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Background: It is possible to find many different visual representations of data values in visualizations, it is less common to see visual representations that include uncertainty, especially in visualizations intended for non-technical audiences. 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: A Bradley-Terry analysis of a pairwise comparison of the glyphs shows participants (n=19) ordered the glyphs as predicted by the visual entropy score (linear regression R2 \textgreater0.97, p\textless0.001). We also evaluate whether the glyphs can effectively represent uncertainty using a signal detection method, participants (n=15) were able to search for glyphs representing uncertainty with high sensitivity and low error rates. Conclusion: visual entropy is a novel cue for representing ordered data and provides a channel that allows the uncertainty of a measure to be presented alongside its mean value.

@article{holliman_visual_2019, title = {Visual {Entropy} and the {Visualization} of {Uncertainty}}, url = {http://arxiv.org/abs/1907.12879}, abstract = {Background: It is possible to find many different visual representations of data values in visualizations, it is less common to see visual representations that include uncertainty, especially in visualizations intended for non-technical audiences. 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: A Bradley-Terry analysis of a pairwise comparison of the glyphs shows participants (n=19) ordered the glyphs as predicted by the visual entropy score (linear regression R2 {\textgreater}0.97, p{\textless}0.001). We also evaluate whether the glyphs can effectively represent uncertainty using a signal detection method, participants (n=15) were able to search for glyphs representing uncertainty with high sensitivity and low error rates. Conclusion: visual entropy is a novel cue for representing ordered data and provides a channel that allows the uncertainty of a measure to be presented alongside its mean value.}, urldate = {2020-10-14}, journal = {arXiv:1907.12879 [cs, math]}, author = {Holliman, Nicolas S. and Coltekin, Arzu and Fernstad, Sara J. and Simpson, Michael D. and Wilson, Kevin J. and Woods, Andrew J.}, month = jul, year = {2019}, note = {ZSCC: 0000002 arXiv: 1907.12879}, keywords = {Computer Science - Graphics, Computer Science - Human-Computer Interaction, Computer Science - Information Theory}, }

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