Ensemble statistics accessed through proxies: Range heuristic and dependence on low-level properties in variability discrimination.

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.