The efficacy of a new experimental drug to reduce allergic reactions

A pharmaceutical company is interested in examining the efficacy of a new
experimental drug to reduce allergic reactions and therefore recruited subjects to
participate in a randomized clinical trial. The researchers exposed participants to a benign
allergen to elicit allergic reactions. Half of the participants were assigned to an
experimental drug treatment condition in which they were administered the new
experimental drug (Drug condition), while the remaining half of participants were placed
in a placebo condition in which they received a sham pharmacological treatment (Placebo
condition). They measured a continuous-valued, composite index of allergic reaction
symptomology to examine whether those who received the experimental drug treatment
showed a reduction in allergic reaction symptomology (see Table 5 below). Upon
preliminary analysis, the researchers discovered that the assumption of homogeneity of
variance was violated:
πΉπ‘šπ‘Žπ‘₯ =
π‘ π‘™π‘Žπ‘Ÿπ‘”π‘’π‘ π‘‘
2
π‘ π‘ π‘šπ‘Žπ‘™π‘™π‘’π‘ π‘‘
2 =
6.79
1.67 = 4.07, πΉπ‘šπ‘Žπ‘₯.π‘π‘Ÿπ‘–π‘‘ = 4.04 .
Furthermore, they realized that the dependent variable was not normally distributed, as
scores were heavily positively skewed. Given these observations, using a parametric
analysis of the mean difference between conditions is not appropriate. What can the
researchers conclude about the efficacy of the drug using a non-parametric analysis? Show
all relevant descriptive statistics.
Table 5. Composite allergic reaction symptomology scores in the Drug and Control
conditions.
Subject Condition Scores
1 Drug 1.05
2 Drug 0.70
3 Drug 2.10
4 Drug 0.20
5 Drug 1.91
6 Drug 1.38
7 Drug 1.09
8 Drug 4.41
9 Drug 0.29
10 Drug 0.02
11 Placebo 5.73
12 Placebo 8.21
13 Placebo 6.70
14 Placebo 1.00
15 Placebo 2.02
16 Placebo 3.33
17 Placebo 6.19
18 Placebo 8.47
19 Placebo 2.67
20 Placebo 5.92

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