ABSTRACT
It is well known that Student’s t test as well as the ANOVA F test are reasonably validity-robust with respect to moderate departures from normality; see e.g. Mudholkar, Mudholkar and Srivastava (1991), Marchetti, Mudholkar and Mudholkar (1998). However, in the absence of normality substantial power loss is associated with the above procedures. The same holds for Hotelling’s T2 and various normal theory MANOVA procedures in multivariate analysis; see Seber (1984), Mudholkar and Srivastava (1999a,b) and the references therein. Recently, Mudholkar and Srivastava (1999c) have proposed a class of robust stepwise tests as alternatives to Hotelling’s problem by incorporating the modification of J. Roy’s (1958) step down argument presented in Mudholkar and Subbaiah (1980). In this paper, we extend their reasoning to construct a class of robust tests for the multivariate analysis of variance for the one way classification and examine their robustness properties. The new procedures use relatively familiar univariate tests and avoid any new distributional problems. The robust stepwise tests have a reasonable type I error control and substantially enhanced power at nonnormal alternatives without significant loss of power in the presence of normality.
