Question

What are the similarities and differences between the two t tests for the difference between two population means? Under what condition should we use the t test for the matched samples?

Answer 1

The two-sample t-test is used when the data of two samples are statistically independent, while the paired t-test is used when data is in the form of matched pairs.

To use the two-sample t-test, we need to assume that the data from both samples are normally distributed and they have the same variances. For paired t-test, we only require that the difference of each pair is normally distributed. An important parameter in the t-distribution is the degrees of freedom.

For two independent samples with equal sample size n, df = 2(n-1) for the two-sample t-test. However, if we have n matched pairs, the actual sample size is n (pairs) although we may have data from 2n different subjects. The paired t-test is, in fact, a one-sample t-test, which makes its df = n-1.