Alpha factor analysis
 Henry F. Kaiser,
 John Caffrey
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A distinction is made between statistical inference and psychometric inference in factor analysis. After reviewing Rao's canonical factor analysis (CFA), a fundamental statistical method of factoring, a new method of factor analysis based upon the psychometric concept of generalizability is described. This new procedure (alpha factor analysis, AFA) determines factors which have maximum generalizability in the KuderRichardson, or alpha, sense. The two methods, CFA and AFA, each have the important property of giving the same factors regardless of the units of measurement of the observable variables. In determining factors, the principal distinction between the two methods is that CFA operates in the metric of the unique parts of the observable variables while AFA operates in the metric of the common (“communality”) parts.
On the other hand, the two methods are substantially different as to how they establish the number of factors. CFA answers this crucial question with a statistical test of significance while AFA retains only those alpha factors with positive generalizability. This difference is discussed at some length. A brief outline of a computer program for AFA is described and an example of the application of AFA is given.
 Title
 Alpha factor analysis
 Journal

Psychometrika
Volume 30, Issue 1 , pp 114
 Cover Date
 196503
 DOI
 10.1007/BF02289743
 Print ISSN
 00333123
 Online ISSN
 18600980
 Publisher
 SpringerVerlag
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 Authors

 Henry F. Kaiser ^{(1)}
 John Caffrey ^{(2)}
 Author Affiliations

 1. University of Wisconsin, USA
 2. System Development Corporation, USA