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

How to use χ² test correctly——the independence test for the data of a multiway table

DOI：10.11886/scjsws20210719002

English keywords:Independence test Weight Weighted χ² test CMH χ² test

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Author Name	Affiliation	Postcode
Hu Chunyan	Graduate School， Academy of Military Sciences PLA China， Beijing 100850， China	100850
Hu Liangping	Graduate School， Academy of Military Sciences PLA China， Beijing 100850， China Specialty Committee of Clinical Scientific Research Statistics of World Federation of Chinese Medicine Societies， Beijing 100029， China	100029

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English abstract:

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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