Satorra and Saris (1985) proposed an approach to estimate statistical power for SEM models. The idea behind the method is when a model is misspecified (but not severely so) the model fit test statistic does not follow a central χ^{2} distribution, but a noncentral χ^{2} distribution. The model χ^{2} statistic of the misspecified model can be considered as an approximation of the noncentrality parameter () of the noncentral χ^{2} distribution (note, the here is not the that denotes factor loadings in our CFA models). Once the parameter has been estimated, statistical power can be obtained either from a table for noncentral χ^{2} distribution for specific degrees of freedom and level (Saris and Stonkhorst, 1984) or calculated using statistical packages, such as SAS or SPSS (Brown, 2006; http://www.statmodel.com/power.shtml).

Several steps are followed in application of Satorra and Saris's method to estimate statistical power and thus sample size ...

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