One tailed p-values for post-hoc tests

Question

Is it okay to calculate one tailed p-values from post-hoc tests? I read this from a source but I just want to confirm it. "First, post hoc tests by their nature are two-tailed (you use them when you have made no specific hypotheses and you cannot predict the direction of hypotheses that don’t exist)."

Answer 1

A post hoc test means that you’re doing the test after seeing some results, such as conducting ANOVA on 4 groups and then testing that group A has a different mean than group B. Since you’ve observed the direction in that case, you must do a two-tailed test, since it’s possible to observe that A has the greater sample mean than B even if B has a greater population mean than A.

(This is for the same reason that, if your two-tailed test gives you a p-value of $1.5\alpha$, you don’t get to do a one-tailed test in the direction you’ve observed the difference and then claim significance at $\alpha$.)

However, it is possible that, prior to seeing results, you know that you specifically want to test that A has a greater mean than B. Then it would be okay to do a one-tailed test of that hypothesis. But if you observe that B has a greater sample mean than A, you still would test that A has a greater mean than B, and even if you skip that test because you know you will get $p>0.50$, you still count this test when you’re counting how many tests you’re doing for multiple comparisons (such as a Bonferroni correction).

I struggle to think of when you’d want to do that, but I suppose it’s possible.