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New Interpretations of Cohen’s Kappa

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  • Matthijs J. Warrens

Abstract

Cohen’s kappa is a widely used association coefficient for summarizing interrater agreement on a nominal scale. Kappa reduces the ratings of the two observers to a single number. With three or more categories it is more informative to summarize the ratings by category coefficients that describe the information for each category separately. Examples of category coefficients are the sensitivity or specificity of a category or the Bloch-Kraemer weighted kappa. However, in many research studies one is often only interested in a single overall number that roughly summarizes the agreement. It is shown that both the overall observed agreement and Cohen’s kappa are weighted averages of various category coefficients and thus can be used to summarize these category coefficients.

Suggested Citation

  • Matthijs J. Warrens, 2014. "New Interpretations of Cohen’s Kappa," Journal of Mathematics, Hindawi, vol. 2014, pages 1-9, September.
    • Handle: RePEc:hin:jjmath:203907
    DOI: 10.1155/2014/203907
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    References listed on IDEAS

    as
    1. Klaus Krippendorff, 1987. "Association, agreement, and equity," Quality & Quantity: International Journal of Methodology, Springer, vol. 21(2), pages 109-123, June.
    2. Matthijs Warrens, 2008. "On the Equivalence of Cohen’s Kappa and the Hubert-Arabie Adjusted Rand Index," Journal of Classification, Springer;The Classification Society, vol. 25(2), pages 177-183, November.
    3. Matthijs Warrens, 2008. "On Similarity Coefficients for 2×2 Tables and Correction for Chance," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 487-502, September.
    4. Matthijs Warrens, 2012. "Some Paradoxical Results for the Quadratically Weighted Kappa," Psychometrika, Springer;The Psychometric Society, vol. 77(2), pages 315-323, April.
    5. Matthijs Warrens, 2008. "On Association Coefficients for 2×2 Tables and Properties That Do Not Depend on the Marginal Distributions," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 777-789, December.
    6. Matthijs Warrens, 2010. "Inequalities Between Kappa and Kappa-Like Statistics for k×k Tables," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 176-185, March.
    7. Matthijs Warrens, 2011. "Cohen’s Linearly Weighted Kappa is a Weighted Average of 2×2 Kappas," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 471-486, July.
    8. Helena Kraemer, 1979. "Ramifications of a population model forκ as a coefficient of reliability," Psychometrika, Springer;The Psychometric Society, vol. 44(4), pages 461-472, December.
    9. F. Baulieu, 1989. "A classification of presence/absence based dissimilarity coefficients," Journal of Classification, Springer;The Classification Society, vol. 6(1), pages 233-246, December.
    10. Ahmed N. Albatineh & Magdalena Niewiadomska-Bugaj & Daniel Mihalko, 2006. "On Similarity Indices and Correction for Chance Agreement," Journal of Classification, Springer;The Classification Society, vol. 23(2), pages 301-313, September.
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