Skip to main content
Log in

Application of a large sampling criterion to some sampling problems in factor analysis

  • Published:
Psychometrika Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bartlett, M. S. Tests of significance in factor analysis.Brit. J. Psychol., Statist. Sect., 1950,3, 77–85.

    Google Scholar 

  2. Coombs, C. H. A criterion for significant common factor variance.Psychometrika, 1941,6, 267–272.

    Google Scholar 

  3. Dwyer, P. S. The evaluation of multiple and partial correlation coefficients from the factorial matrix.Psychometrika, 1940,5, 211–232.

    Google Scholar 

  4. Guttman, L. Multiple rectilinear prediction and the resolution into components.Psychometrika, 1940,5, 75–79.

    Google Scholar 

  5. Hoel, P. G. A significance test for minimum rank in factor analysis.Psychometrika, 1939,4, 149–158.

    Google Scholar 

  6. Hoel, P. G. A significance test for component analysis.Ann. math. Statist., 1937,8, 149–158.

    Google Scholar 

  7. Holzinger, K. J., and Harman, H. H. Factor analysis. Chicago: Univ. Chicago Press, 1936.

    Google Scholar 

  8. Hotelling, H. Analysis of a complex of statistical variables into principal components.J. educ. Psychol., 1933,24, 417–441, 498–520.

    Google Scholar 

  9. Lawley, D. N. Factor loadings by the method of maximum likelihood.Proc. roy. Soc. Edinb., 1940,60, 64–82.

    Google Scholar 

  10. Lawley, D. N. Further investigations in factor estimation.Proc. roy. Soc. Edinb., 1942,61, 176–183.

    Google Scholar 

  11. Lawley, D. N. Problems in factor analysis.Proc. roy. Soc. Edinb., 1947,62, 394–399.

    Google Scholar 

  12. McNemar, Q. On the number of factors.Psychometrika, 1942,7, 9–18.

    Google Scholar 

  13. Wald, A. Notes on the theory of statistical estimation and testing hypothesis. Unpublished lecture notes, Columbia University.

  14. Wilks, S. S. Mathematical statistics. Princeton, N. J.: Princeton Univ. Press, 1946.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

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.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rippe, D.D. Application of a large sampling criterion to some sampling problems in factor analysis. Psychometrika 18, 191–205 (1953). https://doi.org/10.1007/BF02289056

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02289056

Keywords

Navigation