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Tests of Symmetry in Three-Way Contingency Tables

Published online by Cambridge University Press:  01 January 2025

Campbell B. Read
Campbell B. Read*
Affiliation:
Southern Methodist University
*
Requests for reprints should be sent to Dr. C. B. Read, Department of Statistics, Southern Methodist University, Dallas, Texas 75275.
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Abstract

Three-dimensional contingency tables are analyzed, with one variable (e.g., sex) as a factor, and with a natural relation between the other variables (e.g. left and right eye vision). Models of special interest, like symmetry and proportional symmetry between the related variables, and homogeneity across the factor levels, are investigated. Maximum likelihood estimators of parameters and partitions of chi-square goodness-of-fit statistics are explicitly presented; the independence of certain models is noted, and an example is discussed.

Keywords

contingency tablesmodel fittingpartition of chi-squaresymmetrythree-dimensional discrete data
Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 3 , September 1978 , pp. 409 - 420
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

The author wishes to thank the editor and referees for helpful suggestions in preparing the final version of this paper.

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