Numerical distance and size effects dissociate in Indo-Arabic number comparison

Abstract

Numerical distance and size effects (easier number comparisons with large distance or small size) are mostly supposed to reflect a single effect, the ratio effect, which is a consequence of activation of the analog number system (ANS), working according to Weber’s law. In an alternative model, symbolic numbers can be processed by a discrete semantic system (DSS), in which the distance and size effects could originate in two independent factors: the distance effect depending on the semantic distance of the units, and the size effect depending on the frequency of the symbols. Whereas in the classic view both symbolic and nonsymbolic numbers are processed by the ANS, in the alternative view only nonsymbolic numbers are processed by the ANS, but symbolic numbers are handled by the DSS. The present work contrasts the two views, investigating whether the sizes of the distance and size effects correlate in nonsymbolic dot comparison and in symbolic Indo-Arabic comparison tasks. If a comparison is backed by the ANS, the distance and size effects should correlate, because the two effects are merely two ways to measure the same ratio effect. However, if a comparison is supported by another system—for example, the DSS—the two effects might dissociate. In the present measurements, the distance and size effects correlated very strongly in the dot comparison task, but they did not correlate in the Indo-Arabic comparison task. Additionally, the effects did not correlate between the Indo-Arabic and dot comparison tasks. These results suggest that symbolic number comparison is not handled by the ANS, but by an alternative representation, such as the DSS.