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| Titel: |
Statistical Independence and Determinants in a Contingency Table – Interpretation of Pearson Residuals based on Linear Algebra – |
| Auteur: |
Tsumoto, Shusaku Hirano, Shoji |
| Verschenen in: |
Fundamenta informaticae |
| Paginering: | Jaargang 90 (2009) nr. 3 pagina's 251-267 |
| Jaar: |
2009-03-16 |
| Inhoud: |
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. |
| Uitgever: |
IOS Press |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
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