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On the Interpretation of Common Factors: A Criticism and a Statement

Published online by Cambridge University Press:  01 January 2025

H. A. Reyburn
Affiliation:
University of Cape Town
J. G. Taylor
Affiliation:
University of Cape Town

Abstract

The concept of simple structure is criticized for lack of objectivity and for failure to produce invariance of (a) factor loadings under change of battery, and (b) individual scores on primary traits under change of tests. It is also criticized on the grounds that simple structure yields at best the factors which were put in and that, by suitable manipulation of tests, any set of factors may be represented in a battery by tests which will yield a simple structure. A procedure for rotation is developed which locates the first rotated axis to pass through a cluster of tests which, by hypothesis, contain a common factor and to project all tests into a hyperplane orthogonal to this factor. The second factor is then located to pass through the projections of a second cluster of tests defining the second factor, and so on, until all hypothecated factors have been located. Any residual interrelations may then be rotated graphically to the most plausible arrangement.

Type
Original Paper
Copyright
Copyright © 1943 The Psychometric Society

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References

* Reyburn, H. A. and Taylor, J. G. Some factors of intelligence. Brit. J. Psychol. (General Section), 1941, 31, 259 f.

* A mathematical account of the procedure described here is given in the appendix to this article.

* Reyburn, H. A. and Taylor, J. G. Some factors of personality. Brit. J. Psychol. (General Section), 1939, 30, 159 ft.