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This paper gives further investigation on correlation between pearson residuals and degree of freedom in a contingency table. An interesting formula is obtained, where an independent variable in a contingency table will be a fundamental granule of degree of freedom. The structure of formula is also closely related with combinatorial natures of given variables.
This paper focuses on residual analysis of statistical independence of multiple variables from the viewpoint of linear algebra. 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.
Marginal distributions play a central role in statistical analysis of a contingency table. However, when the number of partition becomes large, the contribution from marginal distributions decreases. This paper focuses on a formal analysis of marginal distributions in a contingency table. The main approach is to take the difference between two matrices with the same sample size and the same marginal...
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