This paper proposes a simple nonparametric statistic using sample quartiles to test differences in distribution, and 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.
The proposed procedure is called the 'D test', where the components of D are sensitive to various disparities in two empirical samples. Simulated comparisons of the power of the D test were made with those of the Kolmogorov-Smirnov test, the rank-sum test, the Siegel-Tukey test, and the runs test. The simulation results suggest that the D test is appropriate when it is suspected that two distributions differ in both location and dispersion and that the latter difference exceeds but does not overwhelm the former. The major implication of the discussion is that simple rank tests based on pooled data aggregated to quartiles are surprisingly effective. The D Test is not the only procedure of this kind. The appendix presents the decision rules in the simulations, and tabular data as well as mathematical equations are provided.
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