Parametric bootstrap procedures for three-factor ANOVA and multiple comparison procedures with unequal group variances

Abstract

The issue of unmet equal variance assumption in multi-factor ANOVA has been addressed in the literature with several methods, and parametric bootstrap (PB) has been found in the one-way and two-way cases to outperform other methods. We extend previously developed PB procedures for one- and two-way ANOVA, and illustrate with a three-way ANOVA model with unequal group variances (heteANOVA model). We develop a framework for working with these models, analogous to usual multi-factor ANOVA procedures, where F-tests and Tukey’s simultaneous multiple comparison procedures are replaced by PB procedures. Using simulation, we compare these methods to F-tests for each step in model selection, as well as to Tukey’s test for multiple comparison procedures (MCP). The results of our simulations indicate that the PB methods outperform F-tests and Tukey’s test in terms of Type I error when data are unbalanced.