IBM® SPSS® Amos™ 28

Hoelter's "critical N" (Hoelter, 1983) is the largest sample size for which one would accept the hypothesis that a model is correct. Hoelter does not specify a significance level to be used in determining the critical N, although he uses .05 in his examples. Amos reports a critical N for significance levels of .05 and .01. Here are the critical N's displayed by Amos for each of the models in Example 6.

Model A, for instance, would have been accepted at the .05 level if the sample moments had been exactly as they were found to be in the Wheaton study, but with a sample size of 164. With a sample size of 165, Model A would have been rejected. Hoelter argues that a critical N of 200 or better indicates a satisfactory fit. In an analysis of multiple groups, he suggests a threshold of 200 times the number of groups. Presumably this threshold is to be used in conjunction with a significance level of .05. This standard eliminates Model A and the independence model in Example 6. Models B, C and D are satisfactory according to the Hoelter criterion. I am not myself convinced by Hoelter's arguments in favor of the 200 benchmark. Unfortunately, the use of critical N as a practical aid to model selection requires some such standard. Bollen and Liang (1988) report some studies of the critical N statistic.

Use the \hfive text macro to display Hoelter's critical N on a path diagram using a significance level of .05. Use \hone for a significance level of .01.