Journal of Classification

, Volume 25, Issue 2, pp 177–183 | Cite as

On the Equivalence of Cohen’s Kappa and the Hubert-Arabie Adjusted Rand Index

  • Matthijs J. Warrens


It is shown that one can calculate the Hubert-Arabie adjusted Rand index by first forming the fourfold contingency table counting the number of pairs of objects that were placed in the same cluster in both partitions, in the same cluster in one partition but in different clusters in the other partition, and in different clusters in both, and then computing Cohen’s κ on this fourfold table.


Correction for chance agreement Partitions Clustering method Matching table Simple matching coefficient Similarity indices Resemblance measures 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. ALBATINEH, A.N., NIEWIADOMSKA-BUGAJ, M., and MIHALKO, D. (2006), “On Similarity Indices and Correction for Chance Agreement,” Journal of Classification, 23, 301–313.CrossRefMathSciNetGoogle Scholar
  2. BATAGELJ, V., and BREN, M. (1995), “Comparing Resemblance Measures,” Journal of Classification, 12, 73–90.zbMATHCrossRefMathSciNetGoogle Scholar
  3. BAULIEU, F.B. (1989), “A Classification of Presence/Absence Based Dissimilarity Coefficients,” Journal of Classification, 6, 233–246.zbMATHCrossRefMathSciNetGoogle Scholar
  4. COHEN, J. (1960), “A Coefficient of Agreement for Nominal Scales,” Educational and Psychological Measurement, 20, 37–46.CrossRefGoogle Scholar
  5. FOWLKES, E.B., and MALLOWS, C. L. (1983), “A Method for Comparing Two Hierarchical Clusterings,” Journal of the American Statistical Association, 78, 553–569.zbMATHCrossRefGoogle Scholar
  6. GOWER, J.C., and LEGENDRE, P. (1986), “Metric and Euclidean Properties of Dissimilarity Coefficients,” Journal of Classification, 3, 5–48.zbMATHCrossRefMathSciNetGoogle Scholar
  7. HUBERT, L.J., and ARABIE, P. (1985), “Comparing Partitions,” Journal of Classification, 2, 193–218.CrossRefGoogle Scholar
  8. RAND, W.M. (1971), “Objective Criteria for the Evaluation of Clustering Methods,” Journal of the American Statistical Association, 66, 846–850.CrossRefGoogle Scholar
  9. SALTSTONE, R., and STANGE, K. (1996), “A Computer Program to Calculate Hubert and Arabie’s Adjusted Rand Index,” Journal of Classification, 13, 169–172.CrossRefGoogle Scholar
  10. SOKAL, R.R., and MICHENER, C.D. (1958), “A Statistical Method for Evaluating Systematic Relationships,” University of Kansas Science Bulletin, 38, 1409–1438.Google Scholar
  11. STEINLEY, D. (2004), “Properties of the Hubert-Arabie Adjusted Rand Index,” Psychological Methods, 9, 386–396.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Psychometrics and Research Methodology GroupLeiden University, Institute for Psychological Research, Leiden UniversityLeidenThe Netherlands

Personalised recommendations