Visual Entropy and the Visualization of Uncertainty

Background: Even though data visualizations (and underlying data) almost always contain uncertainty, it remains complex to communicate and interpret uncertainty representations. Consequently, uncertainty visualizations for non-expert audiences are rare. Objective: our aim is to rigorously define and evaluate the novel use of visual entropy as a measure of shape that allows us to construct an ordered scale of glyphs for use in representing both uncertainty and value in 2D and 3D environments. Method: We use sample entropy as a numerical measure of visual entropy to construct a set of glyphs using R and Blender which vary in their complexity. Results: an exact binomial analysis of a pairwise comparison of the glyphs shows a majority of participants (n = 87) ordered each glyph as predicted by the visual entropy score with large effect size (Cohen's g > 0.25). We also evaluate whether the glyphs effectively represent uncertainty using a signal detection method in a search task. Participants (n = 15) were able to find glyphs representing uncertainty with high sensitivity and low error rates. Conclusion: visual entropy is a successful novel approach to representing ordered data and provides a channel that can allow the uncertainty of a measure to be presented alongside its mean value.