Maria Mathias (A-13) conducted a study of hyperactive children. She measured the children’s attitude, hyperactivity, and social behavior before and after treatment. The following table shows for 31 subjects the age and improvement scores from pre-treatment to post-treatment for attitude (ATT), social behavior (SOC), and hyperactivity (HYP). A negative score for HYP indicates an improvement in hyperactivity; a positive score in ATT or SOC indicates improvement. Perform an analysis to determine if there is evidence to indicate that age (years) is correlated with any of the three outcome variables. Let a ¼ :05 for all tests.

Subject No. AGE ATT HYP SOC 1 9 1:2 1:2 0.0 2 9 0.0 0.0 1.0 3 13 0:4 0.0 0.2 4 6 0:4 0:2 1.2 5 9 1.0 0:8 0.2 6 8 0.8 0.2 0.4 7 8 0:6 0:2 0.6 8 9 1:2 0:8 0:6 9 7 0.0 0.2 0.8 10 12 0.4 0:8 0.4 11 9 0:8 0.8 0:2 12 10 1.0 0:8 1.2 13 12 1.4 1:6 0.6 14 9 1.0 0:2 0:2 15 12 0.8 0:8 1.0 16 9 1.0 0.4 0.4 17 10 0.4 0:2 0.6 18 7 0.0 0:4 0.6 19 12 1.1 0:6 0.8 20 9 0.2 0:4 0.2 21 7 0.4 0:2 0.6 22 6 0.0 3:2 1.0 23 11 0.6 0:4 0.0 24 11 0.4 0:4 0.0 25 11 1.0 0:7 0:6 26 11 0.8 0:8 0.0 27 11 1.2 0.6 1.0 28 11 0.2 0.0 0:2 29 11 0.8 1:2 0.3 30 8 0.0 0.0 0:4 31 9 0.4 0:2 0.2 Source: Data provided courtesy of Maria Mathias, M.D. and the Wright State University Statistical Consulting Center.