Numerical cognition
Do we compare digits and dot clouds with the same mental system?
Open access · cc by · source: Europe PMC
A Weber's-law 'approximate number' model described how people compare dot clouds well, but it systematically mispredicted how they compare written digits, suggesting digits use a different system.
Study at a glance
- Design
- Human experiment — Within-subject number comparison task: each participant chose the larger of two digits (1-9) and of two dot arrays (ratio-matched 5-45) over many trials; error rates, reaction times and diffusion-model drift rates were fitted against Analog Number System predictions.
- N
- N=20 · 24 university students tested; 4 excluded for high error rates, leaving 20.
- Population
- Hungarian university students aged 19-24
- Outcome
- Error rates, reaction times and EZ-diffusion drift rates for every number pair in symbolic (digit) and non-symbolic (dot) comparison
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Key findings
For dots, one Weber ratio (about 0.19) predicted both the mean error rate and the shape of errors across pairs, and drift rates fell toward zero as pairs became indistinguishable, as the ANS predicts. For digits, the Weber ratio implied by mean errors (about 0.09) did not produce the best-fitting error pattern: the model predicted too many errors for close pairs and too few for medium pairs. Digit drift rates stayed well above zero even for the hardest pairs, and digit and dot reaction-time patterns were not simple rescalings of each other.
Methodology
20 students chose the larger of two numbers in two conditions: Arabic digits from 1 to 9, and dot arrays using the same ratios scaled up to 5-45 dots to avoid instant counting. Every pair was shown many times, giving 720 trials per condition. The authors fitted Analog Number System (ANS) predictions to error rates, compared reaction-time patterns across notations, and used a diffusion model to recover drift rates (the quality of evidence) for each pair.
Limitations
The sample was small and the analysis rests on group-mean patterns across number pairs rather than a formal comparison against a fitted alternative model. The authors themselves say the reaction-time analysis follows older reasoning and is not a reliable test, and the simple EZ diffusion method has known limits. The dot stimuli did not control all visual cues such as density and area. The study argues digits are not processed by the ANS but does not identify which system does process them.
How this study connects
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