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Oakyoon Cha, Randolph Blake, Isabel Gauthier; Judgments of average and variance within object ensembles rely on a common ability. Journal of Vision 2020;20(11):841. doi: https://doi.org/10.1167/jov.20.11.841.
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Visual estimation of statistical properties can help us grab the ‘gist’ from a group of objects while discounting redundant information. For instance, we say “green leaves” to describe leaves whose color is generally (i.e., on average) green, and “colorful fall leaves” to describe the color variation for a group of leaves. Abilities to judge averages correlate among low-level features (color and orientation; Haberman, Brady & Alvarez, 2005) and among objects from different categories, suggesting that average estimation relies on common abilities for visual features of similar complexity. In contrast, prior work has concluded that abilities to judge different statistical summaries (e.g., average and variance of size) are uncorrelated (e.g., Yang, Tokita, & Ishiguch, 2018). That work however suffers from limitations. First, claims about the absence of correlation were based on small samples. Second, estimates of common variance across tasks did not control for participants’ discrimination abilities with single items. Third, the estimation tasks differed for different statistical summaries being estimated. Here, in a sample of 97 participants, we measured performance in judging: i) the size of a single circle, ii) the size variance within an array of six circles, and iii) the average size within an array of six circles. In our versions of both estimation tasks, participants compared two arrays of circles presented sequentially and judged which array had more variance or a larger average size. We calculated the partial correlation between performance on the average and on the variance estimation tasks, controlling for participants’ discrimination abilities in judgments with single circles. We found that average and variance estimation abilities for the same objects were positively correlated. These results suggest involvement of a common mechanism for ensemble processing of different statistical summaries, over and above perceptual abilities relevant to judgments about single objects.
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