Cochran–Mantel–Haenszel statistics
Encyclopedia
In statistics
, the Cochran–Mantel–Haenszel statistics are a collection of test statistics used in the analysis of stratified categorical data
.. They are named after William G Cochran, Nathan Mantel
and William Haenszel. One of these test statistics is the Cochran–Mantel–Haenszel (CMH) test, which allows the comparison of two groups on a dichotomous/categorical response. It is used when the effect of the explanatory variable on the response variable is influenced by covariate
s that can be controlled. It is often used in observational studies where random assignment of subjects to different treatments cannot be controlled, but influencing covariates can.
In the CMH test, the data are arranged in a series of associated 2 × 2 contingency tables, the null hypothesis is that the observed response is independent of the treatment used in any 2 × 2 contingency table. The CMH test's use of associated 2 × 2 contingency tables increases the ability of the test to detect associations (the power of the test is increased).
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, the Cochran–Mantel–Haenszel statistics are a collection of test statistics used in the analysis of stratified categorical data
Categorical data
In statistics, categorical data is that part of an observed dataset that consists of categorical variables, or for data that has been converted into that form, for example as grouped data...
.. They are named after William G Cochran, Nathan Mantel
Nathan Mantel
Nathan Mantel was a biostatistician best known for his work with William Haenszel which led to the Mantel–Haenszel test and its associated estimate, the Mantel–Haenszel odds ratio...
and William Haenszel. One of these test statistics is the Cochran–Mantel–Haenszel (CMH) test, which allows the comparison of two groups on a dichotomous/categorical response. It is used when the effect of the explanatory variable on the response variable is influenced by covariate
Covariate
In statistics, a covariate is a variable that is possibly predictive of the outcome under study. A covariate may be of direct interest or it may be a confounding or interacting variable....
s that can be controlled. It is often used in observational studies where random assignment of subjects to different treatments cannot be controlled, but influencing covariates can.
In the CMH test, the data are arranged in a series of associated 2 × 2 contingency tables, the null hypothesis is that the observed response is independent of the treatment used in any 2 × 2 contingency table. The CMH test's use of associated 2 × 2 contingency tables increases the ability of the test to detect associations (the power of the test is increased).