Ensemble Statistics Accessed through Proxies: Range Heuristic and Dependence on Low-Level Properties in Variability Discrimination

Abstract

People can quickly and accurately compute not only the mean size of a set of items but also the size variability of the items. However, it remains unknown how these statistics are estimated. Here we show that neither parallel access to all items nor random subsampling of just a few items is sufficient to explain participants' estimations of size variability. In three experiments, we had participants compare two arrays of circles with different variability in their sizes. In the first two experiments, we manipulated the congruency of the range and variance of the arrays. The arrays with congruent range and variability information were judged more accurately, indicating the use of range as a proxy for variability. Experiments 2B and 3 showed that people also are not invariant to low-or mid-level visual information in the arrays, as comparing arrays with different low-level characteristics (filled vs. outlined circles) led to systematic biases. Together, these experiments indicate that range and low-or mid-level properties are both utilized as proxies for variability discrimination, and people are flexible in adopting these strategies. These strategies are at odds with the claim of parallel extraction of ensemble statistics per se and random subsampling strategies previously proposed in the literature.

Color ensembles: Sampling and averaging spatial hue distributions

“…Therefore, our results support a more global mechanism with distributed attention in averaging hue, which has been suggested in some form in ensemble perception of other stimulus types (e.g., Alvarez & Oliva, 2008 ; Chong & Treisman, 2003 ; Corbett & Oriet, 2011 ; Im & Halberda, 2013 ). We cannot directly rule out an alternative strategy, such as smart subsampling (i.e., directing sampling to the most meaningful targets), which would reduce the required number of samples and allow for focal attention (see Lau & Brady, 2018 ). However, smart subsampling would presumably affect the high-noise condition—where the hues are more variable—more than the conditions with low or no noise, whereas our noise model accounts for the data from all noise conditions with a single set of parameters.…”

Emotional judgments of scenes are influenced by unintentional averaging

“…It is robust to variations in time (Albrecht & Scholl, 2010;Haberman, Harp, & Whitney, 2009;Hubert-Wallander & Boynton, 2015), spatial position (Alvarez & Oliva, 2009;Chong & Treisman, 2005b), and impoverished visual information (Haberman & Ulrich, 2019), and conscious access may not even be necessary (Alvarez & Oliva, 2008;Fischer & Whitney, 2011;Haberman & Whitney, 2011). Summary representation is not restricted to the central moment, as observers represent other summary statistical information, such as variance and range (Haberman, Lee, & Whitney, 2015;Lau & Brady, 2018;Solomon, 2010). Ensembles are so efficiently accessed, they tend to be the default representation when faced with memory or perceptual uncertainty about line length (Duffy, Huttenlocher, Hedges, & Crawford, 2010), time judgments (Jazayeri & Shadlen, 2010), emotional expression , and internal and external perceptual noise (Olkkonen, McCarthy, & Allred, 2014).…”