Partitions of Pearson’s Chi-square statistic for frequency tables: a comprehensive account

Sébastien Loisel () and Yoshio Takane ()
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Sébastien Loisel: Heriot-Watt University
Yoshio Takane: University of Victoria

Computational Statistics, 2016, vol. 31, issue 4, No 10, 1429-1452

Abstract: Abstract Pearson’s Chi-square statistic for frequency tables depends on what is hypothesized as the expected frequencies. Its partitions also depend on the hypothesis. Lancaster (J R Stat Soc B 13:242–249, 1951) proposed ANOVA-like partitions of Pearson’s statistic under several representative hypotheses about the expected frequencies. His expositions were, however, not entirely clear. In this paper, we clarify his method of derivations, and extend it to more general situations. A comparison is made with analogous decompositions of the log likelihood ratio statistic associated with log-linear analysis of contingency tables.

Keywords: One-way tables; Two-way tables; Three-way tables; Orthogonal transformations; Metric matrix; Helmert-like contrasts; ANOVA-like partitions; Likelihood ratio (LR) statistic (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s00180-015-0619-1

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