In a study of blood pressure, 12 subjects have their BP measured, then the drug is given and BP rechecked after one hour. The drug will be approved if there is no evidence that the average increase exceeds 20 points. Which test is used?

In a study of blood pressure, 12 subjects have their BP measured, then the drug is given and BP rechecked after one hour. The drug will be approved if there is no evidence that the average increase exceeds 20 points. Which test is used?

• A. One-sample t-test
• B. Two-sample t-test
• C. Matched pairs t-test with 11 degrees of freedom
• D. Sign test

Answer: (C)

When measurements are taken on the same subjects before and after an intervention, the data are paired. To decide if the average change in blood pressure is greater than 20 points, you look at the differences for each subject (post minus pre) and test whether the mean of these differences is more than 20. This is a matched-pairs t-test (equivalently, a one-sample t-test on the differences) with degrees of freedom equal to the number of pairs minus one. Here, there are 12 subjects, so df = 12 − 1 = 11. Why this fit matters: using the paired approach accounts for the natural linkage within each subject, reducing variability and giving a more accurate test of the mean change against the 20-point threshold. The sign test would ignore how big the changes are, only their direction, making it less powerful if the differences are roughly normal. A two-sample t-test would treat pre and post as independent groups, which misuses the data since each subject contributes both measurements. So, the correct approach is a paired (matched) t-test on the differences, with 11 degrees of freedom.

When measurements are taken on the same subjects before and after an intervention, the data are paired. To decide if the average change in blood pressure is greater than 20 points, you look at the differences for each subject (post minus pre) and test whether the mean of these differences is more than 20. This is a matched-pairs t-test (equivalently, a one-sample t-test on the differences) with degrees of freedom equal to the number of pairs minus one. Here, there are 12 subjects, so df = 12 − 1 = 11.

Why this fit matters: using the paired approach accounts for the natural linkage within each subject, reducing variability and giving a more accurate test of the mean change against the 20-point threshold. The sign test would ignore how big the changes are, only their direction, making it less powerful if the differences are roughly normal. A two-sample t-test would treat pre and post as independent groups, which misuses the data since each subject contributes both measurements.

So, the correct approach is a paired (matched) t-test on the differences, with 11 degrees of freedom.