Hotelling One Sample Tsquare

 Dataplot Vol 2 Vol 1

# HOTELLING ONE SAMPLE TSQUARE

Name:
HOTELLING ONE SAMPLE TSQUARE (LET
Type:
Let Subcommand
Purpose:
Compute the 1-sample Hotelling t 2 test.
Description:
The 1-sample Hotelling t 2 tests the following hypothesis:

H0: U=U0

Here, U0 is a vector of population means, that is, the hypothesized means for each column of the matrix.

The 1-sample t 2 test statistic is defined as:

where U0 is the vector of hypothesized means, contains the sample means for each of the columns, and (1/N) is the sample variance-covariance matrix of .

T 2 is distributed as ((n-1)p/(n-p))F(p,n-p) where n is the number of obserations, p is the number of columns, 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 ONE SAMPLE TSQUARE <mat1> <x>
where <mat1> is a matrix containing the data for the 1-sample Hotelling t 2 test;
<x> is a vector containing the hypothesized means;
and where <par> is a parameter where the value of the 1-sample Hotelling t 2 test statistic is saved.
Examples:
LET A = 1-SAMPLE HOTELLING T-SQUARE M X
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 ONE SAMPLE TSQUARE:

HOTELLING ONE SAMPLE T2
HOTELLING 1 SAMPLE TSQUARE
HOTELLING 1 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. HOTELLING TWO SAMPLE TSQUARE = Compute the 2-sample Hotelling t 2 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 SEPLENG SEPWIDTH PETLENG PETWIDTH TAG
SKIP 0
LET NTOT = SIZE SEPLENG
LET M = MATRIX DEFINITION SEPLENG NTOT 4
LET X = DATA 0 0 0 0
LET A = HOTELLING ONE SAMPLE TSQUARE M X
PRINT "1-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