| 胡纯严,胡良平.如何正确运用χ2检验——高维表资料独立性检验与SAS实现[J].四川精神卫生杂志,2021,34(4):314-317.Hu Chunyan,Hu Liangping,How to use χ2 test correctly——the independence test for the data of a multiway table[J].SICHUAN MENTAL HEALTH,2021,34(4):314-317 |
| 如何正确运用χ2检验——高维表资料独立性检验与SAS实现 |
| How to use χ2 test correctly——the independence test for the data of a multiway table |
| 投稿时间：2021-07-19 |
| DOI：10.11886/scjsws20210719002 |
| 中文关键词: 独立性检验 权重 加权χ2检验 CMH χ2检验 |
| 英文关键词:Independence test Weight Weighted χ2 test CMH χ2 test |
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| 中文摘要: |
| 本文目的是介绍一种特殊高维表（即g×2×2表）资料的独立性检验方法及SAS实现。在SAS软件和统计学教科书中，有三种方法可用于进行高维表资料的独立性检验，分别为广义CMH χ2检验（简称为“方法1”）、公式中含有权重系数的加权χ2检验（简称为“方法2”）和公式中没有权重系数的加权χ2检验（简称为“方法3”）。本文通过公式推导和变形，揭示出“方法2”与“方法3”在本质上是完全相同的加权χ2检验，但具有不同的表现形式；还揭示出加权χ2检验统计量的估计值与“方法1”中的CMH χ2检验统计量的估计值近似相等。本文结合一个实例，介绍基于SAS软件实现g×2×2表资料独立性检验的具体方法，对输出结果进行解释，并做出统计结论和专业结论。 |
| 英文摘要: |
| The purpose of this article was to introduce the methods for the independence test of a special high-dimensional table （ie g×2×2 table） and its SAS implementation. There were three approaches， in the SAS software and the statistical textbooks， which could be used to perform the independence test for the data of a multiway table. The three kinds of methods were the generalized CMH χ2 test （for short， approach-1）， the weighted χ2 test with the weighted coefficients in its formula （for short， approach-2）， and the weighted χ2 test without the weighted coefficients in its formula （for short， approach-3）， respectively. This article revealed that the “approach-2” and “approach-3” were the same weighted χ2 test essentially， but with different manifestations. It also revealed that the weighted χ2 test statistic estimation was approximately equal to the CMH χ2 test statistic estimation in the “approach-1”. Based on an example and the SAS software， the article introduced the concrete approaches for the independence test of the g×2×2 table data， explained the output results， and made the statistical and professional conclusions. |
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