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Reliability for the Law of Comparative Judgment

Published online by Cambridge University Press:  01 January 2025

Harold Gulliksen  and
John W. Tukey
Harold Gulliksen
Affiliation:
Princeton University and Educational Testing Service
John W. Tukey
Affiliation:
Princeton University
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Abstract

A variance-components analysis is presented for paired comparisons in terms of three components: s, the scale value of the stimuli; d, a deviation from the linear model specified by the law of comparative judgment; and b, a binomial error component. Estimates are given for each of the three variances, σs2, σd2, and σb2. Several coefficients, analogous to reliability coefficients, based on these three variances are indicated. The techniques are illustrated in a replicated comparison of handwriting specimens.

Type
Original Paper
Information
Psychometrika , Volume 23 , Issue 2 , June 1958 , pp. 95 - 110
Copyright
Copyright © 1958 The Psychometric Society

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Footnotes

*

This research was jointly supported in part by Princeton University, the Office of Naval Research under contract Nonr-1858(15), and the National Science Foundation under grant NSF G-642, and in part by Educational Testing Service. Reproduction in whole or in part is permitted for any purpose of the United States Government.

Thanks are due to Ledyard Tucker and Frederic Lord for valuable suggestions on the development presented here.

References

Ayres, L. P. A scale for measuring the quality of handwriting of school children, New York: Russell Sage Foundation, 1912.Google Scholar
Bennett, C. A. and Franklin, N. L. Statistical analysis in chemistry and the chemical industry, New York: Wiley, 1954.Google Scholar
Cochran, W. G. The χ2 test of goodness of fit. Ann. math. Statist., 1952, 23, 315–345.CrossRefGoogle Scholar
Davies, O. L. Design and analysis of industrial experiments, New York: Hafner, 1954.Google Scholar
Duncan, A. J. Quality control and industrial statistics, Chicago: Richard D. Irwin, 1952.Google Scholar
Fisher, R. A. Statistical methods for research workers 10th ed., London: Oliver and Boyd, 1946.Google Scholar
Fisher, R. A. and Yates, F. Statistical tables for biological, agricultural and medical research, New York: Hafner, 1953.Google Scholar
Freeman, M. F. and Tukey, J. W. Transformations related to the angular and the square root. Ann. math. Statist., 1950, 21, 607–611.CrossRefGoogle Scholar
Hald, A. Statistical tables and formulas, New York: Wiley, 1952.Google Scholar
Kendall, M. G. Rank correlation methods, London: Griffin, 1948.Google Scholar
Kendall, M. G. and Babington-Smith, B. On the method of paired comparisons. Biometrika, 1940, 31, 324–345.CrossRefGoogle Scholar
Mood, A. M. Introduction to the theory of statistics, New York: McGraw-Hill, 1950.Google Scholar
Mosteller, F. Remarks on the method of paired comparisons. III. A test of significance for paired comparisons when equal standard deviations and equal correlations are assumed. Psychometrika, 1951, 16, 207–218.CrossRefGoogle Scholar
Thurstone, L. L. Psychophysical analysis. Amer. J. Psychol., 1927, 38, 368–389.CrossRefGoogle Scholar
Thurstone, L. L. A law of comparative judgment. Psychol. Rev., 1927, 34, 273–286.CrossRefGoogle Scholar
Tippett, L. H. C. The methods of statistics 4th ed., New York: Wiley, 1952.Google Scholar