Theory & Methods: Partitioning Pearson's Chi-squared Statistic for Singly Ordered Two-way Contingency Tables
Article first published online: 18 DEC 2002
Australian Statistical Publishing Association Inc. 2001
Australian & New Zealand Journal of Statistics
Volume 43, Issue 3, pages 327–333, September 2001
How to Cite
Beh, E. J. (2001), Theory & Methods: Partitioning Pearson's Chi-squared Statistic for Singly Ordered Two-way Contingency Tables. Australian & New Zealand Journal of Statistics, 43: 327–333. doi: 10.1111/1467-842X.00179
- Issue published online: 18 DEC 2002
- Article first published online: 18 DEC 2002
- Cited By
- dispersion and higher order components;
- ordinal log-linear analysis;
- orthogonal polynomials;
- singly ordered contingency table;
- singular values.
This paper presents a partition of Pearson's chi-squared statistic for singly ordered two-way contingency tables. The partition involves using orthogonal polynomials for the ordinal variable while generalized basic vectors are used for the non-ordinal variable. The benefit of this partition is that important information about the structure of the ordered variable can be identified in terms of locations, dispersion and higher order components. For the non-ordinal variable, it is shown that the squared singular values from the singular value decomposition of the transformed dataset can be partitioned into location, dispersion and higher order components. The paper also uses the chi-squared partition to present an alternative to the maximum likelihood technique of parameter estimation for the log-linear analysis of the contingency table.