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.

中文翻译：

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分层的两样本设计：非参数方法的回顾

在本文中，对实际使用的两样本分层设计中最有希望的非参数测试进行了比较。我们比较了具有良好小样本性质的方法，以便与最常见的层大小一起使用。从文献中，我们确定了以下有希望的解决方案：对齐秩检验，基于所有分布的未加权平均值的ANOVA型统计量的小样本近似值以及Wald型统计量的渐近置换分布。我们还使用非参数组合过程开发了基于Mann-Whitney统计量的排列秩次检验的排列版本和另一个排列检验程序。通过模拟研究比较了所有选择的方法。结果表明，在大多数考虑的情况下，对齐秩检验及其排列版本均表现更好。来自真实工业问题的数据用于说明目的并确认模拟结果。