There are several well-known statins drugs on the market these days; Lipitor, Zo

Question

There are several well-known statins drugs on the market these days; Lipitor, Zocor, Mevacor, Crestor, and the list goes on... If you have high cholesterol, meaning your total cholesterol level is 240 milligrams per deciliter (mg/dL) or higher, or your low-density lipoprotein cholesterol (LDL, or "bad" cholesterol) level is 130 mg/dLor higher, your doctor may recommend you begin to take a statin. But the numbers alone won't tell you or your doctor the whole story If you're following the recommended lifestyle behaviors and the advice of your doctor but your cholesterolparticularly your low-density lipoprotein (LDL) cholesterol, the "bad" cholesterol _ remains high, statins might be an option for youu Anyhow, a new Statins drug is vying for some of the market space and to this end, offers a challenge to the other statins drugs. At a nearby hospital, patients with a history of high cholesterol were recruited for a comparison study of this new Statins and Lipitor. The LDL levels for all participants were recorded before the study and then the patients were divided into two groups. One group received the new drug and the other their own prescription of Lipitor (both at the dosage originally prescribed for the Lipitor). Both groups were deemed low-risk for heart attacks and stroke and were only on Lipitor as a preventive medication. After 6 months into this study, their LDL cholesterol levels were again recorded and the differences tabulated. The results are as follows Six-Month Differences in LDL (mg/dL) Group A Group B 10 9 19 13 17 19 19 Since this is a double-blind test, use the Mann-Whitney U-Test to test the claim at 95% confidence that there is a difference in the two products. In a double-blind study, no one knows the identity of either group (hence a two-tail test.)

Explanation / Answer

Mann Whitney test :

Here we have to test the hypothesis that,

H0 : There is no difference in the two products.

H1 : There is difference in the two products.

Assume alpha = 5% = 0.05

STEP ONE: Rank all scores together, ignoring which group they belong to.

STEP TWO: Add up the ranks for Brand X, to get T1

T1 = 2+1+5+3+4 = 15

STEP THREE: Add up the ranks for Brand Y, to get T2

T2 = 1+2+6+4.5+3+7+4.5 = 28

STEP FOUR: Select the larger rank. In this case it’s T2

STEP FIVE: Calculate n1, n2 and nx These are the number of participants in each group, and the number of people in the group that gave the larger rank total.

n1 = 5

n2 = 7

nx = 7

STEP SIX: Find U (Note: Tx is the larger rank total)

U = n1*n2 + nx*(nx+1) / 2 - Tx

= 5*7 + 7*(7+1) / 2 - 28

= 35 + 28 -28

= 35

STEP SEVEN: Use a table of critical U values for the Mann-Whitney U Test

At 5% level of significance, the critical value is 7.

STEP EIGHT:

U > critical value

The results are not significant.

That is accept H0 at 5% level of significance.

Conclusion :  There is no difference in the two products.

Group A rank group B rank 10 2 11 1 9 1 13 2 19 5 22 6 13 3 19 4.5 17 4 17 3 26 7 19 4.5

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