How to use χ2 test correctly——CMH χ2 tests for the data collected from the three kinds of R×C contingency tables

Abstract

The purpose of this paper was to introduce the CMH χ2 test and SAS software implementation of the three kinds of R×C contingency table data. The first type was called “two-way unordered R×C contingency table data”. The CMH χ2 test corresponding to this type of data was essentially the Pearson’s χ2 test. The second type was called “R×C contingency table data with an ordinal outcome variable”. The CMH χ2 test corresponding to this kind of data was essentially a rank sum test. The third type was called “R×C contingency table data which was of two ordinal variables with different attributes”. The CMH χ2 test corresponding to the data was essentially Pearson’s correlation analysis or Spearman’s rank correlation analysis. When there were 1 or 2 “ordinal variables” in the R×C contingency table data， it was necessary to “assign or score” the ordinal variables before performing statistical analysis. In the FREQ procedure of SAS/STAT， there were four scoring methods. With different scoring approach， both the expression form and the calculation results of CMH χ2 test statistics could change accordingly.

Keywords

• ordinal variables
• cmh χ2 test
• rank sum test
• rank correlation analysis
• sas software
• r software