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 Ftests 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.