Analytical and simulation-based power analyses for mixed-design ANOVAs

May 22, 2013

In this post I show some R-examples on how to perform power analyses for mixed-design ANOVAs. The first example is analytical — adapted from formulas used in G*Power (Faul et al., 2007), and the second example is a Monte Carlo simulation. The source code is embedded at the end of this post.

Both functions require a dataframe, containing the parameters that will be used in the power calculations. Here is an example using three groups and three time-points.

Here is a plot of our hypothetical study design.
Study design for power analysis for mixed-design ANOVA. By Kristoffer Magnusson Now, we will use this design to perform a power analysis using anova.pwr.mixed and anova.pwr.mixed.sim.

Comparison of analytical and monte carlo power analysis

Now let’s compare the two functions’ results on the time x group-interaction. Hopefully, the two methods will yield the same result.

Comparison of analytical versus monte carlo power analysis for mixed design anova. By Kristoffer Magnusson

Luckily, the analytical results are consistent with the Monte Carlo results.


Faul, F., Erdfelder, E., Lang, A. G., & Buchner, A. (2007). G* Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences.Behavior research methods, 39(2), 175-191.

Source code

You can find the source here and here.