Serendipity Tails: A Note on Two Tailed Hypothesis Tests with Asymmetric Regions of Rejection1

Abstract

Typical criteria for deciding whether to use one or two tailed tests of significance are examined in this paper and found to be too ambiguous to give the researcher useful guidance. This is unfortunate in that the decision creates a dilemma for the researcher. On the one hand, always using symmetric two tailed tests involves a substantial loss of power in the test. On the other hand, using the one tailed test may create the suspicion that the researcher 'peeked' at his data when the results are narrowly signifi cant, and, moreover, should the results substantially differ from the pre diction, the researcher may be unable to attach any statistical weight to the findings. It is suggested here that this dilemma can be satisfactorily sur mounted by avoiding the use of one tailed tests entirely in hypothesis- centered research; instead where the researcher has clear outcome ex pectations, using asymmetric two tailed tests with 90% of the probability in the expected tail and 10% in the unexpected direction to enable the researcher to pick up the serendipidous finding.