Summary statistics for size over space and time

A number of studies have investigated how the visual system extracts the average feature-value of an ensemble of simultaneously or sequentially delivered stimuli. In this study we model these two processes within the unitary framework of linear systems theory. The specific feature value used in this investigation is size, which we define as the logarithm of a circle's diameter. Within each ensemble, sizes were drawn from a normal distribution. Average size discrimination was measured using ensembles of one and eight circles. These circles were presented simultaneously (display times: 13–427 ms), one at a time, or eight at a time (temporal-frequencies: 1.2–38 Hz). Thresholds for eight-item ensembles were lower than thresholds for one-item ensembles. Thresholds decreased by a factor of 1.3 for a 3,200% increase in display time, and decreased by the same factor for a 3,200% decrease in temporal frequency. Modeling and simulations show that the data are consistent with one readout of three to four items every 210 ms