Confidence Intervals for Gamma-Family Measures of Ordinal Association

Psychological Methods

Volumn 12, Issue 2, 2007, Pages 185-204

  Woods, Carol M ^a  

^a WASHINGTON UNIVERSITY   (United States)

Author keywords

confidence interval; ordinal; ordinal association; ordinal measurement; standard error

Indexed keywords

ARTICLE; CONFIDENCE INTERVAL; HUMAN; NOMOGRAM; PSYCHOLOGIC TEST; PSYCHOMETRY; REPRODUCIBILITY; STATISTICS;

CONFIDENCE INTERVALS; HUMANS; NOMOGRAMS; PSYCHOLOGICAL TESTS; PSYCHOMETRICS; REPRODUCIBILITY OF RESULTS;

EID: 34548437715     PISSN: 1082989X     EISSN: None     Source Type: Journal    
DOI: 10.1037/1082-989X.12.2.185     Document Type: Article

References (50)

1. Agresti A. The effect of category choice on some ordinal measures of association. Journal of the American Statistical Association 71 (1976) 49-55
2. Agresti A. Analysis of ordinal categorical data (1984), Wiley, New York
3. Agresti A. Categorical data analysis. 2nd ed. (2002), Wiley, Hoboken, NJ
4. Bonett D.G., and Wright T.A. Sample size requirements for estimating Pearson, Kendall, and Spearman correlations. Psychometrika 65 (2000) 23-28
5. Brown M.B., and Benedetti J.K. Sampling behavior of tests for correlation in two-way contingency tables. Journal of the American Statistical Association 72 (1977) 309-315
6. Caruso J.C., and Cliff N. Empirical size, coverage, and power of confidence intervals for Spearman's rho. Educational and Psychological Measurement 57 (1997) 637-654
7. Chandra M.J. Statistical quality control (2000), CRC Press, Boca Raton, FL
8. Cliff N. Ordinal methods for behavioral data analysis (1996), Erlbaum, Mahwah, NJ
9. Cliff N., and Charlin V. Variances and covariances of Kendall's tau and their estimation. Multivariate Behavioral Research 26 (1991) 693-707
10. Clogg C.C., and Shihadeh E.S. Statistical models for ordinal variables (1994), Sage, Thousand Oaks, CA
11. Costner H.L. Criteria for measures of association. American Sociological Review 30 (1965) 341-353
12. Costner H.L. Reply to Somers. American Sociological Review 33 (1968) 292
13. Daniels H.E. The relation between measures of correlation in the universe of sample permutations. Biometrika 33 (1944) 129-135
14. Daniels H.E., and Kendall M.G. The significance of rank correlations where parental correlation exists. Biometrika 34 (1947) 197-208
15. David F.N., and Mallows C.L. The variance of Spearman's rho in normal samples. Biometrika 48 (1961) 19-28
16. Fieller E.C., Hartley H.O., and Pearson E.S. Tests for rank correlation coefficients: I. Biometrika 44 (1957) 470-481
17. Fieller E.C., and Pearson E.S. Tests for rank correlation coefficients: II. Biometrika 48 (1961) 29-40
18. Freeman L.C. Order-based statistics and monotonicity: A family of ordinal measures of association. Journal of Mathematical Sociology 12 (1986) 49-69
19. Gonzalez R., and Nelson T.O. Measuring ordinal association in situations that contain tied scores. Psychological Bulletin 119 (1996) 159-165
20. Goodman L.A., and Kruskal W.H. Measures of association for cross classifications. Journal of the American Statistical Association 49 (1954) 732-764
21. Goodman L.A., and Kruskal W.H. Measures of association for cross classifications: IV. Simplification of asymptotic variances. Journal of the American Statistical Association 67 (1972) 131-146
22. Higgins J.J. An introduction to modern nonparametric statistics (2004), Brooks/Cole, Pacific Grove, CA
23. Kendall M.G. A new measure of rank correlation. Biometrika 30 (1938) 81-93
24. Kendall M.G. The treatment of ties in ranking problems. Biometrika 33 (1945) 239-251
25. Kendall M.G. Rank correlation methods. 4th ed. (1970), Griffin, London
26. Kim J. Predictive measures of ordinal association. American Journal of Sociology 76 (1971) 891-907
27. Knuth D.E. The art of computer programming: Vol. 2. Seminumerical algorithms (1981), Addison-Wesley, Reading, MA
28. Kraemer H.C. On estimation and hypothesis testing problems for correlation coefficients. Psychometrika 40 (1975) 473-485
29. Leik R.K., and Gove W.R. The conception and measurement of asymmetric monotonic relationships in sociology. American Journal of Sociology 74 (1969) 696-709
30. Leik R.K., and Gove W.R. Integrated approach to measuring association. Sociological Methodology 3 (1971) 279-301
31. Liebetrau A.M. Measures of association (1983), Sage, Newbury Park, CA
32. Long J.D., and Cliff N. Confidence intervals for Kendall's tau. British Journal of Mathematical and Statistical Psychology 50 (1997) 31-41
33. Lovie A.D. Who discovered Spearman's rank correlation?. British Journal of Mathematical and Statistical Psychology 48 (1995) 255-269
34. Marsaglia G., and Zaman A. A new class of random number generators. Annals of Applied Probability 1 (1991) 462-480
35. Olsson U. Maximum likelihood estimation of the polychoric correlation coefficient. Psychometrika 44 (1979) 443-460
36. Pearson K. 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 (1901) 1-47
37. Pearson K., and Pearson E.S. On polychoric coefficients of correlation. Biometrika 14 (1922) 127-156
38. Quade D. Nonparametric partial correlation. In: Blalock H.M. (Ed). Measurement in the social sciences: Theories and strategies (1974), Aldine Publishing, Chicago 369-398
39. Rosenthal I. Distribution of the sample version of the measure of association, gamma. Journal of the American Statistical Association 61 (1966) 440-453
40. Somers R.H. A new asymmetric measure of association for ordinal variables. American Sociological Review 27 (1962) 799-811
41. Somers R.H. A similarity between Goodman and Kruskal's tau and Kendall's tau with a partial interpretation of the latter. Journal of the American Statistical Association 57 (1962) 804-812
42. Somers R.H. On the measurement of association. American Sociological Review 33 (1968) 291-292
43. Spearman C.S. The proof and measurement of association between two things. American Journal of Psychology 15 (1904) 72-101
44. Stevens S.S. On the theory of scales of measurement. Science 103 (1946, June 7) 677-680
45. Stuart A. The estimation and comparison of strengths of association in contingency tables. Biometrika 40 (1953) 105-110
46. Velleman P.F., and Wilkinson L. Nominal, ordinal, interval, and ratio typologies are misleading. American Statistician 47 (1993) 65-72
47. Wilson T.P. A proportional-reduction-in-error interpretation for Kendall's tau-b. Social Forces 47 (1969) 340-342
48. Wilson T.P. A critique of ordinal variables. Social Forces 49 (1971) 432-444
49. Wilson T.P. Measures of association for bivariate ordinal hypotheses. In: Blalock H.M. (Ed). Measurement in the social sciences: Theories and strategies (1974), Aldine Publishing, Chicago 327-342
50. Yule G.U. On the association of attributes in statistics: With illustrations from the material of the Childhood Society. Philosophical Transactions of the Royal Society of London, Series A 194 (1900) 257-319