Authors: Christine Nothelfer, Steven Franconeri
Abstract: The power of data visualization is not to convey absolute values of individual data points, but to allow the exploration of relations among them. We explored how 7 different ways of encoding pairs of data values can lead to vast differences in the efficiency of visually processing the relations between those pairs. In Exp. 1a and 1b, participants located a pair of data values with a given relation (e.g., small bar to the left of a tall bar) among pairs of the opposite relation. In Exp. 2, participants judged which of two relation types was more prevalent in a briefly presented display of data pairs (e.g., 30 positively sloped lines and 20 negatively sloped lines). Across all experiments, the choice of data depiction led to strong differences in efficiency of processing relations between values, with slope graphs, benchmark graphs, connected dashes performing the best. The ranking is also strikingly unrelated to prescriptions stemming from measurements of perceptual precision of visual encodings  (e.g., while an orientation encoding is only moderately precise, it provided a highly efficient encoding for relation perception here).