16. To see whether regular exercise could reduce carotid intima media thickness

Question

16. To see whether regular exercise could reduce carotid intima media thickness test (CIMT) levels among hypertensive patients, researchers measured the CIMT on seven hypertensive patients, before and after participation in a 10-week exercise program CIMT levels BeforeAfter 0.87 1.00 1.14 2.14 1.60 1.18 1.60 ID 0.57 0.88 1.00 1.00 0.20 1.21 1.51 4 (a) Use parametric and nonparametric tests to compare whether there is a significant difference between the before and after serum triglyceride values. The tabulated test statistic values are given as 2.447 (parametric) and 1.96 (nonparametric) (b) Specify the degree of freedom for the parametric test. (c) Comment which test would be most appropriate for the dataset. (d) Comment if nonparametric test is used then which version (t-based or z-based)

Explanation / Answer

a) Using paired t test (parametric) we get

H0: There is no significant difference in the before and after serum triglyceride value.

H1: There is significant difference in the before and after serum triglyceride value.

The P value is much higher than 0.05 so we accept the null hypothesis that there is no significant difference in the before and after serum triglyceride value.

Lets use the Wilcoxon Signed rank test (Non Parametric) test for the same hypothesis

The P value is lower than 0.05 so we reject the null hypothesis hence the test says that there is significant difference in the before and after serum triglyceride value.

b) the degree of freedom for parametric is 6

c) The two sample t-test is one of the most comonly used statistical tests. This is used to test the hypothesis that the means of two groups are the same. The t test assumes that the variable is normally distributed. When we cannot prove the assumption of Normality the non-parametric Wilcoxon-Mann-Whitney (or rank sum ) test is used as an alternative.

if our studt is to test for equality of means, the Wilcoxon test would mislead us, since the two groups will have almost identical means . In such cases Wilcoxon tests rejects the null hypothesis more than 5% of the time.

So t test would be a better approach to the problem to get a realistic view.

d) A T-test is appropriate when you are using small samples (n < 30) while a Z-test is appropriate when you are using large samples (n > 30).

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