The Analysis of Covariance Structures

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Abstract
A major problem encountered in covariance structure analyses involves decisions concerning whether or not a given theoretical model adequately represents the data used for its assessment. Given that X2 goodness-of-fit tests are joint functions of the difference between theoretical and empirical covariance structures and sample size, gauging the impact of sample size on such tests is essential. In this paper, we propose a simple index (critical N) and tentative acceptance criterion, which, by focusing on sample size, provide an improved method for assessing goodness-of-fit. Both small- and large-sample examples are presented, illustrating the utility of the proposed method for assessing theoretical models.