The Indo-Arabic distance effect originates in the response statistics of the task

Petia Kojouharova, Attila Krajcsi

In the number comparison task distance effect (better performance with larger distance between the two numbers) and size effect (better performance with smaller numbers) are used extensively to find the representation underlying numerical cognition. According to the dominant analog number system (ANS) explanation, both effects depend on the extent of the overlap between the noisy representations of the two values. An alternative discrete semantic system (DSS) account supposes that the distance effect is rooted in the association between the numbers and the "small-large" properties with better performance for numbers with relatively high differences in their strength of association, and that the size effect depends on the everyday frequency of the numbers with smaller numbers being more frequent and thus easier to process. A recent study demonstrated that in a new, artificial digit notation-where both association and frequency can be arbitrarily manipulated-the distance and size effects change according to the DSS account. Here, we investigate whether the same manipulations modify the distance and size effects in Indo-Arabic notation, for which associations and frequency are already well established. We found that the distance effect depends on the association between the numbers and the "small-large" responses. It was also found that while the distance effect is flexible, the size effect seems to be unaltered, revealing a dissociation between the two effects. This result challenges the ANS view, which supposes a single mechanism behind the distance and size effects, and supports the DSS account, supposing two independent, statistics-based mechanisms behind the two effects.