Theory & Methods: Partitioning Pearson’s chi‐squared statistic for a partially ordered three‐way contingency table

Abstract

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.