Understanding the difference between one-tailed and two-tailed tests is fundamental to hypothesis testing. The choice between these tests depends on the research question and the directionality of the effect you want to detect. A one-tailed test is used when you are interested in deviations in only one direction—either greater than or less than a specified value. In contrast, a two-tailed test is appropriate when you want to detect deviations in both directions, meaning you are interested in any significant difference, regardless of direction.

A one-tailed test is suitable when your hypothesis predicts the direction of the effect. For example, if you want to know whether a new feature increases conversion rate, you would use a one-tailed test with the alternative hypothesis "conversion rate is greater than before." The entire significance level ($α$) is placed in one tail of the distribution, making it more sensitive to effects in that direction but unable to detect effects in the opposite direction.

A two-tailed test is used when you are interested in any significant difference, regardless of direction. For instance, if you want to know whether a new feature changes the conversion rate in any way (either increase or decrease), you would use a two-tailed test. Here, $α$ is split equally between both tails, allowing you to detect effects in both directions but requiring a larger effect to reach significance in either direction.

Selecting the correct test is crucial for valid results. Using a one-tailed test when a two-tailed test is appropriate (or vice versa) can lead to incorrect conclusions and affect the integrity of your experiment.