Sample Size Effects on Chi Square and Other Statistics Used in Evaluating Causal Models

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Abstract
A simulation study of the effects of sample size on the overall fit statistic provided by the LISREL program indicates the statistic is well behaved over a wide range of sample sizes for simple models. However, this statistic is apparently not chi square distributed for more complex models when samples are relatively small, and will reject the hypothesized model too often. A set of additional measures suggested by various researchers for evaluating causal models also is examined. These statistics are well behaved for both models tested as they converge to the true value and their variance approaches zero as sample size increases.