Ensemble perception: Extracting the average of perceptual versus numerical stimuli.

Recent research has established that humans can extract the average perceptual feature over briefly presented arrays of visual elements or the average of a rapid temporal sequence of numbers. Here we compared the extraction of the average over briefly presented arrays, for a perceptual feature (orientations) and for numerical values (1-9 digits), using an identical experimental design for the two tasks. We hypothesized that the averaging of numbers, more than of orientations, would be constrained by capacity limitations. Arrays of Gabor elements or digits were simultaneously presented for 300 ms and observers were required to estimate the average on a continuous response scale. In each trial the elements were sampled from normal distributions (of various means) and we varied the set size (4-12). We found that while for orientation the averaging precision remained constant with set size, for numbers it decreased with set size. Using computational modeling we also extracted capacity parameters (the number of elements that are pooled in the average extraction). Despite marked heterogeneity between observers, the capacity for orientations (around eight items) was much larger than for numbers (around four items). The orientation task also had a larger fraction of participants relying on distributed attention to all elements. Our study thus supports the idea that numbers more than perceptual features are subject to capacity or attentional limitations when observers need to evaluate the average over an ensemble of stimuli.