exact cochran-mantel-haenszel method
The Cochran-Mantel-Haenszel (CMH) method is a statistical technique used to analyze the association between two categorical variables while controlling for a third variable, often referred to as a covariate. It is commonly used in epidemiological and biomedical research.
Here's how the CMH method works:
1. Define the variables: Identify the three variables you want to analyze. Let's call them A, B, and C.
- Variable A: The exposure or independent variable of interest with two or more categories.
- Variable B: The outcome or dependent variable with two or more categories.
- Variable C: The covariate or stratification variable with two or more categories.
2. Create a contingency table: Construct a 2x2 table that shows the frequency distribution of the outcomes (variable B) by the exposure group (variable A) within each level of the cov
ariate (variable C). This table is often called a stratified or contingency table.
3. Calculate the CMH statistic: The CMH statistic is a measure of association that takes into account the covariate (variable C). It is calculated by comparing the observed frequencies in each cell of the table with the expected frequencies under the assumption of no association.
4. Test the null hypothesis: Conduct a statistical test to determine whether there is evidence of an association between variables A and B after adjusting for variable C. The test is typically performed using a chi-square test or Fisher's exact test, depending on sample size and assumptions.
5. Interpret the results: If the p-value is below a predetermined significance level (e.g., 0.05), it suggests that there is a significant association between variables A and B after controlling for variable C. Conversely, if the p-value is above the significance level, there is no evidence of an association.
The CMH method allows researchers to examine the relationship between variables A and B while accounting for potential confounding effects of variable C. This control for the covariate ensures more accurate estimates and provides insights into the specific relationship of interest.

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