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Theory & Methods: Partitioning Pearson's Chi‐squared Statistic for Singly Ordered Two‐way Contingency Tables
Author(s) -
Beh Eric J.
Publication year - 2001
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00179
Subject(s) - contingency table , mathematics , statistic , partition (number theory) , statistics , ordinal data , combinatorics
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.