Lin Jyh-Jiuan, Chang Ching-Hui, Pal Nabendu
a Department of Statistics , Tamkang University , Tamsui , Taipei , Taiwan.
J Biopharm Stat. 2015;25(3):438-58. doi: 10.1080/10543406.2014.920851.
To test the mutual independence of two qualitative variables (or attributes), it is a common practice to follow the Chi-square tests (Pearson's as well as likelihood ratio test) based on data in the form of a contingency table. However, it should be noted that these popular Chi-square tests are asymptotic in nature and are useful when the cell frequencies are "not too small." In this article, we explore the accuracy of the Chi-square tests through an extensive simulation study and then propose their bootstrap versions that appear to work better than the asymptotic Chi-square tests. The bootstrap tests are useful even for small-cell frequencies as they maintain the nominal level quite accurately. Also, the proposed bootstrap tests are more convenient than the Fisher's exact test which is often criticized for being too conservative. Finally, all test methods are applied to a few real-life datasets for demonstration purposes.
为了检验两个定性变量（或属性）的相互独立性，通常的做法是基于列联表形式的数据进行卡方检验（皮尔逊卡方检验以及似然比检验）。然而，需要注意的是，这些常用的卡方检验本质上是渐近的，当单元格频数“不太小”时才有用。在本文中，我们通过广泛的模拟研究探索了卡方检验的准确性，然后提出了它们的自助法版本，这些自助法版本似乎比渐近卡方检验效果更好。自助法检验即使对于小单元格频数也很有用，因为它们能相当准确地保持名义水平。此外，所提出的自助法检验比费舍尔精确检验更方便，费舍尔精确检验常因过于保守而受到批评。最后，为了演示目的，将所有检验方法应用于一些实际数据集。
