We examine the power of different exact tests of differentiation for d
iploid populations. Since there is not necessarily random mating withi
n populations, the appropriate hypothesis to construct exact tests is
that of independent sampling of genotypes. There are two categories of
tests, F-ST-estimator tests and goodness of fit tests. In this latter
category, we distinguish ''allelic statistics'', which account for th
e nature of alleles within genotypes, from ''genotypic statistics'' th
at do not. We show that the power of F-ST-estimator tests and of allel
ic goodness of fit tests are similar when sampling is balanced, and hi
gher than the power of genotypic goodness of fit tests. When sampling
is unbalanced, the most powerful tests are shown to belong to the alle
lic goodness of fit group.