Question

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

Answer 1

Ans:

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.

There are also some technical differences between them. 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. As discussed above, the paired t-test is in fact one-sample t-test, which makes its df = n-1.

Matched samples (also called matched pairs, paired samples or dependent samples) are paired up so that the participants share every characteristic except for the one under investigation. A “participant” is a member of the sample, and can be a person, object or thing. A common use for matched pairs is to assign one individual to a treatment group and another to a control group. This process, called “matching” is used in matched pairs design. The “pairs” don’t have to be different people — they could be the same individuals at different time. For example:

• The same study participants are measured before and after an intervention.
• The same study participants are measured twice for two different interventions.