When is a paired t-test appropriate?

• A. When observations are from the same subjects before and after; differences are normally distributed.
• B. When observations are collected from two independent groups.
• C. When data are binary outcomes.
• D. When observations are paired and the difference scores are approximately normally distributed.

Answer: (D)

A paired t-test is appropriate when you have matched or paired observations and you assess the change within each pair by looking at the difference between the two measurements. The crucial assumption is that those difference scores are approximately normally distributed, which lets the test determine whether the average difference is zero. This setup comes up when you measure the same subjects before and after a treatment or when you compare paired subjects (like twins) in related groups, because the pairing reduces variability and makes the test more powerful. If the differences aren’t roughly normal, especially with small samples, a nonparametric alternative like the Wilcoxon signed-rank test is more appropriate. Binary outcomes aren’t suitable for a paired t-test, since the method relies on continuous difference scores.