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I am looking to see if the mean of group A is higher than the mean of group B using an unpaired t-test. I don't really care if group B is lower than group A (it might actually mean something, but it isn't very useful). Given that my hypothesis is looking for an effect in one direction, is it justifiable to use a one-tailed t-test? If I clearly state my hypothesis in such a way that I am looking for an effect in a single direction, do I need to explicitly state that the p-value is one-tailed?

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    $\begingroup$ One question you might want to answer in the body of your question is what you would do if the test happened to be significant and in the opposite direction? $\endgroup$ – John Dec 28 '14 at 19:06
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    $\begingroup$ Yes. Acceptance of use of one-tailed tests varies (some application areas tend to be a bit prejudiced against them, probably because of past experience of significance-hunting by people deciding to use a one-tailed test post hoc), but if your justification is one that will seem obvious (that is, that a reader would understand would quite naturally be one-sided) there should be no problem at all. $\endgroup$ – Glen_b -Reinstate Monica Dec 28 '14 at 22:22
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Yes, if you are only talking about the probability that $\mu_A > \mu_B$ then one would expect you to be using a one-tailed t-test and p-value.

More formally, your null hypothesis is $\text{H}_{0}: \mu_A \leq \mu_B$ and your alternative hypothesis, $\text{H}_{1}: \mu_A > \mu_B$, is one-sided.

(Granted, to avoid confusion I would clarify and reiterate the fact that the p-value is single-tailed wherever possible.)

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