Power calculation using simulation -- should I use empirical distribution? In most tutorials on power calculation using simulation (e.g. this example in R), the analyst simulates the outcome variable using some convenient distribution such as the normal distribution.
It seems to me that it is much more logical to sample from the empirical distribution of the outcome variable instead. Is this thinking correct? If no, why? If yes, is it commonly done?
 A: I suspect the potential appeal of sampling from an empirical distribution of the outcome (presumably using data from a pilot study) is that the empirical distribution will better capture nuances in the distribution such as non-normality. This could yield a more accurate power simulation. However, the pilot dataset would need to be fairly large to realize this potential benefit. 
I would find sampling from a small pilot dataset less compelling than sampling from an idealized distribution with a plausible or conservative standard deviation. When judging the quality of a power calculation, I find the plausibility of the assumed effect size and standard deviation to be much more important than accounting for the potential of modest deviations from normality in the outcome distribution.
What you really care about is the distribution of your estimator. The distribution of your outcome influences the distribution of your estimator, but in many circumstances the central limit theorem limits that influence. So getting that distribution exactly right is less important than justifying your assumed standard deviation.
