Reports the probability that the two multivariate means of the selected Covariances are equal.

Settings

Covariances are equal

determines whether the test is performed as if the two covariance matrices are equal or not.

Algorithm

For equal covariance matrices the test is via Hotelling's T² as described in Morrison (1990, page 141). The test statistic is F = (N₁+N₂-p-1)/((N₁+N₂-2)p)· T², with p and N₁+N₂-p-1 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 = (ν-p+1)/(pν)· T², 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 t-test with unequal variances.)