Both exhaustive processing and limited-sample amplification contribute to ensemble averaging
It has been shown that multiple objects can be efficiently represented as ensemble summary statistics, such as the average. Recently, Kanaya et al. (2018) demonstrated the amplification effect in the perception of average. Their participants judged the mean size or temporal frequency of ensembles, and they tended to exaggerate their estimates, especially larger set sizes. Kanaya et al. explained it by non-exhaustive sampling mechanism favoring ~sqrt(N) most salient items, which are either largest or most frequently ones. But how do the rest of elements contribute to ensemble perception? In our study, we used orientation averaging (which does not have any inevitably salient values) and manipulated the salience of individual items via size. Participants had to adjust the average orientation of 4, 8, or 16 triangles. We measured systematic biases, like Kanaya et al. (2018), and SD of errors that are known to correlate with the physical ensemble range. In Experiment 1, most clockwise elements could be bigger, counterclockwise, middle, or all elements were same-size. We found strong clockwise and counterclockwise biases in the corresponding conditions. The biases increased with set size replicating Kanaya et al. (2018). But we found no SD difference between the conditions suggesting that all items were somehow taken into account. In Experiment 2, we compared distributions with same ranges (full-sets) but salient elements being middle or extreme (most clockwise and counterclockwise). We used distribution with only middle elements or only extremes as controls (half-sets). We found that SD in the full-sets were greater than in the middle half-sets and smaller than in the extreme half-sets suggesting that all items were taken into account. We also found that SD in the extreme full-sets were greater than in the middle full-sets in large set size. We conclude that both exhaustive and amplification types of sampling work in averaging.