Journal of Classification

, Volume 33, Issue 3, pp 507–522 | Cite as

Kappa Coefficients for Circular Classifications

  • Matthijs J. Warrens
  • Bunga C. Pratiwi
Open Access


Circular classifications are classification scales with categories that exhibit a certain periodicity. Since linear scales have endpoints, the standard weighted kappas used for linear scales are not appropriate for analyzing agreement between two circular classifications. A family of kappa coefficients for circular classifications is defined. The kappas differ only in one parameter. It is studied how the circular kappas are related and if the values of the circular kappas depend on the number of categories. It turns out that the values of the circular kappas can be strictly ordered in precisely two ways. The orderings suggest that the circular kappas are measuring the same thing, but to a different extent. If one accepts the use of magnitude guidelines, it is recommended to use stricter criteria for circular kappas that tend to produce higher values.


Cohen’s kappa Weighted kappa Inter-rater agreement Linear scale Circular scale. 


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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.GIONUniversity of GroningenGroningenThe Netherlands
  2. 2.Leiden UniversityLeidenThe Netherlands

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