The ANOVA F test can still be used in some balanced designs with unequal variances and nonnormal data

Consider the factorial ANOVA model with m fixed factors, interactions, and error terms that are not necessarily normally distributed. We examine the asymptotic sensitivity against unequal variances of the ANOVA F test statistics for testing main factor effects and interactions, under the assumption that the number of levels of one factor A(1) tends to infinity while the number of levels is fixed for the other factors A(2),... A(m), and the number of replications per factor level remains also finite. Heteroscedasticity is allowed across the levels of factors A(2),...,A(m). We show that the ANOVA F test on factor A(1), designed for a homoscedastic model, can still be used in the presence of this form of heterosceclasticity. That is, as long as the variance of the error term does not depend on the level of factor A(1), the F test for the main effect of factor A(1) is asymptotically almost unaffected by different variances in different levels of the other factors. The theoretical results derived in this paper are supported by simulation studies. (C) 2003 Elsevier B.V. All rights reserved.