A new drug for pain relief is being tested within a given palliative care popula

Question

A new drug for pain relief is being tested within a given palliative care population. The new drug is being compared to an already approved pain relief drug that is commonly used in providing palliative care to patients who experience chronic severe pain. Assume the patients are asked to rate the pain on a scale from 1 to 10, and the data presented below was obtained from a small study designed to compare the effectiveness of the two drugs. Set up and interpret the results of a Mann-Whitney U test with an alpha of .05.

                        Pain Rating as Reported by Patients

Old Drug           1          3          3          4          6         

New Drug         1          2          3          3          7

We fail to reject H0, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 10.5 is greater than the critical U value of 2.

We fail to reject H0, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 14.5 is greater than the critical U value of 2.

We reject H0 in favor of H1, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 10.5 is greater than the critical U value of 2.

We reject H0 in favor of H1, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 14.5 is greater than the critical U value of 2.

Explanation / Answer

Testing of Hypothesis :

H0 : The two populations are equal at the alpha equals .05 level of significance

against,

H1 : The two populations are not equal at the alpha equals .05 level of significance.

Test statistics,

Wilcoxon-Mann-Whitney rank sum test and Mann-Whitney U test.

> wilcox.test(old_drug,New_drug,correct=TRUE)

Wilcoxon rank sum test with continuity correction

data: old_drug and New_drug

W = 14.5, p-value = 0.7457

alternative hypothesis: true location shift is not equal to 0

Decision Rule : The p-value is greater than 0.05 , so accept null hypothesis at 5 % level of significance.

I.e.

We fail to reject H0, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 10.5 is greater than the critical U value of 2.

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