I have data from an experiment in which each subject was assigned to one of 4 experimental conditions (CONDITION, a between-subject factor), and then faced 4 similar but distinct tasks (TASK, a within-subject factor). My DV is a continuous variable (DV), and the hypothesis is with respect to an interaction between CONDITION and TASK.

For the analysis I am using the lme4 package in R, and the model looks like this:

m = lmer(DV ~ CONDITION * TASK + (1+ORDER|SUBJ), data)

where ORDER is simply the order by which a subject faced the task (1, 2, 3, or 4), and SUBJ is a unique subject Id.

This was an exploratory study, and I now would like to use it to perform a power analysis for a larger study. My question regards the way to perform a power analysis considering my goal is to find a significant interaction between a between-subject factor and a within-subject factor.

I tried looking at package SIMR, which seems the most flexible one for performing power analysis of mixed models, but cannot figure out how to do this.

Thanks in advance.

  • $\begingroup$ maybe you could try GPower. Please see the page 182 of this, in which the table 3 talked about the between-within two factor ANOVA power analysis. $\endgroup$
    – WCMC
    May 25, 2018 at 20:46
  • $\begingroup$ Excellent! Thanks for the quick reference. This is very helpful. The one thing I am missing from this document to complete the analysis is determination of "nonsphericity correction ε". Can you perhaps refer to something on that? $\endgroup$
    – Cuenco
    May 25, 2018 at 21:12
  • $\begingroup$ Please have a look at statistics.laerd.com/statistical-guides/…. It talks about how to calculate and correct for the sphericity. Sometimes people just use 0.75. $\endgroup$
    – WCMC
    May 25, 2018 at 21:14
  • $\begingroup$ Great, thank you! (how can I accept a comment as an answer?) $\endgroup$
    – Cuenco
    May 25, 2018 at 21:27
  • $\begingroup$ Glad to help. I am afraid you cannot accept a comment as an answer. No worries! $\endgroup$
    – WCMC
    May 25, 2018 at 21:28


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