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Approaches to Univocal Factor Scores

Published online by Cambridge University Press:  01 January 2025

J. P. Guilford  and
William B. Michael
J. P. Guilford
Affiliation:
University of Southern California Princeton University and the College Entrance Examination Board
William B. Michael
Affiliation:
University of Southern California Princeton University and the College Entrance Examination Board
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Abstract

Two current methods of deriving common-factor scores from tests are briefly examined and rejected. One of these estimates a score from a multiple-regression equation with as many terms as there are tests in the battery. The other limits the equation to a few tests heavily saturated with the desired factor, with or without tests used to suppress the undesired factors. In the proposed methods, the single best test for each common factor is the starting point. Such a test ordinarily has a very few undesired factors to be suppressed, frequently only one. The suppression test should be univocal, or nearly so. Fortunately, there are relatively univocal tests for factors that commonly require suppression. Equations are offered by which the desired-factor test and a single suppression test can be weighted in order to achieve one or more objectives. Among the objectives are (1) maximizing the desired factor variance, (2) minimizing the undesired factor variance, (3) a compromise, in which the undesired variance is materially reduced without loss in desired variance, and (4) a change to any selected ratio of desired to undesired variance. A more generalized solution is also suggested. The methods can be extended in part to the suppression of more than one factor. Equations are derived for the suppression of two factors.

Type
Original Paper
Information
Psychometrika , Volume 13 , Issue 1 , March 1948 , pp. 1 - 22
Copyright
Copyright © 1948 The Psychometric Society

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Footnotes

*

This paper is based upon a report read by the senior author at a joint meeting of the Western Psychological Association and the Institute of Mathematical Statistics at San Diego, California, June 19, 1947.

References

Guilford, J. P. Army Air Forces Aviation Psychology Program Research Reports, Washington, D. S.: M. S. Government Printing Office, 1947.Google Scholar
Guilford, J. P. and Zimmerman, W. S. The Guilford-Zimmerman Aptitude Survey, Beverly Hills: Sheridan Supply Company, 1947.Google Scholar
Thurstone, L. L. Primary mental abilities, Chicago: University of Chicago Press, 1938.Google Scholar