Chi-squared and Fisher-Irwin tests of two-by-two tables with small sample recommendations
Chi-squared and Fisher-Irwin tests of two-by-two tables with small sample recommendations
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DOI：
10.1002/sim.2832
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发表时间：
2007-08-30
影响因子：
2
通讯作者：
Campbell, Ian
中科院分区：
文献类型：
--
作者：
Campbell, Ian
二乘二表格通常出现在比较试验和横断面研究中。在医学研究中，由于疾病的罕见性或资源有限，二乘二表可能具有较小的样本量。目前关于适当统计检验的建议大多指定最小预期数至少为5的表的卡方检验（遵循Fisher和Cochran），否则使用Fisher-Irwin检验;但对于卡方和Fisher-Irwin检验的哪个版本存在分歧应该使用。另一个不确定性是，根据科克伦，数字5是任意选择的。在这项研究中使用计算机密集型技术，比较七个双边测试的两个由两个表的第一类错误。测试结果为K。Pearson和Yates的卡方检验和'N-F卡方检验（首先由E. Pearson），以及四个版本的Fisher-Irwin检验（包括两个中间P版本）。当最小预期数至少为1时，通过“N - 1”卡方检验分析发现最佳测试策略，否则，通过欧文规则的Fisher-欧文检验（取任一尾部中表的总概率与观察到的表的概率相同或更小）。与科克伦的建议相比，这一政策被发现具有更大的权力。版权所有（c）2007约翰威利父子有限公司。
Two-by-two tables commonly arise in comparative trials and cross-sectional studies. In medical studies, two-by-two tables may have a small sample size due to the rarity of a condition, or to limited resources. Current recommendations on the appropriate statistical test mostly specify the chi-squared test for tables where the minimum expected number is at least 5 (following Fisher and Cochran), and otherwise the Fisher-Irwin test; but there is disagreement on which versions of the chi-squared and Fisher-Irwin tests should be used. A further uncertainty is that, according to Cochran, the number 5 was chosen arbitrarily. Computer-intensive techniques were used in this study to compare seven two-sided tests of two-by-two tables in terms of their Type I errors. The tests were K. Pearson's and Yates's chi-squared tests and the 'N - F chi-squared test (first proposed by E. Pearson), together with four versions of the Fisher-Irwin test (including two mid-P versions). The optimum test policy was found to be analysis by the 'N - 1' chi-squared test when the minimum expected number is at least 1, and otherwise, by the Fisher-Irwin test by Irwin's rule (taking the total probability of tables in either tail that are as likely as, or less likely than the one observed). This policy was found to have increased power compared to Cochran's recommendations. Copyright (c) 2007 John Wiley & Sons, Ltd.