samplesizeCMH: Sample Size Calculation for the Cochran-Mantel-Haenszel Test

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by Paul W. Egeler M.S.


This package provides functions relating to power and sample size calculation for the CMH test. There are also several helper functions for interconverting probability, odds, relative risk, and odds ratio values.

Please see the package website for more information on how this package is used, including documentation and vignettes.

The Cochran Mantel Haenszel Test

The Cochran-Mantel-Haenszel test (CMH) is an inferential test for the association between two binary variables, while controlling for a third confounding nominal variable. Two variables of interest, X and Y, are compared at each level of the confounder variable Z and the results are combined, creating a common odds ratio. Essentially, the CMH test examines the weighted association of X and Y. The CMH test is a common technique in the field of biostatistics, where it is often used for case-control studies.

Sample Size Calculation

Given a target power which the researcher would like to achieve, a calculation can be performed in order to estimate the appropriate number of subjects for a study. The power.cmh.test function calculates the required number of subjects per group to achieve a specified power for a Cochran-Mantel-Haenszel test.

Power Calculation

Researchers interested in estimating the probability of detecting a true positive result from an inferential test must perform a power calculation using a known sample size, effect size, significance level, et cetera. The power.cmh.test function can compute the power of a CMH test, given parameters from the experiment.


Installation of the CRAN release can be done with install.packages(). From the R console:


Downloading and installing the latest version from GitHub is facilitated by remotes. To do so, type the following into your R console:

if (!require("remotes")) install.packages("remotes")