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Heeyoung Choo, Steven Franconeri; Small collections violate Weber’s law during relative number judgments.. Journal of Vision 2012;12(9):509. doi: https://doi.org/10.1167/12.9.509.
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© ARVO (1962-2015); The Authors (2016-present)
People can produce exact counts of small collections (1-4 objects) quickly and accurately, while for larger collections people must either create rough estimates or serially count (e.g., Trick & Pylyshyn, 1994). It is controversial whether this pattern results from Weber’s law, where precision of number estimates are only precise enough to produce exact counts of small collections, or whether counts of small collections instead rely on a distinctive mechanism. We asked observers to make relative number judgments within both small and large collections, with equal Weber spacing within each collection. A reference collection had either 3 or 30 objects, and a target collection had 1, 2, 4, 5 or 10, 20, 40, 50 objects. Observers judged if the target had more or fewer than the reference. We tested the relative precision of number estimates for small and large collections by comparing judgments of more difficult comparisons for small collections (e.g. 2 vs. 3) with large (e.g. 20 vs. 30) collections, using easier comparisons within each collection size as a baseline (e.g., 1 vs. 3; 10 vs. 30). That is, we examined the magnitude of the ‘distance effect,’ where closer judgments are more difficult. According to Weber’s law, as long as the ratios among these values are the same, performance should be identical. In contrast, we found that distance effects were significantly smaller for comparisons involving 1-3 than 10-30 objects. Distance effects were identical for comparisons involving larger numbers such as 3-5 and 30-50 objects. Our results suggest distinctive processing of a small set of objects in the visual system.
Meeting abstract presented at VSS 2012
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