Non Parametric Methods
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HomeWork.docx
A Polyunsaturated fatty acids in the diet favorably affect several risk factors for cardiovascular disease. The principal dietary polyunsaturated fat is linoleic acid. To test the effects of dietary supplementation with linoleic acid on blood pressure, 17 adults consumed 23 g/day of safflower oil, high in linoleic acid, for 4 weeks. Systolic blood pressure (SBP) measurements were taken at baseline (before ingestion of oil) and 1 month later, with the mean values over several readings at each visit given in Table 2.
Table 2 Effect of linoleic acid on SBP
|
Subject |
Baseline SBP |
1-month SBP |
Baseline − 1-month SBP |
|
1 |
119.67 |
117.33 |
2.34 |
|
2 |
100.00 |
98.78 |
1.22 |
|
3 |
123.56 |
123.83 |
–0.27 |
|
4 |
109.89 |
107.67 |
2.22 |
|
5 |
96.22 |
95.67 |
0.55 |
|
6 |
133.33 |
128.89 |
4.44 |
|
7 |
115.78 |
113.22 |
2.56 |
|
8 |
126.39 |
121.56 |
4.83 |
|
9 |
122.78 |
126.33 |
–3.55 |
|
10 |
117.44 |
110.39 |
7.05 |
|
11 |
111.33 |
107.00 |
4.33 |
|
12 |
117.33 |
108.44 |
8.89 |
|
13 |
120.67 |
117.00 |
3.67 |
|
14 |
131.67 |
126.89 |
4.78 |
|
15 |
92.39 |
93.06 |
–0.67 |
|
16 |
134.44 |
126.67 |
7.77 |
|
17 |
108.67 |
108.67 |
0.00 |
7 What parametric test could be used to test for the effect of linoleic acid on SBP?
8 Perform the test in Problem 7, and report a p-value.
9 What nonparametric test could be used to test for the effect of linoleic acid on SBP?
10 Perform the test in Problem 9, and report a p-value.
11 Compare your results in Problems 8 and 10, and discuss which method you feel is more appropriate here.
*1 Assess the impact of the program statistically (use a two-sided test). Suppose patients are graded on the degree of change in periodontal status on a 7-point scale, with +3 indicating the greatest improvement, 0 indicating no change, and −3 indicating the greatest decline. The data are given in Table 1.
2 What nonparametric test can be used to determine whether a significant change in periodontal status has occurred over time?
3 Implement the procedure in Problem 2, and report a p-value.
Table 1 Degree of change in periodontal status
|
Change score |
Number of patients |
|
+3 |
4 |
|
+2 |
5 |
|
+1 |
6 |
|
0 |
5 |
|
−1 |
4 |
|
−2 |
2 |
|
−3 |
2 |
4 Suppose there are two samples of size 6 and 7, with a rank sum of 58 in the sample of size 6. Using the Wilcoxon rank-sum test, evaluate the significance of the results, assuming there are no ties. 5 Answer Problem 4 for two samples of size 7 and 10, with a rank sum of 47 in the sample of size 7. Assume there are no ties. 6 Answer Problem 4 for two samples of size 12 and 15, with a rank sum of 220 in the sample of size 12. Assume there are no ties.
