Is there a cost in forming statistical summary representations at multiple spatial scales?

Visual processing often entails forming statistical summary representations (SSRs) to encode properties of groups of similar objects. It has been debated whether forming these representations-also referred to as ensemble coding-requires limited capacity resources. We ask for the first time whether forming SSRs at multiple spatial scales incurs a cost in visual processing efficiency. Inspired by Navon's hierarchical stimuli, we spatially arrange several small tilted rectangles to create multiple large tilted rectangles. Participants estimate the mean orientation of either the large rectangles (low spatial frequency) or the small rectangles (high spatial frequency). Experiment 1a uses a cueing paradigm to demonstrate a cost in the formation of SSRs at multiple spatial scales. We propose a two-part SSR formation framework, according to which SSR formation involves the formation of single-item representations (Part 1) followed by the averaging of the single-item representations (Part 2). SSR formation cost could arise from Part 1, Part 2, or both. Experiment 1b shows that estimating the single-item orientation at multiple spatial scales incurs a cost also. Comparing results from both experiments reveals that there is no cost associated with SSR formation above and beyond the single-item formation cost (i.e., the averaging part is cost free). We replicate this finding in Experiment 2, in which "task" (SSR estimation vs. single-item estimation) is varied within subject. These findings can potentially address the debate surrounding whether SSR formation incurs a cost-the averaging operation is perhaps cost free, and whether or not SSR formation incurs a cost depends on whether single-item formation incurs a cost.