Contingency matrix theory I: rank and statistical independence in a contigency table

Authors:
Shusaku Tsumoto;Shoji Hirano
Affiliations:
Department of Medical Informatics, Faculty of Medicine, Shimane University, Izumo, Shimane, Japan;Department of Medical Informatics, Faculty of Medicine, Shimane University, Izumo, Shimane, Japan
Venue:
Transactions on computational science II
Year:
2008

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Abstract

A contingency table summarizes the conditional frequenciesof two attributes and shows how these two attributes are dependent oneach other with the information on a partition of universe generatedby these attributes. This paper discusses statistical independence in acontingency table from the viewpoint of matrix theory. Statistical independenceis equivalent to linear dependence of all columns or rows.Also, the equations of statistical independence are equivalent to thoseon collinearity of projective geometry.