This paper develops a statistically unbiased and simple method for measuring the difference of independent empirical distributions estimated by bootstrapping or other simulation approaches. This complete combinatorial method is compared with other unbiased and biased methods that have been suggested in the literature, first in Monte Carlo simulations and then in a field test of external and internal scope testing in contingent valuation. Tradeoffs between methods are discussed. When the empirical distributions are not independent a straightforward difference test is suggested.