A Robust Test in the Multivariate Two-Sample Location Problem

SYNOPTIC ABSTRACTA frequently employed test for the equality of two mean vectors is Hotelling's two-sample T2, which assumes multinormality of the populations. When the multinormality assumption is violated, modified versions of T2 and/or nonparametric statistics are utilized. In this paper, it is shown that if Hotelling's T2 statistic is computed as a function of the ranks (instead of the original observations), the resulting statistic is a monotone function of a nonparametric statistic. Just as T2 reduces to the square of a t-statistic in univariate distributions, the rank T2 reduces to a rank transform statistic TR proposed by Conover and Iman (1981). For several bivariate distributions, Monte Carlo results are presented, which suggest robustness of rank T2.