The Time-Limited Visual Statistician

The visual system can calculate summary statistics over time. For example, the multiple frames of a movie showing a dynamically changing disk can be collapsed to form a single representation of that disk's mean size. Summary representations of dynamic information may engage online updating processes that establish a running average of the mean by continuously adjusting the persisting representation of the average in tandem with the arrival of incoming information. Alternatively, summary representations may involve subsampling strategies that reflect limitations in the degree to which the visual system can integrate information over time. Observers watched movies of a disk that changed size smoothly at different rates and then reported the disk's average size by adjusting the diameter of a response disk. Critically, the movie varied in duration. Size estimates depended on the duration of the movie. They were constant and fairly accurate for movie durations up to approximately 600 ms, at which point accuracy decreased with increasing duration to imprecise levels by about 1,000 ms. Summary statistics established over time are unlikely to be updated continuously and may instead be restricted by subsampling processes, such as limited temporal windows of integration.