A Quartile Test for Differences in Distribution

Abstract

We propose a simple nonparametric statistic using sample quartiles to test differences in distribution. Simulation results suggest that the test is about equal in power over a wide range of alternatives to the familiar procedure of Kolmogorov and Smirnov. When the two distributions compared differ in both location and dispersion, the quartile test may be more sensitive than the Kolmogorov-Smirnov, Wilcoxon rank-sum, Siegel-Tukey, and runs tests.