
HOTELLING ONE SAMPLE TSQUAREName:
Here, U0 is a vector of population means, that is, the hypothesized means for each column of the matrix. The 1sample t ^{2} test statistic is defined as:
where U_{0} is the vector of hypothesized means, contains the sample means for each of the columns, and (1/N) is the sample variancecovariance matrix of . T ^{2} is distributed as ((n1)p/(np))F(p,np) 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.
where <mat1> is a matrix containing the data for the 1sample Hotelling t ^{2} test; <x> is a vector containing the hypothesized means; and where <par> is a parameter where the value of the 1sample Hotelling t ^{2} test statistic is saved.
HOTELLING 1 SAMPLE TSQUARE HOTELLING 1 SAMPLE T2
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 "1SAMPLE HOTELLING TSQUARE 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
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