. A small pilot study is run to compare a new drug for chronic pain to one that
ID: 3048440 • Letter: #
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. Use the appropriate test to assess whether there is a significant difference in self-reported improvement in pain, and report your test statistic.
New Drug: 4 5 3 3 4 2
Standard Drug: 2 3 4 1 2 3
Explanation / Answer
(A)
(B)
(C)
(D)
(E)
(F)
(G)
Pain Category
Frequency in New Drug
Frequency in Standard Drug
Proportion in New Drug
Proportion in Standard Drug
Combined Proportion
Z value
Worse
0
1
0
0.166667
0.083333
-1.04447
Slightly worse
1
2
0.166667
0.333333
0.25
-0.66667
No change
2
2
0.333333
0.333333
0.333333
0
Improved Slightly
2
1
0.333333
0.166667
0.25
0.666667
Much Improved
1
0
0.166667
0
0.083333
1.044466
In this example data is provided on 5-point ordinal scale. In the above table column A shows pain category, B shows frequency of patients in each category receiving new drug. Column C shows frequency of patients in each category receiving standard drug. Column D and E gives proportion of patients in each category corresponding to the new and standard drug. Column F gives combined proportion of patients in each category. Lastly column F gives value of Z for testing equality of proportions in each category receiving new and standard drug. From values of Z it seems that all absolute values of Z are less than 1.64 and hence in each category the effect of both drugs is insignificant, it means drug is at par with standard drug
(A)
(B)
(C)
(D)
(E)
(F)
(G)
Pain Category
Frequency in New Drug
Frequency in Standard Drug
Proportion in New Drug
Proportion in Standard Drug
Combined Proportion
Z value
Worse
0
1
0
0.166667
0.083333
-1.04447
Slightly worse
1
2
0.166667
0.333333
0.25
-0.66667
No change
2
2
0.333333
0.333333
0.333333
0
Improved Slightly
2
1
0.333333
0.166667
0.25
0.666667
Much Improved
1
0
0.166667
0
0.083333
1.044466
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