Table of Contents
Advances in Statistics
Volume 2014, Article ID 759527, 6 pages
Research Article

On Marginal Dependencies of the 2 × 2 Kappa

Methodology and Statistics Unit, Institute of Psychology, Leiden University, P.O. Box 9555, 2300 RB Leiden, The Netherlands

Received 19 July 2014; Accepted 1 November 2014; Published 19 November 2014

Academic Editor: Lynn Kuo

Copyright © 2014 Matthijs J. Warrens. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.