Numbers are an interesting thing. We all have an innate sense of quantities, but numbers are a culturally agreed upon format for representing those quantities. When we are trying to convey quantitative information to other people, the choice between “7 days” vs. “1 week” or “100 out of 300” vs. “1 out of 3” often feels like an aesthetic preference. However, the way we represent quantitative information to other people can have a large impact on how people think about what those numbers represent. As data scientists, it is our job to be aware of the ways in which people represent quantities to ensure that survey respondents’ perception of numbers accurately represents reality.
In creating survey instruments, I am always acutely aware of these factors. At the annual meeting of the Society for Personality and Social Psychology that I recently attended, I was fascinated by new research by Andrew White and Virginia S.Y. Kwan on the matter. They hypothesized that a small number of large units (e.g. 1 week) feels more distant and less probable than a large number of small units (e.g. 7 days). In one study, they described a fictional disease and then told people that someone in their community had been infected. The location of the infected person was either described as 1 mile away or as 5280 feet away. They then asked people how willing they were to receive the vaccination for the disease. People were much more willing to receive the vaccine when the location of the infected person was described as 5280 ft relative to when the location was described as 1 mile. This research is fascinating because the two conditions described the exact same amount of physical distance; however, the units used to describe the distance changed people’s perception of the threat.
I think I could hypothesize that the reverse is also true. That is, people might use large numbers of smaller units to describe things that feel closer and more probable and, on the other hand, might use smaller numbers of large units to describe things that feel far away and less probable. So if someone thinks a deadline is urgent, she might describe it as only 14 days away, instead of describing it as two weeks away. When designing surveying and analyzing people’s responses, it is important to understand how numbers can convey more than just quantitative information. As data scientists, we design research methods that capture not only data, but also the nuances of quantitative information.