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Theory & Methods: Partitioning Pearson’s chi‐squared statistic for a partially ordered three‐way contingency table
Author(s) -
Beh Eric J.,
Davy Pamela J.
Publication year - 1999
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.00077
Subject(s) - contingency table , mathematics , statistic , partition (number theory) , statistics , pearson's chi squared test , chi square test , generalization , quadratic equation , combinatorics , test statistic , discrete mathematics , statistical hypothesis testing , mathematical analysis , geometry
This paper presents a generalization of the partition of the chi‐squared statistic presented in Beh & Davy (1998). For a three‐way contingency table with one or two sets of ordered categories, the chi‐squared statistic partition is defined using orthogonal polynomials. Using this partition, information about the relationship between the variables can be obtained by identifying important associations in terms of the location (linear), dispersion (quadratic) and higher order components. The paper compares these partitions with log‐linear models for ordinal data.