Effect of Outliers on the Relative Power of Parametric and Nonparametric Statistical Tests

Abstract

It is known that parametric statistical tests, such as t and F, are more powerful than their nonparametric counterparts, such as the Wilcoxon-Mann-Whitney test or the Kruskal-Wallis test, when the assumption of a normal population distribution is satisfied. However, it has been found that, for quite a few nonnormal distributions, the Wilcoxon-Mann-Whitney test ( W) is more powerful than the Student t-test ( t) both in the asymptotic limit and for small samples. The present computer-simulation study examined the role of outliers in determining the relative power of W and t. In a series of five steps, a standard normal distribution, as well as a uniform distribution, was altered so that extreme scores occurred with increasingly higher probability. It was found that the initial power advantage of t gradually diminished in favor of W. In contrast, in a series of five steps, exponential and Cauchy distributions were truncated at less and less extreme values, so that the influence of outliers was reduced, and the initial power advantage of W gradually diminished in favor of t. For all distributions, the ordinary Student t-test performed on the ranks of measures instead of the measures was affected by addition or elimination of outliers in the same way as W and yielded the same probabilities of Type I and Type II errors as W.