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

Sébastien Loisel; Yoshio Takane

doi:10.1007/s00180-015-0619-1

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

Sébastien Loisel, Yoshio Takane^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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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.

Original language	English
Pages (from-to)	1429–1452
Number of pages	24
Journal	Computational Statistics
Volume	31
Issue number	4
Early online date	4 Sept 2015
DOIs	https://doi.org/10.1007/s00180-015-0619-1
Publication status	Published - Dec 2016

Keywords

ANOVA-like partitions
Helmert-like contrasts
Likelihood ratio (LR) statistic
Metric matrix
One-way tables
Orthogonal transformations
Three-way tables
Two-way tables

ASJC Scopus subject areas

Statistics and Probability
Computational Mathematics
Statistics, Probability and Uncertainty

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

Abstract

Keywords

ASJC Scopus subject areas

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