SIMPLIFIED INTERACTION TESTS FOR NONNORMAL DATA IN PSYCHOLOGICAL-RESEARCH

This study examined three simple transformations which increase the power of F tests of main effects and interaction in 2 x 2 factorial designs under violation of normality. The study obtained Monte Carlo results from various heavy-tailed densities, including mixed-normal, exponential, Cauchy and Laplace densities, which are associated with grossly distorted probabilities of Type I and Type II errors. Transformation of scores to ranks made the F test for interaction robust and comparable in power to the Mann-Whitney-Wilcoxon test for the same distributions. Transformation to 'modular ranks', having one-fourth the number of values of conventional ranks, was equally effective. Detection and downweighting of outliers before performing the F test was more effective than rank methods for several distributions. Implications of these findings for the role of scales of measurement and nonparametric methods in psychological research are discussed.