Let's consider how to analyze the data from the "ADHD Treatment" case study. These data consist of the scores of 24 children with ADHD on a delay of gratification (DOG) task. Each child was tested under four dosage levels. In this section, we will be concerned only with testing the difference between the mean of the placebo (D0) condition and the mean of the highest dosage condition (D60). The first question is why the difference between means should not be tested using the procedure described in the section Difference Between Two Means (Independent Groups). The answer lies in the fact that in this experiment we do not have independent groups. The scores in the D0 condition are from the same subjects as the scores in the D60 condition. There is only one group of subjects, each subject being tested in both the D0 and D60 conditions.
Figure 1 shows a scatter plot of the 60-mg scores (D60) as a function of the 0-mg scores (D0). It is clear that children who get more correct in the D0 condition tend to get more correct in the D60 condition. The correlation between the two conditions is high: r = 0.80. Clearly these two variables are not independent.