On the use of one-sided statistical tests in biomedical research.

There is a tendency to automatically use two-sided tests to assess the statistical significance of experimental results. Yet if a theory predicts the direction of an experimental outcome, or if for some practical (eg clinical) reason an outcome in that direction is the only one of interest, then it makes sense to use a one-sided test. The use of a two-sided test in these situations will lead to too many false negatives. Consequently treatment effects that corroborate a theory or that are of practical importance may be missed. This problem becomes particularly acute in the case of borderline results. Following a nonsignificant one-sided test, the possibility of an effect in the direction opposite to that predicted or required can be assessed in an exploratory fashion by computing the odds in favour of such an effect. Anyone is then at liberty to pursue this possibility as they see fit. The question of whether to use a one-sided or two-sided statistical test should always be decided on logical grounds not statistical ones, and suspicions regarding the motives of the investigator(s) should be disregarded. On the other hand, this choice can be avoided altogether by assuming that a treatment always has some effect (however small) and then computing the strength of the evidence in favour of the observed or predicted/required effect (ie 1-P, where P is the one-sided significance level of the test). With this approach one-sided and two-sided tests yield identical results, and so there is effectively only one type of test.