Texture density discrimination is more precise than number discrimination

Density information is a possible primitive for the perception of numerosity. It has been argued, however, that the perception of numerosity is more precise than density perception at low numbers, whereas density is more precise for high numbers. An interpretive problem with the stimuli used to make those claims is that actual stimulus density was often mis-specified owing to an ambiguity regarding the idealized versus actual filled area. This ambiguity had the effect of underestimating density precision at low numerosities. Here we used a novel method of stimulus generation that allows us to accurately specify stimulus density independent of patch size and number, while varying patch size from trial to trial to dissociate numerosity and density. For both numerosity discrimination and density discrimination, we presented single stimuli in central vision for comparison with an internal standard. Feedback was given after each judgment. Using well-defined densities, density discrimination was more precise than numerosity perception at all densities and showed no evidence of varying as a function of density, as previously hypothesized. This was found with 8 practiced observers, and then replicated in a pre-registered study with 32 observers. As expected, feedback nullified size biases on number judgments, showing that observers were adaptively combining density and size. Reanalysis of data from a recent investigation of downward sloping Weber fractions for numerosity showed that the square root-like effects in those sorts of studies were most likely owing to reductions in patch size variance that were correlated with increases in density.