Statistical power with respect to true sample and true population paths: a PLS-based SEM illustration

Monte Carlo experiments aimed at assessing the statistical power of structural equation modeling (SEM) techniques typically focus on true population path coefficients, ignoring true sample path coefficients. We demonstrate the limitations stemming from such practice in statistical power assessments. This is done in the context of SEM techniques employing the partial least squares (PLS) method, where power claims have led to much recent debate. We show that the sample sizes at which power is greater than .8 differ significantly when we consider true population and true sample paths, and that the difference increases with decreases in the magnitudes of the paths being considered. Finally, we illustrate empirically how these differences affect the conclusions we can draw from the analysis of a relatively small sample of size 193.