Please Solve using R The Wilcoxon Signed-Rank Test Suppose we want to compare the effective-ness of two ointments A and B in reducing excessive red-ness in people who cannot otherwise be exposed to sun-light. Ointment A is randomly applied to either the left or right arm, and Ointment B to the corresponding areaon the other arm. The person is then exposed to 1 hourof sunlight, and the two arms are compared for degrees ofredness. Suppose the following qualitative assessments canbe made:(1) Arm A is not as red as arm B.(2) Arm B is not as red as arm A.(3) Both arms are equally red.Of 45 people tested with the condition, 22 are better off onarm A, 18 are better off on arm B, and 5 are equally well offon both arms. Further, assume the degree of sunburn canbe quantified on a 10-point scale, with 10 being the worstburn and 1 being no burn at all. We can now computeddi = xi − yi, where xi = degree of burn for ointment A andyi = degree of burn for ointment B. Is there any evidenceto show that the ointments are equally effective?Sample data are in Table 9.1. Let’s assume that the di’shave an underlying continuous distribution. δ is the medianscore difference between the ointment A and ointment Barms. Hypothesis Testing H0 : δ = 0 vs. H1 : δ 6= 0.
Please Solve using R
The Wilcoxon Signed-Rank Test
Suppose we want to compare the effective-
ness of two ointments A and B in reducing excessive red-
ness in people who cannot otherwise be exposed to sun-
light. Ointment A is randomly applied to either the left or right arm, and Ointment B to the corresponding area
on the other arm. The person is then exposed to 1 hour
of sunlight, and the two arms are compared for degrees of
redness. Suppose the following qualitative assessments can
be made:
(1) Arm A is not as red as arm B.
(2) Arm B is not as red as arm A.
(3) Both arms are equally red.
Of 45 people tested with the condition, 22 are better off on
arm A, 18 are better off on arm B, and 5 are equally well off
on both arms. Further, assume the degree of sunburn can
be quantified on a 10-point scale, with 10 being the worst
burn and 1 being no burn at all. We can now computed
di = xi − yi, where xi = degree of burn for ointment A and
yi = degree of burn for ointment B. Is there any evidence
to show that the ointments are equally effective?
Sample data are in Table 9.1. Let’s assume that the di’s
have an underlying continuous distribution. δ is the median
score difference between the ointment A and ointment B
arms.
Hypothesis Testing H0 : δ = 0 vs. H1 : δ 6= 0.
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