On the degree of the dependence in a contingency matrix

This paper gives a relation between the degree of granularity and that of dependence of contingency tables. From the results of determinantal divisors, it seems that the divisors provide information on the degree of dependencies between the matrix of the whole elements and its submatrices and the increase of the degree of granularity may lead to that of dependence. However, this paper shows that a constraint on the sample size of a contingency table is very strong, which leads to the evaluation formula where the increase of degree of granularity gives the decrease of dependency.