Symbolic Number Comparison Is Not Processed by the Analog Number System: Different Symbolic and Non-symbolic Numerical Distance and Size Effects.

Attila Krajcsi,Gábor Lengyel,Petia Kojouharova

doi:10.3389/fpsyg.2018.00124

Abstract

HIGHLIGHTS We test whether symbolic number comparison is handled by an analog noisy system.Analog system model has systematic biases in describing symbolic number comparison.This suggests that symbolic and non-symbolic numbers are processed by different systems.Dominant numerical cognition models suppose that both symbolic and non-symbolic numbers are processed by the Analog Number System (ANS) working according to Weber's law. It was proposed that in a number comparison task the numerical distance and size effects reflect a ratio-based performance which is the sign of the ANS activation. However, increasing number of findings and alternative models propose that symbolic and non-symbolic numbers might be processed by different representations. Importantly, alternative explanations may offer similar predictions to the ANS prediction, therefore, former evidence usually utilizing only the goodness of fit of the ANS prediction is not sufficient to support the ANS account. To test the ANS model more rigorously, a more extensive test is offered here. Several properties of the ANS predictions for the error rates, reaction times, and diffusion model drift rates were systematically analyzed in both non-symbolic dot comparison and symbolic Indo-Arabic comparison tasks. It was consistently found that while the ANS model's prediction is relatively good for the non-symbolic dot comparison, its prediction is poorer and systematically biased for the symbolic Indo-Arabic comparison. We conclude that only non-symbolic comparison is supported by the ANS, and symbolic number comparisons are processed by other representation.

Highlights

Specialty section: This article was submitted to Cognition, a section of the journal Frontiers in Psychology
Because the reaction time analysis applied here follows the reasoning of the early analysis, the current results cannot be considered as a reliable test of the Analog Number System (ANS) model, but we examine whether evidence offered formerly really support the common mechanism for symbolic and non-symbolic number processing
The present work investigated whether symbolic Indo-Arabic number comparison and non-symbolic dot comparison can be described by the same model, as predicted by the widely accepted ANS model, or whether the two notations show systematic differences as suggested by the increasing body of evidence and some alternative accounts of symbolic number processing

Summary

Introduction

Specialty section: This article was submitted to Cognition, a section of the journal Frontiers in Psychology. We conclude that only non-symbolic comparison is supported by the ANS, and symbolic number comparisons are processed by other representation In their seminal work Moyer and Landauer (1967) described that in an Indo-Arabic single digit number comparison task the performance is worse (i.e., reaction time is slower and error rate is higher) when the difference between the two numbers is relatively small (numerical distance effect) or when the numbers are relatively large (numerical size effect). They proposed that the effects are the expression of a general ratio-based effect in which number pairs with smaller ratio are harder to process. Moyer and Landauer (1967) demonstrated that the reaction time pattern can be described appropriately with a function used at that time in physical property comparison tasks: a K × log (large_number/(large_number–small_number))

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