A Comparison of Efficient Permutation Tests for Unbalanced Anova in Two by Two Designs and Their Behavior Under Heteroscedasticity

Abstract

We outlined various procedures that aim to compensate shortcomings of classical ANOVA. Some procedures are only valid under normality and possibly heteroscedastic variances (ATS). CSP and USP are valid under non-normally distributed error terms and homoscedastic variances. Both the WTS and WTPS are asymptotically valid even under non-normality and heteroscedasticity, respectively. Most of these procedures are intended to be used for small samples (ATS, WTPS, CSP, and USP), only the WTS requires a sufficiently large sample size. In the following simulation we vary additionally the aspect of balanced vs. unbalanced designs, as heteroscedasticity is especially problematic in the latter one