Suppose one has a large body of data on many variables and, for many variables, no clear rationale for a test of one-sided alternative exists. In such circumstances, a procedure which may be followed is to do two-sided testing on a sub-set of the data, and then a one-sided test in the direction suggested by the data providing the sub-sample test is, in some sense, significant. Under some particular assumptions (normality, known variance) we investigate the appropriate choice of significance levels and relative size of sub-sample for comparison of means to maximize power when the alternative selected is true. Results are compared with the alternate of performing a single two-tailed test.