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.

Many studies have shown that observers can accurately estimate the average feature of a group of objects. However, the way the visual system relies on the information from each individual item is still under debate. Some models suggest some or all items sampled and averaged arithmetically. Another strategy implies “robust averaging,” when middle elements gain greater weight than outliers. One version of a robust averaging model was recently suggested by Teng et al. (2021), who studied motion direction averaging in skewed feature distributions and found systematic biases toward their modes. They interpreted these biases as evidence for robust averaging and suggested a probabilistic weighting model based on minimization of the virtual loss function. In four experiments, we replicated systematic skew-related biases in another feature domain, namely, orientation averaging. Importantly, we show that the magnitude of the bias is not determined by the locations of the mean or mode alone, but is substantially defined by the shape of the whole feature distribution. We test a model that accounts for such distribution-dependent biases and robust averaging in a biologically plausible way. The model is based on well-established mechanisms of spatial pooling and population encoding of local features by neurons with large receptive fields. Both the loss functions model and the population coding model with a winner-take-all decoding rule accurately predicted the observed patterns, suggesting that the pooled population response model can be considered a neural implementation of the computational algorithms of information sampling and robust averaging in ensemble perception.

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