# What is the Cochran–Mantel–Haenszel Test?

Quantitative Results

The Cochran–Mantel–Haenszel test is also known as the Mantel-Haenszel test or the Mantel-Haenszel chi-square test. Researchers use this statistical procedure to evaluate the association between two categorical variables while controlling for the effects of a third categorical variable. Typically, contingency tables, also known as cross-tabulations, display the distribution of observations among multiple categories.

##### The Cochran–Mantel–Haenszel Test

The test is named after its three developers, William Cochran, Nathan Mantel, and William Haenszel. The test was first introduced in the 1950s. It has since become a widely used tool in the field of epidemiology for assessing the relationship between risk factors and the occurrence of a particular disease or outcome. Other fields, including sociology and psychology, widely use the test.

The test determines if there is a significant association between two categorical variables by stratifying the data with respect to a third variable. The chi-square statistic is the test statistic that determines whether the observed frequencies in the contingency table deviate significantly from the expected frequencies, assuming independence between the two variables. The test does not necessitate normal distribution of the data, but it does require independent observations.

One of the key advantages of the Cochran–Mantel–Haenszel test is its ability to control for the effects of confounding variables. The presence of a third variable can distort the relationship between two variables, causing confounding to occur. By stratifying the data by the confounding variable, the test can account for its effects and provide a more accurate estimate of the association between the two variables of interest.

Another advantage of the test is its ability to handle multi-way contingency tables. By extending the test to handle more than three variables, researchers can use it as a useful tool for analyzing complex data sets.

##### Final Remarks

In conclusion, the Cochran–Mantel–Haenszel test is a useful statistical method for evaluating the association between two categorical variables while controlling for the effects of a third categorical variable. Many fields widely use it because it is robust to departure from the assumption of normality. It is also useful to handle multi-way contingency tables. However, it is important to ensure the observations are independent before applying the test.