Top

Gepubliceerd in:

21-07-2018 | Original Article

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

Auteurs: Petia Kojouharova, Attila Krajcsi

Gepubliceerd in: Psychological Research | Uitgave 2/2020

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.

vorige artikel Action plan interrupted: resolution of proactive interference while coordinating execution of multiple action plans during sleep deprivation

volgende artikel Event segmentation and the temporal compression of experience in episodic memory

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.

Dehaene, S. (2007). Symbols and quantities in parietal cortex: Elements of a mathematical theory of number representation and manipulation. In P. Haggard, Y. Rossetti & M. Kawato (Eds.), Sensorimotor foundations of higher cognition (Vol. XXII, pp. 527–574). Cambridge: Harvard University Press.

Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122(3), 371–396. https://doi.org/10.1037/0096-3445.122.3.371.CrossRef

Dehaene, S., & Mehler, J. (1992). Cross-linguistic regularities in the frequency of number words. Cognition, 43(1), 1–29. https://doi.org/10.1016/0010-0277(92)90030-L.CrossRefPubMed

Fischer, M. H., Mills, R. A., & Shaki, S. (2010). How to cook a SNARC: Number placement in text rapidly changes spatial–numerical associations. Brain and Cognition, 72(3), 333–336. https://doi.org/10.1016/j.bandc.2009.10.010.CrossRefPubMed

Goffin, C., & Ansari, D. (2016). Beyond magnitude: Judging ordinality of symbolic number is unrelated to magnitude comparison and independently relates to individual differences in arithmetic. Cognition, 150, 68–76. https://doi.org/10.1016/j.cognition.2016.01.018.CrossRefPubMed

Krajcsi, A. (2016). Numerical distance and size effects dissociate in Indo-Arabic number comparison. Psychonomic Bulletin and Review. https://doi.org/10.3758/s13423-016-1175-6.CrossRef

Krajcsi, A., & Kojouharova, P. (2017). Symbolic numerical distance effect does not reflect the difference between numbers. Frontiers in Psychology. https://doi.org/10.3389/fpsyg.2017.02013.CrossRefPubMedPubMedCentral

Krajcsi, A., Lengyel, G., & Kojouharova, P. (2016). The source of the symbolic numerical distance and size effects. Frontiers in Psychology. https://doi.org/10.3389/fpsyg.2016.01795.CrossRefPubMedPubMedCentral

Leibovich, T., & Ansari, D. (2016). The symbol-grounding problem in numerical cognition: A review of theory, evidence, and outstanding questions. Canadian Journal of Experimental Psychology/Revue Canadienne de Psychologie Expérimentale, 70(1), 12–23. https://doi.org/10.1037/cep0000070.CrossRefPubMed

Lyons, I. M., Ansari, D., & Beilock, S. L. (2015). Qualitatively different coding of symbolic and nonsymbolic numbers in the human brain: Neural coding of numbers. Human Brain Mapping, 36(2), 475–488. https://doi.org/10.1002/hbm.22641.CrossRefPubMed

Lyons, I. M., Nuerk, H.-C., & Ansari, D. (2015). Rethinking the implications of numerical ratio effects for understanding the development of representational precision and numerical processing across formats. Journal of Experimental Psychology: General, 144(5), 1021–1035. https://doi.org/10.1037/xge0000094.CrossRef

Lyons, I. M., Vogel, S. E., & Ansari, D. (2016). On the ordinality of numbers. In Progress in brain research (Vol. 227, pp. 187–221). Amsterdam: Elsevier. https://doi.org/10.1016/bs.pbr.2016.04.010.CrossRef

Moyer, R. S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215(5109), 1519–1520. https://doi.org/10.1038/2151519a0.CrossRefPubMed

Peirce, J. W. (2007). PsychoPy—Psychophysics software in Python. Journal of Neuroscience Methods, 162(1–2), 8–13. https://doi.org/10.1016/j.jneumeth.2006.11.017.CrossRefPubMedPubMedCentral

Ratcliff, R., & McKoon, G. (2008). The diffusion decision model: Theory and data for two-choice decision tasks. Neural Computation, 20(4), 873–922. https://doi.org/10.1162/neco.2008.12-06-420.CrossRefPubMedPubMedCentral

Ratcliff, R., & Tuerlinckx, F. (2002). Estimating parameters of the diffusion model: Approaches to dealing with contaminant reaction times and parameter variability. Psychonomic Bulletin and Review, 9(3), 438–481. https://doi.org/10.3758/BF03196302.CrossRefPubMed

Reynvoet, B., & Sasanguie, D. (2016). The symbol grounding problem revisited: A thorough evaluation of the ANS mapping account and the proposal of an alternative account based on symbol–symbol associations. Frontiers in Psychology. https://doi.org/10.3389/fpsyg.2016.01581.CrossRefPubMedPubMedCentral

Sasanguie, D., Göbel, S. M., Moll, K., Smets, K., & Reynvoet, B. (2013). Approximate number sense, symbolic number processing, or number–space mappings: What underlies mathematics achievement? Journal of Experimental Child Psychology, 114(3), 418–431. https://doi.org/10.1016/j.jecp.2012.10.012.CrossRefPubMed

Schneider, M., Beeres, K., Coban, L., Merz, S., Susan Schmidt, S., Stricker, J., & De Smedt, B. (2017). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science, 20(3), e12372. https://doi.org/10.1111/desc.12372.CrossRef

Smith, P. L., & Ratcliff, R. (2004). Psychology and neurobiology of simple decisions. Trends in Neurosciences, 27(3), 161–168. https://doi.org/10.1016/j.tins.2004.01.006.CrossRefPubMed

Verguts, T., Fias, W., & Stevens, M. (2005). A model of exact small-number representation. Psychonomic Bulletin and Review, 12(1), 66–80. https://doi.org/10.3758/BF03196349.CrossRefPubMed

Verguts, T., & Van Opstal, F. (2014). A delta-rule model of numerical and non-numerical order processing. Journal of Experimental Psychology: Human Perception and Performance, 40(3), 1092–1102. https://doi.org/10.1037/a0035114.CrossRefPubMed

Wagenmakers, E.-J., Van Der Maas, H. L. J., & Grasman, R. P. P. P. (2007). An EZ-diffusion model for response time and accuracy. Psychonomic Bulletin and Review, 14(1), 3–22. https://doi.org/10.3758/BF03194023.CrossRefPubMed

Titel: The Indo-Arabic distance effect originates in the response statistics of the task
Auteurs: Petia Kojouharova
Attila Krajcsi
Publicatiedatum: 21-07-2018
Uitgeverij: Springer Berlin Heidelberg
Gepubliceerd in: Psychological Research / Uitgave 2/2020
Print ISSN: 0340-0727
Elektronisch ISSN: 1430-2772
DOI: https://doi.org/10.1007/s00426-018-1052-1

Andere artikelen Uitgave 2/2020

Task instructions modulate unit–decade binding in two-digit number representation

Original Article

Individual differences in processing resources modulate bimanual interference in pointing

Open Access
Original Article

Attentional bias on motor control: is motor inhibition influenced by attentional reorienting?

Original Article

Shared attention for action selection and action monitoring in goal-directed reaching

Open Access
Original Article

Food deprivation disrupts normal holistic processing of domain-specific stimuli

Original Article

Co-thought gesturing supports more complex problem solving in subjects with lower visual working-memory capacity

Open Access
Original Article