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Changes in Common-Factor Loadings as Tests are Altered Homogeneously in Length

Published online by Cambridge University Press:  01 January 2025

J. P. Guilford  and
William B. Michael
J. P. Guilford
Affiliation:
University of Southern California
William B. Michael
Affiliation:
Princeton University
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Abstract

Formulas are derived by which, given the factor loadings and the internal reliability of a test of unit length, the following estimates can be made: (1) the common-factor loadings for a similar (homogeneous) test of length n; (2) the number of times (n) that a test needs to be lengthened homogeneously to achieve a factor loading of a desired magnitude; and (3) the correlation between two tests, either or both of which have been altered in length, as a function of (a) the new factor loadings in the altered tests or (b) the original loadings in the unit-length tests. The appropriate use of the derived formulas depends upon the fulfillment of four assumptions enumerated.

Type
Original Paper
Information
Psychometrika , Volume 15 , Issue 3 , September 1950 , pp. 237 - 249
Copyright
Copyright © 1950 The Psychometric Society

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Footnotes

*

This article is based on a paper read by the authors at the annual meeting of the Western Psychological Association in Eugene, Oregon, June 25, 1949.

References

Kelley, Truman L. Fundamentals of statistics, Cambridge: Harvard Univ. Press, 1947.Google Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947.Google Scholar
Tucker, Ledyar. The role of correlated factors in factor analysis. Psychometrika, 1940, 5, 141–152.CrossRefGoogle Scholar