One-sided ttests in regression analysis with a clear prior This question has been asked virtually the same in this post:
Regression Slope and a Bilateral Test
However, I still don't get my head around why when I have a clear hypothesis of a positive relationship between my covariate of interest and the outcome in mind I should "waste" the power of testing whether the relationship could be negative. This is particularly strange to me in the case of experiments where the extra needed power implies having to spend more ressources to collect additional data. Does anybody have an opinion on this or knows statistical literature to read up on?
 A: The linked thread considers a case where the alternative $H_1$ and the corresponding rejection region are chosen after the test statistic has been observed. This is bad practice as it distorts the $p$-value and may change the decision (in comparison to the valid way of conducting the test). Now if you choose $H_1$ before observing the test statistic, the problematic aspect of the former approach is eliminated.
One-sided tests exist and can be used and yield valid results. If you know $\theta<c$ to be impossible, you can formulate and test $H_0\colon \ \theta=c$ against a one-sided alternative $H_1\colon \ \theta>c$ no problem. Regarding power, indeed it would be a waste of time to employ the two-sided $H_1\colon \ \neq c$ instead. However, if $\theta<c$ is merely unlikely according to our understanding / is out of line with our favourite theory, this is usually not deemed sufficient to exclude this possibility from the alternative.
Regarding references, I think this is introductory level material and should be found in most classical textbooks, both theoretical and applied. A list of free statistics textbooks is available in this thread. This one contains some more (not necessarily free).
