Estimating the Correlation Between Two Variables When Individuals are Measured Repeatedly
In many research projects, individuals are measured on two or more variables under different conditions. Often the main question concerns the possibility of mean differences between conditions on the variables. In the research that motivated this work, the conditions were several treatments that were evaluated for a skin ailment. Although the treatments were not the same, they did not differ markedly from each other in their effect on the disorder. The two variables were (x) the patient’s rating of his or her general comfort level under the treatment, and (y) a clinician’s rating of the effectiveness of the treatment in reducing symptoms. The principle issue was the correlation between the variables. There were two complicating problems however. The ﬁrst was that each individual was assessed under several different conditions. Consequently, the observations were not independent but rather were nested within individuals. The second complication was that the conditions administered to each subject varied from person to person, and also the number of conditions was unequal. To illustrate, the ﬁrst three participants had n1 = 3, n2 = 2, and n3 = 4 pairs of measurements, giving the data shown in Table 2.1. This kind of study also arises in
28 90 12 95 30 45 36 80 0 80 48 80 24 95 16 93
educational problems where different teachers evaluate several children, and also for rater-ratee problems that are common in personnel psychology, at least for those in which one class is assumed to be hierarchically nested within the other. With this method, there is no requirement that all raters evaluate all ratees.