A Study on Comparison of Generalized Kappa Statistics in Agreement Analysis

Agreement analysis is conducted to assess reliability among rating results performed repeatedly on the same subjects by one or more raters. The kappa statistic is commonly used when rating scales are categorical. The simple and weighted kappa statistics are used to measure the degree of agreement between two raters, and the generalized kappa statistics to measure the degree of agreement among more than two raters. In this paper, we compare the performance of four different generalized kappa statistics proposed by Fleiss (1971), Conger (1980), Randolph (2005), and Gwet (2008a). We also examine how sensitive each of four generalized kappa statistics can be to the marginal probability distribution as to whether marginal balancedness and/or homogeneity hold or not. The performance of the four methods is compared in terms of the relative bias and coverage rate through simulation studies in various scenarios with different numbers of raters, subjects, and categories. A real data example is also presented to illustrate the four methods.