Robust tests for the multivariate Behrens-Fisher problem

Hotelling's T2 procedure is used to test the equality of means in two-group multivariate designs when covariances are homogeneous. A number of alternatives to T2, which are robust to covariance heterogeneity, have been proposed in the literature. However, all are sensitive to departures from multivariate normality. We demonstrate how to obtain multivariate tests that are robust to covariance heterogeneity and non-normality with estimators of location and scale based on trimming and Winsorizing. The performance of six alternatives to T2 was examined via Monte Carlo methods when characteristics of the research design, degree of covariance heterogeneity, and degree of non-normality were manipulated. We have recently developed a program written in the SAS/IML language that can be used to implement these robust multivariate tests. Recommendations are provided on the specific data-analytic conditions under which these tests should be adopted.