Consider studying whether drug A and drug B are equally effective in lowering blood pressure. For each of (a), (b), and (c) answer two questions (you do not need to explain your answers):
(I) What kind of paired design is this (i.e.. What is the nature of the pairing)?
(II) True or false: "It is legitimate to conduct a paired / test analysis on these differences (assuming that the A-B differences follow a normal distribution).
(a) We get a sample of 20 patients and record their ages, ranking them from 1 to 20. We match patient 1 with patient 2, patient 3 with patient 4, and so forth. In each pair, one patient gets drug A, and one gets drug B (randomly). Then we record change in blood pressure and look at the differences within each pair.
(b) For each of 10 consecutive weeks, we randomly select two patients, give one of them drug A and the other drug B (randomly), and record change in blood pressure. We then look at the differences within the pair from the first week, the pair from the second week, and so forth.
(c) We get a sample of 20 patients and give 10 of them drug A and the other 10 drug B (randomly). Then, we measure change in blood pressure. We match the patient with the greatest change on A with the patient with the greatest change on B, the second greatest change on A with the second greatest change on B, and so forth. Then, we look at the differences within each pair.