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

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.

Keywords

• independence test
• weight
• weighted χ2 test
• cmh χ2 test