The correlation statistic is one of the statistics used in the generalized Cochran-Mantel-Haenszel tests. It is applicable when both the treatment (rows) and response (columns) are measured on an ordinal scale.
In case of independence between the two variables in all strata, the asymptotic distribution of the correlation statistic is the chi-square distribution with one degree of freedom
The correlation statistic has more power than either the general association statistic or the mean score statistic to detect of linear association between the “treatment” and “response” variables.