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

Author

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  • Sébastien Loisel

    (Heriot-Watt University)

  • Yoshio Takane

    (University of Victoria)

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.

Suggested Citation

  • Sébastien Loisel & Yoshio Takane, 2016. "Partitions of Pearson’s Chi-square statistic for frequency tables: a comprehensive account," Computational Statistics, Springer, vol. 31(4), pages 1429-1452, December.
    • Handle: RePEc:spr:compst:v:31:y:2016:i:4:d:10.1007_s00180-015-0619-1
    DOI: 10.1007/s00180-015-0619-1
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    Cited by:

    1. Rosaria Lombardo & Yoshio Takane & Eric J. Beh, 2020. "Familywise decompositions of Pearson’s chi-square statistic in the analysis of contingency tables," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(3), pages 629-649, September.
    2. Alzbeta Kucharcikova & Martin Miciak & Eva Malichova & Maria Durisova & Emese Tokarcikova, 2019. "The Motivation of Students at Universities as a Prerequisite of the Education’s Sustainability within the Business Value Generation Context," Sustainability, MDPI, vol. 11(20), pages 1-25, October.
    3. Abbas Alhakim, 2024. "Hadamard matrices, quaternions, and the Pearson chi-square statistic," Statistical Papers, Springer, vol. 65(8), pages 5273-5291, October.
    4. Rosaria Lombardo & Eric J. Beh & Francesco Prattichizzo & Giuseppe Lucisano & Antonio Nicolucci & Björn Eliasson & Hanne Krage Carlsen & Rosalba La Grotta & Valeria Pellegrini & Antonio Ceriello, 2024. "Testing and Visualization of Associations in Three-Way Contingency Tables: A Study of the Gender Gap in Patients with Type 1 Diabetes and Cardiovascular Complications," Mathematics, MDPI, vol. 12(14), pages 1-13, July.

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