Rerandomizing the median in matched-pairs designs

Abstract

When a rerandomization or permutation test is applied to a matched-pairs design, the observed mean difference is typically compared with the null distribution of means that would have occurred under all possible randomizations. It is shown that rerandomizing the median instead of the mean transforms a formidable computational problem into one amenable to a hand calculator. Moreover, the robustness derived from rerandomizing the median rather than the mean is illustrated with an example where outliers were anticipated. Computational methods for constructing confidence intervals are also presented, and extensions to trimmed means are discussed.