A cognitive mathematical modeling method for comparing stacked bar graphs in descriptive visual data science

A great deal of research in data science has been devoted to data visualization techniques but not to their effectiveness from a perceptual, and more generally, cognitive standpoint. This is important because the way that human observers perceive and judge the graphic representation of numerical data can ultimately determine its interpretation. As proof of concept, we introduce and test a quantitative method for replacing human judges in the comparative assessment of simple stacked bar graphs (SBGs). As suggested, the method involves the application of Shepard’s similarity assessment model, a well-known cognitive mathematical model which determines similarities between exemplars as a function of their distance in psychological space. In addition, the method involves a simple technique for transforming each SBG into an appropriate representation that makes the application of the model possible and a cognitively meaningful method for scaling the representation. Specifically, the method assumes that humans form a psychological distance baseline (computed as a median or a mean across the SBGs) as the basis for scaling the representation. The effectiveness of the method was tested with an experiment on similarity judgments between SBGs. Results indicate that our method effectively predicts people’s similarity judgments with respect to pairs of SBGs ( r ²  = 0.88, p  < 0.001). Bootstrapping tests confirmed the stability of the model fit. Among other applications, this method may be used to replace human judges with AI agents in situations where researchers wish to determine how well a SBG representing quantitative predictions from some model reflects the proportional distribution of the SBG representing the empirical data. The method also contributes to the automated quantitative interpretation of visual data in ways that are consistent with the perception of proportional visual relations by humans. Such automation may eventually find wide applications in the interpretation of visual data by AI agents, model evaluation, and UX design.