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One-tailed vs. two-tailed tests

It is easier to reject the null with a one-tailed test than two-tailed test.

A one-tailed test is used when we predict the direction of the difference in advance (e.g. one mean will be larger than the other). With that assumption, the probability of incorrectly rejecting the null is only calculated from one tail of the distribution. In standard testing, the probability is calculated from both tails. Thus, the p-value from a two-tailed test ($p_2$) is twice the p-value of a one-tailed test ($p_1$).

p_{2} = 2\: p_{1}

It is rarely correct to perform a one-tailed test; usually we want to test whether any difference exists.

Maureen Hillenmeyer 2006-05-09