Let's say I have sampled all adult males (N=30) and females (N=25) in a group. There is a property (z) that emerges from pairing male A with female B. I run a Monte Carlo simulation of size 25 (every female is paired with one random male). For every iteration sampling 25 pairs, I calculate the average z [zmean = sum(z)/25]. I run this 100,000 times and draw the distribution of all 100,000 zmeans. I then plot the observed z mean (mean z in field observations = Ozmean) to test for a significant difference of Ozmean from the simulated data.
My question is: What is the best way to test the power of this analysis? Would the power of a Z-test be appropriate? If so, which sigma should I use (the simulated/population, or the observed)?
My goal is to determine if my sample size of observed "z" is good enough to reject the null hypothesis (zmean = Ozmean) in a two.tailed test.
I appreciate any help!