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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Bollen et al. (1988) studied this question.
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