Familywise decompositions of Pearson’s chi-square statistic in the analysis of contingency tables

Rosaria Lombardo (), Yoshio Takane () and Eric J. Beh ()
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Rosaria Lombardo: University of Campania “Luigi Vanvitelli”
Yoshio Takane: University of Victoria
Eric J. Beh: University of Newcastle

Advances in Data Analysis and Classification, 2020, vol. 14, issue 3, No 7, 629-649

Abstract: Abstract Pearson’s chi-square statistic is well established for testing goodness-of-fit of various hypotheses about observed frequency distributions in contingency tables. A general formula for ANOVA-like decompositions of Pearson’s statistic is given under the independence assumption along with their extensions to higher-order tables. Mathematically, it makes the terms in the partitions and orthogonality among them obvious. Practically, it enables simultaneous analyses of marginal and joint probabilities in contingency tables under a variety of hypotheses about the marginal probabilities. Specifically, this framework accommodates the specification of theoretically driven probabilities as well as the well known cases in which the marginal probabilities are fixed or estimated from the data. The former allows tests of prescribed marginal probabilities, while the latter allows tests of the associations among variables after eliminating the marginal effects. Mixtures of these two cases are also permitted. Examples are given to illustrate the tests.

Keywords: Pearson’s chi-square statistic; Orthogonal projectors; Familywise decompositions; Hypothesised probabilities; Observed proportions; 15A03; 15A09 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11634-019-00374-7

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