Hostname: page-component-745bb68f8f-b95js Total loading time: 0 Render date: 2025-01-08T09:49:48.711Z Has data issue: false hasContentIssue false
  • English
  • Français

Application of a Large Sampling Criterion to Some Sampling Problems in Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Dayle D. Rippe
Dayle D. Rippe*
Affiliation:
Operations Analysis Office, Strategic Air Command
Get access Rights & Permissions [Opens in a new window]

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.

Type
Original Paper
Information
Psychometrika , Volume 18 , Issue 3 , September 1953 , pp. 191 - 205
Copyright
Copyright © 1953 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

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
Lawley, D. N. Problems in factor analysis. Proc. roy. Soc. Edinb., 1947, 62, 394–399.Google Scholar
McNemar, Q. On the number of factors. Psychometrika, 1942, 7, 9–18.Google Scholar
Wald, A. Notes on the theory of statistical estimation and testing hypothesis. Unpublished lecture notes, Columbia University.Google Scholar
Wilks, S. S. Mathematical statistics, Princeton, N. J.: Princeton Univ. Press, 1946.Google Scholar