Cohen’s weighted kappa is a popular descriptive statistic for summarizing interrater agreement on an ordinal scale. An agreement table with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$n\in \mathbb N _{\ge 3}$$</EquationSource> </InlineEquation> ordered categories can be collapsed into <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$n-1$$</EquationSource> </InlineEquation> distinct <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$2\times 2$$</EquationSource> </InlineEquation> tables by combining adjacent categories. Weighted kappa with linear weights is a weighted average of the kappas corresponding to the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$2\times 2$$</EquationSource> </InlineEquation> tables, where the weights are the denominators of the <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$2\times 2$$</EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$$2\times 2$$</EquationSource> </InlineEquation> 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
