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:
πΉπππ₯ =
π ππππππ π‘
2
π π ππππππ π‘
2 =
6.79
1.67 = 4.07, πΉπππ₯.ππππ‘ = 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
Sample Solution
fe, Alfred was surrounded by science. His father taught him basic principles of engineering and explosives, this went on to be his main interests later in life. Alfred grew up in Stockholm, Sweden, born: 21st October 1833. However, his family moved to Saint Petersburg in 1842 due to his fatherβs various business failures. Once in the city his father became successful as a manufacturer of tools and explosives. Now wealthy, Alfredβs parents were able to send him to private tutors and he excelled in his studies, specifically chemistry and languages. Fun fact: Alfred Nobel was fluent in English, French, German, Russian and of course Swedish. In 1850, Alfred moved to Paris to continue his studies. He met Ascanio Sobrero, who invented nitroglycerin 3 years earlier. Alfred was intrigued by the instability of Nitroglycerin and went to America to research further. After the Crimean War (1853-1856) Alfredβs father had difficulty switching back to domestic production, so he declared the company bankrupt. In 1859, Immanuel ( his father ) handed the company down to his second son, Ludvig Nobel who went on to greatly improve the business. Nobel devoted himself to the obdurate study of explosives, especially the safe manufacture and use of nitroglycerin. On the 3rd of September 1864, part of a nitroglycerin factory exploded in Heleneborg, Stockholm, killing 5 people including Alfredβs younger brother Emil. However, Alfred continued building factories and developing new technology, unfazed by this. Finally in 1866 Nobel invented dynamite. A more stable compound of Nitroglycerin and Diatomaceous earth, which is a soft rock mostly made of fossilised algae. He moulded it into cylinder shaped sticks and used blasting caps (which he invented a few years earlier) to allow for the safe ignition of such a powerful explosive. He lived the rest of his life being showered in awards from multiple universities and had an award named after him, The Nobel Prize. He was very rich and his money ended up being used to fund these yearly prizes that bear his name. Alfred was a lonely person, he never made a family of his own or got married. He had an interest in literature and often wrote poetry, novels and plays. He once wrote, βNumerous friends are to be found only among dog>
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