I am planning a research experiment with a 4x2 within-subjects design, and am currently trying to determine an appropriate sample size for my project (in order to achieve desired power with an effect size determined by the literature).

Unlike many within-subjects designs that have time as one variable, I am testing all participants on two factors at once; i.e. they will be rating words in 8 different conditions (factor A 4 levels, factor B 2 levels). The plan is to run an ANOVA as well as identify main comparisons (a priori, based on previous literature) between the 8 conditions that could be analysed with t-tests.

To my understanding G*Power is able to do this sort of power analysis (and I have managed to run one), but assumes the same correlation among all repeated measurements which in my case isn't as straight-forward as with the example of time as an IV, as I am quite certain that certain conditions will be strongly correlated while others will not. I've also tried running power simulations in R but unfortunately, my skills are inadequate to completely understand what I'm doing (I'm willing to try again though).

Any help with how to go forward from here would be greatly appreciated!

  • $\begingroup$ If you don't have homogeneity of covariance you probably don't have sphericity, and that's going to mess with your power in (slightly) unpredictable ways. $\endgroup$ – Jeremy Miles Sep 26 '18 at 21:26
  • $\begingroup$ Simulations shouldn't be hard. Generate correlated data with MASS::mvrnorm. Then multiply by SDs and add means. You can also do it with SEM (if you're familiar with that.) $\endgroup$ – Jeremy Miles Sep 26 '18 at 21:28

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