Stratified two‐sample design: A review on nonparametric methods

Abstract

AbstractIn this article, a comparison between the most promising nonparametric tests in a two‐sample stratified design for practical uses is performed. We compared methods that exhibit good small‐sample properties in order to be used with the most common stratum sizes. From the literature we identified as promising the following solutions: the aligned rank test, a small‐sample approximation for the ANOVA‐type statistic based on an unweighted average of all the distributions, and an asymptotic permutation distribution for the Wald‐type statistic. We also developed a permutation version of the aligned rank test and another permutation testing procedure based on the Mann‐Whitney statistic using the nonparametric combination procedure. All selected methods were compared by means of a simulation study. The results show that the aligned rank test and its permutation version perform better in most of the considered situations. Data from a genuine industrial problem were used for illustration purposes and to confirm the simulation results.