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Factoring Test Scores and Implications for the Method of Averages

Published online by Cambridge University Press:  01 January 2025

Karl J. Holzinger
Karl J. Holzinger*
Affiliation:
The University of Chicago
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Abstract

The general procedure and detailed steps for attaining complete factor analyses of scores are presented. Both orthogonal and oblique factors are considered. It is shown that a single average by conventional procedure gives an incomplete summarization of the data when the rank exceeds one. There should be as many averages as there are common factors.

Type
Original Paper
Information
Psychometrika , Volume 9 , Issue 3 , September 1944 , pp. 155 - 167
Copyright
Copyright © 1944 The Psychometric Society

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References

* The reason the analysis of scores has been overlooked so long is probably due to the fact that alternate interpretations of the word “variable” have not been clear. If w 1 denotes the variable “height” we may imagine a continuum on which an indefinitely large number of values may be indicated. If a finite set of heights

W1i: ‖ 62, 63, 69, 64, ...,68 ‖

is given, this row matrix or “vector” may also be considered as a variable. It is this latter interpretation of “variable” that makes possible the geometric vector representation of variables, and suggests the factoring of scores instead of correlations.

* Karl J. Holzinger and H. H. Harman, Factor Analysis, Appendix A, Chicago: University of Chicago Press, 1941.

* Ibid., pp. 325-27.

† Ibid., pp. 386-87.

‡ Ibid., p. 252.