A parametric bootstrap approach for two-way ANOVA in presence of possible interactions with unequal variances

Abstract

In this article we consider the Two-Way ANOVA model with unequal cell frequencies without the assumption of equal error variances. For the problem of testing no interaction effects and equal main effects, we propose a parametric bootstrap (PB) approach and compare it with existing the generalized $F$ (GF) test. The Type I error rates and powers of the tests are evaluated using Monte Carlo simulation. Our studies show that the PB test performs better than the generalized F-test. The PB test performs very satisfactorily even for small samples while the GF test exhibits poor Type I error properties when the number of factorial combinations or treatments goes up.