When is a one-tailed test most appropriate?

A one-tailed test is most appropriate when a researcher has a specific directional hypothesis, meaning that they predict not just that there will be a difference between groups, but also the direction of that difference. For example, if a researcher proposes that one group's scores will be higher than another's, they are making a directional prediction and should use a one-tailed test. This approach allows the researcher to determine if the observed data supports the predicted direction of the effect.

In contrast, a test for any difference between groups is more general and does not specify a direction. Therefore, it would be more appropriate to use a two-tailed test, which evaluates both directions of a potential effect. The conditions of variances being unequal or having a small sample size do not inherently dictate the need for a one-tailed test; rather, they may influence the choice of statistical methods or adjustments, but they don't determine the directionality of the hypothesis being tested.