Two-Way ANOVA with unequal cell frequencies and unequal variances

In this article we consider the Two-Way ANOVA model with unequal cell frequencies without the assumption of equal error variances. By taking the generalized approach to finding p-values, classical F-tests for no interaction effects and equal main effects are extended under heteroscedasticity. The generalized F-tests developed in this article can be utilized in significance testing or in fixed level testing under the Neyman-Pearson theory. An example is given to illustrate the proposed test and to demonstrate its advantage over the classical F-test. A simulation study is carried out to demonstrate that, despite its increased power under heteroscedasticity, the size of the test does not exceed the intended level.