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The Relation Between Results Obtainable with Raw and Corrected Correlation Coefficients in Multiple Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Merrill Roff
Merrill Roff*
Affiliation:
Indiana University
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Abstract

This paper presents three theorems concerning the relation between results with obtained and corrected correlation coefficients in the Thurstone method of multiple factor analysis. (1) The rank of the correlational matrix, and thus the number of factors involved, is unaffected by correcting the obtained coefficients for attenuation. (2) The communality of a variable when the obtained coefficients have been corrected for attenuation is equal to the communality with obtained coefficients divided by the reliability coefficient of the variable. (3) The relationship is shown between the factorial matrix of a correlational matrix of raw correlation coefficients and the factorial matrix of a correlational matrix of corrected correlation coefficients, and a method of obtaining either of these factorial matrices from the other is indicated.

Type
Original Paper
Information
Psychometrika , Volume 2 , Issue 1 , March 1937 , pp. 35 - 39
Copyright
Copyright © 1937 The Psychometric Society

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References

Bocher, M.Introduction to Higher Algebra, New York: Macmillan, 1931.Google Scholar
Cullis, C. E.Matrices and Determinoids. Vol. II, Cambridge: University Press, 1918.Google Scholar
Hotelling, H.Analysis of a Complex of Statistical Variables into Principal Components, Baltimore: Warwick & York, 1933.Google Scholar
Kelley, T. L.Essential traits of Mental Life, Cambridge: Harvard Univ. Press, 1935.Google Scholar
Spearman, C. E. The Abilities of Man, New York: Macmillan, 1927.Google Scholar
Thurstone, L. L.The Vectors of Mind, Chicago: Univ. of Chicago Press, 1935.Google Scholar