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Erschienen in:
01.03.2013 | Regular Article
Cohen’s weighted kappa with additive weights
Erschienen in: Advances in Data Analysis and Classification | Ausgabe 1/2013
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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.