Fitting Bell Curves to Data Distributions using Visualization

Eric Newburger, Michael Correll, Niklas Elmqvist

Room: 109

2023-10-26T00:21:00ZGMT-0600Change your timezone on the schedule page
Exemplar figure, described by caption below
Can people fit a normal curve to a data distribution through visual interactions alone? In other words, do we have the visual intuitions to see the connection between an image of a sample distribution and the population distribution from which those samples might have been drawn? And does graphic design matter? Our experiment sought answers to these questions.
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Graphical inference;visual statistics;statistics by eye;fitting distributions;crowdsourcing


Idealized probability distributions, such as normal or other curves, lie at the root of confirmatory statistical tests. But how well do people understand these idealized curves? In practical terms, does the human visual system allow us to match sample data distributions with hypothesized population distributions from which those samples might have been drawn? And how do different visualization techniques impact this capability? This paper shares the results of a crowdsourced experiment that tested the ability of respondents to fit normal curves to four different data distribution visualizations: bar histograms, dotplot histograms, strip plots, and boxplots. We find that the crowd can estimate the center (mean) of a distribution with some success and little bias. We also find that people generally overestimate the standard deviation---which we dub the "umbrella effect" because people tend to want to cover the whole distribution using the curve, as if sheltering it from the heavens above---and that strip plots yield the best accuracy.