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

between-subjects (groups) factor A with j=1,...,p levels and nj observations at each j and a single within-subjects (occasions) factor B with k=1,...,q levels is very frequent in almost all scientific fields (Shoukri & Pause, 1999). Although the nature of these designs is typically multivariate, the effects of design (occasions main effect and groups x occasions interaction) can be tested by using univariate or multivariate approach. The validity of these procedures rests on the nature of the assumptions that the researcher is willing to make about the data. When the assumptions of multivariate normality, homogeneity of the covariance matrices, and multisample sphericity are satisfied, such designs are analyzed by Scheffé’s (1956) univariate mixed model. When the multisample sphericity assumption is not satisfied either an adjusted degrees of freedom univariate test or multivariate model perspective may be used. Under a multivariate model, no restrictions are placed on the structure of the covariance matrix. However, the number of experimental observations must be greater or equal to the of repeated measurements and, as the univariate model, the assumptions of dispersion matrix equality and normality must be satisfied. If sphericity assumption is met, the conventional univariate procedure is more powerful than the multivariate approach (Davidson, 1972). However, if sphericity appears untenable no clearcut rule emerged for choosing between the adjusted degrees of freedom univariate tests and their multivariate counterparts (Mendoza, Toothaker, & Nicewander, 1974). When covariance matrices are unequal and the design is balanced (equal g roup sizes), Keselman and Keselman (1990) have shown that both procedures are generally robust to the violation of dispersion matrix equality. In this case, the choice between univariate or multivariate technique depends, especially, on differences in their statistical power. HoAn examination of the robustness of the modified Brown-Forsythe and the Welch-James tests in the multivariate Split-Plot designs