Impact of vertical scaling on probability density function plots

Left to right: Question reading "why would anyone compress a PDF plot?". Next, picture of a research paper with just enough space for a small figure. Next, vertically stacked PDFs that overlap with each other. Next, vertically stacked PDFs that are spaced out but use a lot of space. Lastly, vertically stacked PDFs that have been compressed to fit in a small space without overlapping followed by a label reading "the perfect solution?" and a follow-up reading "what are the implications of squishing PDF plots?"
A decision flow that may lead to visualization designers compressing some PDF plots at different rates. Findings from our experiments show that this "perfect solution" can lead to imperfect interpretation. Panel A shows equal-area PDFs with occlusion, B shows equal-area PDFs without occlusion, and C shows equal-height PDFs that have different areas.
Abstract
Probability density function (PDF) curves are among the few charts on a Cartesian coordinate system that are commonly presented without y-axes. This design decision may be due to the lack of relevance of vertical scaling in normal PDFs. In fact, as long as two normal PDFs have the same means and standard deviations (SDs), they can be scaled to occupy different amounts of vertical space while still remaining statistically identical. Because unfixed PDF height increases as SD decreases, visualization designers may find themselves tempted to vertically shrink low-SD PDFs to avoid occlusion or save white space in their figures. Although irregular vertical scaling has been explored in bar and line charts, the visualization community has yet to investigate how this visual manipulation may affect reader comparisons of PDFs. In this paper, we present two preregistered experiments (n = 600, n = 401) that systematically demonstrate that vertical scaling can lead to misinterpretations of PDFs. We also test visual interventions to mitigate misinterpretation. In some contexts, we find including a y-axis can help reduce this effect. Overall, we find that keeping vertical scaling consistent, and therefore maintaining equal pixel areas under PDF curves, results in the highest likelihood of accurate comparisons. Our findings provide insights into the impact of vertical scaling on PDFs, and reveal the complicated nature of proportional area comparisons.
Materials
PDF | Preprint | Supplement | Preregistration (Exp 1) | Preregistration (Exp 2) | BibTeX
Authors
Citation

Khoury Vis Lab — Northeastern University
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