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On Approximate Confidence Intervals for Measures of Concordance

Published online by Cambridge University Press:  01 January 2025

Albert D. Palachek  and
William R. Schucany
Albert D. Palachek
Affiliation:
University of Cincinnati
William R. Schucany*
Affiliation:
Southern Methodist University
*
Requests for reprints should be sent to William R. Schucany, Department of Statistics, Southern Methodist University, Dallas, TX. 75275.
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Abstract

The use of U-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 studentized U-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.

Keywords

Concordanceconfidence intervalsjackkniferank correlationU-Statistics

Information

Type
Original Paper
Information
Psychometrika , Volume 49 , Issue 1 , March 1984 , pp. 133 - 141
Copyright
Copyright © 1984 The Psychometric Society

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Footnotes

Research partially supported on ONR Contract N00014-82-K-0207.

References

Ehrenberg, A. S. C. (1952). On sampling from a population of rankers. Biometrika, 39, 82–87.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Hinkley, D. V. (1977). Jackknife confidence limits using Studentt approximations. Biometrika, 64, 21–28.CrossRefGoogle Scholar
Hoeffding, W. (1948). A class of statistics with asymptotically normal distribution. Annals of Mathematical Statistics, 19, 293–325.CrossRefGoogle Scholar
Kendall, M. G. (1938). A new measure of rank correlation. Biometrika, 30, 81–93.CrossRefGoogle Scholar
Kendall, M. G. and Babington-Smith, B. (1939). The problem ofm rankings. Annals of Mathematical Statistics, 10, 275–287.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Mallows, C. L. (1957). Non-null ranking models I. Biometrika, 44, 114–130.CrossRefGoogle Scholar
Quade, D. (1972). Average internal rank correlation. Technical Report, Mathematical Centre, University of Amsterdam.Google Scholar
Quade, D., Doerfler, D. L. and Flexner, A. L. (1977). Calculation of the variance in a test for concordance of two groups of judges, Chapel Hill: University of North Carolina.Google Scholar
Sen, P. K. (1960). On some convergence properties ofU-statistics. Calcutta Statistical Association Bulletin, 10, 1–18.CrossRefGoogle Scholar
Spearman, C. (1904). The proof and measurement of association between two things. American Journal of Psychology, 15, 72–101.CrossRefGoogle Scholar