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.

Pairwise comparisons: 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

Use Tukey's procedure to look at pairwise comparisons between treatments, and use 99% confidence intervals to answer the following questions. Note: answer question 6 without taking into account your answers from question 5; this way you will not have to worry about the overall experiment-wide error rate being too large.

a. Which two treatments result in the most weight loss? Are the weight losses for those two treatments significantly different from one another?

b. Which two treatments are the least effective in terms of weight loss (not counting the standard treatment)? Are the weight losses for those two treatments significantly different from one another? Justify your answer.

c. A researcher would like to test the hypothesis that weight loss in group A4 is more than one pound greater, on average, than weight loss in group A3. What would be the results of this hypothesis test? Justify your answer.

d. A researcher would like to test the hypothesis that weight loss in group A4 is more than one pound greater, on average than weight loss in group S. What would be the results of this hypothesis test? Justify your answer.

e. Which groups are significantly different from the Standard?

f. What would your recommendation be regarding the different weight loss agents? Be specific about what treatment you recommend, and also under what conditions you recommend it (that is, is this treatment recommended for everyone, or just certain people?).

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