What's the difference between a one-tailed and two-tailed test?

A one-tailed test looks for an effect in one direction, while a two-tailed test looks for an effect in either direction.

In statistical testing, the choice between a one-tailed and a two-tailed test is determined by the nature of the research question. A one-tailed test, also known as a directional hypothesis, is used when the researcher has a specific prediction about the direction of the relationship between variables. For example, if a psychologist is studying the impact of a new therapy technique and predicts that it will improve patient outcomes, they would use a one-tailed test. This test will only look for an effect in one direction, i.e., improvement.

On the other hand, a two-tailed test, also known as a non-directional hypothesis, is used when the researcher does not have a specific prediction about the direction of the relationship. They are simply interested in whether there is a relationship, regardless of whether it is positive or negative. For instance, if a psychologist is studying the relationship between stress levels and a new medication, without predicting whether the medication will increase or decrease stress levels, they would use a two-tailed test. This test will look for an effect in either direction, i.e., increase or decrease.

The choice between a one-tailed and a two-tailed test also impacts the statistical significance of the results. In a one-tailed test, all the statistical power is directed towards detecting an effect in one direction, making it more likely to find a significant result if one exists in that direction. However, it will not detect an effect in the opposite direction. In contrast, a two-tailed test splits the statistical power between two directions. It is less likely to find a significant result in either direction, but it can detect an effect in either direction.

In conclusion, the choice between a one-tailed and a two-tailed test depends on the nature of the research question and the specific predictions made by the researcher. It's crucial to make the right choice, as it can significantly impact the results and interpretations of the study.