Statisticians are not only one of the earliest professional adopters of data visualization, but also some of its most prolific users. Understanding how these professionals utilize visual representations in their analytic process may shed light on best practices for visual sensemaking. We present results from an interview study involving 18 professional statisticians (19.7 years average in the profession) on three aspects: (1) their use of visualization in their daily analytic work; (2) their mental models of inferential statistical processes; and (3) their design recommendations for how to best represent statistical inferences. Interview sessions consisted of discussing inferential statistics, eliciting participant sketches of suitable visual designs, and finally, a design intervention with our proposed visual designs. We analyzed interview transcripts using thematic analysis and open coding, deriving thematic codes on statistical mindset, analytic process, and analytic toolkit. The key findings for each aspect are as follows: (1) statisticians make extensive use of visualization during all phases of their work (and not just when reporting results); (2) their mental models of inferential methods tend to be mostly visually based; and (3) many statisticians abhor dichotomous thinking. The latter suggests that a multi-faceted visual display of inferential statistics that includes a visual indicator of analytically important effect sizes may help to balance the attributed epistemic power of traditional statistical testing with an awareness of the uncertainty of sensemaking.

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 article 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.