Perceptual estimation of variance in orientation and its dependence on sample size

Recent research has shown that participants are very good at perceptually estimating summary statistics of sets of similar objects (e.g., Ariely, 2001; Chong & Treisman, 2003; 2005). While the research has focused on first-order statistics (e.g., the mean size of a set of discs), it is unlikely that a mental representation of the world includes only a list of mean estimates (or expected values) of various attributes. Therefore, a comprehensive theory of perceptual summary statistics would be incomplete without an investigation of the representation of second-order statistics (i.e., variance). Two experiments were conducted to test participants' ability to discriminate samples that differed in orientation variability. Discrimination thresholds and points of subjective equality for displays of oriented triangles were measured in Experiment 1. The results indicated that participants could discriminate variance without bias and that participant sensitivity (measured via relative thresholds, i.e., Weber fractions) was dependent upon sample size but not baseline variance. Experiment 2 investigated whether participants used a simpler second-order statistic, namely, sample range to discriminate dispersion in orientation. The results of Experiment 2 showed that variance was a much better predictor of performance than sample range. Taken together, the experiments suggest that variance information is part of the visual system's representation of scene variables. However, unlike the estimation of first-order statistics, the estimation of variance depends crucially on sample size.M.S.Includes abstractIncludes bibliographical referencesby Steven A. Cholewia