Frank Konietschke

Existing tests for factorial designs in the nonparametric case are based on hypotheses formulated in terms of distribution functions. Typical null hypotheses, however, are formulated in terms of some parameters or effect measures, particularly in heteroscedastic settings. In this talk, we extend this idea to nonparametric models by introducing a novel nonparametric ANOVA-type-statistic based on ranks which is suitable for testing hypotheses formulated in meaningful nonparametric treatment effects in general factorial designs. This is achieved by a careful in-depth study of the common distribution of rank-based estimators for the treatment effects. Since the statistic is asymptotically not a pivotal quantity, we propose different approximation techniques, discuss their theoretic properties, and compare them in extensive simulations together with two additional Wald-type tests. An extension of the presented idea to general repeated measures designs is briefly outlined. The proposed rank-based procedures maintain the pre-assigned Type-I error rate quite accurately, also in unbalanced and heteroscedastic models. A real data example illustrates the application of the proposed methods.