In this article, we are concerned about testing the homogeneity on paired samples with or without confounding variables. These problems usually arise in clinical trials, psychological or sociological studies. We introduce new nonparametric tests for equality of two distributions or two conditional distributions of random vectors on paired samples. We show that their test statistics are consistent but have different asymptotic distributions under the null hypothesis, depending on whether confounding variables exist. The limit distribution of the test statistic is a mixed $\chi^2$ distribution when testing the equality of two paired distributions, while it is a normal distribution when testing the equality of two conditional distributions of paired samples. We conduct several simulation studies to evaluate the finite-sample performance of our tests. Finally, we apply our tests on real data to illustrate their usefulness in the applications.

中文翻译：

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带/不带混杂变量的同质性配对样本检验

在本文中，我们关注的是在有或没有混杂变量的情况下测试配对样本的同质性。这些问题通常出现在临床试验、心理学或社会学研究中。我们引入了新的非参数检验，以检验配对样本上随机向量的两个分布或两个条件分布的相等性。我们表明，它们的检验统计量是一致的，但在原假设下具有不同的渐近分布，这取决于是否存在混杂变量。检验统计量的极限分布在检验两个配对分布是否相等时为混合$\chi^2$分布，而在检验配对样本的两个条件分布相等时为正态分布。我们进行了几项模拟研究来评估我们测试的有限样本性能。