如何正确运用χ^(2)检验--高维表资料独立性检验与SAS实现

How to use χ^(2) test correctly--the independence test for the data of a multiway table

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CMHχ^(2)检验(简称为“方法1”)、公式中含有权重系数的加权χ^(2)检验(简称为“方法2”)和公式中没有权重系数的加权χ^(2)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χ^(2)检验,但具有不同的表现形式;还揭示出加权χ^(2)检验统计量的估计值与“方法1”中的CMHχ^(2)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。

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 CMHχ^(2) test(for short,approach-1),the weightedχ^(2) test with the weighted coefficients in its formula(for short,approach-2),and the weightedχ^(2) 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 weightedχ^(2) test essentially,but with different manifestations.It also revealed that the weightedχ^(2) test statistic estimation was approximately equal to the CMHχ^(2) 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.