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Journal of Probability and Statistics
Volume 2013, Article ID 325831, 9 pages
Research Article

Weighted Kappas for Tables

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

Received 10 April 2013; Accepted 26 May 2013

Academic Editor: Ricardas Zitikis

Copyright © 2013 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.


Weighted kappa is a widely used statistic for summarizing inter-rater agreement on a categorical scale. For rating scales with three categories, there are seven versions of weighted kappa. It is shown analytically how these weighted kappas are related. Several conditional equalities and inequalities between the weighted kappas are derived. The analytical analysis indicates that the weighted kappas are measuring the same thing but to a different extent. One cannot, therefore, use the same magnitude guidelines for all weighted kappas.