CONSEQUENCES OF ASSUMPTION VIOLATIONS REVISITED - A QUANTITATIVE REVIEW OF ALTERNATIVES TO THE ONE-WAY ANALYSIS OF VARIANCE-F TEST

The presence of variance heterogeneity and nonnormality in educational and psychological data may frequently invalidate the use of the analy sis of variance (ANOVA) F test in one-way independent groups designs. This article offers recommendations to applied researchers on the use of various parametric and nonparametric alternatives to the F test und er assumption violation conditions. Meta-analytic techniques were used to summarize the statistical robustness literature on the Type I erro r properties of the Brown-Forsythe (Brown & Forsythe, 1974), James (19 51) second-order, Kruskal-Wallis (Kruskal & Wallis, 1952), and Welch ( 1951) tests. Two variables, based on the theoretical work of Box (1954 ), are shown to be highly effective in deciding when a particular alte rnative procedure should be adopted. Based on the meta-analysis findin gs, it is recommended that researchers gain a clear understanding of t he nature of their data before conducting statistical analyses. Of all of the procedures, the James and Welch tests performed best under vio lations of the variance homogeneity assumption, although their sensiti vity to certain types of nonnormality may preclude their use in all da ta-analytic situations. Opportunities for further methodological studi es of ANOVA alternative procedures are also discussed.