  In this paper, we show that the likelihood-ratio measure (a) is invariant
with respect to dominating sigma-finite measures, (b) satisfies logical
consequences which are not satisfied by standard $p$-values, (c) respects
frequentist properties, i.e., the type I error can be properly controlled, and,
under mild regularity conditions, (d) can be used as an upper bound for
posterior probabilities. We also discuss a generic application to test whether
the genotype frequencies of a given population are under the Hardy-Weinberg
equilibrium, under inbreeding restrictions or under outbreeding restrictions.
