Universität zu Köln

Results from several simulation studies in the last two decades showed that ranking procedures for the comparison of means may lead to an inflation of the type I error rate when the underlying distribution is lognormal and the variances are heterogeneous, even in the case of equal sample sizes. In this study the error rates of the parametric F-test as well as those of seven nonparametric tests are compared in a two-way between subjects anova design. The methods under consideration are: rank transform (RT), inverse normal transform (INT), aligned rank transform (ART), a combination of ART and INT, Puri & Sen‘s L statistic, van der Waerden and Akritas & Brunners ATS. The type I error rates for the tests of the null model are computed for several lognormal distributions with varying degrees if skewness, varying sample sizes from 5 to 50, several degrees of variance heterogeneity as well as for balanced and unbalanced designs. It is shown that the error rates of main and interaction effects for all nonparametric methods increase above any acceptable limit for moderate cell counts of 20 and more, while the parametric F-test keeps the error completely under control at least in the case of equal sample sizes. These results show that nonparametric methods are not always acceptable substitutes for parametric methods such as the F test in research studies when parametric assumptions are not satisfied

English