Statistical Independence and Contingency Matrix

This paper shows the meaning of Pearson residuals as an indicator of statistical independence. While information granules of statistical independence of two variables can be viewed as determinants of 2times2-submatrices, those of three variables consist of several combinations of linear equations which will become residuals for odds ratio (outer products) when they are equal to 0. Interestingly, the residuals can be an expansion series of the product of marginal distributions and the residuals for odds ratio (outer products).