Register today for our Generative AI Foundations course. Use code GenAI99 for a discount price of $99!
Skip to content

Generalized Cochran-Mantel-Haenszel tests

Generalized Cochran-Mantel-Haenszel test:

The Generalized Cochran-Mantel-Haenszel test is a family of tests aimed at detecting of association between two categorical variables observed in K strata.

The initial data are represented as a series of K RxC contingency table s, where K is the number of strata and at least one of the variables (“group”, “response”) takes on more than 2 values. Typically, in each table the rows correspond to the “Treatment group” values (e.g “Placebo”, “Low dose”, “High dose) and the columns to the “Response” values (e.g “Worsening”, “No change” “Improvement”).

The stratification of the subjects into K groups (according to the values of controlled variables – e.g. “Age group”) increases the power of the test to detect association. This increase in power comes from comparing like subjects to like subjects.

The alternative hypotheses vary across the generalized CMH tests, depending on the type of the scale of the two “treatment” and “response” variables.

The general feature of the test statistics used in the generalized CMH tests is that they all are quadratic forms of the differences

nijk mijk;   i=1,…,(R1);   j=1,…,(C1);   k=1,…,K;
nijk mijk;   i=1,…,(R1);   j=1,…,(C1);   k=1,…,K;nijk mijk;   i=1,…,(R1);   j=1,…,(C1);   k=1,…,K;
nijk mijk;   i=1,…,(R1);   j=1,…,(C1);   k=1,…,K;
nijk mijk;   i=1,…,(R1);   j=1,…,(C1);   k=1,…,K;

where nijk and mijk is the observed and expected counts in the (ij)th cell of the (k)th table. For details on the major three generalized CMH statistics, see the General association statistic, the Mean score statistic, and the Correlation statistic.

See also the Cochran-Mantel-Haenszel test – the prototype of the generalized CMH tests.

Note: The CMH tests and corresponding statistics should not be confused with Cochran Q statistic, Mantel-Cox test.

Browse Other Glossary Entries

Test Yourself

Planning on taking an introductory statistics course, but not sure if you need to start at the beginning? Review the course description for each of our introductory statistics courses and estimate which best matches your level, then take the self test for that course. If you get all or almost all the questions correct, move on and take the next test.

Data Analytics

Considering becoming adata scientist, customer analyst or our data science certificate program?

Analytics Quiz

Advanced Statistics Quiz

Statistics Quiz

Statistics

Looking at statistics for graduate programs or to enhance your foundational knowledge?

Statistics 1 Quiz

Regression Quiz

Regression Quiz

Biostatistics

Entering the biostatistics field? Test your skill here.

Biostatistics Quiz

Advanced Statistics Quiz

Statistics 2 Quiz

Stay Informed

Our Blog

Read up on our latest blogs

Certificates

Learn about our certificate programs

Courses

Find the right course for you

Contact Us

We'd love to answer your questions

Our mentors and academic advisors are standing by to help guide you towards the courses or program that makes the most sense for you and your goals.

300 W Main St STE 301, Charlottesville, VA 22903

(434) 973-7673

ourcourses@statistics.com

By submitting your information, you agree to receive email communications from Statistics.com. All information submitted is subject to our privacy policy. You may opt out of receiving communications at any time.