2-Sample Hotelling T-Square

 Dataplot Vol 2 Vol 1

# HOTELLING TWO SAMPLE TSQUARE

Name:
HOTELLING TWO SAMPLE TSQUARE (LET)
Type:
Let Subcommand
Purpose:
Compute the 2-sample Hotelling t 2 test for two matrices.
Description:
The 2-sample Hotelling t2 tests the following hypothesis:

H0: U1=U2

Here, U1 is a vector of population means from sample 1, that is, the hypothesized means for each column of matrix 1. Likewise, U2 is a vector of population means from sample 2, that is, the hypothesized means for each column of matrix 2.

The 2-sample t 2 test statistic is defined as:

where contains the sample means for each of the columns of matrix 1, contains the sample means for each of the columns of matrix 2, N1 is the sample size for matrix 1, N2 is the sample size for matrix 2, and is the inverse of the pooled variance-covariance matrices of and .

T 2 is distributed as F(p,n1+n2-p-1) where n1 is the number of obserations for matrix 1, n2 is the number of observations for matrix 2, p is the number of columns (variables), and F is the F distribution. We reject the null hypothesis if the t 2 test statistic is greater than the critical value from the F distribution.

This command returns a parameter that contains the value of the Hotelling T 2 test statistic. The critical values corresponding to alpha = .10, .05, .01, and .005 are saved in the internal parameters B90, B95, B99, and B995 respectively.

Syntax:
LET <par> = HOTELLING TWO SAMPLE TSQUARE <mat1> <mat2>
where <mat1> is a matrix containing the data for the first sample of the 2-sample Hotelling t 2 test;
where <mat2> is a matrix containing the data for the second sample of the 2-sample Hotelling t 2 test;
and where <par> is a parameter where the value of the 2-sample Hotelling t 2 test statistic is saved.
Examples:
LET A = 2-SAMPLE HOTELLING T-SQUARE M Z
Note:
Matrices are created with either the READ MATRIX command or the MATRIX DEFINITION command. Enter HELP MATRIX DEFINITION and HELP READ MATRIX for details.
Default:
None
Synonyms:
The following are synonyms for HOTELLING TWO SAMPLE TSQUARE:
HOTELLING TWO SAMPLE T2
HOTELLING 2 SAMPLE TSQUARE
HOTELLING 2 SAMPLE T2
Related Commands:
Dataplot Reference Manual
Volume 1: Commands
Auxiliary Chapter
 READ MATRIX = Read a matrix. MATRIX COLUMN DIMENSION = Dimension maximum number of columns for Dataplot matrices. 1-SAMPLE HOTELLING T-SQUARE TEST = Compute the 1-sample Hotelling t-square test. QUADRATIC FORM = Compute the quadratic form of a matrix and a vector. LINEAR COMBINATION = Compute a linear combination of a matrix and a vector.
Reference:

"Applied Multivariate Statistical Analysis", Third Edition, Johnson and Wichern, Prentice-Hall, 1992.
Applications:
Multivariate Analysis
Implementation Date:
1998/8
Program:
DIMENSION 200 COLUMNS
SKIP 25
READ IRIS.DAT X1 X2 X3 X4 TAG
SKIP 0
LET Z1 = X1
LET Z2 = X2
LET Z3 = X3
LET Z4 = X4
RETAIN X1 X2 X3 X4 SUBSET TAG = 1
RETAIN Z1 Z2 Z3 Z4 SUBSET TAG = 2
LET N1 = SIZE X1
LET N2 = SIZE Z1
LET M = MATRIX DEFINITION X1 N1 4
LET N = MATRIX DEFINITION Z1 N2 4
LET A = 2-SAMPLE HOTELLING T-SQUARE M N
PRINT "2-SAMPLE HOTELLING T-SQUARE TEST STATISTIC = ^A"
PRINT "90% CRITICAL VALUE = ^B90"
PRINT "95% CRITICAL VALUE = ^B95"
PRINT "99% CRITICAL VALUE = ^B99"

Date created: 6/5/2001
Last updated: 7/9/2001
Please email comments on this WWW page to alan.heckert@nist.gov.