Psychometrika

, Volume 49, Issue 1, pp 133–141 | Cite as

On approximate confidence intervals for measures of concordance

  • Albert D. Palachek
  • William R. Schucany
Article

Abstract

The use ofU-statistics based on rank correlation coefficients in estimating the strength of concordance among a group of rankers is examined for cases where the null hypothesis of random rankings is not tenable. The studentizedU-statistics is asymptotically distribution-free, and the Student-t approximation is used for small and moderate sized samples. An approximate confidence interval is constructed for the strength of concordance. Monte Carlo results indicate that the Student-t approximation can be improved by estimating the degrees of freedom.

Key words

Concordance confidence intervals jackknife rank correlation U-Statistics 

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References

  1. Ehrenberg, A. S. C. (1952). On sampling from a population of rankers.Biometrika, 39, 82–87.Google Scholar
  2. Feigin, P. D. and Cohen, A. (1978). On a model for concordance between judges.Journal of the Royal Statistical Society, Series B, 40, 203–213.Google Scholar
  3. Friedman, M. (1937). The use of ranks to avoid the assumption of normality implicit in the analysis of variance.Journal of the American Statistical Association, 32, 675–701.Google Scholar
  4. Hinkley, D. V. (1977). Jackknife confidence limits using Studentt approximations.Biometrika, 64, 21–28.Google Scholar
  5. Hoeffding, W. (1948). A class of statistics with asymptotically normal distribution.Annals of Mathematical Statistics, 19, 293–325.Google Scholar
  6. Kendall, M. G. (1938). A new measure of rank correlation.Biometrika, 30, 81–93.Google Scholar
  7. Kendall, M. G. and Babington-Smith, B. (1939). The problem ofm rankings.Annals of Mathematical Statistics, 10, 275–287.Google Scholar
  8. Kraemer, H. C. (1976). The small sample nonnull properties of Kendall's coefficient of concordance for normal populations.Journal of the American Statistical Association, 71, 608–613.Google Scholar
  9. Kraemer, H. C. and Korner, A. F. (1976). Statistical alternatives in assessing reliability, consistency, and individual differences in quantitative measures: application to behavioral measures of neonates.Psychological Bulletin, 83, 914–921.Google Scholar
  10. Mallows, C. L. (1957). Non-null ranking models I.Biometrika, 44, 114–130.Google Scholar
  11. Quade, D. (1972).Average internal rank correlation. Technical Report, Mathematical Centre, University of Amsterdam.Google Scholar
  12. Quade, D., Doerfler, D. L. and Flexner, A. L. (1977).Calculation of the variance in a test for concordance of two groups of judges. Technical Report, University of North Carolina, Chapel Hill.Google Scholar
  13. Sen, P. K. (1960). On some convergence properties ofU-statistics.Calcutta Statistical Association Bulletin, 10, 1–18.Google Scholar
  14. Spearman, C. (1904). The proof and measurement of association between two things.American Journal of Psychology, 15, 72–101.Google Scholar

Copyright information

© The Psychometric Society 1984

Authors and Affiliations

  • Albert D. Palachek
    • 1
  • William R. Schucany
    • 2
  1. 1.University of CincinnatiUSA
  2. 2.Department of StatisticsSouthern Methodist UniversityDallas

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