Recently i've learned about Cochran-Mantel-Haenszel (CMH) test and its application for data analysis. I'm wondering why i have to perform a single CMH test, but not just a multiple Chi-square tests. E.g. if i have 8 2X2 contingency tables. Why i can not make 8 Chi-square tests instead of single CMH test? What is advantage of CMH test versus multiple Chi-square tests ?
$\begingroup$
$\endgroup$
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
2
If you run 8 separate Chi-square tests you will inflate your type 1 error (chance of false positive) due to the multiple comparisons problem.
-
$\begingroup$ Thank you very much! I'm wondering if there are any additional advantages of using
CMHtest? $\endgroup$– DenisCommented Aug 4, 2020 at 9:00 -
1$\begingroup$ Not sure about advantages as such, but if you have a 2x2x8 set of data and want to test the association across the groups it is the correct one to be using. The other approach could be log-linear modelling (aka Poisson regression) where you set and interpret model parameters for the associations you are interested in. $\endgroup$ Commented Aug 4, 2020 at 9:23
$\begingroup$
$\endgroup$
I am using the CMH test to interpret 2 x 2 relationships with a moderating variable (that would be your 8-level variable). Basically the CMH test takes a moderating variable into account - so you really have to think about what your outcome measure is, what your predictor variable is, and then what might be moderating that relationship/contingency. The CMH Risk Ratio gives you a more "true" risk ratio - as it takes moderation into account. The raw 2 x 2 risk ratio (and odds ratio) is less accurate because of this (i.e., "this" being collapsing across the moderator). In a way, a 2 x 2 is like looking at only a main effect (or multiple main effects) when there might be an interaction. The main effects must be interpreted in the context of the interaction.
