Comparing the medians of dependent groups

Abstract

Investigations of the characteristics of real data indicate that psychometric measures can have highly skewed distributions with heavy tails and outliers. In terms of power, the paired t test is known to be unsatisfactory when distributions have heavy tails, and there is the issue of whether some measure of location, other than the mean, might be more appropriate when distributions are skewed. This paper proposes a method for comparing the medians of two dependent groups. Simulations indicate that the proposed procedure controls the probability of a Type I error to a reasonable degree. In terms of power, the new procedure is much less affected by contamination than the paired t test or the Wilcoxon signed rank test. Brief consideration is also given to an extension of the proposed procedure to more than two groups.