Combinatorics of Information Granule in Contingency Table


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This paper focuses on the degree of freedom and number of subdeterminants in a Pearson residual in a multiway contingency table. The results show that multidimensional residuals are represented as linear sum of determinants of 2 × 2 submatrices, which can be viewed as information granules measuring the degree of statistical dependence. Geometrical interpretation of Pearson residual is investigated. Furthermore, the number of subdeterminants in a residual is equal to the degree of freedom in χ2-test statistic. Since the way of calculation of the number of subdeterminants corresponds to the construction of a statistical model for a contingency table, it has been found that the combinatorics of the number subdeterminants is closely related with permutation of attributes in a given table, where symmetric group may play an important role.