The three most common versions of the t-test are: one-sample t-test, independent samples t-test, and the paired samples t-test. The one sample t-test is used to test whether a sample mean could have come from a particular population. The independent samples t-test is used in between-subjects designs, to test whether the sample mean in one condition is different from the sample mean in another condition. The paired samples t-test is used in within-subjects designs, to test whether the sample mean in one condition is different from the sample mean in the other condition.

To do this, we , or average over the observations in the hat conditions.