Roswell Park Cancer Institute, Department of Biostatistics and Bioinformatics, Elm and Carlton Streets, Buffalo, NY 14623, United States.
Roswell Park Cancer Institute, Department of Biostatistics and Bioinformatics, Elm and Carlton Streets, Buffalo, NY 14623, United States.
Comput Methods Programs Biomed. 2023 Oct;240:107725. doi: 10.1016/j.cmpb.2023.107725. Epub 2023 Jul 19.
In this paper, we build upon the work of DiCiccio and Romano (2017) by extending their permutation test approach, based on the Pearson correlation coefficient in the continuous case, to ordinal measures of association. We investigate commonly used ordinal measures such as the Spearman correlation, Kendall's tau-b, and gamma, which are widely implemented in commercial and open-source software packages for exact testing routines based on generalized hypergeometric probabilities. Similar to DiCiccio and Romano's method, we apply studentization to correct the test statistic, which yields asymptotically valid inference for testing no ordinal association. We present a comprehensive theoretical framework for our approach, followed by a simulation study. Furthermore, we use toy examples to highlight the differences between the exact tests and the asymptotically valid tests. Our findings align with those of DiCiccio and Romano, indicating that exact permutation tests based on ordinal measures of association are often not exact, whereas the asymptotically correct tests perform well for moderate to large sample sizes.
在本文中，我们通过将 DiCiccio 和 Romano（2017）基于 Pearson 相关系数的连续情形的排列检验方法扩展到有序关联度量，从而扩展了他们的工作。我们研究了常用的有序关联度量，如 Spearman 相关系数、Kendall's tau-b 和 gamma，这些度量广泛应用于商业和开源软件包中，用于基于广义超几何概率的精确检验例程。与 DiCiccio 和 Romano 的方法类似，我们应用学生化来修正检验统计量，这为检验无有序关联提供了渐近有效的推断。我们提出了我们方法的综合理论框架，随后进行了模拟研究。此外，我们使用玩具示例来突出精确检验和渐近有效检验之间的差异。我们的研究结果与 DiCiccio 和 Romano 的结果一致，表明基于有序关联度量的精确排列检验通常不精确，而渐近正确的检验在中等至大样本量下表现良好。
