Set size and ensemble perception of numerical value.

There is a growing body of research on ensemble perception, or our ability to form ensemble representations based on perceptual features for stimuli of varying levels of complexity, and more recently, on ensemble cognition, which refers to our ability to perceive higher-level properties of stimuli such as facial attractiveness or gaze direction. Less is known about our ability to form ensemble representations based on more abstract properties such as the semantic meaning associated with items in a scene. Previous work examining whether the meaning associated with digits can be incorporated into summary statistical representations suggests that numerical information from digit ensembles can be extracted rapidly, and likely using a parallel processing mechanism. Here, we further investigate whether participants can accurately generate summary representations of numerical value from digit sets and explore the effect of set size on their ability to do so, by comparing psychometric functions based on a numerical averaging task in which set size varied. Steeper slopes for ten- and seven-item compared to five-item digit sets provide evidence that displays with more digits yield more reliable discrimination between larger and smaller numerical averages. Additionally, consistent with previous reports, we observed a response bias such that participants were more likely to report that the numerical average was "greater than 5" for larger compared to smaller sets. Overall, our results contribute to evidence that ensemble representations for semantic attributes may be carried out via similar mechanisms as those reported for perceptual features.