On association coefficients for 2 × 2 tables and properties that do not depend on the marginal distributions

Psychometrika

Volumn 73, Issue 4, 2008, Pages 777-789

  Warrens, Matthijs J ^a  

^a LEIDEN UNIVERSITY   (Netherlands)

Author keywords

Agreement indices; Cohen's kappa; Cole's C 7; Correction for chance; Correction for maximum value; Hubert Arabie adjusted Rand index; Loevinger's H; Phi coefficient; Resemblance measures; Yule's Q

Indexed keywords

EID: 62949147818     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11336-008-9070-3     Document Type: Article

References (47)

1. A.N. Albatineh M. Niewiadomska-Bugaj D. Mihalko 2006 On similarity indices and correction for chance agreement Journal of Classification 23 301 313
2. F.B. Baulieu 1989 A classification of presence/absence based dissimilarity coefficients Journal of Classification 6 233 246
3. F.B. Baulieu 1997 Two variant axiom systems for presence/absence based dissimilarity coefficients Journal of Classification 14 159 170
4. Benini, R. (1901). Principii di demografie. No. 29 of manuali Barbèra di science giuridiche sociali e poltiche. Firenzi: G. Barbèra.
5. R.L. Boyce P.C. Ellison 2001 Choosing the best similarity index when performing fuzzy set ordination on binary data Journal of Vegetational Science 12 711 720
6. R.L. Brennan R.J. Light 1974 Measuring agreement when two observers classify people into categories not defined in advance British Journal of Mathematical and Statistical Psychology 27 154 163
7. N.J. Castellan 1966 On the estimation of the tetrachoric correlation coefficient Psychometrika 31 67 73
8. J. Cohen 1960 A coefficient of agreement for nominal scales Educational and Psychological Measurement 20 37 46
9. L.C. Cole 1949 The measurement of interspecific association Ecology 30 411 424
10. max∈ Psychometrika 24 89 91
11. E.C. Davenport N.A. El-Sanhurry 1991 Phi/phimax: review and synthesis Educational and Psychological Measurement 51 821 828
12. L.R. Dice 1945 Measures of the amount of ecologic association between species Ecology 26 297 302
13. P.G.N. Digby 1983 Approximating the tetrachoric correlation coefficient Biometrics 39 753 757
14. D.R. Divgi 1979 Calculation of the tetrachoric correlation coefficient Psychometrika 44 169 172
15. J.M. Duarte J.B. Santos L.C. Melo 1999 Comparison of similarity coefficients based on RAPD markers in the common bean Genetics and Molecular Biology 22 427 432
16. A.W.F. Edwards 1963 The measure of association in a 2×2 table Journal of the Royal Statistical Society, Series A 126 109 114
17. J.L. Fleiss 1975 Measuring agreement between two judges on the presence or absence of a trait Biometrics 31 651 659
18. L.A. Goodman W.H. Kruskal 1954 Measures of association for cross classifications Journal of the American Statistical Association 49 732 764
19. J.C. Gower P. Legendre 1986 Metric and Euclidean properties of dissimilarity coefficients Journal of Classification 3 5 48
20. J.P. Guilford 1965 The minimal phi coefficient and the maximal phi Educational and Psychological Measurement 25 3 8
21. Z. Hubálek 1982 Coefficients of association and similarity based on binary (presence-absence) data: an evaluation Biological Reviews 57 669 689
22. L.J. Hubert P. Arabie 1985 Comparing partitions Journal of Classification 2 193 218
23. S.H. Hurlbert 1969 A coefficient of interspecific association Ecology 50 1 9
24. P. Jaccard 1912 The distribution of the flora in the Alpine zone The New Phytologist 11 37 50
25. S. Janson J. Vegelius 1981 Measures of ecological association Oecologia 49 371 376
26. S. Janson J. Vegelius 1982 The J-index as a measure of nominal scale response agreement Applied Psychological Measurement 6 111 121
27. K. Krippendorff 1987 Association, agreement, and equity Quality and Quantity 21 109 123
28. Loevinger, J.A. (1947). A systematic approach to the construction and evaluation of tests of ability. Psychometrika Monograph No. 4.
29. J.A. Loevinger 1948 The technique of homogeneous tests compared with some aspects of scale analysis and factor analysis Psychological Bulletin 45 507 530
30. A.E. Maxwell A.E.G. Pilliner 1968 Deriving coefficients of reliability and agreement for ratings British Journal of Mathematical and Statistical Psychology 21 105 116
31. Mokken, R.J. (1971). A theory and procedure of scale analysis. Hague: Mouton.
32. A. Ochiai 1957 Zoogeographic studies on the soleoid fishes found in Japan and its neighboring regions Bulletin of the Japanese Society for Fish Science 22 526 530
33. K. Pearson 1900 Mathematical contributions to the theory of evolution. VII. On the correlation of characters not quantitatively measurable Philosophical Transactions of the Royal Society of London, Series A 195 1 47
34. Popping, R. (1983). Overeenstemmingsmaten Voor Nominale Data. Unpublished doctoral dissertation, Rijksuniversiteit Groningen, Groningen, The Netherlands.
35. R. Popping 1984 Traces of agreement. On some agreement indices for open-ended questions Quality and Quantity 18 147 158
36. W. Rand 1971 Objective criteria for the evaluation of clustering methods Journal of the American Statistical Association 66 846 850
37. 8 coefficients of interspecific association Ecology 50 1 9
38. Sijtsma, K., & Molenaar, I.W. (2002). Introduction to nonparametric item response theory. Thousand Oaks: Sage.
39. G.G. Simpson 1943 Mammals and the nature of continents American Journal of Science 24 11 31
40. R.R. Sokal C.D. Michener 1958 A statistical method for evaluating systematic relationships University of Kansas Science Bulletin 38 1409 1438
41. Sokal, R.R., & Sneath, P.H. (1963). Principles of numerical taxonomy. San Francisco: Freeman.
42. D. Steinley 2004 Properties of the Hubert-Arabie adjusted Rand index Psychological Methods 9 386 396
43. Warrens, M.J. (in press). On the equivalence of Cohen's kappa and the Hubert-Arabie adjusted Rand index. Journal of Classification.
44. G.U. Yule 1900 On the association of attributes in statistics Philosophical Transactions of the Royal Society A 75 257 319
45. G.U. Yule 1912 On the methods of measuring the association between two attributes Journal of the Royal Statistical Society 75 579 652
46. Zegers, F.E. (1986). A general family of association coefficients. Unpublished doctoral dissertation, Rijksuniversiteit Groningen, Groningen, The Netherlands.
47. P.V. Zysno 1997 The modification of the phi-coefficient reducing its dependence on the marginal distributions Methods of Psychological Research Online 2 41 52