The apparent and effective dimensionality of representations of objects

Information displays commonly use 2-D and 3-D objects even though the numbers represented are 1-D. This practice may be problematic because the psychophysical relation between perceived and physical magnitudes is generally nonlinear for areas and volumes. Nonetheless, this research shows that apparent 2-D and 3-D objects can produce linear psychophysical functions if only one dimension shows variation. Processing time increases with the number of dimensions in the objects that show variation, not with the apparent dimensionality. Indeed, when only one dimension showed variation, apparent 3-D objects were judged more quickly than were apparent 2-D or 1-D objects. These results present a challenge for computational models of size perception and have implications for the design of information displays. Actual or potential applications of this research include the design and use of statistical graphs and information displays; objects that display variation in more than one dimension should not be used to represent single (1-D) numerical variables if they are to be judged accurately and rapidly.