Paired Comparisons for Multiple Characteristics: An ANOCOVA Approach

  • Pranab Kumar Sen
Chapter

Abstract

An analysis of covariance model is developed for paired comparisons to situations in which responses (on a preference order) to paired comparisons are obtained on some primary as well as concomitant traits. Along with the general rationality of the proposed test, its asymptotic properties are studied.

Key Words

Association parameters Bradley-Terry model concordance dichotomous attributes MANOCOVA 
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References

  1. Bahadur, R.R. (1961). A representation of the joint distribution of responses to n dichotomous items. In: H. Solomon, Ed., Studies in Item Analysis and Prediction, Stanford, CA: Stanford Univ. Press, pp. 158–176.Google Scholar
  2. Bradley, R.A., and Terry, M.E. (1952). Rank analysis of incomplete block designs, I. The method of paired comparison. Biometrika, 39, 324–345.MathSciNetMATHGoogle Scholar
  3. Chatterjee, S.K. (1966). A bivariate sign-test for location. Ann. Math. Statist., 37, 1771–1782.MathSciNetMATHCrossRefGoogle Scholar
  4. David, H.A. (1988). The Method of Paired Comparisons. Second Edition. New York: Oxford Univ. Press.Google Scholar
  5. Davidson, R.R., and Bradley, R.A. (1969). Multivariate paired comparisons: The extension of a univariate model and associated estimation and test procedures. Biometrika, 56, 81–94.MATHCrossRefGoogle Scholar
  6. Davidson, R.R., and Bradley, R.A. (1970). Multivariate paired comparisons: Some large sample results on estimation and test of equality of preference. In: M. L. Puri, Ed., Nonparametric Techniques in Statistical Inference, New York: Cambridge Univ. Press, pp. 111–125.Google Scholar
  7. Huber, P.J. (1965). A robust version of the probability ratio test. Ann. Math. Statist., 36, 1753–1758.MathSciNetMATHCrossRefGoogle Scholar
  8. Keating, J.P., Mason, R.L., and Sen, P.K. (1993). Pitman’s Measure of Closeness: A Comparison of Statistical Estimators. Philadelphia: SIAM.MATHGoogle Scholar
  9. Mantel, N., and Haenszel, W. (1959). Statistical aspects of the analysis of data from retrospective studies of disease. J. Nat. Cancer Inst., 22, 719–748.Google Scholar
  10. Pitman, E.J.G. (1937). The closest estimate of statistical parameters. Proc. Cambridge Phil. Soc., 33, 212–222.CrossRefGoogle Scholar
  11. Puri, M.L., and Sen, P.K. (1985). Nonparametric Methods in General Linear Models. New York: Wiley.MATHGoogle Scholar
  12. Scheffé, H. (1959). The Analysis of Variance. New York: Wiley.MATHGoogle Scholar
  13. Sen, P.K. (1988). Combination of statistical tests for multivariate hypotheses against restricted alternatives. In: S. Dasgupta and J.K. Ghosh, Eds., Multivariate Analysis, Calcutta: ISI, India, pp. 377–402.Google Scholar
  14. Sen, P.K. (1993). Perspectives in multivariate nonparametrics: conditional functionals and ANOCOVA models. Sankhyā Ser. A, 55, 516–532.MATHGoogle Scholar
  15. Sen, P.K., and David, H.A. (1968). Paired comparisons for paired characteristics, Ann. Math. Statist., 39, 200–208.MathSciNetMATHCrossRefGoogle Scholar
  16. Sen, P.K., and Singer, J.M. (1993). Large Sample Methods in Statistics: An Introduction with Applications. New York: Chapman-Hall.MATHGoogle Scholar
  17. Wald, A. (1943). Tests of statistical hypotheses concerning several parameters when the number of observations is large. Trans. Amer. Math. Soc., 54, 426–482.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1996

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  • Pranab Kumar Sen

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