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Another Interpretation of a Model for Paired Comparisons

Published online by Cambridge University Press:  01 January 2025

Ralph A. Bradley
Ralph A. Bradley*
Affiliation:
Florida State University
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Abstract

The first contribution of this paper is to demonstrate that the paired-comparison model may be derived from a variety of different initial assumptions about the nature of paired comparisons, some of these assumptions appearing to the author to be more appropriate to a description of the preference-decision process than others. The second contribution of this paper is to note that the generalization of the model to triple comparisons chosen earlier is not the one compatible with the Lehmann model even though it possesses other desirable properties. Limited numerical calculations suggest that both models for triple comparisons give comparable results in applications. Their asymptotic properties should be similar.

Type
Original Paper
Information
Psychometrika , Volume 30 , Issue 3 , September 1965 , pp. 315 - 318
Copyright
Copyright © 1965 Psychometric Society

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Footnotes

*

Research supported by the Office of Naval Research contract number Nonr-988108, Task Order NR042-004. Reproduction in whole or in part is permitted for any purpose of the United States Government.

References

Bradley, R. A. and Terry, M. E. Rank analysis of incomplete block designs. I. The method of paired comparisons. Biometrika, 1952, 39, 324–345.Google Scholar
Bradley, R. A. Some statistical methods in taste testing and quality evaluation. Biometrics, 1953, 9, 22–38.CrossRefGoogle Scholar
Kendall, M. G. A new measure of rank correlation. Biometrika, 1938, 30, 81–93.CrossRefGoogle Scholar
Lehmann, E. L. The power of rank tests. Ann. math. Statist., 1953, 24, 23–43.CrossRefGoogle Scholar
Luce, R. D. Individual choice behavior, New York: Wiley, 1959.Google Scholar
Pendergrass, R. N. and Bradley, R. A. Ranking in triple comparisons. In Olkin, I. (Eds.), Contributions to probability and statistics. Stanford, Calif.: Stanford Univ. Press, 1960, 331–351.Google Scholar
Savage, I. R. Contributions to the theory of rank order statistics—the two-sample case. Ann. math. Statist., 1956, 27, 580–615.CrossRefGoogle Scholar
Thompson, W. A. Jr. Characterization of the Bradley-Terry model. Florida State Univ. Statistics Report (mimeo.).Google Scholar
Wilcoxon, F., Rhodes, L. J., and Bradley, R. A. Two sequential two-sample grouped rank tests with application to screening experiments. Biometrics, 1963, 19, 385–397.CrossRefGoogle Scholar