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Some Paradoxical Results for the Quadratically Weighted Kappa

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, Institute of Psychology, Unit Methodology and Statistics, Leiden University, P.O. Box 9555, 2300 RB Leiden, The Netherlands. E-mail: warrens@fsw.leidenuniv.nl
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Abstract

The quadratically weighted kappa is the most commonly used weighted kappa statistic for summarizing interrater agreement on an ordinal scale. The paper presents several properties of the quadratically weighted kappa that are paradoxical. For agreement tables with an odd number of categories n it is shown that if one of the raters uses the same base rates for categories 1 and n, categories 2 and n−1, and so on, then the value of quadratically weighted kappa does not depend on the value of the center cell of the agreement table. Since the center cell reflects the exact agreement of the two raters on the middle category, this result questions the applicability of the quadratically weighted kappa to agreement studies. If one wants to report a single index of agreement for an ordinal scale, it is recommended that the linearly weighted kappa instead of the quadratically weighted kappa is used.

Keywords

Cohen’s kappaweighted kappanominal agreementordinal agreementagreement studiesradiologyquadratic weights
Type
Original Paper
Information
Psychometrika , Volume 77 , Issue 2 , April 2012 , pp. 315 - 323
Copyright
Copyright © 2012 The Psychometric Society

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