# Dissociation of Size and Distance Effect in Numerical Magnitude Comparison in Less Familiar Number Ranges

## TL;DR

The study investigates whether symbolic and non-symbolic number comparisons use different systems by analyzing correlations between size and distance effects in less familiar number ranges.

## Contribution

The study introduces less familiar number ranges to test the dissociation between symbolic and non-symbolic numerical magnitude comparison mechanisms.

## Key findings

- Size and distance effects in symbolic number comparisons were uncorrelated, supporting the dual system model.
- Non-symbolic comparisons showed a negative correlation between size and distance effects.
- A subsample of participants showed significant correlations between size and distance effects in symbolic comparisons.

## Abstract

The approximate number system (ANS) is thought to mediate symbolic and non-symbolic numerical magnitude comparison. Challenging this view, the dual system model stipulates that non-symbolic comparisons rely on the ANS while symbolic comparisons rely on a discrete semantic system (DSS). In three experiments, the current study tests whether symbolic and non-symbolic magnitude comparisons rely on a common ANS or a DSS by examining the correlation between the size and distance effects in numerical magnitude comparison. We replicated previous studies, which used one-digit numbers 1 to 9, but also aimed to increase variance by using less familiar number ranges. Experiment 1 used a fixed-reference paradigm (reference = 55) with two-digit integers (11–99). Experiments 2 and 3 extended the design to decimals (0.01–0.98) with variable (Experiment 2) or fixed reference (Experiment 3). All experiments additionally included non-symbolic dot comparison in which the expected negative correlation between size and distance effect emerged. Across experiments, size and distance effects in less familiar number ranges were uncorrelated when presented in symbolic format, corroborating the idea that symbolic number comparison relies on a DSS. These findings were moderated by the observation of a significant correlation between size and distance effects in a subsample of participants who showed significant size and distance effects at the individual level. Interpretation of the current results must take into account limitations concerning specificities of multi-digit number processing, the reliability of the effects, and the possible role of unmeasured external factors in shaping the observed correlations.