Abstract
Fislrier's well-known omnibus tcst for compounding evidence from several tests is modified to find a test that is more powerful for a certain class of alternatives. The idea to the modification comes from a similar result in the theory of statistical inference under order restrictions. Four test statistics for compounding evidence from several one-sided tests concerning normal means are compared, Two of the tests are based on p-valus, thus extending the validity to any distributional assumptions and also to any kind of hypothesis. The four tests are: Fisher's test, the modified version of it, the likelihood ratio test, and the most powerful test against the sub-alternative of equal means.