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Factor Analysis and the Index of Clustering

Published online by Cambridge University Press:  01 January 2025

Gale Young
Gale Young*
Affiliation:
The University of Chicago
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Abstract

The initial problem of factor analysis is described as a search for clustering of the test vectors. Curves are developed which give a visual picture of the clustering tendency, and an index of clustering is derived which provides a simple estimate for the number of factors.

Type
Original Paper
Information
Psychometrika , Volume 4 , Issue 3 , September 1939 , pp. 201 - 207
Copyright
Copyright © 1939 Psychometric Society

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Footnotes

*

Based, in part, on a paper “Matrix Approximation Criteria” read at the District meeting of the Psychometric Society, Chicago, April 3, 1937. The author wishes to acknowledge suggestions gained in conversations with Dr. A. S. Householder and Mr. Clyde Coombs, of the University of Chicago.

References

Any power or root of ζ would vary from 0 to 1 monotonically with ζ, and hence would also serve as an index. In an application to theory of single tests it has been found that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\sqrt[4]{\zeta }$$ \end{document} makes close contact with the usual index of reliability (Young, Gale and Libby, J. E. P. On the index of reliability. Unpublished manuscript).Google Scholar
Dickson, L. E. First course in the theory of equations, New York: John Wiley & Sons, 1922.Google Scholar
Mosier, C. I. Influence of chance errors on simple structure. Psychometrika, 1939, 4, 33–44.CrossRefGoogle Scholar