, Volume 77, Issue 2, pp 315–323 | Cite as

Some Paradoxical Results for the Quadratically Weighted Kappa

  • Matthijs J. Warrens


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.

Key words

Cohen’s kappa weighted kappa nominal agreement ordinal agreement agreement studies radiology quadratic weights 



The author thanks three anonymous reviewers for their helpful comments and valuable suggestions on an earlier versions of this article. This research is part of project 451-11-026 funded by the Netherlands Organisation for Scientific Research.


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Copyright information

© The Psychometric Society 2012

Authors and Affiliations

  1. 1.Institute of Psychology, Unit Methodology and StatisticsLeiden UniversityLeidenThe Netherlands

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