Researchers conducted an experiment to compare the effectiveness of four new weight-reducing agents to that of an existing agent. The researchers randomly divided a random sample of 50 males into five equal groups with preparation A1 assigned to the first group, preparation A2 to the second group, and so on. The fifth group was given the standard preparation, labeled S. They gave a prestudy physical to each person in the experiment and told him how many pounds overweight he was. A comparison of the mean numbers of pounds overweight for the groups showed no significant differences. The researchers then began the study program, and each group took the prescribed preparation for a fixed period of time. The weight losses recorded at the end of the study were recorded, and can be found in the attached data set. Answer the following questions using SAS, and append your code

Contrasts: suppose the weight-loss agents were of the following form:

A1: Drug therapy with exercise but no counseling

A2: Drug therapy with no exercise but counseling

A3: Drug therapy with no exercise and no counseling

A4: Drug therapy with exercise and counseling

S: Standard agent

For each of the following situations, construct a linear contrast and use SAS to test it. In your homework, write the contrast and your conclusion (both statistical significance and interpretation; it's fine to say the outcome is inconclusive if that's so):

a. Compare the mean for the standard agent (S) to the average of the means for the four new agents. Are the new agents an improvement over the standard?

b. Compare the mean for the agents with counseling to those without counseling, ignoring the standard. Does counseling result in improved outcomes?

c. Compare the mean for the agents with exercise to those without exercise, ignoring the standard treatment. Does exercise result in improved outcomes?

d. What is the overall experiment-wide error rate if you test each of these three contrasts at 5%? Adjust alpha using Bonferroni's correction so that the overall error rate is no more than 5%, and run the contrasts again. What level alpha did you use? Which (if any) results changed?

loss regime

12.4 A1

10.7 A1

11.9 A1

11 A1

12.4 A1

12.3 A1

13 A1

12.5 A1

11.2 A1

13.1 A1

9.1 A2

11.5 A2

11.3 A2

9.7 A2

13.2 A2

10.7 A2

10.6 A2

11.3 A2

11.1 A2

11.7 A2

8.5 A3

11.6 A3

10.2 A3

10.9 A3

9 A3

9.6 A3

9.9 A3

11.3 A3

10.5 A3

11.2 A3

12.7 A4

13.2 A4

11.8 A4

11.9 A4

12.2 A4

11.2 A4

13.7 A4

11.8 A4

12.2 A4

11.7 A4

8.7 S

9.3 S

8.2 S

8.3 S

9 S

9.4 S

9.2 S

12.2 S

8.5 S

9.9 S