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.