Numerous papers have shown that the conventional F test is not robust to unequal variances in the one-way fixed effects ANOVA model, and several methods have been proposed for dealing with this problem. Here I describe and compare two methods for handling unequal variances in the two-way fixed effects ANOVA model. One is based on an improved Wilcox (1988) method for the one-way model, which forms the basis for considering this method in the two-way ANOVA model. The other is an extension of James’s (1951) second order method.
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Rand R. Wilcox (1989) studied this question.
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