The International Conference on Harmonization (ICH) E9 guideline recommends using a significance level of α/2 for one-sided tests in regulatory sellings. Two arguments are presented to demonstrate that this approach may not be universally sensible. First, a two-sided p-value is not always twice the minimum of the two tail probabilities, that is, the two possible one-sided p-values. Based on Fisher's exact test, examples are presented in which the one-sided p-value is larger than α/2 although the corresponding two-sided p-value is smaller than α. Second, the choice between one- and two-sided tests is an artificial dichotomy since there is a continuum of choices when using asymmetrical critical regions. Such an unequal split of α is implicitly used when Fisher's exact test is applied two-sided. Furthermore, a test intermediate to one- and two-sided tests is sometimes appropriate in group sequential designs.
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