Descriptive Statistics

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Descriptive Statistics

Information in this document is subject to change without notice and does not represent a commitment on the part of Aptech Systems, Inc. The software described in this document is furnished under a license agreement or nondisclosure agreement. The software may be used or copied only in accordance with the terms of the agreement. The purchaser may make one copy of the software for backup purposes. No part of this manual may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, for any purpose other than the purchaser’s personal use without the written permission of Aptech Systems, Inc. c

Copyright 1984-2002 by Aptech Systems, Inc., Maple Valley, WA. All Rights Reserved.

GAUSS, GAUSS Engine, GAUSS Light are trademarks of Aptech Systems, Inc. All other trademarks are the properties of their respective owners.

Documentation Version: March 22, 2002

Part Number: 000027

Contents

1 Installation

1

1.1 UNIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.1.1

Download . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.1.2

Floppy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.1.3

Solaris 2.x Volume Management . . . . . . . . . . . . . . . . . . .

2

1.2 Windows/NT/2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.2.1

Download . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.2.2

Floppy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.3 Differences Between the UNIX and Windows/NT/2000 Versions

. . . . .

2 Descriptive Statistics 2.1 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1

3 5 5

README Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

2.2 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

2.3 Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

2.3.1

Data Transformations . . . . . . . . . . . . . . . . . . . . . . . . .

6

2.3.2

Creating Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

2.3.3

3

The Uppercase/Lowercase Convention for Distinguishing Character and Numeric Data . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.4 Error Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.4.1

Tests for Error Codes . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.4.2

Error Code Values . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.5 Using the On-Line Help System . . . . . . . . . . . . . . . . . . . . . . . .

9

2.6 Compatibility with Previous Versions . . . . . . . . . . . . . . . . . . . . .

9

Descriptive Statistics Reference

11

dstatset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

corr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

crosstab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

freq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

freqstat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

getfreq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

tblstat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

ttest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

Index

ii

41

Installation

Chapter 1

Installation

1.1 UNIX If you are unfamiliar with UNIX, see your system administrator or system documentation for information on the system commands referred to below. The device names given are probably correct for your system.

1.1.1 Download 1. Copy the .tar.gz file to /tmp. 2. Unzip the file. gunzip appxxx.tar.gz 3. cd to the GAUSS or GAUSS Engine installation directory. We are assuming /usr/local/gauss in this case. cd /usr/local/gauss 4. Untar the file. tar xvf /tmp/appxxx.tar

1.1.2 Floppy 1. Make a temporary directory. mkdir /tmp/workdir 1

1. INSTALLATION 2. cd to the temporary directory. cd /tmp/workdir 3. Use tar to extract the files. tar xvf device name If this software came on diskettes, repeat the tar command for each diskette. 4. Read the README file. more README 5. Run the install.sh script in the work directory. ./install.sh The directory the files are install to should be the same as the install directory of GAUSS or the GAUSS Engine. 6. Remove the temporary directory (optional). The following device names are suggestions. See your system administrator. If you are using Solaris 2.x, see Section 1.1.3. Operating System Solaris 1.x SPARC Solaris 2.x SPARC Solaris 2.x SPARC Solaris 2.x x86 Solaris 2.x x86 HP-UX IBM AIX SGI IRIX

3.5-inch diskette /dev/rfd0 /dev/rfd0a (vol. mgt. off) /vol/dev/aliases/floppy0 /dev/rfd0c (vol. mgt. off) /vol/dev/aliases/floppy0 /dev/rfloppy/c20Ad1s0 /dev/rfd0 /dev/rdsk/fds0d2.3.5hi

1/4-inch tape /dev/rst8 /dev/rst12 /dev/rst12

DAT tape /dev/rmt/1l /dev/rmt/1l /dev/rmt/1l /dev/rmt/1l /dev/rmt/0m

/dev/rmt.0

1.1.3 Solaris 2.x Volume Management If Solaris 2.x volume management is running, insert the floppy disk and type volcheck to signal the system to mount the floppy. The floppy device names for Solaris 2.x change when the volume manager is turned off and on. To turn off volume management, become the superuser and type /etc/init.d/volmgt off To turn on volume management, become the superuser and type /etc/init.d/volmgt on 2

1. INSTALLATION

Installation

1.2 Windows/NT/2000 1.2.1 Download Unzip the .zip file into the GAUSS or GAUSS Engine installation directory.

1.2.2 Floppy 1. Place the diskette in a floppy drive. 2. Call up a DOS window 3. In the DOS window log onto the root directory of the diskette drive. For example: A: cd\ 4. Type: ginstall source drive target path source drive

Drive containing files to install with colon included For example: A:

target path

Main drive and subdirectory to install to without a final \ For example: C:\GAUSS

A directory structure will be created if it does not already exist and the files will be copied over. target path\src source code files library files target path\lib target path\examples example files

1.3 Differences Between the UNIX and Windows/NT/2000 Versions • If the functions can be controlled during execution by entering keystrokes from the keyboard, it may be necessary to press Enter after the keystroke in the UNIX version. 3

1. INSTALLATION • On the Intel math coprocessors used by the Windows/NT/2000 machines, intermediate calculations have 80-bit precision, while on the current UNIX machines, all calculations are in 64-bit precision. For this reason, GAUSS programs executed under UNIX may produce slightly different results, due to differences in roundoff, from those executed under Windows/NT/2000.

4

Chapter 2

The DESCRIPTIVE STATISTICS module is a set of procedures which generates basic sample statistics of the variables in GAUSS data sets. These statistics describe the numerical characteristics of the random variables, and provide information for further statistical analysis.

2.1 Getting Started GAUSS 3.1.0+ is required to use these routines.

2.1.1 README Files The file README.ds contains any last minute information on this module. Please read it before using the procedures in this module.

2.2 Setup In order to use the procedures in the DESCRIPTIVE STATISTICS module, the DSTAT library must be active. This is done by including dstat in the LIBRARY statement at the top of your program: library dstat,quantal,pgraph; 5

Descriptive Statistics

Descriptive Statistics

2. DESCRIPTIVE STATISTICS This enables GAUSS to find the DESCRIPTIVE STATISTICS procedures. If you plan to make any right-hand references to the global variables, you also need the statement: #include dstat.ext; To reset global variables in succeeding executions of the program the following instruction can be used: dstatset; This could be included with the above statements without harm and would insure the proper definition of the global variables for all executions of the program.

2.3 Data Sets A GAUSS data set is a binary disk file. Under DOS, each data set has two disk files associated with it: the first file, containing the data, has a .dat extension; the second file, containing the names of the variables associated with each column of the data set, is called the “header file” and has a .dht extension. For example, the files mydata.dat and mydata.dht are the two files associated with the GAUSS data set named “mydata”. Under UNIX, everything is combined into one file with a .dat extension. For the data set “mydata”, then, there would only be the file mydata.dat.

2.3.1 Data Transformations It is assumed that the data set for analysis is ready before you call the procedures. If you need to modify your data, use DATALOOP. The data loop allows selection of observations, transformation of variables, selection of variables, deletion of missing values, etc. For more details on DATALOOP, please consult the GAUSS manual.

2.3.2 Creating Data Sets There are three ways to create a GAUSS data set. 1. If you have an ASCII format data file, use the ATOG utility to convert it into a GAUSS data set. For details, see ATOG in the UTILITIES section of the GAUSS manual. 2. If you have a matrix in memory, use the command CREATE or SAVED to create a data set. See the COMMAND REFERENCE section of the GAUSS manual. 6

2. DESCRIPTIVE STATISTICS 3. If you already have a GAUSS data set and want to create a new GAUSS data set from the existing one, use a data loop. See the DATA TRANSFORMATIONS section of the GAUSS manual. To look at a GAUSS data set, use the keyword DATALIST. The syntax is: DATALIST filename [variables];

Descriptive Statistics

For details, see DATALIST in the GAUSS manual.

2.3.3 The Uppercase/Lowercase Convention for Distinguishing Character and Numeric Data To distinguish numeric variables from character variables in GAUSS data sets, GAUSS recognizes an “uppercase/lowercase” convention: if the variable name is uppercase, the variable is assumed to be numeric; if it is lowercase, the variable is assumed to be character. ATOG implements this convention automatically when you use the $ and # operators to toggle between character and numeric variable names listed in the INVAR statement. When creating a data set using the SAVED command, this convention can be established as follows: data = { M 32 21500, F 27 36000, F 28 19500, M 25 32000 }; dataset = "MYDATA"; vnames = { "sex" AGE PAY }; call saved(data,dataset,vnames); It is necessary to put “sex” into quotes in order to prevent it from being forced to uppercase. The procedure GETNAME can be used to retrieve the variable names: names = getname("mydata"); print $names; The names are: sex AGE PAY 7

2. DESCRIPTIVE STATISTICS When you are selecting data using DATALOOP, the selection is case-insensitive. That is: keep

AGE, PAY, SEX;

keep age PAY sex; perform the same selection. Only when you are writing or creating a data set (as the above example using SAVED does) is the case of the variable names important. If you have data sets which do not conform to the uppercase/lowercase convention, set the global variable vtype to specify which of your variables are character and which are numeric.

2.4 Error Codes If problems are encountered in data being analyzed, the procedures attempt to trap the errors. Errors are handled with the low order bit of the trap flag. Depending on the value of the trap flag, the procedure either sends an error message indicating the nature of the problem and terminates the program, or returns an error code without termination. TRAP 0 terminate with error message TRAP 1 return scalar error code Error codes are particularly helpful if you are running a large program and need to obtain values to pass to other programs.

2.4.1 Tests for Error Codes If an error is encountered and a procedure returns an error code, it will appear as a missing value. Use the SCALERR procedure to return the value of the error code. For example: { t, n } = crosstab(dataset,varnm); errcode = scalerr(t); if errcode /= 0; print "Error " errcode " was encountered."; end; endif; The error code returned by SCALERR is an integer. 8

2. DESCRIPTIVE STATISTICS

2.4.2 Error Code Values The following error codes are common to all of the procedures in the DESCRIPTIVE STATISTICS module: 1 2 32

Descriptive Statistics

33 41 77

the data file was not found. undefined variables in input argument. too many categories in frequency or crosstable. If this happens, the user may change the value of the global variable maxvec and try again. cannot create crosstable with only one variable. the global variable miss = 0, but missing values are found. no observations left after deleting missing values.

2.5 Using the On-Line Help System All of the procedures are automatically accessible through GAUSS’s on-line help system. If the DSTAT library is active, pressing Alt-H, then “H” again, then entering the name of a procedure listed in the library displays information about syntax, arguments, and globals used by that procedure. The help system uses the same search path that GAUSS uses when it is attempting to compile your programs. That is, if the help system can find the procedure you request information on, then GAUSS can too. This feature can be particularly useful if you are getting “Undefined Symbol” errors, or if it appears that GAUSS is finding the wrong definition of a procedure being called. If, when you attempt to locate the procedure through the help system, nothing appears on the screen or you are returned to your edit file or command mode, then GAUSS is not finding the procedure you requested. Check your SRC PATH and check to see that the library file (with .lcg extension on the lib subdirectory) is active. If a file is found, check the top of the help screen for the name and location of the file.

2.6 Compatibility with Previous Versions This new version of the DESCRIPTIVE STATISTICS module requires GAUSS 3.1.0+. Any programs that you had running under the previous modules may require minor changes before they run successfully under this new version. If you used DTRAN for data transformations, you need to use DATALOOP instead. A new global variable range is now used. This global variable enables the user to specify the range of rows in the data set for analysis. The default is that the whole data set is used. If you need to sample part of your data set, you should set the global variable range before you call the procedures. 9

2. DESCRIPTIVE STATISTICS

10

Chapter 3

Descriptive Statistics Reference

A summary table listing the main procedures is displayed below.

Description

corr crosstab freq means ttest

Computes the correlations Creates contingency tables from raw or weighted data Computes frequency distributions Computes the descriptive statistics Tests the differences of means between two groups

Reference

Procedure

Page 13 17 21 29 35

11

dstatset

3. DESCRIPTIVE STATISTICS REFERENCE

dstatset Purpose Resets DESCRIPTIVE STATISTICS global variables to default values.

Library dstat

Format dstatset;

Remarks It is generally good practice to put this instruction at the top of all programs that invoke procedures in the DESCRIPTIVE STATISTICS module. This prevents globals from being inappropriately defined when a program is run either several times or after another program that also calls DESCRIPTIVE STATISTICS procedures. dstatset calls GAUSSET.

Source dstatset.src

12

corr

3. DESCRIPTIVE STATISTICS REFERENCE

corr Purpose Computes the correlations for variables in a GAUSS data set.

Library dstat

Format { cor,vc,n,nms,des } = corr(dataset,vars);

Input string, name of data file.

vars

K×1 character vector, names of variables. – or – K×1 numeric vector, indices of variables.

Reference

dataset

If 0, all variables are included.

Output cor

K×K matrix, correlations in the order of vars.

vc

K×K matrix, covariances in the order of vars.

n

scalar, number of observations for listwise correlations. – or – K×K matrix of number of observations for each correlation. A matrix is returned if and only if pairwise correlations are selected.

nms

K×1 character vector, variable names in the order of vars.

des

K×7 matrix, descriptive statistics: des[.,1] Means des[.,2] Standard deviations des[.,3] Variances 13

corr

3. DESCRIPTIVE STATISTICS REFERENCE des[.,4] Minimum des[.,5] Maximum des[.,6] Number of valid cases des[.,7] Number of missing cases Error handling is controlled by the low order bit of the trap flag. TRAP 0 terminate with error message. TRAP 1 return scalar error code in all return arguments. The function SCALERR can be used to return the value of the error code. The error codes returned are: 1

data file not found

2

undefined variables in input argument

41

miss = 0 but missing values were encountered

77 no cases left after deleting missing observations

Globals dscor

scalar, if 1, print correlation matrix. Default = 1.

dstat

scalar, if 1, print univariate descriptive statistics. Default = 1.

dsmmt

scalar, if 1, print moment matrix. Default = 0.

dst

scalar, if 1, print t-tests of hypothesis H 0 : r = 0. Based on the formula: √ r n − 1√ ∼ t(n − 2) 1 − r2 Default = 1.

dsvc

scalar, if 1, print covariance matrix. Default = 0.

header string, specifies the format for the output header. zero or more of the following characters: t l d v f

header can contain

print title (see title) bracket title with lines print date and time print procedure name and version number print file name being analyzed

Example: __header = "tld"; If 14

header == “”, no header is printed. Default = “tldvf”.

corr

3. DESCRIPTIVE STATISTICS REFERENCE miss

scalar, determines how missing data is handled. 0

Missing values are not checked for, and so the data set must not have any missing observations. This is the fastest option.

1

Listwise deletion. Removes from computation any observation containing a missing value for any variable included in the analysis.

2

Pairwise deletion. corr does not require a complete set of data for each observation. This procedure deals separately with each pair of variables in the matrix, computing the covariance and correlation between that pair on the basis of all cases for which there is data. With pairwise deletion, any pair of variables containing missing values is excluded from the computation of their covariance.

Default = 0. output scalar, determines printing of intermediate results. nothing is written.

1

serial ASCII output format suitable for disk files or printers.

2

(NOTE: DOS version only) output is suitable for screen only. ANSI.SYS must be active.

Reference

0

Under UNIX, default = 1; under DOS, default = 2. range

2×1 vector, the range of records in the data set used for analysis. The first element is the starting row index, the second element is the ending row index. Default is range = { 0, 0 }, the whole data set. For example, if one wants the range of data from row 100 to the end of data, then range should be set as: __range = { 100, 0 };

row

scalar, specifies how many rows of the data set are read per iteration of the read loop. If row = 0, the number of rows to be read is calculated by corr. Default = 0.

rowfac scalar, “row factor”. If a DESCRIPTIVE STATISTICS procedure fails due to insufficient memory while attempting to read a GAUSS data set, then rowfac may be set to some value between 0 and 1 to read a proportion of the original number of rows of the GAUSS data set. For example, setting __rowfac = 0.8; causes GAUSS to read in only 80% of the rows that were originally calculated. This global only has an effect when

row = 0.

Default = 1. 15

corr

3. DESCRIPTIVE STATISTICS REFERENCE title

string, this is the title used by

header. Default = “”.

weight string or scalar, name or index of weight variable. By default, unweighted correlations are calculated.

Example library dstat; #include dstat.ext; dstatset; var = { pub1, pub3, pub6, job, enrol }; __weight = "PUB1"; __miss = 2; __header = "tl"; __title = "corr.e: WEIGHTED PAIRWISE - ALL OPTIONS"; output file = corr.out reset; call corr("scigau",var); output off;

Source destat.src

16

crosstab

3. DESCRIPTIVE STATISTICS REFERENCE

crosstab Purpose Creates contingency tables from raw or weighted data contained in a GAUSS data set.

Library dstat

Format { t,n } = crosstab(dataset,vars);

Input string, name of data set.

vars

K×1 character vector of variable names for the table. – or – K×1 numeric vector of column indices of variables for the table.

Reference

dataset

K must be at least 2. The first variable in vars is the row variable, the second variable is the column variable, the remaining variables are levels of the control variables.

Output t

N×K matrix, table indices.

n

N×1 vector, table counts. Error handling is controlled by the low order bit of the trap flag. TRAP 0 terminate with error message. TRAP 1 return scalar error code in all return arguments. The function SCALERR can be used to return the value of the error code. The error codes returned are: 1

data file not found

2

undefined variables in input argument 17

crosstab

3. DESCRIPTIVE STATISTICS REFERENCE 32 too many cells in crosstable 33 cannot create crosstable with only one variable

Globals dscase

scalar, if 1, case sensitivity turned on for character variables. Default = 0.

dscol

scalar, number of columns to print per section of a table. If a table is large, this allows printing it in sections. Default = 6.

dscolp

scalar, if 1, list column percentages. Default = 0.

dspause scalar, if 1, pause between tables. Default = 1. dsrow

scalar, number of rows to print per section of a table. If a table is large, this allows printing it in sections. Default = 3.

dsrowp

scalar, if 1, list row percentages. Default = 0.

dstat

scalar, if 1, print statistics. See documentation of tblstat for details on statistics printed. Default = 1.

dstotp

scalar, if 1, list total percentages. Default = 0.

miss

scalar, determines how missing data are handled. 0

Missing values are included in the table as a separate category if there are missing observations in the data.

1

Listwise deletion. Removes from computation any observation with a missing value for any variable included in the analysis.

Default = 0. output scalar, determines printing of intermediate results. 0

nothing is written.

1

serial ASCII output format suitable for disk files or printers.

2

(NOTE: DOS version only) output is suitable for screen only. ANSI.SYS must be active.

Under UNIX, default = 1; under DOS, default = 2. range

18

2×1 vector, the range of records in the data set used for analysis. The first element is the starting row index, the second element is the ending row index. Default is range = { 0, 0 }, the whole data set. For example, if one wants the range of data from row 100 to the end of data, then range should be set as:

crosstab

3. DESCRIPTIVE STATISTICS REFERENCE __range = { 100, 0 }; row

scalar, specifies how many rows of the data set are read per iteration of the read loop. If row = 0, the number of rows to be read is calculated by crosstab. Default = 0.

rowfac scalar, “row factor”. If crosstab fails due to insufficient memory while attempting to read a GAUSS data set, then rowfac may be set to some value between 0 and 1 to read a proportion of the original number of rows of the GAUSS data set. For example, setting __rowfac = 0.8; causes GAUSS to read in only 80% of the rows that were originally calculated. This global only has an effect when

row = 0.

Default = 1. vtype

scalar or vector, indicates the types of the variables included in the analysis. Set vtype only if you are NOT following the uppercase/lowercase convention.

Reference

If you have: all character data all numeric data mixed data

vtype = 0. set set vtype = 1. set vtype to a vector of 0’s and 1’s, 0 for character variables, 1 for numeric.

vtype should be a K×1 or a (K+1)×1 vector, If you have mixed data, depending on whether or not a weight variable is specified (see weight below). Set the elements of vtype as follows: [1:K] [K+1]

types of vars variables type of weight variable (if specified)

By default, vtype = −1. That is, data type is determined by looking at the case of each variable name. See section 2.3.3 for a discussion of the uppercase/lowercase convention. weight scalar or string, name or index of weight variable. By default, no weighting is used.

Remarks This procedure handles both character and numeric data. To indicate the type of each variable to be included in the analysis, you may either follow the uppercase/lowercase convention (see Section 2.3.3), or set the global variable vtype as described above under Globals. 19

crosstab

3. DESCRIPTIVE STATISTICS REFERENCE crosstab constructs a K-way table from variables V i (i = 1, K) in vars, with variable Vi having Ki categories. The resulting table contains N = K 1 × K2 × . . . KK cells. The observed variables for this table are contained in the N×1 vector n. The N cell indices associated with n are contained in the K×N matrix t, where element t ij is the category level of variable Vj for ni . The matrices t and n that are returned by crosstab are in the appropriate form for input to the programs in the LOGLINEAR ANALYSIS module. A table can contain at most MAXVEC cells.

Example Print a two-way table. library dstat; #include dstat.ext; dstatset; dataset = "mydata"; call crosstab(dataset,2|5); /* crosstab 2nd variable by 5th */

Source crosstab.src

See also tblstat, freq

20

freq

3. DESCRIPTIVE STATISTICS REFERENCE

freq Purpose Computes frequency distributions for variables contained in a GAUSS data set.

Library dstat

Format { cats,ncats,freqn } = freq(dataset,vars);

Input string, name of data set.

vars

K×1 character vector, names of variables – or – K×1 numeric vector, indices of variables

Reference

dataset

for which frequency distributions are requested. If vars = 0, all the variables in the data set are used.

Output PK

cats

L×1 vector of categories for each variable, where L = is the number of categories of the ith variable.

ncats

K×1 vector of (cat1 , cat2, . . ., catK ), where each element is the number of categories for the corresponding variable.

freqn

L×1 vector of frequencies for each variable.

i=1

cati , and cati

Error handling is controlled by the low order bit of the trap flag. TRAP 0 terminate with error message. TRAP 1 return scalar error code in all return arguments. The function SCALERR can be used to return the value of the error code. The error codes returned are: 21

freq

3. DESCRIPTIVE STATISTICS REFERENCE 1

data file not found

2

undefined variables in input argument

32 too many cells in frequency 77 no cases left after deleting missing observations

Globals dscase

scalar, if 1, case sensitivity turned on for character variables. Default = 0.

dspause scalar, if 1, pause between tables. Default = 1. dstat miss

scalar, if 1, print descriptive statistics. Default = 1. scalar, determines how missing data are handled. 0

Missing values are included in the table as a separate category if there are missings in the data.

1

Listwise deletion. Removes from computation any observation with a missing value for any variable included in the analysis.

Default = 0. output scalar, determines printing of intermediate results. 0

nothing is written.

1

serial ASCII output format suitable for disk files or printers.

2

(NOTE: DOS version only) output is suitable for screen only. ANSI.SYS must be active.

Under UNIX, default = 1; under DOS, default = 2. range

2×1 vector, the range of records in data set used for analysis. The first element is the starting row index, the second element is the ending row index. Default is range = { 0, 0 }, the whole data set. For example, if one wants the range of data from row 100 to the end of data, then range should be set as: __range = { 100, 0 };

row

scalar, specifies how many rows of the data set are read per iteration of the read loop. If row = 0, the number of rows to be read is calculated by freq. Default = 0.

rowfac scalar, “row factor”. If freq fails due to insufficient memory while attempting to read a GAUSS data set, then rowfac may be set to some value between 0 and 1 to read a proportion of the original number of rows of the GAUSS data set. For example, setting 22

freq

3. DESCRIPTIVE STATISTICS REFERENCE __rowfac = 0.8; causes GAUSS to read in only 80% of the rows that were originally calculated. This global only has an effect when

row = 0.

Default = 1. sort

scalar, if 1, output is sorted by the names of the variables in vars. Default = 0.

vtype

scalar or vector, indicates the types of the variables included in the analysis. Set vtype only if you are NOT following the uppercase/lowercase convention. If you have: all character data all numeric data mixed data

vtype = 0. set set vtype = 1. set vtype to a vector of 0’s and 1’s, 0 for character variables, 1 for numeric.

[1:K] [K+1]

types of vars variables type of weight variable (if specified)

By default, vtype = −1. That is, data type is determined by looking at the case of each variable name. See section 2.3.3 for a discussion of the uppercase/lowercase convention. weight scalar or string, the name or index of the weight variable. By default, no weighting is used in calculations.

Remarks This procedure handles both character and numeric data. To indicate the type of each variable to be included in the analysis, you may either follow the uppercase/lowercase convention (see section 2.3.3), or set the global variable vtype as described above under Globals. If there are missing data for a variable, counts excluding the missing category are also made. For each variable in vars, freq returns a sorted list of all categories of that variable, the number of categories for that variable, and the number of cases in each category. The procedure getfreq gets the categories and frequencies for a specified variable. 23

Reference

vtype should be a K×1 or a (K+1)×1 vector, If you have mixed data, depending on whether or not a weight variable is specified (see weight below). Set the elements of vtype as follows:

freq

3. DESCRIPTIVE STATISTICS REFERENCE The total number of cells in the frequency distributions for all variables in vars cannot exceed MAXVEC.

Example Using freq: library dstat; #include dstat.ext; dstatset; dataset = "mydata"; call freq(dataset,2|5); /* <=== Frequencies for the */ /* 2nd and 5th variables */ Using freq, getfreq and HISTF: library dstat,pgraph; #include dstat.ext; graphset; dstatset; print "FR4.E: Using getfreq and HISTF"; print; dataset = "freq"; output file = fr1.out reset; __miss = 1; /* get rid of missing category */ { cats,ncats,freqs } = freq(dataset,1|2|3); output off; /* get frequencies for var 1 */ histf(getfreq(1,cats,ncats,freqs));

Source freq.src

See also getfreq, freqstat

24

freqstat

3. DESCRIPTIVE STATISTICS REFERENCE

freqstat Purpose Prints percentages, descriptive statistics and simple histogram given category values and number of cases in each category.

Library dstat

Format freqstat(nm,freq,val,c);

Input string, name of variable.

freq

L×1 vector, number of observations in each category.

val

L×1 character vector, label of each category. – or – L×1 numeric vector, value of each category.

c

scalar, 1 if numeric variable, 0 if character variable.

Reference

nm

Output None.

Globals dsfreq

scalar, if 1, print frequencies. Default = 1.

dstat

scalar, if 1, print descriptive statistics. Default = 1.

Remarks freqstat prints frequencies, percentages, descriptive statistics and a histogram. freqstat works with matrices in memory; if your data is in a GAUSS data set, you should use the procedure freq, which works with data sets. 25

freqstat

3. DESCRIPTIVE STATISTICS REFERENCE

Example library dstat; dstatset; output file = frst.out reset; freq = { 10, 3, 4 }; cats = { 1, 2, 3 }; freqstat("VAR", freq, cats, 1); output off;

Source freqstat.src

See also freq

26

getfreq

3. DESCRIPTIVE STATISTICS REFERENCE

getfreq Purpose Gets frequencies and categories for a particular variable from the results returned by freq.

Library dstat

Format { vfreq,vcat } = getfreq(var,cats,ncats,freqs);

var

scalar, the index of the variable for which frequencies are desired.

cats

K×1 character vector, labels – or – K×1 numeric vector, category values

Reference

Input

for all counts in the freqs vector. ncats

L×1 vector, number of categories associated with each variable in the freqs vector.

freqs

M×1 vector, frequencies associated with cats and ncats.

Output vfreq

Q×1 vector, frequencies associated with specified variable.

vcat

P×1 vector, categories associated with specified variable.

27

getfreq

3. DESCRIPTIVE STATISTICS REFERENCE

Remarks The variables cats, ncats and freqs are the results returned from freq. freq returns vectors for all variables specified. getfreq returns the frequencies for a specified variable.

Example library dstat,pgraph; #include dstat.ext; dstatset; { cats,ncats,freqs } =

freq(dataset,1|2|3);

{ f,c } = getfreq(1,cats,ncats,freqs);

histf(f,c);

Source getfreq.src

See also freq

28

/* <=== Get frequencies */ /* for VAR 1 */

/* <=== Plot histogram for VAR 1 */

means

3. DESCRIPTIVE STATISTICS REFERENCE

means Purpose Computes the descriptive statistics for variables in a GAUSS data set.

Library dstat

Format { nms,mn,std,min,max ,valid,missing } = means(dataset,vars);

Input string, name of data file.

vars

K×1 character vector, names of variables. – or – K×1 numeric vector, indices of variables.

Reference

dataset

If vars = 0, all variables are included.

Output nms

K×1 character vector of variable names.

mn

K×1 vector of means.

std

K×1 vector of standard deviations.

min

K×1 vector of minimum values.

max

K×1 vector of maximum values.

valid

K×1 vector of the number of valid cases for each selected variable.

missing

K×1 vector of the number of missing cases in each selected variable. Error handling is controlled by the low order bit of the trap flag. TRAP 0 terminate with error message. 29

means

3. DESCRIPTIVE STATISTICS REFERENCE TRAP 1 return scalar error code in all return arguments. The function SCALERR can be used to return the value of the error code. The error codes returned are: 1

data file not found

2

undefined variables in input argument

77 no cases left after deleting missing observations

Globals miss

scalar, determines how missing data are handled. 0

Missing values are not checked for, so the data set must not have any missing observations. This is the fastest option.

1

Listwise deletion. Removes from computation any observation with a missing value for any variable included in the analysis.

2

Pairwise deletion. means does not require a complete set of data for each observation. This procedure deals separately with each variable in the matrix, computing the mean of that variable on the basis of all cases for which there is data. With pairwise deletion, missing values are excluded from computation, so the number of cases used in calculating the mean of each variable differs from variable to variable.

Default = 0. output scalar, determines printing of intermediate results. 0

nothing is written.

1

serial ASCII output format suitable for disk files or printers.

2

(NOTE: DOS version only) output is suitable for screen only. ANSI.SYS must be active.

Under UNIX, default = 1; under DOS, default = 2. range

2×1 vector, the range of records in data set used for analysis. The first element is the starting row index, the second element is the ending row index. Default is range = { 0, 0 }, the whole data set. For example, if one wants the range of data from row 100 to the end of data, then range should be set as: __range = { 100, 0 };

row

30

scalar, specifies how many rows of the data set are read per iteration of the read loop. If row = 0, the number of rows to be read is calculated by means. Default = 0.

means

3. DESCRIPTIVE STATISTICS REFERENCE rowfac scalar, “row factor”. If means fails due to insufficient memory while attempting to read a GAUSS data set, then rowfac may be set to some value between 0 and 1 to read a proportion of the original number of rows of the GAUSS data set. For example, setting __rowfac = 0.8; causes GAUSS to read in only 80% of the rows that were originally calculated. This global only has an effect when

row = 0.

Default = 1. sort

scalar, if 1, output is sorted by the names of the variables in vars. Default = 0.

vtype

scalar or vector, indicates the types of the variables included in the analysis. Set vtype only if you are NOT following the uppercase/lowercase convention. If you have: vtype = 0. set set vtype = 1. set vtype to a vector of 0’s and 1’s, 0 for character variables, 1 for numeric.

Reference

all character data all numeric data mixed data

If you have mixed data, vtype should be a K×1 or a (K+1)×1 vector, depending on whether or not a weight variable is specified (see weight below). Set the elements of vtype as follows: [1:K] [K+1]

types of vars variables type of weight variable (if specified)

By default, vtype = −1. That is, data type is determined by looking at the case of each variable name. See section 2.3.3 for a discussion of the uppercase/lowercase convention. weight string or scalar, name or index of weight variable. By default, calculations are unweighted.

Remarks This procedure handles both character and numeric data. To indicate the type of each variable to be included in the analysis, you may either follow the uppercase/lowercase convention (see section 2.3.3), or set the global variable vtype as described above under Globals.

Example 31

means

3. DESCRIPTIVE STATISTICS REFERENCE library dstat; #include dstat.ext; dstatset; dsn = "cook"; output file = means.exp reset; { nms,mn,std,min,max,valid,missing } = means(dsn,0); output off;

Source destat.src

32

tblstat

3. DESCRIPTIVE STATISTICS REFERENCE

tblstat Purpose Computes statistics and measures of association for an I×J contingency table.

Library dstat

Format tblstat(x );

Input I×J matrix of cell frequencies.

Reference

x

Output Measures of fit and association for table are sent to the output device.

Remarks The following statistics are computed and printed. Statistic Pearson’s Chi Square Likelihood Chi Square Yate’s Corrected Chi Square (2×2) McNemar’s Symmetry Chi-Square Phi Cramer’s V (not for 2×2) Contingency (Pearson’s P) Spearman’s Rho (Correlation) Cohen’s Kappa (symmetric tables) Yule’s Q (2×2) Yule’s Y (2×2) Goodman-Kruskal Gamma Kendall’s Tau-B Stuart’s Tau-C Somer’s D Lambda Uncertainty

Reference BFH, 124 BFH, 124 BFH, 124 Agresti, 175 BFH, 386 BFH, 385 BFH, 381 BFH, 395 BFH, 378 BFH, 378 Agresti, 159 Agresti, 161 Agresti, 177 Agresti, 161 BFH, 388

33

tblstat

3. DESCRIPTIVE STATISTICS REFERENCE Agresti: Agresti, Alan. 1984. Analysis of Ordinal Categorical Data. New York: John Wiley and Sons. BFH: Bishop, Yvonne, Stephen Fienberg and Paul Holland 1975. Discrete Multivariate Analysis: Theory and Practice. Cambridge, Mass.: MIT Press.

Example library dstat; dstatset; x = { 10 23, 34 47 }; tblstat(x);

Source tblstat.src

See also crosstab

34

ttest

3. DESCRIPTIVE STATISTICS REFERENCE

ttest Purpose Tests the differences of means between two groups.

Library dstat

Format { varl,descstat,mntest,vartest } = ttest(dataset,grpvar,varnm);

Input string, name of data file.

grpvar

string, name of the group variable. – or – scalar, index of the group variable.

Reference

dataset

grpvar may be the name of a variable that contains character data. varnm

K×1 character vector, names of variables to be tested. – or – K×1 numeric vector, indices of variables to be tested. – or – scalar 0, all variables but grpvar are tested.

Output varl

(K+1)×1 character vector, variable names.

descstat

L×6 matrix of descriptive statistics, where descstat[.,1] means of group 0 descstat[.,2] means of group 1 descstat[.,3] standard deviation of group 0 descstat[.,4] standard deviation of group 1 descstat[.,5] number of valid cases 35

ttest

3. DESCRIPTIVE STATISTICS REFERENCE descstat[.,6] number of missing cases mntest

L×6 matrix, results of test of the hypothesis that the true means are the same. Columns are: mntest[.,1] t value for assumption that the two groups have equal variances mntest[.,2] degrees of freedom for equal variances mntest[.,3] probability for equal variances mntest[.,4] t value for unequal variances mntest[.,5] degrees of freedom for unequal variances mntest[.,6] probability for unequal variances

vartest

L×4 matrix of results from test of variances. Columns are: vartest[.,1] F value for test of differences vartest[.,2] degrees of freedom for equal variances vartest[.,3] degrees of freedom for unequal variances vartest[.,4] probability of the F statistic Error handling is controlled by the low order bit of the trap flag. TRAP 0 terminate with error message. TRAP 1 return scalar error code in all return arguments. The function SCALERR can be used to return the value of the error code. The error codes returned are: 1

data file not found

2

undefined variables in input argument

41

miss = 0 but missing values were encountered

77 no cases left after deleting missing observations

Globals dsgrpnm 2×1 character vector of names of groups. By default, the names “Group 0” and “Group 1” are used. dscut

scalar or 2×1 vector. The groups are defined by follows: scalar

36

dscut and the conditioning variable grpvar as

dscut, numeric grpvar:

ttest

3. DESCRIPTIVE STATISTICS REFERENCE first group second group scalar

grpvar < grpvar ≥

dscut dscut

grpvar = grpvar 6=

dscut dscut

grpvar = grpvar =

dscut[1] dscut[2]

dscut, character grpvar:

first group second group vector (2×1)

dscut, character or numeric grpvar:

first group second group Default = 0. miss

scalar, determines how missing data are handled. Missing values are not checked for, and so the data set must not have any missing observations. This is the fastest option.

1

Listwise deletion. Removes from computation any observation containing a missing value for any variable included in the analysis.

2

Pairwise deletion. ttest does not require a complete set of data for each observation. This procedure deals separately with each pair of variables in the matrix, computing the covariance and correlation between that pair on the basis of all cases for which there is data. With pairwise deletion, any pair of variables containing missing values is excluded from the computation of their covariance.

Default = 0. output scalar, determines printing of intermediate results. 0

nothing is written.

1

serial ASCII output format suitable for disk files or printers.

2

(NOTE: DOS version only) output is suitable for screen only. ANSI.SYS must be active.

Under UNIX, default = 1; under DOS, default = 2. range

2×1 vector, the range of records in data set used for analysis. The first element is the starting row index, the second element is the ending row index. Default is range = { 0, 0 }, the whole data set. For example, if one wants the range of data from row 100 to the end of data, then range should be set as: __range = { 100, 0 };

row

scalar, specifies how many rows of the data set are read per iteration of the read loop. If row = 0, the number of rows to be read is calculated by ttest. Default = 0. 37

Reference

0

ttest

3. DESCRIPTIVE STATISTICS REFERENCE rowfac scalar, “row factor”. If ttest fails due to insufficient memory while attempting to read a GAUSS data set, then rowfac may be set to some value between 0 and 1 to read a proportion of the original number of rows of the GAUSS data set. For example, setting __rowfac = 0.8; causes GAUSS to read in only 80% of the rows that were originally calculated. This global only has an effect when

row = 0.

Default = 1. vtype

scalar or vector, indicates the types of the variables included in the vtype only if you are NOT following the analysis. Set uppercase/lowercase convention. If you have: all character data all numeric data mixed data

set vtype = 0. set vtype = 1. set vtype to a vector of 0’s and 1’s, 0 for character variables, 1 for numeric.

vtype should be a (K+1)×1 vector. Set the If you have mixed data, elements of vtype as follows: [1] [2:K+1]

type of grpvar variable types of varnm variables

By default, vtype = −1. That is, data type is determined by looking at the case of each variable name. See section 2.3.3 for a discussion of the uppercase/lowercase convention.

Remarks This procedure handles both character and numeric data. To indicate the type of each variable to be included in the analysis, you may either follow the uppercase/lowercase convention (see section 2.3.3), or set the global variable vtype as described above under Globals. Descriptive statistics for each group and tests of differences of means are sent to the output device.

Example library dstat; dstatset; dataset = "scigau"; vars = { cit1, pub1 }; 38

ttest

3. DESCRIPTIVE STATISTICS REFERENCE grpvar = { job }; _dsgrpnm = { Lo_Job, Hi_Job }; __miss = 2; _dscut = 2; output file = ttest.out reset; { desc,mtest,vtest } = ttest(dataset,grpvar,vars); output off;

Source ttest.src

Reference

39

ttest

3. DESCRIPTIVE STATISTICS REFERENCE

40

Index contingency tables, 33 corr, 13 crosstab, 17, 20 crosstab.src, 20

D

E error codes, 8, 9

F freq, 21, 23 freq.src, 24

G GAUSSET, 12 getfreq, 23, 27 getfreq.src, 28

H header, 14 histogram, 25

I Installation, 1

L library, DSTAT, 5 LOGLINEAR ANALYSIS module, 20

M MAXVEC, 20, 24 means, 29 means, differences, 35 measures of association, 33 measures of fit, 33 miss, 18, 22, 30 missing values, 6

O output, 15, 18, 22, 30, 37

R

Index

destat.src, 16, 32 dscase, 18, 22 dscol, 18 dscolp, 18 dscor, 14 dscut, 36 dsdesc, 14 dsfreq, 25 dsgrpnm, 36 dsmmt, 14 dspause, 18, 22 dsrow, 18 dsrowp, 18 dst, 14 dstat, 18, 22, 25 dstat.ext, 6 dstatset, 6, 12 dstatset.src, 12 dstotp, 18 dsvc, 14

freqstat, 25 freqstat.src, 26

INDEX range, 15, 18, 22, 30, 37 row, 15, 19, 22, 30, 37 rowfac, 15, 19, 22, 31, 38

S sort, 23, 31 statistics, descriptive, 25, 38

T tblstat, 33 tblstat.src, 34 tests for error codes, 8 TRAP, 14, 17, 21, 29, 36 ttest, 35 ttest.src, 39

U UNIX, 1, 3

V vtype, 19, 23, 31, 38

W weight, 16, 19, 23, 31 Windows/NT/2000, 3

42

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Descriptive Statistics

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