# Surveys as RCTs: an exercise in analogy

Surveys use probability samples from a finite population to estimate a quantity of that population, e.g., the percentage of people holding a particular view. What happens if we try to understand surveys using the concepts of a randomised controlled trial?

Those assigned to intervention get the survey questions – the questions are the intervention. Those assigned to control get nothing and are ignored entirely. Typically the probability of being assigned to intervention (being surveyed) is much smaller than that of being assigned to control (ignored).

We wish to estimate the percentage of people in the population who hold a particular view following the intervention (the survey questions). This percentage is the outcome measure. We observe the outcome for people randomly assigned to the survey. For the control group, we want to know what percentage would have held that view, if they had been assigned to the survey.

An interesting feature of this “intervention” of a survey is that we hope it does not change the percentage outcome. So, viewing a survey through this RCT lens, the average treatment effect (mean difference between intervention and control, survey and ignore) is assumed to be 0. But this might not hold. There may be a mean difference between people who have been asked to reflect on something and tell a researcher versus those who hold a view but have not told anyone. We cannot tell using this design.

Where did the population come from? Across in the RCT analogy, it would be the (typically nonprobability) sample of people who consented to take part in the trial. In the survey, it is a collection of people who found themselves living in a particular area, having the demographic profile of interest (satisfying the inclusion criteria), and being reachable via a sample frame. We usually do not care how they got there. Other researchers might, e.g., demographers studying migration or births. People often end up in an area because they found a job nearby or because they were born there – both events with an element of chance.

Researchers often worry whether an RCT’s results transfer to other settings. This is not an issue for surveys. In fact we might assume that people living in different areas hold different views. One aspect we might hope does transfer is how people interpret the questions.