Rank and Normal Scores Alternatives to Hotelling's T²

Monte Carlo methods were used to compare the Type I error rates and powers of two-sample multivariate rank and normal scores procedures to those of Hotelling's T(2). The 20 conditions investigated include heteroscedastic cases and nonnormal conditions in which the marginal densities were slightly leptokurtic and had a moderate negative skew. Results showed that under normal homoscedastic conditions, the parametric test was, as expected, the most powerful procedure. The parametric and rank tests were more powerful than the normal scores procedure in the normal heteroscedastic case. In the nonnormal homoscedastic conditions, the parametric and normal scores tests performed better than the rank procedure. In the nonnormal heteroscedastic case, the rank test was superior to its competitors.