A model of symbol size discrimination in scatterplots

Symbols are used in scatterplots to encode data in a way that is appropriate for perception through human visual channels. Symbol size is believed to be the second dominant channel after color. We study symbol size perception in scatterplots in the context of analytic tasks requiring size discrimination. More specifically, we performed an experiment to measure human performance in three visual analytic tasks. Circles are used as the representative symbol, with eight, linearly varying radii; 24 persons, divided across three groups, participated; and both objective and subjective measures were obtained. We propose a model to describe the results. The perception of size is assumed to be an early step in the complex cognitive process to mediate discrimination, and psychophysical laws are used to describe this perceptual mapping. Different mapping schemes are compared by regression on the experimental data. The results show that approximate homogeneity of size perception exists in our complex tasks and can be closely described by a power law transformation with an exponent of 0.4. This yields an optimal scale for symbol size discrimination.