XLSTAT: Cochran-Mantel-Haenszel test in Excel

This tutorial shows how to compute and interpret a Cochran-Mantel-Haenszel CMH analysis in Excel using the XLSTAT software.

Not sure this is the statistical test you are looking for? Check out this guide.

Background

The Cochran-Mantel-Haenszel test is a statistical method to analyze the association between two categorical variables while controlling for a third confounding variable. 

Dataset for Example

The dataset has first been used in [Mantel N. (1963). Chi-Square Tests with One Degree of Freedom; Extensions of the Mantel- Haenszel Procedure. Journal of the American Statistical Association, 58, 303, 690-700] and corresponds to an experiment in which rabbits were injected with beta-hemolytic streptococci, and then immediately or after 90 minutes with a dose of penicillin varying from 1/8 to 4.

The aim of the experiment is to check first if there is a dependency between the survival or death of the rabbit and the delay in injection of penicillin.

Setting Up

• Open XLSTAT.
• Click on the Nonparametric tests menu and select the Cochran-Mantel-Haenszel test feature:

• Once you've clicked the button, the dialog box appears.

In the General tab:

• In the Data format, select Contingency tables. Note: For illustration the two data formats are presented in the datasheet. However, for the tutorial, only the format  Contingency Table is used.
• Select the 5  contingency tables  on the Excel sheet (each representing a level of penicillin).
• Check the Column label option since the first row includes the response categories ("Cured" and "Died").

In the Options tab:

• In the Alternative hypothesis field, select Common odds ratio ≠ 1, as it is valid for 2×2 contingency tables.
• Since all selected tables are 2×2, leave the exact p-value option activated to obtain more accurate results.

• Click on the OK button to launch the computations.
• The results are displayed on a new Excel sheet.

Interpreting the results of a Cochran-Mantel-Haenszel test

The Cramer's V has the advantage of being interpretable in terms of strength of link between variables. In the case of 2x2 tables, it is indeed close to 0 when there is no link, -1 if the cross categories (1 and 2, 2 and 1) are related, and close to 1 when categories with the same index (1 and 1, 2 and 2) are linked.

However, when taking the tables all together for a Cochran-Mantel-Haenszel test, we obtain a common odds ratio of 0.143, with a 95% confidence interval that does not include the value 1. The exact p-value of 0.04 (we would obtain 0.047 if the exact option was not selected) leads to the conclusion that there is generally a link between the delay and the fact that a rabbit will survive or not the injection of streptococci.

This result may seem surprising because none of the sub-tables showed a dependency. By combining the tables, we show though that there is a dependence. As the odds ratio is different from 1, there is a positive effect of an immediate injection of penicillin on the survival.

The Cochran-Mantel-Haenszel should be used with caution. It is particularly not recommended when there is a level of 3 interaction between the 3 variables. In our case, this would correspond to the situation where a higher dose of penicillin would increase the impact of delay on the survival. This situation can correspond to an evolution of Cramer's V from a value close to -1 to 1. And despite an obvious strong dependence, the Cochran-Mantel-Haenszel could conclude that there is independence. Hence the interest that the Cramer's V are almost homogeneous when one concludes there is independence.