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On Association Coefficients for 2×2 Tables and Properties That Do Not Depend on the Marginal Distributions

Published online by Cambridge University Press:  01 January 2025

Matthijs J. Warrens
Matthijs J. Warrens*
Affiliation:
Leiden University Institute for Psychological Research
*
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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We discuss properties that association coefficients may have in general, e.g., zero value under statistical independence, and we examine coefficients for 2×2 tables with respect to these properties. Furthermore, we study a family of coefficients that are linear transformations of the observed proportion of agreement given the marginal probabilities. This family includes the phi coefficient and Cohen’s kappa. The main result is that the linear transformations that set the value under independence at zero and the maximum value at unity, transform all coefficients in this family into the same underlying coefficient. This coefficient happens to be Loevinger’s H.

Keywords

agreement indicesresemblance measurescorrection for chancecorrection for maximum valuephi coefficientCohen’s kappaHubert–Arabie adjusted Rand indexYule’s QLoevinger’s HCole’s C7
Type
Original Paper
Information
Psychometrika , Volume 73 , Issue 4 , December 2008 , pp. 777 - 789
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NC
This 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)

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