It is useful for researchers to be able to estimatethe sample size necessary to have an impressiveprobability of obtaining a difference between sample locations of two independent groups that isclose to the difference between corresponding population locations. The present manuscript provides the necessary equations. To increase generality, the derivations presented are not basedon the typical assumption that the samples comefrom the family of normally distributed populations but rather from the much larger family ofskew normal distributions. In addition, counter tomany researchers' intuitions, we demonstrate thatgreater sampling precision ensues from skewnessthan from normality, all else being equal, withsimulation results. Finally a real data example onfaculty salaries of New Mexico State University isgiven for the illustration of our main results.