Permutation tests for multi-factorial analysis of variance

Several permutation strategies are often possible for tests of individual terms in analysis-of-variance (ANOVA) designs. These include restricted permutations, permutation of whole groups of units, permutation of some form of residuals or some combination of these. It is unclear, especially for complex designs involving random factors, mixed models or nested hierarchies, just which permutation strategy should be used for any particular test. The purpose of this paper is two-fold: (i) we provide a guideline for constructing an exact permutation strategy, where possible, for any individual term in any ANOVA design; and (ii) we provide results of Monte Carlo simulations to compare the level accuracy and power of…