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The Effects of Selection in Factor Analysis

Published online by Cambridge University Press:  01 January 2025

L. L. Thurstone
L. L. Thurstone*
Affiliation:
The University of Chicago
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Abstract

Factorial results are affected by selection of subjects and by selection of tests. It is shown that the addition of one or more tests which are linear combinations of tests already in a battery causes the addition of one or more incidental factors. If the given test battery reveals a simple structure, the addition of tests which are linear combinations of the given tests leaves the structure unaffected unless the number of incidental factors is so large that the common factors become indeterminate.

Type
Original Paper
Information
Psychometrika , Volume 10 , Issue 3 , September 1945 , pp. 165 - 198
Copyright
Copyright © 1945 Psychometric Society

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References

* The importance of experimental dependence in factor analysis was first pointed out by Ledyard Tucker.

* Thomson, Godfrey tt. “The influence of univariate selection on the factorial analysis of ability. Brit. J. Psych. (Gen. Sec.) 1938, 28, Part 4.

Ledermann, Walter. Note on Professor Godfrey H. Thomson’s article “The influence of univariate selection on the factorial analysis of ability.” Brit. J. Psychol. (Gen. Sec.) 1938, 29, Part 1.

Thomson, Godfrey H. and Ledermann, Walter. The influence of multivariate selection on the factorial analysis of ability. Brit. J. Psychol. (Gen Sec.) 1939, 29, Part 3.

Thomson, Godfrey H. The factorial analysis of human ability, Chapters 11 and 12.

* Godfrey Thomson, who has contributed fundamental theory on the problem of univariate and multivariate selection in relation to factor analysis, has expressed doubt as to whether the primary factors can be interpreted as basic and identifiable psychological processes. His reason is mainly that the correlations between the primary factors of a simple structure are altered and determined in part by the conditions of selection and, further that incidental factors can be added by certain conditions of multivariate selection. Our interpretation is that the primary factors represent the same basic processes in different conditions of selection and that it is the correlations between these parameters that are altered rather than the fundamental meaning of the parameters themselves. The incidental factors can be classed with the residual factors which reflect the conditions of particular experiments. These extraneous factors do not show the invariant characteristics that have been shown for the more basic primary factors. In presenting Godfrey Thomson’s theoretical work on the selection problem, we are giving a less pessimistic interpretation of the factorial results.

* Thomson, Godfrey. The factorial analysis of human ability, page 187.

* Ibid.