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:
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
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?