A New Algorithm for the Partition of Pearson's Chi-Squared Statistic for Multiway Contingency Table

Pearson's chi-squared statistic is one of the most common statistical tools used to assess the association between two or more categorical variables that have been cross-classified to form a contingency table. In many practical settings, multiple categorical variables are "paired-off" and analysed by identifying association structures between two variables only. However, there are less well-known tools that allow the analyst to explore the association structure of categorical variables that form a multi-way contingency table. This paper presents an ANOVA-like decomposition of the chi-squared statistic for four-way and five-way contingency tables and can be extended for the analysis of higher-way contingency tables. Furthermore, we propose an efficient algorithm for partitioning the statistic that leads to two-way and higher-way terms. The proposed algorithm reduces the complexity involved in the calculation of the terms of the partition and will be demonstrated by way of a simulation and practical example.