Rank Tests for Main and Interaction Effects in Analysis of Variance

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Abstract
A class of rank tests for analysis of variance based on linear functions of the Wilcoxon/Mann-Whitney statistics between cells is studied. This class includes many popular procedures. Assuming a location-family model, a condition for optimal Pitman efficacy of tests of main effects in this class is given. Tests for main effects in two-way layouts that achieve this optimality are shown to improve on previous proposals when the sample sizes are unbalanced. Nested orthogonal contrasts are introduced that can be used to decompose the overall test statistics into independent components to assess the contribution of individual contrasts. A new definition of interaction appropriate for rank-based analysis of variance is suggested, and test procedures are proposed.

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