Parametric and Non-Parametric Hypothesis Tests
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Re-analyze the data in Table 8.18 using nonparametric methods. Assume the samples are unpaired.
Table 8.18 Birthweights in a clinical trial to test a drug for preventing low-birthweight deliveries
Baby weight (lb)
Patient number Treatment Group Control Group
1 6.9 6.4
2 7.6 6.7
3 7.3 5.4
4 7.6 8.2
5 6.8 5.3
6 7.2 6.6
7 8.0 5.8
8 5.5 5.7
9 5.8 6.2
10 7.3 7.1
11 8.2 7.0
12 6.9 6.9
13 6.8 5.6
14 5.7 4.2
15 8.6 6.8
9.8 Would such methods be preferable to parametric methods in analyzing the data? Why or why not?
Hypertension
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 supplements of linoleic acid on blood pressure, 17 adults consumed 23 g/day of safflower oil, high in linoleic acid, for 4 weeks. Blood-pressure 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 9.10
Subject Baseline SBP 1-month SBP Baseline minus 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
9.19 What parametric test could be used to test for the effect of linoleic acid on SBP?
9.20 Perform the test in Problem 9.19, and report a p-value.
9.21 What nonparametric test could be used to test for the effect of linoleic acid on SBP?
9.22 Perform the test in Problem 9.21 and report a p-value.
9.23 Compare your results in Problems 9.20 and 9.22, and discuss which method you feel is more appropriate here.
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Solution Summary
The solution provides step-by-step method of performing a non-parametric Wilcoxon Signed Rank Test and a parametric T-Test. All the steps of hypothesis testing (formulation of null and alternate hypotheses, selection of significance level, choosing the appropriate test-statistic, decision rule, calculation of test-statistic and conclusion) have been explained and the statistical analysis has been shown in details. The calculations have also been shown in EXCEL for better understanding.
Education
- MSc, Osmania University
- MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
- BSc, Banaras Hindu University
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