A Psychophysical Investigation of Size as a Physical Variable.

Physical visualizations, or data physicalizations, encode data in attributes of physical shapes. Despite a considerable body of work on visual variables, "physical variables" remain poorly understood. One of them is physical size. A difficulty for solid elements is that "size" is ambiguous - it can refer to either length/diameter, surface, or volume. Thus, it is unclear for designers of physicalizations how to effectively encode quantities in physical size. To investigate, we ran an experiment where participants estimated ratios between quantities represented by solid bars and spheres. Our results suggest that solid bars are compared based on their length, consistent with previous findings for 2D and 3D bars on flat media. But for spheres, participants' estimates are rather proportional to their surface. Depending on the estimation method used, judgments are rather consistent across participants, thus the use of perceptually-optimized size scales seems possible. We conclude by discussing implications for the design of data physicalizations and the need for more empirical studies on physical variables.