A Systematic Investigation of Accuracy and Response Time Based Measures Used to Index ANS Acuity.

Julia Felicitas Dietrich,Klaus Willmes,Elise Klein,Silvia Pixner,Stefan Huber,Korbinian Moeller

doi:10.1371/journal.pone.0163076

Julia Felicitas Dietrich, Klaus Willmes + Show 4 more

Open Access

https://doi.org/10.1371/journal.pone.0163076

Copy DOI

Abstract

The approximate number system (ANS) was proposed to be a building block for later mathematical abilities. Several measures have been used interchangeably to assess ANS acuity. Some of these measures were based on accuracy data, whereas others relied on response time (RT) data or combined accuracy and RT data. Previous studies challenged the view that all these measures can be used interchangeably, because low correlations between some of the measures had been observed. These low correlations might be due to poor reliability of some of the measures, since the majority of these measures are mathematically related. Here we systematically investigated the relationship between common ANS measures while avoiding the potential confound of poor reliability. Our first experiment revealed high correlations between all accuracy based measures supporting the assumption that all of them can be used interchangeably. In contrast, not all RT based measures were highly correlated. Additionally, our results revealed a speed-accuracy trade-off. Thus, accuracy and RT based measures provided conflicting conclusions regarding ANS acuity. Therefore, we investigated in two further experiments which type of measure (accuracy or RT) is more informative about the underlying ANS acuity, depending on participants’ preferences for accuracy or speed. To this end, we manipulated participants’ preferences for accuracy or speed both explicitly using different task instructions and implicitly varying presentation duration. Accuracy based measures were more informative about the underlying ANS acuity than RT based measures. Moreover, the influence of the underlying representations on accuracy data was more pronounced when participants preferred accuracy over speed after the accuracy instruction as well as for long or unlimited presentation durations. Implications regarding the diffusion model as a theoretical framework of dot comparison as well as regarding the relationship between ANS acuity and math performance are discussed.

Highlights

A prominent theory in numerical cognition postulates that the origins of our symbolic math abilities are rooted in a nonverbal, evolutionary old system for approximately representing non-symbolic numerical quantities, which we share with many nonhuman species [1,2,3,4,5,6,7,8,9,10,11]
These results enable us to investigate the relationship between the approximate number system (ANS) measures ruling out the possible alternative explanation that low correlations might be caused by poor reliabilities
In order to clarify whether the reported correlations reflect the “true” relationship between the measures or whether these correlations where artificially reduced due to poor reliability, we evaluated the relationship between accuracy and response time (RT) based measures ensuring sufficient reliability

Summary

Introduction

A prominent theory in numerical cognition postulates that the origins of our symbolic math abilities are rooted in a nonverbal, evolutionary old system for approximately representing non-symbolic numerical quantities, which we share with many nonhuman species [1,2,3,4,5,6,7,8,9,10,11]. Using single-cell recordings, Nieder and colleagues found numerosity-selective neurons in lateral prefrontal and posterior parietal cortex of monkeys [16,17,18]. These neurons showed maximum firing rate for one specific numerosity (i.e., their “preferred numerosity”). Using a representational similarity approach, Lyons et al (2015) demonstrated that numerosities are represented by overlapping tuning curves, which show an increasing overlap for larger numerosities [20]

Methods

Results

Discussion

Conclusion