The Type I error and power properties of the parametric F test and three nonparametric competitors were compared in terms of a 3x 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 Ierror 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.
Headrick, Todd C. and Vineyard, George. "An Empirical Investigation of Four Tests for Interaction in the Context of Factorial Analysis of Covariance." (Jan 2001).