The most powerful non-asymptotic unconditioned method for comparing two proportions (independent samples) is that of Barnard (1945), but the complexity of computation has led to several simplifying versions being produced. There is no complete global comparison of these (though there are some partial ones, such as Haber's, 1987), nor has there been an evaluation of the loss incurred by not using Barnard's method. In this paper all existing relevant versions (including Barnard's, and one proposed by the authors) for a wide range of sample sizes are compared, as well as for one-and two-tailed tests (only the second case has been dealt with in recent literature), and a conclusion is drawn about the suitability of the new method proposed. The comparison is effected on the basis of the new criterion of ''mean power'', and the other customary criteria for comparing methods, based on the comparison of their powers in each point of the parametric space, are criticized. The new criterion can be applied to all tests based on discrete random variables. Finally, given the large number of methods proposed in the relevant literature for solving this problem, the authors classify the same in function of their precision and their complexity of computation.
