Geometrical interpretation of pearson residuals

This paper focuses on geometrical intepretation of pearson residual, which measures the degree of statistical depedendence of a given cell. An information granule of statistical independence at a given cell is represented as a square whose origin is the given cell. Interestingly, the degree of freedom of each cell is equal to the number of squares at the cell, which can be extended to mult-way contingency table. Moreover, combinatorial analysis of squares shows that the degree of freedom will not represent the global nature of a contingency table in general.