Calculating non-centrality parameter for power analysis under structural equation modelling: An alternative

Identifying the most parsimonious model in structural equation modelling is of utmost importance and the appropriate power estimation methods minimize the probabilities of Type I and Type II errors. The power of a test depends on the sample size, Type I error, degrees of freedom and effect size. In this study, a modified approach of using effect size in calculating the non-centrality parameter for power is proposed. This is compared to the approach in Maccallum et al. (1996) at different degrees of freedom and sample size specifications --- taken from 50 to 2000. As the sample size increased the difference between the power of a test for both methods reduced to zero. The results showed that the values for power of a test are the same for the modified and original approaches for large sample sizes and degrees of freedom. The findings also revealed that the sample discrepancy function ($\hat{F}$) is asymptotically unbiased.