This study examined three simple transformations which increase the power of F tests of main effects and interaction in 2 × 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. 1994 The British Psychological Society

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Journal British Journal of Mathematical and Statistical Psychology
Zimmerman, D.W. (Donald W.). (1994). Simplified interaction tests for non‐normal data in psychological research. British Journal of Mathematical and Statistical Psychology, 47(2), 327–335. doi:10.1111/j.2044-8317.1994.tb01040.x