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

• Autorzy: Tsumoto S. , Hirano S.
• Języki publikacji: EN

Abstrakty

EN

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_{i,j/sub> 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.}

Słowa kluczowe

EN

contingency table; Chi-square distribution; matrix theory

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2009
• Tom: Vol. 90, nr 3
• Strony: 251--267
• Opis fizyczny: bibliogr. 22 poz.

Twórcy

autor

Tsumoto S.

autor

Hirano S.

• Department of Medical Informatics, Faculty of Medicine, Shimane University, Enya-cho Izumo City, Shimane 693-8501 Japan,

Bibliografia

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