One-tailed tests: Hypothesis tests in which the entire alpha is placed in either the upper (positive) or lower (negative) tail such that there is only one critical value of the test statistic. Also called directional tests.
The choice of a one-tailed test versus a two-tailed test is generally made on a case-by-case basis. It depends on whether a researcher has a good reason to believe that the relationship under examination should be positive or negative. Suppose that you are studying an in-prison treatment program that focuses on improving participants’ literacy skills. You would measure their reading levels before the program began and then again after it had ended, and would expect to see an increase—you have good reason to predict that post- intervention literacy skills would be greater than pre-intervention ones. In this case, a one-tailed test would be in order (these are also called directional tests, since a prediction is being made about the direction of a relationship). Now suppose you want to know whether that literacy program works better for men or for women. You do not have any particular reason for thinking that it would be more effective for one group than the other, so you set out merely to test for any difference at all, regardless of direction. This would be cause for using a two-tailed test (also called a nondirectional test). Let us work our way through some examples and discuss one-tailed and two-tailed tests as we go.