
Reports the probability that the two multivariate means of the selected Covariances are equal.
For equal covariance matrices the test is via Hotelling's T^{2} as described in Morrison (1990, page 141). The test statistic is F = (N_{1}+N_{2}p1)/((N_{1}+N_{2}2)p)· T^{2}, with p and N_{1}+N_{2}p1 degrees of freedom.
If the covariance matrices are not equal, we apply a correction on the number of degrees of freedom as proposed by Krishnamoorthy & Yu (2004). The test statistic in this case is F = (νp+1)/(pν)· T^{2}, with p and ν degrees of freedom. Here ν is a corrected number of degrees of freedom.
(The test for unequal covariances simplifies to Welch's approximate solution for the univariate ttest with unequal variances.)
© djmw, June 27, 2009