Alpha factor analysis
 Henry F. Kaiser,
 John Caffrey
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
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.
 Anderson, T. W., Rubin, H. (1956) Statistical inference in factor analysis. Proc. third Berkeley Symp. math. Statist. and Prob. 5: pp. 1150
 Bargmann, R. A study of independence and dependence in multivariate normal analysis. Institute of Statistics, Univ. North Carolina, Mimeographed Series No. 186, 1957.
 Caffrey, J. (1961) Algorithm 66. INVRS. Communications of the ACM 4: pp. 322322
 Cronbach, L. J. (1951) Coefficient alpha and the internal structure of tests. Psychometrika 16: pp. 297334
 Cronbach, L. J., Rajaratnam, N., Gleser, G. C. (1963) Theory of generalizability: a liberalization of reliability theory. Brit. J. statist. Psychol. 16: pp. 137163
 Cronbach, L. J., Hartmann, W. (1954) A note on negative reliabilities. Educ. psychol. Measmt 14: pp. 342346
 Dickman, K., Kaiser, H. F. (1961) Program for inverting a Gramian matrix. Educ. psychol. Measmt 21: pp. 721727
 Guttman, L. (1945) A basis for analyzing testretest reliability. Psychometrika 10: pp. 255282
 Guttman, L. (1956) “Best possible” systematic estimates of communalities. Psychometrika 21: pp. 273286
 Guttman, L. (1958) To what extent can communalities reduce rank?. Psychometrika 23: pp. 297308
 Harris, C. W. (1962) Some RaoGuttman relationships. Psychometrika 27: pp. 247263
 Holzinger, K. J., Harman, H. (1941) Factor analysis. Univ. Chicago Press, Chicago
 Hotelling, H. (1933) Analysis of a complex of statistical variables into principal components. J. educ. Psychol. 24: pp. 417441
 Hoyt, C. (1941) Test reliability estimated by analysis of variance. Psychometrika 6: pp. 153160
 Jackson, R. W. and Ferguson, G. A. Studies on the reliability of tests. Bulletin No. 12, Dept. of Educ. Res., Univ. Toronto, 1941.
 Kaiser, H. F. The varimax method of factor analysis. Unpublished doctoral dissertation, Univ. Calif., 1956.
 Kaiser, H. F. (1958) The varimax criterion for analytic rotation in factor analysis. Psychometrika 23: pp. 187200
 Kaiser, H. F. (1960) The application of electronic computers in factor analysis. Educ. psychol. Measmt 20: pp. 141151
 Kaiser, H. F. Comments on communalities and the number of factors. Unpublished manuscript, 1960.
 Kuder, G. F., Richardson, M. W. (1937) The theory of the estimation of test reliability. Psychometrika 2: pp. 151160
 Lawley, D. N. (1940) The estimation of factor loadings by the method of maximum likelihood. Proc. roy. Soc. Edinburgh 60: pp. 6482
 Lord, F. M. (1958) Some relations between Guttman's principal components of scale analysis and other psychometric theory. Psychometrika 23: pp. 291296
 Rao, C. R. (1955) Estimation and tests of significance in factor analysis. Psychometrika 20: pp. 93111
 Thurstone, L. L. (1947) Multiplefactor analysis. Univ. Chicago Press, Chicago
 Tryon, R. C. (1957) Reliability and behavior domain validity: Reformulation and historical critique. Psychol. Bull. 54: pp. 229249
 Title
 Alpha factor analysis
 Journal

Psychometrika
Volume 30, Issue 1 , pp 114
 Cover Date
 19650301
 DOI
 10.1007/BF02289743
 Print ISSN
 00333123
 Online ISSN
 18600980
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 Authors

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

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