# Finding post-hoc power of a repeated measures ANOVA using G*Power (Am I entering the right parameters?)

I would like to report the power observed with my mixed model analysis (or repeated measures ANOVA). My experiment followed a completely within subject design with 2 independent factors (two levels & 5 levels, respectively). 12 participants were recruited to run the 10 combos (5x2) twice (repeated observations), yielding 240 observations. There were some missing data, so the actual total observations was 230.

I have never used G*Power before but it seems like a pretty powerful tool. I attempted to run a post-hoc analysis as shown below. The resulting power is so high (0.933) that I'm a little skeptical. I've taken the sample size to mean # of subjects (12) and that the number of groups refers to levels for between-subject factors, which I have none. The corr among rep measures was just something I estimated [edit: I thought this parameter isn't making a big difference, but it is. Changing it to 0.5 actually lowers the power to 0.5]

Did I enter anything wrong? I would appreciate it if anyone could help me figure out this power analysis.

Analysis:   Post hoc: Compute achieved power
Input:  Effect size f   =   0.2
α err prob  =   0.05
Total sample size   =   12
Number of groups    =   1
Number of measurements  =   10
Corr among rep measures =   0.8
Nonsphericity correction ε  =   1

Output: Noncentrality parameter λ   =   24.0000000
Critical F  =   1.9758061
Numerator df    =   9.0000000
Denominator df  =   99.0000000
Power (1-β err prob)    =   0.9333319

• I'm a bit confused about your analysis. When you ran (or run) the ANOVA, how many repeated measures variables did you have? – Jeremy Miles Apr 16 '13 at 21:22
• Also, observed power is a curious thing, because it's a function of your p-value (if I've understood correctly, again). If you p is 0.05, your power is 50%. Lower p, higher power, so what was p? – Jeremy Miles Apr 16 '13 at 21:23
• @JeremyMiles 10 combinations of the two factors (5x2) were run twice for each participant. There's only 1 dependent measure taken for each observation/trial. As for the ANOVA results, one factor was non significant (p=0.7) and the other one was significant (p=0.015). I am interested in the power because I want to report that for the non-significant factor (type II error). My understanding is that it has more to do with the effect size and sample size, but since it's repeated measures I am not sure about how to proceed and turned to G*Power. – Wynn Apr 16 '13 at 21:46
• Ah, I just saw your edit. Changing the correlation should make a huge difference. I find gpower beyond me for repeated measures analysis (unless they're simple). I'm not very sure about the effect size - I wrote a paper about the method I use, here: biomedcentral.com/1471-2288/3/27 , although it's pretty time consuming, you've got to really want to know the power to do it. – Jeremy Miles Apr 16 '13 at 23:53