Question 1: A researcher wants to study whether an existing drug causes a particular kind of skin reaction. She collects data from an existing medical database; she samples individuals who showed the skin reaction as well as individuals without a reaction. She then examines how many individuals had taken the drug of interest.
- (a) [2 points] What kind of study is this? Be as specific as possible, and explain your answer.
- (b) [2 points] Suppose the researcher finds that those who took the drug had a higher chance of developing a skin reaction. Do you believe this result? Can you think of other specific factors that might a↵ect the conclusion? Explain your answers.
Question 2: [2 points] A researcher runs a randomized experiment where study partic- ipants are randomized to be given either a drug or a placebo. Another researcher wants to perform an additional study on this same study group. He asks participants whether they get more or less than 3 hours of exercise per week. He concludes that individuals with more than 3 hours of exercise per week have lower blood pressure than those who get less than 3 hours, on average. Are you worried about confounders in this conclusion? Explain.
Question 3: We want to study the genetics of colour distribution in a population of unicorns. Suppose that in unicorns there is a single gene that determines colour; there are two variants of the gene, one called A and the other called a. Each unicorn has two copies of the gene (one from each parent). The combination of the gene variants for copy 1 and copy 2 of the gene determines colour as follows:
Copy 1 Copy 2 Colour A A Red A a Pink
a A Pink a a White
We want to determine if “random mating” is happening in this unicorn population. This would mean that the probability that a newly born unicorn inherits variant A or a with probability equal to the prevalence of each variant in the overall population.
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(a) [3 points] Let p be the proportion of the A variant in the population, and q be the proportion of the variant a, so that q = 1p. Under random mating, each newborn unicorn inherits A with probability p and a with probability q and the two copies inherited in each unicorn are independent of one another. Calculate the expected proportions of unicorn colours under random mating.
(b) [5 points] Suppose you know that p = 0.75 and q = 0.25, and that you collect the following data from a sample of unicorns:
Colour
Red Pink White
Number of unicorns
45 49 12
Use the appropriate statistical test to determine whether the random mating as- sumption holds in this population. Write out your calculations for this part; using R for this part will not result in credit.
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