Cohen's linearly weighted kappa is a weighted average

Authors:
Matthijs J. Warrens
Affiliations:
Department of Methodology and Statistics, Tilburg University, Tilburg, The Netherlands 5000 LE
Venue:
Advances in Data Analysis and Classification
Year:
2012

Citing 4
Cited 2

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
On the Equivalence of Cohen's Kappa and the Hubert-Arabie Adjusted Rand Index

Journal of Classification
Inequalities between multi-rater kappas

Advances in Data Analysis and Classification
A Formal Proof of a Paradox Associated with Cohen’s Kappa

Journal of Classification

The problem with kappa

EACL '12 Proceedings of the 13th Conference of the European Chapter of the Association for Computational Linguistics
Cohen's weighted kappa with additive weights

Advances in Data Analysis and Classification

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Abstract

An n 脳 n agreement table F = {f ij } with n 驴 3 ordered categories can for fixed m (2 驴 m 驴 n 驴 1) be collapsed into $${\binom{n-1}{m-1}}$$ distinct m 脳 m tables by combining adjacent categories. It is shown that the components (observed and expected agreement) of Cohen's weighted kappa with linear weights can be obtained from the m 脳 m subtables. A consequence is that weighted kappa with linear weights can be interpreted as a weighted average of the linearly weighted kappas corresponding to the m 脳 m tables, where the weights are the denominators of the kappas. Moreover, weighted kappa with linear weights can be interpreted as a weighted average of the linearly weighted kappas corresponding to all nontrivial subtables.