Once you have considered the questions below, I would recommend that you consider the clinically contextualized examples in the tutorial Fundamentals of Hypothesis Testing with a view to constructing your own null and alternative hypotheses.
· Q 1. I wish to compare pain scores between two groups of patients. How do I decide whether to use a one-tailed (one-sided) or two-tailed (two-sided) test?
A. I think that one of the main issues here is whether or not we have good reason in advance to convince us that the overall values will have changed in a particular direction when we progress from considering one group to another.
For example, if we expect pain levels to decrease after use of a particular analgesic, we might choose to use a one-tailed test. However, if we are comparing pain levels according as to which of two types of analgesic were used, we might wish to be more cautious.
The debate is ongoing (even amongst statisticians) re whether one-tailed tests are a ‘no-no’. Those who dislike them are often troubled about the fact that since for a one-tailed test, we use a p-value which is half that for a two-tailed test, it is much easier to conclude that we have a significant effect and therefore much easier to wrongly conclude that there is a real effect.
As you may know, when the chance of making the above error increases, the chance of failing to detect a real effect decreases (and so the statistical power of the test increases). Thus, those on the side of the defence for a one-tailed test might argue that a one-tailed test is less likely to dismiss clinically valuable interventions as non-significant, as such tests are less conservative.
Taking both sides of the argument into consideration, for me, the bottom line is just as I said at the start – one ought to be absolutely sure from the outset that a one-tailed test makes sense relative to the data under consideration. It is conceptually unsound and deceitful  to start with a two-tailed test (as you do not know in advance what direction the change should occur in) and then having obtained the outcome, to switch to a one-tailed test (by halving the p-value) so as to argue for (or ‘fudge’) a significant effect in a particular direction. Please don’t do this.
· Q 2. I would like to refer my readers to published literature when writing up my research findings. Can you recommend any literature explaining the rationale for using two-tailed tests, except in the special type of case described above?
A. Yes, there is a lot of relevant literature available to help here. A helpful example is Defending the Rationale for the Two-Tailed Test in Clinical Research.
One-Tailed versus Two-Tailed Hypotheses Tests by Margaret MacDougall is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
