Roles of saliency and set size in ensemble averaging

Ensemble statistics are often thought of as a reliable impression of numerous items despite limited capacities to consciously represent each individual. However, whether all items equally contribute to ensemble summaries (e.g., mean) and whether they might be affected by known limited-capacity processes, such as focused attention, is still debated. We addressed these questions via a recently described "amplification effect," a systematic bias of perceived mean (e.g., average size) towards the more salient "tail" of a feature distribution (e.g., larger items). In our experiments, observers adjusted the mean orientation of sets of items varying in set size. We made some of the items more salient or less salient by changing their size. While the whole orientation distribution was fixed, the more salient subset could be shifted relative to the set mean or differ in range. We measured the bias away from the set mean and the standard deviation (SD) of errors, as it is known to reflect the physical range from which ensemble information is sampled. We found that bias and SD changes followed the shifts and range changes in salient subsets, providing evidence for amplification. However, these changes were weaker than those expected from sampling only salient items, suggesting that less salient items were also sampled. Importantly, the SD decreased as a function of set size, which is only possible if the number of sampled elements increased with set size. Overall, we conclude that orientation summary statistics are sampled from an entire ensemble and modulated by the amplification effect of attention.