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Separation of Data as a Principle in Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Chester W. Harris
Chester W. Harris*
Affiliation:
University of Wisconsin
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Abstract

Two systems of factor analysis—factoring correlations with units in the diagonal cells and factoring correlations with communalities in the diagonal cells—are considered in relation to the commonly used statistical procedure of separating a set of data (scores) into two or more parts. It is shown that both systems of factor analysis imply the separation of the observed data into two orthogonal parts. The matrices used to achieve the separation differ for the two systems of factor analysis.

Type
Original Paper
Information
Psychometrika , Volume 20 , Issue 1 , March 1955 , pp. 23 - 28
Copyright
Copyright © 1955 The Psychometric Society

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References

Aitken, A. C. On the independence of linear and quadratic forms in samples of normally distributed variables. Proc. royal Soc. Edinburgh, 1939, 60, 40–46CrossRefGoogle Scholar
Bartlett, M. S. Multivariate analysis. J. royal stat. Soc. Sup, 1947, 9, 176–190CrossRefGoogle Scholar
Cochran, W. G. The distribution of quadratic forms in a normal system with applications to the analysis of variance. Proc. Cambridge phil. Soc., 1934, 30, 178–191CrossRefGoogle Scholar
Cramér, Harald. Mathematical methods of statistics, Princeton, N.J.: Princeton Univ. Press, 1946Google Scholar
Eckart, Carl, and Young, Gale. The approximation of one matrix by another of lower rank. Psychometrika, 1936, 1, 211–218CrossRefGoogle Scholar
Harris, Chester W. The symmetrical idempotent matrix in factor analysis. J. exp. Educ., 1951, 19, 239–246CrossRefGoogle Scholar
Holzinger, Karl J. Factoring test scores and implications for the method of averages. Psychometrika, 1944, 9, 155–167CrossRefGoogle Scholar
Rao, C. R. Estimation and tests of significance in factor analysis. (mimeographed).Google Scholar
Thomson, Godfrey. The factorial analysis of human ability 4th edition, Boston: Houghton Mifflin Co., 1950Google Scholar