| Historically, there has been a lack of nonparametric tests available for use in detecting interactions in Analysis of Variance. Over the past 25 years, new nonparametric tests for interactions have been developed. The purpose of this study was to determine the comparative robustness with respect to departures from normality (i.e., Type I error) and power properties of four tests of interaction in the 2 x 2 x 2 ANOVA layout. The four tests were: (a) Analysis of Variance, a parametric test; (b) Bradley's Collapsed and Reduced Technique, a distribution-free test; (c) Harwell and Serlin's L test, which is based on the Puri and Sen (1985) test; and (d) Blair and Sawilowsky's Adjusted Rank Transform test, which is similar to Fawcett and Salter's (1984) aligned rank test, and is a conditionally distribution-free test. The study used Monte Carlo techniques to compare the four tests under four theoretical distributions and two real (psychological and educational) data sets from Micceri (1989). Sample sizes of 7, 21, and 35 and effect sizes of.2-1.2(.2) were used.;The results indicated that the Analysis of Variance F test shows superior power properties and is robust with data from symmetric and light tailed distributions, when compared to Bradley's Collapsed and Reduced Technique or Harwell and Serlin's L test. Blair and Sawilowsky's Adjusted Rank Transform test, however, was only slightly less powerful than ANOVA under these conditions.;If the distribution is heavy-tailed or skewed, the results indicated that the Blair-Sawilowsky statistic is robust and shows superior power properties when compared to ANOVA, Bradley's Collapsed and Reduced Technique, and Harwell and Serlin's L Test. In addition, when using a real psychometric data set, discrete mass at zero, Blair-Sawilowsky was much more powerful than ANOVA. When using a real achievement data set, multi-modal lumpy, Blair-Sawilowsky was slightly more powerful when the effect size was small and slightly less powerful than ANOVA when the effect size was large.;Harwell and Serlin's L test was conservatively and liberally nonrobust when the effect size was large. When the number of non-null effects increased from one to seven, Harwell-Serlin's power decreased. Bradley's Collapsed and Reduced Technique was usually the least powerful test in this study. It was consistently robust. However, it demonstrated meager power properties. For these reasons, neither the Harwell-Serlin or Bradley test is recommended. |
