Computing Cohen’s kappa coefficients using SPSS MATRIX

Abstract

This short paper proposes a general computing strategy to compute Kappa coefficients using the SPSS MATRIX routine. The method is based on the following rationale. If the contingency table is considered as a square matrix, then the observed proportions of agreement lie in the main diagonal’s cells, and their sum equals the trace of the matrix, whereas the proportions of agreement expected by chance are the joint product of marginals. The generalization to weighted kappa, which requires an additional square matrix of disagreement weights, both matrices having the same order, becomes possible by the use of the Hadamard product-that is, the elementwise direct product of two matrices.

This research was supported by a grant from the Quebec Health Research Fund (Canada). We thank Christopher Earls, Stéphane Sabourin, and Marc Valiquette for critical and enlightening comments on earlier drafts.