Re: Test for equality of means (multivariate) and unequal variance matrices

In article <1146987966.387810.37140@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
bob <bob_bobene@xxxxxx> wrote:
Hi all -

I am after a solution for testing equality of two means from trivariate
normal distributions. Hotelling T2 requires that the covariance
matrices of both would be approqimately equal. Is there an accepted
solution for cases where the covariance matrices are not equal?

There is a randomized solution, which I have previously
posted for the univariate case; it works in the
multivariate as well. If the sample sizes are equal,
just make a random comparison between the samples, and
use the one-sample test.

In the unequal sample size, take the usual difference
of the means. To get an estimate of the variance of
the difference, it is sigma_1/n_1 + sigma_2/n_2. Now
if n_1 < n_2, take n_1 - 1 other rows of an orthogonal
matrix in which one row is constant, form their values
and divide by the square roots of the appropriate n's,
take their difference and form the covariance matrix of
these with means assumed 0. This will be the appropriate
estimate of the covariance matrix of the difference of
the means with n_1 - 1 degrees of freedom.

This procedure is certainly not optimal, but I doubt that
it is at all bad if one cannot assume that the covariance
matrices are equal.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

Relevant Pages