A Non-Parametric Test for Comparing Two Non-Independent Distributions

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1978 · Volume 40 · Issue 2

DOI: 10.1111/j.2517-6161.1978.tb01671.x

Abstract

Using a sample from an unknown bivariate distribution, we propose a test for the hypothesis that one marginal distribution is stochastically larger than the other. We show that the test statistic has an asymptotic normal distribution, and that the proposed test is asymptotically non-parametric. This test is compared to the pairedt-test for large samples in terms of asymptotic relative efficiency and for samples of size 20 by simulation estimates of size and power. There are important cases in which the power of the proposed test exceeds that of the pairedt-test; whereas even under normality its power is near that of the pairedt-test.

Keywords

stochastic ordering, u-statistic, asymptotic normality, asymptotic non-parametric test, pairedt-test

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