A selective sampling account of forming numerosity representations.

Abstract

Two leading models of numerosity judgments describe numerical representations as Gaussian distributions on a mental number line. The linear model posits that both the mean and standard deviation of the distributions increase linearly with number, while the logarithmic model assumes logarithmic increases in the mean with constant variability. In this study, we use the selective sampling account, which proposes that information is gathered selectively based on goals and available resources, to explore the cognitive processes underlying variations in variability and scaling. In intermingled displays of blue and yellow dots (blue/yellow task), participants relied on incomplete representations of dots positioned near the center, where spatial resolution is highest, leading to increasing variability with set size. In contrast, spatially separated displays (left/right task) facilitated more comprehensive sampling, resulting in approximately constant variability across set sizes. Behavioral patterns and modeling analyses suggest that the type of scale used is also shaped by the display format, with a more sensitive linear scale applied to compute numerical differences in intermingled displays, and a less sensitive logarithmic scale used to estimate magnitudes for each side in spatially separated displays. Eye-tracking data provide further support for our account, emphasizing the role of selective attention in forming numerical representations and providing a unified framework for understanding variability and scaling across tasks. (PsycInfo Database Record (c) 2025 APA, all rights reserved).