Representation of similar objects as a group: effects of variance on ensemble representations

Abstract

Previous research has shown that the visual system forms accurate statistical summary representations, but little research to date has directly investigated how variance is represented as an ensemble statistics. In the first set of experiments (Experiments 1, 2A and 2B), we examined the effects of group variance on ensemble statistics. We presented viewers with either a single circle/line or with displays that had nine circles/lines, and asked them to estimate the mean size of these circles/lines by adjusting the size of a test circle/line. Across conditions we manipulated variance in the displays while keeping mean size constant. In Experiments 1 and 2A, participants were equally accurate in estimating the mean size of nine same-size circles/lines and a single circle/line. However, more irregular displays of Experiment 2B resulted in more error in the estimations of the size of nine same-sized lines. More critically, in higher variance displays, participants were more likely to overestimate mean size suggesting that variance biases mean size estimations. In a second set of experiments (Experiments 3 and 4), we directly tested whether variance is represented as an ensemble statistics. Participants judged whether two consecutively presented displays consisting of circles of various sizes and yet with identical means and variance. When the second display had higher as opposed to lower variance, accuracy was significantly lower suggesting that people were overestimating the variance of the initial display. The results support the notion of the automaticity of the ensemble statistics. The overestimation of variance representations might lead to overestimation bias in the mean size estimations.