Type I Error Rate and Power of Rank Transform ANOVA When Populations are Non-Normal and Have Equal Variance

Abstract

The rank transformation approach to analysis of variance as a solution to the Behrens-Fisher problem is examined. Using simulation methodology four parameters were manipulated for the two group design: (1) ratio of.population variances; (2) distribution form; (3) sample size and (4) population mean difference. The results indicated that while the rank transform approach was less sensitive to variance inequality than the parametric ANOVA F-ratio, unacceptably high Type I error rates were obtained when cell frequencies and group variances were inversely related. With equal cell frequencies and/or when cell frequencies were directly related to group variances, appropriate Type I error rates were obtained. Under these conditions however, the Brown-Forsythe procedure for comparing, group· means provided greater power except when the sampled distribution was leptokurtic.