Greater power of one-sided tests?
An argument in favour of choosing a one-sided test is that it has greater statistical power than the corresponding two-sided test. Let us assume that we are planning a randomised, controlled trial and want a high probability of claiming a difference in effect if the probabilities of success with the standard treatment and new treatment are 0.6 and 0.8, respectively. If we plan to use a two-sided test, we would need 82 patients in each group to achieve statistical power of 80 % at a significance level of 0.05. If we plan to use a one-sided test, on the other hand, 64 patients in each group will be sufficient.
Let us assume that this trial was undertaken with 100 patients in each group. In the group that received the standard treatment 64 patients recovered, while in the group with the new treatment 76 recovered. The estimated difference in the probability of success is 76/100–64/100 = 0.12. Pearson's chi-square test gives a two-sided p-value of 0.064, meaning that the difference is not statistically significant at a significance level of 0.05. However, if the alternative hypothesis were one-sided, the p-value would be half of this, i.e. 0.032. In general, a two-sided p-value is equal to twice the corresponding one-sided p-value.
Around the 1990 s, there was some debate on the choice of one-sided versus two-sided tests in medical statistics (1, 2). However, one issue has always remained beyond dispute: the choice of a one-sided or two-sided hypothesis test must be made in advance. This rule seems to have been frequently disregarded. In his textbook from 1991, Altman wrote: 'The small number of one-sided tests that I have seen reported in published papers have usually yielded P values between 0.025 and 0.05, so that the result would have been non-significant with a two-sided test. I doubt that most of these were pre-planned one-sided tests' ((3), p. 171)