Nonparametric alternatives to the F statistic in analysis of variance

Populations are frequently nonnormally distributed in applied behavioral and social science research, affecting the properties of the F test in Analysis of Variance designs. The purpose of this study is to compare some of the most promising nonparametric alternatives to the F test for interaction: McSweeney (Marascuilo and McSweeney, 1977), Harwell and Serlin (1989; Harwell, 1991), and Blair and Sawilowsky (1990). The properties of the competing statistics were examined on data sampled from four theoretical distributions and two real data sets in the context of the balanced 2 x 2 x 2 design. Cell sample sizes of n = 7, 21, and 35 were obtained, and statistics were calculated at the nominal alpha = 0.05 and 0.01 levels. The number of repetitions was set at 20,000 per experiment. Results indicated that Harwell and Serlin's L test was conservatively and liberally nonrobust, and not a powerful competitor. Although robust, McSweeney's test was conservative when the effect size was large, and as the number of nonnull effects increased, the test's power decreased. If the distribution is heavy-tailed or skewed, the Blair and Sawilowsky test statistic demonstrated superior power properties when compared with ANOVA. The F test retained a slight power advantage over the Blair and Sawilowsky statistic when testing for interactions on data sampled from populations that are symmetric with light tails, such as the normal or uniform.