Hotelling's T-squared Distribution
Hotelling's T-squared distribution is a multivariate generalization of the t distribution.
Description
The T-squared distribution is used for the generalization of t tests for multiple jointly normally distributed variables. It is in fact a scaled version of the F distribution.
Consider the univariate case: there are
two samples of size n1 and n2
a pooled variance as s2.
These sample means are characterized by the t distribution with n1 + n2 - 2 degrees of freedom.
The T-squared distribution generalizes this to p variables. The distribution is notated as T2(p, n1+n2-2).
Usage
Probability Tests
Much like how the t distribution is used for t tests, this distribution is used for multivariate t tests.