A class of rank-score tests in factorial designs

Abstract The analysis of factorial designs in a nonparametric setup has been restricted mainly to the one-way layout. Procedures for higher-way layouts are either restricted to semiparametric models or to special designs. Moreover, the continuity of the underlying distribution functions is assumed in general. The aim of this paper is to provide a general theory for the analysis of nonparametric factorial designs with fixed factors. Rank procedures for nonparametric hypotheses based on the distribution functions are proposed and the results are derived for score functions with bounded second derivatives. Unlike in most of the literature, we do not assume the continuity of the underlying distribution functions or the equality of the sample sizes. This means that data from continuous distributions as well as discrete ordinal data are covered by our approach. The results obtained are applied to some special factorial designs. For small sample sizes, the Box-approximation is applied to compute approximate p -values for the statistics. Within this framework, also the question of the rank transform property of rank statistics is briefly addressed. The application of the proposed tests is demonstrated by the analysis of real data for a two-way layout.

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