Top histogram: simulated sample of size N = 1000 drawn from a superposition of two Gaussian distributions separated by r = 2.0 standard deviations. The solid curve is the best-fitting single Gaussian. In this case the null hypothesis, that the sample was drawn from a single Gaussian, cannot be rejected. Bottom histogram: simulation with separation r = 2.4 standard deviations. The solid curve is again the best-fitting single Gaussian. In this case the null hypothesis would be rejected and a much better fit could be obtained by fitting two Gaussians (not shown).