Estimating the Statistical Power in Small Samples by Empirical Distributions

Summary

Model selection is an important issue in Structural Equation Modeling. This issue is in particular important if the sample size is small. In such a case the power may be very small, so it is hard to decide which model is the most appropriate, because alternative models may also fit the data well. There is a lot of theoretical papers on this subject, however they are almost always dealing with asymptotic theory. In cases with small samples this assumption may lead to wrong results. We will use resampling methods, like the parametric bootstrap, to investigate the empirical distribution of certain statistics. On the basis of this empirical distribution we can investigate the power of some tests, even in cases with small samples. An example will be given.