Statistical Independence and Determinants in a Contingency Table - Interpretation of Pearson Residuals based on Linear Algebra -

Authors:
Shusaku Tsumoto;Shoji Hirano
Affiliations:
(Correspd.) Department of Medical Informatics, Shimane University, School of Medicine, Enya-cho Izumo City, Shimane 693-8501 Japan. tsumoto@computer.org, hirano@ieee.org;Department of Medical Informatics, Shimane University, School of Medicine, Enya-cho Izumo City, Shimane 693-8501 Japan. tsumoto@computer.org, hirano@ieee.org
Venue:
Fundamenta Informaticae - Cognitive Informatics, Cognitive Computing, and Their Denotational Mathematical Foundations (I)
Year:
2009

Citing 8
Cited 0

A decision theoretic framework for approximating concepts

International Journal of Man-Machine Studies
Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic

Fuzzy Sets and Systems - Special issue: fuzzy sets: where do we stand? Where do we go?
Rough Sets in Knowledge Discovery 2: Applications, Case Studies, and Software Systems

Rough Sets in Knowledge Discovery 2: Applications, Case Studies, and Software Systems
Proceedings of the Third Pacific-Asia Conference on Methodologies for Knowledge Discovery and Data Mining

PAKDD '99 Proceedings of the Third Pacific-Asia Conference on Methodologies for Knowledge Discovery and Data Mining
Data Mining: Granular Computing Approach

PAKDD '99 Proceedings of the Third Pacific-Asia Conference on Methodologies for Knowledge Discovery and Data Mining
An Analysis of Quantitative Measures Associated with Rules

PAKDD '99 Proceedings of the Third Pacific-Asia Conference on Methodologies for Knowledge Discovery and Data Mining
Medicine

Handbook of data mining and knowledge discovery
Foreword to the Special Section on Granular Computing

IEEE Transactions on Fuzzy Systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper analyzes pearson residuals, which is an important element of chi-square test statistic, in a contingency table from the viewpoint of matrix theory as follows. First, a given contingency table is viewed as a matrix and the residual of each element in a matrix are obtained as the difference bewteen observed values and expected values calculated by marginal distributions. Then, each residual σ$_{ij}$ is decomposed into the linear sum of the 2 × 2 subderminants of a original matrix, except for i-th column and j-th row. Furthermore, the number of the determinants is equal to the degree of freedom for the chi-square test statistic for a given contingency table. Thus, 2 × 2 subdeterminants in a contingencymatrix determine the degree of statistical independence of two attributes as elementary granules.