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I'm studying use cases for Cochran-Mantel-Haenszel (CMH) test. All the examples i've found deal with 2X2 contingency tables. I'm wondering if CMH test is applicable for tables larger than 2x2?

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Yes you can. You can read some of the theory on recent extensions of CHH tests by Rayner & Rippon

For 3 dimensional table examples you can look at Mangiafico's website

And for doing it in R the CMHtest function is a good start

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