A Note on the Influence of Outliers on Parametric and Nonparametric Tests

Abstract

Extremely deviant scores, or outliers, reduce the probability of Type I errors of the Student t test and, at the same time, substantially increase the probability of Type II errors, so that power declines. The magnitude of the change depends jointly on the probability of occurrence of an outlier and its extremity, or its distance from the mean. Although outliers do not modify the probability of Type I errors of the Mann-Whitney-Wilcoxon test, they nevertheless increase the probability of Type II errors and reduce power. The effect on this nonparametric test depends largely on the probability of occurrence and not the extremity. Because deviant scores influence the t test to a relatively greater extent, the nonparametric method acquires an advantage for outlier-prone densities despite its loss of power.