An examination of the robustness of the modified Brown-Forsythe and the Welch-James tests in the multivariate Split-Plot designs

Abstract

The aim of this paper is to evaluate the robustness of the Welch-James multivariate solution given by Johansen (1980), and the improved multivariate Brown-Forsythe (1974) procedure when covariance matrices are heterogeneous. The results indicate that when design is unbalanced and the data are multivariate normally distributed, both approaches show a good control of error rates for the within-subjects main effect. When normality and homogeneity assumptions are jointly violated, none of the pr ocedures was able to control the error rates in all of the investigated conditions. With regard to the test of the interaction effect, our results indicate that the modified Brown-Forsythe procedure can ef fectively control the rate of Type I errors when dispersion matrices are heterogeneous, and also when the data are sampled from a skewed distribution. This finding held even when the degree of heterogeneity of the covariance matrices was varied across the design. The Welch-James test is not a adequate solution, since the sample sizes required to achieve robustness could be unreasonably large, particularly when the multivariate normality assumption is violated.