One- and Two-Tailed Tests (2 of 4)
A probability computed considering differences in both directions is called a "two-tailed" probability. The name makes sense since both tails of the sampling distribution are considered.
There are situations in which an experimenter is concerned only with differences in one direction. For example, an experimenter may be concerned with whether or not μ1 - μ2 is greater than zero. However, if μ1 - μ2 is not greater than zero, the experimenter may not care whether it equals zero or is less than zero. For instance, if a new drug treatment is developed, the main issue is whether or not it is better than a placebo. If the treatment is not better than a placebo, then it will not be used. It does not really matter whether or not it is worse than the placebo.
When only one direction is of concern to an experimenter, then a "one-tailed" test can be performed. If an experimenter were only concerned with whether or not μ1 - μ2 is greater than zero, then the one-tailed test would involve calculating the probability of obtaining a statistic as great or greater than the one obtained in the experiment.