Stratified two-sample design: A review on nonparametric methods

In 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.