Study Design
The t test for dependent means requires a specific type of research design. We use the t test for dependent means when we collect data two different times on a single sample drawn from a population or when two different people are sampled as a pair because they are linked in some fashion in the population.

In this design, we have one group of subjects/paired subjects, collect data on these subjects twice, compute the difference between pairs or pretest and posttest scores, and compare the average sample difference (M_Diff) to the population parameter (m_Diff). The population parameter tells us what to expect if there were no effect or difference in the population.

If our sample statistic is very different (beyond what we would expect from sampling error), then our statistical test allows us to conclude that our sample came from a population in which members of a pair were different or Time 1 and Time 2 scores were different. In the
t test for dependent means, we are comparing the mean difference (M₁ - M₂) calculated on linked/dependent data to an expectation that there is no difference in the population (μ₁ - μ₂ = 0).