# How power was calculated in this study

In this high protein study here (http://www.mdpi.com/2072-6643/9/9/1007/htm), comparing high protein to low protein in obese sedentary women, the authors described their methods here

An a priori power analysis was performed (G*Power v. 3.0.10, Heinrich-Heine-University Düsseldorf, Düsseldorf, Germany ) for an F test (repeated measures, within-between interaction factors for 2 time points) to calculate the required number of participants in each group. On the basis of a statistical power ($1–β$ err prob) of $0.80$, a moderately large effect size ($0.5$), and an overall level of significance of $0.05$, 12 subjects were required for this study."

How is this possible to get a total sample size of 12? I ran the numbers on G*power myself and got similar numbers.

These were the parameters for my calculation:

Input:
Effect size f = 0.5
α err prob = 0.05
Power (1-β err prob) = 0.8
Number of groups = 2
Number of measurements = 2
Corr among rep measures = 0.5
Nonsphericity correction ε = 1

Output:
Noncentrality parameter λ = 12.0000000
Critical F = 4.9646027
Numerator df = 1.0000000
Denominator df = 10.0000000
Total sample size = 12
Actual power = 0.8764178

Is this analysis wrong, and was this study with an actual n=23 statistically underpowered?

• It would be helpful if you could provide a few more details about G*Power or as a minimum the full reference  from the study you quote. – user77876 Sep 13 '17 at 15:07
• Is your issue that you are surprised that the number can be as small/large as 12? – mdewey Sep 13 '17 at 15:16
• @user77876 that's odd, are you unable to see the high-protein study I linked? In any case, here's the reference about G*power, it's considered to be one of the easiest power calculators around. What I'm trying to know is, is this study powered enough? – user177098 Sep 13 '17 at 15:17
• @mdewey yes, that's also another thing I'm wondering – user177098 Sep 13 '17 at 15:17
• ncbi.nlm.nih.gov/pubmed/17695343 – user177098 Sep 13 '17 at 15:29