Multivariate tests of means in independent groups designs. Effects of covariance heterogeneity and nonnormality

Health evaluation research often employs multivariate designs in which data on several outcome variables are obtained for independent groups of subjects. This article examines statistical procedures for testing hypotheses of multivariate mean equality in two-group designs. The conventional test for multivariate means, Hotelling's T2, rests on certain assumptions about the distribution of the data and the population variances and covariances. When these assumptions are violated, which is often the case in applied health research, T2 will result in invalid conclusions about the null hypothesis. This article describes parametric procedures that are robust, or insensitive, to assumption violations. A numeric example illustrates the statistical concepts that are presented and a computer program to implement these robust solutions is introduced.