A Non-Parametric Test for Comparing Two Non-Independent Distributions
- 1 January 1978
- journal article
- research article
- Published by Oxford University Press (OUP) in Journal of the Royal Statistical Society Series B: Statistical Methodology
- Vol. 40 (2) , 253-261
- https://doi.org/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 paired t‐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 paired t‐test; whereas even under normality its power is near that of the paired t‐test.This publication has 5 references indexed in Scilit:
- Robustness of the Wilcoxon Test to a Certain Dependency Between SamplesThe Annals of Statistics, 1974
- Some Probability Paradoxes in Choice from among Random AlternativesJournal of the American Statistical Association, 1972
- A Note on the Generation of Random Normal DeviatesThe Annals of Mathematical Statistics, 1958
- The Efficiency of Some Nonparametric Competitors of the $t$-TestThe Annals of Mathematical Statistics, 1956
- A Class of Statistics with Asymptotically Normal DistributionThe Annals of Mathematical Statistics, 1948