Hostname: page-component-7dd5485656-hw7sx Total loading time: 0 Render date: 2025-10-31T04:43:19.439Z Has data issue: false hasContentIssue false
  • English
  • Français

A Least Squares Solution for Paired Comparisons with Incomplete Data

Published online by Cambridge University Press:  01 January 2025

Harold Gulliksen
Harold Gulliksen*
Affiliation:
Princeton University and Educational Testing Service
Get access Rights & Permissions [Opens in a new window]

Abstract

A precise and rapid procedure has been devised for dealing with a matrix of incomplete data in paired comparisons. This method should increase the general applicability of paired comparisons since experiments involving large numbers of stimuli may now be shortened to feasible experimental proportions. Also, we may now use sets of stimuli which cover a wide range, resulting in a considerable number of 100 per cent vs. 0 per cent judgments, and still give a precise solution depending equally on each of the observations.

Information

Type
Original Paper
Information
Psychometrika , Volume 21 , Issue 2 , June 1956 , pp. 125 - 134
Copyright
Copyright © 1956 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

*

This study was supported in part by the Office of Naval Research Contract N6onr-270-20 with Princeton University and by the National Science Foundation Grant G-642. The opinions expressed are, of course, those of the author and do not represent attitudes or policies of the Office of Naval Research or of the National Science Foundation.

†

The author wishes to acknowledge helpful suggestions and comments received from Frederic M. Lord, Warren S. Torgerson, and Ledyard R Tucker. Thanks are also due to Mrs. Gertrude Diederich for some of the tabulating and computing for the illustrative problem.

References

Garner, W. R., and Hake, H. W.. The amount of information in absolute judgments. Psychol. Rev., 1951, 58, 446–459CrossRefGoogle Scholar
Horst, P. The prediction of personal adjustment. Social Science Research Council Bulletin No. 48, 1941.Google Scholar
Kempthorne, O. The design and analysis of experiments (pp. 96–98). New York: Wiley, 1952Google Scholar
Kendall, M. G. The advanced theory of statistics, Vol. II (pp. 229–230). London: Griffin, 1948Google Scholar
Mosteller, F. Remarks on the method of paired comparisons: I. The least squares solution assuming equal standard deviations and equal correlations. Psychometrika, 1951, 16, 3–9CrossRefGoogle Scholar
Thurstone, L. L. The zero point in scaling. (Unpublished study.)Google Scholar