Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Polyunsaturated fatty acids in the diet favorably affect several risk factors fo

ID: 3204057 • Letter: P

Question

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 below, where SBPb is SBP measured at baseline, SBP1m is SBP measured at 1 month later and SBPd is (SBPb-SBP1m).

a) What parametric test could be used to test for the effect of linoleic acid on SBP?

b) Use Stata to perform the test in (a) and report a p-value.

c) What nonparametric test could be used to test for the effect of linoleic acid on SBP?

d) Use Stata to perform the test in (c) and report a p-value.

e) Compare your results in (b) and (d), and discuss which method you feel is more appropriate here.

subject

SBPb

SBP1m

SBPd

1

119.67

117.33

2.34

2

100

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

4.33

12

117.33

108.44

8.89

13

120.67

117

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

subject

SBPb

SBP1m

SBPd

1

119.67

117.33

2.34

2

100

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

4.33

12

117.33

108.44

8.89

13

120.67

117

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

Explanation / Answer

a) Since the subjects of the test remains the same and the test has to check the difference between means of the two cases, the appropriate parametric test would be paired t-test

b) On performing the paired t-test, the p-value obtained = 0.00186

c) The non-parametric test suitable for this case would be Wilcoxon Signed rank test

d)

Result Details

W-value: 12
Mean Difference: 18.89
Sum of pos. ranks: 124
Sum of neg. ranks: 12

Z-value: -2.8957
Mean (W): 68
Standard Deviation (W): 19.34

Sample Size (N): 16

Result 1 - Z-value

The Z-value is -2.8957. The p-value is 0.00374. The result is significant at p 0.05.

Result 2 - W-value

The W-value is 12. The critical value of W for N = 16 at p 0.05 is 29. Therefore, the result is significant at p 0.05.

Both the results give a similar output wherein the null hypothesis should be rejected, which shows that the mean value of cholesterol has changed.

Hope this helps.