Document Type


Publication Date

Summer 2023


While the F-test is the recommended method for detecting interaction in two-way ANOVA when the data are normally distributed, nonparametric procedures are shown to be more powerful in the cases of non-normal distributions. We computed extensive null critical values for the aligned rank-based tests (APCSSA and APCSSM) in additional settings where the numbers of levels of the factors are between 2 and 6. The performance of these new procedures, the ANOVA F-test for interaction, the adjusted rank transform test (ART), Conover’s rank transform procedure, and the raov function in the Rfit package were compared using Monte Carlo simulations. There is no single dominant test in detecting interaction effects for non-normal data, but nonparametric procedures APCSSM and ART are more powerful than the F-test for Cauchy data. Our hope is that these recently developed nonparametric methods will be more widely considered.



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