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Kappa coefficients for dichotomous-nominal classifications

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  • Matthijs J. Warrens

    (University of Groningen)

Abstract

Two types of nominal classifications are distinguished, namely regular nominal classifications and dichotomous-nominal classifications. The first type does not include an ‘absence’ category (for example, no disorder), whereas the second type does include an ‘absence’ category. Cohen’s unweighted kappa can be used to quantify agreement between two regular nominal classifications with the same categories, but there are no coefficients for assessing agreement between two dichotomous-nominal classifications. Kappa coefficients for dichotomous-nominal classifications with identical categories are defined. All coefficients proposed belong to a one-parameter family. It is studied how the coefficients for dichotomous-nominal classifications are related and if the values of the coefficients depend on the number of categories. It turns out that the values of the new kappa coefficients can be strictly ordered in precisely two ways. The orderings suggest that the new coefficients are measuring the same thing, but to a different extent. If one accepts the use of magnitude guidelines, it is recommended to use stricter criteria for the new coefficients that tend to produce higher values.

Suggested Citation

  • Matthijs J. Warrens, 2021. "Kappa coefficients for dichotomous-nominal classifications," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(1), pages 193-208, March.
    • Handle: RePEc:spr:advdac:v:15:y:2021:i:1:d:10.1007_s11634-020-00394-8
    DOI: 10.1007/s11634-020-00394-8
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    References listed on IDEAS

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    2. Yang, Zhao & Zhou, Ming, 2015. "Weighted kappa statistic for clustered matched-pair ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 1-18.
    3. Matthijs Warrens, 2014. "Corrected Zegers-ten Berge Coefficients Are Special Cases of Cohen’s Weighted Kappa," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 179-193, July.
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    6. Matthijs J. Warrens & Bunga C. Pratiwi, 2016. "Kappa Coefficients for Circular Classifications," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 507-522, October.
    7. Matthijs Warrens, 2010. "Inequalities between multi-rater kappas," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(4), pages 271-286, December.
    8. Matthijs Warrens, 2012. "Some Paradoxical Results for the Quadratically Weighted Kappa," Psychometrika, Springer;The Psychometric Society, vol. 77(2), pages 315-323, April.
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