A small pilot study is run to compare a new drug for chronic pain to one that is

Question

A small pilot study is run to compare a new drug for chronic pain to one that is currently available. Participants are randomly assigned to receive either the new drug or the currently available drug and report improvement in pain on a 5-point ordinal scale. 1 = Pain is much worse, 2 = Pain is slightly worse, 3 = No change, 4 = Pain improved slightly, 5 = Pain much improved.

Use the Mann-Whitney U test to determine if the new drug is significantly better in improvement in pain with a 5% level of significance (i.e. one-sided).

NewDrug: 3 5 4 3 4 2 5

StandardDrug: 3 1 4 1 2 3 2

What is the critical value?

a. 8

b. 9

c. 10

d. 11

Define Group 1 to be those who received the New Drug. What is R1?

a. 37

b. 13.5

c. 68

d. 7.5

Define Group 2 to be those who received the Standard Drug. What is R2?

a. 68

b. 37

c. 11

d. 1.5

What is U1? a. 49 b. 28 c. 37

d. 9

What is U2?

a. 40

b. 49

c. 28

d. 37

14. True or False: Reject the null hypothesis as the test statistic is less than the critical value.

Explanation / Answer

The given test of Mann - Whitley is a one tailed test

Null Hypothesis : H0: There is no significant difference between both drugs.

Alternative Hypothesis: Ha : New drug is significantly effective than the old drug.

I am attaching here the rank table

(A) The critical Value of U for one tailed alpha = 0.05 and n1= n2= 7 is 11 as we can see it in U- table.

(B) R1= Sum of all ranks for new drug= 4+ 7.5 + 7.5 +11 + 11 + 13.5 +13.5 = 68

(C) R2= sum of all ranks for old drug = 1.5 +1.5 +4 + 4 +7.5+ 7.5 +11 = 37

(D ) U1= n1n2+n2(n2+1)/2 - Max (R1,R2) = 7 * 7 + 7 * 4 - 37 = 9

(E) U2 = n1n2- U1= 49 - 9 = 40

so minimum of these two U values will be the U value for the test which is equal to 9

The U-value is 9. The critical value of U at p < .05 is 11. Therefore, the result is significant at p < .05.

Q>14 so we can reject the null hypothesis as the test statistic is less than the critical value. The statement is true.

New Drug Rank Standard Drug Rank Combined values Rank 3 4 3 1.5 1 1.5 5 7.5 1 1.5 1 1.5 4 7.5 4 4 2 4 3 11 1 4 2 4 4 11 2 7.5 2 4 2 13.5 3 7.5 3 7.5 5 13.5 2 11 3 7.5 3 7.5 3 7.5 4 11 4 11 4 11 5 13.5 5 13.5

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