An Empirical Investigation of Four Tests for Interaction in the Context of Factorial Analysis of Covariance

Abstract

The Type I error and power properties of the parametric F test and three nonparametric competitors were compared in terms of a 3 × 4 factorial analysis of covariance layout. The focus of the study was on the test for interaction either in the presence and/or absence of main effects. A variety of conditional distributions, sample sizes, levels of variate and covariate correlation, and treatment effect sizes were investigated. The Puri and Sen (1969a) test had ultra-conservative Type I error rates and power losses when main effect(s) were present. The adjusted rank transform (Blair & Sawilowsky, 1990; Salter & Fawcett; 1993) had liberal Type I error rates when sampling was from moderate to extremely skewed distributions. The Hettmansperger (1984) chi-square test displayed acceptable Type I error rates for all distributions considered when sample sizes were ten or twenty. It is suggested that the Hettmansperger (1984) test be considered as an alternative to the parametric F test provided sample sizes are relatively equal and at least as large as ten.