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Related Experiment Videos

Can test statistics in covariance structure analysis be trusted?

L T Hu1, P M Bentler, Y Kano

  • 1Department of Psychology, University of California, Los Angeles 90024-1563.

Psychological Bulletin
|September 1, 1992
PubMed
Summary
This summary is machine-generated.

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The adequacy of chi-squared goodness-of-fit tests in covariance structure analysis is uncertain. The Satorra-Bentler scaled test statistic demonstrated the best overall performance across various conditions in a Monte Carlo study.

Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Covariance structure analysis relies on chi-squared goodness-of-fit tests.
  • Model conclusions can be inaccurate if assumptions regarding sample size, independence, and distribution are violated.

Purpose of the Study:

  • To evaluate the performance of six different test statistics under various distributional conditions and sample sizes.
  • To identify robust test statistics for covariance structure analysis.

Main Methods:

  • A Monte Carlo simulation study was employed.
  • Confirmatory factor analysis models were analyzed.
  • Six distinct goodness-of-fit test statistics were compared across seven distributional conditions and six sample sizes.

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Main Results:

  • Test statistics exhibited significant performance variations.
  • Normal-theory tests failed under certain conditions.
  • A distribution-free test performed poorly across most conditions.
  • The Satorra-Bentler scaled test statistic showed the most consistent and superior performance.

Conclusions:

  • The choice of test statistic significantly impacts the validity of covariance structure analysis.
  • The Satorra-Bentler scaled test statistic is recommended for its robustness.
  • Researchers must be cautious about assumption violations and their effect on test statistic performance.