Abstract
In a comparison task, the larger the distance between the two numbers to be compared, the better the performance—a phenomenon termed as the numerical distance effect. According to the dominant explanation, the distance effect is rooted in a noisy representation, and performance is proportional to the size of the overlap between the noisy representations of the two values. According to alternative explanations, the distance effect may be rooted in the association between the numbers and the small-large categories, and performance is better when the numbers show relatively high differences in their strength of association with the small-large properties. In everyday number use, the value of the numbers and the association between the numbers and the small-large categories strongly correlate; thus, the two explanations have the same predictions for the distance effect. To dissociate the two potential sources of the distance effect, in the present study, participants learned new artificial number digits only for the values between 1 and 3, and between 7 and 9, thus, leaving out the numbers between 4 and 6. It was found that the omitted number range (the distance between 3 and 7) was considered in the distance effect as 1, and not as 4, suggesting that the distance effect does not follow the values of the numbers predicted by the dominant explanation, but it follows the small-large property association predicted by the alternative explanations.
Highlights
Reviewed by: Herbert Heuer, Leibniz Research Centre for Working Environment and Human Factors (LG), Germany Fuhong Li, Jiangxi Normal University, China
It is possible that participants learn that 9 is the largest number in the actual session; when 9 is displayed, no further consideration is required in a comparison task
In a new artificial number notation with omitted numbers, the distance effect measured with reaction time and drift rate did not follow the values of the numbers, as it would have been suggested in the mainstream Analog Number System (ANS) model (Moyer and Landauer, 1967; Dehaene, 2007) or in the value-based explanation of the Discrete Semantic System (DSS) model
Summary
Reviewed by: Herbert Heuer, Leibniz Research Centre for Working Environment and Human Factors (LG), Germany Fuhong Li, Jiangxi Normal University, China. The larger the distance between the two numbers to be compared, the better the performance—a phenomenon termed as the numerical distance effect. The distance effect may be rooted in the association between the numbers and the small-large categories, and performance is better when the numbers show relatively high differences in their strength of association with the small-large properties. In a symbolic number comparison task, performance is better (i.e., error rates are lower and reaction times are shorter) when the numerical distance is relatively large, e.g., comparing 1 vs 9 is easier than comparing 5 vs 6 (Moyer and Landauer, 1967). The distance effect is the consequence of this ratio effect because larger
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