Articlegreen1988

Some Properties of Hoelter's CN

70 citations0/0 files storedSociological Methods & Research

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Psychometric Methodologies and Testing Statistical Distribution Estimation and Applications Statistical Methods and Bayesian Inference

Abstract

Reviews, critiques, and simulation studies are available for the chi-square and other measures of goodness of fit for structural equation models. The main exception is Hoelter's critical N (CN) statistic. In this article we present some of the properties of CN, explain why a fixed cutoff value for CN often favors large samples over small ones, and illustrate some of these characteristics with simulated and empirical data. We also describe the ambiguities involved in treating CN as a gauge of the power of the chi-square test.

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References

1980Significance tests and goodness of fit in the analysis of covariance structures.1989Structural Equations with Latent Variables 1973A Reliability Coefficient for Maximum Likelihood Factor Analysis 1969A General Approach to Confirmatory Maximum Likelihood Factor Analysis 1984The Effect of Sampling Error on Convergence, Improper Solutions, and Goodness-of-Fit Indices for Maximum Likelihood Confirmatory Factor Analysis 1983The Analysis of Covariance Structures 1985Power of the Likelihood Ratio Test in Covariance Structure Analysis 1986Sample Size and Bentler and Bonett's Nonnormed Fit Index

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