The Numeric Ebbinghaus Effect: Evidence for a Density-Area Mechanism of Numeric Estimation?

Abstract

One model of numeric perception is a density-area mechanism: a process that estimates both density and area of an array, then multiplies them to create an estimate of number. One line of evidence that supports this is the surprising numeric Ebbinghaus illusion: smaller context circles lead to greater perceived number than larger context circles, potentially via larger perceived area. This registered report re-tested this effect with a number of simple but potentially important improvements in the method and analysis. Participants were asked to indicate the number of blue dots in arrays that were surrounded by grey context circles of three different sizes. Both experiments confirmed that larger context circles lead to a proportional increase in perceived number. Experiment 1 (N = 50) did so with denser, more texture-like arrays (50-100 dots filling 35% of the area). Experiment 2 (N = 50) did so with sparser, more scatter-like arrays (10-30 dots filling 5% of the area). These findings confirm the existence of the numeric Ebbinghaus effect. This in turn confirms a specific prediction derived from a density-area mechanism and rules out alternatives that begin by stripping away context to non-verbally count discrete entities. No further significant evidence was found to suggest that this depends on the array being particularly dense or texture-like, nor to suggest that anything moderates the impact of increasing perceived area as a direct proportional effect on increasing perceived number. This further builds the case that this kind of numeric perception relies on a density-area mechanism.