The 2-sample Hotelling t2 tests the following
hypothesis:
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: