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

The aim of this paper is to evaluate the robustness of the Welch-James mult ivariate solution given by Johansen (1980), and the improved multivariate B rown-Forsythe (1974) procedure when covariance matrices are heterogeneous. The results indicate that when design is unbalanced and the data are multiv ariate normally distributed, both approaches show a good control of error r ates for the within-subjects main effect. When normality and homogeneity as sumptions are jointly violated, none of the procedures was able to control the error rates in all of the investigated conditions. With regard to the t est of the interaction effect, our results indicate that the modified Brown -Forsythe procedure can effectively control the rare of Type I errors when dispersion matrices are heterogeneous, and also when the data are sampled f rom a skewed distribution. This finding held even when the degree of hetero geneity of the covariance matrices was varied across the design. The Welch- James test is not a adequate solution, since the sample sizes required to a chieve robustness could be unreasonably large, particularly when the multiv ariate normality assumption is violated.