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 to 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. Is there a significant difference in self-reported improvement in pain? Use the Mann-Whitney U test with a 5% level of significance.New Drug:  4      5      3     3      4     2Standard Drug:  2     3     4     1     2     3

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Asked Dec 15, 2019
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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 to 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. Is there a significant difference in self-reported improvement in pain? Use the Mann-Whitney U test with a 5% level of significance.

New Drug:  4      5      3     3      4     2

Standard Drug:  2     3     4     1     2     3

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Expert Answer

Step 1

Given data and calculation of Rank is shown below

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Scale of pain Type of Drug New Drug New Drug New Drug New Drug New Drug New Drug Standard Drug Standard Drug Standard Drug Standard Drug Standard Drug Standard Drug Rank 4 10 5 12 3 6.5 6.5 4 10 3 3 6.5 3 4 10 3 3 6.5

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Step 2

Formulation of Hypothesis

Null Hypothesis : - There is no difference in the self-reported improvement in pain

Alternative Hypothesis : - There is difference in the self-reported improvement in pain

Sum of Ranks of new drug

R1 = 10 + 12 + 6.5 + 6.5 + 10 + 3  = 48

Sum of Ranks of standard Drug

R2 = 3 + 3 + ...

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6 x (6 + 1) п(п + 1) 48 = 9 = 6 x 6 + - Rn U1 n¡n2 + 2

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