The Relationship Between the Numerical Distance Effect and Approximate Number System Acuity is Non-Linear

People can estimate numerical quantities, like the number of grapes in a bunch, using the Approximate Number System (ANS). Individual differences in this ability (ANS acuity) are emerging as an important predictor in research areas ranging from math skills to judgment and decision making. One commonly used ANS acuity metric is the size of the Numerical Distance Effect (NDE): the amount of savings in RT or errors when distinguishing stimuli values as the numerical distance between them increases. However, the validity of this metric has recently been questioned. Here, we model the relationship between the NDE-size and ANS acuity. We demonstrate that the relationship between NDEsize and ANS acuity should not be linear, but rather should resemble an inverted J-shaped distribution, with the largest NDE-sizes typically being found for near average ANS acuities.