APA Dictionary of Psychology

a statistical test of one hypothesis against another that has the greatest power among all tests available at a given alpha value. Suppose the two hypotheses are the null hypothesis of no difference between two groups (Sample 1 mean = Sample 2 mean) and the alternative hypothesis of some difference between the groups (Sample 1 mean ≠ Sample 2 mean). Because the latter is actually a composite of several possibilities, a UMP test is one defined by a critical region that is best suited to test the null hypothesis against each of the simple hypotheses comprising the larger alternative hypothesis.