISTICA system case selection conditions and then verifies whether each case meets those conditions.  When selection conditions are in use, it reports the conditions and lists the cases which meet the current case selection conditions.  Otherwise it reports that selection conditions are not specified.

Related topic:  SelectionConditionsGet.

For a complete listing of data management functions, see STATISTICA BASIC Library of Data Management Functions.


STATISTICA BASIC - SelectionConditionsGet

  STATISTICA BASIC Library of Data Management Functions - SelectionConditionsGet (Include, Seltext$)

Parameters:

Include	variable to which a value of one is assigned if the currently specified STATISTICA case selection conditions are inclusive (i.e., "include if..."); otherwise (i.e., if they are exclusive, "exclude if...") a value of zero is assigned to the variable.

Seltext$	text variable to which the text of the current case selection conditions will be assigned.

Return value:	0 - Selection Conditions are not on, 1 - Selection Conditions are on

The SelectionConditionsGet function will retrieve the current STATISTICA system case selection conditions.

Example:

selon := SelectionConditionsGet (include, seltext$);

if selon then

begin

  Write ('Selection Conditions:');

  if include then

    Write ('Include if ')

  else

    Write ('Exclude if ');

  WriteLn (seltext$);

end

else

  WriteLn ('Selection conditions are not specified');

This program determines whether or not the STATISTICA case selection conditions are currently in use (on).  When the selection conditions are in use, it reports their contents (status (include/exclude) and text).  Otherwise it reports that selection conditions are not specified.

Related topic:  SelectionConditions.

For a complete listing of data management functions, see STATISTICA BASIC Library of Data Management Functions.


STATISTICA BASIC - MatrixDuplicate

  STATISTICA BASIC Library of Matrix Functions - MatrixDuplicate (Matrix, MatrixResult)

Parameters:

Matrix	name of source data matrix (see Arrays in Functions).

MatrixResult	name of destination data matrix (see Arrays in Functions).

The MatrixDuplicate function will copy all values from the specified Matrix (see Arrays in Functions) and place the values in the specified MatrixResult.

Example:

RandomAccess;

Dim array1(4,5),  array2(4,5);

MatrixRead('c:\mat1.txt', array1);

MatrixDuplicate(array1, array2);

This program will read a data matrix from a text file into the matrix array1, then copy all values into the matrix array2.

Related topics:  MatrixCopy, MatrixExtract, MatrixGetColumn, MatrixGetRow.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixDuplicate (Data, Array)

  STATISTICA BASIC Library of Matrix Functions - MatrixDuplicate (Data, Array)

This application of the general matrix function MatrixDuplicate allows the user to perform data management operations on the current data file.

Parameters:

Data	current data file.

Array	name of destination data array (see Arrays in Functions).

The MatrixDuplicate function will copy all values from the current data file and place the values in the specified destination Array (see Arrays in Functions).

Example:

RandomAccess;

Dim array(NCases,NVars);

MatrixDuplicate(Data, array);

This program will copy the contents of the current data file into the matrix array.

Related topics:  MatrixCopy, MatrixExtract, MatrixGetColumn, MatrixGetRow.

For more information on using arrays, see Arrays in Functions.

For a complete listing of data management functions, see STATISTICA BASIC Library of Data Management Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixDuplicate(Var, Array)
  STATISTICA BASIC Library of Data Management Functions - MatrixDuplicate (Var, Array)

This application of the general matrix function MatrixDuplicate allows the user to perform data management operations on the current data file.

Parameters:

Var	name of source data variable from the current data file.

Array	name of destination data array (see Arrays in Functions).

The MatrixDuplicate function will copy all values from the specified variable and place the values in the specified destination Array (see Arrays in Functions; the destination array can be another variable from the current data file, if desired).

Example:

RandomAccess;

MatrixDuplicate(v2, v3);

This program will copy all values from variable 2 into variable 3 of the current data file.

Related topics:  MatrixCopy, MatrixExtract, MatrixGetColumn, MatrixGetRow.

For more information on using arrays, see Arrays in Functions.

For a complete listing of data management functions, see STATISTICA BASIC Library of Data Management Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixEigenvalues

  STATISTICA BASIC Library of Matrix Functions - MatrixEigenvalues (Matrix, Eigenvalues, NumEigen)

Parameters:

Matrix	name of source symmetric data matrix (see Arrays in Functions).

Eigenvalues	name of vector (see Arrays in Functions) which will contain eigenvalues.

NumEigen	STATISTICA BASIC variable which will contain number of positive eigenvalues.

The MatrixEigenvalues function will compute the eigenvalues of the specified symmetric Matrix, as well as the number of positive eigenvalues.  There will be as many eigenvalues as there are columns and rows in the source matrix.

Example:

RandomAccess;

ReDim corr(NVars, NVars);

ReDim eigenval(NVars);

MatrixCorrelations(Data, 1, corr);

MatrixDisplay(corr, 'Correlations');

MatrixEigenvalues(corr, eigenval, numeigen);

MatrixDisplay(eigenval, 'Eigenvalues');

This program will compute eigenvalues from the matrix of correlations between variables in the current data file, and display them in a Scrollsheet with the title Eigenvalues.

Related topics:  MatrixEigenvectors, MatrixCorrelations, MatrixCrossProductOfDev.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixEigenvectors

  STATISTICA BASIC Library of Matrix Functions - MatrixEigenvectors (Matrix, Eigenvalues, Eigenvectors, NumEigen)

Parameters:

Matrix	name of source square symmetric data matrix (see Arrays in Functions).

Eigenvalues	name of vector(see Arrays in Functions) which will contain eigenvalues.

Eigenvectors	name of matrix(see Arrays in Functions) which will contain eigenvectors.

NumEigen	STATISTICA BASIC variable which will contain number of positive eigenvalues.

The MatrixEigenvalues function will compute the eigenvalues and eigenvectors of the specified Matrix, as well as the number of positive eigenvalues.  For each eigenvalue λi (the i' th element of vector EigenValues) and eigenvector xi (in the i' th column of EigenVectors), this function solves the equation Matrix * xi = λi * xi.

Example:

RandomAccess;

ReDim corr(NVars, NVars);

ReDim eigenvect(NVars, NVars);

ReDim eigenval(NVars);

MatrixCorrelations(Data, 1, corr);

MatrixDisplay(corr, 'Correlations');

MatrixEigenvectors(corr, eigenval, eigenvect, numeigen);

MatrixDisplay(eigenvect, 'Eigenvectors');

MatrixDisplay(eigenval, 'Eigenvalues');

This program will compute eigenvalues and eigenvectors from the matrix of correlations between variables in the current data file, and display them in separate Scrollsheets with the titles Eigenvalues and Eigenvectors, respectively.

Related topics:  MatrixEigenvalues, MatrixCorrelations, MatrixCrossProductOfDev.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixElemAdd

  STATISTICA BASIC Library of Matrix Functions - MatrixElemAdd (Matrix, Scalar, MatrixResult)

Parameters:

Matrix	name of source data matrix (see Arrays in Functions).

Scalar	value to be added to each element of the source matrix.

MatrixResult	destination matrix (see Arrays in Functions; may be the same as source Matrix, if desired).

The MatrixElemAdd function will add the specified Scalar value to each element of the specified source Matrix (see Arrays in Functions) and place the resulting values in the specified destination MatrixResult.  Note that MatrixResult may be the same as the source Matrix if you wish to overwrite the original values of that array.

Example:

RandomAccess;

Dim array(4,6);

MatrixRead('c:\mat1.txt', array);

MatrixElemAdd(array, 10, array);

MatrixDisplay(array, 'Array1 + 10');

This program will read a data matrix from a text file, add 10 to each element of the matrix, and display the result in a Scrollsheet with the title Array1 + 10.

Related topics:  MatrixElemDivide, MatrixElemMultiply, MatrixElemSubtract.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixElemAdd

  STATISTICA BASIC Library of Data Management Functions - MatrixElemAdd (Data, Scalar, Data)

This application of the general matrix function MatrixElemAdd allows the user to perform data management operations on the current data file.

Parameters:

Data	current data file.

Scalar	value to be added to each element of the current data file.

Data	current data file.

The MatrixElemAdd function will add the specified Scalar value to each value of the current data file.

Example:

RandomAccess;

MatrixElemAdd(Data, 10, Data);

MatrixDisplay(Data, 'Data + 10');

This program will add 10 to each value of the current data file and display the data in a Scrollsheet with the title Data + 10.

Related topics:  MatrixElemDivide, MatrixElemMultiply, MatrixElemSubtract.

For more information on using arrays, see Arrays in Functions.

For a complete listing of data management functions, see STATISTICA BASIC Library of Data Management Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixElemDivide

  STATISTICA BASIC Library of Matrix Functions - MatrixElemDivide (Matrix, Scalar, MatrixResult)

Parameters:

Matrix	name of source data matrix (see Arrays in Functions).

Scalar	value by which to divide each element of the source matrix.

MatrixResult	destination matrix (see Arrays in Functions; may be the same as source Matrix, if desired).

The MatrixElemDivide function will divide each element of the specified source Matrix (see Arrays in Functions) by the specified Scalar value and place the resulting values in the specified destination MatrixResult.  Note that MatrixResult may be the same as the source Matrix if you wish to overwrite the original values of that array.

Example:

RandomAccess;

Dim array(4,6);

MatrixRead('c:\mat1.txt', array);

MatrixElemDivide(array, 10, array);

MatrixDisplay(array, 'Array1/10');

This program will read a data matrix from a text file, divide each element by 10, and display the result in a Scrollsheet with the title Array1/10.

Related topics:  MatrixElemAdd, MatrixElemMultiply, MatrixElemSubtract.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixElemDivide

  STATISTICA BASIC Library of Data Management Functions - MatrixElemDivide (Data, Scalar, Data)

This application of the general matrix function MatrixElemDivide allows the user to perform data management operations on the current data file.

Parameters:

Data	current data file.

Scalar	value by which to divide each element of the current data file.

Data	current data file.

The MatrixElemDivide function will divide each element of the current data file by the specified Scalar value.

Example:

RandomAccess;

MatrixElemDivide(Data, 10, Data);

MatrixDisplay(Data, 'Data/10');

This program will divide each element of the current data file by 10, and display the result in a Scrollsheet with the title Data/10.

Related topics:  MatrixElemAdd, MatrixElemMultiply, MatrixElemSubtract.

For more information on using arrays, see Arrays in Functions.

For a complete listing of data management functions, see STATISTICA BASIC Library of Data Management Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixElemMultiply

  STATISTICA BASIC Library of Matrix Functions - MatrixElemMultiply (Matrix, Scalar, MatrixResult)

Parameters:

Matrix	name of source data matrix (see Arrays in Functions).

Scalar	value by which to multiply each element of the source matrix.

MatrixResult	destination matrix (see Arrays in Functions; may be the same as source Matrix, if desired).

The MatrixElemMultiply function will multiply each element of the specified source Matrix (see Arrays in Functions) by the specified Scalar value and place the resulting values in the specified destination MatrixResult.  Note that MatrixResult may be the same as the source Matrix if you wish to overwrite the original values of that array.

Example:

RandomAccess;

Dim array(4,6);

MatrixRead('c:\mat1.txt', array);

MatrixElemMultiply(array, 10, array);

MatrixDisplay(array, 'Array1 * 10');

This program will read a data matrix from a text file, multiply each element by 10, and display the result in a Scrollsheet with the title Array1 * 10.

Related topics:  MatrixElemAdd, MatrixElemDivide, MatrixElemSubtract.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixElemMultiply

  STATISTICA BASIC Library of Data Management Functions - MatrixElemMultiply (Data, Scalar, Data)

This application of the general matrix function MatrixElemMultiply allows the user to perform data management operations on the current data file.

Parameters:

Data	current data file.

Scalar	value by which to multiply each element of the current data file.

Data	current data file.

The MatrixElemMultiply function will multiply each element of the current data file by the specified Scalar value and place the resulting values in the specified destination MatrixResult.  Note that MatrixResult may be the same as the source Matrix if you wish to overwrite the original values of that array.

Example:

RandomAccess;

MatrixElemMultiply(Data, 10, Data);

MatrixDisplay(Data, 'Data * 10');

This program will multiply each element of the current data file by 10, and display the result in a Scrollsheet with the title Data * 10.

Related topics:  MatrixElemAdd, MatrixElemDivide, MatrixElemSubtract.

For more information on using arrays, see Arrays in Functions.

For a complete listing of data management functions, see STATISTICA BASIC Library of Data Management Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixElemSubtract

  STATISTICA BASIC Library of Matrix Functions - MatrixElemSubtract (Matrix, Scalar, MatrixResult)

Parameters:

Matrix	name of source data matrix (see Arrays in Functions).

Scalar	value to be subtracted from each element of source matrix.

MatrixResult	destination matrix (see Arrays in Functions; may be the same as source Matrix, if desired).

The MatrixElemSubtract function will subtract the specified Scalar value from each element of the specified source Matrix (see Arrays in Functions) and place the resulting values in the specified destination MatrixResult.  Note that MatrixResult may be the same as the source Matrix if you wish to overwrite the original values of that array.

Example:

RandomAccess;

Dim array(4,6);

MatrixRead('c:\mat1.txt', array);

MatrixElemSubtract(array, 10, array);

MatrixDisplay(array, 'Array1 - 10');

This program will read a data matrix from a text file, subtract 10 from each element, and display the result in a Scrollsheet with the title Array1 - 10.

Related topics:  MatrixElemAdd, MatrixElemDivide, MatrixElemMultiply.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixElemSubtract

  STATISTICA BASIC Library of Data Management Functions - MatrixElemSubtract (Data, Scalar, Data)

This application of the general matrix function MatrixElemSubtract allows the user to perform data management operations on the current data file.

Parameters:

Data	current data file.

Scalar	value to be subtracted from each element of current data file.

Data	current data file.

The MatrixElemSubtract function will subtract the specified Scalar value from each element of the current data file.

Example:

RandomAccess;

MatrixElemSubtract(Data, 10, Data);

MatrixDisplay(Data, 'Data - 10');

This program will subtract 10 from each element of the current data file, and display the result in a Scrollsheet with the title Data - 10.

Related topics:  MatrixElemAdd, MatrixElemDivide, MatrixElemMultiply.

For more information on using arrays, see Arrays in Functions.

For a complete listing of data management functions, see STATISTICA BASIC Library of Data Management Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixExtract

  STATISTICA BASIC Library of Matrix Functions - MatrixExtract (Matrix, Row, Column, ?NoOfRows, ?NoOfCols, SubMatrix)

Parameters:

Matrix	name of source data matrix (see Arrays in Functions).

Row	initial row number to extract

Column	initial column number to extract

NoOfRows	number of rows to extract

NoOfCols	number of columns to extract

SubMatrix	destination matrix (see Arrays in Functions).

The MatrixExtract function will extract the specified number of rows and columns from the source Matrix and place the resulting values in the destination matrix specified as SubMatrix.  If the NoOfRows or NoOfCols is set to zero, then the respective height or width of the SubMatrix is used.

Example:

RandomAccess;

Dim array1(4,6);

Dim array2(3,3);

MatrixRead('c:\mat1.txt', array1);

MatrixExtract(array1, 1, 2, 0, 0, array2);

MatrixDisplay(array2, 'Extracted Matrix');

This program will read a data matrix from a text file, extract a submatrix of 3 rows and 3 columns, beginning in the first row, second column, and display the results in a Scrollsheet with the title Extracted Matrix.

Related topics:  MatrixGetColumn, MatrixGetDiagonal, MatrixGetRow, MatrixCopy MatrixDuplicate.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixExtract

  STATISTICA BASIC Library of Data Management Functions - MatrixExtract (Data, Row, Column, ?NoOfRows, ?NoOfCols, Array)

This application of the general matrix function MatrixExtract allows the user to perform data management operations on the current data file.

Parameters:

Data	current data file.

Row	initial case number to extract

Column	initial variable number to extract

NoOfRows	number of cases to extract

NoOfCols	number of variables to extract

Array	destination array (see Arrays in Functions).

The MatrixExtract function will extract the specified number of cases and variables from the current data file and place the resulting values in the destination Array.  If the NoOfRows or NoOfCols is set to zero, then the respective height or width of the destination Array is used.

Example:

RandomAccess;

Dim array(4,6);

MatrixExtract(Data, 1, 2, 0, 0, array);

MatrixDisplay(array, 'Extracted Matrix');

This program will extract from the current data file a submatrix of 4 rows and 6 columns, beginning in the first case, second variable, and display the results in a Scrollsheet with the title Extracted Matrix.

Related topics: MatrixGetColumn, MatrixGetDiagonal, MatrixGetRow, MatrixCopy MatrixDuplicate.

For more information on using arrays, see Arrays in Functions.

For a complete listing of data management functions, see STATISTICA BASIC Library of Data Management Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixFill

  STATISTICA BASIC Library of Matrix Functions - MatrixFill (Scalar, DestMatrix, DestRow, DestCol, ?NoOfRows, ?NoOfCols)

Parameters:

Scalar	value with which to fill matrix

DestMatrix	name of data matrix to be filled (see Arrays in Functions).

DestRow	number of first row into which values will be filled.

DestCol	number of first column into which values will be filled.

?NoOfRows	number of rows to be filled (0 = all remaining rows in matrix).

?NoOfCols	number of columns to be filled (0 = all remaining columns in matrix).

The MatrixFill function will fill the specified number of rows and columns in the specified destination DestMatrix with the specified Scalar value.

Example:

RandomAccess;

Dim array(5,5);

MatrixFill(Rnd(1), array, 1, 2, 0, 2);

MatrixDisplay(array, 'Array');

This program will select a random number from 0 to 1, place it into all rows of the second and third columns of the matrix, and display the results in a Scrollsheet with the title Array.

Related topics:  MatrixSetToZero, MatrixExtract, MatrixSetColumn, MatrixSetDiagonal, MatrixSetRow.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixFill

  STATISTICA BASIC Library of Data Management Functions - MatrixFill (Scalar, Data, DestRow, DestCol, ?NoOfRows, ?NoOfCols)

This application of the general matrix function MatrixFill allows the user to perform data management operations on the current data file.

Parameters:

Scalar	value with which to fill specified cases and variables

Data	the current data file

DestRow	number of first row into which values will be filled.

DestCol	number of first variable into which values will be filled.

?NoOfRows	number of cases to be filled (0 = all remaining cases in file).

?NoOfCols	number of variables to be filled (0 = all remaining variables in file).

The MatrixFill function will fill the specified number of cases and variables in the current data file with the specified Scalar value.

Example:

RandomAccess;

MatrixFill(Rnd(1), array, 1, 2, 0, 2);

This program will select a random number from 0 to 1, place it into all cases of the second and third variables of the current data file.

Related topics:  MatrixSetToZero, MatrixExtract, MatrixSetColumn, MatrixSetDiagonal, MatrixSetRow.

For more information on using arrays, see Arrays in Functions.

For a complete listing of data management functions, see STATISTICA BASIC Library of Data Management Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixGeneralPseudoInverse

  STATISTICA BASIC Library of Matrix Functions - MatrixGeneralPseudoInverse (Matrix, MatrixResult)

Parameters:

Matrix	name of source data matrix (n,m) (see Arrays in Functions).

MatrixResult	name of destination data matrix (m,n) (see Arrays in Functions).

The MatrixGeneralPseudoInverse function will compute the generalized inverse of the specified source Matrix(n,m) (see Arrays in Functions) and place the values in the specified destination MatrixResult(m,n).  The values in MatrixResult are computed such that Matrix*MatrixResult*Matrix=Matrix and MatrixResult*Matrix*MatrixResult=MatrixResult.  Also, Matrix*MatrixResult and MatrixResult*Matrix will be symmetric.

Example:

RandomAccess;

Dim array(4,5),  arrayresult(5,4);

MatrixRead('c:\mat1.txt', array);

MatrixGeneralPseudoInverse(array, arrayresult);

MatrixDisplay(arrayresult, 'Pseudo Inverse Matrix');

This program will read a data matrix from a text file into the matrix array, then compute the generalized inverse of that matrix as arrayresult and display the result in a Scrollsheet.

Related topics:  MatrixInverse.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixGetColumn

  STATISTICA BASIC Library of Matrix Functions - MatrixGetColumn (Matrix, Column, ColVector)

Parameters:

Matrix	name of source data matrix (see Arrays in Functions).

Column	number of the column to be retrieved.

ColVector	destination vector (see Arrays in Functions) to contain column retrieved from source matrix.

The MatrixGetColumn function will copy the values from the specified Column in the source Matrix (see also Arrays in Functions) and place them in the destination vector specified as ColVector.

Example:

RandomAccess;

Dim array(4,5),  colvect(4);

MatrixRead('c:\mat1.txt', array);

MatrixGetColumn(array, 3, colvect);

MatrixDisplay(colvect, 'Values from Column 3');

This program will read a data matrix from a text file into the matrix array, retreive the values of the third column as the vector colvect and display them in a Scrollsheet with the title Values from Column 3.

Related topics: MatrixGetDiagonal, MatrixGetRow, MatrixExtract, MatrixSetColumn, MatrixSetDiagonal, MatrixSetRow, MatrixCopy MatrixDuplicate.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixGetDiagonal

  STATISTICA BASIC Library of Matrix Functions - MatrixGetDiagonal (Matrix, DiagVector)

Parameters:

Matrix	name of source data matrix (see Arrays in Functions).

DiagVector	destination vector (see Arrays in Functions) to receive values in the main diagonal from source matrix.

The MatrixGetColumn function will copy the values from the main diagonal of the specified source Matrix (see also Arrays in Functions) into the destination vector specified as DiagVector.

Example:

RandomAccess;

Dim array(5,5),  diagonal(5);

MatrixRead('c:\mat1.txt', array);

MatrixGetDiagonal(array, diagonal);

MatrixDisplay(diagonal, 'Values from Main Diagonal');

This program will read a data matrix from a text file into the matrix array, retreive the values of the main diagonal as the vector diagonal and display them in a Scrollsheet with the title Values from Main Diagonal.

Related topics: MatrixGetColumn, MatrixGetRow, MatrixExtract, MatrixSetColumn, MatrixSetDiagonal, MatrixSetRow, MatrixCopy MatrixDuplicate.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixGetRow

  STATISTICA BASIC Library of Matrix Functions - MatrixGetRow (Matrix, Row, RowVector)

Parameters:

Matrix	name of source data matrix (see Arrays in Functions).

Row	number of the row to be retrieved.

RowVector	destination vector (see Arrays in Functions) to contain the row retrieved from the source matrix.

The MatrixGetRow function will copy the values from the specified Row in the source Matrix (see also Arrays in Functions) and place them in the destination vector specified as RowVector.

Example:

RandomAccess;

Dim array(4,5),  rowvect(5);

MatrixRead('c:\mat1.txt', array);

MatrixGetRow(array, 3, rowvect);

MatrixDisplay(rowvect, 'Values from Row 3');

This program will read a data matrix from a text file into the matrix array, retreive the values of the third row as the vector rowvect and display them in a Scrollsheet with the title Values from Row 3.

Related topics: MatrixGetColumn, MatrixGetDiagonal, MatrixExtract, MatrixSetColumn, MatrixSetDiagonal, MatrixSetRow, MatrixCopy MatrixDuplicate.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixGramSchmidtOrt

  STATISTICA BASIC Library of Matrix Functions - MatrixGramSchmidtOrt (Matrix, MatrixResult)

Parameters:

Matrix	name of source data matrix (see Arrays in Functions).

MatrixResult	name of destination matrix of results (see Arrays in Functions).

The MatrixGramSchmidtOrt function will transform successive columns of the specified source Matrix (see also Arrays in Functions) so that each column vector in the destination matrix MatrixResult will have a length of 1 (i.e., the sum of the squared column elements will be equal to 1) and will be orthogonal to all other columns (i.e., the vector product of all column vectors Vi' * Vj will be equal to 0).  To increase precision, a modified Gram-Schmidt algorithm is used (see Bock, 1975).

Example:

RandomAccess;

Dim array(4,4),  arrayresult(4,4);

MatrixRead('c:\mat1.txt', array);

MatrixGramSchmidtOrt(array, arrayresult);

MatrixDisplay(arrayresult, 'Orthonormalized Values');

This program will read a data matrix from a text file into the matrix array, orthonormalize the values of the matrix, and display the results in a Scrollsheet with the title Orthonormalized Values.

Related topics:  MatrixSingularValuesDecomp.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixIdentity

  STATISTICA BASIC Library of Matrix Functions - MatrixIdentity (Matrix)

Parameters:

Matrix	name of square matrix (see Arrays in Functions) to be set to identity matrix.

The MatrixIdentity function will set the specified square source Matrix to the identity matrix (see also Arrays in Functions), with values of 1 along the main diagonal, and 0 in all other elements of the matrix.

Example:

RandomAccess;

Dim array(4,4);

MatrixIdentity(array);

MatrixDisplay(array, 'Identity Matrix');

This program will define a new data matrix array, set it to the identity matrix, and display it in a Scrollsheet with the title Identity Matrix.

Related topics:  MatrixInverse, MatrixGeneralPseudoInverse.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixInverse

  STATISTICA BASIC Library of Matrix Functions - MatrixInverse (Matrix, MatrixResult)

Parameters:

Matrix	name of symmetric, non-singular, source data matrix (see Arrays in Functions).

MatrixResult	destination matrix (see Arrays in Functions; may be the same as source Matrix, if desired).

The MatrixInverse function will compute the inverse of the specified symmetric, non-singular, source Matrix (see also Arrays in Functions) and place the result in the specified MatrixResult.  The inverse of a matrix A is usually denoted as A**-1 (matrix A to the power of minus 1).  It is the matrix equivalent of the same operation performed on numbers.  Specifically, for numbers, a*a**-1=a/a=1; in matrix form: A*A**-1=I, where I stands for the identity matrix (see MatrixIdentity).

Example:

RandomAccess;

Dim array(4,4),  arrayresult(4,4);

MatrixRead('c:\mat1.txt', array);

MatrixInverse(array, arrayresult);

MatrixDisplay(arrayresult, 'Matrix Inverse');

This program will read a data matrix from a text file, compute the matrix inverse, and display the results in a Scrollsheet with the title Matrix Inverse.

Related topics:  MatrixIdentity, MatrixGeneralPseudoInverse.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixIsEqual

  STATISTICA BASIC Library of Matrix Functions - MatrixIsEqual (Matrix1, Matrix2, MatrixResult)

Parameters:

Matrix1	name of first data matrix (see Arrays in Functions).

Matrix2	name of second data matrix (see Arrays in Functions).

MatrixResult	destination matrix (see Arrays in Functions).

The MatrixIsEqual function will compare each element of Matrix1 and Matrix2 (see also Arrays in Functions).  Each element in MatrixResult will contain a 1 if the corresponding elements of the two matrices are equal, and a 0 otherwise.

Example:

RandomAccess;

Dim array1(4,4),  array2(4,4),  arrayresult(4,4);

MatrixRead('c:\mat1.txt', array1);

MatrixRead('c:\mat2.txt', array2);

MatrixIsEqual(array1, array2, arrayresult);

MatrixDisplay(arrayresult, 'Matrix Comparison');

This program will read two data matrices from text files, compare the equality of each element of the two matrices, and display the results of the comparison in a Scrollsheet with the title Matrix Comparison.

Related topics:  MatrixIsGreater, MatrixIsGreaterEqual, MatrixIsLess, MatrixIsLessEqual, MatrixIsNotEqual.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixIsGreater

  STATISTICA BASIC Library of Matrix Functions - MatrixIsGreater (Matrix1, Matrix2, MatrixResult)

Parameters:

Matrix1	name of first data matrix (see Arrays in Functions).

Matrix2	name of second data matrix (see Arrays in Functions).

MatrixResult	destination matrix (see Arrays in Functions).

The MatrixIsGreater function will compare each element of Matrix1 and Matrix2 (see also Arrays in Functions).  Each element in MatrixResult will contain a 1 if the corresponding element of Matrix1 is greater than that of Matrix2, and a 0 otherwise.

Example:

RandomAccess;

Dim array1(4,4),  array2(4,4),  arrayresult(4,4);

MatrixRead('c:\mat1.txt', array1);

MatrixRead('c:\mat2.txt', array2);

MatrixIsGreater(array1, array2, arrayresult);

MatrixDisplay(arrayresult, 'Matrix Comparison');

This program will read two data matrices from text files, compare whether each element of array1 is greater than the corresponding element of array2, and display the results of the comparison in a Scrollsheet with the title Matrix Comparison.

Related topics:  MatrixIsEqual, MatrixIsGreaterEqual, MatrixIsLess, MatrixIsLessEqual, MatrixIsNotEqual.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixIsGreaterEqual

  STATISTICA BASIC Library of Matrix Functions - MatrixIsGreaterEqual (Matrix1, Matrix2, MatrixResult)

Parameters:

Matrix1	name of first data matrix (see Arrays in Functions).

Matrix2	name of second data matrix (see Arrays in Functions).

MatrixResult	destination matrix (see Arrays in Functions).

The MatrixIsGreater function will compare each element of Matrix1 and Matrix2 (see also Arrays in Functions).  Each element in MatrixResult will contain a 1 if the corresponding element of Matrix1 is equal to or greater than that of Matrix2, and a 0 otherwise.

Example:

RandomAccess;

Dim array1(4,4),  array2(4,4),  arrayresult(4,4);

MatrixRead('c:\mat1.txt', array1);

MatrixRead('c:\mat2.txt', array2);

MatrixIsGreaterEqual(array1, array2, arrayresult);

MatrixDisplay(arrayresult, 'Matrix Comparison');

This program will read two data matrices from text files, compare whether each element of array1 is equal to or greater than the corresponding element of array2, and display the results of the comparison in a Scrollsheet with the title Matrix Comparison.

Related topics:  MatrixIsEqual, MatrixIsGreater, MatrixIsLess, MatrixIsLessEqual, MatrixIsNotEqual.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixIsLess

  STATISTICA BASIC Library of Matrix Functions - MatrixIsLess (Matrix1, Matrix2, MatrixResult)

Parameters:

Matrix1	name of first data matrix (see Arrays in Functions).

Matrix2	name of second data matrix (see Arrays in Functions).

MatrixResult	destination matrix (see Arrays in Functions).

The MatrixIsLess function will compare each element of Matrix1 and Matrix2 (see also Arrays in Functions).  Each element in MatrixResult will contain a 1 if the corresponding element of Matrix1 is less than that of Matrix2, and a 0 otherwise.

Example:

RandomAccess;

Dim array1(4,4),  array2(4,4),  arrayresult(4,4);

MatrixRead('c:\mat1.txt', array1);

MatrixRead('c:\mat2.txt', array2);

MatrixIsLess(array1, array2, arrayresult);

MatrixDisplay(arrayresult, 'Matrix Comparison');

This program will read  two data matrices from text files, compare whether each element of array1 is less than the corresponding element of array2, and display the results of the comparison in a Scrollsheet with the title Matrix Comparison.

Related topics:  MatrixIsEqual, MatrixIsGreater, MatrixIsGreaterEqual, MatrixIsLessEqual, MatrixIsNotEqual.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixIsLessEqual

  STATISTICA BASIC Library of Matrix Functions - MatrixIsLessEqual (Matrix1, Matrix2, MatrixResult)

Parameters:

Matrix1	name of first data matrix (see Arrays in Functions)

Matrix2	name of second data matrix (see Arrays in Functions).

MatrixResult	destination matrix (see Arrays in Functions).

The MatrixIsLessEqual function will compare each element of Matrix1 and Matrix2 (see also Arrays in Functions).  Each element in MatrixResult will contain a 1 if the corresponding element of Matrix1 is equal to or less than that of Matrix2, and a 0 otherwise.

Example:

RandomAccess;

Dim array1(4,4),  array2(4,4),  arrayresult(4,4);

MatrixRead('c:\mat1.txt', array1);

MatrixRead('c:\mat2.txt', array2);

MatrixIsLessEqual(array1, array2, arrayresult);

MatrixDisplay(arrayresult, 'Matrix Comparison');

This program will read two data matrices from text files, compare whether each element of array1 is equal to or less than the corresponding element of array2, and display the results of the comparison in a Scrollsheet with the title Matrix Comparison.

Related topics:  MatrixIsEqual, MatrixIsGreater, MatrixIsGreaterEqual, MatrixIsLess, MatrixIsNotEqual.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixIsNotEqual

  STATISTICA BASIC Library of Matrix Functions - MatrixIsNotEqual (Matrix1, Matrix2, MatrixResult)

Parameters:

Matrix1	name of first data matrix (see Arrays in Functions).

Matrix2	name of second data matrix (see Arrays in Functions).

MatrixResult	destination matrix (see Arrays in Functions).

The MatrixIsNotEqual function will compare each element of Matrix1 and Matrix2 (see also Arrays in Functions).  Each element in MatrixResult will contain a 1 if the corresponding element of Matrix1 is not equal to that of Matrix2, and a 0 otherwise.

Example:

RandomAccess;

Dim array1(4,4),  array2(4,4),  arrayresult(4,4);

MatrixRead('c:\mat1.txt', array1);

MatrixRead('c:\mat2.txt', array2);

MatrixIsNotEqual(array1, array2, arrayresult);

MatrixDisplay(arrayresult, 'Matrix Comparison');

This program will read two data matrices from text files, compare whether each element of array1 is not equal to the corresponding element of array2, and display the results of the comparison in a Scrollsheet with the title Matrix Comparison.

Related topics: MatrixIsEqual, MatrixIsGreater, MatrixIsGreaterEqual, MatrixIsLess, MatrixIsLessEqual,.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixKroneckerMultiply

  STATISTICA BASIC Library of Matrix Functions - MatrixKroneckerMultiply (Matrix1, Matrix2, MatrixResult)

Parameters:

Matrix1	name of first data matrix (see Arrays in Functions).

Matrix2	name of second data matrix (see Arrays in Functions).

MatrixResult	destination matrix (see Arrays in Functions).

The MatrixKroneckerMultiplyl function will perform a Kronecker multiplication of Matrix1 and Matrix2 (see also Arrays in Functions)and place the result in the destination matrix MatrixResult.  The number of rows in the destination matrix MatrixResult must be the product of the number of rows in Matrix1 and Matrix2, and the number of columns in the destination matrix MatrixResult must be the product of the number of columns in Matrix1 and Matrix2.

Example:

RandomAccess;

Dim array1(3,4),  array2(3,4),  arrayresult(9,16);

MatrixRead('c:\mat1.txt', array1);

MatrixRead('c:\mat2.txt', array2);

MatrixKroneckerMultiply(array1, array2, arrayresult);

MatrixDisplay(arrayresult, 'Kronecker Multiplication Result');

This program will read two data matrices from text files, perform a Kronecker multiplication of array1 and array2, and display the results of the computation in a Scrollsheet with the title Kronecker Multiplication Result.

Related topics:  MatrixMultiply, MatrixElemMultiply.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixLogicalAnd

  STATISTICA BASIC Library of Matrix Functions - MatrixLogicalAnd (Matrix1, Matrix2, MatrixResult)

Parameters:

Matrix1	name of first data matrix. (see Arrays in Functions)

Matrix2	name of second data matrix (see Arrays in Functions).

MatrixResult	destination matrix (see Arrays in Functions).

The MatrixLogicalAnd function will compare each element of Matrix1 and Matrix2 (see also Arrays in Functions).  Each element in MatrixResult will contain a 1 if the corresponding elements of the two matrices are true (i.e., greater than 0), and a 0 otherwise.

Example:

RandomAccess;

Dim array1(4,6),  array2(4,6),  arrayresult(4,6);

MatrixRead('c:\mat1.txt', array1);

MatrixRead('c:\mat2.txt', array2);

MatrixLogicalAnd(array1, array2, arrayresult);

MatrixDisplay(arrayresult, 'Logical Comparison');

This program will read two data matrices from text files, compare their elements to determine whether the respective elements in each matrix are true (greater than 0), and display the results in a Scrollsheet with the title Logical Comparison.

Related topics:  MatrixLogicalNot, MatrixLogicalOr.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixLogicalNot

  STATISTICA BASIC Library of Matrix Functions - MatrixLogicalNot (Matrix1, MatrixResult)

Parameters:

Matrix1	name of data matrix (see Arrays in Functions).

MatrixResult	destination matrix (see Arrays in Functions).

The MatrixLogicalNot function will perform a logical negation of each element of Matrix1 (see also Arrays in Functions).  Each element in MatrixResult will contain a 0 if the corresponding elements of Matrix1 is true (i.e., greater than 0), and a 1 otherwise.

Example:

RandomAccess;

Dim array(4,6),  arrayresult(4,6);

MatrixRead('c:\mat1.txt', array);

MatrixLogicalNot(array, arrayresult);

MatrixDisplay(arrayresult, 'Logical Negation');

This program will read a data matrix from a text file, perform a logical negation of each element of the matrix, and display the results in a Scrollsheet with the title Logical Negation.

Related topics:  MatrixLogicalAnd, MatrixLogicalOr.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixLogicalOr

  STATISTICA BASIC Library of Matrix Functions - MatrixLogicalOr (Matrix1, Matrix2, MatrixResult)

Parameters:

Matrix1	name of first data array (see Arrays in Functions).

Matrix2	name of second data array (see Arrays in Functions).

MatrixResult	destination matrix (see Arrays in Functions).

The MatrixLogicalOr function will compare each element of Matrix1 and Matrix2 (see also Arrays in Functions).  Each element in MatrixResult will contain a 1 if either of the corresponding elements of the two matrices are true (i.e., greater than 0), and a 0 otherwise.

Example:

RandomAccess;

Dim array1(4,6),  array2(4,6),  arrayresult(4,6);

MatrixRead('c:\mat1.txt', array1);

MatrixRead('c:\mat2.txt', array2);

MatrixLogicalOr(array1, array2, arrayresult);

MatrixDisplay(arrayresult, 'Logical Comparison');

This program will read two data matrices from text files, compare their elements to determine whether either of the respective elements in each matrix are true (greater than 0), and display the results in a Scrollsheet with the title Logical Comparison.

Related topics:  MatrixLogicalAnd, MatrixLogicalNot.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixMeans

  STATISTICA BASIC Library of Matrix Functions - MatrixMeans (Matrix, Vector)

Parameters:

Matrix	name of data array (see Arrays in Functions).

Vector	destination vector (see Arrays in Functions).

The MatrixMeans function will compute the mean of each column of the specified Matrix (see Arrays in Functions) and place the resulting values in the specified destination Vector.

Example:

RandomAccess;

Dim array(4,6),  means(6);

MatrixRead('c:\mat1.txt', array);

MatrixMeans(array, means);

MatrixDisplay(means, 'Means of Array Columns');

This program will read a data matrix from a text file, computes the mean of each column of the matrix, and displays the results in a Scrollsheet with the title Means of Array Columns.

Related topics:  MatrixCorrelations.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixMultiply

  STATISTICA BASIC Library of Matrix Functions - MatrixMultiply (Matrix1, Matrix2, MatrixResult)

Parameters:

Matrix1	name of first data matrix (m,n) (see Arrays in Functions).

Matrix2	name of second data matrix (n,m2) (see Arrays in Functions).

MatrixResult	destination matrix (m,m2) (see Arrays in Functions).

The MatrixMultiply function will perform matrix multiplication of Matrix1(m,n) by Matrix2(n,m2) (see also Arrays in Functions) and place the result in the destination matrix MatrixResult(m,m2).  The destination matrix must have the same number of rows as Matrix1, and the same number of columns as Matrix2.

Example:

RandomAccess;

Dim array1(3,4),  array2(4,5),  arrayresult(3,5);

MatrixRead('c:\mat1.txt', array1);

MatrixRead('c:\mat2.txt', array2);

MatrixMultiply(array1, array2, arrayresult);

MatrixDisplay(arrayresult, 'Matrix Multiplication Result');

This program will read two data matrices from text files, perform a matrix multiplication of array1 by array2, and display the results of the computation in a Scrollsheet with the title Matrix Multiplication Result.

Related topics:  MatrixElemMultiply, MatrixKroneckerMultiply.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixRank

  STATISTICA BASIC Library of Matrix Functions - MatrixRank (Matrix, Result)

Parameters:

Matrix	name of input matrix (see Arrays in Functions).

Result	destination variable (see Variables in STATISTICA BASIC).

The MatrixRank function will compute the so-called rank of the input Matrix (see also Arrays in Functions) and place the result in the destination variable Result.  The rank of a matrix is equal to the number of columns or rows that are not exactly linear combinations of other columns or rows.  Thus, the rank of a matrix is, in a sense, a measure of the amount of independent information contained in it.  Note that the maximum rank of a matrix A(n,m) is equal to min(n,m) (i.e., the minimum number of rows and columns).

Example:

RandomAccess;

Dim array(3,4);

MatrixRead('c:\mat1.txt', array);

MatrixRank(array, rank);

This program will read a data matrix from a text file, compute the rank of the matrix, and store the rank in the STATISTICA BASIC variable rank.

Related topics:  MatrixInverse, MatrixGeneralPseudoInverse, MatrixSingularValues.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixRead

  STATISTICA BASIC Library of Matrix Functions - MatrixRead (FileName$, Matrix)

Parameters:

FileName$	name of source text file.

Matrix	name of data matrix (see Arrays in Functions).

The MatrixRead function will read the specified text file into the array Matrix (see Arrays in Functions).  In the text file, columns should be delimited by non-numeric characters (e.g., tabs, blanks, and commas are all valid separators).  Rows should be delimited by carriage returns.  If the defined matrix is larger than the contents of the text file, the unused cells are set to 0.  If the defined matrix is smaller than the contents of the text file, the extra rows and/or columns are ignored.

Example:

RandomAccess;

Dim array(4,6);

MatrixRead('c:\mat1.txt', array);

MatrixDisplay(array, 'Array');

This program will read the data matrix from a text file and displays its contents in a Scrollsheet with the title Array.

Related topics:  MatrixReadFromDataFile, MatrixCopy, MatrixWrite, MatrixSetColumn, MatrixSetDiagonal, MatrixSetRow, MatrixFill, MatrixExtract.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixRead

  STATISTICA BASIC Library of Data Management Functions - MatrixRead (FileName$, Data)

This application of the general matrix function MatrixRead allows the user to perform data management operations on the current data file.

Parameters:

FileName$	name of source text file.

Data	current data file.

The MatrixRead function will read the specified text file into the current data file.  In the text file, columns should be delimited by non-numeric characters (e.g., tabs, blanks, and commas are all valid separators).  Rows should be delimited by carriage returns.  If the current data file is larger than the contents of the text file, the unused cells are set to 0.  If the current data file is smaller than the contents of the text file, the extra rows and/or columns are ignored.

Example:

RandomAccess;

MatrixRead('c:\data.txt', Data);

MatrixDisplay(Data, 'New Data');

This program will read a text file into the current data file and displays its contents in a Scrollsheet with the title New Data.

Related topics:  MatrixReadFromDataFile, MatrixCopy, MatrixWrite, MatrixSetColumn, MatrixSetDiagonal, MatrixSetRow, MatrixFill, MatrixExtract.

For more information on using arrays, see Arrays in Functions.

For a complete listing of data management functions, see STATISTICA BASIC Library of Data Management Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixReadFromDataFile

  STATISTICA BASIC Library of Matrix Functions - MatrixReadFromDataFile (FileName$, ?FirstCase, ?FirstVar, ?NoOfCases, ?NoOfVars, Matrix)

Parameters:

FileName$	name of source STATISTICA data file.

?FirstCase	number of first case from data file to read (0 = first case)

?FirstVar	number of first variable from data file to read (0 = first variable)

?NoOfCases	number of cases to read from data file (0 = all remaining cases in source file or destination matrix, whichever is smaller)

?NoOfVars	number of variables to read from data file (0 = all remaining variables in source file or destination matrix, whichever is smaller)

Matrix	name of data matrix (see Arrays in Functions).

The MatrixReadFromDataFile function will read the specified STATISTICA data file into the array Matrix (see Arrays in Functions).  If the defined matrix is larger than the contents of the data file, the unused cells are set to 0.  If the defined matrix is smaller than the contents of the data file, the extra cases and/or variables are ignored.

Example:

RandomAccess;

ReDim array(NCases, NVars);

MatrixReadFromDataFile('c:\data.sta', 0, 0, 0, 0, array);

MatrixDisplay(array, 'Array from data');

This program will read the data matrix from a STATISTICA data file and displays its contents in a Scrollsheet with the title Array from data.

Related topics:  MatrixRead, MatrixCopy, MatrixWrite, MatrixSetColumn, MatrixSetDiagonal, MatrixSetRow, MatrixFill, MatrixExtract.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixReadFromDataFile

  STATISTICA BASIC Library of Data Management Functions - MatrixReadFromDataFile (FileName$, ?FirstCase, ?FirstVar, ?NoOfCases, ?NoOfVars, Matrix)

This application of the general matrix function MatrixReadFromDataFile allows the user to perform data management operations on the current data file.

Parameters:

FileName$	name of source STATISTICA data file.

?FirstCase	number of first case from data file to read (0 = first case)

?FirstVar	number of first variable from data file to read (0 = first variable)

?NoOfCases	number of cases to read from data file (0 = all remaining cases in source file or destination matrix, whichever is smaller)

?NoOfVars	number of variables to read from data file (0 = all remaining variables in source file or destination matrix, whichever is smaller)

Matrix	name of data matrix (see Arrays in Functions).

The MatrixReadFromDataFile function will read the specified STATISTICA data file into the array Matrix (see Arrays in Functions).  If the defined matrix is larger than the contents of the data file, the unused cells are set to 0.  If the defined matrix is smaller than the contents of the data file, the extra cases and/or variables are ignored.

Example:

RandomAccess;

ReDim array(NCases, NVars);

MatrixReadFromDataFile('c:\data.sta', 0, 0, 0, 0, array);

MatrixDisplay(array, 'Array from data');

This program will read the data matrix from a STATISTICA data file and displays its contents in a Scrollsheet with the title Array from data.

Related topics:  MatrixRead, MatrixCopy, MatrixWrite, MatrixSetColumn, MatrixSetDiagonal, MatrixSetRow, MatrixFill, MatrixExtract.

For more information on using arrays, see Arrays in Functions.

For a complete listing of data management functions, see STATISTICA BASIC Library of Data Management Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixSetColumn

  STATISTICA BASIC Library of Matrix Functions - MatrixSetColumn (Matrix, Column, ColVector)

Parameters:

Matrix	name of target data matrix (see Arrays in Functions).

Column	number of the column to be changed.

ColVector	source vector (see Arrays in Functions) containing the values to be placed into the source matrix.

The MatrixSetColumn function will place the values from the specified ColVector into the specified column of the target Matrix (see also Arrays in Functions).

Example:

RandomAccess;

Dim array(4,5),  colvect(4);

MatrixRead('c:\mat1.txt', colvect);

MatrixSetColumn(array, 3, colvect);

MatrixDisplay(array, 'Values in Column 3');

This program will read a data matrix from a text file into the vector colvect, then place them in the third column of the matrix array and display the matrix in a Scrollsheet with the title Values in Column 3.

Related topics:  MatrixSetDiagonal, MatrixSetRow, MatrixFill, MatrixRead, MatrixExtract, MatrixGetColumn, MatrixGetDiagonal, MatrixGetRow.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixSetDiagonal

  STATISTICA BASIC Library of Matrix Functions - MatrixSetDiagonal (Matrix, DiagVector)

Parameters:

Matrix	name of target data matrix (see Arrays in Functions).

DiagVector	source vector (see Arrays in Functions) containing the values to be placed into the source matrix.

The MatrixSetDiagonal function will place the values from the specified DiagVector into the main diagonal of the target Matrix (see also Arrays in Functions).

Example:

RandomAccess;

Dim array(4,4),  diagvect(4);

MatrixRead('c:\mat1.txt', diagvect);

MatrixSetDiagonal(array, diagvect);

MatrixDisplay(array, 'Values in Main Diagonal');

This program will read a data matrix from a text file into the vector diagvect, then place them in the main diagonal of the matrix array1 and display the matrix in a Scrollsheet with the title Values in Main Diagonal.

Related topics:  MatrixSetColumn, MatrixSetRow, MatrixFill, MatrixRead, MatrixExtract, MatrixGetColumn, MatrixGetDiagonal, MatrixGetRow.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixSetRow

  STATISTICA BASIC Library of Matrix Functions - MatrixSetRow (Matrix, Row, RowVector)

Parameters:

Matrix	name of target data matrix (see Arrays in Functions).

Row	number of the row to be changed.

RowVector	source vector (see Arrays in Functions) containing the values to be placed into the source matrix.

The MatrixSetRow function will place the values from the specified RowVector into the specified row of the target Matrix (see also Arrays in Functions).

Example:

RandomAccess;

Dim array(4,5),  rowvect(5);

MatrixRead('c:\mat1.txt', rowvect);

MatrixSetRow(array, 3, rowvect);

MatrixDisplay(array, 'Values in Row 3');

This program will read a data matrix from a text file into the vector rowvect, then place them in the third row of the matrix array and display the matrix in a Scrollsheet with the title Values in Row 3.

Related topics:  MatrixSetColumn, MatrixSetDiagonal, MatrixFill, MatrixRead, MatrixExtract, MatrixGetColumn, MatrixGetDiagonal, MatrixGetRow.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixSetToZero

  STATISTICA BASIC Library of Matrix Functions - MatrixSetToZero (Matrix)

Parameters:

Matrix	name of target data matrix (see Arrays in Functions).

The MatrixSetToZero function will set to zero all values of the target Matrix (see also Arrays in Functions).

Example:

RandomAccess;

Dim array(4,5);

MatrixSetToZero(array);

MatrixDisplay(array, 'All Values Zero');

This program will define matrix array, set all values to zero, and display the matrix in a Scrollsheet with the title All Values Zero.

Related topics:  MatrixFill, MatrixIdentity.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixSetToZero

  STATISTICA BASIC Library of Data Management Functions - MatrixSetToZero (Data)

This application of the general matrix function MatrixSetToZero allows the user to perform data management operations on the current data file.

Parameters:

Data	current data file.

The MatrixSetToZero function will set to zero all values of the current data file.

Example:

RandomAccess;

MatrixSetToZero(Data);

MatrixDisplay(Data, 'All Values Zero');

This program will set all values of current data file to zero, and display the data file in a Scrollsheet with the title All Values Zero.

Related topics:  MatrixFill, MatrixIdentity.

For more information on using arrays, see Arrays in Functions.

For a complete listing of data management functions, see STATISTICA BASIC Library of Data Management Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixSingularValues

  STATISTICA BASIC Library of Matrix Functions - MatrixSingularValues (Matrix, SingularValues)

Parameters:

Matrix	name of source data matrix(m,n) (see Arrays in Functions).

SingularValues	vector(n) to contain singular values computed from source matrix (see Arrays in Functions).

The MatrixSingularValues function will compute the singular values for the specified Matrix(m,n) (see also Arrays in Functions) into the vector SingularValues(n).  If the Matrix is of reduced rank, that is, it has some columns or rows that are linear combinations of other columns or rows, then the vector SingularValues will contain as many non-zero singular values as there are independent column/row vectors.  Thus, the number of positive singular values in the vector SingularValues is equal to the rank of the source Matrix (for further discussion, see also MatrixSingularValuesDecomp).

Example:

RandomAccess;

Dim array(6,5),  singval(5);

MatrixRead('c:\mat1.txt', array);

MatrixSingularValues(array, singval);

MatrixDisplay(singval, 'Singular Values of Array');

This program will read a data matrix from a text file into the matrix array, compute the singular values of that matrix and place them in the vector SingVal, then display the values in a Scrollsheet with the title Singular Values of Array.

Related topics:  MatrixSingularValuesDecomp, MatrixRank.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixSingularValuesDecomp

  STATISTICA BASIC Library of Matrix Functions - MatrixSingularValuesDecomp (Matrix, U, W, V)

Parameters:

Matrix	name of source data matrix (see Arrays in Functions).

U	result matrix (see Arrays in Functions).

W	vector to contain singular values computed from source matrix (see Arrays in Functions).

V	result matrix (see Arrays in Functions).

The MatrixSingularValuesDecomp function will perform the singular value decomposition for the specified Matrix (see also Arrays in Functions).  Given an input Matrix(m,n), the program will compute matrices U(m,n), W(n), V(n,n), so that Matrix=U*W-diag.*V' (where V' stands for the transposed V matrix, and W-diag. stands for a diagonal matrix(n,n), with the elements of vector W in the diagonal).  If the Matrix is of reduced rank, that is, it has some columns or rows that are linear combinations of other columns or rows, then the function will return as many non-zero singular values (in vector W) as there are independent column vectors that can be constructed from the columns and rows of the singular Matrix.  Thus, the number of positive singular values in vector SingularValues is equal to the rank of the source Matrix (for further discussion, see also MatrixSingularValues).  Matrix U will contain a set of orthonormal vectors for each non-singular value.

Example:

RandomAccess;

Dim array(4,5),  u(4,5),  w(5),  vm(5,5);

MatrixRead('c:\mat1.txt', array);

MatrixSingularValuesDecomp(array, u, w, vm);

MatrixDisplay(u, 'Singular Value Decomposition');

This program will read a data matrix from a text file into the matrix array, compute the singular value decomposition of that matrix and place the results in the arrays u, w, and vm, then display the values in a Scrollsheet with the title Singular Value Decomposition.

Related topics:  MatrixSingularValues, MatrixRank, MatrixGramSchmidtOrt.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixSolve

  STATISTICA BASIC Library of Matrix Functions - MatrixSolve (Matrix, MatrixSolution, MatrixResult)

Parameters:

Matrix	name of first source data matrix (see Arrays in Functions).

MatrixSolution	name of second source data matrix (see Arrays in Functions).

MatrixResult	solution matrix (see Arrays in Functions).

The MatrixSolve function will solve the linear sets of equations Matrix*MatrixResult = MatrixSolution, for the square Matrix(n,n), MatrixSolution(n,m),  and MatrixResult(n,m) (see also Arrays in Functions).  Note that MatrixSolution and MatrixResult can also be vectors with n elements.

Example:

RandomAccess;

Dim array(2,2),  vect(2),  resultvect(2);

MatrixFill(1, array, 1, 1, 0, 0);

array(2,2) := -1; vect(1) := 12; vect(2) := 6;

MatrixSolve(array, vect, resultvect);

MatrixDisplay(resultvect, 'Solution Vector');

This program will solve the set linear set of equations x+y=12, x-y=6, then display the solution in a Scrollsheet with the title Solution Vector.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixSubtract

  STATISTICA BASIC Library of Matrix Functions - MatrixSubtract (Matrix1, Matrix2, MatrixResult)

Parameters:

Matrix1	name of first data array (see Arrays in Functions).

Matrix2	name of second data array (see Arrays in Functions).

MatrixResult	destination matrix (see Arrays in Functions; may be the same as Matrix1 or Matrix2, if desired).

The MatrixSubtract function will subtract each element of Matrix2 from the corresponding element of Matrix1 (see Arrays in Functions) and place the resulting values in the matrix specified as MatrixResult (the result matrix may be the same as either Matrix1 or Matrix2 if you wish to overwrite the original values of that array).

Example:

RandomAccess;

Dim array1(4,6),  array2(4,6);

MatrixRead('c:\mat1.txt', array1);

MatrixRead('c:\mat2.txt', array2);

MatrixSubtract(array1, array2, array2);

MatrixDisplay(array2, 'Array1 - Array2');

This program will read two data matrices from text files, subtract the elements of array2 from those of array1, and display the results in a Scrollsheet with the title Array1 - Array2.

Related topics:  MatrixAdd, MatrixMultiply, MatrixElemSubtract.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixSumOfSquares

  STATISTICA BASIC Library of Matrix Functions - MatrixSumOfSquares (Matrix, Result)

Parameters:

Matrix	name of source data matrix (see Arrays in Functions).

Result	destination variable (see Variables in STATISTICA BASIC) .

The MatrixSumOfSquares function will compute the sum of squares of each element of the specified Matrix (see Arrays in Functions) and place the resulting value in the STATISTICA BASIC variable specified as Result.

Example:

RandomAccess;

Dim array(4,6);

MatrixRead('c:\mat1.txt', array);

MatrixSumOfSquares(array, ssq);

This program will read a data matrix from a text file, compute the sums of squares of all elements, and store the result in the temporary variable ssq.

Related topics:  MatrixMeans.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixSweep

  STATISTICA BASIC Library of Matrix Functions - MatrixSweep (Matrix, From, To, Dir)

Parameters:

Matrix	name of symmetric data matrix (see Arrays in Functions; results will overwrite original values).

From	number of first column in which to begin sweeping.

To	number of last column in which to perform sweeping.

Dir	direction of sweeping (1 = forward, -1 = backward).

The MatrixSweep function will perform the sweeping transformation (see Dempster, 1969) on the specified square symmetric Matrix (see Arrays in Functions).  The sweeping transformation is commonly used to efficently perform stepwise multiple regression (see Jennrich, 1977) or similar analyses.  The forward sweeping transformation for a column k can be summarized in the following four steps:

1. e   = e   - e   * e   / e   for i<>k, j<>k

    ij    ij    jk    kj    kk

2. e   = e   / e

    kj    kj    kk

3. e   = e   / e

    ik    ik    kk

4. e   = -1 / e

    kk         kk

The reverse sweeping operation reverses the changes effected by these transformations.

Example:

RandomAccess;

Dim array(4,4);

MatrixRead('c:\mat1.txt', array);

MatrixSweep(array, 1, 4, 1);

MatrixDisplay(array, 'Sweep Matrix');

This program will read a data matrix from a text file, perform the forward sweeping transformation, and display the results in a Scrollsheet with the title Sweep Matrix.

Related topics:  MatrixInverse, MatrixDet, MatrixGeneralPseudoInverse, MatrixSolve.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixTrace

  STATISTICA BASIC Library of Matrix Functions - MatrixTrace (Matrix, Result)

Parameters:

Matrix	name of source data matrix (see Arrays in Functions).

Result	destination variable (see Variables in STATISTICA BASIC).

The MatrixTrace function will calculate the trace of the source Matrix (see Arrays in Functions), that is, the sum of the main diagonal elements, and place the result in the STATISTICA BASIC variable specified as Result.

Example:

RandomAccess;

Dim array(4,4);

MatrixRead('c:\mat1.txt', array);

MatrixTrace(array, trace);

This program will read a data matrix from a text file, compute the sum of the main diagonal elements, and store the result in the temporary variable trace.

Related topics:  MatrixInverse.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixTranspose

  STATISTICA BASIC Library of Matrix Functions - MatrixTranspose (Matrix, MatrixResult)

Parameters:

Matrix	name of source data matrix (see Arrays in Functions).

MatrixResult	destination matrix (see Arrays in Functions; may be the same as source Matrix, if desired).

The MatrixTranspose function will transpose the specified source Matrix (see Arrays in Functions) and place the resulting values in the matrix specified as MatrixResult.  (The destination MatrixResult may be the same as the source Matrix if it is a square matrix and you wish to overwrite the original values of the source array.)

Example:

RandomAccess;

Dim array1(4,6),  array2(6,4);

MatrixRead('c:\mat1.txt', array1);

MatrixTranspose(array1, array2);

MatrixDisplay(array2, 'Transposed Matrix');

This program will read a data matrix from a text file, transpose it, and display the results in a Scrollsheet with the title Transposed Matrix.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixWrite

  STATISTICA BASIC Library of Matrix Functions - MatrixWrite (FileName$, Matrix)

Parameters:

FileName$	name of output text file.

Matrix	name of source data matrix (see Arrays in Functions).

The MatrixWrite function will write the specified Matrix (see Arrays in Functions) into a text file.  In the text file, columns will be delimited by tabs, and rows will be delimited by carriage returns.

Example:

RandomAccess;

Dim array(4,4);

MatrixRead('c:\mat1.txt', array);

MatrixTranspose(array, array);

MatrixWrite('c:\transpos.txt', array);

This program will read a data matrix from a text file, transpose it, and write the transposed matrix to the disk as the text file Transpos.txt.

Related topics:  MatrixRead, ScrollsheetSetMatrix.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - MatrixWrite

  STATISTICA BASIC Library of Matrix Functions - MatrixWrite (FileName$, Data)

This application of the general matrix function MatrixWrite allows the user to perform data management operations on the current data file.

Parameters:

FileName$	name of output text file.

Data	current data file.

The MatrixWrite function will write the contents of the current data file into a text file.  In the text file, columns will be delimited by tabs, and rows will be delimited by carriage returns.

Example:

RandomAccess;

MatrixWrite('c:\data.txt', Data);

This program will write the the contents of the current data file to the disk as the text file Data.txt.

Related topics:  MatrixReadFromDataFile, ScrollsheetSetMatrix.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - VectorDualSort

  STATISTICA BASIC Library of Matrix Functions - VectorDualSort (Vector, IndexVector, Direction)

Parameters:

Vector	name of vector to sort (see Arrays in Functions).

IndexVector	name of index vector (see Arrays in Functions) to rearrange, following the sort in Vector.

Direction	direction of sort (SORT_ASCENDING, SORT_DESCENDING)

The VectorDualSort function will sort the values in Vector (see Arrays in Functions) into ascending or descending order, depending on the value of Direction (either SORT_ASCENDING or SORT_DESCENDING, respectively).  The values in IndexVector will be rearranged accordingly, so that all pairs of values Vector(i) and IndexVector(i) will remain unchanged.

Example:

RandomAccess;

Dim array1(100),  array2(100);

for i:=1 to 100 do begin

  array1(i):=normal(1);

  array2(i):=i;

end;

VectorDualSort(array1, array2, SORT_ASCENDING);

NewScrollsheet(0, 0, array1, 'Array 1', '', '');

NewScrollsheet(0, 0, array2, 'Array 2', '', '');

This program will create two vectors, fill the first one with standard normal random values and the second one with consecutive integers, and then sort array1 into ascending order, maintaining the equivalent order of values in array2; the two vectors are then shown in two Scrollsheets.

Related topics:  VectorRank, VectorSort.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - VectorDualSort

  STATISTICA BASIC Library of Matrix Functions - VectorDualSort (Variable, IndexVariable, Direction)

This application of the general matrix function MatrixDualSort allows the user to perform data management operations on the current data file.

Parameters:

Variable	variable from current data file to sort.

IndexVariable	index variable to rearrange, following the sort in Variable.

Direction	direction of sort (SORT_ASCENDING, SORT_DESCENDING)

The VectorDualSort function will sort the values in the specified Variable into ascending or descending order, depending on the value of Direction (either SORT_ASCENDING or SORT_DESCENDING, respectively).  The values in IndexVariable will be rearranged accordingly, so that all pairs of values Variable(i) and IndexVariable(i) will remain unchanged.

Example:

RandomAccess;

VectorDualSort(v3, v4, SORT_ASCENDING);

MatrixDisplay(Data, 'Sorted v3 and v4');

This program will sort variable 3 into ascending order, maintaining the equivalent order of values in variable 4; the data file is then shown in a Scrollsheet.

Related topics:  VectorRank, VectorSort.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - VectorRank

  STATISTICA BASIC Library of Matrix Functions - VectorRank (Vector, Direction, DupControl)

Parameters:

Vector	name of vector to rank (see Arrays in Functions).

Direction	direction of rank (SORT_ASCENDING - rank from smallest to largest value, SORT_DESCENDING - rank from largest to smallest value)

DupControl	assignment of ranks to duplicate (identical) values (RANK_FIRST, RANK_LAST, RANK_MEAN

The VectorRank function will rank (assign integer values to) the values in Vector (see Arrays in Functions), either from the smallest value to the largest value (SORT_ASCENDING), or from the largest value to the smallest value (SORT_DESCENDING).  Parameter DupControl determines how identical (duplicated) values in Vector are handled; if DupControl is set to RANK_FIRST, then the smallest possible rank (for the respective set of identical values) is assigned to each duplicate value in Vector; if DupControl is set to RANK_LAST, then the largest possible rank is assigned to each duplicate value in Vector (tied ranks); if DupControl is set to RANK_MEAN, then the average rank for all duplicate values will be assigned to each duplicate value in Vector (tied ranks).

Example:

RandomAccess;

Dim array1(100),  array2(100);

for i:=1 to 100 do

  array1(i):=normal(1);

MatrixDuplicate(array1, array2);

VectorRank(array2, SORT_ASCENDING, RANK_MEAN);

NewScrollsheet(0, 0, array1, 'Array 1' , '', '');

NewScrollsheet(0, 0, array2, 'Array 2' ,'' , '');

This program will create two vectors, fill the first one with random standard normal values, duplicate this array (copy it to array2), and then rank array2 from the smallest to the largest value; the two vectors are shown in two Scrollsheets.

Related topics:  VectorDualSort, VectorSort.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - VectorRank

  STATISTICA BASIC Library of Matrix Functions - VectorRank (Variable, Direction, DupControl)

Parameters:

Variable	variable from the current data file to rank.

Direction	direction of rank (SORT_ASCENDING - rank from smallest to largest value, SORT_DESCENDING - rank from largest to smallest value)

DupControl	assignment of ranks to duplicate (identical) values (RANK_FIRST, RANK_LAST, RANK_MEAN

The VectorRank function will rank (assign integer values to) the values in the specified Variable, either from the smallest value to the largest value (SORT_ASCENDING), or from the largest value to the smallest value (SORT_DESCENDING).  Parameter DupControl determines how identical (duplicated) values in the specified Variable are handled; if DupControl is set to RANK_FIRST, then the smallest possible rank (for the respective set of identical values) is assigned to each duplicate value in the specified Variable; if DupControl is set to RANK_LAST, then the largest possible rank is assigned to each duplicate value in the specified Variable (tied ranks); if DupControl is set to RANK_MEAN, then the average rank for all duplicate values will be assigned to each duplicate value in the specified Variable (tied ranks).

Example:

RandomAccess;

VectorRank(v2, SORT_ASCENDING, RANK_MEAN);

MatrixDisplay(Data, 'Ranking of v2');

This program will rank variable 2 from the smallest to the largest value; the data file is then shown in a Scrollsheet.

Related topics:  VectorDualSort, VectorSort.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - VectorSort

  STATISTICA BASIC Library of Matrix Functions - VectorSort (Vector, Direction)

Parameters:

Vector	name of vector to rank (see Arrays in Functions).

Direction	direction of sort (SORT_ASCENDING, SORT_DESCENDING)

The VectorSort function will sort the values in Vector (see Arrays in Functions) into ascending or descending order, depending on the value of Direction (either SORT_ASCENDING or SORT_DESCENDING, respectively).

Example:

RandomAccess;

Dim array(100);

for i:=1 to 100 do

   array(i):=normal(1);

VectorSort(array, SORT_ASCENDING);

NewScrollsheet(0,0,array,'Sorted Values','','');

This program will create a vector, fill it with random standard normal values, and sort it into ascending order; the sorted vector is then shown in a Scrollsheet.

Related topics:  VectorDualSort, VectorRank.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


STATISTICA BASIC - VectorSort

  STATISTICA BASIC Library of Matrix Functions - VectorSort (Variable, Direction)

This application of the general matrix function MatrixSort allows the user to perform data management operations on the current data file.

Parameters:

Variable	variable from the current data file to sort.

Direction	direction of sort (SORT_ASCENDING, SORT_DESCENDING)

The VectorSort function will sort the values in the specified Variable into ascending or descending order, depending on the value of Direction (either SORT_ASCENDING or SORT_DESCENDING, respectively).

Example:

RandomAccess;

VectorSort(v2, SORT_ASCENDING);

MatrixDisplay(Data, 'Sorted values of v2');

This program will sort variable 2 into ascending order; the display the data file in a Scrollsheet.

Related topics:  VectorDualSort, VectorRank.

For more information on using arrays, see Arrays in Functions.

For a complete list of matrix functions, see Matrix Library of STATISTICA BASIC.


  Advanced Examples of STATISTICA BASIC Programs

The following example application programs (written in STATISTICA BASIC) are included in the directory \STAT\EXAMPLES\STBASIC.  For more information, please read the comments included in each of the programs.

Note that additional example programs can be viewed on the Frequently Asked Questions topic of the StatSoft WEB page.  To copy the StatSoft WEB page address to the Clipboard, select WEB page from the Help pull-down menu.

PROGRAM	Description

2STLS.STB	This program illustrates many of the available matrix functions in an example of a two-stage least squares regression analysis.

BOXCOX.STB	This program will compute the best parameter for a Box-Cox transformation of the dependent variable in a multiple regression analysis; the user can choose between an automatic search algorithm and a graphical procedure for determining the best parameter.

BOXCOXP.STB	This program will generate plots of the means versus the standard deviations, and the log(means) versus log(standard deviations) from the Display Scrollsheet in Experimental Design.  These plots are useful for determining an appropriate Box-Cox transformation for the dependent variable values in an experiment.

BOXTID.STB	This program will compute the parameters for a Box-Tidwell transformation of the independent variable values in a multiple regression analysis.

CASEPLOT.STB	This program will produce a multiple line plot for selected cases, and for selected variables.  Each line will represent the values for one case, across the selected variables.

DOTPLOT.STB	This program will produce dot-plots for selected variables.  Dot-plots show the distribution of the values over the range of values for the respective variables.

ETA-TRAN.STB.	This program will compute the standard (Taguchi) Signal-to-Noise ratios for a user-specified list of variables.  These indices can be used  (as the dependent or Y-variables) together with all types of designs available in the Experimental Design module of STATISTICA, or in any other type of analysis.   For more information about Taguchi methods, see Experimental Design.

FACTORAN.STB	This program allows you to perform a principal components analysis, based on correlations, covariances, or the moment matrix (also, very large problems can be analyzed, e.g., >300 variables).  The program will also perform a varimax rotation of the factor space, and compute the factor scores.

FILCOMP.STB	This program will compare the values for selected variables in two data files, and produce a summary report of the "mismatches."

HENON.STB	This program will compute the successive values for the Henon strange attractor, and plot them in 2D and 3D scatterplots.

HISTRES.STB	This program will produce a histogram for a selected variable, and fit to it the normal distribution.  The results are presented in a compound graph document, which shows the histogram and a line plot indicating the deviations of the normal expected frequencies from the observed frequencies.

LILLIEF.STB	This program will compute critical values for the Kolmogorov-Smirnov D statistic, based on a user-defined sample size and number of replications, for normal samples with means and standard deviations unknown. These critical values are also called Lilliefors critical values (see Lilliefors, 1967).

MANOVA.STB	This program will perform a multivariate analysis of variance and compute various results, statistics and graphs.

MANTHAEN.STB	This program will compute the Mantel-Haenszel test for a user-defined three-way table.

MANYGRPS.STB	This program will produce and print a line plot, scatterplot, or step plot for each case in a data file, for a selected set of variables.

METAHIST.STB	This program will produce a histogram "built from" user-defined clipart, and based on a frequency table, as produced via the Basic Statistics module or the Quick Basic Stats options. The bars in the histogram will be made up from a specified metafile, and it is assumed that the Scrollsheet with frequencies is the top-most Scrollsheet.

REGRESSN.STB	This program will perform a complete multiple regression analysis for selected variables, and produce various diagnostic plots of the residuals.

REPMEAS.STB	This program will restructure a data file, so that the values for selected variables become consecutive "groups" in a new data file; that data file will also include a grouping variable with text values that are identical to the original variable names.  This program is useful if you need to restructure a data file that contains the data for several independent samples in different columns of data (one for each sample); in order to analyze such data via the numerous statistical and graphical tools available in STATISTICA, you first need to restructure your data file (as can be accomplished via this program) to the standard form (i.e., so that each row in the data file represents one "case" or observations, and each column represents one measurement for that case).

RESPLOTS.STB	This program will retrieve the data from the Predicted & Residual Values Scrollsheet in Multiple Regression (accessible via the Residual Analysis dialog), and produce:

1. a 2D scatterplot plot of the case numbers versus the standardized residual values; in this plot all standardized residuals with absolute values greater than 2 will be highlighted and labeled;

2. a 3D scatterplot of the case numbers (x) by observed values (y) by standardized residuals (z).

SAMPLE.SCL	This SCL (STATISTICA Command Language) program illustrates a simple standard SCL application.

SCLHELP.STB	This program is called from the SCL (STATISTICA Command Language) program sclstb.scl.

SORT.STB	This program will sort the rows of the current Scrollsheet by the user-specified column.

WLS.STB	This program will compute the parameters for a multiple regression equation via weighted least squares.

SCALES.STB	This program generates a simple custom scale to the right of an existing graph.  You can modify this program to place custom scales in any place on a graph.

SCLSTB.SCL	This program illustrates how to use STATISTICA BASIC programs from within SCL (STATISTICA Command Language) programs to provide elements of the run-time user interface (in this case, selecting variables for the analysis).  The program will first append a variable (new variable 26) to the example data file adstudy.sta; then the STATISTICA BASIC program sclhelp.stb is executed; that program will prompt the user to select a variable that is to be used as the dependent variable in a multiple regression analysis.  The BASIC program will copy the selected variable to the new variable 26; then this SCL program will continue by running the multiple regression procedure with variable 26 as the dependent variable.


  STATISTICA BASIC User-defined Functions and Subroutines

STATISTICA BASIC supports user-defined subroutines and functions, allowing the user to build large structured programs.  Libraries of subroutines and functions can be saved in separate files, and included in programs via the Include metacommand ({$I:'FileName'}).

In general, user-defined subroutines and functions allow you to build compact and structured programs, which are more easily debugged and maintained; libraries of subroutines and functions can also be "reused" in separate projects.

Example 1:

Here is a simple example of a function:

Function Factorial(x)                      {declaration of function}

begin                                      {beginning of body of function}

 Factorial:=1;

 For i:=1 to x do Factorial:=Factorial*i;

end;                                       {end of function}

x:=Factorial(5);                           {main program, calling the function}

First, the user-defined function Factorial(x) is declared.  This function computes the factorial function X! = 1 * 2 * ... * X; as a result of running the program shown above, X will be equal to: 1 * 2 * 3 * 4 * 5 = 120.

Example 2:

Using the function declared in Example 1 above, one could now write a subroutine to compute the number of ways of selecting r distinct objects from N objects, irrespective of order; the formula is: (N!/(r!*(N-r!)).  Here is the subroutine:

Sub NoverR(n,r, byref x)

begin

 x:=Factorial(n)/(Factorial(r)*Factorial(n-r));

end;

Passing Arguments by Reference

Note that the subroutine shown above changes the value of X, and passes it back to the program, subroutine, or function from which it was called; the keyword byref is used to denote that the value of X is to be passed back (i.e., it is passed to the subroutine by reference).  By default (if keyword byref is not used), all single-value arguments passed to a subroutine will be the same after the subroutine was executed (i.e., they are passed by value); note that arrays are always passed by reference (see the description of Arguments below).  Of course, single-value arguments passed to a subroutine can be changed inside a subroutine, but upon exiting, the arguments will retain their original values inside the calling program.  Thus, to change the value of X in the program that calls NoverR, the declaration byref x is necessary.

One could now write the following line (main program) to call the subroutine (which calls the function):

Noverr(5,3,x);

writeln('Number of ways to select 3 objects from 5 objects:',X);

Functions vs. Subroutines

As illustrated in the two example programs shown above, functions will return a value to the calling program, subroutine, or function.  Thus, the statement x:=Factorial(n); will assign to variable x the value returned by function Factorial(n).  In general, function procedures can be used on the right-hand side of expressions in the same way you use any intrinsic function, such as Sqr, Cos, or Chr.  Subroutines cannot be used on the right-hand side of expressions.  To return values from subroutines, the respective arguments have to be passed to the subroutine by reference, i.e., using the keyword byref (see above).  Of course, arguments can also be passed to functions by reference.

Declaration of Functions

The general format of function definitions is:

Function Name [(Arguments)] ;

begin

  [Declarations]

  { [Instruction] | [Name := Expression] | [Exit Function]

    [;[Instruction] | [Name := Expression] | [Exit Function], ...] }

end [Function];

The components of the function definition are:

Name	name of the function; the name also determines the function type; if the function name ends with a dollar character ($) then the function will return a string; otherwise it will return a number

Arguments	list of variables representing arguments that are passed to the function when it is called; multiple variables are separated by commas; arguments that are to be changed when returning to the calling program have to be passed by reference, and declared using the keyword byref (see above)

begin ... end	block denoting the body of the function

Declarations	contains declarations of any array arguments and other local variables

Instruction	instructions to be executed inside the body of the function

Name := Expression	instruction assigning a return value of the function

Exit Function	instruction causing an immediate exit from the function; several Exit Function instructions can appear anywhere in a function

Declaration of Subroutines

The general format of subroutine definitions is very similar to that of functions (see above), except that no return value can be specified:

SUB Name [(Arguments)] ;

begin

  [Declarations]

  { [Instruction] | [Exit SUB]

    [;[Instruction] | [Exit SUB], ...] }

end [Subroutine];

Arguments

The general syntax for arguments in a function or subroutine declaration is:

[Sub | Function] Name ( [BYREF | BYVAL] ArgName [,[BYREF | BYVAL] ArgName, ...] )

•	Arguments are optional.

•	BYREF indicates that an argument is passed by reference (see also Passing Arguments by Reference, above).  When an argument is passed by reference, the function or subroutine has access to the actual variable.  As a result, the variable's value can be changed by the procedure to which it is passed, and the changed value will be passed back to the calling program, function, or subroutine.

•	BYVAL indicates that an argument is passed by value (this is the default).  When an argument is passed by value, the function or subroutine only has access to a "copy" of the variable.  As a result, the variable's value in the calling program cannot be changed by the procedure to which it is passed.

•	ArgName is the name of a variable representing the argument.  Strings are denoted by argument names with a dollar sign ($) at the end.  Arrays are defined in the function or subroutine body, as usual, via the Dim statement.  Multiple arguments are separated by comma.

Array Arguments

Arrays are always passed by reference, which means that any assignments to parameters which are arrays are retained after the function or subroutine terminates.  Array arguments have to be explicitly declared in the respective subroutine or function; for example:

Sub fillarray(x,n)

begin

 dim x(n);

 for i:=1 to n do x(i):=1/i;

end;

fillarray(data(1,5),ncases);

This program will fill the fifth column (variable) in the data file (referenced via the reserved array name data) with the values 1/i.  Note that you cannot increase or decrease the size of arrays that are arguments (from inside the function or subroutine to which it is passed).

Local and Global Arrays and Variables

Variables that can be used in subroutine and function procedures fall into three categories:  Arguments that are passed to the procedure, local variables, and global variables.  Arguments are described above.

All variables that are not arguments passed by reference are by default local.  Local means that the values of those variables are only accessible within the respective procedure, and no naming conflicts will arise if the same variable name is used in another procedure or the main program.

All variables or arrays that are defined (e.g., explicitly declared) at some higher level outside the procedure are global.  Global means that the values of those variables can be accessed and changed inside the respective procedures, even though they were not passed as arguments.  For example, the reserved array name data(i,j) and the variable ncases can be used in every subroutine or function to access the current data file:

SUB FILLARRAY(Y)

begin

 for I:=1 to ncases do data(I,1):=y/I;

end;

FILLARRAY(2);

In this example, the first column of the data file will be filled with the successive values of 2/i.  Note that in this example, both array DATA and variable ncases can be used inside the subroutine (i.e., they are visible to the subroutine).

Declaring Global Variables

To make other arrays and variables globally visible to the procedures that follow, declare them in the program prior to the respective procedures, using the Dim keyword.  For example:

Dim x(10);

Dim n;

SUB FILLARRAY(Y)

begin

 FOR I:=1 TO N DO x(I):=y/I;

end;

n:=10;

FILLARRAY(2);

This program will fill the 10 elements of array X with successive values of 2/i.  Instead of declaring variable n via the dim  statement, you could also use a simple assignment statement at the beginning of the program:

dim x(10);

n:=10;

SUB FILLARRAY(Y)

             ...

             ...

Note that all arrays that are explicitly declared inside a procedure, and which are not arguments of the procedure, will be treated as local arrays, even if they also exist as global arrays.  For example:

dim x(10);

Dim n;

SUB FILLARRAY(Y)

begin

 Dim x(10);

 For I:=1 to N do x(I):=y/I;

 MatrixDisplay (x, 'Local X');

end;

n:=10;

FILLARRAY(2);

MatrixDisplay (x, 'Global X');

This program will fill the elements of the local array X, but on return, all elements of X in the main program will be unchanged (i.e., equal to zero).

In general, a procedure can use a variable that is not explicitly declared in the procedure, but a name conflict can occur if anything you have defined has the same name.  If your procedure refers to an undeclared variable that has the same name as another procedure, constant or variable, it is assumed that your procedure is referring to that name.

Other Conventions and Rules

•	All goto statements must reference addresses within the same subroutine or function.  You cannot jump into a subroutine from a main program or another subroutine, etc.

•	The pauseandedit statement cannot access local variables inside procedures.

•	Functions and subroutines cannot be recursive.

Using Libraries of Procedures via the Include ({$I:'FileName'}) Metacommand

You may want to develop sets (libraries) of routines and functions to be used repeatedly in different programs.  You can keep such libraries in separate files, and include them in a current program via the Include metacommand.  For example:

{$I:'c:\stat\libraries\combinat.stb'}

noverr(5,3,x);

writeln('Number of ways to combine 3 objects from 5 objects:',X);

This program assumes that the subroutine noverr is located in the include file c:\stat\libraries\combinat.stb.

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Expressions

Operators

Compound Instructions (Begin..End)

Conditional Constructions

Loops

GOTO Statements

Recoding Statements

Missing data

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Include Metacommand

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


STATISTICA BASIC Include Metacommand

  STATISTICA BASIC Metacommand {$I:'FileName'} (Include File)

This metacommand will cause the program to include the statements and instructions from the respective STATISTICA BASIC file FileName when executing the current program.  Metacommands In STATISTICA BASIC are placed in curly brackets, and thus may look similar to comments, but they always begin with a dollar sign.

The syntax of the metacommand for specifying include files is as follows:

{$I:'FileName'}

If a full path is not specified the program will look for the file in the STATISTICA subdirectory (where the STATISTICA program files are).

Default Include Files

Note that there are six predefined include files that will be loaded before any program statements are analyzed:

Graphlib.inc	all graphics functions

Uilib.inc	user interface functions

Statlib.inc	statistical functions

Scrlib.inc 	Scrollsheet functions

Matrlib.inc	matrix functions

Userlib.inc	an optional file with user-defined functions, subroutines, and declarations

You can modified the contents of these include files if necessary.  Also, STATISTICA will always look for the file Userlib.inc, so if you want to write some functions or interfaces that will be available without including them explicitly via the {$I:'FileName'} metacommand, you can create file Userlib.inc and place it in the STATISTICA subdirectory.  The functions, subroutines, and declarations in that file will then automatically be "visible" to all programs.

Nested Inclusion of Files

You can include the {$I:'FileName'} metacommand in files which are themselves included in other programs, that is, STATISTICA BASIC supports nested inclusion of files.

For other General Conventions topics, see:

General Operation (Sequential vs. RandomAccess Mode)

General Syntax Conventions (Instruction, Line Length, Separators, Uppercase/lowercase, Comments in programs)

Referencing STATISTICA Variables

Elementary Instructions (Assignments)

Expressions

Operators

Compound Instructions (Begin..End)

Conditional Constructions

Loops

GOTO Statements

User-defined Functions and Subroutines

Recoding Statements

Missing data

Transferring Values Between Cases

Calling Functions or Subroutines Defined in External DLL Files

Reversing the Changes to Data Made in STATISTICA BASIC

Format of STATISTICA BASIC Source Code Files

STATISTICA BASIC Compiler (Technical Note)


  STATISTICA BASIC Output - Data Files, Text/graphics Reports, External Files

The output from STATISTICA BASIC can be handled in a variety of ways.  First, the values (numeric or text) can be written directly to the current or a new STATISTICA data file (e.g., when you need to perform data transformations or cleaning).  It can also be directed to the printer, disk files, interactive dialogs, or the report window (where it can combine graphs with text or tables in a single document).  Also, text or tabular output can be sent to new Scrollsheets (see Scrollsheets).  See also Graphics Output.


  STATISTICA BASIC Output - Scrollsheets

Creating Output Scrollsheets.  In addition to the various report, external file, or data file output options (see Output), you can create new Scrollsheets or cascades of Scrollsheets (directly from within your BASIC program) and display your tabular or text results in a way that is most efficient to review.  Creating a simple output Scrollsheet takes just one line of code, and as a result, you get a "tool" to review tables and values that is incomparably more efficient and user-friendly than traditional text-output editors.  For example, the value display format, column width, etc., can be interactively customized by the user of your STATISTICA BASIC application program, edited (including Drag-and-Drop, AutoFill, etc.), printed as tables with high-resolution grid lines, selectively copied, exported, etc.; the values can also be interactively visualized in graphs of any type supported in STATISTICA.  Moreover, if you need to create specific, highly customized Scrollsheets that look like those created by the standard STATISTICA procedures (with titles, custom formatting, fonts, colors, highlighting, etc.), a comprehensive set of functions is provided and can be used in your BASIC programs.

Accessing (input) data from existing Scrollsheets, "follow-up analyses."  You can also easily write procedures to manage existing Scrollsheets.  This includes not only global operations (e.g., save, open, print Scrollsheets), but Scrollsheets can also be used for input.  Specifically, you can read data from existing Scrollsheets created by other STATISTICA procedures, and thus your BASIC programs can be designed to "continue" or "follow up" on analyses completed by other procedures of STATISTICA.  For example, you can write procedures to further analyze frequency data from a crosstabulation or from complex sequences of means displayed in a multiple-classification table; you can analyze output from Monte Carlo procedures, or just rearrange the layout of an existing Scrollsheet (e.g., by reading its contents into a BASIC data array and writing them to new, custom-designed Scrollsheets); you can merge or split Scrollsheets, save them as STATISTICA data sets, Scrollsheet or ASCII files.  Like all functions in STATISTICA BASIC, Scrollsheet functions are easy to use because they can be inserted with the help of the Wizard.

See also, Scrollsheets Overview.


Graphics (Overview of Graphics Options in STATISTICA)

In addition to the specialized graphs which are available from the output dialogs of all statistical procedures, there are two general types of graphs accessible from the Graphs Gallery, pull-down menu Graphs, and toolbar and flying menus of all Scrollsheets and spreadsheets:

•	Stats Graphs (see Stats Graphs and Quick Stats Graphs), and

•	Custom Graphs.

The most important difference between these two types is that Stats Graphs produce statistical summaries or other representations of raw data in the selected variables of the current data file, whereas Custom Graphs provide a general tool to visualize numeric values in the currently highlighted block (which may contain values from custom defined subsets of numerical output or arbitrarily selected subsets of raw data).

See also,

Block Stats Graphs

Multiple Graph Layouts (Wizards, Templates)

Blank Graphs

Stats User-defined Graphs

  Graphs gallery

See also Customizing Graphs.


Graphics (Overview of Graphics Options in STATISTICA) - Other Specialized Graphs

In addition to the standard selection of Quick Stats Graphs, some Scrollsheets also offer other, more specialized statistical graphs (e.g., plots of interactions in ANOVA, icon plots of regression residuals, or contour plots in cluster analysis).

As mentioned before, other, specialized statistical graphs which are related not to a specific Scrollsheet but to a type of analysis (e.g., nonlinear estimation results) are accessible directly from results dialogs (i.e., the dialogs which contain output options from the current analysis).

See also Quick Stats Graphs, Stats Graphs, Custom Graphs and Graphs gallery.


  Quick Stats Graphs

Quick Stats Graphs include the most-commonly used types of Stats Graphs (which are available from the pull-down menu Graphs, or by pressing the Graphs Gallery [image] toolbar button).  Quick Stats Graphs do not offer as many options as Stats Graphs, however, they are quicker to select because unlike Stats Graphs:

•	Quick Stats Graphs can be called directly from flying menus and toolbars,

•	Quick Stats Graphs do not require the user to select variables (the variable selection is determined by the current cursor position within a Scrollsheet or spreadsheet), and

•	Quick Stats Graphs do not require the user to select options from any intermediate dialogs (default formats of the respective graphs are produced).

Selecting the Quick Stats Graphs option (either from the toolbar button, flying menu, or the pull-down menu Graphs) will open a menu from which you may choose one of the statistical graphs applicable to the current variable, that is, to the variable indicated by the current cursor position in the Scrollsheet or spreadsheet.  If the Scrollsheet has a matrix format or a format where a cursor position may indicate not one but two variables, then predefined bivariate graphs for the specified pair of variables will be available from the Quick Stats Graphs menu.

If no variables are indicated by the current cursor position, then selecting any of the Quick Stats Graphs will prompt you to select a variable from a list.  As the Quick Stats Graphs are generated, STATISTICA will take into account the current case selection and weighting conditions for the variables that are being plotted.

For specific information on Quick Stats Graphs, click on the topic name below.

Specific Graphs

  Values/Stats of...	  2D Histogram by...

  Histogram of ...	  3D Histogram by...

  Box-Whisker of ...	  Box-Whisker by...

  Probability Plot of ...	  Probability Plot by...

  Scatterplot by...	  Matrix Scatterplot

  Scatterplot with Histograms	  Scatterplot with Box Plots

  Swap Variables (available from the right-mouse button Quick Stats Graphs menu)

See also Stats Graphs, Custom Graphs, Block Stats Graphs, and Graphs gallery.


Custom Graphs

Custom Graphs allow you to visualize any custom-defined combination of values from Scrollsheets and spreadsheets (from rows, columns, or both, and/or their subsets).  When you select one of the global types of these graphs (Custom 2D Graphs, Custom 3D Sequential Graphs, Custom 3D XYZ Graphs, Custom Matrix Graphs, or Custom Icon Graphs), a respective dialog will open allowing you to specify the parts of the current Scrollsheet or spreadsheet to be plotted.  The layout of this dialog depends on the global type of the Custom graph which you have selected (e.g., Custom 2D Graphs).  The initial selection of the data to be plotted (suggested in that dialog) depends on the current block (or cursor) position in the current Scrollsheet or spreadsheet.  Each of these Custom graph definition dialogs allow you to select the specific types of graph (within the global type).  However, the graph type can also be adjusted later, after the graph is created (via the General Layout or Plot Layout dialogs accessible by clicking on the graph background or from the graph pull-down menu Layouts).

For specific information on Custom Graphs, click on the graph name below.

  2D Graphs	  Matrix Plots

  3D Sequential Graphs	  Icon Plots

  3D XYZ	  Ternary Plots

See also Quick Stats Graphs, Stats Graphs, Block Stats Graphs, and Graphs gallery.


Stats Graphs

Unlike Custom Graphs (which provide general tools to create custom visualizations of numerical Scrollsheet output, or spreadsheet data, see above), Stats Graphs are pre-defined statistical graphs.  They are available from the pull-down menu Graphs or by pressing the Graphs Gallery [image] toolbar button, and offer hundreds of types of graphical representations and analytic summaries of data.  They are not limited to the values in the current Scrollsheet, and they do not depend on highlighted blocks or the current cursor position; instead, they process data directly from the current data file.  They represent either standard methods to graphically summarize raw data (e.g., various scatterplots, histograms, or plots of central tendencies such as medians) or standard graphical analytic techniques (e.g., categorized normal probability plots, detrended probability plots, or plots of confidence intervals of regression lines).  As the Stats Graphs are generated, STATISTICA will take into account the current case selection and weighting conditions for the variables selected to be plotted.

For specific information on Stats Graphs, click on the graph name below.  You can also click on the [image] toolbar button in order to open a dialog displaying each of these graphics options and their summary descriptions.

  Stats 2D Graphs

  2D Histograms	  2D Box Plots

  2D Scatterplots	  Bar/Column Plots

  Scatterplots w/Histograms	  2D Line Plots (Variables)

  Scatterplots w/Box Plots	  2D Line Plots (Case Profiles)

  Probability Plots	  Sequential/Stacked Plots

  Quantile-Quantile Plots	  Pie Charts

  Probability-Probability Plots	  Missing/Range Data Points

  2D Range Plots	  2D Custom Function Plots

  Stats 3D Sequential Graphs

  Raw Data Plots	  Range Plots

  Bivariate Histograms	  Box Plots

  Stats 3D XYZ Graphs

  Scatterplots	  Ternary Plots

  Surface Plots	  Categorized Plots

  Contour Plots	  Categorized Ternary Plots

  Trace Plots	  Custom Function Plots

  Stats Matrix Plots

  Stats Icon Plots

  Stats Categorized Graphs

  Histograms	  Box Plots

  Scatterplots	  Pie Charts

  Probability Plots	  Missing/Range Data Plots

  Quantile-Quantile Plots	  3D XYZ Plots

  Probability-Probability Plots	  3D Ternary Plots

  Line Plots

  Stats User-defined Graphs

See also Quick Stats Graphs, Custom Graphs, Block Stats Graphs, and Graphs gallery.


  Graphs Gallery

Click on the [image] toolbar button (or this button in a graph definition dialog) in order to open the Graphs Gallery dialog.  This dialog displays a 'gallery'-style menu of STATISTICA graphs and allows you to quickly and easily "switch" between the different types of graphs (e.g., Stats Graphs, Custom Graphs, etc.).  The following graphs are available in this dialog:

  Stats 2D Graphs	  Multiple Graph Layouts

  Stats 3D Sequential Graphs	  Blank Graphs

  Stats 3D XYZ Graphs	  Custom Graphs

  Stats Matrix Plots	  Block Stats Graphs

  Stats Icon Plots	  Stats User-defined Graphs

  Stats Categorized Graphs

Graph button:  When you click on this button, a STATISTICA Help window will open in which the topic for the highlighted graph will be displayed.

Overview button:  Click on this button in order to open the STATISTICA Help window and display the Graphics window Overview topic.


  Stats 2D Graphs

  2D Histograms	  2D Box Plots

  2D Scatterplots	  Bar/Column Plots

  Scatterplots w/Histograms	  2D Line Plots (Variables)

  Scatterplots w/Box Plots	  2D Line Plots (Case Profiles)

  Probability Plots	  Sequential/Stacked Plots

  Quantile-Quantile Plots	  Pie Charts

  Probability-Probability Plots	  Missing/Range Data Points

  2D Range Plots	  2D Custom Function Plots


  Stats 3D Sequential Graphs

  Raw Data Plots	  Range Plots

  Bivariate Histograms	  Box Plots


  Stats 3D XYZ Graphs

  Scatterplots	  Ternary Plots

  Surface Plots	  Categorized Plots

  Contour Plots	  Categorized Ternary Plots

  Trace Plots	  Custom Function Plots


  Stats Categorized Graphs

  Histograms	  Box Plots

  Scatterplots	  Pie Charts

  Probability Plots	  Missing/Range Data Plots

  Quantile-Quantile Plots	  3D XYZ Plots

  Probability-Probability Plots	  3D Ternary Plots

  Line Plots


Customizing Graphs

All graph customization facilities in STATISTICA are available when a graph window is active (thus, after a graph has been shown).  Usually, graphs appear on the screen instantaneously, and typically, it is preferable to first see the default appearance of the graph before proceeding with any customizations.  However, in the rare cases when producing a graph takes more time (e.g., in case of complex multi-graphs or graphs based on very large data sets), you can also make the customization before the drawing of the default graph is completed.  Specifically, you can always interrupt the drawing with a single click (press any key or click the mouse anywhere on the screen).  Then, you can access some customization tools or facilities and resume redrawing after making the desired adjustments.

For more information on graph customization, see:

Adding/Editing Custom Graphic Objects

Customizing the Structural Components of the Graph

Using the Right-Mouse-Button (Flying Menus in Graphs)

Using the Left-Mouse-Button (Direct Access to Customization Dialogs)

Customization of Custom Graphic Objects (Drawings, Embedded Objects)

Margins, Graph Proportions, Plot Area, Zooming

Moving a Graph Object


Customizing Graphs - Adding/Editing Custom Graphic Objects

The tools to add and edit custom graphic objects to the current graph (such as drawing, managing and customizing objects, pasting, embedding, linking, etc.) can be accessed from the graphics toolbar. Those options are also accessible via the keyboard (from the graph pull-down menu Edit), and many of them can also be accessed from the flying menus accessible by clicking on specific parts of the graph with the right-mouse-button.


Customizing Graphs - Customizing the Structural Components of the Graph

Almost all facilities to change the structural properties of graphs (such as proportions, scales, patterns, features of individual plots, etc.) can be accessed from two types of dialogs: General Layout and Plot Layout. These two types of dialogs can be accessed from the graph pull-down menu Layouts or by double-clicking on the graph background.

The General Layout dialogs for the various general types of graphs available in STATISTICA are listed below:

2D Graphs	Icon Plots

3D Scatterplots and Surfaces	Matrix Plots

3D Sequence Graphs	Ternary Scatterplots and Surfaces

3D Histograms

The Plot Layout dialogs for the various general types of graphs available in STATISTICA are listed below:

2D Graphs

3D Scatterplots and Surfaces

3D Sequence Graphs

Note that for 3D Histograms, Icon Plots, and Matrix Plots, the customization options controlling the patterns and colors of individual plots are included in their respective General Layout dialogs.


 Customizing Graphs - Using the Left-Mouse-Button (Direct Access to Customization Dialogs)

You can use the left-mouse-button to access customization facilities for specific elements of the graph by double-clicking on the specific graph object or component.  If the element you have selected this way is one of the structural components of the graph (such as a scale, point marker, or a title), then the dialog which is most-commonly used to customize that type of the object will automatically open.

Options accessible by double-clicking on an object with the left-mouse-button vs. options accessible from the flying menus (clicking the right-mouse-button).  By pointing with the right-mouse-button to a graph object, a list of customization dialogs and options applying to that object will be displayed in a flying menu.  On the other hand, double-clicking using the left-mouse-button opens directly the dialog most-commonly used, or the global dialog which applies to the object.  Therefore, double-clicking with the left button saves you one step whenever you are accessing the most-commonly used option.

Accessing the General Layout dialog.  The same principle also applies to calling the General Layout dialog.  To access it, simply double-click on the empty graph space outside the graph axes.  Alternatively, you can select it from the "main" flying menu accessible by clicking with the right-mouse-button on the empty graph space outside the graph axes.


Customizing Graphs - Customization of Custom Graphic Objects (Drawings, Embedded Objects)

The general principles of selecting objects by mouse and accessing their customization facilities [see Using the Right-Mouse-Button (Flying Menus in Graphs) and Using the Left-Mouse-Button (Direct Access to Customization Dialogs)] also apply to all custom graphic objects, such as drawings, arrows, and embedded/linked objects.  The graphics toolbar buttons can also be used to access most of those customization facilities.  For example, the buttons can be used to change the dynamic vs. fixed coordinates of objects, their patterns, sizes and colors, properties of predefined objects (such as arrows or error bars), or foreign objects (e.g., pasted, linked, or embedded artwork).


Customizing Graphs - Margins, Graph Proportions, Plot Area, Zooming

These global graph attributes can be adjusted by using the respective buttons on the graphics toolbar; these options are also available on the graph pull-down menu View.

See also:

Adjust Graph Margins, Plot Area

Fixed Graph Proportion (Maintain Graph Aspect Ratio)

Change Graph Proportion

Graphics Zoom In Tool

Graphics Zoom Out Tool


Customizing Graphs - Using the Right-Mouse-Button (Flying Menus in Graphs)

The easiest way to access the two main types of customization dialogs (i.e., General Layout and Plot Layout) as well as all other customization facilities, is to use the flying menus accessible by clicking on the graph with the right-mouse-button.  Using the flying menus is also often faster because they provide shortcuts allowing you to directly access the nested (i.e., "second-" or "third-level") dialogs controlling the attributes of specific graph components while bypassing the General Layout and Plot Layout dialogs.

One of the graph flying menus has a different status than others.  Specifically, unlike all other flying menus which are associated with specific objects, the "main" (or "background") flying menu accessible by pressing the right-mouse-button anywhere outside the graph axes contains global graph customization and multi-graphics management options.


If Data Point Labels Overlap

If the labels overlap in a graph, try to rotate the 3D graph (via the Perspective and Rotation Graph Window toolbar button) or double-click on any data point label to access the Data Point Labels dialog and then click on the Font button in order to adjust (reduce) the size of font used to label the points.  You can also use the Display Filters option from the Graphics View pull-down menu in order to select the degree of filtering (removal of overlapping points or text) in the current graph (the default setting, Level 2, suppresses the display of only those labels which overlap to a large degree).  Finally, you may also adjust the location of specific labels one at a time:  double-click on any point label to bring up the Data Point Labels dialog.  Now, click on the Edit button in this dialog to open the Edit Text Labels dialog.  In this dialog, highlight the label to be adjusted and cut it (by pressing CTRL+X); press OK to return to the plot.  Now, paste (CTRL+V) the label into the graph, then position the label as desired (you may need to adjust the font and other attributes of the label if the current defaults of the custom text are different from the defaults set for the data labels, but you will need to make this adjustment only once - the next repositioned label will use the previously set attributes).

NOTE:  Use the Brushing tools to turn off individual (or all) data point labels that were created using the Brushing tools.


Fitted Functions for Histograms

Choose to fit an equation to the histogram or smooth the histogram by selecting one of the predefined functions.  (The maximum likelihood method is used to estimate the distribution parameters.)

  Normal	  Laplace

  Beta	  Logistic

  Exponential	  Lognormal

  Extreme	  Poisson

  Gamma	  Rayleigh

  Geometric	  Spline

  Weibull

Note that for the Beta distribution, the data are required to be in the valid range of 0<x<1.  For the Gamma, Lognormal, Weibull, Extreme, and Rayleigh distributions, the valid range is x>0.  If the data fall outside of the valid range, then STATISTICA will give an error message ("Fit not drawn because of invalid range of values") in the title of the graph.


2D Graphs Fitted Functions

Choose to fit an equation to the data or smooth the data by selecting one of the predefined functions (see below), or custom define a function to be overlaid.

  Linear	  Polynomial

  Logarithmic	  Least Squares

  Exponential	  Negative Exponential

  Spline	  Custom Function

To custom define a function (mathematical expression), select either the Custom Function option or click on the Custom Function button to bring up the User-Defined Functions dialog.  Note:  User-defined functions which can be specified here or in graph Plot Layout dialogs are plotted over (i.e., overlaid) and not fitted to the data.  In order to fit (and plot) user-defined functions to the data, use the Nonlinear Estimation module.

If you wish, you can use the fitted function equation as a graph title via control characters.  The Control Characters for the fitted function are @F[plot number, subgraph number] where you specify the desired plot number and optionally the subgraph number (for categorized graphs).  Once the Control Characters for the fitted function have been entered into the Titles dialog, you can edit the fitted function by re-entering this dialog (double-click on the displayed fitted function).  The fitted function will be displayed after the Control Characters in curly brackets (e.g., @F{PRICE = -0.145+0.152log10(x)+eps@}, where eps represents random error).  Now, delete the @F Control Character, the curly brackets, and the @ symbol after the function (e.g., PRICE = -0.145+0.152log10(x)+eps) so that the edited function will be treated as regular text instead of a fitted function.


3D Graphs Fitted Functions

Choose to fit an equation to the data or smooth the data by selecting one of the predefined functions (see below), or custom define a function to be overlaid.

  Linear Smooth	  Negative Exp/Wght

  Quadratic Smooth	  Spline Smooth

  Least Squares	  Custom Function

To custom define a function (mathematical expression), select either the Custom Function option or click on the Custom Function button to bring up the User-Defined Functions dialog.  Note:  User-defined functions which can be specified here or in graph Plot Layout dialogs are plotted over (i.e., overlaid) and not fitted to the data.  In order to fit (and plot) user-defined functions to the data, use the Nonlinear Estimation module.


Method of Categorization

Categorization is used in two classes of graphs in STATISTICA:  categorized graphs (e.g., Categorized Scatterplots) and graphs that include grouping or categorized variables (e.g., 2D Histograms, or 2D Box Plots).  You can choose from several methods of categorization which are described below.

•	Integer Mode

•	Categories

•	Boundaries

•	Codes

•	Multiple Subsets

Note:  You can change the number of significant digits that are used when labeling the category levels in the graph by specifying the desired number of digits in the No. of decimals in category description option in the Options dialog.  You can also specify alphanumeric category labels or the equivalent numeric category labels on the graph axes by using the Display text values (or dates) as axis values option in the Options dialog.


Method of Categorization - Integer Mode

When you select this method, STATISTICA will truncate each encountered value of the selected variable to an integer value, and create one category (or graph in the case of categorized graphs) for each integer.  When you select this option, the Change Variable button in this box allows you to select a different variable whose values will be categorized in the graph.  Note that if the number of integer categories exceeds 256, then STATISTICA will automatically change the method of categorization to Categories (see below) with 16 categories.

In the case of histograms (2D or 3D), the Integer categorization method offers an additional option designed to automatically identify the most informative method of categorization if the encountered distribution of values does not lend itself to a simple integer categorization (e.g., when it contains fractions or wide ranges of values).  The specific manner in which this method will categorize the respective variable depends on whether or not the Auto check box is set.  In general, if you want to force single integer categories (as described under the simple Integer Mode above; e.g., if you want to produce a histogram for 100 different integer values), deselect the Auto check box.  If you want "neat" categorization, then leave the Auto check box selected.  When you select the Auto option, STATISTICA will perform integer categorization as described above, unless one of the following conditions is met:  (1) if the range of values is greater than 20, or (2) if there are any non-integer values in the respective variable.  In that case, STATISTICA will create a "neat" categorization for the histogram.  "Neat" categories in this context means that the program will choose a step size with the only significant digit being either 1, 2, or 5 (e.g., possible step sizes could be .1, .05, 50, 200, etc.).  The minimum will be chosen (1) so that it includes the smallest value in the respective variable, and (2) so that it will produce "neat" scale values, that is, scale values with the last significant digit of either 0, 2, or 5 (e.g., 10.5, .002, .004, 1000, etc.).


Method of Categorization - Categories

Enter the desired number of categories in the edit box to the right of this option.  The program will divide the entire range of values of the selected variable (from minimum to maximum) into the requested number of equal length intervals.  Cases with values of the selected variable that belong to each interval will compose one category.  When you select this option, the Change Variable button in this box allows you to select a different variable whose values will be categorized in the graph.


Method of Categorization - Boundaries

After you select this option, click on the Specify Boundaries button and enter a list of the desired boundaries for the selected variable in the Specify Boundaries for ... dialog.  For example, if you enter 1 3 4 9, then the following five ranges (i.e., categories) of values of the selected variable will be created:  (1) x<=1, (2) 1<x<=3, (3) 3<x<=4, (4) 4<x<=9, and (5) 9<x.  As you can see from this example, the intervals do not have to be of equal width, but the boundaries do need to be of consecutive numbers (e.g., 1 3 9, not 1 3 1 9).


Method of Categorization - Codes

Choose this option if the selected variable contains codes from which you want to specify the categories.  After you select this option, click on the Specify Codes button and enter the desired codes in the Category Codes dialog.


Method of Categorization - Mark Selected Subsets

Method of Categorization - Multiple Subset

When you select this option, click on the Specify Subsets button to open the Specify Multiple Subsets dialog in which you can define the selection conditions that define specific categories.  This method allows you to custom-define the categories and enables you to use more than one variable to define the category.  See Specify Multiple Subsets for more information on this method of categorization.  Note:  When this categorization method is selected, then the current selection of the respective categorical variable is ignored, because several different variables can be used to define the categories.


Mark Selected Subsets

When you click on the Specify Multiple Subset button, the Specify Multiple Subsets dialog will open in which you can specify selection conditions that will subset (i.e., categorize) the cases in the plot.  After you define the subset conditions, STATISTICA assigns the points in the plot which satisfy the first condition a point marker which is different from that given to the points which satisfy the second condition, etc.

For example, cases which satisfy the conditions given in the categories below,

Category 1:  Include if:  v5 = 1 and v6 < 0

Category 2:  Include if:  v5 = 2 and v6 > 0

Category 3:  Include if:  v5 = 3 or v6 = 'A'

will be assigned the following point markers: category 1 will be assigned a "cross" point marker, category 2 will be assigned a "filled triangle" point marker, and category 3 will be assigned a "hollow circle" point marker.  The text of these conditions along with the appropriate point marker will become the plot legends so that you will be able to easily discern between categories in the graph.

The default selection of point markers used to identify the marked cases (subsets) of points can be adjusted in the Selected Point Default Patterns dialog.  For more information on selection conditions for subsetting cases, see Specify Multiple Subsets.

Note that overlaid Categorized Scatterplots automatically mark the points in each overlaid plot differently (i.e., each plot is represented in the same manner as multiple subsets which are based on categorization options).  Use the overlaid format of Categorized Scatterplots when you need to treat each subset as a separate plot in the graph (e.g., in order to fit a separate function to each subset).  Use the Mark Selected Subset option in the regular Scatterplots if you intend to include all subsets in one plot (e.g., in order to be able to fit one function to combined data from all subsets).


Specify Multiple Subsets

This dialog is accessible by clicking on either the Mark Selected Subsets or Specify Subsets buttons.  In either case, this dialog is used to specify the selection conditions which will subset or categorize (respectively) the cases in a data file to be assigned to different graphs (in categorized graphs), categories (e.g., histograms or box plots), or marked classes (e.g., in multiple subset scatterplots).  The subsetting conditions that you specify here will be used as legends of the respective plots.

Non-exclusive categories.  Even though you can specify non-exclusive categories, when the selection (categorization) conditions are processed, they will always assign each case only once (to the first category where it "fits").  Thus, multiple subsets or categories created via this option will always be mutually exclusive.

Example

Specify Multiple Subsets dialog:

Category

Review Vars

Open All

Save All

Print


Specify Multiple Subsets - Category

Use up to 16 categories to subset or categorize a variable.

Include, Exclude if:  When you choose Include if and the subset condition evaluates to true, the values of the selected variable for cases (observations) that meet the condition will be placed in the category (or subset) defined by that condition.  Exclude if will exclude the value from the category if the case meets the condition.  However, remember that each case will only be assigned to a category once (resulting in mutually exclusive categories); thus, if a case fits a particular selection condition (e.g., Subset 3), but it also fits a previous condition (e.g., Subset 2), then the case will not be assigned to Subset 3, but only to Subset 2.

Subset condition:  Specify the subset condition in the blank Subset line following the standard STATISTICA Case Selection Conditions.

•	Operators:  =, <>, <, >, <=, >=, NOT, AND, OR

•	Variable Names:  Specify either variable numbers (e.g., v1, v2, v3, . . . ) or variable names (e.g., GENDER, Date, time, . . .).

•	Case Number:  v0

•	Examples:  v1=0 OR v2>=0;

(v1<1 OR v9='YES' ) AND v4<>0

•	Note:  Be sure to use single quotation marks to reference the text values of variables, e.g., 'Yes'.  In order to reference date values, use the Julian value representing that date (e.g., use the Julian date 24858 instead of 1/21/1968; see Dates).

•	Note:  Since the text specified here will be used as plot legends, you can use the shortcut symbols for certain operators in order to save space when specifying the selection conditions.  Use the following shortcut symbols:

& for the operation AND

!  for the operation OR

# for the operation NOT EQUAL

~ for the operation NOT

Open, Save button:  Use this option to open (and use for subsetting) an existing standard STATISTICA Case Selection Conditions file (those which can be used to select/filter cases for all analyses in the program) as well as save the current condition in each Category.  Clicking on the Open, Save button will open the Case Selection Conditions dialog where you can edit, save or open case selection conditions (these are the same conditions which are used for processing subsets of cases throughout the program).  Case selection conditions saved in this dialog are saved under the file name extension *.sel.  These case selection conditions are then used as subsetting conditions when you click OK in the Case Selection Conditions dialog.


Specify Multiple Subsets - Review Vars

Clicking this button will open the Variables dialog from which you can view the variables in the current data file.


Specify Multiple Subsets - Open All

This button opens the Open File with Frequency Categories dialog from which you can select a file (containing all of the subsetting categories) to open into the Specify Multiple Subsets dialog.  Files opened from this dialog are standard text files with the file name extension *.txt.


Specify Multiple Subsets - Save All

This button opens the Save File with Frequency Categories dialog from which you can designate a file into which all of the subsetting conditions can be saved.  This file will be saved in text file format (*.txt extension).


Specify Multiple Subsets - Print

Clicking this button will print the contents of all currently defined subsetting conditions.  You can send the contents of this dialog either to a printer file, the printer, and/or Text/output Window depending on your selection in the Page/Output Setup dialog.


Specifying Multiple Subsets

Subset 1:  Include if:  v1<=10

Subset 2:  Include if:  v1>10 AND v2 = 'YES'

If this dialog was accessed by clicking on the Mark Selected Subsets button, then all cases (observations) which meet the condition specified in Subset 1 (i.e., cases for which the value of variable 1 is less than or equal to 10) will be assigned a specific point marker in the graph (e.g., a star).  All cases which meet the condition outlined in Subset 2 (i.e., cases for which the value of variable 1 is greater than 10 and the value of variable 2 is equal to 'YES') will be assigned a different point marker in the graph (e.g., a circle).  In this way, the points in a single graph are subsetted or categorized according to some user-defined conditions.

If this dialog was accessed by clicking on the Specify Subsets button, then the first category (i.e., small graph) will contain all cases (observations) which meet the condition specified in Subset 1 (i.e., cases for which the value of variable 1 is less than or equal to 10).  The second category (i.e., small graph) will contain all cases which meet the condition outlined in Subset 2 (i.e., cases for which the value of variable 1 is greater than 10 and the value of variable 2 is equal to 'YES').


Stats Graphs Options

In this dialog, you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.  The options can be saved either for the current session or as program defaults (see below).

STATISTICA Defaults: Stats Graphs dialog:

Optimize

Cases

Display

Save As Program Defaults

X-Y Axis Orientation

2D Graphs Coordinates

Order of Polynomial Fit

Base of Logarithm

Show Buttons on the Last Graph

Add as User-defined Graph to Menu

Display Progress Bar


Stats Graphs Options - 2D Graphs Coordinates

This option allows you to select the desired coordinate display for the 2D graph.

Normal:  Select this option in order to display the graph using Cartesian coordinates.

Polar:  Select this option in order to convert the standard (Cartesian) coordinates into a graph with polar coordinates.  Categorized graphs with polar coordinates can also be produced.

Layered Graph:  Selecting this option will reduce the main graph plotting area to leave space for Margin Graphs in the upper and right side of the display (and a miniature graph in the corner).  The Margin Graphs represent vertically and horizontally compressed images (respectively) of the main graph.  This so-called layered compression is an exploratory data analysis technique that may facilitate the identification of otherwise obscured trends and patterns in 2-dimensional data sets.


Stats Graphs Options - Display Progress Bar

This option allows you to control the display of the Progress Bar when a Stats Graph or Quick Stats Graph is being produced.  You can choose to display the Progress Bar each time a graph is produced (select ON) or only when a time-consuming graph is being produced (more than 10,000 data points) and you need to keep track of the progress (select AUTO).  In the latter case, STATISTICA will determine when to display the Progress Bar.  You can also choose OFF in order to turn off the display of the Progress Bar.


Stats Graphs Options - Optimize

This option allows you to reduce the data set in order to speed up graph production (this option is most useful when you have a very large data file).  When you select On and specify an integer value n less than the number of cases in the data file (after any Case Selection Conditions or the Cases option below has been satisfied), STATISTICA will randomly select approximately n cases from the available cases and create the plot based on these cases only.


Stats Graphs Options - Cases

Select either All or a range of cases (From, To) to be plotted with this option.

All Cases:  Deselect this check box to enable selection of a range of cases in the data file for the selected variables.

From, To:  Specify here the number of the first and last case (inclusive) to be plotted; note that the same (or more complex case selection conditions) can be specified using the Case Selection Conditions dialog.  If you use both Case Selection Conditions and the From, To option here, STATISTICA will first perform the Case Selection Conditions and then to the resulting subset of cases, apply the From, To condition (note that in this situation, the case numbers specified in the From, To edit boxes may not reference the original case numbers in the data file).


Stats Graphs Options - Display

These options affect the display of specific components of Stats Graphs.

Case Labels:  Choose either no case labels (select Off), Case Names as case labels (select Case Names), or a selected variable's values as case labels (select Var: and then specify the variable name).

Display Text Values (or Dates) as Axes Values:  Select this option in order to use text (or dates) category labels on the graph axes.  If this option is de-selected, then the equivalent numeric values (or Julian date value) will be used as category labels.

Display Fitted Functions (equations) and Display Fitted Functions as Custom Text options:  Selecting the Display Fitted Functions (equations) option enables the display of the selected fitted function(s) equation(s) in the graph.  If the Display Fitted Functions as Custom Text option is also selected, then the fitted function(s) equation(s) will be displayed in a movable legend in the graph.  If the Display Fitted Functions as Custom Text option is not selected, then the fitted function(s) equations(s) will be displayed in the title area of the graph, or if there is not enough room in the title area, then STATISTICA will place the equation(s) in a movable legend.  If a function cannot be fitted (e.g., in categorized graphs, where one category may not contain any or not enough points), then a blank line will be displayed in place of that function.

Selecting the Display Fitted Functions as Custom Text option will force the text of the fitted functions (equation) into the custom (movable) text format even if the number of equations is less than 5 and thus the functions would fit in the fixed title of the graph (see the previous section).  This option is useful when you intend to extensively edit or integrate the text of functions with other text or when the length of the functions exceed the capacity of the fixed titles.  Note that if there are more equations to be displayed than fit in the fixed title of the graph, they are always displayed as custom text.

Create Long Legends for Mult. Subset Graphs:  When this option is de-selected, STATISTICA will place the multiple subset legend as a fixed legend in the graph, thereby limiting the size of the legend to 24 characters (sometimes not long enough for multiple subset legends).  Select this option in order to place the multiple subset legend in the graph as a movable legend, thereby increasing the length of the legend.  This option applies to scatterplots, matrix plots, and icon plots, and not to multiple subsets as categorization methods because in categorized graphs the category labels must be placed next to the respective category (component) graphs.

Job Header:  Select this option to include the current Output Header as specified in the Page/Output Setup dialog as the first title for the Stats Graphs.

Graph Header:  Select this option and then enter a title in the edit box which will then be used as the second title for the Stats Graphs.

No. of decimals in category descriptions:  Specify here the number of significant digits displayed in the labels of category levels in categorized graphs, histograms, box and whisker graphs and other graphs based on interval categorization.


Stats Graphs Options - Save as Program Defaults

When this dialog is called from the Stats Graphs option in the Options pull-down menu, you can use this option to save the selections that you make in this dialog as default selections.  The saved selections will apply to all subsequent Stats Graphs created in STATISTICA.  Any selections that you make in this dialog when it is called from a Stats Graphs dialog (click on the Options button), will apply only to the current STATISTICA session.


Stats Graphs Options - X-Y Axis Orientation

Select the orientation of the variables in the 2D graph.  If you select Standard orientation, then the selected X variables will be displayed on the x-axis and the selected Y variables will be displayed on the y-axis.  Selecting Reversed orientation of the variables will display the selected X variable(s) on the y-axis and the selected Y variable(s) on the x-axis.  This option applies only to 2D Stats Graphs.


Stats Graphs Options - Order of Polynomial Fit

Select the order for the fitted polynomial (choose either a second, third, fourth or fifth order polynomial) in Stats Graphs.  This setting can be modified after the graph is selected in the appropriate Plot Layout dialog.


Stats Graphs Options - Base of Logarithm

Select either the natural log (base e) or the base 10 logarithmic function for the fitted Logarithmic function in Stats Graphs.  This setting can be modified after the graph is selected in the appropriate Plot Layout dialog.


Stats Graphs Options - Show Buttons on the Last Graph

Select this option in order to display the Next and Quit buttons on the last graph produced.  If a cascade of graphs are being produced, STATISTICA will only display as many graphs on screen as specified in the Graphs queue.  Therefore, after viewing or customizing the graphs on screen, click on the Next button to view the next series of graphs in the cascade.  In this case, pressing the Quit button will interrupt displaying the sequence of graphs.  If only one graph was produced (or the last graph in the sequence is displayed), then clicking the Next button will return you to the appropriate Stats Graphs dialog and clicking on the Quit button will discontinue the connection to that dialog (however, you can always return to that dialog by clicking on the option from the spreadsheet or Scrollsheet Graphs pull-down menu).


Stats Graphs Options - Add as User-Defined Graph

This option is available only if this dialog was called by clicking on the Options button in a Stats Graphs graph definition dialog (that is, this option is available only when you are defining a specific graph, and not when setting general options for all graphs in the Options pull-down menu option Stats Graphs ...).  When you click on this button, the New User-defined Graph dialog will open in which you can save the current Stats Graphs selections as a user-defined graph.


  Stats Graphs - 2D Histograms

The Stats 2D Graphs - Histogram option (in the Graphs pull-down menu), allows you to create several types of 2D histograms.

2D Histograms dialog:

Variables

Graph Type:  You can select the type of 2D histogram to be plotted from the Graph Type list in this dialog.  Click on the type of the histogram below, to obtain a brief description of that type of graph.

  Regular	  Double-Y

  Multiple	  Hanging Bars

Fitted Functions for Histograms

Categories

Options

Cumulative Counts

Breaks between columns

  Graphs gallery

Note:  Other options which control the arrangement and appearance of various components of this graph can be adjusted in the 2D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 2D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).

In order to produce frequency distributions of values in cases (and not variables), use the Block Stats Graphs - Histograms of Rows option from the Graphs pull-down menu (instead of transposing your data file).


  Stats Graphs 2D Histograms - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Stats Graphs 2D Histograms - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the variable(s) to be plotted.  When you select more than one variable for one of the univariate graphs types (i.e., Regular or Hanging Bars), then a sequence of graphs will be produced (one for each of the variables).  The selection that you make will then be displayed in the area of the dialog below the Variables button.


  Stats Graphs 2D Histograms - Categories

This option allows you to choose a method of categorization of the values in the histogram for the selected variable(s).  Each of the methods is discussed in the Method of Categorization topic.  For multivariate histograms (e.g., Double-Y), the categorization is based on the values of the first variable selected in the list.  For example, if you first select a grouping variable with two codes (1 and 2), the categorization would be based on those two values of the grouping variable.  If you select Integer categorization, then the program would scan this grouping variable, select all of the integer values (which in this variable are the values 1 and 2) and base the frequencies of the rest of the selected variables on those integer values.


  Stats Graphs 2D Histograms - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


  Stats Graphs 2D Histograms - Cumulative Counts

When you select this option, the consecutive columns in the resulting histogram will represent cumulative frequencies (i.e., the frequencies of all preceding categories) instead of the raw data.


  Stats Graphs 2D Histograms - Breaks Between Columns

Check this option if you would like the histogram columns to be separated from each other.  According to a common convention, histograms of continuous variables should be displayed with no breaks (the breaks signify discrete values).


  Stats Graphs - 2D Scatterplots

This Stats Graphs dialog will allow you to create several types of 2D scatterplots.  Each of the options in the 2D Scatterplots dialog is described below.

2D Scatterplots dialog:

Variables

Graph Type:  You can select the type of 2D scatterplot to be plotted from the Graph Type list in this dialog.

  Regular	  Frequency

  Multiple	  Quantile

  Double-Y	  Voronoi

Style

No of Freq.

Fit:  You can choose to fit either none (select Off) or one of several equations to the data in the scatterplot by selecting one of the predefined functions in this dialog or click on the Custom: button to custom-define a function that will be overlaid in the graph.

  Linear	  Polynomial

  Logarithmic	  Least Squares

  Exponential	  Negative Exponential

  Spline	  Custom Function

Ellipse

Confidence bands

Mark Selected Subsets

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 2D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 2D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).


  Stats Graphs 2D Scatterplots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Stats Graphs 2D Scatterplots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X and Y variables to be plotted.  When you select more than one variable for one of the univariate graphs types (i.e., Regular, Frequency, or Voronoi), then a sequence of graphs will be produced (one for each of the variables).  The selection that you make will then be displayed in the area of the dialog below the Variables button.    If you select marked subsets, then the method of categorization selected will apply to all scatterplots.


  Stats Graphs 2D Scatterplots - Style

Normal:  Select this option in order to display the graph using Cartesian coordinates.

Polar:  Select this option in order to convert the standard (Cartesian) coordinates into a graph with polar coordinates.  Categorized graphs with polar coordinates can also be produced.

Layered Graph:  Selecting this option will reduce the main graph plotting area to leave space for Margin Graphs in the upper and right side of the display (and a miniature graph in the corner).  The Margin Graphs represent vertically and horizontally compressed images (respectively) of the main graph.  This so-called layered compression is an exploratory data analysis technique that may facilitate the identification of otherwise obscured trends and patterns in 2-dimensional data sets.


  Stats Graphs 2D Scatterplots - No. of Freq.

This option (available for Frequency scatterplots) allows you to specify the number of classes of frequencies (min=2, max=16) for the plot.  For example, if you specify 3 frequencies, then STATISTICA will search the selected variables for overlapping points, categorize (i.e., divide) those frequencies into 3 ranges, and then assign a small point marker for frequencies from the first range (e.g., 1-3 points), a larger point marker for frequencies from the second range (e.g., 4-6 points), and the largest point marker for frequencies from the this range (e.g., more than 6 points).  Note that the default point markers used in the frequency scatterplot can be adjusted in the Selected Point Default Patterns dialog.


  Stats Graphs 2D Scatterplots - Ellipse

Superimpose an ellipse on the data in the scatterplot with this option.  You can choose to display one of two types of ellipses (Conf or Range, see below), or leave it off (select Off).

Confidence Area (Conf) Ellipse:  This option will produce an ellipse based on the the assumption that the two variables follow the bivariate normal distribution.  The orientation of the ellipse is determined by the sign of the linear correlation between the two variables (the major axis of the ellipse is superimposed on the regression line).  The probability that the values will fall within the area marked by the ellipse is determined by the current setting of the Coefficient (see below).

Range Ellipse:  This option will produce a fixed size ellipse such that the length of its horizontal and vertical projection onto the X- and Y- axes (respectively) is equal to the mean ± (Range * I) where the mean and range refer to the X or Y variable, and I is the current value of the coefficient field.

Coeff:  Specify the coefficient that controls the ellipses described above.


  Stats Graphs 2D Scatterplots - Confidence Bands

This option (applicable when Linear Fit or Polynomial Fit is selected, see Fitted Functions) will allow you to select (On) confidence bands around the fitted (regression) line.  You can enter the probability value (Level ) which represents the probability that the "true" fitted line (in the population) falls between the bands.  The standard error for the fitted line (which represents the predicted values, given the respective linear or polynomial fit) is computed based on the polynomial regression model (it is assumed that the data and their polynomial transformations are normally distributed, e.g., see Neter, Wasserman, & Kutner, 1985, p. 246).


  Stats Graphs 2D Scatterplots - Mark Selected Subsets

When you click on this button, the Specify Multiple Subsets dialog will open in which you can specify selection conditions that will subset (i.e., categorize) the cases in one plot.  For more information about this option, see Mark Selected Subsets.


  Stats Graphs 2D Scatterplots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


  Stats Graphs - 2D Scatterplots w/Histograms

This type of Stats Graph creates a compound graph containing a regular scatterplot of the specified two (X and Y) variables and frequency distribution histograms for the X and Y variables displayed along the X- and Y-axis of the scatterplot, respectively.  Each component graph in this compound graph can be edited by double-clicking it.  See below for more information on the options available in this dialog.

2D Scatterplots with Histograms dialog:

Variables

Scatterplot Fit:  This option applies only to the scatterplot component graph.  You can choose to fit either none (select Off) or one of several equations to the data in the scatterplot by selecting one of the predefined functions in this dialog or click on the Custom: button to custom-define a function that will be overlaid in the graph.

  Linear	  Polynomial

  Logarithmic	  Least Squares

  Exponential	  Negative Exponential

  Spline	  Custom Function

X-Axis/Y-Axis Histogram Categories

Options

  Graphs gallery

Histogram Fit:  This option applies only to each histogram component graph.  For a listing of the available distributions, see Fitted Functions for Histograms.

Breaks between columns

Note:  Other options which control the arrangement and appearance of various components of each graph in this compound graph can be adjusted in the respective 2D General Layout dialog (accessible by double-clicking on the component graph background or from the graphics Layouts pull-down menu) and the respective 2D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the component graph or from the graphics Layouts pull-down menu).


2D Scatterplots w/Histograms - Variables

  Stats Graphs 2D Scatterplots w/Histograms - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X and Y variables to be plotted in the conponent scatterplot graph.  A histogram will also be produced for each variable (the X variable histogram will be placed above the scatterplot while the Y variable histogram will be placed to the right of the scatterplot in the compound graph display).  The selection that you make will then be displayed in the area of the dialog below the Variables button.


2D Scatterplots w/Histograms - X-Axis/Y-Axis Histogram Categories

  Stats Graphs 2D Scatterplots w/Histograms - X-Axis/Y-Axis Histogram Categories

These options allow you to choose a method of categorization of the values for each of the component histograms.  Each of the methods is discussed in the Method of Categorization topic.

Histogram Size:  This option allows you to adjust the size of the component histogram with respect to the size of the graph window (e.g., 30% of the graph window size).  Note that the size of the scatterplot will adjust accordingly.


2D Scatterplots w/Histograms - Options

  Stats Graphs 2D Scatterplots w/Histograms - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


2D Scatterplots w/Histograms - Graphs Gallery

  Stats Graphs 2D Scatterplots w/Histograms - Graphs Gallery

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


2D Scatterplots w/Histograms - Breaks between Columns

  Stats Graphs 2D Scatterplots w/Histograms - Breaks Between Column

Check this option if you would like the columns in each component histogram to be separated from each other.  According to a common convention, histograms of continuous variables should be displayed with no breaks (the breaks signify discrete values).


- 2D Scatterplots w/Box Plots

  Stats Graphs - 2D Scatterplots w/Box Plots

This type of Stats Graph creates a compound graph containing a regular scatterplot of the specified two (X and Y) variables and box plots for the X and Y variables displayed along the X- and Y-axis of the Scatterplot, respectively.  Each component graph in this compound graph can be edited by double-clicking it.  See below for more information on the options available in this dialog.

2D Scatterplots with Box Plots dialog:

Variables

Scatterplot Fit:  This option applies only to the scatterplot component graph.  You can choose to fit either none (select Off) or one of several equations to the data in the scatterplot by selecting one of the predefined functions in this dialog or click on the Custom: button to custom-define a function that will be overlaid in the graph.

  Linear	  Polynomial

  Logarithmic	  Least Squares

  Exponential	  Negative Exponential

  Spline	  Custom Function

Box Plots:  These options apply only to the box plot component graphs.

Graph Type:  You can select the type of box plot to be plotted in this area of the dialog.  Click on the desired plot below, to obtain a brief description of that type of box plot.

  Box Whiskers	  Boxes

  Whiskers	  Columns

Box Plot Icon

Outliers

Middle Point, Box, and Whisker options

Options

  Graphs Gallery

Box Plot Size

Note:  Other options which control the arrangement and appearance of various components of each graph in this compound graph can be adjusted in the respective 2D General Layout dialog (accessible by double-clicking on the component graph background or from the graphics Layouts pull-down menu) and the respective 2D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the component graph or from the graphics Layouts pull-down menu).


2D Scatterplots w/Box Plots - Variables

  Stats Graphs 2D Scatterplots w/Box Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X and Y variables to be plotted in the component scatterplot graph.  A box plot will also be produced for each variable (the X variable box plot will be placed above the scatterplot while the Y variable box plot will be placed to the right of the scatterplot in the compound graph display).  The selection that you make will then be displayed in the area of the dialog below the Variables button.


2D Scatterplots w/Box Plots - Box Plot Icon

  Stats Graphs 2D Scatterplots w/Box Plots - Box Plot Icon

The Box Plot icon represents the currently selected Graph Type, and the selection of values for the Box, Middle Point, and Whiskers.  This icon will preview these three selections and the specific statistics which define the current box plot.


2D Scatterplots w/Box Plots - Outliers and Extremes

  Stats Graphs 2D Scatterplots w/Box Plots - Outliers and Extremes

Select to display none (select Off), only Outliers, only Extreme values, or both Outliers & Extremes in the component box plots.

For more information, see Outliers and Extremes.


2D Scatterplots w/Box Plots - Middle Point, Box, and Whisker

  Stats Graphs 2D Scatterplots w/Box Plots - Middle Point, Box, and Whisker

Middle Point

In the component box and whisker plots of this compound graph, first select the desired mid-point value to be represented by the selected style (point or line) in these plots.  The mid-point can be either the Mean or Median of the selected variable and this setting determines the range of choices (statistics) available for other parts of the box plot (box, whiskers, and outliers).  The options that are available for the Box and Whiskers will depend on the selection that you make here.

Box

If you selected the Median as the mid-point, then the range (box) can be represented by Percentiles or the Min-Max values of the selected variable, or a specified Constant value (when you want a fixed size box around the medians).

If you selected Mean as the mid-point, then the range (box) can be defined in terms of standard deviations (Std. Dev), standard errors (Std. Error), or Min-Max values of the selected variable, or a specified Constant value (when you want a fixed size box around the means).

You can also specify a Coefficient by which the selected range value will be multiplied (by default, the Coeff is equal to 1).  Note that except for unusual applications, the default value of the coefficient (1) should not be changed if the Box type is Min-Max.

Whisker

If you selected the Median as the mid-point, then the range (whiskers) can be represented by Percentiles or the Min-Max values of the selected variable, a specified Constant value, or Non-outlier range (see, Outliers and Extremes).

If you selected Mean as the mid-point, then the range (whiskers) can be defined in terms of standard deviations (Std. Dev), standard errors (Std. Error), or Min-Max values of the selected variable, or Non-outlier range.

If you select Non-outlier range, then STATISTICA will determine which points in the data set are outliers (see Outliers and Extremes) and then use the highest and lowest data points which are closest to the outliers (but are not outliers) as the whiskers in the plot.

You can also specify a Coefficient by which the selected range value will be multiplied (by default, the Coeff is equal to 1).  In most typical applications the coefficient should be set to 1 when the value of the whisker is Min-Max or Non-outlier range.


2D Scatterplots w/Box Plots - Options

  Stats Graphs 2D Scatterplots w/Box Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


2D Scatterplots w/Box Plots - Graphs Gallery

  Stats Graphs 2D Scatterplots w/Box Plots - Graphs Gallery

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


2D Scatterplots w/Box Plots - Box Plot Size

  Stats Graphs 2D Scatterplots w/Box Plots - Box Plot Size

This option allows you to adjust the size of the component box plot with respect to the size of the graph window (e.g., 30% of the graph window size).  Note that the size of the scatterplot will adjust accordingly.


  Stats Graphs - Probability Plots

The options in this Stats Graphs dialog will allow you to produce three types of probability plots:  Normal, Half-Normal, and Detrended.  See below for more information about these graphs.

Probability Plots dialog:

Variables

Graph Type:  You can select the type of probability plot to be plotted from the Graph Type list in this dialog.  Click on the desired plot below, to obtain a brief description of that type of graph.

  Normal

  Half-Normal

  Detrended

Options

  Graphs gallery

Notes:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 2D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 2D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).

In order to produce normal probability plots of the values in cases (and not variables), use the Block Stats Graphs - Normal Prob. Plots of Rows option from the Graphs pull-down menu (instead of transposing your data file).  Note that if more than one row is highlighted, then a multiple normal probability plot will be produced.

See also, Stats Graphs - Quantile-Quantile Plots and Stats Graphs - Probability-Probability Plots.


  Stats Graphs Probability Plots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Stats Graphs Probability Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the variable(s) to be plotted.  If you select more than one variable, then a sequence of graphs (one for each variable selected) will be produced.  The selection that you make will then be displayed in the area of the dialog below the Variables button.


  Stats Graphs Probability Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


  Stats Graphs - Quantile-Quantile Plots

The options in this Stats Graphs dialog will allow you to produce a Quantile-Quantile (or Q-Q) plot.  This plot is useful for finding the best fitting distribution within a family of distributions.  The first step therefore, is to choose which of the theoretical distributions to fit to the data.  After selecting the distribution from the list in this dialog (see below), you may or may not need to specifiy certain parameters for that distribution.

In order to assess the fit of the theoretical distribution to the observed data, the nonmissing observed values of the variable are ordered (x1 < ... < xn) and then these values (xi) are plotted against the inverse probability distribution function denoted as F**-1 [specifically, F**-1(i - rankadj/n + nadj), where F**-1 depends on the distribution, and rankadj and nadj are user-defined adjustments].  A regression line is then fitted to the data in the resulting scatterplot.  If the observed values fall on the regression line (fitting line), then it can be concluded that the observed values follow the specified distribution.  The equation of the fitting line (Y=a + bx, given in the third title of the resulting Q-Q plot) provides parameter estimates (a and b, where a is the Threshold parameter and b is the Scale parameter) for the best fitting distribution (see the respective distribution for more information on these parameters).

For the Exponential, Extreme, Normal, and Raleigh distributions, the standardized distribution function is used and no additional parameters are needed.

For the Beta, Gamma, Lognormal, and Weibull distributions, the standardized distribution with specific Shape parameters is used.  The Shape parameters can be specified in one of two ways:

(1)	The Shape parameters are user-defined (de-select the Compute parameters from option).

(2)	The Shape parameters are estimated (select the Compute parameters from option) based on user-defined Threshold and Scale parameters and using either the maximum likelihood or matching moments approximation (see below).

The Shape parameters are given in the second title of the graph.

Quantile-Quantile Plots dialog:

Variables

Distribution:  Select the desired theoretical distribution for this graph.

Parameters.  Specific parameters may be required for some of the distributions.  In those cases, the parameters will be described when the distribution is described.  See below for more information.

  Beta	  Lognormal

  Exponential	  Normal

  Extreme Value	  Rayleigh

  Gamma	  Weibull

Probability Scale

Fitting Line

Adjustments

Graphs Gallery

Options


Quantile-Quantile Plots - Variables

  Stats Graphs Quantile-Quantile Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the variable(s) to be plotted.  If you select more than one variable, then a sequence of graphs (one for each variable selected) will be produced.  The selection that you make will then be displayed in the area of the dialog below the Variables button.


Quantile-Quantile Plots - Probability Scale

  Stats Graphs Quantile-Quantile Plots - Probability Scale

This option will scale the upper-X axis nonlinearly, according to the probability values given in the respective edit field (by default, .01, .05, .1, .25, .5, .75, .9, .96, .99).  Vertical grid lines will be positioned along these percentiles.  If this option is de-selected, then no scale will be displayed on the upper-X axis.


Quantile-Quantile Plots - Fitting Line

  Stats Graphs Quantile-Quantile Plots - Fitting Line

Display linear fit:  When you select this option, the program will calculate and display the linear fitting line.  The equation of the linear fitting line (Y=a + bx, given in the third title of the resulting Q-Q plot) provides estimates for the Threshold (a, location) and the Scale (b) parameters of the specified distribution.

Custom fit:  You can custom-define a fitting line to be included in the graph (in addition to the linear fit) by setting the Custom fit check box and then entering user-defined Scale and Threshold (location) values.  This option is useful for comparing the linear fitting line (see above) with custom fitting lines based on known distributions in the family of distributions.

Note that both the linear fit and custom fit lines can be displayed in the graph (set both check boxes).  Note also that the equation for the custom-defined line can be displayed in a title in the graph using Control Characters (enter @[F2] in the Titles dialog, the number 2 denotes the fact that this is the equation for the second plot in the graph).


Quantile-Quantile Plots - Adjustments

  Stats Graphs Quantile-Quantile Plots - Adjustments

These options allow you to adjust the values which are used in the determination of the theoretical quantiles:  [(i - rankadj)/(n + nadj)] where i is the i'th ordered observation, n is the number of non-missing values and rankadj and nadj are user-defined adjustments to insure that this quantity is greater than 0 and less than 1, see below.

Ranks:  Specify here the rank adjustment (rankadj; by default, .375) which is added to the ranks of the observed values when the theoretical quantiles are computed.

N:  Specify here the sample size adjustment (nadj; by default, .25) which is added to the observed sample size when the theoretical quantiles are computed.

For more information, see Hahn and Shapiro, 1967.


Quantile-Quantile Plots - Graphs Gallery

  Stats Graphs Quantile-Quantile Plots - Graphs Gallery

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


Quantile-Quantile Plots - Options

  Stats Graphs Quantile-Quantile Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


  Beta Distribution for Quantile-Quantile Plots

The beta distribution has the probability density function:

                                 ν-1          ω-1    ν+ω-1

f(x) = Γ(ν+ω)/[Γ(ν)Γ(ω)] * [(x-θ)    * (σ+θ-x)    ]/σ

0 ≤ x ≤ 1, ν > 0, ω > 0

where

Γ	(gamma) is the Gamma function (of argument alpha)

ν, ω	are the Shape parameters

θ	is the Threshold (location) parameter

σ	is the Scale parameter

The inverted Beta distribution is related to the B(ν, ω) variate by:  IB(ν,ω)~B(ν,ω)/[1-B(ν,ω)]

The standardized Beta distribution with Shape parameters Shape1 and Shape2 will be used to find the best fitting distribution function.  The Shape parameters can be specified in one of two ways:

(1)	Enter user-defined values for Shape1 and Shape2 and de-select the Compute parameters from option.

(2)	Estimate the Shape1 and Shape2 parameters by selecting the Compute parameters from option and entering user-defined Threshold and Scale parameters.  The Shape parameters will be estimated using either the maximum likelihood or matching moments approximation (see below).

In general if the points in the Q-Q plot form a straight line, then the respective family of distributions (Beta distribution with the respective ν and ω parameters in this case) provides a good fit to the data; in that case, the intercept and slope of the fitted line can be interpreted as graphical estimates of the threshold (θ) and scale (σ) parameters, respectively.

Use Max. Likelihood:  When this option is checked, STATISTICA will use the maximum likelihood parameter method to estimate the Shape parameters of the Beta distribution (see Evans, Hastings, & Peacock, 1993, for details).  If de-selected, then the method of matching moments will be used.


  Exponential Distribution for Quantile-Quantile Plots

The exponential distribution has the probability density function:

         [-λ(x-θ)]

f(x) = λe

0 ≤ x < ∞

λ > 0, θ<x

where

θ	is the Threshold (location) parameter

λ	is the Scale parameter (an alternative parameterization is scale parameter λ=1/b)

e	is Euler's constant (2.71...)

The inverse distribution function (of probability α) is:  -1/λ*log(1-α)

The standardized exponential distribution function is used to determine the best fitting distribution.

In general if the points in the Q-Q plot form a straight line, then the respective family of distributions (Exponential distribution) provides a good fit to the data; in that case, the intercept and slope of the fitted line can be interpreted as graphical estimates of the threshold (θ) and scale (λ) parameters, respectively.


Extreme Value Distribution for Quantile-Quantile Plots

  Extreme Value (Gumbel) Distribution for Quantile-Quantile Plots

The extreme value (Type I) distribution has the probability density function:

                           -(x-a)/b

              -(x-a)/b   -e

f(x) = 1/b * e        * e

-∞ < x < ∞

b > 0

where

a	is the Threshold (location) parameter

b	is the Scale parameter

e	is Euler's constant (2.71...)

The inverse distribution function (of probability α) is:  (a-b)*loglog(1/α)

The standardized extreme value distribution function is used to determine the best fitting distribution.

In general if the points in the Q-Q plot form a straight line, then the respective family of distributions (Extreme Value distribution) provides a good fit to the data; in that case, the intercept and slope of the fitted line can be interpreted as graphical estimates of the threshold (a) and scale (b) parameters, respectively.


  Gamma Distribution for Quantile-Quantile Plots

The gamma distribution has the probability density function:

                            c−1  [-(x-θ)/b]

f(x) = {1/[bΓ(c)]}*[(x-θ)/b]   *e

0 ≤ x, c > 0

where

Γ	(gamma) is the Gamma function (of argument alpha)

c	is the Shape parameter

θ	is the Threshold (location) parameter

b	is the Scale parameter

e	is Euler's constant (2.71...)

The inverted gamma variate has probability distribution function (with quantile y) is:

            c        c+1

[exp(-λ/y)*λ  * (1-y)    ]/Γ(c)

where

λ = 1/b

The standardized Gamma distribution (Scale = 1, Threshold = 0) with Shape parameter will be used to find the best fitting distribution function.  The Shape parameter can be specified in one of two ways:

(1)	Enter a user-defined value for the Shape parameter and de-select the Compute parameters from option.

(2)	Estimate the Shape parameter by selecting the Compute parameters from option and entering a user-defined Threshold parameter.  The Shape parameter will be estimated using either the maximum likelihood or matching moments approximation (see below).

In general if the points in the Q-Q plot form a straight line, then the respective family of distributions (Gamma distribution with the Shape parameter c in this case) provides a good fit to the data; in that case, the intercept and slope of the fitted line can be interpreted as graphical estimates of the threshold (θ) and scale (b) parameters, respectively.

Use Max. Likelihood:  When this option is checked, STATISTICA will use the maximum likelihood parameter method to estimate the Shape parameter of the gamma distribution (see Evans, Hastings, & Peacock, 1993, for details).  If de-selected, then the method of matching moments will be used.


  Lognormal Distribution for Quantile-Quantile Plots

The lognormal distribution has the probability density function:

                                         2   2

                   1/2     -{log(x-θ)-μ]} /2σ

f(x) = 1/[(x-θ)σ(2)  ] * e

θ < x < ∞

μ > 0

σ > 0

where

μ	is the Scale parameter

σ	is the Shape parameter

θ	is the Threshold (location) parameter

e	is Euler's constant (2.71...)

The standardized Lognormal distribution with Shape parameter will be used to find the best fitting distribution function.  The Shape parameter can be specified in one of two ways:

(1)	Enter a user-defined value for the Shape parameter and de-select the Compute parameters from option.

(2)	Estimate the Shape parameter by selecting the Compute parameters from option and entering a user-defined Threshold parameter.  The Shape parameter will be estimated using either the maximum likelihood or matching moments approximation (see below).

In general if the points in the Q-Q plot form a straight line, then the respective family of distributions (Lognormal distribution with the Shape parameter σ in this case) provides a good fit to the data; in that case, the intercept and slope of the fitted line can be interpreted as graphical estimates of the threshold (θ) and scale (μ) parameters, respectively.

Use Max. Likelihood:  When this option is checked, STATISTICA will use the maximum likelihood parameter method to estimate the Shape parameter of the lognormal distribution (see Evans, Hastings, & Peacock, 1993, for details).  If de-selected, then the method of matching moments will be used.


  Normal Distribution for Quantile-Quantile Plots

The normal distribution function is determined by the following formula:

               1/2                        2

f(x) = 1/[(2*π)   * σ] * e^{-1/2*[(x-μ)/σ] }

-∞ < x < ∞

where

μ	is the mean

σ	is the standard deviation

e	is Euler's constant (2.718...)

π	is the constant Pi (3.14...)

The standardized normal distribution function is used to determine the best fitting distribution.

In general if the points in the Q-Q plot form a straight line, then the respective family of distributions (Normal distribution) provides a good fit to the data; in that case, the intercept and slope of the fitted line can be interpreted as graphical estimates of the mean (μ) and standard deviation (σ) parameters, respectively.


  Rayleigh Distribution for Quantile-Quantile Plots

The Rayleigh distribution has the probability density function:

                          2   2

              2    -[(x-θ) /2b ]

f(x) = (x-θ)/b  * e

θ ≤ x < ∞

b > 0

where

b	is the Scale parameter

θ	is the Threshold (location) parameter

e	is Euler's constant (2.71...)

The inverse distribution function (of probability α) is (for θ=0):  {-2b**2[log(1-α)]}**1/2

The standardized Rayleigh distribution function is used to determine the best fitting distribution.

In general if the points in the Q-Q plot form a straight line, then the respective family of distributions (Rayleigh distribution) provides a good fit to the data; in that case, the intercept and slope of the fitted line can be interpreted as graphical estimates of threshold (θ) and scale (b) parameters, respectively.


  Weibull Distribution for Quantile-Quantile Plots

The Weibull distribution has the probability density function:

                                     c

                    c-1    -[(x-θ)/b]

f(x) = c/b*[(x-θ)/b]    * e

0 ≤ x < ∞

b > 0

c > 0

θ > 0

where

b	is the Scale parameter

c	is the Shape parameter

θ	is the Threshold (location) parameter

e	is Euler's constant (2.71...)

The inverse distribution function (of probability α) is (for θ=0):  b{log[1/(1-α)]}**1/c

The standardized Weibull distribution with Shape parameter will be used to find the best fitting distribution function.  The Shape parameter can be specified in one of two ways:

(1)	Enter a user-defined value for the Shape parameter and de-select the Compute parameters from option.

(2)	Estimate the Shape parameter by selecting the Compute parameters from option and entering a user-defined Threshold parameter.  The Shape parameter will be estimated using either the maximum likelihood or matching moments approximation (see below).

In general if the points in the Q-Q plot form a straight line, then the respective family of distributions (Weibull distribution with Shape parameter c in this case) provides a good fit to the data; in that case, the intercept and slope of the fitted line can be interpreted as graphical estimates of threshold (θ) and scale (b) parameters, respectively.

Use Max. Likelihood:  When this option is checked, STATISTICA will use the maximum likelihood parameter method to estimate the Shape parameter of the Weibull distribution (see Evans, Hastings, & Peacock, 1993, for details).  If de-selected, then the method of matching moments will be used.


  Stats Graphs - Probability-Probability Plots

The Probability-Probability (or P-P) plot is useful for determining how well a specific theoretical distribution fits the observed data.  In the P-P plot, the observed cumulative distribution function (the proportion of nonmissing values ≤ x) is plotted against a theoretical cumulative distribution function in order to assess the fit of the theoretical distribution to the observed data.  If all points in this plot fall onto a diagonal line (with intercept 0 and slope 1), then you can conclude that the theoretical cumulative distribution approximates the observed distribution well.  If the data points do not all fall on the diagonal line, then you can use this plot to visually assess where the data do and do not follow the distribution (e.g., if the points form an S shape along the diagonal line, then the data may need to be transformed in order to bring them to the desired distribution pattern).

In order to create this plot, the theoretical distribution function must be completely specified.  Therefore, the parameters for the distribution must either be defined by the user or computed from the data (see the specified distribution for more information on the respective parameters).  Note that you can also use the Quantile-Quantile plot to obtain the parameter estimate(s) (for the best fitting distribution from a family of distributions) to be used here.

Probability-Probability Plots dialog:

Variables

Distribution:  Select the desired theoretical distribution for this graph.

Parameters.  The parameters for each distribution are described along with the distribution.  See below for more information.

  Beta	  Lognormal

  Exponential	  Normal

  Extreme Value	  Rayleigh

  Gamma	  Weibull

Graphs Gallery

Options


Probability-Probability Plots - Variables

  Stats Graphs Probability-Probability Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the variable(s) to be plotted.  If you select more than one variable, then a sequence of graphs (one for each variable selected) will be produced.  The selection that you make will then be displayed in the area of the dialog below the Variables button.


Probability-Probability Plots - Graphs Gallery

  Stats Graphs Probability-Probability Plots - Graphs Gallery

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


Probability-Probability Plots - Options

  Stats Graphs Probability-Probability Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


Beta Distribution for Quantile-Quantile Plots

  Beta Distribution for Probability-Probability Plots

The beta distribution has the probability density function:

                                 ν-1          ω-1    ν+ω-1

f(x) = Γ(ν+ω)/[Γ(ν)Γ(ω)] * [(x-θ)    * (σ+θ-x)    ]/σ

0 ≤ x ≤ 1

ν > 0, ω > 0

where

Γ	(gamma) is the Gamma function (of argument alpha)

ν, ω	are the Shape parameters

θ	is the Threshold (location) parameter

σ	is the Scale parameter

De-select Compute from data.  When you de-select this option in the dialog, you will need to specify the two Shape parameters ν and ω as well as the Threshold and Scale parameters θ and σ, respectively.

Select Compute from data.  When you select this option and specify the Threshold and Scale parameters (θ and σ, respectively), STATISTICA will estimate both Shape parameters ν and ω from the data.

In general, if the observed points follow the Beta distribution with the respective parameters, then they will fall onto the straight line in the P-P plot.  Note that you can use the Quantile-Quantile plot to obtain the parameter estimates (for the best fitting distribution from a family of distributions) to enter here.

Use Max. Likelihood:  When this option is checked, STATISTICA will use the maximum likelihood method to estimate the Shape parameters of the Beta distribution (see Evans, Hastings, & Peacock, 1993, for details).  If de-selected, then the method of matching moments will be used.


Exponential Distribution for Quantile-Quantile Plots

  Exponential Distribution for Probability-Probability  Plots

The exponential distribution has the probability density function:

         [-λ(x-θ)]

f(x) = λe

0 ≤ x < ∞

λ > 0, θ<x

where

θ	is the Threshold (location) parameter

λ	is the Scale parameter (an alternative parameterization is Scale parameter λ=1/b)

e	is Euler's constant (2.71...)

De-select Compute from data.  When you de-select this option, you will need to specify the Scale and Threshold parameters (λ and θ, respectively).

Select Compute from data.  When you select this option and specify the Threshold parameter θ, STATISTICA will estimate the Scale parameter λ from the data.

In general, if the observed points follow the Exponential distribution with the respective parameters, then they will fall onto the straight line in the P-P plot.  Note that you can use the Quantile-Quantile plot to obtain the parameter estimates (for the best fitting distribution from a family of distributions) to enter here.


Extreme Value Distribution for Quantile-Quantile Plots

  Extreme Value (Gumbel) Distribution for Probability-Probability Plots

The extreme value (Type I) distribution has the probability density function:

                           -(x-a)/b

              -(x-a)/b   -e

f(x) = 1/b * e        * e

-∞ < x < ∞

b > 0

where

a	is the Threshold (location) parameter

b	is the Scale parameter

e	is Euler's constant (2.71...)

De-select Compute from data.  When you de-select this option, you will need to specify the Threshold and Scale parameters (a and b, respectively).

Select Compute from data.  When you select this option  STATISTICA will estimate the Threshold parameter a and the Scale parameter b from the data.

In general, if the observed points follow the Extreme Value distribution with the respective parameters, then they will fall onto the straight line in the P-P plot.  Note that you can use the Quantile-Quantile plot to obtain the parameter estimates (for the best fitting distribution from a family of distributions) to enter here.


Gamma Distribution for Quantile-Quantile Plots

  Gamma Distribution for Probability-Probability Plots

The gamma distribution has the probability density function:

                            c−1  [-(x-θ)/b]

f(x) = {1/[Γ(c)b]}*[(x-θ)/b]   *e

0 ≤ x, c > 0, b > 0

where

Γ	(gamma) is the Gamma function (of argument alpha)

c	is the Shape parameter

θ	is the Threshold (location) parameter

b	is the Scale parameter

e	is Euler's constant (2.718...)

De-select Compute from data.  When you de-select this option, you will need to specify the Shape and Scale parameters (c and b, respectively) as well as the Threshold parameter θ.

Select Compute from data.  When you select this option and specify the Threshold parameter θ, STATISTICA will estimate both the Shape and Scale parameters (c and b, respectively) from the data.

In general, if the observed points follow the Gamma distribution with the respective parameters, then they will fall onto the straight line in the P-P plot.  Note that you can use the Quantile-Quantile plot to obtain the parameter estimates (for the best fitting distribution from a family of distributions) to enter here.

Use Max. Likelihood:  When this option is checked, STATISTICA will use the maximum likelihood method to estimate the Shape and Scale parameters of the Gamma distribution (see Evans, Hastings, & Peacock, 1993, for details).  If de-selected, then the method of matching moments will be used.


  Lognormal Distribution for Probability-Probability Plots

The lognormal distribution has the probability density function:

                                         2   2

                   1/2     -{log(x-θ)-μ]} /2σ

f(x) = 1/[(x-θ)σ(2)  ] * e

θ < x < ∞

μ > 0

σ > 0

where

μ	is the Scale parameter

σ	is the Shape parameter

θ	is the Threshold (location) parameter

e	is Euler's constant (2.71...)

De-select Compute from data.  When you de-select this option, you will need to specify the Shape and Scale parameters (σ and μ, respectively) as well as the Threshold parameter θ.

Select Compute from data.  When you select this option and specify the Threshold parameter θ, STATISTICA will estimate both the Shape and Scale parameters (σ and μ, respectively) from the data.

In general, if the observed points follow the Lognormal distribution with the respective parameters, then they will fall onto the straight line in the P-P plot.  Note that you can use the Quantile-Quantile plot to obtain the parameter estimates (for the best fitting distribution from a family of distributions) to enter here.


  Normal Distribution for Probability-Probability Plots

The normal distribution function is determined by the following formula:

                1/2                        2

f(x) = [1/{(2*π)   * σ}] * e^[-1/2*{(x-μ)/σ} ]

where

μ	is the mean

σ	is the standard deviation

e	is Euler's constant (2.71...)

π	is the constant Pi (3.14...)

De-select Compute from data.  When you de-select this option, you will need to specify both the Mu (μ) and Sigma (σ) parameters.

Select Compute from data.  When you select this option, STATISTICA will estimate Mu (μ) and Sigma (σ) from the data.

In general, if the observed points follow the Normal distribution with the respective parameters, then they will fall onto the straight line in the P-P plot.  Note that you can use the Quantile-Quantile plot to obtain the parameter estimates (for the best fitting distribution from a family of distributions) to enter here.


  Rayleigh Distribution for Probability-Probability Plots

The Rayleigh distribution has the probability density function:

                          2   2

              2    -[(x-θ) /2b ]

f(x) = (x-θ)/b  * e

θ ≤ x < ∞

b > 0

where

b	is the Scale parameter

θ	is the Threshold (location) parameter

e	is Euler's constant (2.71...)

De-select Compute from data.  When you de-select this option, you will need to specify the Scale parameter b as well as the Threshold parameter θ.

Select Compute from data.  When you select this option and specify the Threshold parameter θ, STATISTICA will estimate the Scale parameter b from the data.

In general, if the observed points follow the Rayleigh distribution with the respective parameters, then they will fall onto the straight line in the P-P plot.  Note that you can use the Quantile-Quantile plot to obtain the parameter estimates (for the best fitting distribution from a family of distributions) to enter here.


  Weibull Distribution for Probability-Probability Plots

The Weibull distribution has the probability density function:

                                     c

                    c-1    -[(x-θ)/b]

f(x) = c/b*[(x-θ)/b]    * e

0 ≤ x < ∞

b > 0

c > 0

θ > 0

where

b	is the Scale parameter

c	is the Shape parameter

θ	is the Threshold (location) parameter

e	is Euler's constant (2.71...)

De-select Compute from data.  When you de-select this option, you will need to specify the Shape and Scale parameters (b and c, respectively) as will as the Threshold parameter θ.

Select Compute from data.  When you select this option and specify the Threshold parameter θ, STATISTICA will estimate both the Shape and Scale parameters (b and c, respectively) from the data.

In general, if the observed points follow the Weibull distribution with the respective parameters, then they will fall onto the straight line in the P-P plot.  Note that you can use the Quantile-Quantile plot to obtain the parameter estimates (for the best fitting distribution from a family of distributions) to enter here.

Use Max. Likelihood:  When this option is checked, STATISTICA will use the maximum likelihood method to estimate the Shape and Scale parameters of the Weibull distribution (see Evans, Hastings, & Peacock, 1993, for details).  If de-selected, then the method of matching moments will be used.


  Stats Graphs - 2D Range Plots

Stats Graphs range plots display ranges of values or error bars related to specific data points in the form of boxes or whiskers.  Unlike the standard Box plots, the ranges or error bars are not calculated from data but defined by the raw values in the selected variables.  One range or error bar is plotted for each case.  In the simplest instance, three variables need to be selected, one representing the mid-points, one representing the upper limits and one representing the lower limits, as illustrated in the example below:

The range variables can be interpreted either as absolute values or values representing deviations from the midpoint.  Simple or multiple variables can be represented in the graph (see below).  To produce simple graphs of sequences of values (without range or error bars) for either style or multiple variables use Bar/Column Plots.

2D Range Plots dialog:

Variables

Graph Type:  You can select the type of range plot from the Graph Type list in this dialog.  Click on the desired plot below, to obtain a brief description of that type of graph.

  Whiskers	  Columns

  Boxes	  High-Low Close

Mode (range values)

Multiple Plot Layout

Display Range Borders

Fit:  You can choose to fit an equation to the mid-points in the range plot by selecting one of the predefined functions in this dialog or click on the Custom: button to custom-define a function that will be overlaid in the graph.

  Linear	  Polynomial

  Logarithmic	  Least Squares

  Exponential	  Negative Exponential

  Spline	  Custom Function

Cases

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 2D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 2D Plot Layout dialog (accessible from the right-mouse-button flying menus related to specific plots on the graph or from the graphics Layouts pull-down menu).

Editing graph data for box and whisker format graphs: see Editing Graph Data for Box and Whisker Format Graphs


2D Range Plots - Graphs Gallery Button

  Stats Graphs 2D Range Plots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


2D Range Plots - Variables

  Stats Graphs 2D Range Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the variables used to define the mid-point and range.  The selection that you make will then be displayed in the area of the dialog below the Variables button.  If more than one variable is selected for the mid-point list, then a multivariate range graph will be produced (the same number of variables must be selected in the mid-point and range lists).  The logic of the arrangement of variables in the graph is illustrated in the example below:


2D Range Plots - Mode

  Stats Graphs 2D Range Plots - Mode

You can choose to interpret the values of variables selected for the ranges in two different ways:

Absolute:  When you select this option, the actual values of the mid-point, minimum, maximum values will be plotted.  For example, for a mid-point value of 9, a minimum value of 1, and a maximum value of 12, the absolute range (as indicated by whiskers, boxes, or columns) would start at 1 and end at 12, with the mid-point at 9.

Relative to the Mid-Point:  This option will display the range (as indicated by whiskers, boxes, or columns, see above) relative to the mid-point value.  For the three points given in the example above, the range relative to the mid-point would start at 8 (the value that is 1 less than the mid-point of 9) and end at 21 (the value that is 12 more than the mid-point) with the mid-point at 9.

See also "One-sided" Ranges or Error Bars in Range Plots.


2D Range Plots - Multiple Plot Layout

  Stats Graphs 2D Range Plots - Multiple Plot Layout

When multiple variables are selected for the graph, you can choose to display the ranges in one of two styles:

  Overlaid:  Series of graphs will be displayed one on top of the other.

  Shifted :  Series of graphs will be displayed side by side.

The overlaid layout is more economical, but can be used only if the ranges of the plotted variables are so different that the whiskers or boxes will not run into each other.


2D Range Plots - Display Range Borders

  Stats Graphs 2D Range Plots - Display Range Borders

When you select this option, the upper and lower range limits will be connected with a line from point to point (i.e., one line will connect the ranges from upper limit to upper limit and another line will connect the ranges from lower limit to lower limit).


2D Range Plots - Cases

  Stats Graphs 2D Range Plots - Cases

Select either All or a range of cases (From, To) to be plotted with this option.

All Cases:  Set this check box to plot all cases in the data file for the selected variable(s).

From, To:  Specify here the number of the first and last case (inclusive) to be plotted; note that the same (or more complex case selection conditions) can be specified using the Case Selection Conditions dialog.  If you use both Case Selection Conditions and the From, To option here, STATISTICA will first perform the Case Selection Conditions and then to the resulting subset of cases, apply the From, To condition.


2D Range Plots - Options

  Stats Graphs 2D Range Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


Outliers and Extremes

Values which are "far" from the middle of the distribution are referred to as outliers and extreme values if they meet the conditions specified below.

  See also the detailed diagram shown below.

Outliers:  For Stats Graphs box plots, a data point is deemed to be an outlier if the following conditions hold:

data point value > UBV + o.c.*(UBV - LBV)

or

data point value < LBV - o.c.*(UBV - LBV)

where:

UBV	is the upper value of the box in the box plot (e.g., the mean + std.err. or the 75th percentile).

LBV	is the lower value of the box in the box plot (e.g., the mean - std.err. or the 25th percentile).

o.c.	is the outlier coefficient specified in the Outliers option of the box plot dialog (by default, the outlier coefficient is 1.5; for example, see 2D Box Plots)

Non-outlier range:  See Non-outlier range.

Extremes:  For Stats Graphs box plots, a data point is deemed to be an extreme value if the following conditions hold:

data point value > UBV + 2*o.c.*(UBV - LBV)

or

data point value < LBV - 2*o.c.*(UBV - LBV)

where:

UBV   is the upper value of the box in the box plot (e.g., the mean + std.err. or the 75th percentile).

LBV   is the lower value of the box in the box plot (e.g., the mean - std.err. or the 25th percentile).

o.c.    is the outlier coefficient specified in the Outliers option of the box plot dialog (by default, the outlier coefficient is 1.5, thus, the extreme values are those which are outside the 3 box length range from the upper and lower value of the box; for example, see 2D Box Plots)

For example, the following diagram illustrates the ranges of outliers and extremes in the "classic" box and whisker plot where the upper box value (UBV) is the 75th percentile, the lower box value (LBV) is the 25th percentile, and the outlier coefficient is equal to 1.5.


  Stats Graphs - 2D Box Plots

In Box Plots, ranges of values of a selected variable (or variables) are plotted separately for groups of cases defined by values of a categorical (grouping) variable.  The central tendency (e.g., median or mean), and range or variation statistics (e.g., quartiles, standard errors, or standard deviations) are computed for each group of cases and the selected values are presented in the style selected in the Graph Type below.  Outliers data points can also be plotted.  Range plots differ from Box plots in that for Range plots, the ranges are defined by the values of the selected variables (e.g., one variable contains the minimum range values and another variable contains the maximum range values) while for Box plots, the ranges are calculated from variable values (e.g., standard deviations, standard errors, or min-max value).

2D Box Plots dialog:

Variables

Graph Type:  You can select the type of box plot to be plotted from the Graph Type list in this dialog.  Click on the desired plot below, to obtain a brief description of that type of graph.

  Box Whiskers	  Boxes

  Whiskers	  Columns

  High-Low Close

Format:

  Regular	  Multiple

Categories

Graph Icon

Middle Point, Box, and Whisker options

Outliers

Multiple Box Layout

Fit:  You can choose to fit an equation to the mid-points in the box plots by selecting one of the predefined functions in this dialog or click on the Custom: button to custom-define a function that will be overlaid in the graph.

  Linear	  Polynomial

  Logarithmic	  Least Squares

  Exponential	  Negative Exponential

  Spline	  Custom Function

Options

Connect Middle Points

Trim distrib. extremes

  Graphs gallery

Notes:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 2D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 2D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).

In order to produce box plots representing the distribution of the values in cases (and not variables), use either the Block Stats Graphs - Box Plot/Means of Rows or Block Stats Graphs - Box Plot/Medians of Rows option from the Graphs pull-down menu (instead of transposing your data file).

Editing graph data for box and whisker format graphs: see Editing Graph Data for Box and Whisker Format Graphs


Box Plots - Connect Middle Points

  Stats Graphs Box Plots - Connect Middle Points

In box plots, you can select the desired mid-point (Mean or Median or trimmed Mean or Medial of the selected variable) to be represented by the selected style (point or line; see Middle Point).  Setting this option will connect the midpoints of the box plots with a line.  With this option, for example, a line plot (or categorized line plot) of means with "error bars" or a line plot (or categorized line plot) of medians with quantiles and min-max range bars can be produced.  Selecting the Overlaid option under Multiple Box Layout will align the respective plots from each line.  This setting of the Connect Middle Points option can also be used to create line plots of means with error bars or line plots of medians with range bars.  Also, this format is used in some statistical procedures to create predefined graphical output.


2D Box Plots - Graph Gallery Button

  Stats Graphs 2D Box Plots - Graph Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to "switch" between different types of Stats Graphs without leaving the current dialog.


2D Box Plots - Variables

  Stats Graphs 2D Box Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the grouping (category) and dependent variables for the graph.  If you select a category variable and more than one dependent variable for Regular box plots (see the Graph Type, Format icons below), then a sequence of graphs (one for each dependent variable) will be produced; if the Format is set to Multiple, then box plots for all selected variables will be combined in one graph.  The selection that you make will then be displayed in the area of the dialog below the Variables button.

Note that if you select only one dependent variable and no category variable, then a single box plot representing the distribution of the dependent variable will be produced.  If you select multiple dependent variables and no category variable, then a single graph with box plots for each selected variable will be produced.  This latter plot is useful for comparing the distribution of several variables.


2D Box Plots - Categories

  Stats Graphs 2D Box Plots - Categories

This option allows you to choose a method of categorization for the selected variable(s).  Each of the methods is discussed in the Method of Categorization topic.


2D Box Plots - Graph Icon

  Stats Graphs 2D Box Plots - Graph Icon

The graph icon in the middle of the dialog, represents the currently selected Graph Type, and the selection of values for the Box, Middle Point, and Whiskers.  The graph icon will preview these three selections and the specific statistics which define the current box plot.


2D Box Plots - Middle Point, Box, and Whisker

  Stats Graphs 2D Box Plots - Middle Point, Box, and Whisker

Middle Point

In box and whisker plots, first select the desired mid-point to be represented by the selected style (point or line) in these plots.  The mid-point can be either the Mean or Median of the selected variable and this setting determines the range of choices (statistics) available for other components of the box plot (box, whiskers, and outliers).  The options which will be available for the Box and Whiskers will depend on your selection here.

Pooled variance estimate:  This option is available when you select Mean as the Midpoint (see above).  The setting of this checkbox determines how the standard deviations and standard errors (for the means) are computed from grouped data.  When this checkbox is set, the program will compute the pooled within-group (category) variance for all groups (categories), and use this value as an estimate of σ (sigma) when computing the standard errors for the means (see, for example, Milliken and Johnson, 1984).  Specifically, the program will compute the pooled within-group (category) variance as:

       2                2                  2

s        = 1/(n-k) * [s  *(n -1) + ... + s  *(n -1)]

 pooled                1    1             k    k

In this equation, k refers to the k groups in the plot, si**2, refers to the variance in the i'th category or group, ni refers to number of valid observations in the i'th category or group, and n is the overall number of valid observations in the plot.

The standard error of the mean for the i'th group is then computed as:

s.e.(mean) = s      /square root(n )

              pooled              i

Box

If you selected the Median as the mid-point, then the range (box) can be represented by Percentiles or the Min-Max values of the selected variable, or a specified Constant value (when you want a fixed size box around the medians).

If you selected Mean as the mid-point, then the range (box) can be defined in terms of standard deviations (Std. Dev), standard errors (Std. Error), or Min-Max values of the selected variable, or a specified Constant value (when you want a fixed size box around the means).

You can also specify a Coefficient by which the selected range value will be multiplied (by default, the Coeff is equal to 1).  Note that except for unusual applications, the default value of the coefficient (1) should not be changed if the Box type is Min-Max.

Whisker

If you selected the Median as the mid-point, then the range (whiskers) can be represented by Percentiles or the Min-Max values of the selected variable, a specified Constant value, or Non-outlier range (see, Outliers and Extremes).

If you selected Mean as the mid-point, then the range (whiskers) can be defined in terms of standard deviations (Std. Dev), standard errors (Std. Error), or Min-Max values of the selected variable, or Non-outlier range.

If you select Non-outlier range, then STATISTICA will determine which points in the data set are outliers (see Outliers and Extremes) and then use the highest and lowest data points which are closest to the outliers (but are not outliers) as the whiskers in the plot.

You can also specify a Coefficient by which the selected range value will be multiplied (by default, the Coeff is equal to 1).  In most typical applications the coefficient should be set to 1 when the value of the whisker is Min-Max or Non-outlier range.


2D Box Plots - Outliers

  Stats Graphs 2D Box Plots - Outliers

Select to display none (select Off), only Outliers, only Extreme values, or both Outliers & Extremes in the box plot.

Outliers and Extremes

Values which are "far" from the middle of the distribution are referred to as outliers and extreme values if they meet the conditions specified below.

Outliers:  For Stats Graphs box plots, a data point is deemed to be an outlier if the following conditions hold:

data point value > UBV + o.c.*(UBV - LBV)

or

data point value < LBV - o.c.*(UBV - LBV)

where:

UBV	is the upper value of the box in the box plot (e.g., the mean + std.err. or the 75th percentile).

LBV	is the lower value of the box in the box plot (e.g., the mean - std.err. or the 25th percentile).

o.c.	is the outlier coefficient specified in the Outliers option of the box plot dialog (by default, the outlier coefficient is 1.5; for example, see 2D Box Plots)

Non-outlier range:  See Non-outlier range.

Extremes:  For Stats Graphs box plots, a data point is deemed to be an extreme value if the following conditions hold:

data point value > UBV + 2*o.c.*(UBV - LBV)

or

data point value < LBV - 2*o.c.*(UBV - LBV)

where:

UBV   is the upper value of the box in the box plot (e.g., the mean + std.err. or the 75th percentile).

LBV   is the lower value of the box in the box plot (e.g., the mean - std.err. or the 25th percentile).

o.c.    is the outlier coefficient specified in the Outliers option of the box plot dialog (by default, the outlier coefficient is 1.5, thus, the extreme values are those which are outside the 3 box length range from the upper and lower value of the box; for example, see 2D Box Plots)

For example, the following diagram illustrates the ranges of outliers and extremes in the "classic" box and whisker plot where the upper box value (UBV) is the 75th percentile, the lower box value (LBV) is the 25th percentile, and the outlier coefficient is equal to 1.5.


2D Box Plots - Multiple Box Layout

  Stats Graphs 2D Box Plots - Multiple Box Layout

When the Multiple box plot style is selected for the graph (see above), you can choose to display the boxes, whiskers, columns or box-whiskers in one of two styles:

  Overlaid:  Series of box plots will be displayed one on top of the other.

  Shifted:  Series of box plots will be displayed side by side.


2D Box Plots - Options

  Stats Graphs 2D Box Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


2D Box Plots - Trim Distrib. Extremes

  Stats Graphs 2D Box Plots - Trim Distrib. Extremes

This option will allow you to specify the percent of cases to be "trimmed" from the extremes (i.e., tails) of the distribution of cases for the selected variable.  For example, if you specify 10%, then for a variable with 100 cases, STATISTICA will remove the first 10 lowest value cases and the 10 highest value cases from the distribution, and only plot the 80 middle cases.  For example, if you select this option for a mean-based box plot, so-called "trimmed means" will be plotted.


  Stats Graphs - 2D Line Plots (Case Profiles)

Unlike in the regular line plots where the values of one variable are plotted as one line (individual data points are connected by a line), in case profile line plots, the values of the selected variables in a case (row) are plotted as one line (i.e., one line plot will be generated for each of the selected cases).  Case profile line plots provide a simple way to visually present the values in a case (e.g., test scores for several tests).  Note that you can use the Block Stats/Columns option from the Analysis pull-down menu to perform some statistics on the cases [e.g., sum the values or take the mean of the values for each test (variable)] and then plot those statistics along with the cases in the block for comparison purposes.

2D Line Plots - Case Profiles dialog:

Variables

Cases

Graph Type:  You can select the type of line plot to be plotted from the Graph Type list in this dialog.

  Regular	  Multiple

Points

Ignore missing data

Fit:  You can choose to fit an equation to the points in the line plots by selecting one of the predefined functions in this dialog or click on the Custom: button to custom-define a function that will be overlaid in the graph.

  Linear	  Polynomial

  Logarithmic	  Least Squares

  Exponential	  Negative Exponential

  Spline	  Custom Function

Control Limits

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 2D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 2D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).


2D Line Plots - Variables

  Stats Graphs 2D Line Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the variable(s) for the graph.  The values of the selected variables will be plotted sequentially (one line for each case).  The selections that you make here will be displayed in the area of the dialog below the Variables button.


2D Line Plots - Cases

  Stats Graphs 2D Line Plots - Cases

Select either All or a range of cases (From, To) to be plotted with this option.  If you select Regular line plots, then a sequence of graphs (one for each selected case) will be produced.  If you select Multiple line plots, then a line plot for each case specified here will be displayed in one graph.

All Cases:  Set this check box to plot all cases in the data file.

From, To:  Specify here the number of the first and last case (inclusive) to be plotted; note that the same (or more complex case selection conditions) can be specified using the Case Selection Conditions dialog.  If you use both Case Selection Conditions and the From, To option here, STATISTICA will first perform the Case Selection Conditions and then to the resulting subset of cases, apply the From, To condition.


2D Line Plots - Control Limits

  Stats Graphs 2D Line Plots - Control Limits

You can use this option to place control limits or boxes in these line plots in order to define simple and data-independent limit ranges.

Display:  Select Off to turn off this option and any existing control limits in the graph.  You can also choose between displaying the control limits as intersecting Lines [image] or as a Box [image] (the box would be drawn at the intersection of the control limit lines).

Values/Axis Selection:  You will need to specify for each of the four limits (X1, X2, Y1, and Y2), whether you want the limit displayed in the graph (set the respective check box), and also the exact coordinate of the limit on the respective axis (i.e., its Value) that will determine its position in the graph.

Note that these options allow you to set the same control limits which can also be set for any type of 2D graph using the Control Limits dialog accessible from the General Layout dialog.  To customize the control limits (change pattern, style, values), use the Control Limits dialog.


  Stats Graphs - 2D Bar/Column Plots

The options in this Stats Graph dialog will allow you to create Bar/Column Plots.  These graphs represent simple sequences of values (one case is represented by one bar/column).  If more than one variable is selected, then either multivariate clusters of bars/columns are plotted (one cluster per case) or each variable is represented in a separate graph, depending on the Graph Type selected (see Regular vs. Multiple below).  A multiple column plot is illustrated below.

To produce column, bar, or box plots with error (or range) bars, use 2D Range Plots or 2D Box Plots.

2D Bar/Column Plots dialog:

Variables

Graph Type:  You can select the type of bar/column plot to be plotted from the Graph Type list in this dialog.

  Regular	  Multiple

Cases

Orientation

Options

Control Limits


2D Bar/Column - Control Limits

  Stats Graphs 2D Bar/Column Plots - Control Limits

You can use this option to place control limits or boxes in these bar/column plots in order to define simple and data-independent limit ranges.

Display:  Select Off to turn off this option and any existing control limits in the graph.  You can also choose between displaying the control limits as intersecting Lines [image] or as a Box [image] (the box would be drawn at the intersection of the control limit lines).

Values/Axis Selection:  You will need to specify for each of the four limits (X1, X2, Y1, and Y2), whether you want the limit displayed in the graph (set the respective check box), and also the exact coordinate of the limit on the respective axis (i.e., its Value) that will determine its position in the graph.

Note that these options allow you to set the same control limits which can also be set for any type of 2D graph using the Control Limits dialog accessible from the General Layout dialog.  To customize the control limits (change pattern, style, values), use the Control Limits dialog.


2D Bar/Column Plots - Cases

  Stats Graphs 2D Bar/Column Plots - Cases

Select either All or a range of cases (From, To) to be plotted with this option.  If you select Regular bar/column plots, then a sequence of graphs (one for each selected case) will be produced.  If you select Multiple bar/column plots, then a bar/column plot for each case specified here will be displayed in one graph.

All Cases:  Set this check box to plot all cases in the data file.

From, To:  Specify here the number of the first and last case (inclusive) to be plotted; note that the same (or more complex case selection conditions) can be specified using the Case Selection Conditions dialog.  If you use both Case Selection Conditions and the From, To option here, STATISTICA will first perform the Case Selection Conditions and then to the resulting subset of cases, apply the From, To condition.


2D Bar/Column Plots - Orientation

  Stats Graphs 2D Bar/Column Plots - Orientation

Select the orientation of the variables in the bar/column graph.  If you select the Vertical [image] orientation, then the values of the selected variable(s) will be plotted as columns (against the y-axis).  If you select the Horizontal [image] orientation , then the values will be plotted as horizontal bars (against the x-axis).

Note that this option corresponds to the global option X-Y Axis Orientation (Standard vs. Reversed) accessible in the Stats Graphs: Options dialog.


2D Bar/Column Plots - Variables

  Stats Graphs 2D Bar/Column - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the variable(s) for the graph.  The values of each of the selected variables will be plotted sequentially (one bar/column for each case).  If more than one variable is selected, then either multivariate clusters of bars/columns are plotted (one cluster per case) or each variable is represented in a separate graph, depending on the Graph Type selected (see Regular vs. Multiple below).  The selections that you make here will be displayed in the area of the dialog below the Variables button.


2D Bar/Column Plots - Options

  Stats Graphs 2D Bar/Column Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


- 2D Line Plots (Variables)

  Stats Graphs - 2D Line Plots (Variables)

In line plots, individual data points are connected by a line.  Line plots provide a simple way to visually present a sequence of many values (e.g., stock market quotes over a number of days); X-Y Trace-type line plots (see below) can be used to display a trace (instead of a sequence).  Line graphs can also be used to plot continuous functions, theoretical distributions, etc.  In the 2D Line Plots dialog, you can select the type of line plot as well as other options.  (Note that 2D Line Plots (Case Profiles) can be used to visualize sequences of values within cases, so that one case is represented by one line.)

2D Line Plots dialog:

Variables

Graph Type:  You can select the type of line plot to be plotted from the Graph Type list in this dialog.  Click on the desired plot below, to obtain a brief description of that type of graph.

  Regular	  XY Trace

  Multiple	  Aggregated

  Double-Y

Style

Fit:  You can choose to fit an equation to the points in the line plots by selecting one of the predefined functions in this dialog or click on the Custom: button to custom-define a function that will be overlaid in the graph.

  Linear	  Polynomial

  Logarithmic	  Least Squares

  Exponential	  Negative Exponential

  Spline	  Custom Function

Points

Ignore missing data

Cases

Aggregated Data

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 2D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 2D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).


2D Line Plots - Graphs Gallery Button

    Stats Graphs 2D Line Plots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


2D Line Plots - Variables

  Stats Graphs 2D Line Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the variable(s) for the graph.  If you select more than one variable for Regular or Trace line plots, then a sequence of graphs (one for each selected variable) will be produced.  The selections that you make will then be displayed in the area of the dialog below the Variables button.


2D Line Plots - Style

  Stats Graphs 2D Line Plots - Style

Normal:  Select this option in order to display the graph using Cartesian coordinates.

Polar:  Select this option in order to convert the standard (Cartesian) coordinates into a graph with polar coordinates.  Categorized graphs with polar coordinates can also be produced.

Layered Graph:  Selecting this option will reduce the main graph plotting area to leave space for Margin Graphs in the upper and right side of the display (and a miniature graph in the corner).  The Margin Graphs represent vertically and horizontally compressed images (respectively) of the main graph.  This so-called layered compression is an exploratory data analysis technique that may facilitate the identification of otherwise obscured trends and patterns in 2-dimensional data sets.


2D Line Plots - Points

    Stats Graphs 2D Line Plots - Points

You can choose to display the line plot with (On) or without (Off) point markers.  If you select Auto, then STATISTICA will automatically determine the display of point markers depending on the number of observations and the closeness of the points (usually, if n>100, then the points are not displayed).


2D Line Plots - Ignore Missing Data

    Stats Graphs 2D Line Plots - Ignore Missing Data

When missing data are present, a discontinuous line will be drawn for that plot.  You can elect to ignore missing data by selecting this option, and a continuous line will be drawn for that plot.


2D Line Plots - Cases

  Stats Graphs 2D Line Plots - Cases

Select either All or a range of cases (From, To) to be plotted with this option.

All Cases:  Set this check box to plot all cases in the data file for the selected variable(s).

From, To:  Specify here the number of the first and last case (inclusive) to be plotted; note that the same (or more complex case selection conditions) can be specified using the Case Selection Conditions dialog.  If you use both Case Selection Conditions and the From, To option here, STATISTICA will first perform the Case Selection Conditions and then to the resulting subset of cases, apply the From, To condition.


2D Line Plots - Aggregrated Data

  Stats Graphs 2D Line Plots - Aggregrated Data

This option (available when Aggregated line plots have been selected) is useful when there are very many differentiated observations in the sequence of points, in order to uncover or expose the overall pattern of the data sequence.  In this case, the means of consecutive sets of n observations are plotted instead of the raw data.

Aggr. Index:  Specify here the number of consecutive observations from which the mean will be calculated.

Value Range Bars:  When you select this option, whiskers representing the range of the n values from which the means are calculated, will be placed in the plot at the respective points.

Note:  A selection of data smoothing and filtering procedures integrated with line plots are available in the Time Series module.


2D Line Plots - Options

    Stats Graphs 2D Line Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


  Stats Graphs - Sequential/Stacked Plots

These types of graphs are used to present sequences of values of selected variables.  The stacked feature of this type of graph is specifically designed to represent the broad category of data sets in which consecutive variables represent parts ("portions") of one whole.  See below for more information about these graphs.

Sequential/Stacked Plots dialog:

Variables

Graph Type:  You can select the type of sequential/stacked plot to be plotted from the Graph Type list in this dialog.  Click on the desired plot below, to obtain a brief description of that type of graph.

  Line	  Step Area

  Area	  Mixed Step

  Mixed Line	  Column

  Step

Style

Cases

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 2D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 2D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).


Sequential/Stacked Plots - Graphs Gallery Button

  Stats Graphs Sequential/Stacked Plots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


Sequential/Stacked Plots - Variables

  Stats Graphs Sequential/Stacked Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the variable(s) for the graph either one or two lists of variables can be selected, depending on the graph type.  The selections that you make will then be displayed in the area of the dialog below the Variables button.


Sequential/Stacked Plots - Style

  Stats Graphs Sequential/Stacked Plots - Style

Normal:  Select this option in order to display the graph using Cartesian coordinates.

Polar:  Select this option in order to convert the standard (Cartesian) coordinates into a graph with polar coordinates.  Categorized graphs with polar coordinates can also be produced.

Layered Graph:  Selecting this option will reduce the main graph plotting area to leave space for Margin Graphs in the upper and right side of the display (and a miniature graph in the corner).  The Margin Graphs represent vertically and horizontally compressed images (respectively) of the main graph.  This so-called layered compression is an exploratory data analysis technique that may facilitate the identification of otherwise obscured trends and patterns in 2-dimensional data sets.


Sequential/Stacked Plots - Cases

  Stats Graphs Sequential/Stacked Plots - Cases

Select either All or a range of cases (From, To) to be plotted with this option.

All Cases:  Set this check box to plot all cases in the data file for the selected variable(s).

From, To:  Specify here the number of the first and last case (inclusive) to be plotted; note that the same (or more complex case selection conditions) can be specified using the Case Selection Conditions dialog.  If you use both Case Selection Conditions and the From, To option here, STATISTICA will first perform the Case Selection Conditions and then to the resulting subset of cases, apply the From, To condition.


Sequential/Stacked Plots - Options

  Stats Graphs Sequential/Stacked Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.  (Note, the Orientation option in the Options dialog does not apply to Area and Step Area graphs.)


  Stats Graphs - Pie Charts

The pie chart is one of the most common graph formats used for representing proportions or values of variables.  Depending on the selected type of graph (see below), the pie chart will display either raw values or counts (i.e., frequencies) of specific values (such as those which can be displayed in Histograms).

Pie Charts dialog:

Variables

Graph Type:  You can select the type of pie chart to be plotted from the Graph Type list in this dialog.  Click on the desired plot below, to obtain a brief description of that type of graph.

  Counts

  Values

  Multi-pattern Bar

Categories

Cases

Pie Legend

Style

Shape

Exploded Slice

Pie Labels - Values

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of the pie chart can be adjusted in the Pie Options dialog (accessible by double-clicking on the pie or by clicking on the Pie Options button in the 2D Plot Layout dialog), 2D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 2D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).


  Stats Graphs Pie Charts - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Stats Graphs Pie Charts - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the variable(s) for the graph.  If you select more than one variable for the pie charts, then a cascade of graphs (one for each selected variable) will be produced.  The selection that you make will then be displayed in the area of the dialog below the Variables button.


  Stats Graphs Pie Charts - Categories

This option applies when the Counts type of pie chart is selected (see above), which displays frequency data, and it allows you to choose a method of categorization for the selected variable(s).  Each of the methods is discussed in the Method of Categorization topic.


  Stats Graphs Pie Charts - Cases

Select either All or a range of cases (From, To) to be plotted with this option.

All Cases:  Set this check box to plot all cases in the data file for the selected variable(s).

From, To:  Specify here the number of the first and last case (inclusive) to be plotted; note that the same (or more complex case selection conditions) can be specified using the Case Selection Conditions dialog.  If you use both Case Selection Conditions and the From, To option here, STATISTICA will first perform the Case Selection Conditions and then to the resulting subset of cases, apply the From, To condition.


  Stats Graphs Pie Charts - Pie Legend

Select one of six formats for pie legends (Off, Percent, Values, Text labels, Text & percent, Text & values) to be placed in the graph.  If you select Counts as the graph type, then selecting the Text labels option will use the category descriptions in the pie legend.  Otherwise (for Values pie charts and Multi-pattern bar charts), the Text labels used will depend on the Pie labels (values) selected (e.g., if you select Case names as pie labels, then the Text labels will display the actual case names instead of Case1, Case2, etc.; if you select a variable in the Pie labels option and then choose Text labels, then STATISTICA will use the text values of the selected variable in the pie legend).


  Stats Graphs Pie Charts - Style

You can change the appearance of the pie by choosing either the 2-dimensional (2D) or 3-dimensional (3D) display in this option; see also the Pie Options dialog.


  Stats Graphs Pie Charts - Shape

The pie shape can be either circular (select Circle) or elliptical (select Ellipse).  However, choosing the Ellipse option may cause the slices to be disproportionate in size (i.e., the slices that follow radii close to the vertical axis of the screen or paper will look relatively larger than their real size as compared to the "horizontal" slices which will be "squeezed" in perspective and will appear smaller); see also the Pie Options dialog.


  Stats Graphs Pie Charts - Exploded Slice

Select this option to "explode" a specified number of slices of the pie; see also the Pie Options dialog for .


  Stats Graphs Pie Charts - Pie Labels-Values

You can choose to label the pie with Case Names (select any of the Text options in the Pie legend option) or the values (text or numeric depending on the setting in the Pie legend option) of a specified variable.  If you do not want any pie labels, select Off.


  Stats Graphs Pie Charts - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


  Stats Graphs - 2D Custom Function Plots

This type of Stats Graphs produces a graph based not on values of variables in a data file but on a user-defined formula (custom function), for example: y = x^2 + x/2.

2D Custom Function Plots dialog:

Custom Function button:  Click on this button to open the User-defined Functions dialog in which you can enter the formula to be plotted.

X Min, X Max:  Specify here the range (i.e., minimum and maximum values) of the X variable for the custom function.

Options button:  Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.

  Graphs Gallery button:  Click on this button ( [image]) in order to bring up the STATISTICA Graphs gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 2D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 2D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).


  Stats 3D Sequential Graphs - Raw Data Plots

These options allow you to plot sequences of raw data from selected variables in a 3-dimensional display.  The selected variables are represented on the Y-axis, the consecutive cases on the X-axis, and the values are plotted against the Z-axis as shown in the following example:

3D Raw Data Plots dialog:

Variables

Graph Type:  You can select the type of raw data chart to be plotted from the Graph Type list in this dialog.  Click on the desired plot below, to obtain a brief description of that type of graph.

  Box Plot	  Spikes

  Block Plot	  Contour/Discrete

  Ribbons	  Surface Plot

  Lines	  Contour Plot

Cases

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 3D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 3D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).


  Stats 3D Sequential Graphs Raw Data Plots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Stats 3D Sequential Graphs Raw Data Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the variable(s) for the graph.  The selection that you make will then be displayed in the area of dialog below the Variables button.


  Stats 3D Sequential Graphs Raw Data Plots - Cases

Select either All or a range of cases (From, To) to be plotted with this option.

All Cases:  Set this check box to plot all cases in the data file for the selected variable(s).

From, To:  Specify here the number of the first and last case (inclusive) to be plotted; note that the same (or more complex case selection conditions) can be specified using the Case Selection Conditions dialog.  If you use both Case Selection Conditions and the From, To option here, STATISTICA will first perform the Case Selection Conditions and then to the resulting subset of cases, apply the From, To condition.


  Stats 3D Sequential Graphs Raw Data Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


  Stats 3D Sequential Graphs - Bivariate Histograms

This option creates a 3D bivariate distribution histogram of the selected variables.  Three-dimensional histograms are used to visualize crosstabulations of values in two variables.  They can be considered a conjunction of two simple (i.e., univariate) histograms, combined such that the frequencies of co-occurrences of values on the two analyzed variables can be examined.  You can selectively highlight individual plots in the graph by pressing the left-mouse-button anywhere on the selected plot.  This "x-raying" option allows you to temporarily highlight complete series of data even if the respective plots are almost entirely covered by other plots.

3D Bivariate Histograms dialog:

Variables

Categories (for X and Y Variables)

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the General Layout and Plot Layout: 3D Histograms dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu).


  Stats 3D Sequential Graphs Bivariate Histograms - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Stats 3D Sequential Graphs Bivariate Histograms - Variables

When you click on this button, the standard two variable selection dialog will open in which you can select the X and Y variables for the graph.  The selection that you make will then be displayed in the area of the dialog below the Variables button.  Variables do not need to be selected if the Multiple Subset categories are analyzed (instead of variables).


  Stats 3D Sequential Graphs Bivariate Histograms - Categories (for X and Y Variables)

These options allow you to choose the method of categorization for each of the selected variables.  Each of the methods is discussed in the Method of Categorization topic.


  Stats 3D Sequential Graphs Bivariate Histograms - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display.


  Stats 3D Sequential Graphs - Range Plots

Similar to Stats Graphs 2D Range Plots, 3D range plots display ranges of values or error bars related to specific data points.  The ranges or error bars are not calculated from data but defined by the raw values in the selected variables.  One range or error bar is plotted for each case.  The range variables can be interpreted either as absolute values or values representing deviations from the midpoint (see below).  Simple or multiple variables can be represented in the graph (see below).

3D Range Plots dialog:

Variables

Graph Type:  Select one type of 3D range plots the Graph Type list in this dialog.  Click on the desired plot type below, to obtain a brief description of that type of graph.

  Point	  Double Ribbon Ranges

  Border-style Ranges	  Flying Boxes

  Error Bar	  Flying Blocks

Mode (range values)

Cases

Style

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 3D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 3D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).


  Stats 3D Sequential Graphs Range Plots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Stats 3D Sequential Graphs Range Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the variables used to define the mid-point and range (i.e., the lower limit and upper limit values).  The selection that you make will then be displayed in the area of the dialog below the Variables button.  If more than one variable is selected for the mid-point list, then a multivariate range graph will be produced (the same number of variables must be selected in the mid-point and range lists).


  Stats 3D Sequential Graphs Range Plots - Mode

You can choose to interpret the values of variables selected for the ranges in two different ways:

Absolute:  When you select this option, the actual values of the mid-point, minimum, maximum values will be plotted.  For example, for a mid-point value of 9, a minimum value of 1, and a maximum value of 12, the absolute range (as indicated by whiskers, boxes, or columns, see above) would start at 1 and end at 12, with the mid-point at 9.

Relative to the Mid-Point:  This option will display the range (as indicated by whiskers, boxes, or columns, see above) relative to the mid-point value.  For the three points given in the above example, the range relative to the mid-point would start at 8 (the value that is 1 less than the mid-point of 9) and end at 21 (the value that is 12 more than the mid-point) with the mid-point at 9.

See also "One-sided" Ranges or Error Bars in Range Plots.


  Stats 3D Sequential Graphs Range Plots - Cases

Select either All or a range of cases (From, To) to be plotted with this option.

All Cases:  Set this check box to plot all cases in the data file for the selected variable(s).

From, To:  Specify here the number of the first and last case (inclusive) to be plotted; note that the same (or more complex case selection conditions) can be specified using the Case Selection Conditions dialog.  If you use both Case Selection Conditions and the From, To option here, STATISTICA will first perform the Case Selection Conditions and then to the resulting subset of cases, apply the From, To condition.


  Stats 3D Sequential Graphs Range Plots - Style

This option (applicable only to Point Ranges, Border-style Ranges, and Error Bar-style Ranges) allows you to customize the style of the 3D range plot.

  Spikes:  When you select this option, the point ranges or error bars will be connected to the base of the graph with lines.


  Stats 3D Sequential Graphs Range Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the appearance of the graph.


  Stats 3D Sequential Graphs - Box Plots

Similar to Stats Graphs 2D Box Plots, in 3D box plots, the ranges of values of a selected variable are plotted separately for groups of cases defined by values of a categorical (grouping) variable.  The central tendency (e.g., median or mean), and range or variation statistics (e.g., quartiles, standard errors, or standard deviations) are computed for each group of cases and the selected values are presented in the style selected in the Graph Type below.  3D Range plots differ from 3D Box plots in that for Range plots, the ranges are the values of the selected variables (e.g., one variable contains the minimum range values and another variable contains the maximum range values) while the ranges are calculated from variable values (e.g., standard deviations, standard errors, or min-max value) for Box plots.

3D Box Plots dialog

Variables

Graph Type:  You can select the type of 3D box plot to be plotted from the Graph Type list in this dialog.  Click on the desired plot below, to obtain a brief description of that type of graph.

  Border-style Ranges	  Double Ribbon Ranges

  Error Bar	  Flying Boxes

  Point	  Flying Blocks

Categories

Graph Icon

Middle Point and Whisker options

Style

Options

Trim distrib. extremes

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 3D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 3D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).


  Stats 3D Sequential Graphs Box Plots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Stats 3D Sequential Graphs Box Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the grouping and dependent variables for the graph.  The selection that you make will then be displayed in the area of the dialog below the Variables button.


  Stats 3D Sequential Graphs Box Plots - Categories

This option allows you to choose a method of categorization for the selected variable(s).  Each of the methods is discussed in the Method of Categorization topic.


  Stats 3D Sequential Graphs Box Plots - Graph Icon

The graph icon in the middle of the dialog, represents the currently selected Graph Type, and the selection of values for the Middle Point and Whiskers.  The graph icon will preview these three selections.


  Stats 3D Sequential Graphs Box Plots - Middle Point and Whisker Options

In box and whisker plots, first select the desired mid-point to be represented by the selected style (point or line) in these plots (the mid-point can be either the Mean or Median of the selected variable).  Then, depending on the selection that you make here, the following options will be available for the Whiskers.

Whisker:  If you selected the Median as the mid-point, then the range (whiskers) can be represented by Percentiles or the Min-Max values of the selected variable, a specified Constant value, or Non-outlier range.

If you selected Mean as the mid-point, then the range (whiskers) can be represented by the Std. Dev., Std. Error, or Min-Max values of the selected variable, Outlier range, or a specified Constant value (when you want a fixed size box around the median).

Outliers and extreme values are not displayed in the 3D box plot, however, if you select Non-outlier range, then the range will be computed as in 2D Box Plots using the outlier coefficient of 1.5.

You can also specify a Coefficient by which the selected range value will be multiplied (by default, the Coeff is equal to 1).  In most typical applications the coefficient should be set to 1 when the value of the whisker is Min-Max or Non-outlier range.


  Stats 3D Sequential Graphs Box Plots - Style

This option allows you to customize the style of the 3D box plot.

Spikes:  When you select this option, the point ranges or error bars will be connected to the base of the graph with lines.


  Stats 3D Sequential Graphs Box Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the appearance of the graph.


  Stats 3D Sequential Graphs Box Plots - Trim Distrib. Extremes

This option will allow you to specify the percent of cases to be "trimmed" from the extremes (i.e., tails) of the distribution of cases for the selected variable.  For example, if you specify 10%, then for a variable with 100 cases, STATISTICA will remove the 10 lowest value cases and the 10 highest value cases from the distribution, and only plot the 80 cases inbetween.  For example, if you select this option for a mean-based box plot, so-called "trimmed means" will be plotted.


  Stats 3D XYZ Graphs - Scatterplots

Three-dimensional scatterplots (also called XYZ scatterplots) represent the most elementary and probably one of the most commonly used forms of 3D data plots.  Its most typical application is to visualize relations between continuous variables.  You can select one of several types of 3D scatterplots in this dialog.

3D Scatterplots dialog:

Variables

Graph Type:  You can select the type of 3D scatterplot to be plotted from the Graph Type list in this dialog.  Click on the desired plot below, to obtain a brief description of that type of graph.

  Scatterplot	  Spectral Plot

  Space Plot	  Deviation Plot

Deviation Level

Number of planes

Mark Selected Subsets

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 3D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 3D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).


  Stats 3D XYZ Graphs Scatterplots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Stats 3D XYZ Graphs Scatterplots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X-, Y-, and one or more Z-axis variables for the graph.  The selection that you make will then be displayed in the area of the dialog below the Variables button.


  Stats 3D XYZ Graphs Scatterplots - Deviation Level

This option (applicable to Deviation and Space plots) allows you to specify a value on the z-axis that determines the level from which deviations are derived; or in the case of Space Plots, this value determines the Z-level of the X-Y plane.


  Stats 3D XYZ Graphs Scatterplots - Number of Planes

This option (applicable to Spectral plots) allows you to specify the number of spectral planes into which the data are segmented (compressed).


  Stats 3D XYZ Graphs Scatterplots - Mark Selected Subsets

When you click on this button, the Specify Multiple Subsets dialog will open in which you can specify selection conditions that will subset (i.e., categorize) the cases in one plot.  For more information about this option, see Mark Selected Subsets.


  Stats 3D XYZ Graphs Scatterplots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the appearance of the graph.


  Stats 3D XYZ Graphs - Surface Plots

Instead of plotting raw data, this type of Stats Graph displays a surface representing a smoothed image of the data following one of the available transformation/fitting procedures (see below).  Options to customize the appearance of the wirenet, shading, color palette, etc. are available in the 3D Graphs/More Options dialog, accessible by double-clicking on the surface (on the graph) or by pressing the More Options button in the 3D General Layout dialog.

3D Surface Plots dialog:

Variables

Fit:  You can choose to fit one of several equations to the data or use one of the data smoothing procedures in the 3D surface plot by selecting one of the predefined functions in this dialog or click on the Custom: button to custom-define a function that will be overlaid in the graph.

  Linear Smooth	  Negative Exp/Wght

  Quadratic Smooth	  Spline Smooth

  Least Squares	  Custom Function

To custom define a function (mathematical expression), select either the Custom Function option or click on the Custom Function button to bring up the User-Defined Functions dialog.  Note:  User-defined functions which can be specified here or in graph Plot Layout dialogs are plotted over (i.e., overlaid) and not fitted to the data.  In order to fit (and plot) user-defined functions to the data, use the Nonlinear Estimation module.

Options

Show Raw Data Points

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 3D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 3D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).


  Stats 3D XYZ Graphs Surface Plots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Stats 3D XYZ Graphs Surface Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X-, Y-, and Z-axis variables for the graph.  The selection that you make will then be displayed in the area of the dialog below the Variables button.


  Stats 3D XYZ Graphs Surface Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the appearance of the graph.


  Stats 3D XYZ Graphs Surface Plots - Show Raw Data Points

Select this option if you want the raw data points to be overlaid on the graph surface.  (If the points are not located directly on the surface, then they will be "connected" to the surface by "spikes.")


Stats 3D XYZ - Contour Plots

  Stats 3D XYZ Graphs - Contour Plots

Instead of plotting raw data, this type of Stats Graph will display a contour representing a smoothed image of the data following one of the available transformation/fitting procedures (see below).  Options to customize the appearance of the wirenet, shading, color palette, distance from the surface to the contour, etc., are available in the 3D Graphs/More Options dialog, accessible by double-clicking on the surface (on the graph) or by pressing the More Options button in the 3D General Layout dialog.

3D Contour Plots dialog:

Variables

Fit:  You can choose to fit one of several equations to the data or use one of the data smoothing procedures in the 3D contour plot by selecting one of the predefined functions in this dialog or click on the Custom: button to custom-define a function that will be overlaid in the graph.

  Linear Smooth	  Negative Exp/Wght

  Quadratic Smooth	  Spline Smooth

  Least Squares	  Custom Function

To custom define a function (mathematical expression), select either the Custom Function option or click on the Custom Function button to bring up the User-Defined Functions dialog.  Note:  User-defined functions which can be specified here or in graph Plot Layout dialogs are plotted over (i.e., overlaid) and not fitted to the data.  In order to fit (and plot) user-defined functions to the data, use the Nonlinear Estimation module.

Contour Style

Show Raw Data Points

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 3D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 3D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).


Stats 3D XYZ Contour Plots - Graphs Gallery button

  Stats 3D XYZ Graphs Contour Plots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


Stats 3D XYZ Contour Plots - Variables

  Stats 3D XYZ Graphs Contour Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X-, Y-, and Z-axis variables for the graph.  The selection that you make will then be displayed in the area of the dialog below the Variables button.


Stats 3D XYZ Contour Plots - Contour Style

  Stats 3D XYZ Graphs Contour Plots - Contour Style

You can choose to display the contour as a series of Lines or Areas.  (See also, Calculating Contour Levels and Distance.)


Stats 3D XYZ Contour Plots - Show Raw Data Points

  Stats 3D XYZ Graphs Contour Plots - Show Raw Data Points

Select this option if you want the raw data points to be overlaid on the graph contour.


Stats 3D XYZ Contour Plots - Options

  Stats 3D XYZ Graphs Contour Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the appearance of the graph.


Stats 3D XYZ - Trace Plots

  Stats 3D XYZ Graphs - Trace Plots

Each data point in Stats Graphs trace plots is represented by its location in 3D space as determined by the values of the variables selected as X, Y, and Z (and interpreted as the X-, Y-, and Z-axis coordinates, respectively).  The individual data points are connected sequentially with a line to form a "trace" of a sequential process (e.g., movement, change of a phenomenon over time, etc.).  See also, 2D XY Trace Plots.

3D Trace Plots dialog:

Variables

Cases

Mark Selected Subsets

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 3D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 3D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).


Stats 3D XYZ Trace Plots - Graphs Gallery

  Stats 3D XYZ Graphs Trace Plots - Graphs Gallery

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


Stats 3D XYZ Trace Plots - Variables

  Stats 3D XYZ Graphs Trace Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X-, Y-, and Z-axis variables for the graph.  The selection that you make will then be displayed in the area of the dialog below the Variables button.  More than one Z-axis variable can be selected to produce a multivariate trace plot.


Stats 3D XYZ Trace Plots - Cases

  Stats 3D XYZ Graphs Trace Plots - Cases

Select either All or a range of cases (From, To) to be plotted with this option.

All Cases:  Set this check box to plot all cases in the data file for the selected variable(s).

From, To:  Specify here the number of the first and last case (inclusive) to be plotted; note that the same (or more complex case selection conditions) can be specified using the Case Selection Conditions dialog.  If you use both Case Selection Conditions and the From, To option here, STATISTICA will first perform the Case Selection Conditions and then to the resulting subset of cases, apply the From, To condition.


Stats 3D XYZ Trace Plots - Mark Selected Subsets

  Stats 3D XYZ Graphs Trace Plots - Mark Selected Subsets

When you click on this button, the Specify Multiple Subsets dialog will open in which you can specify selection conditions that will subset (i.e., categorize) the cases in one plot.  For more information about this option, see Mark Selected Subsets.


Stats 3D XYZ Trace Plots - Options

  Stats 3D XYZ Graphs Trace Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the appearance of the graph.


  Stats Graphs - 3D Categorized Plots

This type of Stats Graph allows you to categorize 3D scatterplots and surface plots by the specified categories of a selected variable.  One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).

3D Categorized Plots dialog:

Variables

Graph Type:  You can select the type of plot from the Graph Type list in this dialog.  Click on the desired plot below, to obtain a brief description of that type of graph.

  Scatterplot	  Surface Plot

  Space Plot	  Contour/Lines

  Spectral Plot	  Contour/Areas

  Deviation Plot

Categories

Fit:  You can choose to fit one of several equations to the data or use a data smoothing procedure in the 3D categorized plot by selecting one of the predefined functions in this dialog or click on the Custom: button to custom-define a function that will be overlaid in the graph.

  Linear Smooth	  Negative Exp/Wght

  Quadratic Smooth	  Spline Smooth

  Least Squares	  Custom Function

To custom define a function (mathematical expression), select either the Custom Function option or click on the Custom Function button to bring up the User-Defined Functions dialog.  Note:  User-defined functions which can be specified here or in graph Plot Layout dialogs are plotted over (i.e., overlaid) and not fitted to the data.  In order to fit (and plot) user-defined functions to the data, use the Nonlinear Estimation module.

Deviation Level

Number of planes

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 3D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 3D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).


3D Categorized Plots - Graphs Gallery Button

  Stats Graphs 3D Categorized Plots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


3D Categorized Plots - Variables

  Stats Graphs 3D Categorized Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X-, Y-, and Z-axis variables and the grouping variable to be categorized for the graph.  The selection that you make will then be displayed in the area of the dialog below the Variables button.  Note that the selected grouping variable does not have to be a categorical variable (e.g., contain codes); you can use one of the Methods of Categorization options to categorize a continuous variable.  (The grouping variable is not necessary if the categories are defined via the Multiple Subset method.)


3D Categorized Plots - Categories

  Stats Graphs 3D Categorized Plots - Categories

This option allows you to choose the method of categorization for the selected grouping variable.  Each of the methods is discussed in the Method of Categorization topic.


3D Categorized Plots - Deviation Level

  Stats Graphs 3D Categorized Plots - Deviation Level

This option (applicable to Deviation and Space plots) allows you to specify a value on the Z-axis that determines the level from which deviations are derived; or in the case of Space Plots, this value determines the Z-level of the X-Y plane.


3D Categorized Plots - Number of Planes

  Stats Graphs 3D Categorized Plots - Number of Planes

This option (applicable to Spectral plots) allows you to specify the number of spectral planes into which the data are segmented (compressed).


3D Categorized Plots - Options

  Stats Graphs 3D Categorized Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the appearance of the graph.


  Stats 3D XYZ Graphs - Custom Function Plots

This type of Stats Graphs produces a 3-dimensional graph based not on values of variables in a data file but on a user-defined formula (custom function), for example:  z = x^2 + y/2.

3D Custom Function Plots dialog:

Custom Function

X Min, X Max

Y Min, Y Max

Options

  Graphs Gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 3D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 3D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).


  Stats 3D XYZ Graphs Custom Function Plots - Custom Function

Click on this button to open the User-defined Functions dialog in which you can enter the equation to be plotted.


  Stats 3D XYZ Graphs Custom Function Plots - X Min, X Max

Specify here the range (i.e., minimum and maximum values) of the X variable for the custom function.


  Stats 3D XYZ Graphs Custom Function Plots - Y Min, Y Max

Specify here the range (i.e., minimum and maximum values) of the Y variable for the custom function.


  Stats 3D XYZ Graphs Custom Function Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the appearance of the graph.


  Stats 3D XYZ Graphs Custom Function Plots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Stats Graphs - Matrix Plots

In Stats Graphs matrix plots, one or two lists of variables are selected and one X-Y style graph is generated for each pair of variables, either within one list (square matrix plot) or between two lists (rectangular matrix plot).  In other words, in the matrix display format, two lists of variables are "crossed" and the crossing of each pair of variables (X and Y) is represented in the display by one X-Y plot.

Matrix Plot dialogs:

Variables

Graph Type:  You can select the type of matrix plot from the Graph Type list in this dialog.  Click on the desired plot below, to obtain a brief description of that type of graph.

  Square Scatter Matrix	  Rectangular Scatter Matrix

  Square Line Matrix	  Rectangular Line Matrix

  Square Column Matrix	  Rectangular Column Matrix

MD Deletion

Fit:  You can choose to fit either none (select Off) or one of several equations to the data in the matrix plots by selecting one of the predefined functions in this dialog or clicking on the Custom: button to custom-define a function that will be overlaid in the plots.

  Linear	  Polynomial

  Logarithmic	  Least Squares

  Exponential	  Negative Exponential

  Spline	  Custom Function

Histogram Scales

Mark Selected Subsets

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the General Layout and Plot Layout - Matrix Plots dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu).  The default point and area colors and patterns used in this graph can be adjusted in the Specific Plots Default Patterns dialog.

In order to produce a scatterplot matrix for each of the selected groups in the grouping variable, see Categorized Scatterplot Matrix.


  Stats Graphs Matrix Plots - MD Deletion

This option will allow you to choose between Pairwise or Casewise deletion of missing data.


  Stats Graphs Matrix Plots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Stats Graphs Matrix Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X- and (optional) Y-axis variables for the graph.  When you select Square matrix plots, you will need to select only variables for the X-axis; when you select Rectangular matrix plots, you will need to select variables for both the X- and Y-axis.  The selection that you make will then be displayed in the area of the dialog below the Variables button.


  Stats Graphs Matrix Plots - Histogram Scales

Frequency histograms are placed on the diagonal of square matrix plots and in the first row and column of rectangular matrix plots.  You can also choose the type of scaling for the histograms in this option.

Common:  When you select a Common scale, then the scale will be based on a common range of all of the histogram ranges and will allow you to compare the histograms.  However, if the individual histogram ranges vary widely (causing a very wide common scale), then some of the histograms may be unreadable.

Independent:  When Independent scale is chosen, STATISTICA will plot each of the histograms based on their individual ranges.  If you select Independent, then comparing histograms would be difficult since they could all possibly have different scales, but they may be better defined than if a Common scale was used.

#  of Bins:  This option allows you to set the number levels (bins) for which the frequencies will be calculated.


  Stats Graphs Matrix Plots - Mark Selected Subsets

When you click on this button, the Specify Multiple Subsets dialog will open in which you can specify selection conditions that will subset (i.e., categorize) the cases in one plot.  For more information about this option, see Mark Selected Subsets.  The point markers which identify specific subsets will be listed in the legend next to the text of the respective case selection conditions (as defined in the Specify Multiple Subsets dialog).


  Stats Graphs Matrix Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


  Stats Graphs - Icon Plots

One of the potentially powerful general techniques of exploratory data analysis are multidimensional icon graphs.  The basic idea of icon plots is to represent individual units of observation as particular graphical objects where values of variables are assigned to specific features or dimensions of the objects (usually one case = one object).  The assignment is such that the overall appearance of the objects changes as a function of the configuration of values.  Thus, the objects are given visual "identities" that are unique for configurations of values and that can be identified by the observer.  Examining such icons may help to discover specific clusters of both simple relations and interactions between variables.

Icon Plots dialog:

Variables

Graph Type:  You can select the type of icon plot from the Graph Type list in this dialog.  Click on the desired icon plot below, to obtain a brief description of that type of graph.

  Chernoff Faces	  Pies

  Stars	  Columns

  Sun Rays	  Lines

  Polygons	  Profiles

Standardize

Cases

Mark Selected Icons

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the General Layout and Plot Layout - Icon Plots dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu).


  Stats Graphs Icon Plots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Stats Graphs Icon Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the variable(s) for the graph.  The selection that you make will then be displayed in the area of the dialog below the Variables button.


  Stats Graphs Icon Plots - Standardize

You can control the standardization of the values of variables selected for the icon plot with this option.

Off:  If you select this option, then the raw data values will be used to create the icon plots.

Variables:  Select this option to standardize the values of the variables across cases.

Cases:  Select this option to standardize the values of the variables within each icon.

Twice:  This option involves one regular standardization (i.e., across cases) followed by a standardization within each case (icon).

Except for unusual cases when you intend the icons to reflect the global differences in ranges of values between the selected variables, the values of the variables should be standardized once to assure the within-icon compatibility of value ranges.  For example, because the largest value sets the global scaling reference point for the icons, then if there are variables that are in a range of much smaller order, they may not appear in the icon at all, e.g., in a star plot, the rays that represent them will be too short to be visible.


  Stats Graphs Icon Plots - Cases

Select either All or a range of cases (From, To) to be plotted with this option.

All Cases:  Set this check box to plot all cases in the data file for the selected variable(s).

From, To:  Specify here the number of the first and last case (inclusive) to be plotted; note that the same (or more complex case selection conditions) can be specified using the Case Selection Conditions dialog.  If you use both Case Selection Conditions and the From, To option here, STATISTICA will first perform the Case Selection Conditions and then to the resulting subset of cases, apply the From, To condition.


  Stats Graphs Icon Plots - Mark Selected Icons

Click on this button to open the Specify Multiple Subsets dialog in which you can specify the cases whose icons will be marked (i.e., frames will be placed around the selected icons) in the plot.  The line patterns of frames which identify specific subsets will be listed in the legend next to the text of the respective case selection conditions (as defined in the Specify Multiple Subsets dialog).


  Stats Graphs Icon Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the appearance of the graph.


  Stats Graphs - Categorized Histograms

When you select this option, a series of standard 2D histograms, one for each category of cases identified by the X or X and Y category variables (or identified by the Multiple Subset criteria) will be produced.

2D Categorized Histograms dialog:

Variables

Layout

Fitted Functions for Histograms

Categories (for X and Y Category Variables)

Categories (for Histogram)

Cumulative Counts

Breaks between columns

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 2D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 2D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).

In order to produce frequency distributions of values in cases (and not variables), use the Block Stats Graphs - Histograms of Rows option from the Graphs pull-down menu (instead of transposing your data file).


Categorized Histograms - Graphs Gallery Button

  Stats Graphs Categorized Histograms - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


Categorized Histograms - Variables

  Stats Graphs Categorized Histograms - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X and (optional) Y grouping variables and the dependent variable(s) to be displayed in the graph.  If more than one dependent variable is selected, then a sequence of graphs (one for each dependent variable) will be produced using the same set of grouping variables.  The selection that you make will then be displayed in the area of the dialog below the Variables button.  Note that the selected grouping variables do not have to be categorical variables (e.g., contain codes); you can use one of the Methods of Categorization to categorize continuous variables.  The selection of grouping variables is not necessary if the categories are defined via the Multiple Subset method.


Categorized Histograms - Layout

  Stats Graphs Categorized Histograms - Layout

Choose either a Separate plot layout (where each subset of cases is displayed in a separate small graph) or an Overlaid plot layout (where all subsets are overlaid in one graph and identified only by patterns and colors) for the categorized histograms.


Categorized Histograms - Categories (for X and Y Category Variables)

  Stats Graphs Categorized Histograms - Categories (for X and Y Category Variables)

These options allow you to choose the method of categorization for each of the selected grouping variables.  (Note that grouping variables do not need to be selected if Multiple Subset categories are selected.)

Categorization is used in two classes of graphs in STATISTICA:  categorized graphs (e.g., Categorized Scatterplots) and graphs that include grouping or categorized variables (e.g., 2D Histograms, or 2D Box Plots).  You can choose from several methods of categorization which are described below.

•	Integer Mode

•	Categories

•	Boundaries

•	Codes

•	Multiple Subsets

Note:  You can change the number of significant digits that are used when labeling the category levels in the graph by specifying the desired number of digits in the No. of decimals in category description option in the Options dialog.  You can also specify alphanumeric category labels or the equivalent numeric category labels on the graph axes by using the Display text values (or dates) as axis values option in the Options dialog.


Categorized Histograms - Categories (for Histogram)

  Stats Graphs Categorized Histograms - Categories (for Histogram)

These options allow you to choose the method of categorization for the histogram (e.g., you can divide the distribution of the variable into a requested number of intervals or custom define the interval boundaries).  Each of the methods is discussed in the Method of Categorization topic.


Categorized Histograms - Cumulative Counts

  Stats Graphs Categorized Histograms - Cumulative Counts

When you select this option, the consecutive columns in the resulting histogram will represent cumulative frequencies (i.e., the frequencies of all preceding categories) instead of the raw data.


Categorized Histograms - Breaks Between Columns

  Stats Graphs Categorized Histograms - Breaks Between Columns

Check this option if you would like the histogram columns in the plot to be separated from each other.  According to a common convention, histograms of continuous variables should be displayed with no breaks (the breaks signify discrete values).


Categorized Histograms - Options

  Stats Graphs Categorized Histograms - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, scale, orientation, etc.


  Stats Graphs - Categorized Scatterplots

When you select this option, a series of standard 2D scatterplots, one for each category of cases identified by the X or X and Y category variables (or identified by the Multiple Subset criteria) will be produced.

(In order to produce a scatterplot matrix for each of the selected groups in the grouping variable, see Categorized Scatterplot Matrix.)

2D Categorized Scatterplots dialog:

Variables

Layout

Categories (for X and Y Category Variables)

Style

Fit:  You can choose to fit one of several equations to the data or use a data smoothing procedure in the scatterplot by selecting one of the predefined functions in this dialog or click on the Custom: button to custom-define a function that will be overlaid in the graph.

  Linear	  Polynomial

  Logarithmic	  Least Squares

  Exponential	  Negative Exponential

  Spline	  Custom Function

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 2D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 2D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).


Categorized Scatterplots - Style

  Stats Graphs Categorized Scatterplots - Style

Normal:  Select this option in order to display the categorized graphs using Cartesian coordinates.

Polar:  Select this option in order to convert the standard (Cartesian) coordinates into a graph with polar coordinates.


Categorized Scatterplots - Graphs Gallery button

  Stats Graphs Categorized Scatterplots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


Categorized Scatterplots - Variables

  Stats Graphs Categorized Scatterplots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X and (optional) Y grouping variables and the variable(s) to be displayed in the scatterplots.  The selection that you make will then be displayed in the area of the dialog below the Variables button.  Note that the selected grouping variables do not have to be categorical variables (e.g., contain codes); you can use one of the Methods of Categorization to categorize continuous variables.  The selection of grouping variables is not necessary if the categories are defined via the Multiple Subset method.


Categorized Scatterplots - Layout

  Stats Graphs Categorized Scatterplots - Layout

Choose either a Separate plot layout (where each subset of cases is displayed in a separate small graph) or an Overlaid plot layout (where all subsets are overlaid in one graph and identified only by patterns and colors) for the categorized scatterplots.

Note that similar to the option Marking Selected Subsets in 2D Scatterplots, overlaid Categorized Scatterplots automatically mark the points in each overlaid plot differently (i.e., each plot is represented in the same manner as multiple subsets which are based on categorization options).


Categorized Scatterplots - Categories (for X and Y Category Variables)

  Stats Graphs Categorized Scatterplots - Categories (for X and Y Category Variables)

These options allow you to choose the method of categorization for each of the selected grouping variables.  (Note that grouping variables do not need to be specified if Multiple Subset categories are selected.)

Each of the methods is discussed in the Method of Categorization topic.


Categorized Scatterplots - Options

  Stats Graphs Categorized Scatterplots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


  Stats Graphs - Categorized Probability Plots

When you select this option, a series of standard 2D probability plots one for each category of cases identified by the X or X and Y category variables (or identified by the Multiple Subset criteria) will be produced.

2D Categorized Probability Plots dialog:

Variables

Graph Type:  You can select the type of probability plot to be plotted from the Graph Type list in this dialog.  Click on the desired plot below, to obtain a brief description of that type of graph.

  Categorized Normal

  Categorized Half-Normal

  Categorized Detrended

Categories (for X and Y Category Variables)

Options

  Graphs gallery

Notes:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 2D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 2D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).

In order to produce normal probability plots of the values in cases (and not variables), use the Block Stats Graphs - Normal Prob. Plots of Rows option from the Graphs pull-down menu (instead of transposing your data file).  Note that if more than one row is highlighted, then a multiple normal probability plot will be produced.

See also, Stats Graphs - Quantile-Quantile Plots and Stats Graphs - Probability-Probability Plots.


Categorized Probability Plots - Graphs Gallery Button

  Stats Graphs Categorized Probability Plots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


Categorized Probability Plots - Variables

  Stats Graphs Categorized Probability Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X and (optional) Y grouping variables and the variable(s) to be displayed in the probability plots.  If more than one dependent variable is selected, then a sequence of graphs (one for each dependent variable) will be produced using the same set of grouping variables.  The selection that you make will then be displayed in the area of the dialog below the Variables button.  Note that the selected grouping variables do not have to be categorical variables (e.g., contain codes); you can use one of the Methods of Categorization to categorize continuous variables.  The selection of grouping variables is not necessary if the categories are defined via the Multiple Subset method.


Categorized Probability Plots - Categories (for X and Y Category Variables)

  Stats Graphs Categorized Probability Plots - Categories (for X and Y Category Variables)

These options allow you to choose the method of categorization for each of the selected grouping variables.  (Note that grouping variables do not need to be specified if Multiple Subset categories are selected.)

Each of the methods is discussed in the Method of Categorization topic.


Categorized Probability Plots - Options

  Stats Graphs Categorized Probability Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the display of the graph.


  Stats Graphs - Categorized Quantile-Quantile Plots

When you select this option, a series of Quantile-Quantile (or Q-Q) plots, one for each category of cases identified by the X or X and Y category variables (or identified by the Multiple Subset criteria) will be produced.  The Q-Q plot is useful for finding the best fitting distribution within a family of distributions.  The first step therefore, is to choose which of the theoretical distributions to fit to the data.  After selecting the distribution from the list in this dialog (see below), you may or may not need to specifiy certain parameters for that distribution.

In order to assess the fit of the theoretical distribution to the observed data, the nonmissing observed values of the variable are ordered (x1 < ... < xn) and then these values (xi) are plotted against the inverse probability distribution function denoted as F**-1 [specifically, F**-1(i - rankadj/n + nadj), where F**-1 depends on the distribution, and rankadj and nadj are user-defined adjustments].  A regression line is then fitted to the data in the resulting scatterplot.  If the observed values fall on the regression line (fitting line), then it can be concluded that the observed values follow the specified distribution.  The equation of the fitting line (Y=a + bx, given in the third title of the resulting Q-Q plot) provides parameter estimates (a and b, where a is the Threshold parameter and b is the Scale parameter) for the best fitting distribution (see the respective distribution for more information on these parameters).

For the Exponential, Extreme, Normal, and Raleigh distributions, the standardized distribution function is used and no additional parameters are needed.

For the Beta, Gamma, Lognormal, and Weibull distributions, the standardized distribution with specific Shape parameters is used.  The Shape parameters can be specified in one of two ways:

(1)	The Shape parameters are user-defined (de-select the Compute parameters from option).

(2)	The Shape parameters are estimated (select the Compute parameters from option) based on user-defined Threshold and Scale parameters and using either the maximum likelihood or matching moments approximation (see below).

The Shape parameters are given in the second title of the graph.

Categorized Quantile-Quantile Plots dialog:

Variables

Categories (for X and Y Category Variables)

Distribution:  Select the desired theoretical distribution for this graph.

Parameters.  Specific parameters may be required for some of the distributions.  In those cases, the parameters will be described when the distribution is described.  See below for more information.

  Beta	  Lognormal

  Exponential	  Normal

  Extreme Value	  Rayleigh

  Gamma	  Weibull

Probability Scale

Fitting Line

Adjustments

Graphs Gallery

Options


Maximum Likelihood Method for Q-Q and P-P Plots

This method can be employed to determine parameter estimates for a distribution (see Quantile-Quantile Plots and Probability-Probability Plots).  In order to estimate a distribution parameter, the maximum likelihood method uses a value in the parameter space that corresponds to the largest "likelihood" for the sample data (i.e., the value that makes the observed data most probable).  Alternatively, you could use the Method of Matching Moments to estimate the parameters.  For more information, see Hahn and Shapiro, 1994.


Categorized Quantile-Quantile Plots - Variables

  Stats Graphs Quantile-Quantile Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X and (optional) Y grouping variables and the variable(s) to be displayed in the Q-Q plots.  If more than one dependent variable is selected, then a sequence of graphs (one for each dependent variable selected) will be produced.  The selection that you make will then be displayed in the area of the dialog below the Variables button.  Note that the selected grouping variables do not have to be categorical variables (e.g., contain codes); you can use one of the Methods of Categorization to categorize continuous variables.  The selection of grouping variables is not necessary if the categories are defined via the Multiple Subset method.


Categorized Quantile-Quantile Plots - Probability Scale

  Stats Graphs Quantile-Quantile Plots - Probability Scale

This option will scale the upper-X axis nonlinearly, according to the probability values given in the respective edit field (by default, .01, .05, .1, .25, .5, .75, .9, .95, .99).  Vertical grid lines will be positioned along these percentiles.  If this option is de-selected, then no scale will be displayed on the upper-X axis.


Categorized Quantile-Quantile Plots - Fitting Line

  Stats Graphs Quantile-Quantile Plots - Fitting Line

Display linear fit:  When you select this option, the program will calculate and display the linear fitting line.  The equation of the linear fitting line (Y=a + bx, given in the third title of the resulting Q-Q plot) provides estimates for the Threshold (a, location) and the Scale (b) parameters of the specified distribution.

Custom fit:  You can custom-define a fitting line to be included in the graph (in addition to the linear fit) by setting the Custom fit check box and then entering user-defined Scale and Threshold (location) values.  This option is useful for comparing the linear fitting line (see above) with custom fitting lines based on known distributions in the family of distributions.

Note that both the linear fit and custom fit lines can be displayed in the graph (set both check boxes).  Note also that the equation for the custom-defined line can be displayed in a title in the graph using Control Characters.


Categorized Quantile-Quantile Plots - Adjustments

  Stats Graphs Quantile-Quantile Plots - Adjustments

These options allow you to adjust the values which are used in the determination of the theoretical quantiles:  [(i - rankadj)/(n + nadj)] where i is the i'th ordered observation, n is the number of non-missing values and rankadj and nadj are user-defined adjustments to insure that this quantity is greater than 0 and less than 1, see below.

Ranks:  Specify here the rank adjustment (rankadj; by default, .375) which is added to the ranks of the observed values when the theoretical quantiles are computed.

N:  Specify here the sample size adjustment (nadj; by default, .25) which is added to the observed sample size when the theoretical quantiles are computed.

For more information, see Hahn and Shapiro, 1967.


Categorized Quantile-Quantile Plots - Graphs Gallery

  Stats Graphs Quantile-Quantile Plots - Graphs Gallery

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


Categorized Quantile-Quantile Plots - Options

  Stats Graphs Quantile-Quantile Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


Categorized Quantile-Quantile Plots - Categories (for X and Y Category Variables)

  Stats Graphs Categorized Quantile-Quantile Plots - Categories (for X and Y Category Variables)

These options allow you to choose the method of categorization for each of the selected grouping variables.  (Note that grouping variables do not need to be specified if Multiple Subset categories are selected.)

Each of the methods is discussed in the Method of Categorization topic.


  Stats Graphs - Categorized Probability-Probability Plots

When you select this option, a series of Probability-Probability (or P-P) plots, one for each category of cases identified by the X or X and Y category variables (or identified by the Multiple Subset criteria) will be produced.  The P-P plot is useful for determining how well a specific theoretical distribution fits the observed data.  In the P-P plot, the observed cumulative distribution function (the proportion of nonmissing values ≤ x) is plotted against a theoretical cumulative distribution function in order to assess the fit of the theoretical distribution to the observed data.  If all points in this plot fall onto a diagonal line (with intercept 0 and slope 1), then you can conclude that the theoretical cumulative distribution approximates the observed distribution well.  If the data points do not all fall on the diagonal line, then you can use this plot to visually assess where the data do and do not follow the distribution (e.g., if the points form an S shape along the diagonal line, then the data may need to be transformed).

In order to create this plot the theoretical distribution function must be completely specified.  Therefore, the parameters for the distribution must either be defined by the user or computed from the data (see the specified distribution for more information on the respective parameters).  Note that you can also use the Quantile-Quantile plot to obtain the parameter estimate(s) (for the best fitting distribution from a family of distributions) to be used here.

Categorized Probability-Probability Plots dialog:

Variables

Categories (for X and Y Category Variables)

Distribution:  Select the desired theoretical distribution for this graph.

Parameters.  The parameters for each distribution are described along with the distribution.  See below for more information.

  Beta	  Lognormal

  Exponential	  Normal

  Extreme Value	  Rayleigh

  Gamma	  Weibull

Graphs Gallery

Options


Categorized Probability-Probability Plots - Variables

  Stats Graphs Categorized Probability-Probability Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X and (optional) Y grouping variables and the variable(s) to be displayed in the P-P plots.  If more than one dependent variable is selected, then a sequence of graphs (one for each dependent variable selected) will be produced.  The selection that you make will then be displayed in the area of the dialog below the Variables button.  Note that the selected grouping variables do not have to be categorical variables (e.g., contain codes); you can use one of the Methods of Categorization to categorize continuous variables.  The selection of grouping variables is not necessary if the categories are defined via the Multiple Subset method.


Categorized Probability-Probability Plots - Graphs Gallery

  Stats Graphs Categorized Probability-Probability Plots - Graphs Gallery

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


Categorized Probability-Probability Plots - Options

  Stats Graphs Categorized Probability-Probability Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


Categorized Probability-Probability Plots - Categories (for X and Y Category Variables)

  Stats Graphs Categorized Probability-Probability Plots - Categories (for X and Y Category Variables)

These options allow you to choose the method of categorization for each of the selected grouping variables.  (Note that grouping variables do not need to be specified if Multiple Subset categories are selected.)

Each of the methods is discussed in the Method of Categorization topic.


  Stats Graphs - Categorized Line Plots

When you select this option, a series of standard 2D line plots, one for each category of cases identified by the X or X and Y category variables (or identified by the Multiple Subset criteria) will be produced.

2D Categorized Line Plots dialog:

Variables

Categories (for X and Y Category Variables)

Cases

Style

Points

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 2D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 2D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).


  Stats Graphs Categorized Line Plots - Style

Normal:  Select this option in order to display the categorized graphs using Cartesian coordinates.

Polar:  Select this option in order to convert the standard (Cartesian) coordinates into a graph with polar coordinates.  Categorized graphs with polar coordinates can also be produced.


  Stats Graphs Categorized Line Plots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Stats Graphs Categorized Line Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X and (optional) Y grouping variables and the variable(s) to be displayed in the line plots.  If more than one dependent variable is selected, then a multiple line plot will be produced using the same set of grouping variables.  The selection that you make will then be displayed in the area of the dialog below the Variables button.  Note that the selected grouping variables do not have to be categorical variables (e.g., contain codes); you can use one of the Methods of Categorization to categorize continuous variables.  The selection of grouping variables is not necessary if the categories are defined via the Multiple Subset method.


  Stats Graphs Categorized Line Plots - Categories (for X and Y Category Variables)

These options allow you to choose the method of categorization for each of the selected grouping variables.  (Note that grouping variables do not need to be specified if Multiple Subset categories are selected.)

Each of the methods is discussed in the Method of Categorization topic.


  Stats Graphs Categorized Line Plots - Cases

Select either All or a range of cases (From, To) to be plotted with this option.

All Cases:  Set this check box to plot all cases in the data file for the selected variable(s).

From, To:  Specify here the number of the first and last case (inclusive) to be plotted; note that the same (or more complex case selection conditions) can be specified using the Case Selection Conditions dialog.  If you use both Case Selection Conditions and the From, To option here, STATISTICA will first perform the Case Selection Conditions and then to the resulting subset of cases, apply the From, To condition.


  Stats Graphs Categorized Line Plots - Points

You can choose to display the line plot with (On) or without (Off) point markers.  If you select Auto, then STATISTICA will automatically determine the display of point markers depending on the number of observations and the closeness of the points (usually, if n>100, then the points are not displayed).


  Stats Graphs Categorized Line Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


  Stats Graphs - Categorized Box Plots

When you select this option, a series of standard 2D box plots, one for each category of cases identified by the X or X and Y category variables (or identified by the Multiple Subset criteria) will be produced.

2D Categorized Box Plots dialog:

Variables

Graph Type:  You can select the type of box plot to be plotted from the Graph Type list in this dialog.  Click on the desired plot below, to obtain a brief description of that type of graph.

  Box Whiskers	  Boxes

  Whiskers	  Columns

  High-Low Close

Categories (for X and Y Category Variables)

Categories (for Box Plot)

Graph Icon

Middle Point, Box, and Whisker options

Fit:  You can choose to fit an equation to the mid-points in the box plots by selecting one of the predefined functions in this dialog or click on the Custom: button to custom-define a function that will be overlaid in the graph.

  Linear	  Polynomial

  Logarithmic	  Least Squares

  Exponential	  Negative Exponential

  Spline	  Custom Function

Outliers

Options

Connect Middle Points

Trim distrib. extremes

  Graphs gallery

Notes:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 2D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the 2D Plot Layout dialog (accessible from the right-mouse-button flying menu related to specific plots on the graph or from the graphics Layouts pull-down menu).

In order to produce box plots representing the distribution of the values in cases (and not variables), use either the Block Stats Graphs - Box Plot/Means of Rows or Block Stats Graphs - Box Plot/Medians of Rows option from the Graphs pull-down menu (instead of transposing your data file).

Editing graph data for box and whisker format graphs: see Editing Graph Data for Box and Whisker Format Graphs


  Stats Graphs Categorized Box Plots - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Stats Graphs Categorized Box Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X and Y grouping variables, the dependent variable(s) to be displayed in the box plots, and the grouping variable that will be used to categorize values of the dependent variable(s) in each small graph.  If more than one dependent variable is selected, then a sequence of graphs (one for each dependent variable) will be produced using the same set of grouping variables.  The selection that you make will then be displayed in the area of the dialog below the Variables button.  Note that the selected grouping variables do not have to be categorical variables (e.g., contain codes); you can use one of the Methods of Categorization to categorize continuous variables.  The selection of grouping variables is not necessary if the categories are defined via the Multiple Subset method.


  Stats Graphs Categorized Box Plots - Categories (for X and Y Category Variables)

These options allow you to choose the method of categorization for each of the selected grouping variables.  (Note that grouping variables do not need to be specified if Multiple Subset categories are selected.)

Each of the methods is discussed in the Method of Categorization topic.


  Stats Graphs Categorized Box Plots - Categories (for Box Plot)

These options allow you to choose the method of categorization for the box plot (i.e., for the grouping variable that will be used to categorize values of the dependent variable(s) in each small graph).  Each of the methods is discussed in the Method of Categorization topic.


  Stats Graphs Categorized Box Plots - Graph Icon

The graph icon in the middle of the dialog, represents the currently selected Graph Type, and the selection of values for the Box, Middle Point, and Whiskers.  The graph icon will preview these three selections.


  Stats Graphs Categorized Box Plots - Middle Point, Box, and Whisker Options

Middle Point

In box and whisker plots, first select the desired mid-point to be represented by the selected style (point or line) in these plots (the mid-point can be either the Mean or Median of the selected variable).  The options which will be available for the Box and Whiskers will depend on your selection here.

Pooled variance estimate:  This option is available when you select Mean as the Midpoint (see above).  The setting of this checkbox determines how the standard deviations and standard errors (for the means) are computed from grouped data.  When this checkbox is set, the program will compute the pooled within-group (category) variance for all groups (categories), and use this value as an estimate of σ (sigma) when computing the standard errors for the means (see, for example, Milliken and Johnson, 1984).  Specifically, the program will compute the pooled within-group (category) variance as:

       2                2                  2

s        = 1/(n-k) * [s  *(n -1) + ... + s  *(n -1)]

 pooled                1    1             k    k

In this equation, k refers to the k groups in the plot, si**2, refers to the variance in the i'th category or group, ni refers to number of valid observations in the i'th category or group, and n is the overall number of valid observations in the plot.

The standard error of the mean for the i'th group is then computed as:

s.e.(mean) = s      /square root(n )

              pooled              i

Box

If you selected Mean as the mid-point, then the range (box) can be represented by the Std. Dev., Std. Error, or Min-Max values of the selected variable, or a specified Constant value (when you want a fixed size box around the mean).

If you selected the Median as the mid-point, then the range (box) can be represented by Percentiles or the Min-Max values of the selected variable, or a specified Constant value (when you want a fixed size box around the median).

You can also specify a Coefficient by which the selected range value will be multiplied (by default, the Coeff is equal to 1).  Note that except for unusual applications, the default value of the coefficient (1) should not be changed if the Box type is Min-Max.

Whisker

If you selected Mean as the mid-point, then the range (whiskers) can be represented by the Std. Dev., Std. Error, or Min-Max values of the selected variable, Non-outlier range, or a specified Constant value.

If you selected the Median as the mid-point, then the range (whiskers) can be represented by Percentiles or the Min-Max values of the selected variable, a specified Constant value, or Non-outlier range.

If you select Non-outlier range, then STATISTICA will determine which points in the data set are outliers (see Outliers and Extremes) and then use the highest and lowest points which are closest to the outliers (but are not themselves outliers) as the whiskers in the plot.

You can also specify a Coefficient by which the selected range value will be multiplied (by default, the Coeff is equal to 1).  In most typical applications the coefficient should be set to 1 when the value of the whisker is Min-Max or Non-outlier range.


  Stats Graphs Categorized Box Plots - Outliers

Select to display none (select Off), only Outliers, only Extreme values, or both Outliers & Extremes in the box plot.

For more information, see Outliers and Extremes.


  Stats Graphs Categorized Box Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


  Stats Graphs Categorized Box Plots - Trim Distrib. Extremes

This option will allow you to specify the percent of cases to be "trimmed" from the extremes (i.e., tails) of the distribution of cases for the selected variable.  For example, if you specify 10%, then for a variable with 100 cases, STATISTICA will remove the first 10 lowest value cases and the 10 highest value cases from the distribution, and only plot the 80 middle cases.  For example, if you select this option for a mean-based box plot, so-called "trimmed means" will be plotted.


  Stats Graphs - Categorized Pie Charts

When you select this option, a series of pie charts displaying counts (see Pie Chart - Counts), one for each category of cases identified by the X or X and Y category variables (or identified by the Multiple Subset criteria) will be produced.

2D Categorized Pie Chart dialog:

Variables

Categories (for X and Y Category Variables)

Categories (for Pie Chart)

Pie Legend

Style

Shape

Exploded Slice

Options

  Graphs gallery

Note:  After the graph is created, other options which control the arrangement and appearance of various components of this graph can be adjusted in the 2D General Layout dialog (accessible by double-clicking on the graph background or from the graphics Layouts pull-down menu) and the Pie Options dialog (accessible by double-clicking on the pie in the graph or by pressing the Pie Options button in the Plot Layout dialog accessible from the graphics Layouts pull-down menu).


  Stats Graphs Categorized Pie Charts - Graphs Gallery Button

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Stats Graphs Categorized Pie Charts - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X and Y grouping variables, the dependent variable(s) to be displayed in the pie charts, and the grouping variable that will be used to categorize values of the dependent variable(s) in each small graph.  If more than one dependent variable is selected, then a sequence of graphs (one for each dependent variable) will be produced using the same set of grouping variables.  The selection that you make will then be displayed in the area of the dialog below the Variables button.  Note that the selected grouping variables do not have to be categorical variables (e.g., contain codes); you can use one of the Methods of Categorization to categorize continuous variables.  The selection of grouping variables is not necessary if the categories are defined via the Multiple Subset method.


  Stats Graphs Categorized Pie Charts - Categories (for X and Y Category Variables)

These options allow you to choose the method of categorization for each of the selected category variables.  (Note that grouping variables do not need to be specified if Multiple Subset categories are selected.)

Each of the methods is discussed in the Method of Categorization topic.


  Stats Graphs Categorized Pie Charts - Categories (for Pie Chart)

These options allow you to choose the method of categorization of values for the pie chart (as mentioned before, the categorized pie charts display the frequencies [i.e., counts, see Pie Chart - Counts]).  Each of the methods is discussed in the Method of Categorization topic.


  Stats Graphs Categorized Pie Charts - Pie Legend

Select one of six pie legends (Off, Percent, Values, Text labels, Text & percent, Text & values) to be placed in the graph.  If you select Counts as the graph type, then selecting the Text labels option will use the category descriptions in the pie legend.  Otherwise (for Values pie charts and Multi-pattern bar charts), the Text labels used will depend on the Pie labels (values) selected (e.g., if you select Case names as pie labels, then the Text labels will display the actual case names instead of Case1, Case2, etc.; if you select a variable in the Pie labels option and then choose Text labels, then STATISTICA will use the text values of the selected variable in the pie legend).


  Stats Graphs Categorized Pie Charts - Style

You can change the appearance of the pie by choosing either the 2-dimensional (2D) or 3-dimensional (3D) display in this option; see also the Pie Options dialog.


  Stats Graphs Categorized Pie Charts - Shape

The pie shape can be either circular (select Circle) or elliptical (select Ellipse).  However, choosing the Ellipse option may cause the slices to be disproportionate in size (i.e., the slices that follow radii close to the vertical axis of the screen or paper will look relatively larger than their real size as compared to the "horizontal" slices which will be "squeezed" in perspective and will appear smaller); see also the Pie Options dialog.


  Stats Graphs Categorized Pie Charts - Exploded Slice

Select this option to "explode" a specified number of slices of the pie; see also the Pie Options dialog.


  Stats Graphs Categorized Pie Charts - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the display of the graph.


  Stats Graphs - User-defined Graphs

Sometimes it may be necessary or desirable to produce more than one graph based on some specific options selected in a Stats Graphs dialog.  In this case, as you define the graph, you can save those selected options as a Stats User-defined Graph and add them to the User-defined Graphs submenu of the pull-down menu Graphs.  Then, at a later time, you can call up that user-defined graph and the appropriate Stats Graphs dialog will open with all of the previous settings as the default settings.  You can then select or change the variables to produce another Stats Graph.

To save the desired Stats Graphs options as a user-defined graph (after selecting the graph type from the Stats Graphs menu), click on the Options button on the respective Stats Graph dialog containing the currently defined graph specifications.  This will open the Stats Graphs:Options dialog.  In this dialog, click on the Add as User-defined Graph to Menu button.  Now, the New User-defined Graph dialog will open.  Here, you can specify the name for the new graph that will be displayed on the Graphs pull-down menu as well as the file name (file name extension *.sug) under which the specifications will be saved.  Up to 16 user-defined graphs can be added to the menu.

You can review or modify the list of user-defined graphs in the Modify the List of User-defined Graphs dialog.  This dialog is opened when you select the User Graphs option from the Options pull-down menu.  In this dialog, you can delete a user-defined graph from the list by highlighting the menu name and then clicking on the Delete button.

A list of user-defined graphs is stored in the Statist.ini file in the section titled [USER GRAPHS].  You can modify this list (add, reorder) by editing the Statist.ini file.

User-defined graphs can also be assigned to buttons of the floating Auto Task Buttons toolbar.

If you need to custom-design a graph using other features than those which can be specified in the Stats Graphs dialogs, use the graphics library of STATISTICA BASIC which allows you to custom design graphics procedures using virtually all facilities of the STATISTICA system graphics library.

For information about other options available from the pull-down menu Graphs, see the following topics:

Graphics (Overview)

Quick Stats Graphs

Stats Graphs

Multiple Graph Layouts

Multiple Graph AutoLayout Wizard

Templates

Blank Graphs

Custom Graphs

Block Stats Graphs

Graph Data Link

See also Graphs Gallery.


Stats Graphs - New User-defined Graph

When you click on the Save as User-defined Graph button in the STATISTICA Defaults: Stats Graphs dialog (when called from a Stats Graphs dialog), the New User-defined Graph dialog will open.  Here, you can save the previously-selected Stats Graphs options as a user-defined graph in order to produce similar graphs at a later time.  Up to 16 user-defined graphs can be added to the menu.

New User-defined Graph dialog

Menu Name:  Enter the name (up to 40 characters) that will be used to identify the user-defined graph on the Graphs pull-down menu (see the hierarchical sub-menu for the option Stats User-Defined Graphs).

File Name button:  Click on this button if you wish to change the default name of the file (file name extension*.sug) under which the Stats Graphs specifications will be saved.

Save Current Vars with the Graph Definition:  When this option is selected, the variable selections (i.e., variable numbers) will be saved as part of the graph definition in the user-defined graph.  When the user-defined graph is later called up, the previously-selected variables will be displayed in the Stats Graphs dialog.

Show the Graph Now:  Select this option if you want to produce the Stats Graph after saving the specifications as a user-defined graph and exiting this dialog.


Modify the List of User-defined Graphs

When you select User Graphs from the Options pull-down menu, the Modify the List of User-defined Graphs dialog will open.

Modify the List of User-defined Graphs dialog:

User Graphs:  The menu names of all of the previously-saved user-defined graphs are listed in this area of the dialog.  Up to 16 user-defined graphs may be saved using the New User-defined Graph dialog.  These graphs are accessible from the Stats User-defined Graphs option of the pull-down menu Graphs.

Delete button:  You can remove a user-defined graph from the list by highlighting its menu name and then clicking on the Delete button.  Note that the respective graph definition file (file name extension *.sug) will not be deleted but only the reference to that file will be removed from the Statist.ini file, so that the user-defined graph will no longer appear in the User-defined Graphs submenu.  They can later be added by clicking on the Add button.

Add button:  You can add a user-defined graph to the list by clicking on the Add button.  Doing this will open the Change User-defined Graph Name dialog which allows you to add a new menu name and select a graph definition file (file name extension *.sug) to associate with that menu name.

Edit button:  You can edit the list of user-defined graphs by highlighting the name of the graph you wish to edit and clicking on the Edit button or by double clicking on the name of the graph.  Doing this will open the Change User-defined Graph Name dialog which allows you to change the currently selected menu name and/or select a graph definition file (file name extension *.sug) to associate with that menu name.

Reordering the User-defined graphs:  To reorder the graphs in this dialog (and the corresponding pull-down menu), select the graph name(s) to be moved, then click between the lines of the new location.


Change User-defined Graph Name

When you click on either the Add button or the Edit button in the Modify the List of User-defined Graphs dialog (available by selecting User Graphs from the Options pull-down menu), the Change User-defined Graph Name dialog will open.

Change User-defined Graph Name dialog:

Menu Name:  Enter the name (up to 40 characters) that will be used to identify the user-defined graph on the Graphs pull-down menu (see the hierarchical sub-menu for the option Stats User-Defined Graphs).

File Name button:  Click on this button if you wish to change the Stats Graphs specifications file (file name extension *.sug) which is associated with this Menu Name.


Specify Boundaries for Categorization Variable

When you click on the Specify Boundaries button in a Stats Graphs dialog, the Specify Boundaries for ... dialog will open.  Here, you can specify the upper limits for the boundaries.  Enter in the Enter upper boundaries box a list of values representing the upper boundaries of ranges to be represented in the plot.

For example, if you list the four values:

-5 .05 15 32.3

then the following five ranges will be used as categories in the graph:

x <= -5

-5 < x <= .05

.05 < x <= 15

15 < x <= 32.3

32.3 < x


Stats Graphs - Missing/Range Data Points

  Stats Graphs - Missing/Range Data Points Plot

This graph allows you to examine the pattern or distribution of missing and/or user-specified 'out of range' data points in the current data set (or in a subset of variables and cases).  This graph is useful in exploratory data analysis to determine the extent of missing (and/or 'out of range') data and whether the patterns of those data occur more or less randomly.

Missing Data and 'Out of Range' Plots dialog:

Variables

Cases

Display Missing Data

Display 'Out of Range' Data Points

Graphs Gallery

Options

Note that a variety of methods are available in STATISTICA to transform and recode data (e.g., spreadsheet formulas, STATISTICA BASIC) including menu-driven techniques to replace or convert missing values (e.g., replace by means, recoding).  In most analyses, missing data can be managed using either pairwise deletion or casewise deletion of missing data, or substitution by means.


Missing/Range Data Points - Variables

  Stats Graphs Missing/Range Data Points Plot - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the variable(s) to be plotted.  The variable(s) that you select here will be plotted on the X-axis in the graph (against Cases on the Y-axis).


Missing/Range Data Points - Cases

  Stats Graphs Missing/Range Data Points Plot - Cases

Select either All or a range of cases (From, To) to be plotted with this option.

All Cases:  Deselect this check box to enable selection of a range of cases in the data file for the selected variables.

From, To:  Specify here the number of the first and last case (inclusive) to be plotted; note that the same (or more complex case selection conditions) can be specified using the Case Selection Conditions dialog.  If you use both Case Selection Conditions and the From, To option here, STATISTICA will first perform the Case Selection Conditions and then to the resulting subset of cases, apply the From, To condition (note that in this situation, the case numbers specified in the From, To edit boxes may not reference the original case numbers in the data file).


Missing/Range Data Points - Display Missing Data

  Stats Graphs Missing/Range Data Points Plot - Display Missing Data

Selecting this option will display missing data points along with 'out of range' points for the specified variables.  Deselect this option in order to display only the 'out of range' points in the graph.


Missing/Range Data Points - Display 'Out of Range' Data Points

  Stats Graphs Missing/Range Data Points Plot - Display 'Out of Range' Data Points

'Out of range' values can be defined using the Min and Max edit fields for the respective variable (selected by clicking on the Variables button).  Values which fall above or below the defined range will be plotted in the graph.  Missing data values can be displayed along with the 'out of range' values by checking the Display Missing Data checkbox.  A different point pattern will be used for each defined range.


Missing/Range Data Points - Graphs Gallery

  Stats Graphs Missing/Range Data Points Plot - Graphs Gallery

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


Missing/Range Data Points - Options

  Stats Graphs Missing/Range Data Points Plot - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


Stats Graphs - Categorized Missing/Range Data Points

  Stats Graphs - Categorized Missing/Range Data Points Plot

This option produces a series of 2D graphs (one for each category of cases identified by the grouping variables or by the Multiple Subset criteria) of missing data points and/or user-specified 'out of range' points from which you can visualize the pattern or distribution of missing data (and/or user-specified 'out of range' points) within each subset of cases (category).  This graph is useful in exploratory data analysis to determine the extent of missing (and/or 'out of range') data and whether the patterns of those data occur randomly.

Categorized Missing Data and 'Out of Range' Plots dialog:

Variables

Category

Cases

Display Missing Data

Display 'Out of Range' Data Points

Graphs Gallery

Options

Note that a variety of methods are available in STATISTICA to transform and recode data (e.g., spreadsheet formulas, STATISTICA BASIC) including menu-driven techniques to replace or convert missing values (e.g., replace by means, recoding).  In most analyses, missing data can be managed using either pairwise deletion or casewise deletion of missing data, or substitution by means.


Categorized Missing/Range Data Points - Variables

  Stats Graphs Categorized Missing/Range Data Points Plot - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the variable(s) to be plotted and the grouping variable to be categorized for the graph.  The variable(s) that you select here will be plotted on the X-axis in the graph (against Cases on the Y-axis).  Note that the selected grouping variable does not have to be categorical (e.g., contain codes); you can use one of the Methods of Categorization to categorize continuous variables.  The selection of a grouping variable is not necessary if the categories are defined via the Multiple Subset method.


Categorized Missing/Range Data Points - Category

  Stats Graphs Categorized Missing/Range Data Points Plot - Category

These options allow you to choose the method of categorization for the missing data or 'out of range' graph (i.e., for the grouping variable that will be used to categorize values of the dependent variable(s) in each small graph).  (Note that grouping variables do not need to be specified if Multiple Subset categories are selected.)

Each of the methods is discussed in the Method of Categorization topic.


Categorized Missing/Range Data Points - Cases

  Stats Graphs Categorized Missing/Range Data Points Plot - Cases

Select either All or a range of cases (From, To) to be plotted with this option.

All Cases:  Deselect this check box to enable selection of a range of cases in the data file for the selected variables.

From, To:  Specify here the number of the first and last case (inclusive) to be plotted; note that the same (or more complex case selection conditions) can be specified using the Case Selection Conditions dialog.  If you use both Case Selection Conditions and the From, To option here, STATISTICA will first perform the Case Selection Conditions and then to the resulting subset of cases, apply the From, To condition (note that in this situation, the case numbers specified in the From, To edit boxes may not reference the original case numbers in the data file).


Categorized Missing/Range Data Points - Display Missing Data

  Stats Graphs Categorized Missing/Range Data Points Plot - Display Missing Data

Selecting this option will display missing data points along with 'out of range' points for the specified variables.  Deselect this option in order to display only the 'out of range' points in the graph.


Categorized Missing/Range Data Points - Display 'Out of Range' Data Points

  Stats Graphs Categorized Missing/Range Data Points Plot - Display 'Out of Range' Data Points

'Out of range' values can be defined using the Min and Max edit fields for the respective variable (selected by clicking on the Vars button).  Values which fall above or below the defined range will be plotted in the graph.  Missing data values can be displayed along with the 'out of range' values by checking the Display Missing Data checkbox.  A different point pattern will be used for each defined range.


Categorized Missing/Range Data Points - Graphs Gallery

  Stats Graphs Categorized Missing/Range Data Points Plot - Graphs Gallery

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


Categorized Missing/Range Data Points - Options

  Stats Graphs Categorized Missing/Range Data Points Plot - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


  Stats 3D XYZ Graphs - Ternary Plots

A ternary (or "trilinear") plot can be used to examine relations between three or more dimensions where three of those dimensions represent components of a mixture (i.e., the relations between them is constrained such that the values of the three variables add up to the same constant for each case).  One typical application of this graph is when the measured response(s) from an experiment depends on the relative proportions of three components (e.g., three different chemicals) which are varied in order to determine an optimal combination of those components (e.g., in mixture designs).  In ternary plots, the triangular coordinate systems are used to plot four (or more) variables (the components X, Y, and Z, and the responses V1, V2, etc.) in two dimensions (ternary scatterplots or contours) or three dimensions (ternary 3D scatterplots or surface plots).  In order to produce ternary graphs, the relative proportions of each component (within each case) are constrained to add up to the same value (e.g., 1).  By default, when the graph is produced, the proportions are rescaled so that they add to 1 in each case.  Other options to manage cases with invalid sums are given below (see Data Range, below).

Ternary Plots dialog:

Graph Type:  You can select the type of ternary plot to be plotted from the Graph Type list in this dialog.  Click on the desired plot below, to obtain a brief description of that type of graph.

  2D Scatterplot	  Trace Plot

  3D Scatterplot	  Surface

  Space Plot	  Contour/Lines

  Deviation Plot	  Contour/Areas

Variables

Fit:  You can choose from four regression functions to fit to the data in a ternary plot.  Click on a function name for more information about that function.  See also Fitting Options for Ternary Plots.

  Linear Smooth	  Special Cubic Smooth

  Quadratic Smooth	  Custom Function

  Full Cubic Smooth

Note:  User-defined functions can be specified in the Plot Layout dialog.  These functions are plotted over (i.e., overlaid) and not fitted to the data.  In order to fit (and plot) user-defined functions to the data, use the Nonlinear Estimation module.

Data Range

Graphs gallery

Options


  Stats 3D XYZ Graphs Ternary Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the X-, Y-, Z-, and one or more V-axis variables for the graph.  The selection that you make will then be displayed in the area of the dialog below the Variables button.


  Stats 3D XYZ Graphs Ternary Plots - Data Range

Plot Pseudo-components:  When you select this option, the component settings are recoded to so-called pseudo-components so that (see also Cornell, 1993, Chapter 3):

x'  = (x -L )/(Total-L)

  i     i  i

Here, x'i stands for the i'th pseudo-component, xi stands for the original component value, Li stands for the lower constraint (limit) for the i'th component, L stands for the sum of all lower constraints (limits) for all components in the design, and Total stands for the mixture total.  This transformation makes the coefficients for different factors comparable in size.

When you select this option, the Ignore cases with invalid sums option will automatically be selected (see below).

Ignore cases with invalid sums:  This option will allow you to manage cases in which the component proportions do not add to the constrained value.  If you select this option, STATISTICA will ignore cases in which the proportions add to a specified expected sum.  If you de-select this option, then STATISTICA will rescale the proportions so that they add to 1 in each case.

Expected sum of x+y+z:  Specify here the sum to which the proportions should add.

Ignore out of range cases:  When selected, this option allows you to specify ranges of values for each of the component variables (X, Y, and/or Z) that will be considered valid.  Cases which have values that fall outside (above or below) the respective ranges will be ignored.


  Stats 3D XYZ Graphs Ternary Plots - Graphs Gallery

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


  Stats 3D XYZ Graphs Ternary Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


  Stats Graphs - Categorized Ternary Plots

A categorized ternary plot can be used to examine relations between three or more dimensions where three of those dimensions represent components of a mixture (i.e., the relations between them is constrained such that the values of the three variables add up to the same constant for each case) for each level of a grouping variable.  One typical application of this graph is when the measured response(s) from an experiment depends on the relative proportions of three components (e.g., three different chemicals) which are varied in order to determine an optimal combination of those components (e.g., in mixture designs).  In a categorized ternary plot, one component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).

In ternary plots, the triangular coordinate systems are used to plot four (or more) variables (the components X, Y, and Z, and the responses V1, V2, etc.) in two dimensions (ternary scatterplots or contours) or three dimensions (ternary surface plots).  In order to produce ternary graphs, the relative proportions of each component within each case are constrained to add up to the same value (e.g., 1).  By default, when the graph is produced, the proportions are rescaled so that they add to 1 in each case.  Other options to manage cases with invalid sums are given below (see Data Range, below).

Categorized Ternary Plots dialog:

Graph Type:  You can select the type of categorized ternary plot to be plotted from the Graph Type list in this dialog.  Click on the desired plot below, to obtain a brief description of that type of graph.

  2D Scatterplot	  Surface

  3D Scatterplot	  Contour/Lines

  Space Plot	  Contour/Areas

  Trace Plot

Variables

Fit:  You can choose from four regression functions to fit to the data in a ternary plot.  Click on a function name for more information about that function.  See also Fitting Options for Ternary Plots.

  Linear Smooth	  Special Cubic Smooth

  Quadratic Smooth	  Custom Function

  Full Cubic Smooth

Note:  User-defined functions can be specified in the Plot Layout dialog.  These functions are plotted over (i.e., overlaid) and not fitted to the data.  In order to fit (and plot) user-defined functions to the data, use the Nonlinear Estimation module.

Category

Data Range

Graphs gallery

Options


Categorized Ternary Plots - Variables

  Stats Graphs Categorized Ternary Plots - Variables

When you click on this button, a standard variable selection dialog will open in which you can select the variable(s) to be plotted and the grouping variable to be categorized for the graph.  Note that the selected grouping variable does not have to be categorical (e.g., contain codes); you can use one of the Methods of Categorization to categorize continuous variables.  The selection of a grouping variable is not necessary if the categories are defined via the Multiple Subset method.


Categorized Ternary Plots - Data Range

  Stats Graphs Categorized Ternary Plots - Data Range

Ignore cases with invalid sums:  This option will allow you to manage cases within specified subsets (categories) in which the component proportions do not add to the constrained value.  If you select this option, STATISTICA will ignore cases in which the proportions add to a specified expected sum.  If you de-select this option, then STATISTICA will rescale the proportions so that they add to 1 in each case.

Ignore out of range cases:  When selected, this option allows you to specify ranges of values within specified subsets (categories) for each of the component variables (X, Y, and/or Z) that will be considered valid.  Cases which have values that fall outside (above or below) the respective ranges will be ignored.


Categorized Ternary Plots - Graphs Gallery

  Stats Graphs Categorized Ternary Plots - Graphs Gallery

Click on this button ( [image]) in order to bring up the STATISTICA Graphs Gallery dialog.  This dialog will allow you to easily "switch" between different types of graphs.


Categorized Ternary Plots - Options

  Stats Graphs Categorized Ternary Plots - Options

Click on this button to open the Stats Graphs: Options dialog from which you can adjust some global options that will affect the graph display, fitted function, scale, orientation, etc.


Categorized Ternary Plots - Category

  Stats Graphs Categorized Ternary Plots - Category

These options allow you to choose the method of categorization for the ternary graph (i.e., for the grouping variable that will be used to categorize values of the component and response variables in each small graph; note that grouping variables do not need to be specified if Multiple Subset categories are selected).

Each of the methods is discussed in the Method of Categorization topic.


  Structural Equation Modeling - Contents

Getting Started with the Structural Modeling Module

Conceptual Overview

The Basic Idea Behind Structural Modeling

Structural Equation Modeling and the Path Diagram

Rules for SEPATH Path Diagrams

Inputting Path Diagrams with the PATH1 Language

Models for Two or More Groups

Structured Means Models with Intercept Variables

Program Operation - Overview

Startup Panel

Path Wizards

Confirmatory Factor Analysis

Structural Modeling

Analysis Parameters

Monte Carlo Setup

Analysis Results

Monte Carlo Results

Examples

1.	Stability of Alienation

2.	Confirmatory Factor Analysis

3.	Confirmatory Factor Analysis with Identifying Constraints

4.	Effects of Peer Influence on Ambition

5.	Standardized Solution for the Effects of Peer Influence on Ambition

6.	Factor Analysis with an Intercept Variable

7.	Comparing Factor Structure in Two Groups

8.	Testing for Circumplex Structure

9.	Testing for Stability of a Correlation Matrix Over Time

10.	A Multiple Regression Model for Home Environment and Mathematics Achievement

11.	Structural Models for Home Environment and Mathematics Achievement

12.	Test Theory Models for Sets of Congeneric Tests

13.	Comparing Dependent Variances

14.	A Multi-Trait Multi-Method Model

15.	A Longitudinal Factor Analysis Model

16.	A Structural Model for 10 Personality and Drug Use Variables

17.	A Test for Compound Symmetry

18. 	Testing the Equality of Correlation Matrices from Different Populations


  Getting Started with the Structural Modeling Module

The Structural Equation Modeling (SEPATH) module is designed to allow you to fit a wide variety of structural equation models to your data in a user-friendly, interactive environment.  You will find many features in this module designed to allow you to move quickly and effectively from conceptualization of a model to its specification and testing.

We suggest that you begin by working through the Introductory Tutorial in the manual.  The tutorial will introduce you to our Wizards and Path Construction Tool, which allow you to specify even the most complicated structural model in just a few moments, with virtually no typing.  The tutorial will also acquaint you with the basic aspects of program operation.

Finally, work through the Examples in the Electronic Manual.  These will introduce you to a few of the kinds of models the program is capable of handling.

See also, Program Operation - An Overview


  Program Operation - An Overview

The Structural Equation Modeling (SEPATH) module offers a huge number of options.  Although program operation is simplified in many ways, relative to similar programs, there are many options to master.  The basic operation of fitting a structural model to data can be broken down into the following basic steps:

(1)	Open the appropriate data file.  This can be done from the Startup Panel.

(2)	Decide on the appropriate structural model.  This requires some familiarity with the basic concepts of structural equation modeling.

(3)	Express your model as a path diagram.

(4)	Translate the path diagram into the PATH1 language.

(5)	Enter the PATH1 commands into a program instruction file (usually with file extension *.cmd).  You can do this by hand, using the program text editor in the SEPATH module (or any ASCII text editor).  However, you will find that this can be done, in a few minutes, with virtually no typing, using the program's user interface, which has been specifically designed to make this task as effortless as possible.  For simple structural models or confirmatory factor models, use the Path Wizards.  For more complex or unusual models, use the Path Construction Tool.

(6)	Set the program Analysis Parameters to the analysis options required for your particular model.

(7)	Start program execution.

(8)	Examine program results.  To enhance the interactive nature of the process, the program will automatically open a text window and display your path model, in the PATH1 language, with numerical estimates for all parameters included.  If you click OK after iteration, the program will open a Results Window, in which you may examine a wide variety of indices reflecting the fit of your model.

For more information, see the following topics:

Conceptual Overview

The Basic Idea Behind Structural Modeling

Structural Equation Modeling and the Path Diagram

Rules for SEPATH Path Diagrams

Inputting Path Diagrams with the PATH1 Language

Models for Two or More Groups

Structured Means Models with Intercept Variables


  Structural Equation Modeling - A Conceptual Overview

Structural Equation Modeling is a very general, very powerful multivariate analysis technique that includes specialized versions of a number of other analysis methods as special cases.  We will assume that you are familiar with the basic logic of statistical reasoning as described in Elementary Concepts.  Moreover, we will also assume that you are familiar with the concepts of variance, covariance, and correlation; if not, we advise that you read the Basic Statistics chapter at this point.  Although it is not absolutely necessary, it is highly desirable that you have some background in factor analysis before attempting to use structural modeling.

Major applications of structural equation modeling include:

(1)	causal modeling, or path analysis, which hypothesizes causal relationships among variables and tests the causal models with a linear equation system.  Causal models can involve either manifest variables, latent variables, or both;

(2)	confirmatory factor analysis, an extension of factor analysis in which specific hypotheses about the structure of the factor loadings and intercorrelations are tested;

(3)	second order factor analysis, a variation of factor analysis in which the correlation matrix of the common factors is itself factor analyzed to provide second order factors;

(4)	regression models, an extension of linear regression analysis in which regression weights may be constrained to be equal to each other, or to specified numerical values;

(5)	covariance structure models, which hypothesize that a covariance matrix has a particular form.  For example, you can test the hypothesis that a set of variables all have equal variances with this procedure;

(6)	correlation structure models, which hypothesize that a correlation matrix has a particular form.  A classic example is the hypothesis that the correlation matrix has the structure of a circumplex (Guttman, 1954; Wiggins, Steiger, & Gaelick, 1981).

Many different kinds of models fall into each of the above categories, so structural modeling as an enterprise is very difficult to characterize.

Most structural equation models can be expressed as path diagrams.  This program uses a command language (PATH1) that looks very much like a path diagram.  Consequently even beginners to structural modeling can perform complicated analyses with a minimum of training.

For more information, see the following topics:

The Basic Idea Behind Structural Modeling

Structural Equation Modeling and the Path Diagram

Rules for SEPATH Path Diagrams

Inputting Path Diagrams with the PATH1 Language

Models for Two or More Groups

Structured Means Models with Intercept Variables


  The Basic Idea Behind Structural Modeling

One of the fundamental ideas taught in intermediate applied statistics courses is the effect of additive and multiplicative transformations on a list of numbers.  Students are taught that, if you multiply every number in a list by some constant K, you multiply the mean of the numbers by K.  Similarly, you multiply the standard deviation by the absolute value of K.

For example, suppose you have the list of numbers 1,2,3.  These numbers have a mean of 2 and a standard deviation of 1.  Now, suppose you were to take these 3 numbers and multiply them by 4.  Then the mean would become 8, and the standard deviation would become 4, the variance thus 16.

The point is, if you have a set of numbers X related to another set of numbers Y by the equation Y = 4X, then the variance of Y must be 16 times that of X, so you can test the hypothesis that Y and X are related by the equation Y = 4X indirectly by comparing the variances of the Y and X variables.

This idea generalizes, in various ways, to several variables inter-related by a group of linear equations.  The rules become more complex, the calculations more difficult, but the basic message remains the same -- you can test whether variables are interrelated through a set of linear relationships by examining the variances and covariances of the variables.

Statisticians have developed procedures for testing whether a set of variances and covariances in a covariance matrix fits a specified structure.  The way structural modeling works is as follows:

(1)	You state the way that you believe the variables are inter-related, often with the use of a path diagram.

(2)	The program works out, via some complex internal rules, what the implications of this are for the variances and covariances of the variables.

(3)	The program tests whether the variances and covariances fit this model of them.

(4)	The program reports the results of the statistical testing, and also returns parameter estimates and standard errors for the numerical coefficients in the linear equations.

(5)	On the basis of this information, you decide whether the model seems like a good fit to your data.

There are some important, and very basic logical points to remember about this process.  First, although the mathematical machinery required to perform structural equations modeling is extremely complicated, the basic logic is embodied in the above 5 steps.  Below, we diagram the process.

Second, we must remember that it is unreasonable to expect a structural model to fit perfectly  for a number of reasons.  A structural model with linear relations is only an approximation.  The world is unlikely to be linear.  Indeed, the true relations between variables are probably nonlinear.  Moreover, many of the statistical assumptions are somewhat questionable as well.  The real question is not so much, "Does the model fit perfectly?" but rather, "Does it fit well enough to be a useful approximation to reality, and a reasonable explanation of the trends in our data?"

Third, we must remember that simply because a model fits the data well does not mean that the model is necessarily correct.  One cannot prove that a model is true  to assert this is the fallacy of affirming the consequent.  For example, we could say "If Joe is a cat, Joe has hair."  However, "Joe has hair" does not imply Joe is a cat.  Similarly, we can say that "If a certain causal model is true, it will fit the data."  However, the model fitting the data does not necessarily imply the model is the correct one.  There may be another model that fits the data equally well.

For more information, see the following topics:

Conceptual Overview

Structural Equation Modeling and the Path Diagram

Rules for SEPATH Path Diagrams

Inputting Path Diagrams with the PATH1 Language

Models for Two or More Groups

Structured Means Models with Intercept Variables


  Structural Equation Modeling and the Path Diagram

Path Diagrams play a fundamental role in structural modeling.  Path diagrams are like flowcharts.  They show variables interconnected with lines that are used to indicate causal flow.

One can think of a path diagram as a device for showing which variables cause changes in other variables.  However, path diagrams need not be thought of strictly in this way.  They may also be given a narrower, more specific interpretation.

Consider the classic linear regression equation

Y = aX + e

Any such equation may be represented in a path diagram as follows:

Such diagrams establish a simple isomorphism.  All variables in the equation system are placed in the diagram, either in boxes or ovals.  Each equation is represented on the diagram as follows:  All independent variables (the variables on the right side of an equation) have arrows pointing to the dependent variable.  The weighting coefficient is placed above the arrow.  The above diagram shows a simple linear equation system and its path diagram representation.

Notice that, besides representing the linear equation relationships with arrows, the diagrams also contain some additional aspects.  First, the variances of the independent variables, which we must know in order to test the structural relations model, are shown on the diagrams using curved lines without arrowheads attached.  We refer to such lines as wires.  Second, some variables are represented in ovals, others in rectangular boxes.  Manifest variables are placed in boxes in the path diagram.  Latent variables are placed in an oval or circle.  For example, the variable E in the above diagram can be thought of as a linear regression residual when Y is predicted from X.  Such a residual is not observed directly, but calculated from Y and X, so we treat it as a latent variable and place it in an oval.

The example discussed above is an extremely simple one.  Generally, we are interested in testing models that are much more complicated than these.  As the equation systems we examine become increasingly complicated, so do the covariance structures they imply.  Ultimately, the complexity can become so bewildering that we lose sight of some very basic principles.  For one thing the train of reasoning which supports testing causal models with linear structural equations testing has several weak links.  The variables may be non-linear.  They may be linearly related for reasons unrelated to what we commonly view as causality.  The ancient adage, "correlation is not causation" remains true, even if the correlation is complex and multivariate.  What causal modeling does allow us to do is examine the extent to which data fail to agree with one reasonably viable consequence of a model of causality.  If the linear equations system isomorphic to the path diagram does fit the data well, it is encouraging, but hardly proof of the truth of the causal model.

Although path diagrams can be used to represent causal flow in a system of variables, they need not imply such a causal flow.  Such diagrams may be viewed as simply an isomorphic representation of a linear equations system.  As such, they can convey linear relationships when no causal relations are assumed.  Hence, although one might interpret the diagram in the above figure to mean that "X causes Y," the diagram can also be interpreted as a visual representation of the linear regression relationship between X and Y.

For more information, see the following topics:

Conceptual Overview

The Basic Idea Behind Structural Modeling

Rules for SEPATH Path Diagrams

Inputting Path Diagrams with the PATH1 Language

Models for Two or More Groups

Structured Means Models with Intercept Variables


Rules for SEM Path Diagram

  Rules for SEPATH Path Diagrams

In this section, we establish rules for path diagrams which will guarantee that the diagram will represent accurately any model which fully accounts for all variances and covariances of all variables, both manifest and latent.  Our rules are based on the following considerations.

Path diagrams consist of variables connected by wires and arrows, representing, respectively, undirected and directed relationships.  These variables must be endogenous or exogenous.  They must also be manifest or latent.  Hence any variable can be classified into 4 categories:  (a) manifest endogenous, (b) manifest exogenous, (c) latent endogenous, and (d) latent exogenous.

If random variables are related by linear equations, then variables which are endogenous have variances and covariances which are determinate functions of the variables on which they regress.  For example if X and Y are orthogonal and [image], then

.

Hence, one way of guaranteeing that a diagram can account for variances and covariances among all its variables is to require:  (1) representation of all variances and covariances among exogenous variables, (2) no variances or covariances to be directly represented in the diagram for endogenous variables, and (3) all variables in the diagram be involved in at least one relationship.

There is a significant practical problem with many path diagrams  lack of space.  In many cases, there are so many exogenous variables that there is simply not enough room to represent, adequately, the variances and covariances among them.  Diagrams which try often end up looking like piles of spaghetti.  For a beautiful example of a spaghetti diagram, see page 147 of James, Mulaik, and Brett (1982).

One way of compensating for this problem is to include rules for default variances and covariances which allow a considerable number of them to be represented implicitly in the diagram.

These considerations lead to the following rules:

(1)	Manifest variables are always represented in boxes (squares or rectangles) while latent variables are always in ovals or circles.

(2)	Directed relationships are always represented explicitly with arrows between two variables.

(3)	Undirected relationships need not be represented explicitly.  (See rule 9 below regarding implicit representation of undirected relationships.)

(4)	Undirected relationships, when represented explicitly are shown by a wire from a variable to itself, or from one variable to another.

(5)	Endogenous variables may never have wires connected to them.

(6)	Free parameter numbers for a wire or arrow are always represented with integers placed on or slightly above the middle of the wire or arrow line.

(7)	Fixed values for a wire or arrow are always represented with a floating point number containing a decimal point.  The number is generally placed on or slightly above the middle of the wire or arrow line.

(8)	Different statistical populations are represented by a line of demarcation and the words Group 1 (for the first population or group), Group 2, etc., in each diagram section.

(9)	All exogenous variables must have their variances represented either explicitly or implicitly.  If variances and covariances are not represented explicitly, then the following rules hold:

a)	For latent variables, variances not explicitly represented in the diagram are assumed to be 1.0, and covariances not explicitly represented are assumed to be 0.

b)	For manifest variables, variances and covariances not explicitly represented are assumed to be free parameters each having a different parameter number.  These numbers are not equal to any number appearing explicitly in the diagram.

By adopting a consistent standard for path diagrams, we can facilitate clear communication of path models, regardless of what system is used to analyze them.  Besides standing on their own as a coherent standard for path diagrams, the above rules for SEPATH PATH diagrams are designed to match the PATH1 language, and allow quick translation from the diagram to the language, and vice-versa.

Within this manual we will adhere to these simplifying conventions.  However, the typical SEPATH user will attempt to use the program to reproduce results from published papers employing a wide variety of standards for their path diagrams.  In some cases this will create no problems, and the user will be able to translate directly to and from the published path diagram to a PATH1 representation of the model.  However, experience indicates that it is often useful to translate published diagrams into an SEPATH diagram, i.e., one which obeys rules 1-9 above, before coding the diagram in the PATH1 language.  Frequently the translation process will draw attention to errors or ambiguities in the published diagram.  (See Resolving Ambiguities in Path Diagrams for a discussion of this problem.)

For more information, see the following topics:

Conceptual Overview

The Basic Idea Behind Structural Modeling

Rules for SEPATH Path Diagrams

Inputting Path Diagrams with the PATH1 Language

Models for Two or More Groups

Structured Means Models with Intercept Variables


  Resolving Ambiguities in Path Diagrams

The figure below shows a portion (this is not a complete diagram and it does not conform to SEPATH diagramming rules) of a path diagram which is quite typical of what is found in the literature.  Some of the diagram is clear and routine, but what do we make of the symbols D1 and D2? Variable L1 is a latent exogenous variable.  It has arrows pointing away from it and no arrows pointing to it.  Since, by rule 9 for SEPATH diagrams, all exogenous variables must have their variances and covariances explained, the most reasonable assumption is that D1 stands for the variance of latent variable L1.  Hence, we modify the diagram to make D1 a parameter attached to a wire from L1 to itself.

A Section From an Ambiguous Path Diagram

But what are we to make of D2?  In the diagram it looks just like D1, but on closer inspection we find it must mean something different.  D2 is connected to L2, and L2 is an endogenous latent variable.  Consequently, the most reasonable interpretation is that D2 represents an error variance for latent variable L2.  We represent it with an error latent variable E2 with variance D2.

The revised path diagram, accurately reflecting the author's model, is shown in the next figure.

In some cases you will have to be creative, tenacious, and lucky to figure out what the author intended.  Even the most accomplished and generally careful authors will leave out paths, forget to mention that some values were fixed rather than free parameters, or simply misrepresent the model actually tested.  Sometimes the only way to figure out what the author actually did is to try several models with SEPATH, until you find coefficients which agree with the published values.  Sometimes even this approach will not work, because on occasion correlation or covariance matrices are printed incorrectly.

Revised Version of the Diagram

Needless to say, if authors were to adopt SEPATH diagramming rules and/or report their models in the PATH1 language, these problems would be reduced.

Some path diagrams do not represent the error variance attached to endogenous latent variables at all -- they leave this to the reader to figure out for him/her self.  Whenever an endogenous latent variable has no error term, you should suspect that an error latent variable has been left out, especially if your degrees of freedom don't agree with those of the published paper.

For more information, see the following topics:

Conceptual Overview

The Basic Idea Behind Structural Modeling

Structural Equation Modeling and the Path Diagram

Rules for SEPATH Path Diagrams

Inputting Path Diagrams with the PATH1 Language

Models for Two or More Groups

Structured Means Models with Intercept Variables


  Inputting Path Diagrams with the PATH1 Language

PATH1 is a computer language designed to mimic the appearance of a path diagram as best as possible within a completely portable, character-based environment.  PATH1 programs are written in ordinary text files, yet they are easy to relate to a typical path diagram.

PATH1 was designed to allow quick conversion of SEPATH path diagrams to a form where they can be read by a computer.  Here are the rules for the PATH1 language.

(1)	Each arrow and wire is represented on a separate line.

(2)	Blanks never count.  They are stripped from the line before parsing.

(3)	Manifest variable names are represented as the FULL variable name enclosed within brackets.  The name enclosed in brackets must follow the rules for a STATISTICA variable name.  The name thus can be at most 8 alphanumeric characters in length.  Characters must be upper case.  The underscore character "_" is also allowed.

Examples.	[MATH1]
[HS_MATH]
[ANXIETY]

(4)	Latent variable names are represented by a variable name in parentheses.  The name can be up to 20 characters in length.  Upper and lower case characters are allowed, and are distinguished.  Underscores are allowed, but dashes are not allowed.

Examples.	(Verbal_Intelligence)
(Explosive_Strength)

(5)	Directed relationships are represented in the following form in a PATH1 input line:

Example.	VNAME1-<#1>{<#2>}->VNAME2

where VNAME1 and VNAME2 are valid manifest or latent variables adhering to rules 3 and 4 above, <#1> is an integer representing the coefficient number, and <#2> is a real value representing the start value.

If VNAME1 is omitted, then the program will find the last preceding line with two variable names and use the first variable name as VNAME1.

<#1> is required if the path has a coefficient which is a free parameter.  If the coefficient is a fixed value, <#1> is omitted.  Otherwise, <#1> is the integer value for the parameter number.  It must be between 1 and 30000 in value.

If the coefficient for the arrow is a free parameter, then <#2> is the starting value used during iteration.  If the coefficient is fixed, then <#2> represents the fixed value.  If both <#1> and <#2> are omitted, then the path is assumed to have a fixed coefficient with a value of 1.

Examples.	(IQ_10)-1->[WECHSLER]
(X)-->[Y]

(6)	Undirected relationships are presented in the following form

VNAME1-<#1>{<#2>}-VNAME2

where VNAME1, VNAME2, <#1>, and <#2> are the same as in the preceding section.  If VNAME1 is omitted, then the program will find the last preceding line with two variable names and use the first variable name as VNAME1.

Examples.	(L1)-1-(L2)
(Intelligence)-{.5}-(Success)

(7)	Different statistical populations are denoted in the PATH1 language by a GROUP statement of the form

GROUP <#>

where <#> is the number of the population.  All PATH1 files begin (implicitly) with a GROUP 1 statement.  All statements are assumed to refer to the group referenced in the last GROUP statement.  Before beginning a new group, you must terminate a block of lines with the command

ENDGROUP

(8)	Blank lines, and any lines beginning with an * (asterisk), are treated as comment lines, and are not analyzed as PATH1 statements.

Each element in a SEPATH path diagram has an obvious corresponding element in PATH1.  However there is one situation where the SEPATH diagram may represent information implicitly which must be expressed explicitly in the PATH1 representation.  This is when the model has manifest exogenous variables.  As noted in section 9b of the rules for path diagrams, the diagram allows you the option of not representing all the variances and covariances among exogenous manifest variables explicitly.  However, for reasons of computational efficiency, the user must follow one of two courses of action.  If either the Fixed or Free option has been checked in the Manifest Exogenous box in the Parameters dialog, then no variances and covariances among exogenous manifest variables are to be expressed explicitly in the diagram.  If the User option is selected, then all variances and covariances among exogenous manifest variables must be expressed explicitly in the PATH1 representation.  This restriction in the program (rather than the PATH1 language itself) presents few problems in practice.

For more information, see the following topics:

Conceptual Overview

The Basic Idea Behind Structural Modeling

Structural Equation Modeling and the Path Diagram

Rules for SEPATH Path Diagrams

Models for Two or More Groups

Structured Means Models with Intercept Variables


  Structural Models for Two or More Groups

SEPATH provides a very simple method for specifying models for several populations, or groups.  Each model is input as a separate unit of code.  Models are specified in exactly the same way as they are for a single group.  Path coefficients that are constrained to be equal across groups are given the same coefficient in all groups.  The model is input in the following form for two groups:

GROUP 1

[program lines for the model for the first group]

.

.

.

ENDGROUP

GROUP 2

[program lines for the model for the first group]

.

.

.

ENDGROUP

The system is extended in the obvious way for models for more than 2 groups.

For more information, see the following topics:

Conceptual Overview

The Basic Idea Behind Structural Modeling

Structural Equation Modeling and the Path Diagram

Rules for SEPATH Path Diagrams

Inputting Path Diagrams with the PATH1 Language

Structured Means Models with Intercept Variables


  Structural Equation Modeling - Startup Panel

For a Table of Contents for the Structural Equation Modeling part of the Electronic Manual, including references to a general conceptual overview of structural modeling, see Structural Equation Modeling - Contents.

You can think of the Startup Panel dialog as a Master Control Panel that directs access to the many functions of the structural modeling program.  Each structural modeling job requires a data (*.sta) file, and a model (*.cmd) file.  The Startup Panel displays the names of these current files, and the number of groups currently selected for analysis.

There is no variable selection dialog in this module.  Whatever variables are included in the model file are selected automatically for analysis.

Basic Options

Cancel button:  This button closes the Startup Panel  window, and places the cursor in the top window underneath the panel.

Open Data button:  This button activates a standard data file selection dialog.  The data file is either raw data or a covariance or correlation matrix previously created via Factor Analysis or another STATISTICA module (e.g., Basic Statistics, Multiple Regression, Canonical Analysis, Reliability and Item Analysis, or directly via Data Management, see also, Matrix File Format).

Cases button:  This button opens a standard case selection dialog.

PATH MODEL Group

Open Model button:  This button opens a standard Open File dialog, for opening a *.cmd file for analysis and/or modification.

New Model button:  This button opens a new model file, with the temporary name New.cmd, in a separate text window.

Edit Text of Model button:  This button brings up the text edit window containing the current program (*.cmd) file.  You may edit the file directly in this window.  This can be especially useful if you wish to format the text in the file to make it more readable, or add last minute comments.

Edit with Path Tool button:  This button activates the Path Tool, a user-friendly interface specially designed for fast, error-free entry of path analysis programs.  The current program (*.cmd file) is automatically opened by the Path Tool for editing.

Use Path Wizards button:  This button activates a dialog to allow you to select one of the special Path Wizards.  These Wizards lead you, step by step, through the construction of certain common types of path models.

OK (Execute Current Model) button:  This button causes the current path model to be tested on the currently entered data, using the analysis options currently selected in the Analysis Parameters dialog.

OPTIONS Group

Specify Groups:  If your data file is a multiple group correlation or covariance matrix file, you may analyze one or several groups.  This button activates a Specify Number of Groups dialog to allow you to define the number of groups to be analyzed.  If your data file is a raw data file, the button activates a Specify Grouping Variable dialog to allow you to specify a variable used to categorize the groups to be analyzed.

Set Parameters:  Before leaving the Startup Panel, you can use this option to activate the Analysis Parameters dialog, in order to adjust the parameters for the analysis.

Review Descriptives:  This button calls up a dialog that allows you to review a variety of descriptive statistics if you have raw data to analyze.

MONTE CARLO Group

The structural equation modeling module has extensive capabilities for performing Monte Carlo analyses.

Perform Analysis:  This button starts the Monte Carlo experiment.  First, you will be presented with the Monte Carlo Setup dialog.  When you terminate the dialog by clicking OK, the Monte Carlo will be executed, using the setup parameters you selected.  Progress will be indicated in the status bar at the bottom of the screen.

Review Results:  This button activates a Monte Carlo Results dialog for reviewing the results from the most recently completed Monte Carlo experiment.


  Structural Equation Modeling - Analysis Parameters

This allows you to select the numerous parameters and options for the analysis.  The following groups of options are available in this dialog.  Double-click on the group description for a full explanation of the options for that group.

Convergence Criteria

Data to Analyze

Discrepancy Function

Global Iteration Parameters

Initial Values

Line Search Method

Line Search Parameters

Manifest Exogenous

Output Options

Standardization


  Analysis Parameters - Data to Analyze

In this box of the Analysis Parameters dialog, you select which type of data to analyze.  For standard path analyses or structural equation models, you choose either Covariances or Correlations, for models specifying intercepts, or structured means, you must specify the Moments option.

Data to Analyze options:

Covariances:  If you select this option, the program will analyze the Covariance Matrix of the input variables, regardless of what kind of data are input.  So, for example, if you input a correlation matrix file with standard deviations, SEPATH will calculate the covariance matrix and analyze it.  If your input file is a covariance matrix file, SEPATH will analyze it directly.  If your file contains raw data, SEPATH will analyze it and calculate the covariance matrix for you.

The statistical distribution of the elements of a covariance matrix is not the same as that of a correlation matrix.  This is obvious if you consider the diagonal elements of a covariance matrix, which are the variances of the variables.  These are random variables  they vary from sample to sample.  On the other hand, the diagonal elements of a correlation matrix are not random variables  they are always 1.  The methods employed by previous structural modeling programs are based on the assumption that a covariance matrix is being analyzed.  The sampling distribution theory they employ is not applicable to a correlation matrix, except in special circumstances.

Recent research has emphasized that it is possible (indeed likely) that you will get some wrong results if you analyze a correlation matrix as if it were a covariance matrix.  However, a number of currently distributed structural modeling programs will analyze a correlation matrix as though it were a covariance matrix.  The fact that such programs yield incorrect results has been described in the literature (see, for example, Cudeck, 1989).  In order to provide compatibility with these other programs, SEPATH will analyze a correlation matrix as if it were a covariance matrix, but it can, unlike most other programs, directly and automatically provide correct analysis of a correlation matrix as well.

Correlations:  If you select this option, SEPATH will calculate the correlation matrix from the input data and analyze it.  SEPATH analyzes the correlation matrix correctly, using constrained estimation theory developed by Michael Browne (see Browne, 1982; Mels, 1989; Browne & Mels, 1992), and implemented first in the computer program RAMONA.  As a result, SEPATH gives the correct standard errors, estimates, and test statistics when a correlation matrix is analyzed directly.  When combined with the Standardization -- New option SEPATH can estimate a completely standardized path model, where all variables are standardized to have unit variance, and standard errors can be estimated as well.

Moments:  If you select this option, SEPATH will analyze the augmented product-moment matrix instead of the covariance matrix.  This option is selected if you are analyzing models involving intercepts or structured means.  SEPATH will also add, to the input variable list, an additional variable called CONSTANT that always takes on the value 1.  CONSTANT is a dummy variable used to represent means in structured means models, i.e., those with an intercept variable.

For more options in the Analysis Parameters dialog, see:

Convergence Criteria

Discrepancy Function

Global Iteration Parameters

Initial Values

Line Search Method

Line Search Parameters

Manifest Exogenous

Output Options

Standardization


  Analysis Parameters - Discrepancy Function

In this section of the Analysis Parameters dialog, the user selects which discrepancy function or functions will be minimized to yield parameter estimates.  Consult the manual section on Statistical Estimation for an in-depth discussion of these methods.

Discrepancy Function options:

Maximum Likelihood (ML):  If this option is selected, SEPATH performs Maximum Wishart Likelihood estimation if Correlations or Covariances are analyzed, and Maximum Normal Likelihood estimation if Moments are analyzed.

Generalized Least Squares (GLS):  If this option is selected, SEPATH performs Generalized Least Squares estimation.

GLS --> ML (GLS followed by ML):  By default, this option is selected.  SEPATH performs 5 iterations using the Generalized Least Squares estimation procedure, regardless of the current setting in the Maximum No. of Iterations field in the Global Iteration Parameters group in the Analysis Parameters dialog.  At that point it shifts to Maximum Likelihood Estimation (see above).

Ordinary Least Squares (OLS):  If this option is selected, SEPATH performs Ordinary Least Squares estimation.

Asymptotically Distribution Free Gramian (ADFG):  SEPATH performs Asymptotically Distribution Free estimation, which does not require the assumption of multivariate normality.  In this variant, the weight matrix is guaranteed to be Gramian.  As a preliminary to ADFG estimation, SEPATH performs GLS estimation.

Asymptotically Distribution Free Unbiased (ADFU):  SEPATH performs Asymptotically Distribution Free estimation, which does not require the assumption of multivariate normality.  In this variant, the weight matrix is an unbiased estimate of the true weight matrix.  However, this estimated matrix may not be Gramian (i.e., invertible) in all cases.  If it is not, SEPATH will give an error message.  At that point, the user should restart the estimation using the ADFG option.  As a preliminary to ADFU estimation, SEPATH performs GLS estimation.

For more options in the Analysis Parameters dialog, see:

Convergence Criteria

Data to Analyze

Global Iteration Parameters

Initial Values

Line Search Method

Line Search Parameters

Manifest Exogenous

Output Options

Standardization


  Analysis Parameters - Standardization

In this section of the Analysis Parameters dialog, the user chooses to generate either a standardized solution (where latent variables all have unit variance) by one of two methods, or an unstandardized solution.

Standardization options:

New:  If this option is selected, SEPATH estimates a standardized solution via constrained estimation.  This approach produces a solution where all latent variables, both independent and dependent, have variances of 1.  Unlike the old method, however, standard errors are available with this option.  Combining this option with the Data to Analyze - Correlations option available in the Analysis Parameters dialog allows one to estimate a completely standardized path model, where all variables, manifest and latent, have unit variances, and standard errors can be estimated for all parameters.

Old:  Older programs generate a standardized solution after iteration is complete, then perform a calculation after the fact to transform the solution to a standardized form.  This method gets a solution faster than the New option described above, because it does not need to use constrained estimation.  However, standard errors cannot be computed.

None:  An unstandardized solution is calculated.

For more options in the Analysis Parameters dialog, see:

Convergence Criteria

Data to Analyze

Discrepancy Function

Global Iteration Parameters

Initial Values

Line Search Method

Line Search Parameters

Manifest Exogenous

Output Options


  Analysis Parameters - Manifest Exogenous

Most models do not have manifest variables that are exogenous.  If a model does have such variables, their variances and covariances must be accounted for.  In most cases (but not all), the variances and covariances estimated under one of the standard estimation techniques will be identical to the observed variances and covariances, and consequently these parameters are not of much interpretive interest.  SEPATH provides two approaches to calculating these parameters automatically and keeping them out of view (the Fixed and Free options below) and also allows them to be declared explicitly.

Manifest Exogenous options:

Fixed:  In this case, the variances and covariances for manifest exogenous variables are fixed (at the value of the observed variances and covariances) during iteration, then treated as if they were free parameters at the end of iteration.  This approach eliminates, in the case of several manifest exogenous variables, the addition of a number of extra free parameters, which can slow down iteration and make it less reliable.  The user should take the output obtained by this approach, and resubmit it using the Free option described below to guarantee correct estimates.  If you select this option and attempt (in the PATH1 input) to specify the variance or covariance of a manifest exogenous variable, you will generate an error message.

Free:  If this option is selected, the variances and covariances among the manifest exogenous variables are treated as free parameters and added to the model, although their values are not shown.  Start values are the observed variances and covariances.  If you select this option and attempt (in the PATH1 input) to specify the variance or covariance of a manifest exogenous variable, you will generate an error message.

User:  If this option is selected, you must specify the variances and covariances of all manifest exogenous variables, using standard PATH1 syntax.

For more options in the Analysis Parameters dialog, see:

Convergence Criteria

Data to Analyze

Discrepancy Function

Global Iteration Parameters

Initial Values

Line Search Method

Line Search Parameters

Output Options

Standardization


  Analysis Parameters - Output Options

The options in this box of the Analysis Parameters dialog allow you some preliminary control over the appearance of your output.  You can preselect the number of decimal places to be printed in output Scrollsheets, and you can select whether or not to print estimated standard errors for model coefficients.

Output options:

No.  of Decimal Places:  Here you can set the number of decimal places displayed by default in the text output, in the Results Text Window and output Scrollsheets.  The number can be between 1 and 6.

Standard Errors:  If this box is checked, the program will display estimated standard errors for all parameters in the PATH1 text output, and Model Summary Scrollsheet.  However, if OLS estimation is performed, or the "old" standardization method is employed, standard errors will not be available.

For more options in the Analysis Parameters dialog, see:

Convergence Criteria

Data to Analyze

Discrepancy Function

Global Iteration Parameters

Initial Values

Line Search Method

Line Search Parameters

Manifest Exogenous

Standardization


  Analysis Parameters - Convergence Criteria

In this box of the Analysis Parameters dialog you can adjust constants that can directly affect when the program decides convergence has occurred during iteration.  The default values produce desirable results for a wide variety of problems, and you will seldom need to adjust these criteria.

Convergence Criteria Parameters:

Maximum Residual Cosine Criterion:  This criterion becomes small when parameter values have stabilized.  You may alter this criterion in the input field.  The default value of .0001 works well across a wide variety of situations.  For a technical definition of this criterion and a discussion of its merits, see the manual discussion of Unconstrained Minimization Techniques.

Relative Function Change Criterion:  This criterion becomes small when the discrepancy function being minimized (see the manual section on Statistical Estimation Theory for a discussion) is no longer changing.  On occasion, especially when boundary cases are encountered, it will not be possible for the program to iterate to a point where a local or global minimum is obtained.  In that case, the Maximum Residual Cosine criterion may not fall below, but the discrepancy function will not change.  At that point, this criterion will stop iteration.  In general, it should be kept very low, or it may cause iteration to terminate prematurely.  For a technical definition of the criterion see the manual discussion of Unconstrained Minimization Techniques.

For more options in the Analysis Parameters dialog, see:

Data to Analyze

Discrepancy Function

Global Iteration Parameters

Initial Values

Line Search Method

Line Search Parameters

Manifest Exogenous

Output Options

Standardization


  Analysis Parameters - Global Iteration Parameters

In this box of the Analysis Parameters dialog, you enter parameters that control the basic iterative process.  For a technical description of the iteration process, see the manual section on Unconstrained Minimization Techniques.

Global Iteration Parameters:

Maximum Number of Iterations:  In this field, you enter the maximum number of iterations allowed.  The default number is 30.  When this number of iterations is reached, the iterative process will automatically terminate, and a message will be issued to indicate that the maximum number of iterations was exceeded.  Minimum is zero (in which case the discrepancy function and estimated covariance matrix will be computed, and control will be returned to the user), maximum is 1000.

Maximum Step Length:  In this field, you enter the maximum length of the step vector that will be allowed.  See the manual section on Unconstrained Minimization Techniques for a discussion of this parameter.  See the manual discussion of Solving Iteration Problems for suggestions on how to use this parameter to solve some problems encountered during iteration.

No.  of Steepest Descent Iterations:  In this field, you enter a number of Steepest Descent Iterations to proceed the standard iterations.  See the discussion of Solving Iteration Problems in the manual for suggestions on how to use this parameter to solve some problems encountered during iteration.

Step Tolerance:  In this field, you enter a Tolerance value for when a parameter is temporarily eliminated from the iterative process.  The tolerance value is basically one minus the squared multiple correlation of a parameter with the other parameters.  If a parameter becomes highly redundant with other parameters during iteration, the approximate Hessian employed during Gauss-Newton iteration becomes unstable.  This parameter controls when a parameter is temporarily removed from the iterative process.  Very low values of this parameter mean that a parameter will never be removed.  This can cause iteration to "blow up" if the approximate Hessian becomes nearly singular.  High Values mean that parameters will not be varied while they are moderately correlated with other parameters.  This can cause iteration to fail if parameters are fairly highly correlated at the solution point.  Change this parameter seldom, and in small increments.  The default value seems to work well on a wide range of problems.

For more options in the Analysis Parameters dialog, see:

Convergence Criteria

Data to Analyze

Discrepancy Function

Initial Values

Line Search Method

Line Search Parameters

Manifest Exogenous

Output Options

Standardization


  Analysis Parameters - Line Search Method

In this box of the Analysis Parameters dialog, you choose a basic line search method.  Once the step direction has been chosen, the minimization problem is basically reduced from a problem in n unknowns to a problem in 1 unknown, i.e., the length of the step.  There are 3 methods for choosing the length of the step.  Their technical aspects are discussed in the manual section on Unconstrained Minimization Techniques.

Line Search Method options:

Cubic Interpolation:  This method is reasonably fast and rather robust.  It works well in the vast majority of circumstances.

Golden Section:  This method tries to solve the one dimensional minimization problem exactly on each iteration.  It often converges in slightly fewer iterations than cubic interpolation, but takes longer, because it requires more function evaluations on each iteration.

Simple Stephalving:  This method is the fastest, but will fail to converge for a fair number of problems that the other two, more sophisticated methods succeed on.

For more options in the Analysis Parameters dialog, see:

Convergence Criteria

Data to Analyze

Discrepancy Function

Global Iteration Parameters

Initial Values

Line Search Parameters

Manifest Exogenous

Output Options

Standardization


  Analysis Parameters - Line Search Parameters

In this box of the Analysis Parameters dialog, you choose numerical parameters that control the performance of the line search method you have chosen.  Only a subset of the parameters are relevant to each line search method.  Only relevant parameters will be enabled for the currently selected line search method.

Line Search Parameters:

Max.  No.  of Stephalves:  This parameter sets the maximum number of stephalves allowed on a single iteration if the Simple Stephalving line search method is used.

Stephalve Fraction:  This parameter sets the fraction the current step is multiplied by when Simple Stephalving is used as the line search method.

Cubic LS Alpha:  This parameter controls how large a reduction in the discrepancy function  has to be made before a step is considered acceptable when the Cubic Interpolation line search method is used.  The default value, .0001, allows virtually any improvement to be considered acceptable.

Golden Section Tau:  This parameter controls how wide a range to which the Golden Section line search is limited.

Golden Search Precision:  This parameter controls the precision of estimation in a Golden Section line search.

For more options in the Analysis Parameters dialog, see:

Convergence Criteria

Data to Analyze

Discrepancy Function

Global Iteration Parameters

Initial Values

Line Search Method

Manifest Exogenous

Output Options

Standardization


  Analysis Parameters - Initial Values

Here in this section of the Analysis Parameters dialog, you select the method employed to find initial values for free parameters.  The default method uses .5 for all free parameters, except variances and covariances (or correlations) of manifest exogenous variables.  These parameters are initialized at the values obtained from the sample data.

Initial Values Options:

Default:  The default method uses .5 for all free parameters, except variances and covariances (or correlations) of manifest exogenous variables.  These parameters are initialized at the values obtained from the sample data.

Automatic:  If this option is selected, the initial values are obtained by a method that is a minor adaptation of the technique described by McDonald and Hartmann (1992).

For more options in the Analysis Parameters dialog, see:

Convergence Criteria

Data to Analyze

Discrepancy Function

Global Iteration Parameters

Line Search Method

Line Search Parameters

Manifest Exogenous

Output Options

Standardization


  Structural Equation Modeling - Iteration Window

During iteration, the Iteration Window opens to report the progress of iteration.  The information reported can be useful in diagnosing problems in convergence.  When iteration is terminated, the user is presented with 2 options:  These options give the user the opportunity to continue the analysis, or terminate without presenting the Results dialog.

The following information is presented:

Itn.  #:  The number of the iteration in the iterative sequence.

Discrepancy:  The current value of the discrepancy function being minimized.

RCos:  The current value of the Maximum Residual Cosine criterion.

Lambda:  The value of the step multiplier used on that iteration.  A value of 1.  means that the first "full" step reduced the discrepancy function "sufficiently" to continue iteration.  A value less than one means that the program had to use a line search along the chosen step direction in order to find a point where the discrepancy function was reduced.  Very small values usually indicate that iteration is about to fail.

MAXCON:  The maximum value of any constraint function.  This value will only be non-zero during constrained estimation, used when the New option is chosen for Standardization, or Correlations are chosen as the Data to Analyze.  If iteration progresses satisfactorily, this value should decrease systematically to a value very close to zero.

NRP:  Number of redundant parameters.  If some parameters are redundant with others, the program may be able to detect the condition, and, if so, will set this value other than zero.

NRC:  Number of redundant constraints.  If some parameter constraints are redundant, the program may be able to detect the condition, and, if so, will set this value other than zero.

NAIC:  Number of active inequality constraints, or "boundary conditions."  During iteration, the program maintains certain inequality constraints on parameters to prevent some "impossible" values from arising.  For example, negative variances are not allowed to occur.  If the program detects a variance will be set to a negative value on the next iteration, it constrains the value at the boundary point (i.e., zero) and only minimizes the discrepancy function relative to the other parameters.  If, for example, you have a "Heywood case" in a confirmatory factor model, you will have a non-zero value of this index at termination of iteration.

StepLen:  The length of the current full iteration step.  If an asterisk appears next to the value, it indicates that the maximum allowable step was taken.  You can control the maximum step length allowed by setting a parameter in the Analysis Parameters dialog.

When iteration stops, the following commands are available:

Cancel:  Clicking this button will terminate the current analysis and return to the Startup Panel.

OK:  The program will calculate results, and present the Results dialog.


  Structural Equation Modeling - Monte Carlo Setup

A Monte Carlo experiment involves executing a specified number of replications of a statistical procedure.  Each replication involves a complete analysis of a random sample created with certain characteristics, so Monte Carlo experiments can be very time consuming.  You may terminate any Monte Carlo experiment prematurely with the Esc key or by clicking on the Cancel button.

In this dialog, you enter the parameters and conditions for a Monte Carlo experiment.  You begin by entering the seed values and number of Replications:

Seed1:  An integer between 1 and 2,147,483,647.  Used to generate random numbers.

Seed2:  Another integer between 1 and 2,147,483,647.  Used in Contaminated Normal generation only.

Number of Replications:  The number of Monte Carlo replications.  Must be no greater than 1000.

You then set the analysis parameters by selecting options from the following boxes:  Click on a box name to obtain further information about that the options for that group.

Store Extra Information

Get Population From

Special Data Types

Group Characteristics

Adjust Distribution

Set Contamination Parameters

Set Monte Carlo Sample Sizes


  Monte Carlo Setup - Store Extra Information

As a Monte Carlo experiment is performed, information about the analysis results for each Monte Carlo replication is stored in memory, and is displayed in an Overall Results Scrollsheet at the end of the experiment.  Results for each replication are stored in a new row of the Scrollsheet.  The basic results, stored for all Monte Carlo experiments, include the Monte Carlo seeds used for each replication, the discrepancy function value, the number of iterations required, and a variety of indicators used to determine whether iteration converged satisfactorily.  These are described in detail in the Monte Carlo Results section of the Electronic Manual.

You may also opt to store additional information about the results of each analysis.  Checking the following boxes in this group causes this information to be added to the Overall Results stored during the experiment.

Parameter Estimates:  Checking this box causes the values for free parameters to be stored.  They are given names corresponding to the numbers actually assigned in the PATH1 program.  The names are PAR_# , where # is the parameter number.  So, if a program had free parameters 1,2,3,6, the variables PAR_1, PAR_2, PAR_3, and PAR_6 would be added to the Overall Results Scrollsheet.

Standard Errors:  Checking this box causes the estimated standard errors to be stored for each free parameter, using the following naming scheme.  Each standard error is named SE_#, where # is the free parameter number.

Fit Indices:  Checking this box causes the available fit indices to be stored for each analysis.

For more information on Monte Carlo setup, see:

Monte Carlo Setup

Get Population From

Special Data Types

Group Characteristics

Adjust Distribution

Set Contamination Parameters

Set Monte Carlo Sample Sizes


  Monte Carlo Setup - Get Population From

In Monte Carlo analysis, the program generates data that simulate samples from a particular population structure.  The option you check in this group determines how that population is obtained.

Model:  If you select this option, the program generates a population structure corresponding to the current model.  Whatever model is active in the current window, with the starting values specified for the parameters, is used to generate a population covariance matrix.  You can specify the numerical value you want for various free parameters by specifying these values as starting values within braces after the free parameter number.  So, for example, if you wanted your population to be based on a factor model where the first factor loads .5 on the first variable, you would have a line like this in your *.cmd file:

(F1)-1{.5}->[X1]

Data:  If you select this option, the program will take your data, calculate the appropriate matrix (correlation, covariance, augmented moment) and generate simulated data from it based on the currently selected distributional characteristics.

It is important that you understand the fine points of how this option works.  If your input data file is a correlation or covariance matrix, the program will treat that as the population matrix, or convert it to the appropriate matrix type if necessary.  If your input file contains raw data, the program will calculate the appropriate matrix type, and sample from that matrix.

This means that, if your file contains raw data, and you have selected the default distributional options, the program will calculate the covariance matrix corresponding to your data, and will generate simulated data from a Multivariate Normal distribution having those characteristics.

If you have a raw data file, and you want a simulated population that exactly mirrors the characteristics of those raw data, you should use the Bootstrap option below.

Bootstrap:  This option may only be selected if the data file contains raw data.  In bootstrapping, a simulated sample of size N is created by treating the current data file as a discrete multivariate population, where each observation vector occurs equally often.  The bootstrapped sample is obtained by sampling, randomly with replacement vectors of observations from the current data file.  So, suppose the current data file contains 100 observations on 10 variables.  If you request the Bootstrap option with Sample Size of 50, the program will, 50 times, sample randomly with replacement from the integers from 1 to 100.  The resulting list of 50 integers is used to select which observations from the data file are included in the bootstrapped sample.  Note, it is possible (likely, in fact) that some of the observations in the resulting data file will be identical.  This occurs if, during the sampling of integers, the same integer is selected more than once.

For more information on Monte Carlo setup, see:

Monte Carlo Setup

Store Extra Information

Special Data Types

Group Characteristics

Adjust Distribution

Set Contamination Parameters

Set Monte Carlo Sample Sizes


  Monte Carlo Setup - Special Data Types

The Monte Carlo module allows you to create special types of non-normal data.  Besides allowing you to adjust the skewness and kurtosis of individual variables (see the Group Characteristics group), the program also allows you to create Monte Carlo data of two special types:

Categorical Data:  If you check this option, the program will, as a last step, change the data from continuous to categorical, using categorization rules that you have specified.  You may select between 2 and 10 categories, and you select the boundaries for the categorization.  (See the Categories option under the Adjust Distribution group for details.)

Outlier Contamination:  This option allows you to create a distribution contaminated by outliers, using a standard mixture distribution technique.  For details, see the Contamination Factors section of the Group Characteristics group.

For more information on Monte Carlo setup, see:

Monte Carlo Setup

Store Extra Information

Get Population From

Group Characteristics

Adjust Distribution

Set Contamination Parameters

Set Monte Carlo Sample Sizes


  Monte Carlo Setup - Group Characteristics

In this group, you enter characteristics for your Monte Carlo groups.

Sample Sizes button:  This button activates a dialog to allow you to enter the sample sizes for each group in the analysis.  Sample sizes should be greater than the number of variables in the analysis, but can be different for each group.

Contamination Factors button:  In this dialog, you enter, for each group, a proportion of outliers, and a multiplier factor.  Outlier contamination is simulated in the Monte Carlo module by a standard mixture distribution technique.  Suppose your data come from a population with mean  and covariance matrix Σ.  We simulate contamination by substituting, a certain proportion p of the time, observations with a mean  and a covariance matrix kΣ, where k is a moderately large multiplier (say, 10).  In effect, the outliers are obtained by taking "what they would have been before the mean was added on" and multiplying by the square root of k.

For each sample, you enter contamination factors k and p.  For each sample, a proportion p of the time, the observations will then have a mean  and a covariance matrix kΣ.

For more information on Monte Carlo setup, see:

Monte Carlo Setup

Store Extra Information

Get Population From

Special Data Types

Adjust Distribution

Set Contamination Parameters

Set Monte Carlo Sample Sizes


  Monte Carlo Setup - Adjust Distribution

In this group, you adjust special distributional characteristics if you are simulating data that are not multivariate normal.  Characteristics may be adjusted separately by group.

Group:  In this field, you enter the number of the group whose characteristics you wish to alter.

Skewnesses button.  This button activates a dialog in which you enter the desired skewnesses for variables in each group.

Kurtoses button.  This button activates a dialog in which you enter the desired kurtoses for variables in each group.

Categories button.  This button activates an "interactive Scrollsheet" in which you enter the parameters for converting each continuous variable to categorical form.  For each variable, you enter the number of categories.  If you have k categories, you will have k-1 cutoff points.  All continuous values below the first cutoff will be given the categorical score 1.  All continuous values exceeding the first cutoff but below the second cutoff will be given the categorical score 2, etc.

For more information on Monte Carlo setup, see:

Monte Carlo Setup

Store Extra Information

Get Population From

Special Data Types

Group Characteristics

Set Contamination Parameters

Set Monte Carlo Sample Sizes


  Monte Carlo Setup - Set Monte Carlo Sample Sizes

In this dialog, you may set the sample sizes for each sample separately, by simply entering them in the appropriate field in the dialog box.  Note that only sample sizes for the groups available for your analysis may be altered.

Restore Defaults button:  This button resets all group sample sizes to the default value of 100.

For more information on Monte Carlo setup, see:

Monte Carlo Setup

Store Extra Information

Get Population From

Special Data Types

Group Characteristics

Adjust Distribution

Set Contamination Parameters


  Monte Carlo Setup - Set Contamination Parameters

In this dialog, you enter, for each group, a proportion of outliers, and a multiplier factor.  Outlier contamination is simulated in the Monte Carlo module by a standard mixture distribution technique.  Suppose your data come from a population with mean  and covariance matrix Σ.  We simulate contamination by substituting, a certain proportion p of the time, observations with a mean  and a covariance matrix kΣ, where k is a moderately large multiplier (say, 10).  In effect, the outliers are obtained by taking "what they would have been before the mean was added on" and multiplying by the square root of k.

For each sample, you enter contamination factors k and p.  For each sample, a proportion p of the time, the observations will then have a mean  and a covariance matrix kΣ.

For more information on Monte Carlo setup, see:

Monte Carlo Setup

Store Extra Information

Get Population From

Special Data Types

Group Characteristics

Adjust Distribution

Set Monte Carlo Sample Sizes


Editing Latent Variable Names

In this dialog, you will see a list of the current latent variables in a series of edit field boxes.  To add a new latent variable name, scroll to the end of the series of names.  You will find empty fields labeled "New Variable Name" on the left.  Simply type in the names of the new latent variables you wish to add.

To delete a latent variable, simply delete its name.

If you delete a latent variable name and return to the path tool, all paths involving this latent variable will be removed from the current model.


  Path Construction Tool

The Path Construction Tool allows you to construct path model files in the PATH1 language, with virtually no typing.  Because you type latent variable names only once, never have to type manifest variable names, and never have to enter paths manually, there is virtually no chance of a syntax error.  Even extremely complicated models can be entered in a few minutes with this tool.

Setting Up - Editing the Latent Variables List

When the Path Construction Tool is first activated, the Latent Variables list will be presented in the To variables column.  The variable names listed will be those already in the *.cmd file being edited.  If the file is a new one, or if you wish to add latent variable names, you will have to edit the latent variable names list.

Edit Latent button:  This button activates the dialog for editing latent variables.  Within this dialog, you can add, delete, or change latent variable names.

Creating Paths - Adding Arrows and Wires

There are two basic types of paths, the arrow and the wire.  Basic operation is as follows:

a)	Choose a type of path by checking either the X-->Y or X--Y option in the Path Type group.

b)	Select the type of variable in the From column of the Variables group.

c)	Highlight the variable(s) from which to draw paths.

d)	Select type of variable in the To column of the Variables group.

e)	Highlight the variables to which paths will be drawn.

f)	Press the Add>> button.

At this point, the requested paths will appear in the Paths List Box on the far right side of the screen.

Creating Paths - Multiple Path Commands

Besides the basic arrow and wire path types, the Path Type group includes options for 3 additional multiple path commands.  These commands automate operations which are (a) highly repetitive, and (b) common to most path diagrams.  They are described below.

Residual option:  This option creates residual (or "disturbance") variables automatically for all currently highlighted variables in the To column.  Suppose, for example, you wished to create residuals ("unique factors") for all the manifest variables (X1,X2,X3,X4,X5,X6) in the Child.sta file.  You would simply (a) select Manifest in the To variables column; (b) highlight all the variables; (c) select Residual as the Path Type option; (d) enter a Base Name (say, EPS) and a Base Number (say, 1) in the Residual Vars dialog; (e) click the Add>> button.  At this point, paths for residual variables EPS1, EPS2, EPS3, EPS4, EPS5, and EPS6 and their variances will be added automatically, and these residual variable names will be added to the latent variables list.

Base Name:  This name will be used for all residual variable names created during the current residual variables operation.

Base Number:  As residual variables are created, this number will be added to the Base Name, then incremented.  So, if the Base Name is DELTA, and the Base Number is 5, the first residual variable created will have the name DELTA5, the second DELTA6, etc.

Correl.  option:  Frequently in a structural model, you need to insert paths for the correlation coefficients among a set of latent or manifest variables.  The program does this automatically for all variables highlighted in the To column.  For example, if you highlight variables X1,X2,X3 and click the Correl. button, you get the following paths:

[X2]-1-[X1]

[X3]-2-[X1]

[X3]-3-[X2]

[X1]-{1.0}-[X1]

[X2]-{1.0}-[X2]

[X3]-{1.0}-[X3]

Covar. option:  This option creates paths for all the variances and covariances for all variables highlighted in the To variables column.  It operates in virtually the same way as the Correl. option.

Adding Paths

Add>> button:  This button causes paths to be created, according to the currently created options.  The new paths will appear immediately in the Paths box.  If you don't like them, simply delete them with the Cut command (see below).

Editing the Paths Already Created

The program offers editing capabilities, to change and/or reorganize the paths already created.  These paths are listed in the Paths list box on the right side of the screen.  Available functions include:

Cut button:  Highlighted paths are deleted, and placed on the Clipboard.

Paste button:  Material currently on the Clipboard is pasted into the Paths window after the current cursor position.

Copy button:  A copy of the currently highlighted material is placed on the Clipboard.

Removing All Paths involving a Latent Variable

The program offers an especially easy way to completely eliminate a latent variable from an analysis.  Simply activate the Edit Latent Variables dialog, and delete the name of the latent variable that you wish to remove from the model.  After you click OK, all paths involving this variable, and the variable itself, will be deleted from the model.

The Parameters Group - Controlling the Parameter Numbers of Paths

The Parameters group contains functions that allow you to control if, and how, free parameter numbers are inserted in the paths you create.

Include option:  If this box is checked, a free parameter will be included in the path.  The number will be the current value in the Par # field (see below).

Increment option:  If this box is checked, the free parameter value in the Par # field (see below) will be increased by 1 after each parameter number is added to a path.

Par #:  This field specifies the parameter number to be added to the next path (if the Include box is checked).  When the Path Construction Tool is first activated, this value is set equal to one more than the highest parameter number currently in the active *.cmd file.

Renumber option:  This button causes all highlighted paths to be renumbered, starting at the value in the Par # field.  The renumbering preserves all order relationships, and same-difference relationships in the parameters of the highlighted paths.  It is important to remember that the action of the Renumber command is affected by the current settings of the Include and Increment boxes!  What this means is that, if you Renumber paths with the Include box not checked, all parameter numbers will be removed from the paths.

The Renumber command is a powerful and convenient one for making your programs easier to read.  It is best, when finishing a program, to renumber the paths, starting at 1.  In this way, it is easy to verify the number of free parameters in a model.

The Renumber command can be especially useful when you are creating a multiple groups model with similar models in each group.  You can simply Copy the model for the first group, then use the Renumber command to renumber the parameters.

The Start Value Group - Controlling Start Values

The fields in the Start Value group control whether a start value is added to a path, and what value is added.

Include option:  If this box is checked, a start value is added to each path.

Value:  The value in this field is added as the start value.

Adding Comments to the Model File

You can add comments to the Model File using the Comment button.

Comment button:  This button calls up a dialog for adding a comment.  Type the text of the comment into the edit field.  Do not add the asterisk to denote the comment field.  The program will do this automatically.

Adding Group and Endgroup Commands

You can add Group and Endgroup commands, using the appropriate buttons.

Group button:  This button has an integer field to its right.  If you click this button, the command

Group #

(where # is the integer in the field) will be added to the Paths file after the current line.

Endgroup button:  This button causes an Endgroup command to be added to the Paths file.

Adjusting Analysis Parameters

You can call up the Analysis Parameters dialog, using the Parameters button.

Parameters button:  This button calls up the Analysis Parameters dialog.


  Structural Equation Modeling Results

When iteration concludes, you can examine the results of the analysis in this dialog.

At the top of the dialog, a large window will present a number of results that can be scanned to determine, quickly and efficiently, (a) whether iteration concluded successfully, and (b) how well the model fit the data.

There are also several groups of buttons that allow you to examine Scrollsheets with various results.  Click on the topics below to see information about them.

Results Text Window

Model Summary

Alpha level for highlighting

Basic Summary Statistics

Goodness-of-Fit Indices

Tests of Assumptions

Analysis of Residuals

Lagrange Multiplier Statistics

Iteration History


Information in the Results Text Window

  Structural Equation Modeling - Information in the Results Text Window

The information on the left side of the text window is designed to enable you to evaluate, quickly and efficiently, whether iteration was successful.

Method of Estimation:  At the top of the window is the Method of Estimation (i.e., the discrepancy function used).

Discrepancy Function Value:  This is the numerical value of the discrepancy function.

Maximum Residual Cosine:  This numerical criterion should be close to zero if iteration was successful.

Maximum Absolute Gradient:  This is the absolute value of the largest element of the gradient.

Maximum Absolute Constraint:  In options requiring constrained estimation, i.e., when correlations are analyzed, or when the New Standardization (see Analysis Parameters for details) method is employed, a number of constraint functions are evaluated, and must iterate to zero if the constraints are maintained.  If this value is not zero, or a very small value, it indicates iteration was unsuccessful.

ICSF Criterion:  This criterion should be close to zero if the structural model is invariant under a constant scaling factor (ICSF).  Most, but not all, structural models are invariant under a constant scaling factor.

ICS Criterion:  This criterion should be close to zero if the structural model is invariant under changes of scale (ICS).  In general, when correlations are analyzed, this index should be close to zero.

Boundary Conditions:  This criterion indicates the number of inequality constraints that were operative at convergence.  This number should be zero, unless there is a boundary case such as a Heywood Case in your model.  If this number is not zero, then the Chi-square statistic will not necessarily have the proper distribution.

The information on the right side of the window is basic statistical information about the fit of the model.

Chi-square Statistic:  Available for all discrepancy functions except OLS, this statistic has an asymptotic Chi-square distribution if the null hypothesis of perfect fit is true.  In multiple group models, this is an overall statistic for all groups.

Degrees of Freedom:  This is the number of degrees of freedom for the Chi-square statistic.

Chi-square p level:  This is the probability level for the Chi-square statistic.

Steiger-Lind RMSEA:  Here the point estimate and 90% confidence interval for the Steiger-Lind RMSEA are given.

RMS Standardized Residual:  This is the root mean square standardized residual.  Roughly, this number must be less than .05 for the fit to be "good" in a practical sense.

For more information on Structural Equation Modeling Results, see:

Model Summary

Alpha level for highlighting

Basic Summary Statistics

Goodness-of-Fit Indices

Tests of Assumptions

Analysis of Residuals

Lagrange Multiplier Statistics

Iteration History


  Structural Equation Modeling Results - Model Summary

The model summary Scrollsheet presents model output in a Scrollsheet form convenient for analysis.  For each path in the model, the following information is given:

Path Representation:  Each row of the Scrollsheet begins with the PATH1 representation of the model statement.

Parameter Value:  This is the actual numerical value of the parameter estimate.

Standard Error:  The estimated standard error of the parameter estimate.

"T"-Statistic:  Actually, this should more properly be called the "asymptotic normal statistic," as it does not actually have a Student's t distribution.  It represents a test of the hypothesis that the parameter value is zero.  Rejecting the hypothesis implies that the parameter value is not zero, and should be included in the model.  By this criterion, paths that are "significant" at the selected level are highlighted.  The alpha level for highlighting may be altered using the Alpha level for highlighting.

Probability Level:  This is the standard normal probability level for the "T"-Statistic.

For more information on Structural Equation Modeling Results, see:

Results Text Window

Alpha level for highlighting

Basic Summary Statistics

Goodness-of-Fit Indices

Tests of Assumptions

Analysis of Residuals

Lagrange Multiplier Statistics

Iteration History


  Structural Equation Modeling Results - Alpha Level for Highlighting

In the current Scrollsheet, statistically significant results (p < alpha) are highlighted.  Enter the desired new alpha level, and a new Scrollsheet will be prepared with highlights reflecting the new significance criterion.  You can later request a different threshold p-level by pressing on the Options Toolbar button on the Scrollsheet Toolbar.

The general logic of significance testing is described in the Elementary Concepts chapter of the manual.

In this dialog, you may enter a cutoff value for alpha to control highlighting of paths in the Model Summary Scrollsheet.  Choose a value greater than zero and less than one. The default value is .05.

For more information on Structural Equation Modeling Results, see:

Results Text Window

Model Summary

Basic Summary Statistics

Goodness-of-Fit Indices

Tests of Assumptions

Analysis of Residuals

Lagrange Multiplier Statistics

Iteration History


  Structural Equation Modeling Results - Basic Summary Statistics

This button produces a Scrollsheet containing some of the basic summary statistics also presented in the Results Text Window.  Having the results in Scrollsheet form allows them to be printed, saved to a file, etc.

For more information on Structural Equation Modeling Results, see:

Results Text Window

Model Summary

Alpha level for highlighting

Goodness-of-Fit Indices

Tests of Assumptions

Analysis of Residuals

Lagrange Multiplier Statistics

Iteration History


  Structural Equation Modeling Results - Goodness-of-Fit Statistics

The options in this box allow you to generate several of the best-known and most useful indices of fit for evaluating structural equation models.  There are, literally, dozens of such indices, and we present only those we think are very widely used, especially valuable, or both.

There are three buttons for generating indices of fit.

Noncentrality-Based Indices button: These indices are all based on the idea, first proposed by Steiger and Lind (1980), of basing goodness-of-fit assessment on an estimation of the population noncentrality parameter.  Steiger, Shapiro, and Browne (1985) proved that, under some realistic simplifying assumptions, the Chi-square test statistic has a distribution which is asymptotically non-central Chi-square, with a non-centrality parameter equal to N times the population discrepancy function.  The population discrepancy function is that value of the discrepancy function that you would obtain if (a) you actually knew the population covariance matrix Σ, and (b) you were to analyze it as if it were sample data.  It is a rather natural index of "badness-of-fit."  The population discrepancy function can be estimated, with a confidence interval, from sample data.  So can other fit indices that are functions of the population discrepancy function.  The following estimates are computed, along with a 90% confidence interval.

The philosophy behind "noncentrality interval estimation" (Steiger, 1990) represents a change of emphasis in assessing model fit.  Instead of testing the hypothesis that the fit is perfect, we ask the questions (a) "How bad is the fit of our model to our statistical population?" and (b) "How accurately have we determined population badness-of-fit from our sample data."

The indices presented here allow us to assess both questions, because they allow confidence interval assessment as well as the more traditional point estimates.  As a result, they reward high sample size, and high power, with a narrower confidence interval expressing high precision of estimate.

Population Noncentrality Parameter:  This index directly estimates the population noncentrality parameter.  We present this here primarily because it can be used to compute other noncentrality-based indices, including some we have not presented because they do not lead to confidence interval estimates.

Steiger-Lind RMSEA Index:  This index corrects the population noncentrality by compensating for model parsimony.  All other things being equal, more parsimonious models (those with fewer parameters) tend not to fit as well as less parsimonious models.  Consequently, an index of fit that fails to compensate for the number of parameters in the model can be somewhat misleading.  The Steiger-Lind index compensates for model parsimony by dividing the estimate of the population noncentrality parameter by the degrees of freedom.  This ratio, in a sense, represents a "mean square badness-of-fit." Taking the square root leads to a measure that is analogous, in a sense, to a root mean square measure of model misfit.

If F* is the population badness-of-fit, and ν the degrees of freedom, the Steiger-Lind index can be written as

In general, values of the RMSEA index below .05 indicate good fit, and values below .01 indicate outstanding fit.  In general, the RMSEA index tends to produce the same conclusions about population fit as the Adjusted Population Gamma Index (see below).

McDonald's Index of Noncentrality:  McDonald proposed this index of noncentrality in a 1989 article in the Journal of Classification.  The index represents one approach to transforming the population noncentrality index F* into the range from 0 to 1.  The index does not compensate for model parsimony, and the rationale for the exponential transformation it uses is primarily pragmatic.

The index may be expressed as

Good fit is indicated by values above .95.

Population Gamma Index:  This index was proposed by Steiger (1989) as an extension of the rationale for the GFI given by Joreskog and Sorbom (1984).  These latter two authors proposed their index as strictly a descriptive (sample based) statistic.  However, Tanaka and Huba (1989) showed that the GFI and AGFI could be justified on the basis of a "coefficient of determination" rationale.  Steiger (1989) noted that this rationale could be extended to the population as well as the sample, and developed the asymptotic sampling theory of the statistic (this result was also derived independently by Maiti and Mukherjee, 1990).  The population gamma index is an estimate of the "population GFI," the value of the GFI that would be obtained if we could analyze the population covariance matrix Σ.

For this index, good fit is indicated by values above .95.

Adjusted Population Gamma Index:  This index is to the Joreskog and Sorbom (1984) AGFI as the Population Gamma Index is to the GFI.  It is, basically, an estimate of the population GFI corrected for model parsimony.  Good fit is indicated by values above .95.

Other Single-Sample Indices button:  This button activates a Scrollsheet with a sampling of some of the better known single sample indices of fit, and some related measures.

Joreskog GFI:  Values above .95 indicate good fit.  This index is a negatively biased estimate of the population GFI, so it tends to produce a slightly pessimistic view of the quality of population fit.  We give this index primarily because of its historical popularity.  The Population Gamma index is a superior realization of the same rationale.

Joreskog AGFI:  Values above .95 indicate good fit.  This index is, like the GFI, a negatively biased estimate of its population equivalent.  As with the GFI, we give this index primarily because of its historical popularity.  The Adjusted Population Gamma index is a superior realization of the same rationale.

Akaike Information Criterion:  This criterion is useful primarily for deciding which of several nested models provides the best approximation to the data.  When trying to decide between several nested models, choose the one with the smallest Akaike criterion.  The criterion is defined, for the k'th model, as:

where

Schwarz's Bayesian Criterion:  This criterion, like the Akaike, is used for deciding among several models in a nested sequence.  When deciding among several nested models, choose the one with the smallest Schwarz criterion value.  The criterion is defined, for the k'th model, as

Browne-Cudeck Cross Validation Index:  Browne and Cudeck (1989) proposed a single sample cross-validation index as a follow-up to their earlier (Cudeck & Browne,1983) paper on cross-validation.  Cudeck and Browne had proposed a cross-validation index which, for the k'th model in a set of competing models is of the form

In this case, F is the maximum likelihood discrepancy function, S is the covariance matrix calculated on a cross-validation sample.

is the reproduced covariance matrix obtained by fitting model k to the original calibration sample.  In general, better models will have smaller cross-validation indices.

The drawback of the original procedure is that it requires two samples, i.e., the calibration sample for fitting the models, and the cross-validation sample.  The new measure estimates the original cross-validation index from a single sample.

The measure is:

Independence Model Chi-square and df:  These are the Chi-square goodness-of-fit statistic, and associated degrees of freedom, for the hypothesis that the population covariances are all zero.  Under the assumption of multivariate normality, this hypothesis can only be true if the variables are all independent.  The "Independence Model" is used as the "Null Model" in several comparative fit indices.

Bentler-Bonett (1980) Normed Fit Index:  One of the most important and original fit indices, the Bentler-Bonett index measures the relative decrease in the discrepancy function caused by switching from a "Null Model" or baseline model, to a more complex model.  It is defined as:

This index approaches 1 in value as fit becomes perfect.  However, it does not compensate for model parsimony.

Bentler-Bonett Non-Normed Fit Index:  This comparative index takes into account model parsimony.  It may be written as

Bentler Comparative Fit Index:  This comparative index estimates the relative decrease in population noncentrality obtained by changing from the "Null Model" to the k'th model.  The index may be computed as:

James-Mulaik-Brett Parsimonious Fit Index:  This index was one of the earliest (along with the Steiger-Lind index) to compensate for model parsimony.  Basically, it operates by rescaling the Bentler-Bonnet Normed fit index to compensate for model parsimony.  The formula for the index is:

Bollen's Rho:  This comparative fit index computes the relative reduction in the discrepancy function per degree of freedom when moving from the "Null Model" to the k'th model.  It is computed as:

Bollen's Delta:  This index is similar in form to the Bentler-Bonnet index, but rewards simpler models (those with higher degrees of freedom).  It is computed as:

For more information on Structural Equation Modeling Results, see:

Results Text Window

Model Summary

Alpha level for highlighting

Basic Summary Statistics

Tests of Assumptions

Analysis of Residuals

Lagrange Multiplier Statistics

Iteration History


  Structural Equation Modeling Results - Lagrange Multiplier Statistics

This button activates a Scrollsheet with Lagrange Multiplier statistics for each constraint required by the fitting procedure.  If the New standardization method is employed, each endogenous latent variable will have its variance constrained to one, and there will be a Lagrange multiplier statistic for each variable.  In the Correlation option of Data to Analyze, each endogenous manifest variable has a dummy latent variable attached to it, with its variance constrained to one.

The Lagrange Multiplier statistics should be zero, if the constraints serve (as they are meant to) solely as identification constraints.  If any are non-zero, or significantly exceed the standard error, then the model has probably been mis-specified, or estimation did not converge properly.

For more information on Structural Equation Modeling Results, see:

Results Text Window

Model Summary

Alpha level for highlighting

Basic Summary Statistics

Goodness-of-Fit Indices

Tests of Assumptions

Analysis of Residuals

Iteration History


  Structural Equation Modeling Results - Tests of Assumptions

This group has options that allow you to analyze raw data to examine whether assumptions of multivariate normality have been violated, and to examine invariance properties of the model being tested.  Formulas are given in the manual.

Measures of Univariate Skewness

Skewness:  This is the standard measure of univariate skewness.  For normally distributed data, it should be zero in the population.

Corrected Skewness:  This is a bias-corrected measure of univariate skewness.

Normalized Skewness:  This is a sample based estimate which, under multivariate normality, has approximately a standard normal distribution with large samples.  This measure may be evaluated roughly like any other standard normal statistic.

Measures of Univariate Kurtosis

Kurtosis:  This is the standard measure of univariate skewness.  For normally distributed data, it should be zero in the population.

Corrected Kurtosis:  This is a bias-corrected measure of univariate kurtosis.

Normalized Kurtosis:  This is a sample based estimate which, under multivariate normality, has approximately a standard normal distribution with large samples.  This measure may be evaluated roughly like any other standard normal statistic.

Measures of Multivariate Kurtosis

Mardia Coefficient of Multivariate Kurtosis:  If the sample comes from a multivariate normal distribution, this coefficient should be close to zero.

Normalized Multivariate Kurtosis:  This normalized version of the Mardia coefficient has a distribution that is approximately standard normal at large samples.  The measure may be evaluated roughly like any other standard normal statistic.

The following additional measures of kurtosis are provided for compatibility with other structural modeling programs.

Mardia-Based Kappa:  The elliptical distribution family includes the multivariate normal distribution as a special case.  In this distribution family, all variables have a common kurtosis parameter

This parameter can be used to rescale the Chi-square statistic if the assumption of an elliptical distribution is valid.  The Mardia-based kappa is an estimate of kappa obtained by rescaling Mardia's coefficient of multivariate kurtosis.  This number should be close to zero if the population distribution is multivariate normal

Mean Scaled Univariate Kurtosis:  This is an alternate estimate of kappa, obtained simply by averaging the rescaled univariate kurtoses.

Adjusted Mean Scaled Univariate Kurtosis:  Distribution theory provides a lower bound for kappa.  It must never be less than −2/(p+2), where p is the number of variables.  The preceding two estimates do not always obey this bound.  This estimate averages the scaled univariate kurtosis, but adjusts each one that falls below this bound to be at the lower bound point.  This coefficient should be close to zero if the distribution is multivariate normal

Relative Multivariate Kurtosis:  This measure is the Mardia-based kappa, rescaled to have a mean of 1.  It should be close to 1 in value if the distribution is multivariate normal.

Reflector Matrix

The reflector matrix is used for evaluating model invariance properties.  Its use is discussed in the manual.

For more information on Structural Equation Modeling Results, see:

Results Text Window

Model Summary

Alpha level for highlighting

Basic Summary Statistics

Goodness-of-Fit Indices

Analysis of Residuals

Lagrange Multiplier Statistics

Iteration History


  Structural Equation Modeling Results - Analysis of Residuals

This group allows you to examine model residuals, to help assess model fit, and, in particular, to find which observed variables are being reproduced poorly by the structural model.

Standardized Residuals button:  Standardized residuals represent the difference between the input matrix and the reproduced matrix, standardized in the correlation metric.  We express the residuals in standardized form to eliminate the effects of the scale of the variable on model residuals.

Normalized Residuals button:  These residuals are divided by an estimate of their variance, to provide a measure that, in large samples, is approximately normally distributed when the model fits perfectly in the population.  These residuals may be interpreted (roughly) like any standardized normal statistic.  Keep in mind that, when evaluating a large matrix of residuals, you need to correct for the fact that you are examining, post hoc, a large number of coefficients.  For example, you expect approximately 5% of these to be "significant" by chance at the 5% level, so a matrix with 45 residuals would have, typically, 2 or 3 "significant" values by chance.

Normal Probability Plot button:  If the proposed structural model fits perfectly in the population, and if the population distribution is multivariate normal, the residuals will be approximately normally distributed.  You can use the normal probability plot of the residuals to detect departures from normality, perfect fit, or both.

Input Matrix button:  This is the matrix actually analyzed by the structural modeling iterative routine, rather than the data matrix.  So, for example, if you input Raw Data, but select Moments as your option under the Data to Analyze group of the Analysis Parameters dialog, you will see an augmented moment matrix here.

Reproduced Matrix button:  This is the matrix calculated from the model, using the final parameter estimates as the numerical values.

For more information on Structural Equation Modeling Results, see:

Results Text Window

Model Summary

Alpha level for highlighting

Basic Summary Statistics

Goodness-of-Fit Indices

Tests of Assumptions

Lagrange Multiplier Statistics

Iteration History


  Structural Equation Modeling - Iteration History

During iteration, the program saves the output that is displayed in the Iteration Window for the last executed sequence of iterations.  By opening this Scrollsheet, you can review these results. You may of course also save them to a data file or analyze them graphically.

For more information on Structural Equation Modeling Results, see:

Results Text Window

Model Summary

Alpha level for highlighting

Basic Summary Statistics

Goodness-of-Fit Indices

Tests of Assumptions

Analysis of Residuals

Lagrange Multiplier Statistics


  Structural Equation Modeling - Monte Carlo Results

This dialog gives you the opportunity to review the results of the most recently completed Monte Carlo Analysis, to regenerate Monte Carlo data for individual replication, and to save those data for other types of analysis.

Display Overall Results button:  This button displays a Monte Carlo Results Scrollsheet containing an extensive summary of the outcome of the Monte Carlo experiment.

Generate Data button:  This button generates a Scrollsheet containing the actual raw data employed in the Monte Carlo analysis, for the replication number currently entered in the Replication field.  These data may, of course, be saved to a file for subsequent analyses.


  Structural Equation Modeling - Monte Carlo Results Scrollsheet

The Monte Carlo Results Scrollsheet contains an extensive summary of the outcome of the Monte Carlo experiment.  The Scrollsheet stores the results with the replications in rows, and the data for each replication in columns.  Which data are stored depends on the options that were selected in the Monte Carlo Setup dialog.

Here are the codes for the variable names:

SEED1 - The first of the two Monte Carlo seeds.

SEED2 - The second seed, used only in Contaminated Normal distribution generation.

TERMCODE - The Termination Code for the analysis.  If this is zero, the analysis apparently converged normally.  If not, then the following codes apply.

1 -	The relative function change criterion was below the criterion value.  This can occur when the function has stabilized, but the gradient and relative cosine criteria do not go to zero, because one of the parameters is on a boundary value.

2 -	The line search algorithm was unable to reduce the discrepancy function along the searched direction.

3 -	The number of iterations reached the maximum permissible value.  If necessary, this value may be altered in the Analysis Parameters dialog.

4 -	Singular covariance matrix was encountered during iteration.  On occasion, the parameters will be changed to values that yield a singular estimated covariance matrix.  When this happens in Maximum Likelihood estimation, the discrepancy function cannot be evaluated, so iteration is stopped.

5 -	(this value is currently not in use)

6 -	The iteration was terminated by user request, i.e., the user stopped iteration with the Esc key or the Cancel button.

DISCREP - The value of the discrepancy function after iteration.

RCOS - The maximum residual cosine criterion.

GRADIENT - The maximum absolute value of the gradient elements after iteration.

NUM_ITER - The number of iterations required before termination.

ICSC - The ICSF invariance criterion.

ICS - The ICS invariance criterion.

RED_PAR - The number of redundant parameters.

RED_CON - The number of redundant constraints.

BOUNDARY - The number of active inequality constraints (NAIC), or "boundary cases," after iteration.

CHI_SQR - The Chi-square goodness-of-fit statistic.

DF - The number of degrees of freedom for the Chi-square statistic.

PLEVEL - The probability level for the Chi-square statistic.

PAR_# - The parameter values, numbered as they are in the PATH1 *.cmd file.  So, for example, PAR_23 is the value for the free parameter numbered 23 in the *.cmd file.

SE_# - The standard errors, numbered in the same way as the parameter numbers.

RMS_LO - The lower endpoint of the 90% confidence interval for the Steiger-Lind (1980) RMS index.

RMS_PT - The point estimate for the Steiger-Lind (1980) RMS index.

RMS_HI - The upper endpoint of the 90% confidence interval for the Steiger-Lind (1980) RMS index.

NCP_LO - The lower endpoint of the 90% confidence interval for the population discrepancy function.

NCP_PT - The point estimate for the population discrepancy function.

NCP_HI - The upper endpoint of the 90% confidence interval for the population discrepancy function.

AIC - The rescaled Akaike information criterion.

BIC - The Schwarz Bayesian criterion.

BR_CUD - The Browne-Cudeck single sample cross-validation index.

GAMMA_LO - The upper endpoint of the 90% confidence interval for the population gamma index.

GAMMA_PT - The point estimate for the population gamma index.

GAMMA_HI - The upper endpoint of the 90% confidence interval for the population gamma index.

GAMAD_LO - The upper endpoint of the 90% confidence interval for the adjusted population gamma index.

GAMAD_PT - The point estimate for the adjusted population gamma index.

GAMAD_HI - The upper endpoint of the 90% confidence interval for the adjusted population gamma index.

IRGLS:  The IRGLS discrepancy function, if maximum likelihood estimates were obtained.


  Analyzing Structured Means Models, and Models with an Intercept Variable

This program can conveniently analyze models for structured means, and models with intercept variables.  There are several examples of such models in the Structural Equation Modeling - Examples section of the Electronic Manual.  Here are the key points:

1.  In order to analyze such models, you must activate the Moments option in the Data to Analyze group of the Analysis Parameters dialog.

2.  The program automatically adds a manifest variable called CONSTANT to the list of available manifest variables.  You indicate structured means or intercept variables in your models by having paths from the CONSTANT variable.

For further information, consult the Examples, and the following topics:

Conceptual Overview

The Basic Idea Behind Structural Modeling

Structural Equation Modeling and the Path Diagram

Rules for SEPATH Path Diagrams

Inputting Path Diagrams with the PATH1 Language

Models for Two or More Groups


  Structural Equation Modeling - Path Wizards

The Path Wizards are a preprogrammed sequences of dialog boxes that take you, step by step, through the construction of the most common kinds of structural models.  The Wizards do most of the work, and they structure the problem for you so that the chances of making a mistake in specifying a model are greatly reduced when a Wizard is guiding you.

There are two Wizards implemented in this version of the Structural Modeling module.  Click on the names below for details on these Wizards.

Confirmatory Factor Analysis Wizard

General Structural Model Wizard


  Structural Equation Modeling - Confirmatory Factor Model Wizard

Confirmatory factor analysis models are just like ordinary common factor models, except that some factor loadings and factor intercorrelations can be constrained to be equal to each other, or to zero.  This allows statistical testing of preconceived notions about the general form of the factor pattern.

The confirmatory factor analysis Wizard allows you to construct any confirmatory factor model in just a few seconds, so long as the model has 8 common factors or less.  Most models encountered in practice fall in this category.  Larger models can be constructed, with a bit more effort, using the generalized Path Construction Tool.

Step 1.  Most of the information about the confirmatory factor model is entered in this step.  First, you decide on factor names, and which manifest variables will load on each latent variable, or factor.

Latent Vars:  On the left side of the dialog, there is a column of edit fields.  You enter the names of the common factors in these fields.

Vars:  Click on this button to activate a list of currently available manifest variables.  Use this list to select which variables will load on a particular factor.

Manifest Vars:  The variables you have already selected to load on a particular latent variable will appear in this field.

Step 2.  Next, you decide on the name for your residual variables, and the numbering of model parameters.

Base name for residual variables:  Enter a Base Name for your residual variables in this field.  The names of the residual variables will be constructed by adding an integer (starting at one) to this Base Name.  So, for example, if you enter EPS as the base name, and you have 4 manifest variables, your residual variables will be named EPS1, EPS2, EPS3, and EPS4.

Starting Parameter Number:  Choose a starting parameter number here.  The free parameters in your model will be numbered consecutively, starting at this value.

Step 3.  Finally, you decide whether or not you want your common factors and residuals to be correlated.

Factors:  Click on the appropriate radio button to indicate whether you want the common factors to be Uncorrelated or Correlated.

Residual Vars:  Click on the appropriate radio button to indicate whether you want the residuals to be Uncorrelated or Correlated.

If you decide to have correlations for either your factors or residual variables, additional dialog boxes will appear to prompt you for these correlations.  They are labeled Confirmatory Factor Model - Correlate Factors and Confirmatory Factor Model - Correlate Residuals.

For information on the other Wizards implemented in this version of the Structural Modeling module, see:

General Structural Model Wizard


  Confirmatory Factor Model Wizard - Correlate Factors

In this dialog, you enter paths for correlations between factors.

List Boxes:  Select the variables you want to correlate in these two boxes.  All non-redundant correlations between the variables selected in the left box and those selected in the right box will be added to the model when you click on the Correlate button.  The far right list box will show all correlations currently queued to be added to the model.

Correlate button:  Click on this button to add correlations for the selected variables.

Delete button:  Click on this button to delete selected correlations from the box on the far right.


  Setting Correlations Among Latent Variables

In this dialog, you enter paths for correlations between factors.

List Boxes:  Select the variables you want to correlate in these two boxes.  All non-redundant correlations between the variables selected in the left box and those selected in the right box will be added to the model when you click on the Correlate button.  The far right list box will show all correlations currently queued to be added to the model.

Correlate button:  Click on this button to add correlations for the selected variables.

Delete button:  Click on this button to delete selected correlations from the box on the far right.


  Confirmatory Factor Model Wizard - Correlate Residuals

In this dialog, you enter paths for correlations between residuals in a confirmatory factor model.

List Boxes:  Select the residuals you want to correlate in these two boxes.  All non-redundant correlations between the residual variables selected in the left box and those selected in the right box will be added to the model when you click on the Correlate button.  The far right list box will show all correlations currently queued to be added to the model.

Correlate button:  Click on this button to add correlations for the selected residual variables.

Delete button:  Click on this button to delete selected correlations from the box on the far right.


  Structural Equation Modeling - General Structural Model Wizard

Many structural equation models can be thought of as two factor models linked by a multiple regression model.  Indeed, the classic LISREL model formulation for structural equations is based on this idea.

If we envision "causal flow" in the path diagram as going from left to right, we have a confirmatory factor, or "measurement" model for one set of exogenous latent variables on the left, a second confirmatory factor, or "measurement" model for a set of endogenous latent variables on the right.  In the center is a "structural model," a multiple regression with arrows pointing to the endogenous latent variables from exogenous latent variables (or possibly from other endogenous latent variables).

A general structural model fitting this description actually consists of 3 models  two factor models and a regression model.  In keeping with this idea, the Structural Model Wizard takes you, step by step, through the process of generating these 3 models.

(1)	Structural Equation Modeling Wizard - Define Exogenous Factors.

(2)	Structural Equation Modeling Wizard -  Define Endogenous Factors.

(3)	Structural Equation Modeling Wizard - Define Structural Equation Paths.

For information on the other Wizards implemented in this version of the Structural Modeling module, see:

Confirmatory Factor Analysis Wizard


  Path Construction Tool - Adding Comments

If you wish to add a comment to your PATH1 program file, simply type in your comment and click OK.  Your text will be entered as a comment in the commands.

Note:  You do NOT need to type the asterisk (*) as the first character to indicate the comment.  The Path Construction Tool will add this for you automatically.


  SEPATH Wizard- Final Dialog

In this dialog, you will have the following options.

Append this model to the existing program:  When you click OK, the result of the wizard procedure will be added to the end of your model.

Replace existing program with new model:  When you click OK, the model currently in the active *.cmd file will be erased, and replaced by the result of the wizard procedure.

OK button:  Click this button to finish, according to the option selected above.

Exit button:  You will leave the wizard.  What was in the *.cmd text window before you began the wizard procedure will remain intact.

Back button:  You will go back to the preceding wizard dialog.


  Structural Equation Modeling Wizard - Define Exogenous Factors

At this stage, a dialog box will pop up to request you to define the Measurement Model for the independent, or exogenous latent variables in your path diagram.  These are the variables with no arrows pointing to them.

This factor model is defined in basically the same way as in the Confirmatory Factor Analysis Wizard.


  Structural Equation Modeling Wizard - Define Endogenous Factors

At this stage, a dialog box will pop up to request you to define the Measurement Model for the dependent, or endogenous latent variables in your path diagram.  These are the variables with at least one arrow pointing to them.

This factor model is defined in basically the same way as in the Confirmatory Factor Analysis Wizard.  However, this step also defines disturbance terms, residuals attached to the endogenous latent variables.  You have the option of defining correlations for these variables as well.


  Structural Equation Modeling Wizard - Define Structural Equation Paths

When this dialog is active, you define structural paths by selecting from a From list and a To list.  The From list will contain all the latent variables.  The To list will automatically contain the endogenous latent variables, and only those variables.  When you click the Add button, all paths from the From variables to the To variables will be generated.


  Structural Equation Modeling - Specify Grouping Variable

If you are analyzing raw data, you may select a grouping variable, to be used to divide your sample into two or more groups.

Grouping Variable Options:

Use:  Selecting this option causes the currently selected grouping variable to be used to divide the sample into groups.

Ignore:  Selecting this option causes the grouping variable to be ignored, and the entire data file will be treated as one sample.

Variable:  Activating this option calls up a list of current variables.  Select which one will be employed to divide your sample into two or more groups.

Codes:  Here you select values of the grouping variable to be used to divide your sample into groups.  One group will be created for each code value you select.


  Structural Equation Modeling - Specifying Number of Groups Dialog

If you are analyzing a stacked correlation or covariance matrix matrix, you may select the number of groups to be analyzed.

Number of Groups:  Enter the number of groups to be analyzed in this edit window.  If the  number you enter is less than the total number of matrices in the stacked matrix file, the matrices to be analyzed must be ordered first in the file.


  Manifest Variable

A manifest variable is a variable that is directly observable or measurable.  In path analysis diagrams used in structural modeling (see Path Diagram), manifest variables are usually represented by enclosing the variable name within a square or a rectangle.


  Latent Variable

A latent variable is a variable that cannot be measured directly, but is hypothesized to underlie the observed variables.  An example of a latent variable is a factor in factor analysis.  Latent variables in path diagrams are usually represented by a variable name enclosed in an oval or circle.


  Circumplex

A circumplex is a set of variables which, when plotted as vectors in N-dimensional space, fall in a circular pattern.  If a set of variables forms a circumplex, the correlation matrix for the variables will have an unusual pattern called circular structure.  In this pattern, the correlations on diagonal strips below the main diagonal tend to be equal, or nearly so, first becoming smaller, then larger again as you move away from the main diagonal.  Below is a circular structure for an 8x8 correlation matrix.

1.00

0.80   1.00

0.60   0.80   1.00

0.40   0.60   0.80   1.00

0.20   0.40   0.60   0.80   1.00

0.40   0.20   0.40   0.60   0.80   1.00

0.60   0.40   0.20   0.40   0.60   0.80  1.00

0.80   0.60   0.40   0.20   0.40   0.60   0.80   1.00

Circumplex is a special case of a more general concept of radex, developed by Louis Guttman (who contributed a number of innovative ideas to the theory of multidimensional scaling and factor analysis, Guttman, 1954).

For an illustration, see Example 8:  Testing for Circumplex Structure.


  Arrow

An element in a path diagram (see Structural Equation Modeling) used to indicate causal flow from one variable to another, or, in narrower interpretation, to show which of two variables in a linear equation is the independent variable and which is the dependent variable.


  Wire

A wire is a line, usually curved, used  in a path diagram to represent variances and covariances of exogenous variables.


  Exogenous Variable

An exogenous variable is a variable that never appears as a dependent variable in any equation in a structural model.  In a path diagram, exogenous variables can be recognized by the fact that they have no arrows pointing to them.


  Endogenous Variable

An endogenous variable is a variable that appears as a dependent variable in at least one equation in a structural model.  In a path diagram, endogenous variables can be recognized by the fact that they have at least one arrow pointing to them.


  Boundary Case

A boundary case occurs when a parameter iterates to the boundary of the permissible parameter space (see Structural Equation Modeling).  For example, a variance can only take on values from 0 to infinity.  If, during iteration, the program attempts to move an estimate of a variance below zero, the program will constrain it to be on the boundary value of 0.

For some problems (for example a Heywood Case in factor analysis), it may be possible to reduce the discrepancy function by estimating a variance to be a negative number.  In that case, the program does the best it can within the permissible parameter space, but does not actually obtain the global minimum of the discrepancy function.


  Heywood Case

A Heywood case in common factor analysis occurs when the minimum of the discrepancy function is obtained with one or more negative values as estimates for the variance of the unique variables.  Such values are of course impossible.  Heywood cases occur frequently when too many factors are extracted, or the sample size is too small.


  Free Parameter

A numerical value in a structural model (see Structural Equation Modeling) that is part of the model, but is not fixed at any particular value by the model hypothesis.  Free parameters are estimated by the program using iterative methods.  Free parameters are indicated in the PATH1 language with integers placed between dashes on an arrow or a wire.  For example, the following paths both have the free parameter 14.

(F1)-14->[X1]

(e1)-14-(e1)

If two different coefficients have the same free parameter number, as in the above example, then both will of necessity be assigned the same numerical value.  Simple equality constraints on numerical coefficients are thus imposed by assigning them the same free parameter number.


  Monte Carlo

A computer-intensive technique for assessing how a statistic will perform under repeated sampling.  In Monte Carlo methods, the computer uses random number simulation techniques to mimic a statistical population.  In the Monte Carlo procedure of the Structural Equation Modeling Module, the computer constructs the population according to the users prescription, then does the following:

For each Monte Carlo replication, the computer:

(1)	Simulates a random sample from the population,

(2)	Analyzes the sample,

(3)	Stores the results.

After many replications, the stored results will mimic the sampling distribution of the statistic.  Monte Carlo techniques can provide information about sampling distributions when exact theory for the sampling distribution is not available.


  Discrepancy Function

A numerical value that expresses how badly a structural model reproduces the observed data.  The larger the value of the discrepancy function, the worse (in some sense) the fit of model to data.  In general, the parameter estimates for a given model are selected to make a discrepancy function as small as possible.

The discrepancy functions employed in structural modeling all satisfy the following basic requirements:

(1)	They are non-negative, i.e., always greater than or equal to zero.

(2)	They are zero only if fit is perfect, i.e., if the model and parameter estimates perfectly reproduce the observed data.

(3)	The discrepancy function is a continuous function of the elements of S, the sample covariance matrix, and Σ(θ), the reproduced estimate of S obtained by using the parameter estimates and structural model.


  Gradient

In the Structural Equation Modeling module the gradient is the vector of first partial derivatives of the discrepancy function with respect to the parameter values.  At a local or global minimum, the discrepancy function should be at the bottom of a valley, where all first partial derivatives are zero, so the elements of the gradient should all be near to zero when a minimum is obtained.

The elements of the gradient, by themselves, can, on occasion, be somewhat unreliable as indicators of when convergence has occurred, especially when the model fit is not good, and the discrepancy function value itself is quite large.  For this reason, the gradient is not employed as a convergence criterion by this program.


  Nested Sequence of Models

In the Structural Equation Modeling module, a set of models M(1), M(2), ... M(k) form a nested sequence if model M(i) is a special case of M(i+1) for i=1 to k-1.  Thus, each model in the sequence becomes increasingly more general, but includes all previous models as special cases.  As an example, consider one factor, two factor, and three factor models for 10 variables.  The two factor model includes the one factor model as a special case (simply let all the loadings on the second factor be 0).  Similarly, the three factor model contains the two and one factor models as special cases.


  Invariance Under Change of Scale (ICS)

A structural model is invariant under change of scale if model fit is not changed by rescaling the variables, i.e., by multiplying them by scale factors (see Structural Equation Modeling).


  Invariance Under a Constant Scale Factor (ICSF)

A structural model is invariant under a constant scale factor (ICSF) if model fit is not changed if all variables are multiplied by the same constant.  Most, but not all, structural models that are of practical interest are ICSF (see Structural Equation Modeling).


  Steepest Descent Iterations

When initial values for the parameters are far from the ultimate minimum, the approximate Hessian used in the Gauss-Newton procedure may fail to yield a proper step direction during iteration.  In this case, the program may iterate into a region of the parameter space from which recovery (i.e., successful iteration to the true minimum point) is not possible.  One option offered by the Structural Equation Modeling module is to precede the Gauss-Newton procedure with a few iterations utilizing the method of steepest descent.  In the steepest descent approach, values of the parameter vector θ on each iteration are obtained as

In simple terms, what this means is that the Hessian is not used to help find the direction for the next step.  Instead, only the first derivative information in the gradient is used.

Hint for beginners.  Inserting a few Steepest Descent Iterations may help in situations where the iterative routine gets lost after only a few iterations.


  Relative Function Change Criterion

The relative function change criterion is used to stop iteration when the function value is no longer changing (see Structural Equation Modeling).  Basically, it stops iteration when the function ceases to change.  The criterion is necessary because, sometimes, it is not possible to reduce the discrepancy function even when the gradient is not close to zero.  This occurs, in particular, when one of the parameter estimates is at a boundary value.  The true minimum, where the gradient actually is zero, includes parameter values that are not permitted (like negative variances, or correlations greater than one).

On the i'th iteration, this criterion is equal to


  Augmented Product Moment Matrix

For a set of p variables, this is a (p + 1) X (p + 1) square matrix.  The first p rows and columns contain the matrix of moments about zero, while the last row and column contain the sample means for the p variables.  The matrix is therefore of the form:

where [image] is a matrix with element

and [image] is a vector with the means of the variables (see Structural Equation Modeling).


  *.CMD File Extension

This file extension is reserved for Structural Equation Modeling module files.  These are files containing structural models specified in the PATH1 language.


  Structural Equation Modeling Examples

The Structural Equation Modeling module includes a number of preworked examples, many of which are classic examples from textbooks and program manuals.  The examples are described below.  Double-click on an example name for a detailed description and analysis.

1.  Stability of Alienation - Wheaton, Muthen, Alwin, and Summers (1977).  This is an excellent example of a standard structural model.  Two versions are given, one without correlated residuals, one with correlated residuals.  Data File: Wheaton.sta.  Model Files: Wheatona.cmd, Wheatonb.cmd.

2.  Confirmatory Factor Analysis - Lawley and Maxwell (1971) present an example of a confirmatory factor analysis of 9 psychological tests.  Besides being a representative example of a typical confirmatory factor analysis, the example demonstrates how incorrect estimates of standard errors can result from analyzing a correlation matrix as if it were a covariance matrix.  Data File:  Lawley.sta.  Model File:  Lawley.cmd.

3.  Confirmatory Factor Analysis with Identifying Constraints - Everitt (1984) presents this example of a confirmatory factor analysis where constraints must be imposed to allow the model to be identified.  Data File:  Child.sta.  Model File:  Child.cmd.

4.  Effects of Peer Influence on Ambition - Duncan, Haller, and Portes (1968) presented this path model that utilizes manifest exogenous variables.  It is one of the better known examples in the literature.  Data File:  Dhp.sta.  Model File: Dhpa.cmd.

5.  Standardized Solution for the Effects of Peer Influence on Ambition - The traditional approach to estimating a standardized model is demonstrated on the Duncan, Haller, and Portes (1968) example.  Then we demonstrate the new, iterative approach to obtaining a standardized solution with standard errors.  Finally we show how to obtain a fully standardized path model, with both manifest and latent variables standardized.  Data File:  Dhp.sta.  Model Files:  Dhpa.cmd, Dhpa3.cmd.

6.  Factor Analysis with an Intercept Variable - This example, discussed in the textbook by Bollen (1989, p. 308-311), shows, in a very simple context, the general technique for measuring factor means.  Data File:  Boll310.sta.  Model File:  Boll310.cmd.

7.  Comparing Factor Structure in Two Groups - This example, discussed in the textbook by Bollen (1989, p. 355-365), shows how to compare two groups for equivalence of factor structure.  It provides a basic introduction to the techniques involved in fitting and comparing factor models in two or more populations.  Data File:  Boll362m.sta.  Model Files:  Boll362a.cmd, Boll362b.cmd.

8.  Testing for Circumplex Structure - A correlational pattern hypothesis is a hypothesis that specifies that correlations are equal to each other, to specified numerical values, or both.  With its ability to test correlation matrices directly, the module can be used to test a correlational pattern hypothesis in one or more populations.  In this example, we show how to test for circumplex structure, using a classic example by Guttman (1954).  Data File:  Guttman.sta.  Model File:  Circle.cmd.

9.  Testing for Stability of a Correlation Matrix Over Time - In this example, we show how to test the hypothesis that a matrix of correlations has remained stable over time.  Data File:  Twocorr.sta.  Model File:  Twocorr.cmd.

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement - This is a path model for the relationship between home environment and mathematics achievement, based on a study by Keeves (1972).  The path model is on manifest, rather than latent variables.  Data File:  Keeves.sta.  Model File:  Keeves1.cmd.

11.  Structural Models for Home Environment and Mathematics Achievement - This is a structural model on the Keeves (1972) data, showing the relationship between home environment and mathematics achievement.  Data File:  Keeves.sta.  Model Files:  Keeves3a.cmd, Keeves3b.cmd.

12.  Test Theory Models for Sets of Congeneric Tests - In this set of examples, we show how to fit various test theory models.  Data File:  Lord.sta.  Model Files:  Lorda.cmd, Lordb.cmd, Lordc.cmd, Lordd.cmd.

13.  Comparing Dependent Variances - This example shows how to compare two variances for variables measured on the same subjects.  Data File:  Var2.sta.  Model File:  Var2.cmd.

14.  A Multi-Trait Multi-Method Model - Kenny (1979) analyzed some data with a Multi-trait Multi-Method model.  We review his analysis in this example.  Data File:  Jaccard.sta.  Model File:  Jaccard.cmd.

15.  A Longitudinal Factor Analysis Model - Everitt (1984) gave an illustrative example of a longitudinal factor model, but analyzed a correlation matrix incorrectly as if it were a covariance matrix.  We review and correct his analysis here.  Data File:  Meyer.sta.  Model File:  Meyer.cmd.

16.  A Structural Model for 10 Personality and Drug Use Variables - Huba and Harlow (1987) illustrated techniques for analyzing non-normal variables with a structural model relating personality variables to drug use in adolescents.  This model illustrates several important aspects of structural modeling.  Data File:  Hh.sta.  Model File:  Hh.cmd.

17.  A Test for Compound Symmetry - In this example, we demonstrate how to test the ANOVA assumption of compound symmetry in a covariance matrix.  Data File:  Winer.sta.  Model File:  Winer.cmd.

18.  Testing the Equality of Correlation Matrices from Different Populations - In this example, we demonstrate how to compare entire correlation matrices based on independent samples from different populations.  Data File:  Jennrich.sta.  Model File:  Jennrich.cmd.


Structrual Equation Modeling Examples -  1.  Stability of Alienation
  Structural Equation Modeling Examples - 1.  Stability of Alienation

Data File: Wheaton.sta.

Model Files: Wheatona.cmd, Wheatonb.cmd.

A familiar example in the structural modeling literature is the study on stability of alienation by Wheaton, Muthen, Alwin, and Summers (1977).  Joreskog and Sorbom, in the LISREL VI manual (1984, pp. 22-30), analyzed two very similar structural models with the Wheaton data.  The covariance matrix for these data, based on a sample size of 932, is in a file called Wheaton.sta.

Below is the structural diagram for the first model analyzed by Joreskog and Sorbom.

This diagram is similar to one in Joreskog and Sorbom (1984).  For reasons not clear to us, they specified their model with a variance for the variable SES equal to a free parameter, rather than fixed at 1, which is the normal convention.  So some of their coefficients will differ from ours in the unstandardized case.  Remember, any arrow without any numerical index attached is assumed to have a fixed coefficient of 1.  Such arrows may be given in the PATH1 language in a simplified form - for example, the arrow from EPSILON1 to ANOMIA67 is denoted as follows:

(EPSILON1)-->[ANOMIA67]

Try setting up this model yourself with SEPATH.  Run the example, using the default options.  If you fit the model correctly, you will obtain a Chi-square value of approximately 71.47 with 6 degrees of freedom.

If you run into difficulty, a version of the PATH1 statements for the model is contained in a file called Wheatona.cmd.

Joreskog and Sorbom (1984) point out that a modified version of the above model, in which EPSILON1 and EPSILON3 are allowed to correlate, fits the data much better than the original version.  This model is represented in the path diagram below.

The only difference between the two models is the wire between EPSILON1 and EPSILON3.  Producing this revised model from your original model should take you about 30 seconds with SEPATH.  The revised model is in the file Wheatonb.cmd.

For other examples, see:

2.  Confirmatory Factor Analysis

3.  Confirmatory Factor Analysis with Identifying Constraints

4.  Effects of Peer Influence on Ambition

5.  Standardized Solution for the Effects of Peer Influence on Ambition

6.  Factor Analysis with an Intercept Variable

7.  Comparing Factor Structure in Two Groups

8.  Testing for Circumplex Structure

9.  Testing for Stability of a Correlation Matrix Over Time

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

11.  Structural Models for Home Environment and Mathematics Achievement

12.  Test Theory Models for Sets of Congeneric Tests

13.  Comparing Dependent Variances

14.  A Multi-Trait Multi-Method Model

15.  A Longitudinal Factor Analysis Model

16.  A Structural Model for 10 Personality and Drug Use Variables

17.  A Test for Compound Symmetry

18.  Testing the Equality of Correlation Matrices from Different Populations


  Structural Equation Modeling Examples - 2.  Confirmatory Factor Analysis

Data File:  Lawley.sta.

Model File:  Lawley.cmd.

Lawley and Maxwell (1971, chapter 7) present techniques for confirmatory factor analysis.  These authors are careful to point out that estimation of standard errors must be adjusted when a correlation matrix is analyzed instead of a covariance matrix.  They give formulae for computing standard errors when a covariance matrix is analyzed, and provide an alternative method for computing standard errors when the sample correlation matrix is analyzed.  The formulae are illustrated with a numerical example, the results of which are presented in their Tables 7.9  (p. 99) and 7.10 (p. 102).

The Lawley-Maxwell example was based on an analysis in a paper by Joreskog and Lawley (1968), which used data from Holzinger and Swineford (1939).  Nine psychological tests were administered to seventh and eighth grade students.  The tests were (1) Visual Perception, (2) Cubes, (3) Lozenges, (4) Paragraph Comprehension, (5) Sentence Completion, (6) Word Meaning, (7) Addition, (8) Counting Dots, and (9) Straight-curved capitals.  The Lawley-Maxwell example is a typical one, in that each factor is restricted to load on only 3 or 4 manifest variables, and the factors are allowed to correlate with each other.

The model is portrayed in the diagram below:

You can reproduce both sets of results in the Lawley and Maxwell tables.  First, to simulate what happens with most covariance structure analysis programs, analyze the correlation matrix incorrectly as though it were a covariance matrix by using the Covariances option in the Data to Analyze section of the Analysis Parameters dialog.  Set the number of decimal places to 2, to make the comparison with the Lawley-Maxwell tables easier.  Before beginning iteration, the program will interrupt you with a warning message, that you are about to analyze a correlation matrix (incorrectly) as if it is a covariance matrix.  You will obtain the erroneous standard errors described by Lawley and Maxwell.

Now, go back to the Analysis Parameters dialog, reset the Data to Analyze to Correlations, and re-execute the iteration.  You will see estimates and standard errors that are identical to those reported by Lawley and Maxwell as the correct values, which they obtained by using corrected formulae.

For other examples, see:

1.  Stability of Alienation

3.  Confirmatory Factor Analysis with Identifying Constraints

4.  Effects of Peer Influence on Ambition

5.  Standardized Solution for the Effects of Peer Influence on Ambition

6.  Factor Analysis with an Intercept Variable

7.  Comparing Factor Structure in Two Groups

8.  Testing for Circumplex Structure

9.  Testing for Stability of a Correlation Matrix Over Time

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

11.  Structural Models for Home Environment and Mathematics Achievement

12.  Test Theory Models for Sets of Congeneric Tests

13.  Comparing Dependent Variances

14.  A Multi-Trait Multi-Method Model

15.  A Longitudinal Factor Analysis Model

16.  A Structural Model for 10 Personality and Drug Use Variables

17.  A Test for Compound Symmetry

18.  Testing the Equality of Correlation Matrices from Different Populations


  Structural Equation Modeling Examples - 3.  Confirmatory Factor Analysis with Identifying Constraints

Data File:  Child.sta.

Model File:  Child.cmd.

Everitt (1984, p. 45-52) discusses, in considerable detail, a confirmatory factor analysis of a data set in Child (1970).  This factor model is similar in some ways to the Lawley-Maxwell example.  However, in this case one factor loads on only two manifest variables.  This, unfortunately, leads to a model which is not identified, unless some identifying constraints are applied.  In this model, two factor loadings are constrained to be equal to each other, and two factor covariances are constrained to be zero.  The path diagram for this model is shown below.

Data for this example are in the file Child.sta.  The PATH1 specification for this model is contained in the file Child.cmd.

Everitts analysis of this example is incorrect, because a correlation matrix was treated as if it were a covariance matrix.  You can reproduce Everitts incorrect results by specifying Covariances as the Data to Analyze in the Analysis Parameters dialog.  Correct results may be obtained by specifying Correlations as the Data to Analyze.

For other examples, see:

1.  Stability of Alienation

2.  Confirmatory Factor Analysis

4.  Effects of Peer Influence on Ambition

5.  Standardized Solution for the Effects of Peer Influence on Ambition

6.  Factor Analysis with an Intercept Variable

7.  Comparing Factor Structure in Two Groups

8.  Testing for Circumplex Structure

9.  Testing for Stability of a Correlation Matrix Over Time

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

11.  Structural Models for Home Environment and Mathematics Achievement

12.  Test Theory Models for Sets of Congeneric Tests

13.  Comparing Dependent Variances

14.  A Multi-Trait Multi-Method Model

15.  A Longitudinal Factor Analysis Model

16.  A Structural Model for 10 Personality and Drug Use Variables

17.  A Test for Compound Symmetry

18.  Testing the Equality of Correlation Matrices from Different Populations


  Structural Equation Modeling Examples - 4.  Effect of Peer Influence on Ambition

Data File:  Dhp.sta.

Model File: Dhpa.cmd.

Duncan, Haller, and Portes (1968) analyzed the effect of peer influences on ambition.  The correlation matrix from their study, based on 329 subjects, is contained in the file Dhp.sta.  Their data have been analyzed in a number of publications, and I will not discuss the substantive content of the example here.  Joreskog and Sorbom (1984) present the results from several path models on these data.  Here we analyze the model the results for which are given in Table III.12 of Joreskog and Sorbom.  The path diagram is shown below.  PATH1 statements corresponding to the diagram are in a file called Dhpa.cmd.

We begin by analyzing the model the way it was analyzed by Joreskog and Sorbom (1984).  Several comments are in order.  First, note from the path diagram that the model has manifest exogenous variables.  In the file Dhpa.cmd, you are reminded to use the Manifest Exogenous Fixed option in the Analysis Parameters dialog with this model.  The command is used because of the existence in the model of a number of manifest exogenous variables (located on the left hand side of the diagram).  We have taken the convenient option here and not specified any of the variance-covariance relationships for these variables.  If you fail to activate the Manifest Exogenous Fixed command in the Analysis Parameters dialog, the program will give an error message and abort the analysis, unless you add paths for all of the variance-covariance relationships among these variables.

Second, note that some paths are constrained to have fixed coefficients of 1.0.  It is a relatively common technique in structural modeling to fix one path coefficient to each endogenous latent variable, in order to identify the variance of the latent variable at some fixed value.  In this case, we see two path coefficients are fixed, in order to identify the variances of the latent endogenous variables ETA1 and ETA2.

For other examples, see:

1.  Stability of Alienation

2.  Confirmatory Factor Analysis

3.  Confirmatory Factor Analysis with Identifying Constraints

5.  Standardized Solution for the Effects of Peer Influence on Ambition

6.  Factor Analysis with an Intercept Variable

7.  Comparing Factor Structure in Two Groups

8.  Testing for Circumplex Structure

9.  Testing for Stability of a Correlation Matrix Over Time

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

11.  Structural Models for Home Environment and Mathematics Achievement

12.  Test Theory Models for Sets of Congeneric Tests

13.  Comparing Dependent Variances

14.  A Multi-Trait Multi-Method Model

15.  A Longitudinal Factor Analysis Model

16.  A Structural Model for 10 Personality and Drug Use Variables

17.  A Test for Compound Symmetry

18.  Testing the Equality of Correlation Matrices from Different Populations


  Structural Equation Modeling Examples - 5.  Standardized Solutions for the Effect of Peer Influence on Ambition

Data File:  Dhp.sta.

Model Files:  Dhpa.cmd, Dhpa3.cmd.

In a standardized solution, the latent variables all have unit variance.  In many structural modeling programs, there is no convenient way to constrain the endogenous latent variables so that they have unit variance.  For such programs to produce a standardized solution, model parameters are estimated with the variances of the endogenous variables identified (at some unspecified value).  After iteration is complete, the standardized coefficients are computed, using well known results from the algebra of multiple linear regression to transform the latent variables to standardized form.

To produce such an old fashioned standardized solution, analyze the data in Dhp.sta with the model in Dhpa.cmd, with the Manifest Exogenous Fixed, and Standardization Old options selected in the Analysis Parameters.

Compare the model parameters for this solution with those from the unstandardized solution obtained previously.  One point is particularly noteworthy here.  Some of the constraints which were specified for the unstandardized model are violated in the standardized model!  For example, the path coefficients to ROASP and FOASP which were fixed at 1.0 in the unstandardized model now have values of .767 and .771, respectively.  This is because the post hoc adjustment which produces the standardized coefficients simply employs the (unstandardized) coefficients and some regression algebra.  The procedure is not aware of any equality constraints on parameters, and cannot be guaranteed to maintain them.

This creates no real problem, since the values were assigned an arbitrary value of 1.0 simply to identify the variances at some value.  On the other hand, two paths were constrained to be equal (those with the coefficient label 9 in the path diagram) for reasons other than identification purposes.  These no longer have equal values in the standardized model estimates.  What this means is that it may not be possible to produce standardized estimates which meet the constraints of the maximum likelihood equations, and also meet the model constraint that two coefficients are equal while maintaining the same model fit.

There is a third issue which is probably already obvious to the reader after comparing standardized and unstandardized solutions.  Standard errors are not provided in the old standardized solution.  This is because the post hoc adjustment of the unstandardized coefficients produces values whose information matrix is not the same as that for the unstandardized values.

We have established three major points so far:

(1)	The old approach to standardization produces the same discrepancy function as obtained in the unstandardized solution.

(2)	Equality constraints on the parameters imposed on the unstandardized solution may not be maintained when the parameters are transformed to the standardized form.

(3)	Standard errors are not available with the Standardization Old option.

Now, we will explore the properties of the new standardization approach.  This approach uses constrained estimation to force endogenous latent variables to have variances of one.  Consequently, fixed parameter values of one which where used to identify the variances of endogenous latent variables should now be changed to free parameters before employing the Standardization New option.

Call up Dhpa.cmd and find the following section of model.

 (ETA1)-12->[REASP]

        -->[ROASP]

 (ETA2)-->[FOASP]

       -13->[FEASP]

Change the fixed coefficients to free parameters, so the revised paths look like this:

 (ETA1)-12->[REASP]

       -21->[ROASP]

 (ETA2)-22->[FOASP]

       -13->[FEASP]

Use the options Manifest Exogenous - Free, and Standardization - New in the Analysis Parameters dialog.  Also, set No. Decimal Places to 4.

Execute the iteration, and observe the results.  You will notice that the Chi-Square statistic for the model is slightly different than it was for the unstandardized solution.  (29.8964 to 29.8987). This is because the Standardization - New option produces standardized coefficients by constraining the estimation process.  All equality constraints you imposed in your model are maintained during estimation.  Notice that the two coefficients constrained to be equal (those with the parameter number 9) are estimated to be the same number.  In the Standardization - Old procedure, these are not actually equal once the post hoc standardization procedure is employed.  This demonstrates an important point which is often lost in discussions of standardization.  Because constraints imposed on the unstandardized solution are usually not maintained in the standardized solution, the Chi-Square statistic obtained in the old standardization approach may not, in fact, be correct.  Another way of putting it is that the old standardization approach may remove your model constraints without your consent.  Some of these constraints may have been artificial ones designed to achieve identification.  However, if the constraints have some important substantive purpose, you should be aware that the old standardization approach may remove them.

The Lagrange multiplier statistics for the variance constraints are an important diagnostic tool for assessing whether model constraints were serving merely to achieve identification, or were accomplishing some other purpose.  In this case, we have removed two constraints on model coefficients. These constraints forced two parameters to be equal to a fixed value of one. We have now removed these constraints, and if forcing latent variable variances to be unity imposes no further constraints on the model fitting process, we should see two indications.

(1)	The Chi-Square statistic for the model in the Standarization - New option should be the same as in the Standardization - Old option.

(2)	LaGrange multiplier statistics for all standardization constraints should all be zero.

We see that, in this case, both indications are not present. We have already noted that the Chi-Square statistic is not the same as in the Standardization - Old solution.  The LaGrange multiplier statistics are slightly greater than zero, indicating that the standardization of latent endogenous variables actually imposes constraints on this model.

If the unit variances were simply an identification condition (as they frequently are) these statistics would all be zero.  But in this case, imposing the standardization restriction on the endogenous latent variables constrains the solution for the path coefficients.  The value of the coefficients which minimizes the discrepancy function, subject to the standardization constraints, is not one of the solutions which is a global minimum when the latent variable variances are unconstrained.

The problem is that the minimum of the discrepancy function, achieved when the two parameters labeled 9 are constrained to be equal, cannot be achieved when the endogenous latent variable variances are constrained at unity.  If we allow the two paths labeled with coefficient 9 to vary freely, by renumbering one of them 99, we find a slightly lower Chi-square value, and zero LaGrange multiplier statistics (input for this example is in the file Dhpa3.cmd).  For this solution, the coefficients will not agree with the old fashioned output produced by the commands in Dhpa.cmd.

The old fashioned output was obtained by standardizing, after the fact, coefficients which were generated under the constraint that the two paths between ETA1 and ETA2 are equal.  Standardization after the fact invalidates that constraint, but the solution will not be the same as it would be if you relaxed the constraint, computed a solution, and then standardized.  If, however, you return to the original input file (Dhpa.cmd), relax the equality constraint for the two paths labeled with coefficient number 9, and recompute, you will find that the standardized coefficients agree precisely with those computed by the new method with the commands in Dhpa3.cmd.  Note that the new procedure allows standard errors to be calculated, while the old procedure does not.

Let's briefly review the points covered in the Stability of Alienation, Confirmatory Factor Analysis, Confirmatory Factor Analysis with Identifying Constraints, and Effects of Peer Influence on Ambition examples.

•	The old fashioned approach to standardization has one advantage  computational simplicity.  However, confidence intervals for standardized parameters cannot be calculated with this method.  Moreover, equality constraints and fixed value constraints which are satisfied by coefficients in the unstandardized solution may not be satisfied in the standardized solution.

•	When converting an old model to the new standardized method, you should free up parameters which were fixed solely for the purpose of identifying the variances of endogenous latent variables.  There should be one such parameter for each endogenous latent variable.

•	If Lagrange multiplier statistics are not zero, relax all equality constraints on parameters, and double-check to make sure you have freed up the parameters which were fixed for identification purposes.

•	If your solution has a significant number of manifest exogenous variables, you can speed up iteration using the Manifest Exogenous Fixed option, then restart the iteration with the Manifest Exogenous Free option after convergence has occurred in order to guarantee correct standard errors and Chi-square values.

•	In the above examples, we analyzed a covariance matrix as though is was a correlation matrix in order to remain consistent with traditional analyses of the data.  Consequently, standard errors are not generally correct.  The program gave warning messages before computing its results.

By setting the Data to Analyze option in the Analysis Parameters dialog to Correlations, you can obtain a fully standardized path model with correct standard errors.

For other examples, see:

1.  Stability of Alienation

2.  Confirmatory Factor Analysis

3.  Confirmatory Factor Analysis with Identifying Constraints

4.  Effects of Peer Influence on Ambition

6.  Factor Analysis with an Intercept Variable

7.  Comparing Factor Structure in Two Groups

8.  Testing for Circumplex Structure

9.  Testing for Stability of a Correlation Matrix Over Time

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

11.  Structural Models for Home Environment and Mathematics Achievement

12.  Test Theory Models for Sets of Congeneric Tests

13.  Comparing Dependent Variances

14.  A Multi-Trait Multi-Method Model

15.  A Longitudinal Factor Analysis Model

16.  A Structural Model for 10 Personality and Drug Use Variables

17.  A Test for Compound Symmetry

18.  Testing the Equality of Correlation Matrices from Different Populations


Structural Equation Modeling Examples - 10.  A Multiple Regression Model for Path Analysis and Home Achievement
  Structural Equation Modeling Examples - 10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

Data File:  Keeves.sta.

Model File:  Keeves1.cmd.

Joreskog and Sorbom (1982) discuss several structural models which they fit to data from a study of home environment and school achievement by Keeves (1972).  Keeves studied 215 sixth grade boys over a one year period, and measured initial mathematics achievement ( [image]), a structural dimension in the home ( [image]), an attitudinal dimension of the home environment( [image]), a process dimension of the home environment ( [image]), and final mathematics achievement ( [image]). The correlation matrix for the Keeves data is in a file called Keeves.sta.

According to Joreskog and Sorbom,

The three home environment dimensions were derived as the principal components of three sets of items which sampled each of the three home domains.  Thus, the structural dimension was based on home interview items which determined the level of father's education, father's occupation, mother's occupation before marriage, religious affiliation, and number of children in the family.  The attitudinal dimension was based on parents' attitudes toward the child's present education, future education, and occupation, and the parents' aspirations for themselves.  The process dimension was based on relations between home and school, use of books and libraries, parents' help with formal school work, and arrangements for doing home assignments.

Cooley and Lohnes (1976) analyzed Keeves' data with a path model on the observed variables.  This model, essentially a standardized multiple regression, is shown in the figure below.

PATH1 statements corresponding to this model can be found in a file Keeves1.cmd.  For other analyses of these data, see 11.  Structural Models for Home Environment and Mathematics Achievement.

For other examples, see:

1.  Stability of Alienation

2.  Confirmatory Factor Analysis

3.  Confirmatory Factor Analysis with Identifying Constraints

4.  Effects of Peer Influence on Ambition

5.  Standardized Solution for the Effects of Peer Influence on Ambition

7.  Comparing Factor Structure in Two Groups

8.  Testing for Circumplex Structure

9.  Testing for Stability of a Correlation Matrix Over Time

12.  Test Theory Models for Sets of Congeneric Tests

13.  Comparing Dependent Variances

14.  A Multi-Trait Multi-Method Model

15.  A Longitudinal Factor Analysis Model

16.  A Structural Model for 10 Personality and Drug Use Variables

17.  A Test for Compound Symmetry

18.  Testing the Equality of Correlation Matrices from Different Populations


  Structural Equation Modeling Examples - 11.  Structural Models for Home Environment and Mathematics Achievement

Data File:  Keeves.sta.

Model Files:  Keeves3a.cmd, Keeves3b.cmd.

Joreskog and Sorbom (1982) fit two structural models of their own to the Keeves (1972) data analyzed in a different manner by Cooley and Lohnes (1976).  The Cooley and Lohnes approach is demonstrated in the example on A Multiple Regression Model for Home Environment and Mathematics Achievement.  A path diagram for the first model is shown below (the data are in the file Keeves.sta).

This model takes measurement errors in the home variables into account and treats them merely as fallible indicators of an aggregate construct variable "home."  PATH1 statements for this model are in a file called Keeves3a.cmd.

A somewhat different model is represented in the diagram in the Figure below.  This model incorporates errors of measurement in the measures of mathematics achievement.  It assumes that reliabilities for the two measures are known to be 0.90.  Consequently the path coefficients representing true score and error variance coefficients are shown as fixed in the diagram.  PATH1 statements for this model are in a file called Keeves3b.cmd.

For other examples, see:

1.  Stability of Alienation

2.  Confirmatory Factor Analysis

3.  Confirmatory Factor Analysis with Identifying Constraints

4.  Effects of Peer Influence on Ambition

5.  Standardized Solution for the Effects of Peer Influence on Ambition

6.  Factor Analysis with an Intercept Variable

7.  Comparing Factor Structure in Two Groups

8.  Testing for Circumplex Structure

9.  Testing for Stability of a Correlation Matrix Over Time

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

12.  Test Theory Models for Sets of Congeneric Tests

13.  Comparing Dependent Variances

14.  A Multi-Trait Multi-Method Model

15.  A Longitudinal Factor Analysis Model

16.  A Structural Model for 10 Personality and Drug Use Variables

17.  A Test for Compound Symmetry

18.  Testing the Equality of Correlation Matrices from Different Populations


  Structural Equation Modeling Examples - 12.  Test Theory Models for Sets of Congeneric Tests

Data File:  Lord.sta.

Model Files:  Lorda.cmd, Lordb.cmd, Lordc.cmd, Lordd.cmd.

A variety of interesting test theory models can be tested and estimated using structural equations modeling.  These models are all special cases of the common factor model, and are discussed in Joreskog (1974) on pages 49-56.  The classical test theory model can be expressed as a common factor model.  Suppose a group of tests are congeneric, i.e., have the same true scores underlying them.  Then if the observed score is equal to the true score plus error, and error is uncorrelated with true scores, we have the path model shown in Model A below for two sets of two congeneric tests.

Model A:

Suppose you wished to assess whether two different tests measure the same trait.  In classical test theory, we would say that the tests measure the same trait if their true scores are perfectly correlated, i.e., if the correlation coefficient between the tests, corrected for attenuation, is unity.  Joreskog (1978) refers to such tests as tau-equivalent.

Lord (1957) proposed a test for tau-equivalence.  His test required the assumption that the elements of each pair of tests have equal variance and equal reliability, i.e., that the tests are parallel.  The model corresponding to the hypothesis tested by Lord's method, i.e. that the tests are both parallel and tau-equivalent, is illustrated in the path diagram below.

Model B:

It is possible to test the assumptions underlying Lord's (1957) test directly, i.e., we can test the hypothesis that the elements of each pair of tests are parallel (i.e., have equal variance and equal reliability) without testing the hypothesis that the disattenuated correlation coefficient is unity.  This hypothesis is shown in the next path diagram.

Model C:

Models B and C form a nested sequence, since B is a special case of C.  If we compute the Chi-square statistics for Models B and C, and take their difference, we obtain a Chi-square difference statistic with one degree of freedom for testing the hypothesis that the disattenuated correlation is 1.

Lord's test is valid provided its assumptions are met.  However, SEPATH allows us to test whether the disattenuated correlation coefficient is unity without requiring the restrictions of Lord's test.  The figure below illustrates a hypothesis that the tests are congeneric (but not necessarily parallel) and tau-equivalent.

Model D:

Model D is a special case of model A, i.e., the two models form a nested sequence.  Consequently, subtracting the Chi-square statistics for model A from that obtained for model D will produce a Chi-square statistic with one degree of freedom.  This provides an alternative test that the disattenuated correlation is 1.

Joreskog tested models A,B,C, and D on some data given in Lord's (1957) paper.  The results of the testing are summarized both in Joreskog (1974) and in Joreskog (1978).

The covariance matrix for this example is in the file Lord.sta.  The PATH1 statements for the 4 models are contained in the file Lorda.cmd, Lordb.cmd, Lordc.cmd, Lordd.cmd.

Both Chi-square difference tests yield the same conclusion:  the hypothesis that the disattenuated correlation coefficient is 1 can be resoundingly rejected.  For example, the Chi-square difference statistic (with one degree of freedom) for Model A versus Model D is 35.51.  On the other hand, the maximum likelihood estimate for the disattenuated correlation is quite high (.899).  Moreover, the standard error for this value is only .019.

1.  Stability of Alienation

2.  Confirmatory Factor Analysis

3.  Confirmatory Factor Analysis with Identifying Constraints

4.  Effects of Peer Influence on Ambition

5.  Standardized Solution for the Effects of Peer Influence on Ambition

6.  Factor Analysis with an Intercept Variable

7.  Comparing Factor Structure in Two Groups

8.  Testing for Circumplex Structure

9.  Testing for Stability of a Correlation Matrix Over Time

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

11.  Structural Models for Home Environment and Mathematics Achievement

13.  Comparing Dependent Variances

14.  A Multi-Trait Multi-Method Model

15.  A Longitudinal Factor Analysis Model

16.  A Structural Model for 10 Personality and Drug Use Variables

17.  A Test for Compound Symmetry

18.  Testing the Equality of Correlation Matrices from Different Populations


  Structural Equation Modeling Examples - 8.  Testing for Circumplex Structure

Data File:  Guttman.sta.

Model File:  Circle.cmd.

A perfect circumplex correlation matrix (Guttman, 1954) has equal correlations on sub-diagonal strips.  For example, a 6x6 correlation matrix would be of the form

A data set used frequently to demonstrate a Guttman circumplex is a correlation matrix among 6 different kinds of abilities for 710 Chicago school children.  This matrix, from Guttman (1954), is in a file called Guttman.sta.

The commands for testing a hypothesis of circumplex structure are in the file Circle.cmd.  Test these commands, using the Correlations option of Data to Analyze.

The sample size is very large in this example.  Hence, we would expect precision of estimate to be very high.  At the same time, we would have to keep in mind that the "reject-support" approach of the Chi-square test would be of very limited usefulness in this situation.  We recognize that a model with this many constraints will almost certainly not fit perfectly in the population, and we have very high power to detect imperfect fit.

The Chi-square statistic yields, in this case, a value of 27.05 with 12 degrees of freedom.  The probability level is .008, indicating that the null hypothesis of perfect fit must be rejected.  Joreskog (1978), analyzing these data, remarked that they "do not fit a circumplex well."

This conclusion seems, in the 20-20 vision of hindsight, unjustified, and incorrect.  The correct conclusion is that it is highly probable that they do not fit a circumplex perfectly.  Goodness-of-fit indices indicate how well these data actually do fit a circumplex.  The 90% confidence interval for the Steiger-Lind (1980) RMS index is between .021 and .064.

The corresponding confidence interval for the adjusted population gamma coefficient is between .972 and .997.

A reasonable conclusion would seem to be that Guttman's data fit a circumplex very well, a fact which we have verified statistically.

1.  Stability of Alienation

2.  Confirmatory Factor Analysis

3.  Confirmatory Factor Analysis with Identifying Constraints

4.  Effects of Peer Influence on Ambition

5.  Standardized Solution for the Effects of Peer Influence on Ambition

6.  Factor Analysis with an Intercept Variable

7.  Comparing Factor Structure in Two Groups

9.  Testing for Stability of a Correlation Matrix Over Time

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

11.  Structural Models for Home Environment and Mathematics Achievement

12.  Test Theory Models for Sets of Congeneric Tests

13.  Comparing Dependent Variances

14.  A Multi-Trait Multi-Method Model

15.  A Longitudinal Factor Analysis Model

16.  A Structural Model for 10 Personality and Drug Use Variables

17.  A Test for Compound Symmetry

18.  Testing the Equality of Correlation Matrices from Different Populations


  Structural Equation Modeling Examples - 9.  Testing for Stability of a Correlation Matrix Over Time

Data File:  Twocorr.sta.

Model File:  Twocorr.cmd.

Suppose you measured a set of variables twice, and wished to test the hypothesis that the correlation coefficient had not changed from time 1 to time 2.  For example, suppose 120 individuals are measured twice on verbal, quantitative, and analytical ability.  In this case, the covariance matrix would be 6x6.

This hypothesis can be tested easily as a correlational pattern hypothesis (see Steiger, 1980).  The key to setting up this problem is to conceptualize the 3 variables measured at 2 times as 6 variables measured on a single group of subjects.

A 6x6 correlation matrix is given in the file Twocorr.sta.

The commands for performing the hypothesis test are in a file called Twocorr.cmd.

The estimated correlations among the alias latent variables are maximum likelihood estimates of the correlations among the manifest variables, under the null hypothesis.

I should add a note of caution here.  The tests performed by SEPATH on correlation matrices are valid asymptotic statistics.  However, the evidence suggests that (especially at smaller sample sizes) tests especially designed for correlational hypotheses (Steiger 1980a, 1980b; Steiger & Browne, 1984; Steiger & Hakstian, 1982; Wilson & Martin, 1983), which use the Fisher transform, may be more accurate and more powerful than tests performed with SEPATH.

1.  Stability of Alienation

2.  Confirmatory Factor Analysis

3.  Confirmatory Factor Analysis with Identifying Constraints

4.  Effects of Peer Influence on Ambition

5.  Standardized Solution for the Effects of Peer Influence on Ambition

6.  Factor Analysis with an Intercept Variable

7.  Comparing Factor Structure in Two Groups

8.  Testing for Circumplex Structure

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

11.  Structural Models for Home Environment and Mathematics Achievement

12.  Test Theory Models for Sets of Congeneric Tests

13.  Comparing Dependent Variances

14.  A Multi-Trait Multi-Method Model

15.  A Longitudinal Factor Analysis Model

16.  A Structural Model for 10 Personality and Drug Use Variables

17.  A Test for Compound Symmetry

18.  Testing the Equality of Correlation Matrices from Different Populations


  Structural Equation Modeling Examples - 13.  Comparing Dependent Variances

Data File:  Var2.sta.

Model File:  Var2.cmd.

SEPATH can be used to perform pattern hypotheses on a covariance matrix.  As a simple example, consider some data gathered by William E. Coffman, and reported by Lord (1963).  These data represent performance on the Stanford Achievement Test for 95 students measured in the seventh and eighth grades.  The covariance matrix for the data is in a file called Var2.sta.  Suppose you wished to test the hypothesis that the population variance had not changed from seventh to eighth grade.  The PATH1 specification for such a hypothesis (contained in the file Var2.cmd) is as follows:

[X1]-1-[X1]
[X2]-1-[X2]
[X1]-2-[X2]

The Chi-square statistic indicates that the hypothesis of equal variances can be rejected, as the probability level is only about .0001.

1.  Stability of Alienation

2.  Confirmatory Factor Analysis

3.  Confirmatory Factor Analysis with Identifying Constraints

4.  Effects of Peer Influence on Ambition

5.  Standardized Solution for the Effects of Peer Influence on Ambition

6.  Factor Analysis with an Intercept Variable

7.  Comparing Factor Structure in Two Groups

8.  Testing for Circumplex Structure

9.  Testing for Stability of a Correlation Matrix Over Time

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

11.  Structural Models for Home Environment and Mathematics Achievement

12.  Test Theory Models for Sets of Congeneric Tests

14.  A Multi-Trait Multi-Method Model

15.  A Longitudinal Factor Analysis Model

16.  A Structural Model for 10 Personality and Drug Use Variables

17.  A Test for Compound Symmetry

18.  Testing the Equality of Correlation Matrices from Different Populations


  Structural Equation Modeling Examples - 14.  A Multi-Trait Multi-Method Model

Data File:  Jaccard.sta.

Model File:  Jaccard.cmd.

When personality traits or characteristics are measured, variation among people can occur for several reasons.  Two obvious contributing factors are variation in the traits themselves, and variations in the way people react to a particular method.

When a trait is measured by only one method, there is a possibility that the variation observed is actually method variance, rather than trait variance.  For example, if a particular questionnaire does not control for acquiescence response set, variation among people due to a problem in the method is confounded with actual trait variation.

One way around this problem is to try to measure both trait and method variation in the same experiment.  The multi-trait - multi-method correlation matrix contains correlations between t traits or characteristics each measured by the same m methods.  Campbell and Fiske (1959) suggested that the multi-trait - multi-method correlation matrix should be examined to provide evidence of construct validity.

In their original work, Campbell and Fiske suggested that two kinds of validity, which they termed convergent validity and discriminant validity, could be evaluated by examining this matrix.  There are 4 kinds of correlations in the matrix; (1) same-trait, same-method; (2) same-trait, different-method; (3) different-trait, same-method; (4) different-trait, different-method.  Convergent validity is demonstrated if same-trait, different method correlations are large.  Discriminant validity is evidenced if same-trait different-method correlations are substantially higher than different-trait, different-method correlations.

Kenny (1979) analyzed data from Jaccard, Weber, and Lundmark (1975).  Their study measured attitude toward cigarette smoking (C) and attitude toward capital punishment (P) with 4 different methods.  The methods were: (1) semantic differential, (2) Likert, (3) Thurstone, (4) Guilford.  The correlation matrix, based on only 35 observations, is in a file called Jaccard.sta.

Kenny used a classic test theory approach to analyzing the data:

The traits are factors whereas the disturbances or unique factors are allowed to be correlated across measures using the same method.  Such a model is identified if there are at least two traits and three methods.  Assuming the model fits the data, then convergent validation is assessed by high loadings on the trait factors, discriminant validation by low to moderate correlations between the trait factors, and method variance by highly correlated disturbances.

The path diagram for the resulting model is shown below:

The PATH1 specification for the model is in the file Jaccard.cmd.

Kenny remarked that the data fit the model well in this case.  With statistically-based fit indices, and the 20-20 vision of hindsight, we can see that the issue is very much in doubt.  The sample size is so small that the confidence intervals for the statistically-based fit indices are quite wide.  For example, the 90% confidence interval for the Steiger-Lind RMS index ranges from 0 to .1056.  In practice, we would prefer a significantly larger sample size.  Notice also in the above output how some of the standard errors differ dramatically when the sample correlation matrix is analyzed correctly.

1.  Stability of Alienation

2.  Confirmatory Factor Analysis

3.  Confirmatory Factor Analysis with Identifying Constraints

4.  Effects of Peer Influence on Ambition

5.  Standardized Solution for the Effects of Peer Influence on Ambition

6.  Factor Analysis with an Intercept Variable

7.  Comparing Factor Structure in Two Groups

8.  Testing for Circumplex Structure

9.  Testing for Stability of a Correlation Matrix Over Time

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

11.  Structural Models for Home Environment and Mathematics Achievement

12.  Test Theory Models for Sets of Congeneric Tests

13.  Comparing Dependent Variances

15.  A Longitudinal Factor Analysis Model

16.  A Structural Model for 10 Personality and Drug Use Variables

17.  A Test for Compound Symmetry

18.  Testing the Equality of Correlation Matrices from Different Populations


  Structural Equation Modeling Examples - 17.  A Test for Compound Symmetry

Data File:  Winer.sta.

Model File:  Winer.cmd.

A test for "compound symmetry" of the covariance matrix is sometimes performed in the context of repeated measures analysis of variance (see, e.g., Winer, 1971, p. 596-598; see also General ANOVA).  This hypothesis states that the covariance matrix equal diagonal elements, and equal off-diagonal elements.  The file Winer.sta contains the pooled covariance matrix analyzed by Winer.  Because the matrix was obtained by pooling two samples of size 5, it would have the same distribution (assuming both populations have the same covariance matrix) as a covariance matrix based on a single sample of size 9.  Hence, that is the sample size recorded in the data file.  We test that the covariance matrix has the form

Commands for testing the hypothesis are in the file Winer.cmd.

Note that the maximum likelihood estimates under the null hypothesis correspond to the results  on page 598 of the Winer text.  We find that the Chi-square statistic, with 4 degrees of freedom, is only .694.  This is not significant.  In fact, the probability level is suspiciously high, as is sometimes seen with artificial data in ANOVA textbooks!  This fact, coupled with the high values for the fit coefficients, suggests that the population matrix deviates only trivially from the hypothesized structure.

1.  Stability of Alienation

2.  Confirmatory Factor Analysis

3.  Confirmatory Factor Analysis with Identifying Constraints

4.  Effects of Peer Influence on Ambition

5.  Standardized Solution for the Effects of Peer Influence on Ambition

6.  Factor Analysis with an Intercept Variable

7.  Comparing Factor Structure in Two Groups

8.  Testing for Circumplex Structure

9.  Testing for Stability of a Correlation Matrix Over Time

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

11.  Structural Models for Home Environment and Mathematics Achievement

12.  Test Theory Models for Sets of Congeneric Tests

13.  Comparing Dependent Variances

14.  A Multi-Trait Multi-Method Model

15.  A Longitudinal Factor Analysis Model

16.  A Structural Model for 10 Personality and Drug Use Variables

18.  Testing the Equality of Correlation Matrices from Different Populations


  Structural Equation Modeling Examples - 15.  A Longitudinal Factor Analysis Model

Data File:  Meyer.sta.

Model File:  Meyer.cmd.

Corballis and Traub (1970) presented a longitudinal factor analysis model, which stipulates that factorial structure underlying a set of tests remains constant over two or more administrations of the tests.  An example of such a model is given by Everitt (1984, pages 52-55).  The data were from a study by Meyer and Bendig (1961), who administered the 5 Thurstone Primary Mental Abilities tests to 49 boys and 61 girls in grades 8 and 11.  The tests are Verbal Meaning (V), Space (S), Reasoning (R), Numerical (N), and word fluency (W).  The correlation matrix for these data are in a file called Meyer.sta.

The model, analyzed by Everitt (1984) stipulates a single common factor underlying the scores on both occasions.  The diagram for the model is in the figure below.

The PATH1 translation of the diagram is contained in a file called Meyer.cmd.  Everitt (1984) analyzed the correlation matrix with LISREL as though it were a covariance matrix.  The standard errors reported in his Table 3.10 are not correct.

The Chi-square value of 51.46 allows us to reject the null hypothesis of perfect fit.  On the other hand, the noncentrality-based fit indices indicate that the jury is, in a sense, still out regarding whether the fit of this model is acceptable.  Consider, for example, the Steiger-Lind RMS index. The point estimate is .076, but the confidence interval ranges from .03 to .11.  Basically, this indicates that the sample size of 110 is insufficient to determine, with adequate precision, the quality of the population fit.

1.  Stability of Alienation

2.  Confirmatory Factor Analysis

3.  Confirmatory Factor Analysis with Identifying Constraints

4.  Effects of Peer Influence on Ambition

5.  Standardized Solution for the Effects of Peer Influence on Ambition

6.  Factor Analysis with an Intercept Variable

7.  Comparing Factor Structure in Two Groups

8.  Testing for Circumplex Structure

9.  Testing for Stability of a Correlation Matrix Over Time

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

11.  Structural Models for Home Environment and Mathematics Achievement

12.  Test Theory Models for Sets of Congeneric Tests

13.  Comparing Dependent Variances

14.  A Multi-Trait Multi-Method Model

16.  A Structural Model for 10 Personality and Drug Use Variables

17.  A Test for Compound Symmetry

18.  Testing the Equality of Correlation Matrices from Different Populations


  Structural Equation Modeling Examples - 16.  A Structural Model for 10 Personality and Drug Use Variables

Data File:  Hh.sta.

Model File:  Hh.cmd.

Huba and Harlow (1987) present a structural model relating personality characteristics to alcohol and marijuana consumption in adolescents.  The correlation matrix (to the two-digit level of precision given in their printed article) for their data, based on 257 observations, is given in a file called Hh.sta.  Their first model corresponds to the path diagram below.  Unless you have a high-resolution video display, you may wish to print this diagram to make it more readable.

The file Hh.cmd contains a PATH1 representation of the above model.

We urge the user to try to produce the PATH1 statements corresponding to the figure before examining the contents of Hh.cmd.  The file Hh.cmd is designed to replicate the analysis in the original article.  Results obtained with SEPATH will correspond very closely, but not exactly, to those reported in the first column of Table 2 in Huba and Harlow (1987).  We assume the discrepancy is due to the fact that we are using the correlations from their article, which they reported to only two digit accuracy.

If you experiment with this example, you will discover a number of interesting things about it.  For one thing, it is difficult to find the solution point for this problem.  Use Automatic starting values and the Correlation option of Data to Analyze.

Try reversing some of the paths.  If you experiment for a while, you will discover that there are other models, besides the one in the above figure, that fit the Huba-Harlow data as well as the one in their article.  The theoretical reason for this can be found in an article by Lee and Hershberger (1990), who gave rules for visually inspecting path diagrams to detect paths that may be reversed without altering model fit.  This example is discussed in detail in the SEPATH Manual.

1.  Stability of Alienation

2.  Confirmatory Factor Analysis

3.  Confirmatory Factor Analysis with Identifying Constraints

4.  Effects of Peer Influence on Ambition

5.  Standardized Solution for the Effects of Peer Influence on Ambition

6.  Factor Analysis with an Intercept Variable

7.  Comparing Factor Structure in Two Groups

8.  Testing for Circumplex Structure

9.  Testing for Stability of a Correlation Matrix Over Time

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

11.  Structural Models for Home Environment and Mathematics Achievement

12.  Test Theory Models for Sets of Congeneric Tests

13.  Comparing Dependent Variances

14.  A Multi-Trait Multi-Method Model

15.  A Longitudinal Factor Analysis Model

17.  A Test for Compound Symmetry

18.  Testing the Equality of Correlation Matrices from Different Populations


  Structural Equation Modeling Examples - 6.  Factor Analysis with an Intercept Variable

Data File:  Boll310.sta.

Model File:  Boll310.cmd.

This example, discussed in the textbook by Bollen (1989, p. 308-311), shows, in a very simple context, the general technique for estimating factor means.

The data file for the example is Boll310.sta, the model is in Boll310.cmd.

In this example, 5 judges were asked to estimate, to the nearest tenth of an inch, the length of lines drawn on 60 index cards, with one line per card.

Judge 1 gave his estimates to the nearest tenth of a centimeter, while the other four judges gave their ratings to the nearest tenth of an inch.

In this example, the rating process is modeled with a single factor model.  The ratings of each judge are modeled as arising through multiplicative (representing a rater-specific variance) and additive (representing rater-specific mean) transformations of the true length, represented by the factor F.  So, for example, the ratings that we see for rater X1 are the true length, multiplied by a factor loading, with a rater-specific constant added on.

The primary purpose for using the factor model in this case is to gauge differences among the raters.  Indeed, the scale for the underlying latent variable is arbitrary.  We fix the scale by setting the factor loading for rater 5 be fixed at 1, and the additive constant for rater 5 be fixed at zero.

The path diagram for the model is shown below

The manifest variable constant is actually an artificial variable with a mean of 1 and a variance of zero.  It contributes no variance, and and adds a  constant to variables that load on it.

To analyze an example using an intercept variable, you must select the Moments option for Data to Analyze in the Analysis Parameters dialog.  In that case, the augmented moment matrix is analyzed, and the artificial variable CONSTANT is added automatically to the list of available manifest variables.

For other examples, see:

1.  Stability of Alienation

2.  Confirmatory Factor Analysis

3.  Confirmatory Factor Analysis with Identifying Constraints

4.  Effects of Peer Influence on Ambition

5.  Standardized Solution for the Effects of Peer Influence on Ambition

7.  Comparing Factor Structure in Two Groups

8.  Testing for Circumplex Structure

9.  Testing for Stability of a Correlation Matrix Over Time

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

11.  Structural Models for Home Environment and Mathematics Achievement

12.  Test Theory Models for Sets of Congeneric Tests

13.  Comparing Dependent Variances

14.  A Multi-Trait Multi-Method Model

15.  A Longitudinal Factor Analysis Model

16.  A Structural Model for 10 Personality and Drug Use Variables

17.  A Test for Compound Symmetry

18.  Testing the Equality of Correlation Matrices from Different Populations


  Structural Equation Modeling Examples - 7.  Comparing Factor Structure in Two Groups

Data File:  Boll362m.sta.

Model Files:  Boll362a.cmd, Boll362b.cmd.

This example, discussed in the textbook by Bollen (1989, p. 355-365), shows how to compare two groups for equivalence of factor structure.  It provides a basic introduction to the techniques involved in fitting and comparing factor models in two or more populations.  The textbook contains an extensive discussion of the example.

In order to process this example, you must select the Fixed option in the Manifest Exogenous Variables box in the Analysis Parameters dialog.

Data for the example are in Boll326m.sta.  The models are in files Boll326a.cmd and Boll326b.cmd.

1.  Stability of Alienation

2.  Confirmatory Factor Analysis

3.  Confirmatory Factor Analysis with Identifying Constraints

4.  Effects of Peer Influence on Ambition

5.  Standardized Solution for the Effects of Peer Influence on Ambition

6.  Factor Analysis with an Intercept Variable

8.  Testing for Circumplex Structure

9.  Testing for Stability of a Correlation Matrix Over Time

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

11.  Structural Models for Home Environment and Mathematics Achievement

12.  Test Theory Models for Sets of Congeneric Tests

13.  Comparing Dependent Variances

14.  A Multi-Trait Multi-Method Model

15.  A Longitudinal Factor Analysis Model

16.  A Structural Model for 10 Personality and Drug Use Variables

17.  A Test for Compound Symmetry

18.  Testing the Equality of Correlation Matrices from Different Populations


  Structural Equation Modeling Examples - 18.  Testing the Equality of Correlation Matrices from Different Populations

SEPATH can perform correlational pattern hypothesis tests either between or within samples (or both).  In this example, we show how to use SEPATH to compare correlations in two or more populations for equality.

The general procedure for comparing two or more correlation matrices for equality is extremely straigtforward.  Before setting up your model file, you will have to enter the appropriate group selection commands.  Once you have specified the groups you wish to compare, set up your model file using the following approach.

1)	Using the Path Construction Tool, enter the GROUP 1 command.

2)	Use the Correl. option in the Path Contruction Tool, select Manifest in the right side variables list, and highlight all the variables for the correlation matrix to be tested.  Then click Add>>.

3)	Add an ENDGROUP command.

4)	Highlight the commands that specify the entire correlation matrix.  Copy them to the clipboard, using  the Copy command.

5)	Then for each group, add a GROUP command, paste in a copy of the correlation matrix commands, and add an ENDGROUP command.

The example described here is taken from an article by Jennrich (1970).  In the article, Jennrich describes a dedicated procedure for comparing two correlation matrices.  His procedure, based on the method of generalized least squares, is somewhat different from the method employed by SEPATH.  Jennrich gives an example in which two groups of subjects, (40 mentally retarded, 89 normal) are both measured on 12 variables.  The correlation matrices are then compared for equality.

The correlation matrices from Jennrichs article are contained in a file called Jennrich.sta, and the commands for comparing the two matrices for equality are in the file Jennrich.cmd.  Jennrich compares GLS and ML test statistics for this problem.  Try running the example with the GLS discrepancy function, then with the ML discrepancy function.  You will find that the GLS statistic fails to reject at the .05 level of significance (Chi square = 56.27, p =.7977), while the ML statistic does reject (Chi square = 102.25, p = .0028).  Depending on ones theoretical predisposition, one might be tempted to accept one result or the other as the right one in this case.  However, such a judgement might be ill-advised and statistically naive.  There are several possible reasons for these conflicting results.  The ML test may be more powerful than the GLS procedure.  On the other hand, both procedures are asymptotic tests, and their exact sampling distributions are not known.  It may be, therefore, that the ML procedure is more liberal at small to moderate sample sizes.  That is, it may be that the ML procedure rejects too often at small sample sizes.

Hardly any information is available in the literature about the performance of correlational pattern hypothesis tests for comparisons across populations.  (Steiger (1980b) presents some evidence in single sample tests that the ML test may be more liberal than the GLS test at small samples, and hence may tend to reject a true null hypothesis too often.)

However, the interested experimenter may generate some evidence on his/her own by using SEPATHs powerful Monte Carlo module.

For other examples, see:

1.  Stability of Alienation

2.  Confirmatory Factor Analysis

3.  Confirmatory Factor Analysis with Identifying Constraints

4.  Effects of Peer Influence on Ambition

5.  Standardized Solution for the Effects of Peer Influence on Ambition

6.  Factor Analysis with an Intercept Variable

7.  Comparing Factor Structure in Two Groups

8.  Testing for Circumplex Structure

9.  Testing for Stability of a Correlation Matrix Over Time

10.  A Multiple Regression Model for Home Environment and Mathematics Achievement

11.  Structural Models for Home Environment and Mathematics Achievement

12.  Test Theory Models for Sets of Congeneric Tests

13.  Comparing Dependent Variances

14.  A Multi-Trait Multi-Method Model

15.  A Longitudinal Factor Analysis Model

16.  A Structural Model for 10 Personality and Drug Use Variables

17.  A Test for Compound Symmetry


This module is not available in this version of STATISTICA/w.  Please contact a sales representative at StatSoft, Inc., (918) 749-1119, fax (918) 749-2217, email info@statsoftinc.com, WEB http://www.statsoftinc.com, for more information on upgrading your program (or for the name of your nearest StatSoft representative).


This module is not available in this version of STATISTICA/w.  Please contact a sales representative at StatSoft, Inc., (918) 749-1119, fax (918) 749-2217, email info@statsoftinc.com, WEB http://www.statsoftinc.com, for more information on upgrading your program (or for the name of your nearest StatSoft representative).


This module is not available in this version of STATISTICA/w.  Please contact a sales representative at StatSoft, Inc., (918) 749-1119, fax (918) 749-2217, email info@statsoftinc.com, WEB http://www.statsoftinc.com, for more information on upgrading your program (or for the name of your nearest StatSoft representative).


  Correspondence Analysis - Index

Introductory Overview

Supplementary Points

Multiple Correspondence Analysis

Burt Tables

Program Overview

Examples

Example 1: Correspondence Analysis and Supplementary Points

Example 2.1: Analyzing an Indicator Matrix (Consumer Preferences)

Example 2.2: Multiple Correspondence Analysis

Example 3: Protein Consumption in Europe

Startup Panel

Correspondence Analysis (CA) Results

Multiple Correspondence Analysis (MCA) Results

Computational Details


Correspondence Analysis - Introductory Overview

  Correspondence Analysis Introductory Overview - Introductory Overview

Correspondence analysis is a descriptive/exploratory technique designed to analyze simple two-way and multi-way tables containing some measure of correspondence between the rows and columns.  The results provide information which is similar in nature to those produced by Factor Analysis techniques, and they allow one to explore the structure of categorical variables included in the table.  The most common kind of table of this type is the two-way frequency crosstabulation table (see, for example, the Basic Statistics or Log-Linear module).

In a typical correspondence analysis, a crosstabulation table of frequencies is first standardized, so that the relative frequencies across all cells sum to 1.0.  One way to state the goal of a typical analysis is to represent the entries in the table of relative frequencies in terms of the distances between individual rows and/or columns in a low-dimensional space.  This is best illustrated by a simple example, which will be described below.  There are several parallels in interpretation between correspondence analysis and Factor Analysis, and some similar concepts will also be pointed out below.

For a comprehensive description of this method, computational details, and its applications (in the English language), refer to the classic text by Greenacre (1984).  These methods were originally developed primarily in France by Jean-Paul Benzérci in the early 1960's and 1970's (e.g., see Benzérci, 1973; see also Lebart, Morineau, and Tabard, 1977), but have only more recently gained increasing popularity in English-speaking countries (see, for example, Carrol, Green, and Schaffer, 1986; Hoffman and Franke, 1986).  (Note that similar techniques were developed independently in several countries, where they were known as optimal scaling, reciprocal averaging, optimal scoring, quantification method, or homogeneity analysis).  In the following paragraphs, a general introduction to correspondence analysis will be presented.  Note that the Correspondence Analysis module will also perform Multiple Correspondence analyses of Burt Tables.  If you are familiar with the general concepts used in correspondence analysis, you may want to refer to the Computational Details section for a brief review of the computational formulas.

Overview.  Suppose you collected data on the smoking habits of different employees in a company.  The following data set is presented in Greenacre (1984, p. 55); this table is also provided in the example data file Smoking.sta.

                           Smoking Category

                      ------------------------

Staff                  (1)    (2)   (3)   (4)    Row

Group                 None  Light Medium Heavy  Totals

------------------------------------------------------

(1) Senior Managers     4     2     3     2      11

(2) Junior Managers     4     3     7     4      18

(3) Senior Employees   25    10    12     4      51

(4) Junior Employees   18    24    33    13      88

(5) Secretaries        10     6     7     2      25

------------------------------------------------------

Column Totals          61    45    62    25     193

One may think of the 4 column values in each row of the table as coordinates in a 4-dimensional space, and one could compute the (Euclidean) distances between the 5 row points in the 4-dimensional space.  The distances between the points in the 4-dimensional space summarize all information about the similarities between the rows in the table above.  Now suppose one could find a lower-dimensional space, in which to position the row points in a manner that retains all, or almost all, of the information about the differences between the rows.  You could then present all information about the similarities between the rows (types of employees in this case) in a simple 1, 2, or 3-dimensional graph.  While this may not appear to be particularly useful for small tables like the one shown above, one can easily imagine how the presentation and interpretation of very large tables (e.g., differential preference for 10 consumer items among 100 groups of respondents in a consumer survey) could greatly benefit from the simplification that can be achieved via correspondence analysis (e.g., represent the 10 consumer items in a two-dimensional space).

Mass. To continue with the simpler example of the two-way table presented above, computationally, the program will first compute the relative frequencies for the frequency table, so that the sum of all table entries is equal to 1.0 (each element will be divided by the total, i.e., 193).  One could say that this table now shows how one unit of mass is distributed across the cells.  In the terminology of correspondence analysis, the row and column totals of the matrix of relative frequencies are called the row mass and column mass, respectively.

Inertia.  The term inertia in correspondence analysis is used by analogy with the definition in applied mathematics of "moment of inertia," which stands for the integral of mass times the squared distance to the centroid (e.g., Greenacre, 1984, p. 35).  Inertia is defined as the total Pearson Chi-square for the two-way table (e.g., as can also be computed in the Basic Statistics  or Log-Linear modules) divided by the total sum (193 in the present example).

Inertia and row and column profiles.  If the rows and columns in a table are completely independent of each other, the entries in the table (distribution of mass) can be reproduced from the row and column totals alone, or row and column profiles in the terminology of correspondence analysis.  According to the well-known formula for computing the Chi-square statistic for two-way tables, the expected frequencies in a table, where the column and rows are independent of each other, are equal to the respective column total times the row total, divided by the grand total.  Any deviations from the expected values (expected under the hypothesis of complete independence of the row and column variables) will contribute to the overall Chi-square statistic (see Computational Details).  Thus, another way of looking at correspondence analysis is to consider it a method for decomposing the overall Chi-square statistic (or Inertia=Chi-square/Total N) by identifying a small number of dimensions in which the deviations from the expected values can be represented.  This is similar to the goal of Factor Analysis, where the total variance is decomposed, so as to arrive at a lower-dimensional representation of the variables that allows one to reconstruct most of the variance/covariance matrix of variables.

Analyzing rows and columns.  This simple example began with a discussion of the row-points in the table shown above.  However, one may rather be interested in the column totals, in which case one could plot the column points in a small-dimensional space, which satisfactorily reproduces the similarity (and distances) between the relative frequencies for the columns, across the rows, in the table shown above.  In fact it is customary to simultaneously plot the column points and the row points in a single graph, to summarize the information contained in a two-way table.

Reviewing results.  Let us now look at some of the results for the table shown above.  First, shown below are the so-called singular values (see Computational Details), eigenvalues, percentages of inertia explained, cumulative percentages, and the contribution to the overall Chi-square.

--------------------------------------------------------

Eigenvalues and Inertia for all Dimensions

Input Table (Rows x Columns): 5 x 4

Total Inertia=.08519 Chi²=16.442

--------------------------------------------------------

No. of  Singular  Eigen-   Perc. of  Cumulatv   Chi

Dims    Values    Values   Inertia   Percent    Squares

------  --------  ------   --------  --------   --------

  1    .273421   .074759   87.75587   87.7559   14.42851

  2    .100086   .010017   11.75865   99.5145    1.93332

  3    .020337   .000414     .48547  100.0000     .07982

Note that the dimensions are "extracted" so as to maximize the distances between the row or column points, and successive dimensions (which are independent of or orthogonal to each other) will "explain" less and less of the overall Chi-square value (and, thus, inertia; refer to the Computational Details section for additional information).  Thus, the extraction of the dimensions is similar to the extraction of principal components in Factor Analysis.

First, it appears that, with a single dimension, 87.76% of the inertia can be "explained," that is, the relative frequency values that can be reconstructed from a single dimension can reproduce 87.76% of the total Chi-square value (and, thus, of the inertia) for this two-way table; two dimensions allow you to explain 99.51%.

Maximum number of dimensions.  Since the sums of the frequencies across the columns must be equal to the row totals, and the sums across the rows equal to the column totals, there are in a sense only (no. of columns-1) independent entries in each row, and  (no. of rows-1) independent entries in each column of the table (once you know what these entries are, you can fill in the rest based on your knowledge of the column and row marginal totals).  Thus, the maximum number of eigenvalues that can be extracted from a two-way table is equal to the minimum of the number of columns minus 1, and the number of rows minus 1.  If you choose to extract (i.e., interpret) the maximum number of dimensions that can be extracted, then you can reproduce exactly all information contained in the table (see the Computational Details section for details concerning the overall "model" equation).

Row and column coordinates.  Next look at the coordinates for the two-dimensional solution.

Row Name            Dim.1    Dim.2

---------------- -------- --------

Senior Managers  -.065768  .193737

Junior Managers   .258958  .243305

Senior Employees -.380595  .010660

Junior Employees  .232952 -.057744

Secretaries      -.201089 -.078911

Of course, you can plot these coordinates in a two-dimensional scatterplot from the Correspondence Analysis Results dialog.  Remember that the purpose of correspondence analysis is to reproduce the distances between the row and/or column points in a two-way table in a lower-dimensional display; note that, as in Factor Analysis, the actual rotational orientation of the axes is arbitrarily chosen so that successive dimensions "explain" less and less of the overall Chi-square value (or inertia).  You could, for example, reverse the signs in each column in the table shown above, thereby effectively rotating the respective axis in the plot by 180° (note that you can quickly achieve this "reversal of scales" via the Reverse scaling option on the Scale Options dialog for the respective axis).

What is important are the distances of the points in the two-dimensional display, which are informative in that row points that are close to each other are similar with regard to the pattern of relative frequencies across the columns.  If you have produced this plot you will see that, along the most important first axis in the plot, the Senior employees and Secretaries are relatively close together on the left side of the origin (scale position 0).  If you looked at the table of relative row frequencies (i.e., frequencies standardized, so that their sum in each row is equal to 100%), you will see that these two groups of employees indeed show very similar patterns of relative frequencies across the categories of smoking intensity.

Percentages of Row Totals

                            Smoking Category

                       --------------------------

Staff                   (1)    (2)    (3)    (4)    Row

Group                  None   Light  Medium Heavy  Totals

---------------------------------------------------------

(1) Senior Managers    36.36  18.18  27.27  18.18  100.00

(2) Junior Managers    22.22  16.67  38.89  22.22  100.00

(3) Senior Employees   49.02  19.61  23.53   7.84  100.00

(4) Junior Employees   20.45  27.27  37.50  14.77  100.00

(5) Secretaries        40.00  24.00  28.00   8.00  100.00

Obviously the final goal of correspondence analysis is to find theoretical interpretations (i.e., meaning) for the extracted dimensions.  One method that may aid in interpreting extracted dimensions is to plot the column points.  Shown below are the column coordinates for the first and second dimension.

Smoking

category   Dim.1    Dim.2

-------- -------- --------

None     -.393308  .030492

Light     .099456 -.141064

Medium    .196321 -.007359

Heavy     .293776  .197766

It appears that the first dimension distinguishes mostly between the different degrees of smoking, and in particular between category None and the others.  Thus one can interpret the greater similarity of Senior Managers with Secretaries, with regard to their position on the first axis, as mostly deriving from the relatively large numbers of None smokers in these two groups of employees.

Note that for more complex tables, with many levels, some of the point labels may overlap in the scatterplots.  You can use the brushing facilities to turn off the points that are of less interest, and only display those points that clearly "mark" the respective axes.

Compatibility of row and column coordinates.  It is customary to summarize the row and column coordinates in a single plot (on the Results Dialog there is an option to plot one-, two-, and three dimensional graphs for row or column coordinates, or both).  However, it is important to remember that in such plots, one can only interpret the distances between row points, and the distances between column points, but not the distances between row points and column points.  To continue with this example, it would not be appropriate to say that the category None is similar to Senior Employees (the two points are very close in the simultaneous plot of row and column coordinates).  However, as was indicated earlier, it is appropriate to make general statements about the nature of the dimensions, based on which side of the origin particular points fall.  For example, because category None is the only column point on the left side of the origin for the first axis, and since employee group Senior Employees also falls onto that side of the first axis, one may conclude that the first axis separates None smokers from the other categories of smokers, and that Senior Employees are different from, for example, Junior Employees, in that there are relatively more non-smoking Senior Employees.

Scaling of the coordinates (standardization options).  Another important decision that the analyst must make concerns the scaling of the coordinates.  The computations following from the choice of the different available options (see the Results Dialog) are described in the Computational Details section.  The nature of the choice pertains to whether or not you want to analyze the relative row percentages, column percentages, or both.  In the context of the example described above, the row percentages were shown to illustrate how the patterns of those percentages across the columns are similar for points which appear more closely together in the graphical display of the row coordinates.  Put another way, the coordinates are based on the analysis of the row profile matrix, where the sum of the table entries in a row, across all columns, is equal to 1.0 (each entry rij in the row profile matrix can be interpreted as the conditional probability that a case belongs to column j, given its membership in row i).  Thus, the coordinates are computed so as to maximize the differences between the points with respect to the row profiles (row percentages).  Therefore, one should choose the option Row Profiles in the Standardization of Coordinates box on the Correspondence Analysis Results dialog, if one is primarily interested in interpreting the differences (distances) between the rows in the table.

Conversely, if you are interested in the similarities and differences between the columns of the table, you should choose the option Column Profiles in the Standardization of Coordinates box; the resulting column coordinates are then derived from the analysis of the column profile matrix (the matrix of column proportions, where the sum of the table entries in each column is equal to 1.0).  This standardization will maximize the distances between the column points in the final coordinate system.

By default, STATISTICA will perform both types of standardizations, prior to reporting the coordinates (option Row and Column Profiles in the Standardization of Coordinates box):  The row coordinates are computed from the row profile matrix, the column coordinates are computed from the column profile matrix.

A fourth option, Canonical standardization (see Gifi, 1981), is also provided, and it amounts to a standardization of the columns and rows of the matrix of relative frequencies.  For more information, refer to the  Computational Details section; this standardization amounts to a rescaling of the coordinates based on the row profile standardization and the column profile standardization, and this type of standardization is not widely used.  Note also that a variety of  other custom standardizations can be easily performed, because STATISTICA will report the raw eigenvalues and eigenvector matrices, which can further be processed with STATISTICA BASIC.

Metric of coordinate system.  In several places in this introduction, the term distance was (loosely) used to refer to the differences between the pattern of relative frequencies for the rows across the columns, and columns across the rows, which are to be reproduced in a lower-dimensional solution as a result of the correspondence analysis.  Actually, these distances represented by the coordinates in the respective space are not simple Euclidean distances computed from the relative row or column frequencies, but rather, they are weighted distances.  Specifically, the weighting that is applied is such that the metric in the lower-dimensional space is a Chi-square metric, provided that (1) you are comparing row points, and chose either row-profile standardization or both row- and column-profile standardization, or (2) you are comparing column points, and chose either column-profile standardization or both row- and column-profile standardization.

In that case (but not if you chose the canonical standardization), the squared Euclidean distance between, for example, two row points i and i' in the respective coordinate system of a given number of dimensions actually approximates a weighted (i.e., Chi-square) distance between the relative frequencies (see Hoffman and Franke, 1986, formula 21):

 2                       2

d   =  Σ(1/c (p   /r  - p    /r  ))

 ii'  j    j  ij   i    i'j   i'

In this formula, dii'² stands for the squared distance between the two points, cj stands for the column total for the j'th column of the standardized frequency table (where the sum of all entries or mass is equal to 1.0), pij stands for the individual cell entries in the standardized frequency table (row i, column j), ri stands for the row total for the i'th column of the relative frequency table, and the summation (Σ) is over the columns of the table.  To reiterate, only the distances between row points, and correspondingly, between column points are interpretable in this manner; the distances between row points and column points cannot be interpreted.

Judging the quality of a solution.  A number of auxiliary statistics are reported, to aid in the evaluation of the quality of the respective chosen numbers of dimensions.  The general concern here is that all (or at least most) points are properly represented by the respective solution, that is, that their distances to other points can be approximated to a satisfactory degree.  Shown below are all statistics reported for the row coordinates for the example table discussed so far, based on a one-dimensional solution only (i.e., only one dimension is used to reconstruct the patterns of relative frequencies across the columns).

----------------------------------------------------------------------

          Row Coordinates and Contributions to Inertia

----------------------------------------------------------------------

                 Coordin.                   Relative  Inertia  Cosine²

Staff Group       Dim.1     Mass    Quality  Inertia  Dim.1    Dim.1

---------------- --------  -------  -------  -------  -------  -------

Senior Managers  -.065768  .056995  .092232  .031376  .003298  .092232

Junior Managers   .258958  .093264  .526400  .139467  .083659  .526400

Senior Employees -.380595  .264249  .999033  .449750  .512006  .999033

Junior Employees  .232952  .455959  .941934  .308354  .330974  .941934

Secretaries      -.201089  .129534  .865346  .071053  .070064  .865346

Coordinates.  The first numeric column shown in the table (Scrollsheet) above contains the coordinates, as discussed in the previous paragraphs.  To reiterate, the specific interpretation of these coordinates depends on the standardization chosen for the solution (see above).  The number of dimensions is chosen by the user (in this case we chose only one dimension), and coordinate values will be shown for each dimension (i.e., there will be one column with coordinate values for each dimension).

Mass.  The Mass column contains the row totals (since these are the row coordinates) for the table of relative frequencies (i.e., for the table where each entry is the respective mass, as discussed earlier in this section).  Remember that, if you chose as the method of standardization the Row profiles option or the default Row and column profiles option, the row coordinates are computed based on the row profile matrix.  Put another way, the coordinates are computed based on the matrix of conditional probabilities shown in the Mass column.

Quality.  The Quality column contains information concerning the quality of representation of the respective row point in the coordinate system defined by the respective numbers of dimensions, as chosen by the user.  In the table shown above, only one dimension was chosen, and the numbers in the Quality column pertain to the quality of representation in the one-dimensional space.  To reiterate, computationally, the goal of the correspondence analysis is to reproduce the distances between points in a low-dimensional space.  If you extracted (i.e., interpreted) the maximum number of dimensions (which is equal to the minimum of the number of rows and the number of columns, minus 1), you could reconstruct all distances exactly.  The Quality of a point is defined as the ratio of the squared distance of the point from the origin in the chosen number of dimensions, over the squared distance from the origin in the space defined by the maximum number of dimensions (remember that the metric here is Chi-square, as described earlier).  By analogy to Factor Analysis, the quality of a point is similar in its interpretation to the communality for a variable in factor analysis.

Note that the Quality measure reported by STATISTICA is independent of the chosen method of standardization, and always pertains to the default standardization (i.e., the distance metric is Chi-square, and the quality measure can be interpreted as the "proportion of Chi-square accounted for" for the respective row, given the respective number of dimensions).  A low quality means that the current number of dimensions does not well represent the respective row (or column).  In the table shown above, the quality for the first row (Senior Managers) is less than .1, indicating that this row point is not well represented by the one-dimensional representation of the points.

Relative inertia.  The Quality of a point (see above) represents the proportion of the contribution of that point to the overall inertia (Chi-square) that can be accounted for by the chosen number of dimensions.  However, it does not indicate whether or not, and to what extent, the respective point does in fact contribute to the overall inertia (Chi-square value).  The relative inertia represents the proportion of the total inertia accounted for by the respective point, and it is independent of the number of dimensions chosen by the user.  Note that a particular solution may represent a point very well (high Quality), but the same point may not contribute much to the overall inertia (e.g., a row point with a pattern of relative frequencies across the columns that is similar to the average pattern across all rows).

Relative inertia for each dimension.   This column contains the relative contribution of the respective (row) point to the inertia "accounted for" by the respective dimension.  Thus, this value will be reported for each (row or column) point, for each dimension.

Cosine² (quality or squared correlations with each dimension).  This column contains the quality for each point, by dimension.  The sum of the values in these columns across the dimensions is equal to the total Quality value discussed above (since in the example table above, only one dimension was chose, the values in this column are identical to the values in the overall Quality column).  This value may also be interpreted as the "correlation" of the respective point with the respective dimension.  The term Cosine² refers to the fact that this value is also the squared cosine value of the angle the point makes with the respective dimension (refer to Greenacre, 1984, for details concerning the geometric aspects of correspondence analysis).

A note about "statistical significance."  It should be noted at this point that correspondence analysis is an exploratory technique.  Actually, the method was developed based on a philosophical orientation that emphasizes the development of models that fit the data, rather than the rejection of hypotheses based on the lack of fit (Benzecri's "second principle" states that "The model must fit the data, not vice versa;" see Greenacre, 1984, p. 10).  Therefore, there are no statistical significance tests that are customarily applied to the results of a correspondence analysis; the primary purpose of the technique is to produce a simplified (low-dimensional) representation of the information in a large frequency table (or tables with similar measures of correspondence).


 Correspondence Analysis - Supplementary Points

The Introductory Overview section provides an Introductory Overview of how to interpret the coordinates and related statistics computed in a correspondence analysis.  An important aid in the interpretation of the results from a correspondence analysis is to include supplementary row or column points, that were not used to perform the original analyses.  The Correspondence Analysis module allows the user to add both row and column points, and to plot their coordinates together with the regular row and column points in a combined graph (see also Computational Details).

For example, consider the following results which are based on the example given in the Introductory Overview section (based on Greenacre, 1984).

Staff Group         Dim.1    Dim.2

---------------- -------- --------

Senior Managers  -.065768  .193737

Junior Managers   .258958  .243305

Senior Employees -.380595  .010660

Junior Employees  .232952 -.057744

Secretaries      -.201089 -.078911

----------------------------------

National Average -.258368 -.117648

----------------------------------

The table above shows the coordinate values (for two dimensions) computed for a frequency table of different types of employees by type of smoking habit.  The row labeled National Average contains the coordinate values for the supplementary point, which is the national average (percentages) for the different smoking categories (which make up the columns of the table; those fictitious percentages reported in Greenacre (1984) are: Nonsmokers: 42%, light smokers: 29%, medium smokers, 20%; heavy smokers: 9%).  If you plotted these coordinates in a two-dimensional scatterplot, along with the column coordinates, it would be apparent that the National Average supplementary row point is plotted close to the point representing the Secretaries group, and on the same side of the horizontal axis (first dimension) as the Nonsmokers column point.  If you refer back to the original two-way table shown in the Introductory Overview section, this finding is consistent with the entries in the table of row frequencies, that is, there are relatively more nonsmokers among the Secretaries, and in the National Average.  Put another way, the sample represented in the original frequency table contains more smokers than the national average.

While this type of information could have been easily gleaned from the original frequency table (that was used as the input to the analysis), in the case of very large tables, such conclusions may not be as obvious.

Quality of representation of supplementary points.  Another interesting result for supplementary points concerns the quality of their representation in the chosen number of dimensions (see the Introductory Overview section for a more detailed discussion of the concept of quality of representation).  To reiterate, the goal of the correspondence analysis is to reproduce the distances between the row or column coordinates (patterns of relative frequencies across the columns or rows, respectively) in a low-dimensional solution.  Given such a solution, one may ask whether particular supplementary points of interest can be represented equally well in the final space, that is, whether or not their distances from the other points in the table can also be represented in the chosen numbers of dimensions.  Shown below are the summary statistics for the original points, and the supplementary row point National Average, for the two-dimensional solution.

                           Cosine²  Cosine²

Staff Group       Quality  Dim.1    Dim.2

----------------  -------  -------  -------

Senior Managers   .892568  .092232  .800336

Junior Managers   .991082  .526400  .464682

Senior Employees  .999817  .999033  .000784

Junior Employees  .999810  .941934  .057876

Secretaries       .998603  .865346  .133257

-------------------------------------------

National Average  .761324  .630578  .130746

-------------------------------------------

The statistics reported in the table above are discussed in the Introductory Overview section.  In short, the Quality of a row or column point is defined as the ratio of the squared distance of the point from the origin in the chosen number of dimensions, over the squared distance from the origin in the space defined by the maximum number of dimensions (remember that the metric here is Chi-square, as described in the Introductory Overview section).  In a sense, the overall quality is the "proportion of squared distance-from-the-overall-centroid accounted for."  The supplementary row point National Average has a quality of .76, indicating that it is reasonably well represented in the two-dimensional solution.  The Cosine² statistic is the quality "accounted for" by the respective row point, by the respective dimension (the sum of the Cosine² values over the respective number of dimensions is equal to the total Quality, see also the Introductory Overview section).


Correspondence Analysis - Multiple Correspondence Analysis

 Multiple Correspondence Analysis (MCA)

Multiple correspondence analysis (MCA) may be considered to be an extension of simple correspondence analysis to more than two variables.  For an introductory overview of simple correspondence analysis, refer to the Introductory Overview section.  Multiple correspondence analysis is a simple correspondence analysis carried out on an indicator (or design) matrix with cases as rows and categories of variables as columns.  Actually, one usually analyzes the inner product of such a matrix, called the Burt Table in an MCA; this will be discussed later.  However, to clarify the interpretation of the results from a multiple correspondence analysis, it is easier to discuss the simple correspondence analysis of an indicator or design matrix.

Indicator or design matrix.  Consider again the simple two-way table presented in the Introductory Overview section:

                           Smoking Category

                      ------------------------

Staff                  (1)    (2)   (3)   (4)    Row

Group                 None  Light Medium Heavy  Totals

------------------------------------------------------

(1) Senior Managers     4     2     3     2      11

(2) Junior Managers     4     3     7     4      18

(3) Senior Employees   25    10    12     4      51

(4) Junior Employees   18    24    33    13      88

(5) Secretaries        10     6     7     2      25

------------------------------------------------------

Column Totals          61    45    62    25     193

Suppose you had entered the data for this table in the following manner, as an indicator or design matrix:

                     Staff Group                           Smoking

       -------------------------------------------  ------------------------

Case   Senior  Junior  Senior   Junior

Number Manager Manager Employee Employee Secretary  None  Light Medium Heavy

--------------------------------------------------  ------------------------

  1      1       0       0        0         0         1     0     0      0

  2      1       0       0        0         0         1     0     0      0

  3      1       0       0        0         0         1     0     0      0

  4      1       0       0        0         0         1     0     0      0

  5      1       0       0        0         0         0     1     0      0

...      .       .       .        .         .         .     .     .      .

...      .       .       .        .         .         .     .     .      .

...      .       .       .        .         .         .     .     .      .

191      0       0       0        0         1         0     0     1      0

192      0       0       0        0         1         0     0     0      1

193      0       0       0        0         1         0     0     0      1

Each one of the 193 total cases in the table is represented by one case in this data file.  For each case a 1 is entered into the category where the respective case "belongs," and a 0 otherwise.  For example, case 1 represents a Senior Manager who is a None smoker.  As can be seen in the table above, there are a total of 4 such cases in the two-way table, and thus there will be four cases like this in the indicator matrix.  In all, there will be 193 cases in the indicator or design matrix.

Analyzing the design matrix.  If you now analyzed this data file (design or indicator matrix) shown above as if it were a two-way frequency table, the results of the correspondence analysis would provide column coordinates that would allow you to relate the different categories to each other, based on the distances between the row points, i.e., between the individual cases.  In fact, the two-dimensional display you would obtain for the column coordinates would look very similar to the combined display for row and column coordinates, if you had performed the simple correspondence analysis on the two-way frequency table (note that the metric will be different, but the relative positions of the points will be very similar).

More than two variables.  The approach to analyzing categorical data outlined above can easily be extended to more than two categorical variables.  For example, the indicator or design matrix could contain two additional variables Male and Female, again coded 0 and 1, to indicate the subjects' gender; and three variables could be added to indicate to which one of three age groups a case belongs.  Thus, in the final display, one could represent the relationships (similarities) between Gender, Age, Smoking habits, and Occupation (Staff Groups).

Fuzzy coding.  It is not necessary that each case is assigned exclusively to only one category of each categorical variable.  Rather than the 0-or-1 coding scheme, one could enter probabilities for membership in a category, or some other measure that represents a fuzzy rule for group membership.  Greenacre (1984) discusses different types of coding schemes of this kind.  For example, suppose in the example design matrix shown earlier, you had missing data for a few cases regarding their smoking habits.  Instead of discarding those cases entirely from the analysis (or creating a new category Missing data), you could assign to the different smoking categories proportions (which should add to 1.0) to represent the probabilities that the respective case belongs to the respective category (e.g., you could enter proportions based on your knowledge about estimates for the national averages for the different categories).

Interpretation of coordinates and other results.  To reiterate, the results of a multiple correspondence analysis are identical to the results you would obtain for the column coordinates from a simple correspondence analysis of the design or indicator matrix.  Therefore, the interpretation of coordinate values, quality values, cosine²'s and other statistics reported as the results from a multiple correspondence analysis can be interpreted in the same manner as described in the context of the simple correspondence analysis (see Introductory Overview), however, these statistics pertain to the total inertia associated with the entire design matrix.

Supplementary column points and "multiple regression" for categorical variables.  Another application of the analysis of design matrices via correspondence analysis techniques is that it allows you to perform the equivalent of a Multiple Regression for categorical variables, by adding supplementary columns to the design matrix.  For example, suppose you added to the design matrix shown earlier two columns to indicate whether or not the respective subject had or had not been ill over the past year (i.e., you could add one column Ill and another column Not ill, and again enter 0's and 1's to indicate each subject's health status).  If, in a simple correspondence analysis of the design matrix, you added those columns as supplementary columns to the analysis, then (1) the summary statistics for the quality of representation (see the Introductory Overview) for those columns would give you an indication of how well you can "explain" illness as a function of the other variables in the design matrix, and (2) the display of the column points in the final coordinate system would provide an indication of the nature (e.g., direction) of the relationships between the columns in the design matrix and the column points indicating illness; this technique (adding supplementary points to an MCA analysis) is also sometimes called predictive mapping.

The Burt table.  The actual computations in multiple correspondence analysis are not performed on a design or indicator matrix (which, potentially, may be very large if there are many cases), but on the inner product of this matrix; this matrix is also called the Burt matrix.  With frequency tables, this amounts to tabulating the stacked categories against each other; for example the Burt table for the two-way frequency table presented earlier would look like this.

                        Employee         Smoking

                     ---------------  ------------

                     (1)(2)(3)(4)(5)  (1)(2)(3)(4)

                     ---------------  ------------

(1) Senior Managers  11  0  0  0  0    4  2  3  2

(2) Junior Managers   0 18  0  0  0    4  3  7  4

(3) Senior Employees  0  0 51  0  0   25 10 12  4

(4) Junior Employees  0  0  0 88  0   18 24 33 13

(5) Secretaries       0  0  0  0 25   10  6  7  2

(1) Smoking:None      4  4 25 18 10   61  0  0  0

(2) Smoking:Light     2  3 10 24  6    0 45  0  0

(3) Smoking:Medium    3  7 12 33  7    0  0 62  0

(4) Smoking:Heavy     2  4  4 13  2    0  0  0 25

The Burt table has a clearly defined structure.  In the case of two categorical variables (shown above), it consists of 4 partitions: (1) the crosstabulation of variable Employee against itself, (2) the crosstabulation of variable Employee against variable Smoking, (3), the crosstabulation of variable Smoking against variable Employee, and (4) the crosstabulation of variable Smoking against itself.  Note that the matrix is symmetrical, and that the sum of the diagonal elements in each partition representing the crosstabulation of a variable against itself must be the same (e.g., there were a total of 193 observations in the present example, and hence, the diagonal elements in the crosstabulation tables of variable Employee against itself, and Smoking against itself must also be equal to 193).

Note that the off-diagonal elements in the partitions representing the crosstabulations of a variable against itself are equal to 0 in the table shown above.  However, this is not necessarily always the case, for example, when the Burt table was derived from a design or indicator matrix that included fuzzy coding of category membership (see above).

Creating a Burt table in STATISTICA.  The Correspondence Analysis module will allow you to use a Burt table directly for input into the analysis.  The module can also automatically create a Burt table from variables coded in the standard manner, that is, if you included in your data file grouping variables to indicate the group membership of each case (e.g., you included a variable Gender, with the two possible values Male and Female).  Thus, in most cases there is no need to recode your data in any special way (e.g., into a design or indicator matrix), and you can analyze categorical variables coded in a manner that also allows you to use, for example, the Log-Linear Analysis module, or Basic Statistics module.  Please refer to the Correspondence Analysis: Table Specifications dialog for additional details on the different ways in which data can be formatted for use with the Correspondence Analysis module.

Creating customized Burt tables.  In case your analysis requires you to employ some customized fuzzy coding scheme for several categorical variables, it is very easy to create a Burt table via STATISTICA BASIC; that table can then be displayed in a Scrollsheet and saved as a data file, for subsequent analysis with the Correspondence Analysis module (remember that the Burt table is simply the inner product of the design or indicator matrix, e.g., if matrix X is the design or indicator matrix, then matrix product X'X is a Burt table).


Correspondence Analysis - Burt Table

  Correspondence Analysis Introductory Overview - Burt Table

Multiple correspondence analysis expects as input (i.e., the program will compute prior to the analysis) a so-called Burt table.  The Burt table is the result of the inner product of a design or indicator matrix, and the multiple correspondence analysis results are identical to the results one would obtain for the column points from a simple correspondence analysis of the indicator or design matrix (see also Introductory Overview - MCA).

For example, suppose you had entered data concerning the Survival for different Age groups in different Locations like this:

          SURVIVAL           AGE                   LOCATION

Case No.  NO   YES  LESST50 A50TO69 OVER69  TOKYO  BOSTON GLAMORGN

          --------  -------------  -------  ----------------------

  1        0    1     0       1       0       0       0      1

  2        1    0     1       0       0       1       0      0

  3        0    1     0       1       0       0       1      0

  4        0    1     0       0       1       0       0      1

  .        .    .     .       .       .       .       .      .

  .        .    .     .       .       .       .       .      .

  .        .    .     .       .       .       .       .      .

762        1    0     0       1       0       1       0      0

763        0    1     1       0       0       0       1      0

764        0    1     0       1       0       0       0      1

In this data arrangement, for each case a 1 was entered to indicate to which category, of a particular set of categories, a case belongs (e.g., Survival, with the categories No and Yes).  For example, case 1 survived (a 0 was entered for variable No, and a 1 was entered for variable Yes), case 1 is between age 50 and 69 (a 1 was entered for variable A50to69), and was observed in Glamorgn).  Overall there are 764 observations in the data set.

If you denote the data (design or indicator matrix) shown above as matrix X, then matrix product X'X is a Burt table); shown below is an example of a Burt table that one might obtain in this manner.

                  SURVIVAL         AGE              LOCATION

                  ---------   -------------   ----------------------

                  NO   YES    <50 50-69 69+   TOKYO  BOSTON GLAMORGN

                  ---------   -------------   ----------------------

SURVIVAL:NO       210    0     68   93   49     60     82     68

SURVIVAL:YES        0  554    212  258   84    230    171    153

AGE:UNDER_50       68  212    280    0    0    151     58     71

AGE:A_50TO69       93  258      0  351    0    120    122    109

AGE:OVER_69        49  84       0    0  133     19     73     41

LOCATION:TOKYO     60  230    151  120   19    290      0      0

LOCATION:BOSTON    82  171     58  122   73      0    253      0

LOCATION:GLAMORGN  68  153     71  109   41      0      0    221

The Burt table has a clearly defined structure.  Overall, the data matrix is symmetrical.  In the case of 3 categorical variables (as shown above), the data matrix consists 3 x 3 = 9 partitions, created by each variable being tabulated against itself, and against the categories of all other variables.  Note that the sum of the diagonal elements in each diagonal partition (i.e., where the respective variables are tabulated against themselves) is constant (equal to 764 in this case).

The off-diagonal elements in each diagonal partition in this example are all 0.  If the cases in the design or indicator matrix are assigned to categories via fuzzy coding (i.e., if probabilities are used to indicate likelihood of membership in a category, rather than 0/1 coding to indicate actual membership), then the off-diagonal elements of the diagonal partitions are not necessarily equal to 0.  Note that complex coding schemes can easily be implemented, and the respective Burt table computed, via STATISTICA BASIC.  You can then specify as input a Burt table directly (choose the option Frequencies w/out grouping variables in the Input box of the Table Specifications dialog).  Refer to the Introductory Overview - MCA section for additional details.


  Correspondence Analysis Examples - Program Overview

The Correspondence Analysis module is a full featured implementation of simple and multiple correspondence analysis techniques (see, for example, Greenacre, 1984; see also the Introductory Overview and Introductory Overview - MCA sections).

Input data.  The program will accept as input data files with grouping (coding) variables that are to be used to compute the crosstabulation table, data files that contain frequencies (or some other measure of correspondence, association, similarity, confusion, etc.) and coding variables that identify (enumerate) the cells in the input table, or data files with frequencies (or other measure of correspondence) only (e.g., the user can directly type in and analyze a frequency  table).  For multiple correspondence analysis the user can also directly specify a Burt table as input for the analysis.

Descriptive statistics.  The program will compute various tables, including the table of row percentages, column percentages, total percentages, expected values, observed minus expected values, standardized deviates, and contributions to the Chi-square values.  All of these statistics can be plotted in 3D histograms, and reviewed via the Animated stratification facility.

Results.  The program will compute the generalized eigenvalues and eigenvectors (see Computational Details), and report all standard diagnostics including the singular values, eigenvalues, and proportions of inertia for each dimension.  The user can either manually choose the number of dimensions, or specify a cutoff value for the maximum cumulative percent of inertia.  The program will compute the standard coordinate values for column and row points.  The user has the choice between row-profile standardization, column-profile standardization, row and column profile standardization, or canonical standardization.  For each dimension and row or column point, the program will compute the inertia, quality, and cosine² values.  In addition, the user can display (in Scrollsheets) the matrices of the generalized singular vectors; like the values in all Scrollsheets, these matrices can be accessed via STATISTICA BASIC, for example, in order to implement a non-standard method of computing the coordinates.

Supplementary points.  The user can compute coordinate values and related statistics (quality and cosine² values) for supplementary points (row or column), and compare the results with the regular row and column points.  Supplementary points can also be specified for multiple correspondence analysis.

Graphical results.  In addition to the 3D histograms that can be computed for all tables, the user can produce a line plot for the eigenvalues, and 1D, 2D, and 3D plots for the row or column points.  Row and column points can also be combined in a single graph, along with any supplementary points (each type of point will use a different color and point marker, so the different types of points can easily be identified in the plots).  All points are labeled, and an option is available to truncate the names for the points to a user-specified number of characters.

Alternative procedures.  The Basic Statistics module contains numerous options for computing multi-way frequency tables, and measures of association for those tables.  The Log-Linear Analysis module will also analyze multi-way frequency tables, and includes facilities for analyzing relationships between categorical variables.  For continuous variables, the Multidimensional Scaling and Factor Analysis modules produce results that are similar in nature and interpretation (see Greenacre, 1984; see also the Introductory Overview section).


Correspondence Analysis - Examples

  Correspondence Analysis Examples - Examples

Example 1: Correspondence Analysis and Supplementary Points

Example 2.1: Analyzing an Indicator Matrix (Consumer Preferences)

Example 2.2: Multiple Correspondence Analysis

Example 3: Protein Consumption in Europe


Correspondence Analysis - Example 1

  Correspondence Analysis Examples - Example 1: Correspondence Analysis of a Two-Way Table, and Supplementary Points

The following example is based on a fictitious data set presented in Greenacre (1984, p. 55) to illustrate how to interpret the results of a correspondence analysis.  This data set is also discussed in the Introductory Overview section.  In this example, the different formats of data files accepted by the Correspondence Analysis module will be illustrated, and the typical results of  correspondence analysis will be explained (see also the Computational Details section).  Also, the use of supplementary points for aiding in the interpretation of results will be demonstrated.

Begin by starting the Correspondence Analysis module; then select the file Smoking.sta.  That file contains the frequency table, as presented in Greenacre (1984, p. 55).

                           Smoking Category

                      ------------------------

                       (1)    (2)   (3)   (4)    Row

Employee              None  Light Medium Heavy  Totals

------------------------------------------------------

(1) Senior Managers     4     2     3     2      11

(2) Junior Managers     4     3     7     4      18

(3) Senior Employees   25    10    12     4      51

(4) Junior Employees   18    24    33    13      88

(5) Secretaries        10     6     7     2      25

------------------------------------------------------

Column Totals          61    45    62    25     193

Formats of data files.  The Correspondence Analysis module provides great flexibility with regard to the permissible formats of input data.  For example, in addition to the raw frequency table as contained in the file Smoking, you could also specify the two-way table by including in the data file two grouping variables (one for the Staff group, another for the Smoking category).  This format for the table is illustrated in the example data file Smoking2.sta.

STAFFGRP  SMOKING  FREQUENCY

--------  -------  ---------

Sr.Manag  None       4

Sr.Manag  Light      2

Sr.Manag  Medium     3

Sr.Manag  Heavy      2

Jr.Manag  None       4

Jr.Manag  Light      3

Jr.Manag  Medium     7

Jr.Manag  Heavy      4

Sr.Empl  None       25

Sr.Empl  Light      10

Sr.Empl  Medium     12

Sr.Empl  Heavy       4

Jr.Empl  None       18

Jr.Empl  Light      24

Jr.Empl  Medium     33

Jr.Empl  Heavy      13

Secretar  None      10

Secretar  Light      6

Secretar  Medium     7

Secretar  Heavy      2

Finally, you can analyze raw data that are not pre-tabulated.  The data in the example file Smoking3.sta are organized in this manner, that is, it only contains two variables (StaffGrp and Smoking) with codes to indicate to which group each case belongs; there are a total of 193 cases in that file.

Specifying the analysis.  For this example, the example data file Smoking.sta will be used.  After loading that file, bring up the Correspondence Analysis (CA): Table Specifications dialog.  In this example, the data files contains Frequencies w/out grouping variables; therefore, check that radio button in the Input box (if you want to use the file Smoking2.sta, you would check the Frequencies with grouping variables button; to use the file Smoking3.sta, check button Raw data (requires tabulation)).

Next select the variables.  Click on the Variables with frequencies button and select all variables.  Note that when you use this data file format (i.e., the input is a tabulated frequency table), then the program will interpret the selected variables as the columns of the table to be analyzed, and the cases as the rows of the table.  Since the data in file Smoking.sta are arranged in that manner, simply click OK to perform the correspondence analysis.  After a few moments the Correspondence Analysis Results dialog will come up.

Reviewing the eigenvalues.  If you are not familiar with the correspondence analysis technique, and the most important statistics that are customarily computed, you may want to review the Introductory Overview section at this point.  To reiterate, if you considered the relative row frequencies as coordinates in a space consisting of as many dimensions as there are columns, and the relative column frequencies as coordinates in a space consisting of as many dimensions as there are rows, then the main goal of the analysis is to reconstruct the distances between the row points, and to reconstruct the distances between the column points, in a space defined by as few dimensions as possible.  First, click on the Eigenvalues button to bring up the Scrollsheet that contains information about the number of dimensions that are necessary to reconstruct the information in the table.

--------------------------------------------------------

Eigenvalues and Inertia for all Dimensions

Input Table (Rows x Columns): 5 x 4

Total Inertia=.08519 Chi²=16.442 df=12 p=.17190

--------+-----------------------------------------------

Number  | Singular  Eigen-  Perc. of  Cumulatv  Chi

of Dims | Values    Values  Inertia   Percent   Squares

--------+-----------------------------------------------

  1     | .273421  .074759  87.75587   87.7559  14.42851

  2     | .100086  .010017  11.75865   99.5145   1.93332

  3     | .020337  .000414    .48547  100.0000    .07982

The first column shows the number of dimensions; a maximum of three dimensions can be extracted, in which case the (relative) frequency table can be reconstructed exactly.  The Singular Values are computed by the so-called generalized singular value decomposition of the table of relative frequencies (see Computational Details).  The Eigenvalues are the squared Singular Values, and they will sum to the total Inertia, which is listed at the top of the Scrollsheet as .08519.  The total inertia is defined as the Chi-square value (16.442) divided by the total number of cases (193).  Thus, as discussed in the Introductory Overview section, the correspondence analysis can also be considered to be a decomposition of the total Chi-square value, in much the same way that principal components analysis (see Factor Analysis) decomposes the total variance/covariance matrix of continuous variables.

As you can see, the dimensions are computed so that the first dimension extracts the most information (i.e., has the highest eigenvalue), the next dimension extracts the second most information, and so on (see also the Computational Details section).  The first dimension in this case extracts 87.76% of the total inertia.  The inclusion of the second dimension increases the "explained" inertia to 99.51%.

Note that the Number of dimensions box on the Correspondence Analysis Results dialog contains options for selecting the number of dimensions to retain in the analysis.  You can either directly request a certain Number of dimensions, or allow the program to determine the number of dimensions based on the respective user-defined value for the Cumulative contribution to inertia.  As described in the Introductory Overview section, correspondence analysis is mostly a descriptive method, rather than a method for hypothesis testing.  Therefore, there are no fixed guidelines as to how to decide on the number of dimensions to interpret.  In this case, it is clear that the first two dimensions will explain practically the total inertia for the table.  Thus, accept the default 2 dimensions, and click on the Row and column coordinates button.

Reviewing the quality and inertias of row and column points.  Two Scrollsheet will be displayed; one for the row coordinates and one for the column coordinates.

---------------------------------------------------------------------------------

Row Coordinates and Contributions to Inertia (smoking.sta)

Input Table (Rows x Columns): 5 x 4

Standardization: Row and column profiles

-----------+---------------------------------------------------------------------

Row        | Row  Coord.   Coord.               Rel.   Inert.  Cos²  Inert.  Cos²

Name       | No.  Dim.1   Dim.2   Mass Quality Inertia Dim.1  Dim.1  Dim.2  Dim.2

-----------+---------------------------------------------------------------------

SR.MANAGER | 1  -.0658   .1937  .0570  .8926  .0314   .0033  .0922  .2136  .8003

JR.MANAGER | 2   .2590   .2433  .0933  .9911  .1395   .0837  .5264  .5512  .4647

SR.EMPLOYEE| 3  -.3806   .0107  .2642  .9998  .4497   .5120  .9990  .0030  .0008

JR.EMPLOYEE| 4   .2330  -.0577  .4560  .9998  .3084   .3310  .9419  .1518  .0579

SECRETARY  | 5  -.2011  -.0789  .1295  .9986  .0711   .0701  .8653  .0805  .1333

---------------------------------------------------------------------------

Column Coordinates and Contributions to Inertia (smoking.sta)

Input Table (Rows x Columns): 5 x 4

Standardization: Row and column profiles

------+--------------------------------------------------------------------

Col.  | Col. Coord. Coord.                Rel.   Inert. Cos²   Inert. Cos²

Name  | No.  Dim.1  Dim.2  Mass  Quality Inertia Dim.1  Dim.1  Dim.2  Dim.2

------+--------------------------------------------------------------------

NONE  | 1  -.3933  .0305  .3161 1.0000   .5774  .6540  .9940  .0293  .0060

LIGHT | 2   .0995 -.1411  .2332  .9840   .0829  .0308  .3267  .4632  .6573

MEDIUM| 3   .1963 -.0074  .3212  .9832   .1480  .1656  .9818  .0017  .0014

HEAVY | 4   .2938  .1978  .1295  .9946   .1917  .1495  .6844  .5058  .3102

The statistics reported in these Scrollsheets are discussed in the Introductory Overview section.  First look at the Quality of the points.  The Quality of a point is defined as the ratio of the squared distance of the point from the origin in the chosen number of dimensions, over the squared distance from the origin in the space defined by the maximum number of dimensions (remember that the metric here is Chi-square, as described in the Introductory Overview).  By analogy to Factor Analysis, the quality of a point is similar in its interpretation to the communality for a variable in factor analysis.  As you can see, both the row and column points are represented quite well in the two-dimensional solution; the quality for all points is .89 or higher.

The Relative inertia values pertain to the proportion of the total inertia "accounted for" by the respective point.  Note that a point may be well represented in a particular solution, but not contribute much to the total inertia.  From the Scrollsheet shown above one can see that the row that contributes most to the overall inertia is that representing the Senior Employees, and the column that contributes most is that representing the None smokers.

The quality for each point, due to each dimension can be found in the columns labeled Cosine².  The Cosine² values summed across the two dimensions is equal to the total Quality value.  The relative contribution of each point to the inertia for each dimension (remember that the Eigenvalues represent the inertias associated with each dimension) is also shown in the Scrollsheets above.

Standardization of row and column coordinates.  There are several options available on the Correspondence Analysis Results dialog for standardizing the row and column coordinates.  Note that the interpretation of the row and column coordinates depends on the method of standardization that is chosen (see also the Introductory Overview section); however, the quality of representation and relative inertia values shown in the Scrollsheets above are not affected by the chosen method of standardization.

The coordinates can be computed based either on the matrix of relative row frequencies (Row profiles standardization; the analysis is based on the so-called row profile matrix, where the sum of all relative frequencies within each row, across the columns, sums to 1.0), or the relative column frequencies (Column profiles standardization; the analysis is based on the so-called column profile matrix, where the sum of all relative frequencies within each column, across the rows, sums to 1.0).  In most cases, the Row and column profiles standardization is most appropriate (the default).  In that case the Euclidean distances between the row points, and the distances between the column points can be interpreted in a meaningful manner (i.e., the distances between the points are Chi-square distances; see the Introductory Overview section).  However, note that the distances between the row and column points have no meaningful interpretation, regardless of standardization.

Reviewing the row and column coordinates.  The best way to quickly review the row and column coordinates is to plot them.  Bring up the Correspondence Analysis Results dialog again, and then, in the Plots of coordinates box, click on the Row & col. - 2D button.  A 2D scatterplot will be displayed, simultaneously showing the row and column points in the two dimensions (see also Greenacare, 1984, p. 66).

To reiterate, direct comparisons between row and column points are not meaningful.  However, one can make meaningful interpretations of the general locations of row and column points, and their relations within each type of point.  For example, if you reviewed the 2D graph of the row and column points, you can see that the first (horizontal) dimension, which "accounts for" most of the inertia (and is, therefore, the most "important" dimension, explaining most of the differences between the patterns of relative frequencies in the rows of the table, and in the columns of the table), is characterized by None smokers on the left, and Light, Medium, and Heavy smokers to the right; the row points that are farthest to the left on this axis are the Secretaries and Senior Employees.  This would suggest that much of the total inertia is due to the difference between non-smokers and smokers, and that there are relatively more non-smokers among Secretaries and Senior Employees.

Reviewing tables of relative frequencies.  You can easily verify this interpretation by reviewing the tables of relative frequencies.  From the Correspondence Analysis Results dialog, select options Row percentages and then Column percentages in the Review tables box.

------------------------------------------------

Percentages of Row Totals (smoking.sta)

Input Table (Rows x Columns): 5 x 4

Total Inertia=.08519 Chi²=16.442 df=12 p=.17190

-----------+----------------------------+-------

           | NONE   LIGHT  MEDIUM HEAVY | Total

-----------+----------------------------+-------

SR.MANAGER | 36.36  18.18  27.27  18.18 | 100.0

JR.MANAGER | 22.22  16.67  38.89  22.22 | 100.0

SR.EMPLOYEE| 49.02  19.61  23.53  7.84  | 100.0

JR.EMPLOYEE| 20.45  27.27  37.50  14.77 | 100.0

SECRETARY  | 40.00  24.00  28.00  8.00  | 100.0

-----------------------------------------------

Percentages of Column Totals (smoking.sta)

Input Table (Rows x Columns): 5 x 4

Total Inertia=.08519 Chi²=16.442 df=12 p=.17190

-----------+-----------------------------------

           | NONE   LIGHT  MEDIUM HEAVY

-----------+-----------------------------------

SR.MANAGER |  6.56   4.44   4.84   8.00

JR.MANAGER |  6.56   6.67  11.29  16.00

SR.EMPLOYEE| 40.98  22.22  19.35  16.00

JR.EMPLOYEE| 29.51  53.33  53.23  52.00

SECRETARY  | 16.39  13.33  11.29   8.00

-----------+---------------------------

Total      |100.00 100.00 100.00 100.00

The relative row and column frequencies shown in these tables support the interpretation of the first dimension:  There are a relatively large percentages of None smokers among Senior Employees and Secretaries.  This makes the respective row profiles in the table of relative row frequencies, and the respective column profile (None) in the table of relative column frequencies different from all the others.

3D histogram of relative frequencies.  Note that the default Quick Stats Graphs for the Scrollsheets produced by the options in the Review tables box is the 3D histogram.  Thus, by clicking on the right mouse button and selecting this default graph, you can quickly produce a 3D representation of the respective data.  For reviewing large tables, the Animated stratification option on the View pull-down menu is particularly useful.  After selecting that option, a floating toolbar will appear that allows you to select the "layers" or "slices" of the 3D histogram, one by one, by clicking on the Continue button.  In this manner, particularly small columns in the graph, which would usually be "hidden behind" the larger columns in the foreground, can be quickly identified.

Supplementary points.  An important aspect of correspondence analysis is to represent row and/or points that were not part of the original analysis in the same coordinate system as the regular points (see also the Introductory Overview section).  Greenacre (1984, Table 3.5) provides an example of this procedure, in the context of this data set.  Specifically, suppose you had available information about the national averages concerning the different categories of smoking, and information about the number of employees in each staff group that did or did not consume alcohol.

                     Smoking Category

                 ------------------------

                  (1)    (2)   (3)   (4)

                 None  Light Medium Heavy

-----------------------------------------

National Average  42%   29%   20%    9%

                       Alcohol

                      ----------

Staff                  (1)   (2)

Group                  Yes   No

--------------------------------

(1) Senior Managers     0    11

(2) Junior Managers     1    17

(3) Senior Employees    5    46

(4) Junior Employees   10    78

(5) Secretaries         7    18

Specifying a supplementary row.  From the Correspondence Analysis Results dialog, first click on the Add row points button.  An empty Scrollsheet will come up where you can specify the supplementary row points.  In this case, simply type in 42, 29, 20, and 9 (remember that in row profile standardization, the analysis is performed on the relative row frequencies, which will sum to 1.0; thus, it does not matter whether you entered here 42 or .42, i.e., percentages or proportions, the results would be the same either way).

To enter a supplementary row, first type a name or label for the row into the first column of the Scrollsheet (e.g., type Average).  Next type in the values 42, 29, 20, and 9 under the respective column headers None, Light, Medium, and Heavy.  To accept these values, exit the Scrollsheet via the Continue button; if you exit the Scrollsheet by closing it, your entries will be discarded.

Specifying supplementary columns.  Next click on the Add column point button, and enter the supplementary column frequencies shown above.  Enter the frequencies row-by-row, and then click Continue again.

Reviewing statistics for supplementary points.  After specifying the supplementary rows, whenever you select any of the plots of the coordinates, or when you select the Scrollsheets of row and column coordinates, the resulting displays will incorporate the results for the supplementary rows and columns.  For example, shown below are the coordinate values and related statistics that will be displayed, along with the statistics for the standard row and column points reviewed earlier, after you click on the Row and column coordinates button.

-------------------------------------------------------------------------------

Row Coordinates and Contributions to Inertia (smoking.sta)

Input Table (Rows x Columns): 5 x 4

Standardization: Row and column profiles

---------+---------------------------------------------------------------------

Row      | Row  Coord.  Coord.               Rel.   Inert.  Cos²   Inert.  Cos²

Name     | No.  Dim.1   Dim.2   Mass Quality Inertia Dim.1  Dim.1  Dim.2  Dim.2

---------+---------------------------------------------------------------------

 ....    |        ----- statistics for regular row points -----

---------+---------------------------------------------------------------------

Average  |     -.2584  -.1176       .7613                   .6306         .1307

-------------------------------------------------------------------------------

Column Coordinates and Contributions to Inertia (smoking.sta)

Input Table (Rows x Columns): 5 x 4

Standardization: Row and column profiles

---------+---------------------------------------------------------------------

Col.     | Col. Coord. Coord.                Rel.   Inert. Cos²   Inert. Cos²

Name     | No.  Dim.1  Dim.2  Mass  Quality Inertia Dim.1  Dim.1  Dim.2  Dim.2

---------+---------------------------------------------------------------------

 ....    |         ----- statistics for regular column points -----

---------+---------------------------------------------------------------------

No Drink |     -.1148 -.3620        .4386                .0401          .3985

Drink    |      .0155  .0490        .4386                .0401          .3985

The interpretation of these statistics is the same as that for the points that were used to perform the analysis (see also the Introductory Overview section).  It appears that the two-dimensional solution represents the new row point Average (i.e., national average) very well (the Quality is .7613).  The new column points are not quite as well represented, however, still, over 40% of the total squared (weighted) distance of these points from the origin in the space defined by the maximum number of dimensions is "accounted for" by the two-factor solution (the Quality is equal to .4386 for both supplementary column points).

At this point, you may want to try to enter as supplementary row and column points the respective column and row totals for the entire table.  You will see that those points will be represented by coordinates that are equal to 0 for all dimensions.  This illustrates that the space defined by the two dimensions is weighted by the respective column and row totals, which define the origin of the coordinate system.  Thus, you could interpret the distances of the points from the origin as (Chi-square) distances from the respective column and row totals.

Plots with supplementary points.  Now produce the combined 2D scatterplot again, for both the row and column points.  The supplementary row point for the national average will be plotted on the left side of the origin for the horizontal axis (the coordinate value is -.2584; see the first table shown above).  Thus, one may infer that there are relatively more None smokers on average in the nation than there are in the current sample.

The supplementary column points No Drink and Drink approximately line up along the second axis, which also appears to distinguish between different degrees of smoking, i.e., Light, Medium, and Heavy (as mentioned above, the first axis appears to distinguish between None smokers and smokers).  Thus, there is some indication that Heavy smokers are also more likely to consume alcohol (specifically, the pattern of frequencies across the staff groups for Drinkers is more similar to the pattern of frequencies for the Heavy and Medium smokers).  However, remember that correspondence analysis is primarily a descriptive and/or exploratory technique to represent categorical data in graphical displays, and no claims of statistical significance are implied (see the Introductory Overview section; see also Elementary Statistical Concepts).

Example 2.1: Analyzing an Indicator Matrix (Consumer Preferences)

Example 2.2: Multiple Correspondence Analysis

Example 3: Protein Consumption in Europe


Correspondence Analysis - Example 2.1

  Correspondence Analysis Examples - Example 2.1: Analysis of Beverage Purchase and Consumption

The following example is based on a data set presented by Hoffman and Franke (1986).  The purpose of this example is to present a brief illustration of a typical application of correspondence analysis in marketing research.  For an introductory example demonstrating the basic principles of correspondence analysis (including the role of supplementary points), see Example 1.  Refer also to the Introductory Overview section for a general discussion of correspondence analysis, and the interpretation of typical results.

The example data file Beverage.sta contains data for a group of male and female MBA students from Columbia University, who were asked to indicate the frequency with which they purchased and consumed various soft drinks in a 1-month period.  The data for the 34 subjects were coded into a binary indicator matrix: a 1 was entered for the respective beverage if the respective subject indicated purchase and consumption at least every other week, and a 0 was entered if the respective subject indicated purchase or consumption less than every other week.  For each of the 8 popular soft drinks used in this study, a second variable was created that was coded as the inverse of the respective first variable, that is, a 1 was entered if the respective beverage had not been consumed or purchased, and a 0 if it had been consumed or purchased over the previous month.  Shown below is a partial listing of the data coded in this manner, for 8 popular soft drinks (see also the example data file Beverage.sta).

                Diet   Diet   Diet

         Coke   Coke   Pepsi  7Up   PEPSI  SPRITE  TAB    7UP

         ----   ----   -----  ----  -----  ------  ----   ----

Subject  Y  N   Y  N   Y  N   Y  N   Y  N   Y  N   Y  N   Y  N

-------  -  -   -  -   -  -   -  -   -  -   -  -   -  -   -  -

 1       1  0   0  1   0  1   0  1   1  0   1  0   0  1   1  0

 2       1  0   0  1   0  1   0  1   1  0   0  1   0  1   0  1

 3       1  0   0  1   0  1   0  1   1  0   0  1   0  1   0  1

 4       0  1   1  0   0  1   1  0   0  1   0  1   1  0   0  1

 5       1  0   0  1   0  1   0  1   1  0   0  1   0  1   0  1

 6       1  0   0  1   0  1   0  1   1  0   1  0   0  1   0  1

 7       0  1   1  0   1  0   1  0   0  1   0  1   1  0   0  1

 8       1  0   1  0   0  1   0  1   1  0   1  0   0  1   1  0

 9       1  0   1  0   0  1   0  1   0  1   1  0   1  0   1  0

 .       .  .   .  .   .  .   .  .   .  .   .  .   .  .   .  .

 .       .  .   .  .   .  .   .  .   .  .   .  .   .  .   .  .

32       0  1   1  0   1  0   0  1   0  1   0  1   1  0   0  1

33       1  0   0  1   0  1   0  1   1  0   0  1   0  1   1  0

34       0  1   1  0   1  0   1  0   0  1   0  1   1  0   0  1

This manner of coding may seem unusual at first; however, indicator matrices are discussed in the Introductory Overview - MCA section.  In particular, the standard correspondence analysis of an indicator matrix will give the same results as a multiple correspondence analysis of the data tabulated in the more standard form (e.g., where there is only one variable Coke, with two codes Yes and No, see example data file Beverage2.sta).  This will briefly be demonstrated in Example 2.2.

Specifying the table.  After starting the Correspondence Analysis module, load the data file Beverage.sta.  In the Input box select the radio button Frequencies w/out grouping variables, then select all variables, and click OK.

Reviewing eigenvalues.  On the Correspondence Analysis Results dialog, first look at the Eigenvalues (i.e., click on that button).

---------------------------------------------------------

Eigenvalues and Inertia for all Dimensions (beverage.sta)

Input Table (Rows x Columns): 34 x 16

Total Inertia=1.0000 Chi²=272.00 df=495 p=1.0000

--------+------------------------------------------------

Number  | Singular  Eigen-  Perc. of  Cumulatv  Chi

of Dims | Values    Values  Inertia   Percent   Squares

--------+------------------------------------------------

  1     | .694078  .481745  48.17449  48.1745 131.0346

  2     | .389141  .151430  15.14304  63.3175  41.1891

  3     | .314954  .099196   9.91959  73.2371  26.9813

  4     | .297800  .088685   8.86851  82.1056  24.1223

  5     | .275500  .075900   7.59004  89.6957  20.6449

  6     | .221580  .049098   4.90976  94.6054  13.3546

  7     | .174100  .030311   3.03109  97.6365   8.2446

  8     | .153736  .023635   2.36348 100.0000   6.4287

The first two dimensions account for approximately 63% of the total variation, and the remaining dimensions only account for less than 10% each.  Thus, let us, therefore, review the 2-dimensional solution.

Reviewing and interpreting the coordinates.  Next, click on the Row and column coordinates button.  The Scrollsheet with the column coordinates will contain the following values:

--------------------------------------------------------------------------------

Column Coordinates and Contributions to Inertia (beverage.sta)

Input Table (Rows x Columns): 34 x 16

Standardization: Row and column profiles

-----------+--------------------------------------------------------------------

Row        | Col  Coord.  Coord.               Rel.   Inert. Cos²   Inert. Cos²

Name       | No.  Dim.1   Dim.2   Mass Quality Inert. Dim.1  Dim.1  Dim.2  Dim.2

-----------+--------------------------------------------------------------------

COKE_Y     |  1  -.742    .112    .074  .803  .051    .084   .785   .006   .018

COKE_N     |  2  1.059   -.159    .051  .803  .074    .120   .785   .009   .018

DCOKE_Y    |  3   .784    .138    .063  .633  .062    .080   .614   .008   .019

DCOKE_N    |  4  -.784   -.138    .063  .633  .062    .080   .614   .008   .019

DPEPSI_Y   |  5  1.146   -.066    .029  .405  .096    .080   .404   .001   .001

DPEPSI_N   |  6  -.353    .020    .096  .405  .029    .025   .404   .000   .001

D7UP_Y     |  7  1.329   -.436    .026  .507  .099    .094   .458   .032   .049

D7UP_N     |  8  -.345    .113    .099  .507  .026    .024   .458   .008   .049

PEPSI_Y    |  9  -.787    .505    .059  .777  .066    .076   .550   .099   .227

PEPSI_N    | 10   .699   -.449    .066  .777  .059    .067   .550   .088   .227

SPRITE_Y   | 11  -.559  -1.056    .040  .683  .085    .026   .149   .298   .533

SPRITE_N   | 12   .267    .505    .085  .683  .040    .013   .149   .142   .533

TAB_Y      | 13  1.220   -.003    .040  .712  .085    .125   .712   .000   .000

TAB_N      | 14  -.584    .001    .085  .712  .040    .060   .712   .000   .000

SEVNUP_Y   | 15  -.709  -1.005    .033  .545  .092    .034   .181   .221   .364

SEVNUP_N   | 16   .255    .362    .092  .545  .033    .012   .181   .080   .364

It appears that all beverages are reasonably well represented by the two-dimensional solution, only Diet Pepsi has a Quality value of less than .5 (see the Introductory Overview for an explanation of the Quality value; see also the Computational Details section).

Now plot the beverages in the two-dimensional space.  From the Correspondence Analysis Results dialog, select the option Column, 2D.  A careful review of the graph suggests that the first axis mostly distinguishes between diet beverages and non-diet beverages, while the second dimension appears to separate the colas from the non-colas.

Plotting the row-coordinates.  You could now also plot the row coordinates, that is, the individual subjects who participated in the study, in the two-dimensional coordinate system.  This would allow you to distinguish ("graphically") between different "segments" of consumers, i.e., those who do or do not drink diet beverages, and who do or do not drink colas.  Moreover, if you carefully review the statistics for the row coordinates you will see that the largest contributors to the inertia for the second dimension are cases number 13 and 28.  These points almost solely "define" the direction of the second dimension.  For a more detailed discussion of this data set, refer to Hoffman and Franke (1986).

Example 1: Correspondence Analysis and Supplementary Points

Example 2.2: Multiple Correspondence Analysis

Example 3: Protein Consumption in Europe


Correspondence Analysis - Example 2.2

  Correspondence Analysis Examples - Example 2.2: Multiple Correspondence Analysis of Beverage Purchase and Consumption

The following example illustrates how multiple correspondence analysis can be used to analyze the data presented in Example 2.1.  As described in the Introductory Overview-MCA section, multiple correspondence analysis is an extension of simple correspondence analysis to more than two categorical variables.  In Example 2.1, a data set presented by Hoffman and Franke (1986) was discussed, which described the preferences of 34 subjects for different beverages.  The data file for that example (data file Beverage.sta) contains an indicator matrix, which was then analyzed via a simple correspondence analysis.

In the current examples, the data are coded in the more typical manner, as shown below (see also data file Beverage2.sta.

               Diet  Diet   Diet

Subject  Coke  Coke  Pepsi  7Up   Pepsi  Sprite  TAB  7Up

-------  ----  ----  -----  ----  -----  ------  ---  ---

 1       Yes   No    No     No    Yes    Yes     No   Yes

 2       Yes   No    No     No    Yes    No      No   No

 3       Yes   No    No     No    Yes    No      No   No

 4       No    Yes   No     Yes   No     No      Yes  No

 5       Yes   No    No     No    Yes    No      No   No

 6       Yes   No    No     No    Yes    Yes     No   No

 7       No    Yes   Yes    Yes   No     No      Yes  No

 8       Yes   Yes   No     No    Yes    Yes     No   Yes

 9       Yes   Yes   No     No    No     Yes     Yes  Yes

10       Yes   No    No     No    Yes    No      No   Yes

11       Yes   No    No     No    Yes    Yes     No   No

12       No    Yes   No     No    No     No      Yes  No

13       No    No    Yes    Yes   No     Yes     No   Yes

14       Yes   No    No     No    No     Yes     No   No

15       No    Yes   Yes    No    No     No      Yes  No

16       No    No    No     No    Yes    Yes     No   No

17       No    Yes   No     No    No     Yes     No   No

18       Yes   Yes   No     No    Yes    No      No   No

19       Yes   No    No     No    No     No      No   Yes

20       Yes   Yes   Yes    No    Yes    No      No   No

21       Yes   No    No     No    Yes    No      No   No

22       Yes   No    No     No    Yes    No      No   No

23       No    Yes   No     Yes   No     No      Yes  No

24       Yes   Yes   No     No    Yes    No      No   No

25       No    Yes   Yes    Yes   No     No      No   No

26       No    Yes   No     Yes   No     No      Yes  No

27       No    Yes   No     No    No     No      Yes  No

28       Yes   No    No     No    No     Yes     No   Yes

29       Yes   No    No     No    No     Yes     No   No

30       No    Yes   Yes    No    No     No      Yes  No

31       Yes   No    No     No    Yes    No      No   Yes

32       No    Yes   Yes    No    No     No      Yes  No

33       Yes   No    No     No    Yes    No      No   Yes

34       No    Yes   Yes    Yes   No     No      Yes  No

The entries in this data file indicate whether or not the respective subject has, over the past month, purchased and consumed the respective beverage.

Specifying the analysis.  After starting the Correspondence Analysis module, load the data file Beverage2.sta. Then click on the Multiple correspondence analysis button in the Method box of the Table Specifications dialog.  The data in the current format contains grouping variables only; therefore, you do not have to change the default in the Input box (Raw data (requires tabulation)).  Simply click OK, and select all variables.  The program will automatically "find" the codes used in the data file, and produce the so-called Burt table, which is the basis for the multiple correspondence analysis (see Introductory Overview - MCA).

Reviewing results.  The results for the column coordinates (i.e., the beverages) are identical to those discussed in Example 2.1.  However, a few things should be noted:  First, the overall Chi-square value that is reported in the info box is only valid if the input table were a standard two-way table, which it is not (see the Introductory Overview - MCA for a discussion of the special structure of a Burt table).  Also, there are no row coordinates available; however, when one is analyzing very large samples, one is usually not interested in individual cases; moreover, if there are several thousand observations, then the simple correspondence analysis of the indicator matrix is not convenient, and sometimes not possible.  In those cases, the multiple correspondence analysis approach is much more efficient.

The interpretation of the coordinate values (i.e., the axes) and auxiliary statistics for the column points is the same as that described in the context of simple correspondence analysis (see Example 2.1, Introductory Overview).

As described in the Introductory Overview section, the orientation of axes in correspondence analysis is arbitrary (i.e., each axis could be rotated by 180°).  If you plot the results for the column points from the multiple correspondence analysis of the data in Beverage2.sta, and compare the graph with that produced in Example 2.1 (i.e., via the simple correspondence analysis of the indicator matrix), you will see that the two axes in the plot are reversed.  Note that you can quickly "flip" over axes by checking the Reverse scaling option on the Scale Options dialog for the respective axis.

Example 1: Correspondence Analysis and Supplementary Points

Example 2.1: Analyzing an Indicator Matrix (Consumer Preferences)

Example 3: Protein Consumption in Europe


Correspondence Analysis - Example 3

  Correspondence Analysis Examples - Example 3: Protein Consumption in Europe

The following example illustrates the analysis of a table containing values that are not frequencies.  As explained in the Introductory Overview, the results of the correspondence analysis are still valid; however, the total Chi-square value and associated p-level should of course not be interpreted.  Remember that correspondence analysis is a descriptive technique which allows you to analyze tables that contain any kind of measure of association, correspondence, similarity, confusion, etc.

This particular example is discussed by Greenacre (1984) in the context of the comparison of principal components analysis (see Factor Analysis) with correspondence analysis.  For details concerning that comparison, refer to Greenacre (1984, p. 280, Example 9.6).  If you are not familiar with the typical results from a correspondence analysis, please refer to the Introductory Overview section.

The data in the example file Protein.sta represent estimates of the protein consumption from 9 different sources, by inhabitants of 25 countries (see Greenacre, 1984, table 9.10; the data were originally reported by Weber, 1973, in a mimeograph published at Kiel University, Institut für Agrarpolitik und Marktlehre, entitled "Agrarpolitik im Spannungsfeld der Internationalen Ernährungspolitik").  Thus, the data are not frequencies, but they are analogous to frequencies in that a total mass of protein is distributed over the cells of the matrix in units of 0.1 gram (per head per day).  Shown below is a listing of this data file.

                                Protein Source

           ------------------------------------------------------

                Pigs &                 Cere- Starchy      Fruits/

Country    Meat Poult. Eggs Milk  Fish  als   Foods  Nuts Veget.

---------- ---- ------ ---- ----  ---- ----- ------- ---- -------

Albania    10.1  1.4    .5   8.9   .2  42.3    .6    5.5   1.7

Austria     8.9 14.0   4.3  19.9  2.1  28.0   3.6    1.3   4.3

Belg./Lux. 13.5  9.3   4.1  17.5  4.5  26.6   5.7    2.1   4.0

Bulgaria    7.8  6.0   1.6   8.3  1.2  56.7   1.1    3.7   4.2

Czechosl.   9.7 11.4   2.8  12.5  2.0  34.3   5.0    1.1   4.0

Denmark    10.6 10.8   3.7  25.0  9.9  21.9   4.8     .7   2.4

E. Germany  8.4 11.6   3.7  11.1  5.4  24.6   6.5     .8   3.6

Finland     9.5  4.9   2.7  33.7  5.8  26.3   5.1    1.0   1.4

France     18.0  9.9   3.3  19.5  5.7  28.1   4.8    2.4   6.5

Greece     10.2  3.0   2.8  17.6  5.9  41.7   2.2    7.8   6.5

Hungary     5.3 12.4   2.9   9.7   .3  40.1   4.0    5.4   4.2

Ireland    13.9 10.0   4.7  25.8  2.2  24.0   6.2    1.6   2.9

Italy       9.0  5.1   2.9  13.7  3.4  36.8   2.1    4.3   6.7

Netherl.    9.5 13.6   3.6  23.4  2.5  22.4   4.2    1.8   3.7

Norway      9.4  4.7   2.7  23.3  9.7  23.0   4.6    1.6   2.7

Poland      6.9 10.2   2.7  19.3  3.0  36.1   5.9    2.0   6.6

Portugal    6.2  3.7   1.1   4.9 14.2  27.0   5.9    4.7   7.9

Rumania     6.2  6.3   1.5  11.1  1.0  49.6   3.1    5.3   2.8

Spain       7.1  3.4   3.1   8.6  7.0  29.2   5.7    5.9   7.2

Sweden      9.9  7.8   3.5  24.7  7.5  19.5   3.7    1.4   2.0

Switzerl.  13.1 10.1   3.1  23.8  2.3  25.6   2.8    2.4   4.9

UK         17.4  5.7   4.7  20.6  4.3  24.3   4.7    3.4   3.3

Russia      9.3  4.6   2.1  16.6  3.0  43.6   6.4    3.4   2.9

W. Germany 11.4 12.5   4.1  18.8  3.4  18.6   5.2    1.5   3.8

Yugoslavia  4.4  5.0   1.2   9.5   .6  55.9   3.0    5.7   3.2

Specifying the table.  After starting the Correspondence Analysis module, open the data file Protein.sta.  Even though the values in this data file are not frequencies, we will treat them as such.  Thus, in the Input box, select option Frequencies w/out grouping variables.  Then select all variables for the analysis, and click on the OK button.

Reviewing eigenvalues.  To reiterate, the Chi-square value and associated p-level should not be interpreted in this case, since the entries in the table are not frequencies.  However, all other results are valid.  First click on the Eigenvalues button.

--------------------------------------------------------

Eigenvalues and Inertia for all Dimensions (protein.sta)

Input Table (Rows x Columns): 25 x 9

Total Inertia=.16901 Chi²=362.47 df=192 p=0.0000

--------+-----------------------------------------------

Number  | Singular  Eigen-  Perc. of  Cumulatv  Chi

of Dims | Values    Values  Inertia   Percent   Squares

--------+-----------------------------------------------

  1     | .294112  .086502  51.18215   51.1821 185.5203

  2     | .197564  .039032  23.09456   74.2767  83.7110

  3     | .141324  .019972  11.81746   86.0942  42.8348

  4     | .103388  .010689   6.32456   92.4187  22.9247

  5     | .073660  .005426   3.21042   95.6291  11.6368

  6     | .061616  .003797   2.24640   97.8755   8.1425

  7     | .051975  .002701   1.59838   99.4739   5.7937

  8     | .029818  .000889    .52607  100.0000   1.9069

The total inertia is equal to .16901, and the first two dimensions account for 74.28% of the total inertia.  Thus, it appears that the first 2 dimensions "account" for most of the inertia in this table.

Reviewing the coordinates.  Shown below are the Scrollsheets for the row and column coordinates, for the 2-dimensional solution (see also Greenacre, 1984, Table 9.11).

----------------------------------------------------------------------------

Row Coordinates and Contributions to Inertia (protein.sta)

Input Table (Rows x Columns): 25 x 9

Standardization: Row and column profiles

-----------+----------------------------------------------------------------

Row        | Col Coord  Coord.             Rel.   Inert. Cos²   Inert. Cos²

Name       | No. Dim.1  Dim.2 Mass Quality Inert. Dim.1  Dim.1  Dim.2  Dim.2

-----------+----------------------------------------------------------------

Albania    | 1   .531   .086  .033  .764   .074   .108   .744   .006   .019

Austria    | 2  -.149   .213  .040  .677   .024   .010   .222   .047   .454

Belgium/Lx.| 3  -.159   .020  .041  .590   .010   .012   .581   .000   .009

Bulgaria   | 4   .517   .093  .042  .910   .076   .130   .881   .009   .029

Czechosl.  | 5   .043   .147  .039  .342   .016   .001   .027   .021   .316

Denmark    | 6  -.387  -.107  .042  .837   .048   .072   .777   .012   .060

E. Germany | 7  -.151  -.030  .035  .196   .025   .009   .189   .001   .007

Finland    | 8  -.312   .043  .042  .429   .058   .047   .421   .002   .008

France     | 9  -.167  -.031  .046  .385   .020   .015   .372   .001   .013

Greece     |10   .221  -.171  .046  .602   .035   .026   .376   .034   .226

Hungary    |11   .294   .163  .039  .615   .043   .039   .470   .027   .145

Ireland    |12  -.281   .185  .043  .883   .032   .039   .617   .037   .267

Italy      |13   .198  -.054  .039  .604   .016   .018   .561   .003   .043

Netherlands|14  -.263   .202  .039  .842   .030   .032   .530   .041   .313

Norway     |15  -.286  -.228  .038  .739   .041   .036   .452   .051   .287

Poland     |16   .014   .061  .043  .086   .012   .000   .004   .004   .082

Portugal   |17   .070  -.757  .035  .941   .128   .002   .008   .518   .933

Rumania    |18   .440   .096  .041  .955   .051   .091   .911   .010   .044

Spain      |19   .157  -.367  .036  .790   .043   .010   .122   .125   .667

Sweden     |20  -.367  -.060  .037  .816   .037   .058   .795   .003   .021

Switzerl.  |21  -.178   .154  .041  .683   .020   .015   .390   .025   .293

UK         |22  -.191   .006  .041  .321   .028   .017   .320   .000   .000

Russia     |23   .182   .021  .043  .469   .018   .016   .463   .000   .006

W. Germany |24  -.309   .122  .037  .802   .030   .041   .694   .014   .108

Yugoslavia |25   .570   .081  .041  .953   .085   .155   .934   .007   .019

----------------------------------------------------------------------------

Column Coordinates and Contributions to Inertia (protein.sta)

Input Table (Rows x Columns): 25 x 9

Standardization: Row and column profiles

-----------+----------------------------------------------------------------

Row        | Col Coord  Coord.             Rel.   Inert. Cos²   Inert. Cos²

Name       | No. Dim.1  Dim.2 Mass Quality Inert. Dim.1  Dim.1  Dim.2  Dim.2

-----------+----------------------------------------------------------------

MEAT       | 1  -.176   .037  .115  .336   .065   .041   .322   .004   .014

PIGPOUL    | 2  -.223   .231  .092  .483   .116   .053   .234   .126   .249

EGGS       | 3  -.284   .082  .034  .639   .028   .032   .590   .006   .050

MILK       | 4  -.315   .105  .199  .754   .173   .229   .679   .056   .075

FISH       | 5  -.355  -.720  .050  .961   .198   .073   .188   .663   .774

CEREALS    | 6   .318   .032  .376  .966   .235   .438   .956   .010   .010

STARCH     | 7  -.203  -.115  .050  .364   .044   .024   .276   .017   .088

NUTS       | 8   .507  -.218  .036  .740   .087   .106   .625   .044   .115

FRUITVEG   | 9   .077  -.246  .048  .354   .054   .003   .032   .075   .322

A review of the inertia values for dimension 2 reveals that it is mostly defined by the row point Portugal and the column point Fish.  If you refer back to the data file you can see that Portugal has a relatively low protein consumption overall.  Greenacre (1984, Table 9.12), therefore, reports the results, treating Portugal as a supplementary point in the analysis.  This can easily be accomplished in the Correspondence Analysis module by using the case selection conditions, and excluding the case representing Portugal.  Then, on the results dialog, enter the values for Portugal as a supplementary point, after clicking on the Add row points button in the Supplementary row and/or column points box on the Correspondence Analysis Results dialog (e.g., you can copy the values for Portugal from the data file, and paste them into the Scrollsheet; see also Example 1).

Either way, if you plot the coordinates for the two-dimensional solution, a "protein map" of the countries emerges, with well defined regions corresponding to southern Europe, eastern Europe, and northern/central Europe (remember that the study was conducted in the early 70's, so some of the clusters of countries may not seem as homogeneous any more).  This pattern will become defined even more clearly when Portugal is removed from the analysis and only displayed as a supplementary point.  The horizontal axis appears to be identified on one end by higher consumption of cereals and nuts (in countries like the former Yugoslavia, Bulgaria, and Rumania), and on the other end by greater consumption of meat and milk; the second axis is characterized on one end by higher consumption of fish (in, for example, Norway, Finland, and Sweden), and on the other end by higher consumption of pork, poultry, and to a lesser extent eggs (in countries like, for example, Austria, the Netherlands, and West Germany).

Example 1: Correspondence Analysis and Supplementary Points

Example 2.1: Analyzing an Indicator Matrix (Consumer Preferences)

Example 2.2: Multiple Correspondence Analysis


Correspondence Analysis - Startup Panel

  Correspondence Analysis - Startup Panel (Table Specifications)

The options in this dialog allow you to select the method of analysis, and to specify the input table.

Method

Input

Raw data (requires tabulation)

Frequencies with grouping variables

Frequencies without grouping variables


  Correspondence Analysis Startup Panel - Method

Method.  To perform a standard (simple) correspondence analysis, click on the Correspondence analysis radio button in the Method box.  To perform Multiple correspondence analysis (MCA), set that radio button in the Method box.  For a description of these methods refer to the Introductory Overview section.  Note that the simple correspondence analysis expects as input a two-way (frequency) table, made up of row and column variables.  Multiple correspondence analysis expects as input either (1) a single list of variables that will be tabulated to compute the Burt table (see Introductory Overview - MCA), or (2) a valid Burt table, specified in the selected variables and cases.


  Correspondence Analysis Startup Panel - Input

The options in this box allow you to specify the input table for the simple or multiple correspondence analysis.  The options for selecting variables and codes depend on the choice of the input data file format, and the method chosen in the Method box.

Raw data (requires tabulation)

Frequencies with grouping variables

Frequencies without grouping variables


Correspondence Analysis Startup Panel - Input: Raw Data

  Correspondence Analysis Startup Panel - Input: Raw Data (Requires Tabulation)

If this radio button is set, then the program expects as input (categorical) grouping variables with code values uniquely identifying to which category each case belongs; the program will then tabulate the respective variables to compute the input table.  For example, the variables may contain the following codes:

STAFFGRP  SMOKING

--------  -------

Sr.Manag  None

Sr.Manag  Light

Sr.Manag  Medium

Sr.Manag  Heavy

Jr.Manag  None

Jr.Manag  Light

Jr.Manag  Medium

Jr.Manag  Heavy

Sr.Empl   None

Sr.Empl   Light

Sr.Empl   Medium

.......   ......

.......   ......

.......   ......

If you selected variables StaffGrp and Smoking for the analysis, the program would cross-tabulate  those variables and compute the two-way frequency table (see also the Basic Statistics module for a discussion of crosstabulation tables).

Selection of variables and codes for simple correspondence analysis.  If the simple Correspondence analysis button is set in the Method box, then you will be prompted to select Row and column variables.  Clicking on that button will bring up the standard two-variable list selection dialog.  If you select one row variable and one column variable, then the analysis will be performed on the two-way table defined by the categories for the two variables.  Use the option Codes for grouping variables to select the codes (numbers or text values) that define the categories for the selected variables.  If more than one variable was selected into the list of row or column variables, then all combinations of the categories of the selected variables in one list (e.g., rows) will be crosstabulated against the respective combinations of categories for the variables in the other list (e.g., columns).  For example, in the following two-way table, the combinations of categories for the two column variables Age and Survival were tabulated against the combinations of categories for the two row variables Inflammation and Location.

     Age:         under 50   50 to 69   over_69

                  --------   --------   --------

Survival:         No   Yes   No   Yes   No   Yes

---------

Inflamm. Location

-------- -------- --   ---   --   ---   --   ---

MIN_MAL  TOKYO     9    26    9    20    2     1

MIN_MAL  BOSTON    6    11    8    18    9    15

MIN_MAL  GLAMORGN 16    16   14    27    3    12

MIN_BEGN TOKYO     7    68    9    46    3     6

MIN_BEGN BOSTON    7    24   20    58   18    26

MIN_BEGN GLAMORGN  7    20   12    39    7    11

GRT_MAL  TOKYO     4    25   11    18    1     5

GRT_MAL  BOSTON    6     4    3    10    3     1

GRT_MAL  GLAMORGN  3     8    3    10    3     4

GRT_BEGN TOKYO     3     9    2     5    0     1

GRT_BEGN BOSTON    0     0    2     3    0     1

GRT_BEGN GLAMORGN  0     1    0     4    0     1

In effect, the resulting table is a 4-way table, where the combinations of categories for the row and column variables are arranged to form a two-way table for the correspondence analysis.

Selection of variables and codes for multiple correspondence analysis.  If the Multiple correspondence analysis button is set, then you will be prompted to select one list of variables.  The Burt table (see also Introductory Overview - MCA) will be computed for the categories of the selected variables.  Use the option Codes for grouping variables to select the codes (numbers or text values) that define the categories for the selected variables.  For example, suppose you selected variables Survival (Yes, No), Age (<50, 50-69, and 69+), and Location (Tokyo, Boston, and Glamorgn) for the analysis.  The program would compute the following type of Burt table for the multiple correspondence analysis.

                  SURVIVAL         AGE              LOCATION

                  ---------   -------------   ----------------------

                  NO   YES    <50 50-69 69+   TOKYO  BOSTON GLAMORGN

                  ---------   -------------   ----------------------

SURVIVAL:NO       210    0     68   93   49     60     82     68

SURVIVAL:YES        0  554    212  258   84    230    171    153

AGE:UNDER_50       68  212    280    0    0    151     58     71

AGE:A_50TO69       93  258      0  351    0    120    122    109

AGE:OVER_69        49  84       0    0  133     19     73     41

LOCATION:TOKYO     60  230    151  120   19    290      0      0

LOCATION:BOSTON    82  171     58  122   73      0    253      0

LOCATION:GLAMORGN  68  153     71  109   41      0      0    221

The Burt table has a clearly defined structure.  Overall, the data matrix is symmetrical.  In the case of 3 categorical variables, the data matrix consists 3 x 3 = 9 partitions, created by each variable being tabulated against itself, and against the categories of all other variables.  Note that the sum of the diagonal elements in each diagonal partition (i.e., where the respective variables are tabulated against themselves) is constant (equal to 764 in this case).  Technically, the Burt table is the result of the inner product of an indicator or design matrix; to analyze tables based on indicator matrices that incorporate fuzzy coding schemes, you can specify as input a Burt table directly (choose the option Frequencies w/out grouping variables in the Input box).  Refer to the Introductory Overview - MCA section for additional details.

In addition to the variables defining the table for the analysis, you can designate some variables as Supplementary columns (variables).  Note that unlike in simple correspondence analysis, where supplementary columns and rows can be added from the Correspondence Analysis Results dialog, in multiple correspondence analysis it is required that the supplementary columns also define a valid Burt table.  Hence, in this case specify all variables for the analysis via the Variables (Factors in Burt table) option, and then select the subset of those variables that are to be treated as supplementary columns via the option Supplementary columns (variables).  The variables selected as supplementary columns will not be used for the computation of eigenvalues and eigenvectors (see Computational Details), but coordinate values will be computed for those columns and reported in the Scrollsheet and plots of coordinates.


  Correspondence Analysis Startup Panel - Input: Frequencies with Grouping Variables

If this radio button is set, then the program expects as input grouping variables with code values uniquely identifying each category, and, in addition, the program expects a variable containing frequencies or some other values with the respective measure of correspondence for the categories indicated by the respective grouping variables. For example, the file may look like this:

STAFFGRP  SMOKING  FREQUENCY

--------  -------  ---------_

Sr.Manag  None       4

Sr.Manag  Light      2

Sr.Manag  Medium     3

Sr.Manag  Heavy      2

Jr.Manag  None       4

Jr.Manag  Light      3

Jr.Manag  Medium     7

Jr.Manag  Heavy      4

Sr.Empl  None       25

Sr.Empl  Light      10

Sr.Empl  Medium     12

.......  ......     ..

.......  ......     ..

.......  ......     ..

If you selected variables StaffGrp and Smoking for the analysis, and variable Frequency as the Variable with frequencies/counts (see below), then to each cell in the table identified by the grouping variables the program would assign the respective value for variable Frequency.

Selection of variables and codes.  The required selection of variables and codes is the same as that described under the option Raw data (requires tabulation) above, except that in addition, the user is prompted to select the Variable with frequencies/counts (i.e., the variable containing the measure of correspondence, similarity, confusion, association, etc.).  Note that only positive values or zero are allowed in that variable (e.g., the program does not permit negative frequencies).

Multiple references to the same cell.  If there are multiple references to the same cell in the table, then the multiple values for the "frequency" variable will be summed up, and the sum of the values assigned to the respective cell in the table.  For example, consider the following data specifying a 2 by 2 table:

GENDER  INCOME    FREQUENCY

------  -------  ---------

MALE    HIGH         4

MALE    HIGH         6

MALE    LOW          3

FEMALE  HIGH         2

FEMALE  LOW          4

There are two references to the cell Male-High (i.e., the first two cases in the listing above).  Thus, the frequency assigned to that cell will be 4+6=10.  This way of handling multiple references will allow you to analyze subsets of tables which are coded in this manner.  For example, suppose you had three grouping variables Gender, Income, and Occupation, and a fourth variable containing the frequencies for each cell in the three-way table.  If you now only selected Gender and Income for the analysis, then the program would sum up all the frequencies in the two-way table defined by those two variables, and, in effect, compute the Gender by Income marginal frequency table, collapsing across the levels of the variable Occupation.


  Correspondence Analysis Startup Panel - Input: Frequencies without Grouping Variables

If this radio button is selected, then the program expects that the selected variables (and cases) contain frequency values only (or some other measure of correspondence).

Selection of variables for simple correspondence analysis.  If a simple correspondence analysis was selected in the Method box, the program will treat each selected variable as a category or level of a categorical (column) variable, and each case as a category or level of a second categorical (row) variable.  For example, the data in the example file Smoking.sta (see Example 1) are organized in this manner:

Case Name     None Light Medium Heavy

-------------------------------------

Sr. ManagerS   4    2      3     2

Jr. Managers   4    3      7     4

Sr. Employees 25   10     12     4

Jr. Employees 18   24     33    13

Secretaries   10    6      7     2

Note that the column variables denote different categories for the (categorical) variable "Smoking frequency."

Selection of variables and codes for multiple correspondence analysis.  If a Multiple correspondence analysis was selected in the Method box, then the data in the selected variables (and cases) are expected to define a valid Burt table (see the Introductory Overview - MCA).  For example, the following data specify a valid Burt table:

                  SURVIVAL         AGE              LOCATION

                  ---------   -------------   ----------------------

                  NO   YES    <50 50-69 69+   TOKYO  BOSTON GLAMORGN

                  ---------   -------------   ----------------------

SURVIVAL:NO       210    0     68   93   49     60     82     68

SURVIVAL:YES        0  554    212  258   84    230    171    153

AGE:UNDER_50       68  212    280    0    0    151     58     71

AGE:A_50TO69       93  258      0  351    0    120    122    109

AGE:OVER_69        49  84       0    0  133     19     73     41

LOCATION:TOKYO     60  230    151  120   19    290      0      0

LOCATION:BOSTON    82  171     58  122   73      0    253      0

LOCATION:GLAMORGN  68  153     71  109   41      0      0    221

The Burt table has a clearly defined structure.  Overall, the data matrix is symmetrical.  In the case of 3 categorical variables, the data matrix consists 3 x 3 = 9 partitions, created by each variable being tabulated against itself, and against the categories of all other variables.  Note that the sum of the diagonal elements in each diagonal partition (i.e., where the respective variables are tabulated against themselves) is constant (equal to 764 in this case).  Technically, the Burt table is the result of the inner product of an indicator or design matrix; if the cases in that indicator matrix are assigned to categories via fuzzy coding (i.e., if probabilities are used to indicate likelihood of membership in a category, rather than 0/1 coding to indicate actual membership), then the off-diagonal elements of the diagonal partitions are not necessarily equal to 0.  Note that complex coding schemes can easily be implemented, and the respective Burt table computed, via STATISTICA BASIC.  Refer also to the Introductory Overview - MCA section for additional details.

In addition to selecting the variables for the analysis, you also need to specify the structure of the Burt table, via the option Specify structure of table.  After clicking on that button, a dialog to Specify the dimensions of the table will come up where you can specify the factor names (e.g., Survival, Age, Location) and the number of levels for each factor (e.g., 2, 3, and 3).  When processing the data, the program will then automatically check whether the respective data specify a valid Burt table.

In addition to the variables defining the table for the analysis, you can designate some variables as Supplementary columns (variables).   Note that unlike in simple correspondence analysis, where supplementary columns and rows can be added from the Correspondence Analysis Results dialog, in multiple correspondence analysis it is required that the supplementary columns also define a valid Burt table.  Hence, in this case, specify all variables for the analysis via the Variables (Factors in Burt table) option, and then select a subset of those variables as supplementary columns via option Supplementary columns (variables).  When processing the data, the program will automatically check whether the selected subset of variables define a valid subset (Burt table) of the overall Burt table.  The variables selected as supplementary columns will not be used for the computation of eigenvalues and eigenvectors (see Computational Details), but coordinate values will be computed for those columns and reported in the Scrollsheet and plots of coordinates.


Correspondence Analysis - Specifying Dimensions of Burt Table

  Correspondence Analysis - Specify the dimensions of the Burt table

It is assumed that you typed the frequencies (or other measure of correspondence, confusion, similarity, association, etc.) for the table directly into the data file.  Specify here the names of the factors in the Burt table, and the number of levels in each partition of the table.  Note that the sum of the levels that you specify must be equal to the number of variables you have selected.

For example, suppose your data file contained the following valid Burt table (see Introductory Overview - MCA for a discussion of Burt tables):

                  SURVIVAL         AGE              LOCATION

                  ---------   -------------   ----------------------

                  NO   YES    <50 50-69 69+   TOKYO  BOSTON GLAMORGN

                  ---------   -------------   ----------------------

SURVIVAL:NO       210    0     68   93   49     60     82     68

SURVIVAL:YES        0  554    212  258   84    230    171    153

AGE:UNDER_50       68  212    280    0    0    151     58     71

AGE:A_50TO69       93  258      0  351    0    120    122    109

AGE:OVER_69        49  84       0    0  133     19     73     41

LOCATION:TOKYO     60  230    151  120   19    290      0      0

LOCATION:BOSTON    82  171     58  122   73      0    253      0

LOCATION:GLAMORGN  68  153     71  109   41      0      0    221

You would specify 3 factors: for the first factor enter 3 in the No. of levels field, and name it, for example, Survival (i.e., type Survival in the Factor Name field).  Specify the remaining 2 factors as Age with 3 levels, and Location with 3 levels.

Supplementary columns (variables).  Note that you need to specify here the structure for the full Burt table, including any supplementary columns, that is, you need to "partition" the entire variable list into levels of factors.


  Correspondence Analysis - Results (CA)

The options on this dialog allow you to review the results of the correspondence analysis, and to specify and evaluate supplementary column and row points.  For details concerning the typical statistics computed in a correspondence analysis and their interpretation, refer to the Introductory Overview section; see also the Computational Details section; for examples, refer to the Examples section.  Note that the number of factors that will be retained for the Scrollsheets of coordinates, and all plots of column and row points, is determined by the choice of options in the Number of dimensions box.  Also, the interpretation of the coordinates for row and column points depends on the method of standardization chosen in the Standardization of Coordinates box (see the description of those options, or the Introductory Overview section for details).  To implement other, non-standard methods for standardizing the coordinates, choose the option Unstandardized matrices, which will report the unstandardized left and right generalized singular vectors from the generalized singular value decomposition (see Computational Details).  The Scrollsheet reporting those matrices can then be easily accessed via STATISTICA BASIC, for any additional computations.

Info Box

Print Summary

Row and Column Coordinates

Eigenvalues

Unstandardized Matrices

Number of Dimensions

Plots of Coordinates

Standardization of Coordinates

Review Tables

Supplementary Row and/or Column Points


  Correspondence Analysis (CA) Results - Info Box

The info box area will show the dimensions of the input table, the eigenvalues, and the value of the Pearson Chi-square for the total two-way table, along with the respective degrees of freedom and p-level.  For additional details concerning the extracted number of dimensions, use the option Eigenvalues (below).


  Correspondence Analysis (CA) Results - Print Summary

This option allows you to print (or direct to a file, or the Text/output Window) the information shown in the info box area, as well as the Scrollsheet of Eigenvalues and the Scrollsheets with the Row and column coordinates.  If you click on this button, and no printer, file, or text-window output has been selected, then the Page/Output Setup dialog will come up.


  Correspondence Analysis (CA) Results - Row and Column Coordinates

This option will bring up a Scrollsheet with the coordinates for the row and column points, as well as various additional statistics that are useful for evaluating the adequacy of the number of dimensions in the current solution.  Also, if you have specified supplementary row and/or column points, then the coordinates for those points, as well as related statistics, will also be included in the Scrollsheet.

Two Scrollsheets will be displayed, one for the row points and one for the column points.  Each Scrollsheet will report the following statistics.

Coordinates for dimension 1, 2, ...  The first several columns in each Scrollsheet will report the coordinates for the chosen number of dimensions (see the options in the Number of dimensions box, below).  The specific method of computation of those coordinate values, and their interpretation, depends on the method of standardization chosen in the Standardization of coordinates box (see also the Introductory Overview, or Computational Details section).

Mass.  The Mass column contains the respective row or column totals for the table of relative frequencies (i.e., for the table where each entry is the respective mass; see the Introductory Overview).

Quality.  The Quality column contains information concerning the quality of representation of the respective row or column point in the coordinate system defined by the respective numbers of dimensions, as chosen by the user.  The Quality of a point is defined as the ratio of the squared distance of the point from the origin in the chosen number of dimensions, over the squared distance from the origin in the space defined by the maximum number of dimensions (remember that the metric here is Chi-square, as described in the Introductory Overview).  By analogy to Factor Analysis, the quality of a point is similar in its interpretation to the communality for a variable in factor analysis.

Note that the Quality measure reported by STATISTICA is independent of the chosen method of standardization, and always pertains to the default standardization (i.e., the distance metric is Chi-square, and the quality measure can be interpreted as the "proportion of Chi-square accounted for" for the respective row, given the respective number of dimensions).  A low quality means that the current number of dimensions does not well represent the respective row or column.

Relative inertia.  The Quality of a point (see above) represents the proportion of the contribution of that point to the overall inertia (Chi-square) that can be accounted for by the chosen number of dimensions.  However, it does not indicate whether or not, and to what extent, the respective point does in fact contribute to the overall inertia (Chi-square value).  The relative inertia represents the proportion of the total inertia accounted for by the respective point, and it is independent of the number of dimensions chosen by the user.  Note that a particular solution may represent a point very well (high Quality), but the same point may not contribute much to the overall inertia (e.g., a row point with a pattern of relative frequencies across the columns that is similar to the average pattern across all rows).

Relative inertia for each dimension.   This column contains the relative contribution of the respective (row or column) point to the inertia "accounted for" by the respective dimension.  Thus, this value will be reported for each (row or column) point, for each dimension.

Cosine² (quality or squared correlations of each dimension).  This column contains the quality for each point, by dimension.  The sum of the values in these columns across the dimensions is equal to the total Quality value.  This value may also be interpreted as the "correlation" of the respective point with the respective dimension.  The term Cosine² refers to the fact that this value is also the squared cosine value of the angle the point makes with the respective dimension (refer to Greenacre, 1984, for details concerning the geometric aspects correspondence analysis).

A note about "statistical significance."  It should be noted at this point that correspondence analysis is a descriptive and/or exploratory technique.  Actually, the method was developed based on a philosophical orientation that emphasizes the development of models that fit the data, rather than the rejection of hypotheses based on the lack of fit (Benzecri's "second principle" states that "The model must fit the data, not vice versa;" see Greenacre, 1984, p. 10).  Therefore, there are no statistical significance tests that are customarily applied to the results of a correspondence analysis; the primary purpose of the technique is to produce a simplified (low-dimensional) representation of the information in a large frequency table (or tables with similar measures of correspondence, association, confusion, similarity, etc.).


  Correspondence Analysis (CA) Results - Eigenvalues

This option will bring up a Scrollsheet with the generalized singular values, eigenvalues, and related statistics.  Note that the dimensions are "extracted" so as to maximize the distances between the row or column points, and successive dimensions (which are independent of or orthogonal to each other) will "explain" less and less of the overall Chi-square value (and, thus, inertia; refer to the Computational Details section for additional information).

Plot of eigenvalues.  The Plot button will bring up a line plot of the eigenvalues for the successive dimensions.


  Correspondence Analysis (CA) Results - Unstandardized Matrices

This option will bring up a Scrollsheet with the relative frequencies (i.e., the values in the input table, divided by the sum of all values), and the matrices of the left and right generalized singular vectors (see also Computational Details).  This option is useful if you want to access those matrices via a STATISTICA BASIC program, for example, in order to implement a non-standard method of standardizing the row and column coordinates.

Specifically, let the table of relative frequencies be denoted as matrix P.  Further, let P = A DuB' denote the generalized singular value decomposition of P.  After you click on this option, the three Scrollsheets will show matrices P, A, and B (matrix Du is a diagonal matrix, where the diagonal elements are equal to the singular values, which are reported when you select the option Eigenvalues).


  Correspondence Analysis (CA) Results - Number of Dimensions

The options in this box allow you to determine the number of dimensions for which to compute row and column coordinates (for Scrollsheets and plots of points).

Number of dimensions.  If you choose this option, you can select a fixed number of dimensions in the edit field to the right of this option.

Cumulative contribution to inertia.  If you set this radio button, the program will determine the minimum number of dimensions necessary so that the cumulative percent of total inertia is equal to or exceeds the respective percentage value, specified in the edit field below this option.

Maximum number of dimensions.  Note that the maximum number of eigenvalues that can be extracted from a two-way table is equal to the minimum of the number of columns or rows, minus 1.  If you choose to extract the maximum number of dimensions that can be extracted, then you can reproduce exactly all information contained in the input table (see the Computational Details section for details concerning the overall "model" equation).


  Correspondence Analysis (CA) Results - Plots of Coordinates

The options in this box allow you to plot the row and/or column points, along with supplementary points (if any were specified) in 1D plots, 2D plots, or 3D plots.  Note that you can use the brushing options to eliminate individual points from the plots (e.g., to leave only points that are clearly spread out along the axes).  Also, the orientation of axes is arbitrary, and can, for example, be rotated by 180°.  Note that you can quickly achieve this "reversal of scales" via the Reverse scaling option on the Scale Options dialog for the respective axis.

1D, 2D, 3D plots of row points, column points, and row and column points.  If you click on any of these buttons, the respective plots will be produced for all dimensions, pairs of dimensions, or triplets of dimensions currently chosen via the options in the Number of dimensions box.  By default, the points will be labeled with the full row and column names from the table.

Plot selected dimensions only.  This option allows you to plot the points for selected dimensions, pairs of dimensions, or triplets of dimensions only.  When this option is set, then after clicking on any of the buttons to produce graphs, a one, two, or three-lists selection dialog will come up where you can select the list of dimensions for which to produce the respective plots.

Truncate labels to x characters.  By default the points in the plots will be labeled with the full names for the row and column points.  For large tables with many points, the plots may be more readable when one abbreviates the row and column point names.  If you set this checkbox, then only the first x number of characters of the respective row and column point names will be displayed in the graphs.

Use identical X/Y/Z scaling.  As described in the Introductory Overview section, by default (depending on the chosen method of Standardization of coordinates) the distances between the points in the plots are actually Chi-square distances.  To achieve compatibility of scales between dimensions (i.e., axes in the plot), you can set this check box to force all axes in 2D and 3D plots to use identical scaling (minima and maxima).


  Correspondence Analysis (CA) Results - Standardization of Coordinates

As described in the Introductory Overview, the computation and interpretation of the coordinates for the row and column points depends on the method of standardization that is chosen.  Following the notation used in Greenacre (1984), correspondence analysis is based on the generalized singular value decomposition of the table of relative frequencies (relative to the total sum of all values in the table); let that table of relative frequencies be denoted as matrix P.  Further, let matrices Dr and Dc be diagonal matrices, with diagonal elements equal to the row totals and column totals of P, respectively.  The program will compute the generalized singular value decomposition of P:

P = A DuB'

so that

A inverse(Dr)A = B' inverse(Dc)B = I

where A is the matrix of the left-side generalized singular vectors, B is the matrix of the right-side generalized singular vectors, Du is a diagonal matrix with the diagonal elements equal to the generalized singular values (reported via the option Eigenvalues), and I stands for the identity matrix (a diagonal matrix with 1's in the diagonal).

The standardization options available in the Standardization of coordinates box can then be summarized as follows:

Row and column profiles.  When this option is chosen, then the row coordinates are computed based on the row profile matrix R = inverse(Dr)P, and the column coordinates are computed based on the column profile matrix computed analogously.  Specifically, the row coordinates are computed as inverse(Dr)ADu, and the column coordinates as inverse(Dc)BDu.  This option is appropriate when you are interested in interpreting both the distances between row points, and the distances between column points (the distances in both coordinate systems for row points and column points are Chi-square distances).  However, note that, as discussed in the Introductory Overview section, distances between column and row points are not meaningful.

Canonical standardization.   When this option is chosen, then the row coordinates are computed as inverse(Dr)ADu**½, and the column coordinates as inverse(Dc)BDu**½.  For details concerning this standardization, see Gifi (1981).

Row profiles.  When this option is chosen, then the row coordinates are computed based on the row profile matrix R = inverse(Dr)P.  Specifically, the (principal) row coordinates are computed as inverse(Dr)ADu, and the standard column coordinates as inverse(Dc)B.  This option is appropriate when you are interested in interpreting the distances between row points; the column coordinates should not be interpreted.

Column profiles.  When this option is chosen, then the column coordinates are computed based on the column profile matrix.  Specifically, the (principal) column coordinates are computed as inverse(Dc)BDu, and the standard row coordinates as inverse(Dr)A.  This option is appropriate when you are interested in interpreting the distances between column points; the row coordinates should not be interpreted.

Computation of quality and inertia.  Note that the choice of the standardardization method does not affect the computation of the quality and inertia values reported in the Scrollsheet that is displayed when you click on option Row and column coordinates.  Those values are always computed based on the Row and column profiles standardization.


  Correspondence Analysis (CA) Results - Review Tables

The options in this box allow you to review the input table (option Observed frequenc.), as well as various values computed based on the input table.  Note that the default Quick Stats Graphs plot for all tables is the 3D Histogram of the respective table entries.

Observed frequencies.  This option will bring up a Scrollsheet showing the input table (e.g., frequencies in the two-way table).

Row percentages.  This option will bring up a Scrollsheet showing the values in the input table, after transformation to row percentages.  Thus, the values in each row, across the columns, will sum to 100%.  Note that the coordinates for the row points are computed based on this table, if you chose as the standardization method Row profiles, or Row and column profiles.

Column percentages.  This option will bring up a Scrollsheet showing the values in the input table, after transformation to column percentages.  Thus, the values in each column, across the rows, will sum to 100%.  Note that the coordinates for the column points are computed based on this table, if you chose as the standardization method Column profiles, or Row and column profiles.

Total percentages.  This option will bring up a Scrollsheet showing the values in the input table, after transformation to percentages of the total sum of all values.  Thus, the sum of all values in the table will be equal to 100%.

Expected (chi-square).  This option will bring up a Scrollsheet with the expected values under the hypothesis that the row and column variables are independent of each other.  The standard formula is used for computing the expected values, based on the marginal totals of the input frequency table.  For example, for row i and column j the expected value is computed as the row total for row i, times the column total for column j, divided by the grand total.

Obs. minus expected.  This option will bring up a Scrollsheet with the differences between the observed table values, and the expected values (see above).

Contribution to chi-square.  This option will bring up a Scrollsheet with the respective cells' contributions to the overall Chi-square value (note that these values are only valid if the input table contains frequencies).  For example, for row i and column j this value is computed as: (observed value - expected value)² /expected value.  The sum of all values is equal to the overall Chi-square value.

Standardized deviates.  The standardized deviate values are computed as the square-root of the contribution-to-chi-square values.


  Correspondence Analysis (CA) Results - Supplementary Row and/or Column Points

The options in this box allow you to specify supplementary row and column points (see the Introductory Overview section for details; see also Example 1).  The results for those points will automatically be included when you choose the option Row and column coordinates, or produce any of the plots of the row and column points.  Refer also to the Computational Details section for more information.

Add row points; Add column points.  If you click on either of these buttons, a Scrollsheet will be displayed that will either be empty, or contain previously specified supplementary row or column points.  You can type in the name and values for the additional points, and then exit the Scrollsheet by clicking on the Continue button.  If you close the Scrollsheet without clicking Continue, all changes made to the Scrollsheet will be ignored.


  Correspondence Analysis - Results (MCA)

The options on this dialog allow you to review the results of the multiple correspondence analysis (MCA).  For details concerning the typical statistics computed in a correspondence analysis and their interpretation refer to the Introductory Overview - MCA section; see also the Computational Details section; for an example of multiple correspondence analysis, refer to Example 2.1 and Example 2.2.  Note that the number of factors that will be retained for the Scrollsheet of coordinates, and all plots of column points, is determined by the choice of options in the Number of dimensions box.  To implement non-standard methods for standardizing the coordinates, choose the option Unstandardized matrices, which will report the matrix of unstandardized generalized singular vectors from the singular value decomposition (see the Computational Details).  The Scrollsheet reporting those matrices can then be easily accessed via STATISTICA BASIC for any additional computations.

Info Box

Print Summary

Column Coordinates

Eigenvalues

Unstandardized Matrices

Number of Dimensions

Plots of Coordinates

Review Tables


  Multiple Correspondence Analysis (MCA) Results - Info Box

The info box area will show the number of factors and categories in the input table (Burt table; see Introductory Overview - MCA), the eigenvalues, and the value of the Pearson Chi-square for the two-way table, along with the respective degrees of freedom and p-level;  however, note that the overall Chi-square value, the degrees of freedom, and associated p-level are only valid if the input table were an ordinary two-way table, which it is not.  For details about the structure of Burt table, see also the Introductory Overview - MCA section.


  Multiple Correspondence Analysis (MCA) Results - Print Summary

This option allows you to print (or direct to a file, or the Text/output Window) the information shown in the info box area, as well as the Scrollsheet of Eigenvalues and the Scrollsheets with the Column coordinates.  If you click on this button, and no printer, file, or text-window output has been selected, then the Page/Output Setup dialog will come up.


  Multiple Correspondence Analysis (MCA) Results - Column Coordinates

This option will bring up a Scrollsheet with the coordinates for the column points, as well as various additional statistics that are useful for evaluating the adequacy of the number of dimensions in the current solution.  Also, if you have specified supplementary column points, then the coordinates for those points, as well as related statistics, will also be included in the Scrollsheet.

The results of a multiple correspondence analysis are identical to a simple correspondence analysis of the indicator or design matrix, whose inner product is the current Burt table (see the Introductory Overview - MCA).  Therefore, the interpretation of the typical statistics reported as the result of a multiple correspondence analysis are analogous to those of the simple correspondence analysis (of an indicator matrix).

Coordinates for dimension 1, 2, ... The first several columns in the Scrollsheet will report the coordinates for the chosen number of dimensions (see the options in the Number of dimensions box, below).  The specific method of computation is described in the Computational Details section (note that in multiple correspondence analysis, the typical standardization for the column points is based on the column profile matrix, see also the description of the standardization options for the Correspondence Analysis Results dialog).

Mass.  The Mass column contains the respective column totals (and row totals, since the Burt table is symmetrical) for the table of relative frequencies (i.e., for the table where each entry is the respective mass; see the Introductory Overview).

Quality.  The Quality column contains information concerning the quality of representation of the respective column point in the coordinate system defined by the respective numbers of dimensions, as chosen by the user.  The Quality of a point is defined as the ratio of the squared distance of the point from the origin in the chosen number of dimensions, over the squared distance from the origin in the space defined by the maximum number of dimensions (remember that the metric here is Chi-square, as described in the Introductory Overview).  A low quality means that the current number of dimensions does not well represent the respective column.

Relative inertia.  The Quality of a point (see above) represents the proportion of the contribution of that point to the overall inertia (Chi-square) that can be accounted for by the chosen number of dimensions.  However, it does not indicate whether or not, and to what extent, the respective point does in fact contribute to the overall inertia (Chi-square value).  The relative inertia represents the proportion of the total inertia accounted for by the respective point, and it is independent of the number of dimensions chosen by the user.  Note that a particular solution may represent a point very well (high Quality), but the same point may not contribute much to the overall inertia (e.g., a column point with a pattern of relative frequencies across the rows that is similar to the average pattern across all columns).

Relative inertia for each dimension.  This column contains the relative contribution of the respective column point to the inertia "accounted for" by the respective dimension.  Thus, this value will be reported for each column point, for each dimension.

Cosine² (quality or squared correlations of each dimension).  This column contains the quality for each point, by dimension.  The sum of the values in these columns across the dimensions is equal to the total Quality value.  This value may also be interpreted as the "correlation" of the respective point with the respective dimension.  The term Cosine² refers to the fact that this value is also the squared cosine value of the angle the point makes with the respective dimension (refer to Greenacre, 1984, for details concerning the geometric aspects correspondence analysis).

A note about "statistical significance."  It should be noted at this point that correspondence analysis is a descriptive and/or exploratory technique.  Actually, the method was developed based on a philosophical orientation that emphasizes the development of models that fit the data, rather than the rejection of hypotheses based on the lack of fit (Benzecri's "second principle" states that "The model must fit the data, not vice versa;" see Greenacre, 1984, p. 10).  Therefore, there are no statistical significance tests that are customarily applied to the results of a correspondence analysis; the primary purpose of the technique is to produce a simplified (low-dimensional) representation of the information in a large frequency table (or tables with similar measures of correspondence).


  Multiple Correspondence Analysis (MCA) Results - Eigenvalues

This option will bring up a Scrollsheet with the generalized singular values, eigenvalues, and related statistics.  Note that the dimensions are "extracted" so as to maximize the distances between the column points, and successive dimensions (which are independent of or orthogonal to each other) will "explain" less and less of the overall inertia (refer to the Computational Details section for additional information).

Plot of eigenvalues.  The Plot button will bring up a line plot of the eigenvalues for the successive dimensions.


  Multiple Correspondence Analysis (MCA) Results - Unstandardized Matrices

This option will bring up a Scrollsheet with the relative frequencies (i.e., the values in the input table, divided by the sum of all values), and the matrix of generalized singular vectors (see also Computational Details; because the Burt table is symmetrical, the left- and right-side singular vectors are the same).  This option is useful if you want to access these matrices via a STATISTICA BASIC program, for example, in order to implement a non-standard method of standardizing the column coordinates.  See also the analogous option on the Correspondence Analysis Results dialog for additional computational details.


  Multiple Correspondence Analysis (MCA) Results - Number of Dimensions

The options in this box allow you to determine the number of dimensions for which to compute column coordinates (for Scrollsheets and plots of points).

Number of dimensions.  If you choose this option, you can select a fixed number of dimensions in the edit field to the right of this option.

Cumulative contribution to inertia.  If you set this radio button, the program will determine the minimum number of dimensions necessary so that the cumulative percent of total inertia exceeds the respective percentage value, specified in the edit field below this option.

Maximum number of dimensions.  Note that the maximum number of eigenvalues that can be extracted from a Burt table is equal to: Sum(no. of categoriesi - 1), where the summation is over the i factors in the Burt table.  If you choose to extract the maximum number of dimensions that can be extracted, then you can reproduce exactly all information contained in the Burt table (see the Computational Details section for details concerning the overall "model" equation).


  Multiple Correspondence Analysis (MCA) Results - Plots of Coordinates

The options in this box allow you to plot the column points, along with supplementary points (if any were specified) in 1D plots, 2D plots, or 3D plots.  Note that you can use the brushing options to eliminate individual points from the plots (e.g., to leave only points that are clearly spread out along the axes).  Also, the orientation of axes is arbitrary, and can, for example, be rotated by 180°.  Note that you can quickly achieve this "reversal of scales" via the Reverse scaling option on the Scale Options dialog for the respective axis.

1D, 2D, 3D plots of column points.  If you click on any of these buttons, the respective plots will be produced for all dimensions, pairs of dimensions, or triplets of dimensions currently chosen via the options in the Number of dimensions box.  By default, the points will be labeled with the full column names from the table.

Plot selected dimensions only.  This option allows you to plot the points for selected dimensions, pairs of dimensions, or triplets of dimensions only.  When this option is set, then after clicking on any of the buttons to produce graphs, a one, two, or three-lists selection dialog will come up where you can select the list of dimensions for which to produce the respective plots.

Truncate labels to x characters.  By default, the points in the plots will be labeled by the full names for the column points; the typical format of each label will be variable:level.  For large tables with many points, the plots may be more readable when one abbreviates the column point names.  If you set this checkbox, then only the first x number of characters of the respective column point's  variable name and level name will be displayed in the graphs (e.g., if you set x to 2, you would see the label va:le, instead of the full label variable:level).

Use identical X/Y/Z scaling.  As described in the Introductory Overview section, the distances between the points in the plots are actually Chi-square distances.  To achieve compatibility of scales between dimensions (i.e., axes in the plot), you can set this check box to force all axes in 2D and 3D plots to use identical scaling (minima and maxima).


  Multiple Correspondence Analysis (MCA) Results - Review Tables

The options in this box allow you to review the input table (i.e., Burt table; use the option Observed frequenc.), as well as various values computed based on the input table.  Note that the default Quick Stats Graphs plot for all tables is the 3D Histogram of the respective table entries.

Include supplementary points.  If this checkbox is set, then the tables will include the partitions of the Burt table that were used to compute the eigenvalues and related statistics, as well as the supplementary columns/rows (subset of the Burt table; remember that the Burt table is symmetrical).  The supplementary columns and rows will be highlighted in the tables.

Observed frequencies.  This option will bring up a Scrollsheet showing the input table (i.e., Burt table).

Row percentages.  This option will bring up a Scrollsheet showing the values in the input table, after transformation to row percentages.  Thus, the values in each row, across the columns, will sum to 100%.

Column percentages.  This option will bring up a Scrollsheet showing the values in the input table, after transformation to column percentages.  Thus, the values in each column, across the rows, will sum to 100%.

Total percentages.  This option will bring up a Scrollsheet showing the values in the input table, after transformation to percentages of the total sum of all values.  Thus, the sum of all values in the table will be equal to 100%.

Expected (chi-square).  This option will bring up a Scrollsheet with the expected values under the hypothesis that the categories making up the rows and columns of the table are independent of each other.  Note that since the input table is a Burt table, these values are usually not of interest in a multiple correspondence analysis.

Obs. minus expected.  This option will bring up a Scrollsheet with the differences between the observed table values, and the expected values (see above).

Contribution to chi-square.  This option will bring up a Scrollsheet with the respective cells' contributions to the overall Chi-square value (note that these values are only valid if the input table were a standard two-way table, and not a Burt table).  For example, for row i and column j this value is computed as: (observed value - expected value)² /expected value.  The sum of all values is equal to the overall Chi-square value.

Standardized deviates.  The standardized-deviate-values are computed as the square-root of the contribution-to-chi-square values.


Correspondence Analysis - Selecting Dimensions for 1D Plots

 Select the dimensions to plot (1D plot of points)

To select a dimension for the plot, click on it.  To select more than one dimension, hold down the CTRL key and click on the additional dimensions for the plot.  To select a list of consecutive dimensions, hold down the left mouse button, and drag the mouse over the respective list of items.  To deselect a particular dimension, hold down the CTRL key and click on the respective dimension.

A 1D plot of the points will be produced for each selected dimension.


Correspondence Analysis - Selecting Dimensions for 2D Plots

 Select the dimensions to plot (2D plot of points)

To select a dimension for the plot from the lists of dimensions, click on it.  To select more than one dimension in a list, hold down the CTRL key and click on the additional dimensions for the plot.  To select a list of consecutive dimensions in a list, hold down the left mouse button, and drag the mouse over the respective list of items.  To deselect a particular dimension, hold down the CTRL key and click on the respective dimension.

2D plots of the points will be produced for all combinations of the selected dimensions.


Correspondence Analysis - Selecting Dimensions for 3D Plots

 Select the dimensions to plot (3D plot of points)

To select a dimension for the plot from the lists of dimensions, click on it.  To select more than one dimension in a list, hold down the CTRL key and click on the additional dimensions for the plot.  To select a list of consecutive dimensions in a list, hold down the left mouse button, and drag the mouse over the respective list of items.  To deselect a particular dimension, hold down the CTRL key and click on the respective dimension.

3D plots of the points will be for all combinations of the selected dimensions.


Correspondence Analysis - Computational Details

 Computational Details

The notation used in this section follows closely that used by Greenacre (1984).  Also, refer to Greenacre (1984) for a detailed discussion of the computations involved.

Notation

The computations are based on the following matrices:

P	is the matrix of relative frequencies, i.e., each element of P is computed as the respective frequency from the input table, divided by the grand total of all values.

r	is the vector of row totals of P.

c	is the vector of column totals of P.

Dr 	is a diagonal matrix, the diagonal elements of Dr are equal to the row totals of P.

Dc 	is a diagonal matrix, the diagonal elements of Dc are equal to the column totals of P.

Singular value decomposition

The computation of the row and column coordinates is based on the generalized singular value decomposition of P, as:

P = A DuB'

so that

A inverse(Dr)A = B' inverse(Dc)B = I

where A is the matrix of the left-side generalized singular vectors, B is the matrix of the right-side generalized singular vectors, Du is a diagonal matrix with the diagonal elements equal to the generalized singular values, and I stands for the identity matrix (a diagonal matrix with 1's in the diagonal).

Coordinates for row and column points

The computation of the coordinates for row and column points depends on the choice of the standardization chosen in the Standardization of Coordinates box on the Correspondence Analysis Results dialog:

Row and column profiles.  When this option is chosen, then the row coordinates are computed based on the row profile matrix R = inverse(Dr)P, and the column coordinates are computed based on the column profile matrix computed analogously.  Specifically, the row coordinates are computed as F = inverse(Dr)ADu, and the column coordinates as G = inverse(Dc)BDu.  This option is appropriate when you are interested in interpreting both the distances between row points, and the distances between column points (the distances in both coordinate systems for row points and column points are Chi-square distances).  However, note that, as discussed in the Introductory Overview section, distances between column and row points are not meaningful.

Canonical standardization.   When this option is chosen, then the row coordinates are computed as F = inverse(Dr)A(Du)**½, and the column coordinates as G = inverse(Dc)B(Du)**½.  For details concerning this standardization, see Gifi (1981).

Row profiles.  When this option is chosen, then the row coordinates are computed based on the row profile matrix R = inverse(Dr)P.  Specifically, the (principal) row coordinates are computed as F = inverse(Dr)ADu, and the standard column coordinates as G = inverse(Dc)B.  This option is appropriate when you are interested in interpreting the distances between row points; the column coordinates should not be interpreted.

Column profiles.  When this option is chosen, or when reviewing the results for column points in multiple correspondence analysis, the column coordinates are computed based on the column profile matrix.  Specifically, the (principal) column coordinates are computed as F = inverse(Dc)BDu, and the standard row coordinates as G = inverse(Dr)A.  This option is appropriate when you are interested in interpreting the distances between column points; the row coordinates should not be interpreted.

"Model" equation

When using the default method of standardization, the following "model" on P in k dimensions shows how the relative frequencies are approximated.

P  rc' + DrF inverse(Du)G'Dc

In this formula F and G stand for the row and column coordinates, respectively.

Computation of quality and inertia

Note that the choice of the standardardization method does not affect the computation of the quality and inertia values reported in the Scrollsheet that is displayed when you click on option Row and column coordinates.  Those values are always computed based on the Row and column profiles standardization.

Specifically, define the diag(x) operator as setting the elements of vector x into the diagonal of a diagonal matrix; define the square(X) operator as squaring each element in matrix or vector X; then the partial contributions of the row and column points to the total inertia are computed as inverse(Dr)square(A) and inverse(Dc)square(B), respectively.

The quality (Cosine²) for the individual dimensions is computed as diag(inverse(square(ADu)1)) square(ADu) and diag(inverse(square(BDu)1)) square(BDu) for the row and column points, respectively, where 1 stands for a column vector with all elements equal to 1.

The inertia for the row and column points is computed as (1/t) inverse(Dr) square(ADu)1 and (1/t) inverse(Dc) square(BDu)1, respectively, where t stands for the total inertia.

Supplementary points, simple correspondence analysis

The computation of the coordinates for supplementary row and column points depends on the choice of the standardization chosen in the Standardization of coordinates box on the Correspondence Analysis Results dialog.  Let Rs and Cs be the matrices of relative row or column frequencies for the supplementary rows and columns, respectively.  The supplementary row and column frequencies are then computed as follows:

Row and column profiles.  When this option is chosen, then the supplementary row and column coordinates are computed as Rs inverse(Dc)B and Cs inverse(Dr) A, respectively.

Canonical standardization.   When this option is chosen, then the supplementary row and column coordinates are computed as Rs inverse(Dc)B(Du)**½ and Cs inverse(Dr) A(Du)**½, respectively.

Row profiles.  When this option is chosen, then the supplementary row and column coordinates are computed as Rs inverse(Dc)B and Cs inverse(Dr) A inverse(Du), respectively.

Column profiles.  When this option is chosen, then the supplementary row and column coordinates are computed as Rs inverse(Dc) B inverse(Du) and Cs inverse(Dr) A, respectively.

Supplementary points, multiple correspondence analysis

In multiple correspondence analysis, supplementary column coordinates are computed as Cs inverse(Dr) A inverse(Du).