Rank and Normal Scores Alternatives to Hotelling's T(2)

Multivariate Tests of Means in Independent Groups Designs

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, T 2 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.

Power and Type I Error Rates for Rank-Score MANOVA Techniques

A Monte Carlo simulation study was performed to compare the power and the Type I errors of the Wilks's lambda statistic and the Purl and Sen (1971) statistic on transformed data in a one-way MANOVA. The behavior of the Wilks's lambda statistic and the Puri and Sen statistic are studied using normal scores and ranks of the data. Both chi-square approximations and F approximations are used to estimate the distribution of these statistics. Various combinations of sample sizes and numbers of variables are used in the simulation study. For the situations considered in both normal and nonnormal homoscedastic conditions, the Wilks's lambda statistic calculated using normal scores and used with the F approximation appeared to be somewhat more robust with respect to maintaining its stated significance level than its competitors. Also, the F approximation for the Puri and Sen statistic is also shown to be more robust with respect to maintaining its stated significance level than the standard chi-square approximation.