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The Foundations of Psychometry: Four Factor Systems

Published online by Cambridge University Press:  01 January 2025

Wm. Stephenson
Wm. Stephenson*
Affiliation:
From the Psychology Laboratory, University of London
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Abstract

Four methods of factorizing the fundamental matrices used in factor analysis are described and illustrated. The first is represented by the techniques already developed. The second is the obverse factor technique. The third and fourth methods are variants of the first and second. The implications of each method for different schools of psychology are pointed out. The methods are complementary, not competitive.

Type
Original Paper
Information
Psychometrika , Volume 1 , Issue 3 , September 1936 , pp. 195 - 209
Copyright
Copyright © 1936 The Psychometric Society

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Footnotes

*

Stephenson, W. The Inverted Factor Technique. Brit. J. Psyehol. XXVI, 1936, p. 344. (Other papers are referred to in the Sequel).

References

* Line, W. Process-Psychology – Individual and General. Psychol. Rev. XL. p. 256.

† Lewin, K. Dynamic Theory of Personality, Chap I. (McGraw-Hill) 1935.

§ Thurstone, L. L. The Vectors of Mind. p. 46. (Chicago Univ. Press )1935.

* The word does not imply that the attributes are distinct, unique, isolated or unitary, in the sense of not having correlation with any others.

* The matrices can be built up in other ways: thus individuals might be measured for their Spearman, g, p, o, w, f, c, etc. in standard terms, and then correlated amongst themselves with these factor estimates as population.

† It seems worth while as an example to pursue an investigation for such measurements. I hope to publish such data in due course.

† As nearly whole as the 100 measureanents allow: a large population of such measurements would allow a still closer approximation to the whole physical person.

* Different units of measurement could be used for each person, so long as the same unit is used for all the measurements of the one person. The units could be inches for one person, centimetres for another, feet for another etc.

† Such as, that if only one factor covered the matrix for system (1), no broad factor could appear in system (3) in the above example.

* Line, W. loc. cir.

* So far as the population of persons is concerned it perpetrates no such distortion.

† Peterman, B. The Gestalt Theory. (Kegan Paul, London, 1932). (I refer to the “principle of the primacy of the whole over its parts”.)

* See Stephenson, W. A new application of correlation to averages. Brit. J. Educ. Psych. VI. 1936. p. 43.

† I shall indicate in due course that factors in system (2) need not be analyzed orthogonally, and that thereby the “ ‘total’ situation” is retained.

* The word ‘whole’ must be taken here to mean relational together with ‘absolute’ aspects of the physical measurements.

† This is merely a literal description of what a theorem such as the Spearman two-factor (a common g and specific s factors) means.

‡ In the Spearman two-factor theorem the amount is:

* The words refer here, and always in the sequel, to differences with respect to a population of persons.

† The word ‘type’ is here and throughout this paper used in a special sense, so far as I know never before used. It is the subject of a paper to follow this one.

‡ See examples in my various introductory papers.

* The word again refers only to the mode of thinking about the attributes. Systems (1) and (4) proceed to show whether the attributes vary proportionately, and when any two so vary neither can be regarded as isolated or distinct.