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On Similarity Coefficients for 2×2 Tables and Correction for Chance

Published online by Cambridge University Press:  01 January 2025

Matthijs J. Warrens
Matthijs J. Warrens*
Affiliation:
Leiden University
*
Requests for reprints should be sent to Matthijs J. Warrens, Psychometrics and Research Methodology Group, Leiden University Institute for Psychological Research, Leiden University, Wassenaarseweg 52, P.O. Box 9555, 2300 RB Leiden, The Netherlands. E-mail: warrens@fsw.leidenuniv.nl
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Abstract

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This paper studies correction for chance in coefficients that are linear functions of the observed proportion of agreement. The paper unifies and extends various results on correction for chance in the literature. A specific class of coefficients is used to illustrate the results derived in this paper. Coefficients in this class, e.g. the simple matching coefficient and the Dice/Sørenson coefficient, become equivalent after correction for chance, irrespective of what expectation is used. The coefficients become either Cohen’s kappa, Scott’s pi, Mak’s rho, Goodman and Kruskal’s lambda, or Hamann’s eta, depending on what expectation is considered appropriate. Both a multicategorical generalization and a multivariate generalization are discussed.

Keywords

indices of associationresemblance measurescorrection for chanceCohen’s kappaScott’s piMak’s rhoGoodman and Kruskal’s lambdaHamann’s etasimple matching coefficientDice/Sørenson coefficient
Type
Theory and Methods
Information
Psychometrika , Volume 73 , Issue 3 , September 2008 , pp. 487 - 502
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NC
This is an article distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Copyright
Copyright © 2008 The Author(s)

Footnotes

The author thanks two anonymous reviewers for their helpful comments and valuable suggestions on earlier versions of this article.

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