Increasing the Power of Nonparametric Tests by Detecting and Downweighting Outliers

TLDR: In this paper, the power of the Student t test and the Wilcoxon-Mann-Whitney test declines substantially when samples are obtained from outlier-prone densities, including mixed-normal, Cauchy, lognormal, and mixed-uniform densities.

Abstract: In this study, methods are examined that can be described, somewhat paradoxically, as robust nonparametric statistics. Although nonparametric tests effectively control the probability of Type I errors through rank randomization, they do not always control the probability of Type II errors and power, which can be grossly inflated or deflated by the shape of distributions. The power of the Student t test and the Wilcoxon-Mann-Whitney test declines substantially when samples are obtained from outlier-prone densities, including mixed-normal, Cauchy, lognormal, and mixed-uniform densities. However, the nonparametric test acquires an advantage, because outliers influence the t test to a relatively greater extent. Under these conditions, an outlier detection and downweighting (ODD) procedure, usually associated with parametric significance tests, augments the power of both the t test and the Wilcoxon-Mann-Whitney test.