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Alpha Factor Analysis of Infallible Variables

Published online by Cambridge University Press:  01 January 2025

Gene V Glass
Gene V Glass*
Affiliation:
University of Illinois
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Abstract

The relationship between the factor pattern, F, derived from fallible (containing measurement error) observations on variables and the factor pattern, F*, derived from infallible observations on variables is investigated. A widely believed relationship between F and F*, viz.,F* = AF where A is a diagonal matrix containing the inverses of the square roots of the reliabilities of the variables, is shown to be false for several factor analytic techniques. Under suitable assumptions, it is shown that for Kaiser and Caffrey's “alpha factor analysis”F* and F are related by F* = AF. Empirical examples for which the corresponding elements of F* and AF are equal to two decimal places are presented. The implications of the equality of F* and AF for alpha factor analysis are discussed.

Type
Original Paper
Information
Psychometrika , Volume 31 , Issue 4 , December 1966 , pp. 545 - 561
Copyright
Copyright © 1966 Psychometric Society

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Footnotes

*

I wish to acknowledge the generous assistance of Drs. Chester W. Harris and Henry F. Kaiser in the execution of the research reported in this paper.

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