What is the difference between paired and independent samples tests?

A given study may produce measurements that are paired or that are totally independent. Statistical tests should be chosen accordingly.

For example, we are interested in studying the effect of a medical treatment on insulin rate. Here are two possible experimental designs that would help answer this question:

• Insulin rate is measured on 30 patients before and after the medical treatment. Data are thus organized by pairs (every patient is associated to two measurements). An appropriate test to use here would be a paired two-sample t-test.

• Insulin rate is measured on 30 patients receiving a placebo and 30 other patients receiving the medical treatment. In this case, all of the measurements are independent. An appropriate test to use here would be an independent two-sample t-test.