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 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

Answer 1

Answer:

Given that:

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

New drug	4	5	3	3	4	2
Standard drug	2	3	4	1	2	3

	New drug	Rank for
A	4	10
A	5	12
A	3	6.5
A	3	6.5
A	4	10
A	2	3
B	2	3
B	3	6.5
B	4	10
B	1	1
B	2	3
B	3	6.5

Ranks

1 = 1

2 = 2+3+4 / 3

= 9 / 3 =3

3 = 3+4+5+6 / 4 =6.5

4 = 5+6+7 / 3 =10

Sample size n1	A	6
Sample size n2	B	6

Rank sum(R1)=	A	48
Rank sum(R2)=	B	30

39 - 48

= 9