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Cohen’s weighted kappa with additive weights

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  • Matthijs Warrens

Abstract

Cohen’s weighted kappa is a popular descriptive statistic for summarizing interrater agreement on an ordinal scale. An agreement table with $$n\in \mathbb N _{\ge 3}$$ ordered categories can be collapsed into $$n-1$$ distinct $$2\times 2$$ tables by combining adjacent categories. Weighted kappa with linear weights is a weighted average of the kappas corresponding to the $$2\times 2$$ tables, where the weights are the denominators of the $$2\times 2$$ kappas. It is shown that the linearly weighted kappa is a special case of a more general weighted kappa that is a weighted average of the $$2\times 2$$ kappas. This weighted kappa has additive weights, that is, given initial weights for pairs of adjacent categories the weight for two non-adjacent categories is obtained by adding the weights of all pairs of adjacent categories between the two. Copyright Springer-Verlag Berlin Heidelberg 2013

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  • Matthijs Warrens, 2013. "Cohen’s weighted kappa with additive weights," 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. 7(1), pages 41-55, March.
    • Handle: RePEc:spr:advdac:v:7:y:2013:i:1:p:41-55
    DOI: 10.1007/s11634-013-0123-9
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    References listed on IDEAS

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    1. 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.
    2. Hubert Schouten, 1986. "Nominal scale agreement among observers," Psychometrika, Springer;The Psychometric Society, vol. 51(3), pages 453-466, September.
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