Cohen’s linearly weighted kappa is a weighted average

Abstract

An n × n agreement table F = {f ij } with n ≥ 3 ordered categories can for fixed m (2 ≤ m ≤ n − 1) be collapsed into $${\binom{n-1}{m-1}}$$ distinct m × 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 × 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 × 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.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 35 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.