ABSTRACT

In a typical medical application, subjects are assigned randomly to two or more treatment groups, one of which may be a placebo or control group. As an example, the treatment may be a medication for hypertension. The subjects are then followed over time, their blood pressure measured during visits to a clinic. In a balanced design, every subject has his or her blood pressure measured at equally spaced intervals of, say, one week until a given number of observations is obtained. The statistical question of interest is whether the mean blood pressures for the two groups are significantly different. Assuming that the responses to the treatment or placebo are statistically independent from subject to subject, a simple solution to this problem exists in the balanced case. The mean blood pressure for each subject can be calculated and the two groups compared using the nonparametric Wilcoxon rank sum test or the equivalent Mann Whitney test. If these means appear normally distributed from subject to subject, the two sample t-test can be used. The mathematical model for this simple application, for subjects in group 1, is https://www.w3.org/1998/Math/MathML"> y i ( 1 ) j = β 1 + γ i ( 1 ) + ϵ i ( 1 ) j , https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780203748640/4fa687a6-cf95-4be5-a509-4d5b776421ec/content/eq1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>