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Application of a Large Sampling Criterion to Some Sampling Problems in Factor Analysis
Published online by Cambridge University Press: 01 January 2025
Abstract
A technique is presented to test the completeness of factor solutions and also to test the significance of common-component loadings. The chisquare test involved is based upon the asymptotic normal properties of the residuals.
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- Original Paper
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- Copyright © 1953 The Psychometric Society
Footnotes
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The research work on which the results presented are based was conducted under the supervision of Prof. P. S. Dwyer, Mathematics Department, University of Michigan. The complete results of this research were presented in a Ph. D. thesis, June, 1951.
References
Bartlett, M. S. Tests of significance in factor analysis. Brit. J. Psychol., Statist. Sect., 1950, 3, 77–85.CrossRefGoogle Scholar
Coombs, C. H. A criterion for significant common factor variance. Psychometrika, 1941, 6, 267–272.CrossRefGoogle Scholar
Dwyer, P. S. The evaluation of multiple and partial correlation coefficients from the factorial matrix. Psychometrika, 1940, 5, 211–232.CrossRefGoogle Scholar
Guttman, L. Multiple rectilinear prediction and the resolution into components. Psychometrika, 1940, 5, 75–79.CrossRefGoogle Scholar
Hoel, P. G. A significance test for minimum rank in factor analysis. Psychometrika, 1939, 4, 149–158.CrossRefGoogle Scholar
Hoel, P. G. A significance test for component analysis. Ann. math. Statist., 1937, 8, 149–158.CrossRefGoogle Scholar
Holzinger, K. J., and Harman, H. H. Factor analysis, Chicago: Univ. Chicago Press, 1936.Google Scholar
Hotelling, H. Analysis of a complex of statistical variables into principal components. J. educ. Psychol., 1933, 24, 417–441.CrossRefGoogle Scholar
Lawley, D. N. Factor loadings by the method of maximum likelihood. Proc. roy. Soc. Edinb., 1940, 60, 64–82.CrossRefGoogle Scholar
Lawley, D. N. Further investigations in factor estimation. Proc. roy. Soc. Edinb., 1942, 61, 176–183.Google Scholar
Wald, A. Notes on the theory of statistical estimation and testing hypothesis. Unpublished lecture notes, Columbia University.Google Scholar
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