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A framework for hypothesis testing and power analysis in the assessment of fit of covariance structure models is presented. We emphasize the value of confidence intervals for fit indices, and we stress the relationship of confidence intervals to a framework for hypothesis testing. The approach allows for testing null hypotheses of not-good fit, reversing the role of the null hypothesis in conventional tests of model fit, so that a significant result provides strong support for good fit. The approach also allows for direct estimation of power, where effect size is defined in terms of a null and alternative value of the root-mean-square error of approximation fit index proposed by J. H. Steiger and J. M. Lind (1980). It is also feasible to determine minimum sample size required to achieve a given level of power for any test of fit in this framework. Computer programs and examples are provided for power analyses and calculation of minimum sample sizes.

A major aspect of the application of covariance structure modeling (CSM) in empirical research is the assessment of goodness of fit of an hypothesized model to sample data. There is considerable literature on the assessment of goodness of fit of such models, providing a wide array of fit indices along with information about their behavior (e.g., Bentler & Bonett, 1980; Browne & Cudeck, 1993; Marsh, Balla, & McDonald, 1988; Mulaik et al., 1989). Empirical applications of CSM typically evaluate fit using two approaches: (a) the conventional likelihood ratio χ²  test of the hypothesis that the specified model holds exactly in the population; and (b) a variety of descriptive measures of fit of...