Fisher's exact approach for post hoc analysis of a chi-squared test
Fisher's exact approach for post hoc analysis of a chi-squared test
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DOI：
10.1371/journal.pone.0188709
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发表时间：
2017-12-20
期刊：
影响因子：
3.7
通讯作者：
Gerstenberger, Shawn
中科院分区：
文献类型：
--
作者：
Shan, Guogen;Gerstenberger, Shawn
这项研究的动机是我们的调查研究之一，以评估潜在的影响，引进斑马贻贝的米德湖国家娱乐区，内华达州。在这项研究中的一个研究问题是调查划船活动类型和斑马贻贝的意识之间的关联。卡方检验通常用于检验具有名义水平的两个因子之间的独立性。当两个因素之间的独立性的零假设被拒绝时，我们经常想知道显著性来自哪里。单元格残差，包括标准化残差和调整残差，传统上用于单元格显著性检验，这通常被称为统计学显著性卡方检验之后的事后检验。在实践中，这些残差的极限分布用于统计推断。然而，他们可能会导致不同的结论的基础上计算的p值，和他们的p值可能会被高估或低估，由于不满意的性能渐近方法方面的第一类错误控制。在这篇文章中，我们提出了新的精确的p值，通过使用Fisher的方法的基础上，三个常用的检验统计量来排序的样本空间。我们从理论上证明了基于这些检验统计量的新的精确p值是相同的。基于我们广泛的模拟研究，我们表明，现有的渐近方法的基础上调整后的残差往往是更有可能拒绝零假设相比，由于所观察到的膨胀的家庭明智的错误率的确切方法。我们建议在实践中使用拟定的精确p值作为卡方分析的有价值的事后分析技术。
This research is motivated by one of our survey studies to assess the potential influence of introducing zebra mussels to the Lake Mead National Recreation Area, Nevada. One research question in this study is to investigate the association between the boating activity type and the awareness of zebra mussels. A chi-squared test is often used for testing independence between two factors with nominal levels. When the null hypothesis of independence between two factors is rejected, we are often left wondering where does the significance come from. Cell residuals, including standardized residuals and adjusted residuals, are traditionally used in testing for cell significance, which is often known as a post hoc test after a statistically significant chi-squared test. In practice, the limiting distributions of these residuals are utilized for statistical inference. However, they may lead to different conclusions based on the calculated p-values, and their p-values could be over-o6r under-estimated due to the unsatisfactory performance of asymptotic approaches with regards to type I error control. In this article, we propose new exact p-values by using Fisher's approach based on three commonly used test statistics to order the sample space. We theoretically prove that the proposed new exact p-values based on these test statistics are the same. Based on our extensive simulation studies, we show that the existing asymptotic approach based on adjusted residual is often more likely to reject the null hypothesis as compared to the exact approach due to the inflated family-wise error rates as observed. We would recommend the proposed exact p-value for use in practice as a valuable post hoc analysis technique for chi-squared analysis.