Homework 11 Practice Problems on Applied Multivariable Statistic | STAT 873, Assignments of Statistics

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Note: This data set is from the SAS System for Mixed Models book by Littell, Milliiken, Stroup, and

Wolfinger (1996). See Chapter 3 of the book for a different analysis of the data.

From p. 88-9, Subjects in an exercise therapy study were assigned to one of three weightlifting programs. In the first program (RI), the number of repetitions of weightlifting was increased as the number of subjects became stronger. In the second program (WI), the amount of weight was increased as subjects became stronger. In the third program (CONT), subjects did not participate in weightlifting. Strengths of the subjects were measured every other day for two weeks following the beginning of the study. Below is the data step to read in the data. Note that s1=strength at time 1, s2=strength at time 2,….

data weights; input subj program$ s1 s2 s3 s4 s5 s6 s7;

• Homework for chapter
  • 1 CONT datalines;
  • 2 CONT
  • 3 CONT
  • 4 CONT
  • 5 CONT
  • 6 CONT
  • 7 CONT
  • 8 CONT
  • 9 CONT
• 10 CONT
• 11 CONT
• 12 CONT
• 13 CONT
• 14 CONT
• 15 CONT
• 16 CONT
• 17 CONT
• 18 CONT
• 19 CONT
• 20 CONT
  • 1 RI
  • 2 RI
  • 3 RI
  • 4 RI
  • 5 RI
  • 6 RI
  • 7 RI
  • 8 RI
  • 9 RI
• 10 RI
• 11 RI
• 12 RI
• 13 RI
• 14 RI
• 15 RI
• 16 RI
  • 1 WI
  • 2 WI
  • 3 WI

4 WI 86 87 87 87 87 87 86

5 WI 82 83 84 85 84 85 86

6 WI 79 80 79 79 80 79 80

7 WI 79 79 79 81 81 83 83

8 WI 87 89 91 90 91 92 92

9 WI 81 81 81 82 82 83 83

10 WI 82 82 82 84 86 85 87

11 WI 79 79 80 81 81 81 81

12 WI 79 80 81 82 83 82 82

13 WI 83 84 84 84 84 83 83

14 WI 81 81 82 84 83 82 85

15 WI 78 78 79 79 78 79 79

16 WI 83 82 82 84 84 83 84

17 WI 80 79 79 81 80 80 80

18 WI 80 82 82 82 81 81 81

19 WI 85 86 87 86 86 86 86

20 WI 77 78 80 81 82 82 82

21 WI 80 81 80 81 81 82 83

;

run ;

Answer the following questions:

1) Let i=(i1,…,i7) for i=1 (RI), 2 (WI), and 3 (CONT). Construct a test to determine if there are

differences between the mean vectors using MANOVA methods.

2) Use ANOVA methods to investigate if there are differences between the means at each

individual time point.

3) Construct a profile plot.

Below are partial answers to the questions.

1)

proc glm data=weights; class program; model s1-s7 = program / ss3; manova H=program / printe printh; run ; Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.67261322 1.50 14 96 0. Pillai's Trace 0.35155260 1.49 14 98 0. Hotelling-Lawley Trace 0.45081028 1.52 14 73.513 0. Roy's Greatest Root 0.34738552 2.43 7 49 0. NOTE: F Statistic for Roy's Greatest Root is an upper bound. NOTE: F Statistic for Wilks' Lambda is exact.

Since the tests are not significant at the =0.05 level (except Roy’s), some people would

suggest not to do the remaining tests in 2).

2) Examine the individual ANOVA output give from PROC GLM. Use a Bonferroni adjusted

significance level of /7 to determine significance.

3)