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Matthew Inverso, Charles Chubb, Charles Wright, Richard Shiffrin, George Sperling; Comparing Efficiencies in Estimating Centroids and Judging Numerosity. Journal of Vision 2016;16(12):1308. doi: 10.1167/16.12.1308.
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© ARVO (1962-2015); The Authors (2016-present)
How efficiently can the visual system use stimulus information in a briefly viewed cloud of dots for two different purposes: judging the number of dots in the cloud (numerosity) versus estimating the cloud's center-of-gravity (its centroid)? These two statistical summary statistics can be estimated rapidly and quite accurately even in very brief stimulus exposures. As judging numerosity requires only knowing the presence of a dot, whereas estimating a centroid requires knowing both a dot's presence and position, we might expect numerosity judgments to be more efficient that centroid estimations. Methods. Subjects viewed a cloud of black dots drawn from a circular, bivariate Gaussian distribution. For N = 9 or 12 , the cloud contained either N (on half the trials) or N+1 dots. In the "Numerosity Task," on each trial, the participant judged whether there were N vs N+1 dots. In the "Centroid Task," on each trial, the participant strove to mouse-click the centroid of the dot cloud. Results. To compare numerosity and centroid performances , we assume that all errors (in both tasks) result from random decimation of the display. Specifically, for each task, we determined the probability E ("Efficiency") for which the participant's performance matched an ideal detector's performance derived by removing dots independently from the display with probability 1- E. When displays comprised either 9 dots or 10, Efficiency was approximately equal in the two tasks; when displays comprised 12 dots or 13, Efficiency was slightly higher estimating centroids task than judging numerosity. Conclusion. Surpisingly, efficiency is equal or higher in estimating centroids than judging numerosity suggesting that position information required for judging centroids is essentially free, i.e., it is very accurate (i.e., position error is small relative to other errors) and that it doesn't require resources that are used for representing the presence of dots.
Meeting abstract presented at VSS 2016
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