Statistical Power in Two-Level Models: A Tutorial Based on Monte Carlo Simulation

The estimation of power in two-level models used to analyze data that are hierarchically structured is particularly complex because the outcome contains variance at two levels that is regressed on predictors at two levels. Methods for the estimation of power in two-level models have been based on formulas and Monte Carlo simulation. We provide a hands-on tutorial illustrating how a priori and post hoc power analyses for the most frequently used two-level models are conducted. We describe how a population model for the power analysis can be specified by using standardized input parameters and how the power analysis is implemented in SIMR, a very flexible power estimation method based on Monte Carlo simulation. Finally, we provide case-sensitive rules of thumb for deriving sufficient sample sizes as well as minimum detectable effect sizes that yield a power >=.80 for the effects and input parameters most frequently analyzed by psychologists. For medium variance components, the results indicate that with lower level (L1) sample sizes up to 30 and higher level (L2) sample sizes up to 200, medium and large fixed effects can be detected. However, small L2 director cross-level interaction effects cannot be detected with up to 200 clusters. The tutorial and guidelines should be of help to researchers dealing with multilevel study designs such as individuals clustered within groups or repeated measurements clustered within individuals.