title: Rank-based permutation approaches for non-parametric factorial designs.
abstract: Inference methods for null hypotheses formulated in terms of distribution functions in general non-parametric factorial designs are studied. The methods can be applied to continuous, ordinal or even ordered categorical data in a unified way, and are based only on ranks. In this set-up Wald-type statistics and ANOVA-type statistics are the current state of the art. The first method is asymptotically exact but a rather liberal statistical testing procedure for small to moderate sample size, while the latter is only an approximation which does not possess the correct asymptotic α level under the null. To bridge these gaps, a novel permutation approach is proposed which can be seen as a flexible generalization of the Kruskal-Wallis test to all kinds of factorial designs with independent observations. It is proven that the permutation principle is asymptotically correct while keeping its finite exactness property when data are exchangeable. The results of extensive simulation studies foster these theoretical findings. A real data set exemplifies its applicability.
authors.affiliation: Institute of Statistics, Ulm University, Germany.
authors.forename: Maria
authors.initials: M
authors.lastname: Umlauft
authors.affiliation: Department of Mathematical Sciences, The University of Texas at Dallas, Texas, USA.
authors.forename: Frank
authors.initials: F
authors.lastname: Konietschke
authors.affiliation: Institute of Statistics, Ulm University, Germany.
authors.forename: Markus
authors.initials: M
authors.lastname: Pauly
mesh_terms: D056808:Biostatistics; D002648:Child; D002649:Child Abuse / Q000523:psychology / Q000706:statistics & numerical data; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D016014:Linear Models; D015233:Models, Statistical; D009034:Mother-Child Relations / Q000523:psychology; D018401:Sample Size; D018709:Statistics, Nonparametric
keywords: Kruskal-Wallis test; Wald-type statistic; factorial designs; heteroscedasticity; non-parametrics; permutation methods; unbalanced designs