Rank-Based Procedures in Factorial Designs: Hypotheses About Non-Parametric Treatment Effects

Abstract

Summary Existing tests for factorial designs in the non-parametric 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. Here this idea is extended to non-parametric models by introducing a novel non-parametric analysis-of-variance type of statistic based on ranks or pseudoranks which is suitable for testing hypotheses formulated in meaningful non-parametric treatment effects in general factorial designs. This is achieved by a careful detailed study of the common distribution of rank-based estimators for the treatment effects. Since the statistic is asymptotically not a pivotal quantity we propose three 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 rank- and pseudorank-based procedures proposed maintain the preassigned type I error rate quite accurately, also in unbalanced and heteroscedastic models.

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