A comparison of different synchronized permutation approaches to testing effects in two-level two-factor unbalanced ANOVA designs

Analysis of variance (ANOVA) is used to compare the means of various samples. Parametric ANOVA approaches assume normally distributed error terms within subsamples. Permutation tests like synchronized permutation tests are computationally intensive and distribution free procedures. Hence they overcome the limitationsofparametricmethods.Unbalanceddesignswithdifferingsubsamplesizes are quite frequent in various disciplines. There is a broad literature about unbalanced designs and parametric testing. For permutation tests this topic received some attentionrecently.Thispaperextendsthesynchronizedpermutationmethodtounbalanced two-level ANOVA designs. A simulation study investigates the behavior of different procedures for various types of unbalanced designs. It compares the results to other permutation approaches. The synchronized permutation method yields comparable results to the best performing competing permutation approaches. However the approach is limited to certain kinds of unbalanced designs.