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Remarks on the Method of Paired Comparisons: I. The Least Squares Solution Assuming Equal Standard Deviations and Equal Correlations

Published online by Cambridge University Press:  01 January 2025

Frederick Mosteller
Frederick Mosteller*
Affiliation:
Harvard University
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Abstract

Thurstone's Case V of the method of paired comparisons assumes equal standard deviations of sensations corresponding to stimuli and zero correlations between pairs of stimuli sensations. It is shown that the assumption of zero correlations can be relaxed to an assumption of equal correlations between pairs with no change in method. Further the usual approach to the method of paired comparisons Case V is shown to lead to a least squares estimate of the stimulus positions on the sensation scale.

Type
Original Paper
Information
Psychometrika , Volume 16 , Issue 1 , March 1951 , pp. 3 - 9
Copyright
Copyright © 1951 The Psychometric Society

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Footnotes

*

This research was performed in the Laboratory of Social Relations under a grant made available to Harvard University by the RAND Corporation under the Department of the Air Force, Project RAND.

References

Guilford, J. P. Psychometric Methods (pp. 227–228). New York: McGraw-Hill Book Co., 1936.Google Scholar
Guttman, L. An approach for quantifying paired comparisons and rank order. Annals of math. Stat., 1946, 17, 144–163.CrossRefGoogle Scholar
Horst, P. A method for determining the absolute affective values of a series of stimulus situations. J. educ. Psychol., 1932, 23, 418–440.CrossRefGoogle Scholar
Thurstone, L. L. Psychophysical analysis. Amer. J. Psychol., 1927, 38, 368–389.CrossRefGoogle Scholar