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Joshua Solomon, Michael Morgan, Charles Chubb; Efficiencies for the statistics of size. Journal of Vision 2011;11(11):1041. doi: 10.1167/11.11.1041.
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© ARVO (1962-2015); The Authors (2016-present)
Different laboratories have achieved a consensus regarding how well human observers can estimate the average orientation in a set of N objects. Such estimates are not only limited by visual noise, which perturbs each object's apparent orientation, they are also inefficient: Observers effectively use only √N objects in their estimates (e.g. Dakin, JOSA A, 2001; Solomon, JoV in press). More controversial is the efficiency with which observers can estimate the average size in an array of circles (e.g. Ariely, Psych. Sci., 2001; Chong et al., P&P, 2008; Myczek & Simons, P&P, 2008). Of course, there are some important differences between orientation and size, nonetheless it seemed sensible to compare the two types of estimate against the same ideal observer. Indeed, quantitative evaluation of statistical efficiency requires this sort of comparison (Fisher, 1925).
Our first step was to measure the noise that limits size estimates when only two circles are compared. Our results (Solomon & Chubb, AVA Christmas, 2009) were consistent with the visual system adding the same amount of Gaussian noise to all logarithmically transduced circle diameters. Imitating and amplifying this visual noise in (uncrowded) 8-circle arrays, we have now measured its effect on discrimination between mean sizes. At present, we have results from 4 observers. Inferred efficiencies range from 37.5% to 87.5%. More consistent are our measurements of just-noticeable differences in size variance. These latter results suggest close to 100% efficiency for variance discriminations. That is, like the ideal, human observers effectively use all 8 circles in their estimates of size variance. Estimates of mean size are less efficient, but our data suggest that these estimates are limited by the same noise that limits estimates of size variance. That's where the analogy between size and orientation breaks down. For orientation, mean estimates are noisier than variance estimates (Solomon, JoV in press).
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