Abstract
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.
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Notes
Note that there is an increasing number of works suggesting that the ANS explanation has serious issues in its original form. For example, it has been proposed that symbolic and non-symbolic number processing might rely on different types of representations (Lyons, Ansari, & Beilock, 2015), that symbolic and non-symbolic number representations may have different role in math achievement (Schneider et al., 2017), or that the variance of the performance should also be considered when measuring the ratio effect (Lyons, Nuerk, & Ansari, 2015). For more issues see, e.g., in the review of Leibovich and Ansari (2016) or Reynvoet and Sasanguie (2016). However, in the present work we specifically test alternative models in which distance and size effects are independent effects, and in which models it is possible that the distance effect is not originated in the value of the numbers, but in the associations of the numbers.
The proportion of being smaller or larger is directly proportional to the order of the values. The ordinality of the numbers has been repeatedly proposed to be an important component of number processing. See a recent review of this issue in Lyons, Vogel, and Ansari (2016).
An additional effect which may appear in a number comparison task is the end effect—reaction time is much faster and error rate is lower for the cells containing the largest number of the set, in this case all cells with number 9. Visual inspection suggests that there might be an end effect in the data. As this effect can distort the stimulus space in a non-linear manner (it flattens the distance effect in the relevant cells), an additional analysis was performed with the cells containing the number 9 excluded. The results were similar to the ones described in the text.
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Acknowledgements
We thank Krisztián Kasos and Ákos Laczkó for their comments on an earlier version of the manuscript.
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Kojouharova, P., Krajcsi, A. The Indo-Arabic distance effect originates in the response statistics of the task. Psychological Research 84, 468–480 (2020). https://doi.org/10.1007/s00426-018-1052-1
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DOI: https://doi.org/10.1007/s00426-018-1052-1