The effects of sampling and internal noise on the representation of ensemble average size

Abstract

Increasing numbers of studies have explored human observers' ability to rapidly extract statistical descriptions from collections of similar items (e.g., the average size and orientation of a group of tilted Gabor patches). Determining whether these descriptions are generated by mechanisms that are independent from object-based sampling procedures requires that we investigate how internal noise, external noise, and sampling affect subjects' performance. Here we systematically manipulated the external variability of ensembles and used variance summation modeling to estimate both the internal noise and the number of samples that affected the representation of ensemble average size. The results suggest that humans sample many more than one or two items from an array when forming an estimate of the average size, and that the internal noise that affects ensemble processing is lower than the noise that affects the processing of single objects. These results are discussed in light of other recent modeling efforts and suggest that ensemble processing of average size relies on a mechanism that is distinct from segmenting individual items. This ensemble process may be more similar to texture processing.

Accurate rapid averaging of multihue ensembles is due to a limited capacity subsampling mechanism

“…In spite of the similarity in simulation assumptions and structure, our finding is somewhat at-odds with other simulations which also incorporate fixed internal noise, which have found sub-sampling models of ensemble perception of faces [8] and size [35] underperform on averaging precision relative to real observers with sample sizes fewer than seven elements. Notably, Haberman and Whitney [30] report that discrimination for the mean emotional expression from an ensemble was at least as good as discrimination for individual expressions -a trend not evident in our data, where precision for homogeneous ensembles (single colors) was better than for heterogeneous.…”

“…The magnitude of the difference between these possible models of internal noise is impossible to assess without an available estimate of how internal noise might change with sub-sample size. Although the assumption of fixed internal noise is conservative, in that it may overestimate the precision of the null hypothesis of sub-sampling (the alternative being holistic averaging), the same assumption is made in other ensemble perception studies which do support the suggestion of holistic averaging for faces [8] and size [35]. Separating the effects of internal noise from sample size is a major theoretical challenge in understanding the possible mechanisms behind ensemble perception [45].…”

“…These simulations, like those used in similar studies [e.g., 8,35,45], assume that the level of internal noise is constant across sample size. It is possible that a sub-sampling mechanism would have noise which increases with sample size, meaning that the benefit of larger samples being more representative is diminished by increased noise [see 16].…”

“…the judgment error [ ] present in all psychophysical measurements. Simulations of sub-sampling which incorporate or estimate internal noise as part of the model tend to perform less well compared to real observer data and suggest that larger sub-samples (around seven items), would in fact be required to simulate the averaging performance of human observers [35]. Likewise, experimental evidence also suggests that observers still outperform subsampling expectations even when explicitly instructed to use such strategies in ensemble perception tasks [36], and when ensembles contain a manageable range of stimuli [29].…”

“…Similarly, Marchant and de Fockert [18] showed that their finding that mean size estimates are affected by set size, for irregular sets (ensembles in which all elements have a unique size) but not regular sets (where some elements are the same size), can be predicted by a limited sub-sampling model. Other simulations [e.g., 8,35] have attempted to better characterize the process of mean estimation by including internal noise into simulations -i.e. the judgment error [ ] present in all psychophysical measurements.…”