Number and density discrimination rely on a common metric: Similar psychophysical effects of size, contrast, and divided attention

Abstract

While observers are adept at judging the density of elements (e.g., in a random-dot image), it has recently been proposed that they also have an independent visual sense of number. To test the independence of number and density discrimination, we examined the effects of manipulating stimulus structure (patch size, element size, contrast, and contrast-polarity) and available attentional resources on both judgments. Five observers made a series of two-alternative, forced-choice discriminations based on the relative numerosity/density of two simultaneously presented patches containing 16–1,024 Gaussian blobs. Mismatches of patch size and element size (across reference and test) led to bias and reduced sensitivity in both tasks, whereas manipulations of contrast and contrast-polarity had varied effects on observers, implying differing strategies. Nonetheless, the effects reported were consistent across density and number judgments, the only exception being when luminance cues were made available. Finally, density and number judgment were similarly impaired by attentional load in a dual-task experiment. These results are consistent with a common underlying metric to density and number judgments, with the caveat that additional cues may be exploited when they are available.