The quantification of Simpson's paradox and other contributions to contingency table theory

The analysis of contingency tables is a powerful statistical tool used in experiments with categorical variables. This study improves parts of the theory underlying the use of contingency tables. Specifically, the linkage disequilibrium parameter as a measure of two-way interactions applied to three...

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Bibliographic Details
Published in:PloS one 2022-02, Vol.17 (2), p.e0262502-e0262502
Main Author: Teuscher, Friedrich
Format: Article
Language:English
Subjects:
Analysis
Contingency
Contingency tables
Data Interpretation, Statistical
Drug Interactions
Entropy
Experiments
Humans
Interior Design and Furnishings
Linkage Disequilibrium
Models, Statistical
Paradoxes
Programming, Linear
Quantitative genetics
Simpson's paradox
Software
Statistical analysis
Symmetry
Variables
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Summary:The analysis of contingency tables is a powerful statistical tool used in experiments with categorical variables. This study improves parts of the theory underlying the use of contingency tables. Specifically, the linkage disequilibrium parameter as a measure of two-way interactions applied to three-way tables makes it possible to quantify Simpson's paradox by a simple formula. With tests on three-way interactions, there is only one that determines whether the partial interactions of all variables agree or whether there is at least one variable whose partial interactions disagree. To date, there has been no test available that determines whether the partial interactions of a certain variable agree or disagree, and the presented work closes this gap. This work reveals the relation of the multiplicative and the additive measure of a three-way interaction. Another contribution addresses the question of which cells in a contingency table are fixed when the first- and second-order marginal totals are given. The proposed procedure not only detects fixed zero counts but also fixed positive counts. This impacts the determination of the degrees of freedom. Furthermore, limitations of methods that simulate contingency tables with given pairwise associations are addressed.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0262502