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Steven A. Cholewiak, Manish Singh; Perceptual estimation of variance in orientation and its dependence on sample size. Journal of Vision 2009;9(8):1019. doi: https://doi.org/10.1167/9.8.1019.
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© ARVO (1962-2015); The Authors (2016-present)
Previous research on statistical perception has shown that subjects are very good at perceptually estimating first-order statistical properties of sets of similar objects (such as the mean size of a set of disks). However, it is unlikely that our mental representation of the world includes only a list of mean estimates of various attributes. Work on motor and perceptual decisions, for example, suggests that observers are implicitly aware of their own motor / perceptual uncertainty, and are able to combine it with an experimenter-specified loss function in a near-optimal manner. The current study investigated the representation of variance by measuring difference thresholds for orientation variance of sets of narrow isosceles triangles with relatively large Standard Deviations (SD): 10, 20, 30 degrees; and for different sample sizes (N): 10, 20, 30 samples. Experimental displays consisted of multiple triangles whose orientations were specified by a von Mises distribution. Observers were tested in a 2IFC task in which one display had a base SD, and the other, test, display had a SD equal to +/−10, +/−30, +/−50, and +/−70% of the base SD. Observers indicated which interval had higher orientation variance. Psychometric curves were fitted to observer responses and difference thresholds were computed for the 9 conditions. The results showed that observers can estimate variance in orientation with essentially no bias. Although observers are thus clearly sensitive to variance, their sensitivity is not as high as for the mean. The relative thresholds (difference threshold SD / base SD) exhibited little dependence on base SD, but increased greatly (from ∼20% to 40%) as sample size decreased from 30 to 10. Comparing the σ of the cumulative normal fits to the standard error of SD, we found that the estimated σ's were on average about 3 times larger than the corresponding standard errors.
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