Characterizing ensemble statistics: mean size is represented across multiple frames of reference.

The visual system represents the overall statistical, not individual, properties of sets. Here we tested the spatial nature of ensemble statistics. We used a mean-size adaptation paradigm (Corbett et al. in Visual Cognition, 20, 211-231, 2012) to examine whether average size is encoded in multiple reference frames. We adapted observers to patches of small- and large-sized dots in opposite regions of the display (left/right or top/bottom) and then tested their perceptions of the sizes of single test dots presented in regions that corresponded to retinotopic, spatiotopic, and hemispheric coordinates within the adapting displays. We observed retinotopic, spatiotopic, and hemispheric adaptation aftereffects, such that participants perceived a test dot as being larger when it was presented in the area adapted to the patch of small dots than when it was presented in the area adapted to large dots. This aftereffect also transferred between eyes. Our results demonstrate that mean size is represented across multiple spatial frames of reference, supporting the proposal that ensemble statistics play a fundamental role in maintaining perceptual stability.