Is there a situation where using a two-sample one-sided test is the right thing to do? In the context of health studies, I have to explain to non-statistician colleagues the difference between performing a one-tailed test at alpha=5% and a two-tailed test at alpha=10% when comparing two samples.
Indeed, being able to present a lower alpha for the apparent same statistical power can be falsely appealing for someone without the comprehension of the concept behind it.
In my comprehension, we should only use one-sample tests when the difference can "physically" only go in one direction (CMIIW). However, when comparing groups, I cannot figure out an instance where it is physically impossible for the value to be, say, higher in the control group.
Reading the numerous material here on SSE (the best one being this one to me) further supports my opinion that performing one-tailed tests is hardly ever the right thing to do in this case.
However, when explaining to non-statisticians (or maybe students), I feel that giving an example of what would be a good use case of one-tailed tests will help them grasp the concept better.
Therefore, using the simple example of two-sample tests such as t-tests or log-rank tests, what would be a legitimate comparison case where a one-tailed test is recommended?
If the answer can be health-related, this is a bonus.

Let's say there are two treatments for a given disease, called A and B. You and your team are used to perform treatment A. Every nurse is used to it, all processes are optimized for it, everything works well. You really only want to change to B if B produces better outcome then A. There is really nothing in it for you whether B's outcome is equal or worse then A. Even if B is inferior by a wide margin to A that does not change anything. In that case a one-sided tests reflects what you want to know.
As soon as you consider writing a report and publish it in the unlikely event of B being largely inferior, a one-sided test won't do anymore.
