On Marginal Dependencies of the 2 × 2 Kappa

Cohen’s kappa is a standard tool for the analysis of agreement in a 2 × 2 reliability study. Researchers are frequently only interested in the kappa-value of a sample. Various authors have observed that if two pairs of raters have the same amount of observed agreement, the pair whose marginal distributions are more similar to each other may have a lower kappa-value than the pair with more divergent marginal distributions. Here we present exact formulations of some of these properties. The results provide a better understanding of the 2 × 2 kappa for situations where it is used as a sample statistic.