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18-01-2020 | Original Article

Numerals do not need numerosities: robust evidence for distinct numerical representations for symbolic and non-symbolic numbers

Auteurs: Mila Marinova, Delphine Sasanguie, Bert Reynvoet

Gepubliceerd in: Psychological Research | Uitgave 2/2021

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Abstract

In numerical cognition research, it has traditionally been argued that the processing of symbolic numerals (e.g., digits) is identical to the processing of the non-symbolic numerosities (e.g., dot arrays), because both number formats are represented in one common magnitude system—the Approximate Number System (ANS). In this study, we abandon this deeply rooted assumption and investigate whether the processing of numerals and numerosities can be dissociated, using an audio-visual paradigm in combination with various experimental manipulations. In Experiment 1, participants performed four comparison tasks with large symbolic and non-symbolic numbers: (1) number word–digit (2) tones–dots, (3) number word–dots, (4) tones–digit. In Experiment 2, we manipulated the number range (small vs. large) and the presentation modality (visual–auditory vs. auditory–visual). Results demonstrated ratio effects (i.e., the signature of ANS being addressed) in all tasks containing numerosities, but not in the task containing numerals only. Additionally, a cognitive cost was observed when participants had to integrate symbolic and non-symbolic numbers. Therefore, these results provide robust (i.e., independent of presentation modality or number range) evidence for distinct processing of numerals and numerosities, and argue for the existence of two independent number processing systems.
Voetnoten
1
With respect to the credibility and the scientific integrity of our research, we report how we determined our sample size, all data exclusions (if any), all manipulations, and all measures in the study (Simmons, Nelson, & Simonsohn, 2012).
 
2
Because our study focused on comparing both symbolic and non-symbolic number pairs, we manipulated the relative difference (i.e., ratio) between the numbers, but not the absolute distance between them. As we mentioned in “Introduction”, the ratio and the distance are two very strongly related metrics.
 
3
Because the duration of the silence is dependent on the amount of tones that have to be presented within the stimulus timeframe, for these experiments, the shortest and the longest inter-tone intervals registered by the program were 20 ms and 1373 ms, respectively.
 
4
The BF10 is the ratio of the likelihood of the alternative hypothesis and the likelihood of the null hypothesis (while BF01 is simply the inverse ratio of these two likelihoods). For the more complicated models involving a larger numbers of factors (e.g., repeated measures ANOVA), we reported the BFInclusion (see Wagenmakers et al., 2018 for the rationale). According to the interpretation of Jeffreys (1961), BF values between 1 and 3 are considered as anecdotal evidence (“not worth more than a bare mention”, Jeffreys, 1961) for the alternative hypothesis, BF values between 3 and 10 are considered as moderate evidence, BF values between 10 and 30 are considered as strong evidence, BF values between 30 and 100 are considered very strong evidence, and BF values above 100 are considered as extreme evidence.
 
5
The confidence intervals (CI) around the effect sizes were computed with an SPSS plug in calculator by Karl Wuensch, freely available from http://​core.​ecu.​edu/​psyc/​wuenschk/​SPSS/​SPSS-Programs.​htm. Following the author`s recommendations (see Wuensch, 2009), and Steigner (2004), we report the 90% CI for partial eta squared (\(\eta_{\text{p}}^{2}\)), and the 95% CI for Cohen’s d.
 
6
In JASP, the highest number that can be displayed as BF is 1e+305. Once this value has exceeded, the computer automatically changes this into an infinity (see Love, 2015; Wagenmakers, 2015).
 
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Metagegevens
Titel
Numerals do not need numerosities: robust evidence for distinct numerical representations for symbolic and non-symbolic numbers
Auteurs
Mila Marinova
Delphine Sasanguie
Bert Reynvoet
Publicatiedatum
18-01-2020
Uitgeverij
Springer Berlin Heidelberg
Gepubliceerd in
Psychological Research / Uitgave 2/2021
Print ISSN: 0340-0727
Elektronisch ISSN: 1430-2772
DOI
https://doi.org/10.1007/s00426-019-01286-z

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