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C. Holley Pitts, Melanie Palomares; Mean vs. range in statistical summary representation. Journal of Vision 2011;11(11):1287. doi: 10.1167/11.11.1287.
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© ARVO (1962-2015); The Authors (2016-present)
Statistical summary representation, the ability to accurately encode global statistical properties of a scene (Oliva & Torralba, 2006), occurs due to our limited attention span and memory capacity. Identifying the mean size of a set is more accurate than identifying the size of individual members (Ariely, 2001; Chong & Treisman, 2005). Whether this relative accuracy is reached by distributing attention across the entire set, or by sampling a subset such as the maximum- and minimum-sized elements is still in contention (Myczek & Simons, 2008). Here, we directly evaluated use of the range in set representation by constraining observers to discriminate the true mean from the mid-range ((minimum + maximum)/2). Arrays of 3 or 9 squares were briefly presented (133 ms) and observers were asked to identify either the mean size or a member of the array. First, sizes were sampled from a normal distribution, and the effect of choice type was examined (mean versus member or mid-range verses the correct response). When the mean was pitted against the member, reporting the mean size was better than identifying the sizes of individual elements. When the mean was pitted against the mid-range, accuracies hovered around chance. Moreover, observers were actually below chance performance when identifying the member against the true mean or against the mid-range. These results suggest that the mid-range was used as heuristics for mean size. Second, sizes were sampled from a skewed distribution. For this condition, observers were reliably better than chance at distinguishing both the mean and member of a set from the mid-range, suggesting that observers were sensitive to the relative frequencies of the sizes. Together, these results show we have flexible representations of statistical information from sets, including the skew.
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