Question 3: Research Design (55 points) Over the semester, we have discussed lots of different

approaches to answering research questions. Typically, we are concerned with causality – what is the

effect of one thing on another. For this question, I’d like your group to think critically about a difficult

research question – the effectiveness of wearing masks for preventing the transmission of the flu. The

effectiveness of this approach is in question – it would be nice to know how much wearing a mask

reduces infection rates so that the government can properly incentivize (or punish) those who do not

follow proper protocols.

For this problem, assume that your observations are counties in the United States and your outcome is

the proportion of people within a county that tested positive for the flu measured in any way you see fit

(daily, monthly, per flu season, etc.). To keep things simple, think of the treatment as having a certain

percentage of people (or more) within a county that wear a mask in crowded public places – T = 1 if

more than 50% of people wear a mask while T = 0 if less than 35% of people wear a mask.

a) (5 points) Let’s say that you went out into the world and collected two numbers for each

county in the United States – whether or not more than 50% of people within the county wore

a mask in crowded public areas and a corresponding flu rate for 2022. You compare the

average flu rate in treated and untreated counties and find that treated counties have lower flu

rates, on average. In a few sentences (and engaging with one or more of the common

inferential errors discussed in class), explain why this number may not provide a good estimate

of the effectiveness of masks. Be sure to engage with topics covered in QTM 110!

b) (10 points) Come up with a research design that would, in theory, guarantee an assumption-

free and bias-free estimate of the effect of at least 50% of a county’s population wearing a

mask on flu rate. Discuss how this approach would solve the problems you pointed out in part

a). Be sure to clearly outline what steps you would take to assign the treatment and compute

your estimate.

c) (10 points) Why is your approach in b) not possible/irresponsible? Come up with at least three

distinct issues that might arise when implementing your proposed research design.

d) (10 points) Come up with a more realistic approach that uses observational data to produce a

bias-free estimate of the effect of at least 50% of a county’s population wearing a mask on flu

rate. Clearly outline what data you would collect, what assumptions you would need to meet,

and how you might assess whether or not those assumptions are met.

e) (10 points) The proposed method in d) is unlikely to be perfect. Give at least three reasons that

your approach in d) could still provide an estimate of the effect that has bias. Don’t simply

restate your assumptions – think about the kinds of real-world messiness that could still lead to

an incorrect estimate and/or violations of your key assumptions.

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