, Volume 51, Issue 3, pp 375–377 | Cite as

Sample size and bentler and Bonett's nonnormed fit index

  • Kenneth A. Bollen


Bentler and Bonett's nonnormed fit index is a widely used measure of goodness of fit for the analysis of covariance structures. This note shows that contrary to what has been claimed the nonnormed fit index is dependent on sample size. Specifically for a constant value of a fitting function, the nonnormed index is inversely related to sample size. A simple alternative fit measure is proposed that removes this dependency. In addition, it is shown that this new measure as well as the old nonnormed fit index can be applied to any fitting function that measures the deviation of the observed covariance matrix from the covariance matrix implied by the parameter estimates for a model.

Key words

nonnormed fit index goodness of fit LISREL analysis of covariance structures 


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  1. Anderson, J. C., & Gerbing, D. W. (1984). The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis.Psychometrika, 49, 155–173.Google Scholar
  2. Bentler, P. M., & Bonett, D. G. (1980). Significance tests and goodness-of-fit in the analysis of covariance structures.Psychological Bulletin, 88, 588–600.Google Scholar
  3. Bentler, P. M., & Lee, S. Y. (1979). A statistical development of three-mode factor analysis.British Journal of Mathematical and Statistical Psychology, 32, 87–104.Google Scholar
  4. Jöreskog, K. G., & Sörbom, D. (1984).LISREL VI: Analysis of linear structural relationships by maximum likelihood, instrumental variables, and least squares. Mooresville, IN: Scientific Software.Google Scholar
  5. Tucker, L. R., & Lewis, C. (1973). A reliability coefficient for maximum likelihood factor analysis.Psychometrika, 38, 1–10.Google Scholar

Copyright information

© The Psychometric Society 1986

Authors and Affiliations

  • Kenneth A. Bollen
    • 1
  1. 1.Department of SociologyUniversity of North CarolinaChapel Hill

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