In this article, we identify a situation in Meta analysis involving independent studies in which the conventional omnibus tests are orthogonal to a certain type of votecounting method. This, in turn, gives partial evidence pointing to the inefficiency of using a conventional omnibus test or a votecounting method alone. Also a method is suggested to combine an omnibus test and the votecounting method when an appropriate situation arises in practice. By simulation, it is demonstrated that the test due to this process of combination has somewhat more power than the omnibus tests for many classical problems