Nonparametric multiple comparisons

Nonparametric multiple comparisons are a powerful statistical inference tool in psychological studies. In this paper, we review a rank-based nonparametric multiple contrast test procedure (MCTP) and propose an improvement by allowing the procedure to accommodate various effect sizes. In the review, we describe relative effects and show how utilizing the unweighted reference distribution in defining the relative effects in multiple samples may avoid the nontransitive paradoxes. Next, to improve the procedure, we allow the relative effects to be transformed by using the multivariate delta method and suggest a log odds-type transformation, which leads to effect sizes similar to Cohen's d for easier interpretation. Then, we provide theoretical justifications for an asymptotic strong control of the family-wise error rate (FWER) of the proposed method. Finally, we illustrate its use with a simulation study and an example from a neuropsychological study. The proposed method is implemented in the 'nparcomp' R package via the 'mctp' function.