Hypothesis
The t test for dependent means is used when we want to know whether there is a difference between populations when the data are "linked" or "dependent". For instance, we may want to know if using tutorials in a statistics class improves knowledge. To assess this, we would have to know a student's knowledge before using the tutorial and again after completing the tutorial. Thus, any data collected from this student are "linked".

The t test for dependent means is used only for tests of the sample means. Thus, our hypothesis tests whether the average difference between scores (M1 - M2) suggests that our students come from a population where tutorials do not affect performance (μ₁ - μ₂ = 0) or whether they come from a different population in which knowledge improves after using the tutorial.

The statistical hypotheses for t-tests for dependent means take one of the following forms, depending on whether your research hypothesis is directional or nondirectional. In the equations below, μ₁ refers to the pretest or Time 1 population from which the study sample was drawn; μ₂ refers to the posttest or Time 2 population.