Two-digit number comparison: Decade-unit and unit-decade produce the same compatibility effect with number words.

2010 ◽  
Vol 64 (1) ◽  
pp. 17-24 ◽  
Author(s):  
Pedro Macizo ◽  
Amparo Herrera
Keyword(s):  
Compatibility Effect ◽  
Digit Number ◽  
Number Words ◽  
Number Comparison

scholarly journals Reversing the Manual Digit Bias in Two-Digit Number Comparison

2017 ◽  
Vol 64 (3) ◽  
pp. 191-204 ◽  
Author(s):  
Thomas J. Faulkenberry ◽  
Alexander Cruise ◽  
Samuel Shaki
Keyword(s):  
Numerical Cognition ◽  
Number Line ◽  
Number Representation ◽  
Digit Number ◽  
Computer Mouse ◽  
Number Comparison ◽  
Number Representations ◽  
Mouse Movements ◽  
Embodied Representation ◽  
Fixed Standard

Abstract. Though recent work in numerical cognition has supported a strong tie between numerical and spatial representations (e.g., a mental number line), less is known about such ties in multi-digit number representations. Along this line, Bloechle, Huber, and Moeller (2015) found that pointing positions in two-digit number comparison were biased leftward toward the decade digit. Moreover, this bias was reduced in unit-decade incompatible pairs. In the present study, we tracked computer mouse movements as participants compared two-digit numbers to a fixed standard (55). Similar to Bloechle et al. (2015) , we found that trajectories exhibited a leftward bias that was reduced for unit-decade incompatible comparisons. However, when positions of response labels were reversed, the biases reversed. That is, we found a rightward bias for compatible pairs that was reduced for incompatible pairs. This result calls into question a purely embodied representation of place value structure and instead supports a competition model of two-digit number representation.

scholarly journals No Evidence for an Influence of Grammatical Number in Two-Digit Magnitude and Place-Value Processing in Adults

2020 ◽  
Author(s):  
Julia Huber ◽  
Mojtaba Soltanlou ◽  
Krzysztof Cipora ◽  
Katarzyna Lipowska ◽  
Frank Domahs ◽  
...  
Keyword(s):  
Distance Effect ◽  
Snarc Effect ◽  
Place Value ◽  
Comparison Task ◽  
Digit Number ◽  
Response Level ◽  
Response Side ◽  
Plural Form ◽  
Number Comparison ◽  
Grammatical Number

Numerous studies revealed effects of some linguistic properties like inversion or reading/writing direction on number processing. However, it remains more controversial, whether influences at a syntactic level, such as singular vs. plural form associated with certain numbers, can also influence magnitude and place-value processing and vice versa. In this study, we investigated for the first time in a classical two-digit number comparison task whether grammatical number also affects magnitude and place-value processing (and vice versa). To do so, we used a peculiarity of the Polish language, where the inflection of a verb depends on the unit digit of a number (singular for 25-29, 35-39, etc. and plural for 22-24, 32-34, etc.). This systematic pattern allows the manipulation of congruency between grammatical number and magnitude information, both on an item and a response level (i.e., the grammatical number is either compatible or incompatible to the magnitude information or the response side). We observed no significant interference effects, neither between grammatical number (i.e., associated singular/ plural inflection of the number) and magnitude information, nor between grammatical number and the response side. Model comparisons revealed that models without grammatical number, could explain our data best. Hence, grammatical number did not contribute to the explanation of the data beyond unit-decade compatibility, distance effect and SNARC effect and, thus, seems to be negligible in two-digit number comparison. Task characteristics, which might contribute to this finding are discussed.

On the Perceptual Generality of the Unit-Decade Compatibility Effect

2004 ◽  
Vol 51 (1) ◽  
pp. 72-79 ◽  
Author(s):  
Hans-Christoph Nuerk ◽  
Ulrich Weger ◽  
Klaus Willmes
Keyword(s):  
Compatibility Effect ◽  
Number Line ◽  
Mental Number Line ◽  
Original Experiment ◽  
Holistic Model ◽  
Magnitude Representation ◽  
Number Magnitude ◽  
Number Comparison ◽  
Arabic Number ◽  
Analog Magnitude

Abstract. Number magnitude is assumed to be holistically represented along a single mental number line. Recently, we have observed a unit-decade-compatibility effect which is inconsistent with that assumption (Nuerk, Weger, & Willmes, 2001) . In two-digit Arabic number comparison, we have demonstrated that compatible comparisons in which separate decade and unit comparisons lead to the same decision (32_47, 3 < 4 and 2 < 7) were faster than incompatible trials (37_52, 3 < 5, but 7 > 2). Because overall distance was matched, a holistic model could not account for the compatibility effect. However, one could argue that the compatibility effect was due to the specific vertical perceptual arrangement of the two-digit numbers in Nuerk et al.’s (2001) experiment where the decade digits and unit digits were presented column-wise above each other. To examine this objection, we studied the perceptual generality of the compatibility effect with diagonal presentation. We replicated the compatibility effect with diagonal presentation. It is concluded that the compatibility effect is not due to encoding characteristics imposed by the perceptual setting of the original experiment. In particular, the assumption of an overall analog magnitude representation for two-digit numbers is not consistent with these data.

Is there cross-language modulation when bilinguals process number words?

2010 ◽  
Vol 31 (4) ◽  
pp. 651-669 ◽  
Author(s):  
PEDRO MACIZO ◽  
AMPARO HERRERA ◽  
DANIELA PAOLIERI ◽  
PATRICIA ROMÁN
Keyword(s):  
Second Language ◽  
Compatibility Effect ◽  
First Language ◽  
Unit Distance ◽  
Number Words ◽  
Language Activation ◽  
Cross Language ◽  
The Way

ABSTRACTThis study explores the possibility of cross-language activation when bilinguals process number words in their first language (Italian) and their second language (German). Italian monolinguals (Experiment 1), German monolinguals (Experiment 2), and Italian/German bilinguals (Experiment 3) were required to decide the larger of two number words while the unit–decade compatibility effect was examined. For compatible trials the decade and unit comparisons lead to the same response (e.g., 24–67), whereas for incompatible trials the decade and unit comparisons lead to different responses (e.g., 27–64). The regular unit–decade compatibility effect was significant when bilinguals and monolinguals performed the comparison in German. However, this effect was not found when bilinguals and monolinguals performed the task in Italian. In addition, the decade distance played a major role when bilinguals processed in their first language, whereas the unit distance was more important when they worked in their second language. These results indicate that the processing of number words in one language is not modulated by the way bilinguals process number words in their alternative language.

Two-digit number comparison: Use of place information.

1981 ◽  
Vol 7 (4) ◽  
pp. 890-901 ◽  
Author(s):  
James V. Hinrichs ◽  
Dale S. Yurko ◽  
Jing-mei Hu
Keyword(s):  
Digit Number ◽  
Number Comparison

scholarly journals Reversing the manual digit bias in two-digit number comparison

2016 ◽  
Author(s):  
Thomas J. Faulkenberry
Keyword(s):  
Numerical Cognition ◽  
Number Line ◽  
Number Representation ◽  
Digit Number ◽  
Computer Mouse ◽  
Number Comparison ◽  
Number Representations ◽  
Mouse Movements ◽  
Embodied Representation ◽  
Fixed Standard

Though recent work in numerical cognition has supported the embodiment of number representations (e.g., a mental number line), little is known about the embodiment of multi-digit number representations. Along this line, Bloechle, Huber, and Moeller (2015) found that pointing positions in two-digit number comparison were biased leftward toward the decade digit. Moreover, this bias was reduced in unit-decade incompatible pairs. In the present study, we tracked computer mouse movements as participants compared two-digit numbers to a fixed standard (55). Similar to Bloechle et al. (2015), we found that trajectories exhibited a leftward bias that was reduced for unit-decade incompatible comparisons. However, when positions of response labels were reversed, the biases reversed. That is, we found a rightward bias for compatible pairs that was reduced for incompatible pairs. This result calls into question a purely embodied representation of place value structure and instead supports a competition model of two-digit number representation.

scholarly journals Pick the smaller number: No influence of linguistic markedness on three-digit number processing

2020 ◽  
Author(s):  
Julia Bahnmueller ◽  
Krzysztof Cipora ◽  
Silke Melanie Goebel ◽  
Hans-Christoph Nuerk ◽  
Mojtaba Soltanlou
Keyword(s):  
Standard Procedure ◽  
Number Processing ◽  
Task Instruction ◽  
Comparison Task ◽  
Digit Number ◽  
Task Instructions ◽  
Base Form ◽  
Number Comparison ◽  
English Speaking ◽  
Underlying Processes

The symbolic number comparison task has been widely used to investigate the cognitive representation and underlying processes of multi-digit number processing. The standard procedure to establish numerical distance and compatibility effects in such number comparison paradigms usually entails asking participants to indicate the larger of two presented multi-digit Arabic numbers rather than to indicate the smaller number. In terms of linguistic markedness, this procedure includes the unmarked/base form in the task instruction (i.e., large). Here we evaluate distance and compatibility effects in a three-digit number comparison task observed in Bahnmueller et al. (2015) using a marked task instruction (i.e., ‘pick the smaller number’). Moreover, we aimed at clarifying whether the markedness of task instruction influences common numerical effects and especially componential processing as indexed by compatibility effects. We instructed German- and English-speaking adults (N=52) to indicate the smaller number in a three-digit number comparison task as opposed to indicating the larger number in Bahnmueller et al. (2015). We replicated standard effects of distance and compatibility in the new pick the smaller number experiment. Moreover, when comparing our findings to Bahnmueller et al. (2015), numerical effects did not differ significantly between the two studies as indicated by both frequentist and Bayesian analysis. Taken together our data suggest that distance and compatibility effects alongside componential processing of multi-digit numbers are rather robust against variations of linguistic markedness of task instructions.

scholarly journals Pick the smaller number: No influence of linguistic markedness on three-digit number processing

2021 ◽  
Vol 7 (3) ◽  
pp. 295-307 ◽  
Author(s):  
Julia Bahnmueller ◽  
Krzysztof Cipora ◽  
Silke Melanie Göbel ◽  
Hans-Christoph Nuerk ◽  
Mojtaba Soltanlou
Keyword(s):  
Standard Procedure ◽  
Number Processing ◽  
Task Instruction ◽  
Comparison Task ◽  
Digit Number ◽  
Task Instructions ◽  
Base Form ◽  
Number Comparison ◽  
English Speaking ◽  
Underlying Processes

The symbolic number comparison task has been widely used to investigate the cognitive representation and underlying processes of multi-digit number processing. The standard procedure to establish numerical distance and compatibility effects in such number comparison paradigms usually entails asking participants to indicate the larger of two presented multi-digit Arabic numbers rather than to indicate the smaller number. In terms of linguistic markedness, this procedure includes the unmarked/base form in the task instruction (i.e., large). Here we evaluate distance and compatibility effects in a three-digit number comparison task observed in Bahnmueller et al. (2015, https://doi.org/10.3389/fpsyg.2015.01216) using a marked task instruction (i.e., ‘pick the smaller number’). Moreover, we aimed at clarifying whether the markedness of task instruction influences common numerical effects and especially componential processing as indexed by compatibility effects. We instructed German- and English-speaking adults (N = 52) to indicate the smaller number in a three-digit number comparison task as opposed to indicating the larger number in Bahnmueller et al. (2015). We replicated standard effects of distance and compatibility in the new pick the smaller number experiment. Moreover, when comparing our findings to Bahnmueller et al. (2015), numerical effects did not differ significantly between the two studies as indicated by both frequentist and Bayesian analysis. Taken together our data suggest that distance and compatibility effects alongside componential processing of multi-digit numbers are rather robust against variations of linguistic markedness of task instructions.

Attentional Strategies in Place-Value Integration

2011 ◽  
Vol 219 (1) ◽  
pp. 42-49 ◽  
Author(s):  
Anne Mann ◽  
Korbinian Moeller ◽  
Silvia Pixner ◽  
Liane Kaufmann ◽  
Hans-Christoph Nuerk
Keyword(s):  
Compatibility Effect ◽  
Developmental Trajectories ◽  
Number System ◽  
Number Processing ◽  
Place Value ◽  
Digit Number ◽  
Magnitude Comparison ◽  
Attentional Processes ◽  
Arabic Number ◽  
Value Integration

To process a multi-digit number its constituting digits need to be integrated into the place-value structure of the Arabic number system. For two-digit numbers, processes of unit-decade integration are reflected by the compatibility effect in magnitude comparison. Recent research in adults indicated that the size of the compatibility effect increases when stimuli prevent to focus on the decade digits as achieved by the inclusion of within-decade items (43_47). In the present study within- and between-decade items (47_62) were used to assess the compatibility effect in children. We observed reliable compatibility effects that increased with grade level and that were larger than in a previous study without within-decade stimuli. Furthermore, evaluation of the developmental trajectories showed that two-digit number processing develops to more automatic parallel processing of the constituent digits of tens and units. From these results we conclude that (i) even for children attentional processes can strongly influence multi-digit number processing and (ii) with increasing age and experience more parallel and automated understanding of two-digit numbers develops which seems to remain relatively stable once achieved.

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