Numerical Association Of Response Codes Research Articles

No conclusive evidence for number-induced attentional shifts in a temporal order judgement task.

The Spatial Numerical Association of Response Codes (SNARC) effect refers to the observation that relatively small (e.g., 1) and large numbers (e.g., 9) elicit faster left- and right-sided manual responses, respectively. In a variation known as the attentional SNARC effect, merely looking at numbers caused a left- or right-ward shift in covert spatial attention, depending on the number's magnitude. In our study, we probed the notion that numbers induce shifts of spatial attention in accordance with their position on a mental number line (MNL). Critically, we removed any putative spatial response code that may contaminate the responses. We used a square and a tilted square as targets, thereby situating the decisive response dimension in the ventral, non-spatial processing stream. In two experiments where numbers were used as non-informative cues preceding a temporal order judgement (TOJ) task, we did not observe a deflection of the locus of spatial attention as a function of the numerical magnitude of the cue. In a third experiment, finding a significant modulation of TOJ performance as a function of the pointing direction of arrow cues allowed us to rule out the possibility that the absence of any significant modulation in Experiments 1 and 2 was due to a lack of sensitivity of our task set-up. We conclude from the current findings that the spatial codes that the perception and naming of numbers potentially elicit are not in and by themselves sufficient to elicit deflections of spatial attention.

Spatio–Numerical Mapping in 3D

The close link between number and space is illustrated by the Spatial Numerical Association of Response Codes (SNARC) effect. The current research focuses on the flexibility of the SNARC across three dimensions. Shaki and Fischer (2018) pointed out that spatial attributes of stimuli and response effectors can favor an ad hoc spatial representation. In this paper, we aimed to broaden this perspective using two Go/NoGo experiments with digits being presented at two spatial locations while a central response was required. In Experiment 1, stimuli appeared either to the left or right (horizontal) and below or above fixation (vertical). In Experiment 2, as the monitor was laying down flat on the desk, stimuli appeared either to the left or right (horizontal) and either close or far from the observer (midsagittal). The results of Experiment 1 show significant effects for the two dimensions (horizontal, vertical), while in Experiment 2, we observe only a barely significant effect for the sagittal axis. We interpret these findings as showing (1) the importance of motor response spatialization in eliciting the SNAs and (2) the dominance of the vertical axis over the horizontal when the spatial component of the motor response is removed.

Exploring the Space-Calorie Association: Preliminary Evidence from Reaction Time Performance.

The present study was designed to investigate the representation of calorie levels in space. Previously an association between numerical magnitude and space has been established, namely, the Spatial Numerical Association of Response Codes (SNARC) effect. The spatial-numerical association reveals representation of smaller and larger numbers by the left and right sides, respectively. In addition, previous studies showed that spatial arrangement of foods in space affects the food selection behavior. In three experiments, the presence of an association between calorie magnitude and space was tested to understand how it could potentially affect food selection behavior. Reaction times were recorded to investigate the speed of information processing. In Experiment 1, locations of low and high calorie food stimuli were (in)congruent in terms of the space-calorie association. In Experiment 2, endogenous spatial cues were used to bias attention to investigate if this bias would lead to formation of the space-calorie association. Finally, Experiment 3 investigated whether green and red colors evoke approach or avoidance behavior and prevent formation of the space-calorie association. In all experiments, results revealed lack of an association between space and calorie, that is, presenting low/high calorie items on the left/right hemispace, respectively, did not modulate the processing speed.

Does Number Perception Cause Automatic Shifts of Spatial Attention? A Study of the Att-SNARC Effect in Numbers and Chinese Months.

The Attentional Spatial Numerical Association of Response Codes (Att-SNARC) effect has shown that number perception induces shifts in spatial attention (Fischer et al., 2003; Dodd et al., 2008). However, many replications were attempted and they often failed. In the present study, we investigated whether the Att-SNARC effect can be found for numbers in different notations: months in Arabic form, Simplified Chinese form, Traditional Chinese form (includes numerical ordinal information) and in Chinese non-numerical form (an ordinal sequence). By varying the cognitive task, we also examined whether the effect is a consequence of automatic perceptual processing. In Experiment 1, an Att-SNARC effect was observed for numbers regardless of notation. In Experiment 2 (order-irrelevant task) and Experiment 3 (order-relevant task), the effect was also found consistently for months in Arabic form, Simplified Chinese form, and Traditional Chinese form. This effect was not observed for months in Chinese non-numerical form in Experiment 3. These results show that number and numerical sequence perception automatically causes a spatial shift of attention. Our study provides positive evidence for the Att-SNARC effect and indicates that the effect can generalize to other numerical ordinal sequences that contain numeric information.

Factoring in the spatial effects of symbolic number representation

Spatial constituents of adult symbolic number representation produce effects of size-value congruity, Spatial Numerical Association of Response Codes (SNARC), and numerical distance. According to behavioral experiments, these effects belong to distinct processing stages. Yet, these effects evoke overlapping responses in both early and late Event Related Potentials (ERPs). To probe whether these overlaps indicate sharing of resources, all relevant stimulus and response conditions were factorially combined in a numerical value comparison task. To secure ERP validity, same numbers were compared against variable reference values. This design resulted in previously unobserved interactions in behavior but inhibited late ERP effects. All effects arose early in the P1 component (around 100 ms) and most showed hemispheric specificity. Independency of congruity and SNARC effects was observed, whereas SNARC and numerical distance were closely intertwined. Differences in hemispheric specificity, rather than stage-wise separation, were key to independence.

Is the SNARC a boojum?

In this essay, the author notes that for the past half-century, psychologists have examined how humans make use of spatial representations when making judgments about numerical properties of sets of items. This line of work was initiated by Frank Restle (1970), who asked college students at Indiana University to choose the larger number, either the sum of A + B or C, as rapidly as possible. Restle found that the timing of people's choices fit an analog model of numerical judgment that had been proposed a few years earlier (Moyer & Landauer, 1967) and that people seemed to judge the magnitude of numbers by their position on a mental number line. The hypothetical number line is now called the "mental number line," and the effect on latency to respond to questions about numbers that results from use of the mental number line has been labeled the "Spatial Numerical Association of Response Codes" or SNARC for short. The author notes that she has parodied Frank Beach's (1950) title for his classic essay about the state of comparative psychology at the mid-20th century for the title of this piece. Beach, in turn, was inspired by Lewis Carroll's nonsense poem, " The Hunting of the Snark," published in 1876. The poem chronicles "the impossible voyage of an improbable crew to find an inconceivable creature," the snark. According to the poem, most species of snarks are relatively harmless. The boojum, however, is a dangerous snark, because those who catch sight of a boojum "suddenly vanish away." Here, the author wants to turn the meaning of the homonym SNARC a bit to suggest that the SNARC might itself vanish, perhaps to metamorphose into a more complex entity. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Limited evidence of number-space mapping in rhesus monkeys (Macaca mulatta) and capuchin monkeys (Sapajus apella).

Humans exhibit evidence of a mental number line that suggests a left-to-right, or sometimes right-to-left, representation of smaller to larger numbers. The Spatial Numerical Association of Response Codes (SNARC) effect is one example of this mental number line and has been investigated extensively in humans. Less research has been done with animals, and results have been inconclusive. Rugani, Vallortigara, Priftis, and Regolin (2015) found that young chicks showed a bias to respond to small quantities presented to their left and large quantities presented to their right when forced to move toward those stimuli to gain food reward. We replicated this design with rhesus macaques and capuchin monkeys using a computerized task, but we did not find this outcome. We also trained monkeys to choose between 2 arrays of dots, and then assessed biases in terms of choice location and response latency on trials with a numerical difference and on trials with equal numbers of items in both sets. There was no evidence of SNARC-like effects in equal trials, although when arrays differed in number, 12 of 19 monkeys showed differential performance depending on whether the smaller array was at the left or at the right onscreen. These results indicate that SNARC-like effects may not emerge in all contexts and may not be phylogenetically widespread. More effort is needed to broaden the number of species assessed and match other methods that are used with human participants so that we can better define the presence and extent of such effects. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Individual Differences in Implicit and Explicit Spatial Processing of Fractions.

Recent studies have explored the foundations of mathematical skills by linking basic numerical processes to formal tests of mathematics achievement. Of particular interest is the relationship between spatial-numerical associations—specifically, the Spatial Numerical Association of Response Codes (SNARC) effect—and various measures of math ability. Thus far, studies investigating this relationship have yielded inconsistent results. Here, we investigate how individual implicit and explicit spatial representations of fractions relate to fraction knowledge and other formal measures of math achievement. Adult participants (n = 105) compared the magnitude of single digit, irreducible fractions to ½, a task that has previously produced a reliable SNARC effect. We observed a significant group-level SNARC effect based on overall fraction magnitude, with notable individual variability. While individual SNARC effects were correlated with performance on a fraction number-line estimation (NLE) task, only NLE significantly predicted scores on a fractions test and basic standardized math test, even after controlling for IQ, mean accuracy, and mean reaction time. This suggests that–for fractions–working with an explicit number line is a stronger predictor of math ability than implicit number line processing. Neither individual SNARC effects nor NLE performance were significant predictors of algebra scores; thus, the mental number line may not be as readily recruited during higher-order mathematical concepts, but rather may be a foundation for thinking about simpler problems involving rational magnitudes. These results not only characterize the variability in adults’ mental representations of fractions, but also detail the relative contributions of implicit (SNARC) and explicit (NLE) spatial representations of fractions to formal math skills.

The association between number magnitude and space is dependent on notation: Evidence from an adaptive perceptual orientation task

Research on adults' numerical abilities suggests that number representations are spatially oriented. This association of numbers with spatial response is referred to as the SNARC (i.e., spatial–numerical association of response codes) effect. The notation-independence hypothesis of numeric processing predicts that the SNARC effect will not vary with notation (e.g., Arabic vs. number word). To test such assumption, the current study introduced an adaptive experimental procedure based on a simple perceptual orientation task that can automatically smooth out the mean reaction time difference between Arabic digits and traditional Chinese number. We found that the SNARC effect interacted with notation, showing a SNARC effect for Arabic digits, but not for verbal number words. The results of this study challenged the commonly held view that notation does not affect numerical processes associated with spatial representations. We introduced a parallel model to explain the notation-dependent SNARC effect in the perceptual orientation judgment task.

The Effect of Spatial Numerical Association of Response Codes in Healthy Individuals and Schizophrenic Patients with Mixed-Reading Habit

Background: Reading habits are believed to have an important role in the association between number and space; however, the effect of the spatial numerical association of response codes (SNARC) as a casual involvement has not been fully documented. Objectives: This study aimed to determine the SNARC effect in individuals with mixed-reading Persian language in which the text is read from right to left but the numbers are read from left to right. Moreover, because of the critical role of visuospatial attention in SNARC effect, which is impaired in patients with schizophrenia, the SNARC effect was also examined in a group of patients with schizophrenia. Methods: Using number comparison tasks and parity judgment tasks, the SNARC effect was first examined in a group of Persian speaking university students and then in a group of Persian speaking schizophrenic patients. Results: The results showed the standard SNARC effect in students with the mixed-reading habit. Moreover, the results revealed a comparable SNARC effect in schizophrenia patients and controls. Conclusions: Our results suggested that the direction of reading of numbers might influence the relationship between numbers and space, not the direction of text reading. Also, the semantic representation of numbers is preserved in patients with schizophrenia.

Automaticity of access to numerical magnitude and its spatial associations: The role of task and number representation.

Generally, people respond faster to small numbers with left-sided responses and large numbers with right-sided responses, a pattern known as the SNARC (spatial numerical association of response codes) effect. The SNARC effect is interpreted as evidence for amodal automatic access of magnitude and its spatial associations, because it occurs in settings where number is task-irrelevant and for different number formats. We report five studies designed to establish the degree to which activation of magnitude and its spatial associations is truly automatic and amodal. Based on the notion of autonomous automaticity, we hypothesized that the mere presence of a number form (to which participants made a color decision) would be sufficient to elicit the SNARC effect. However, we found no evidence of a SNARC effect for simple color decisions to Arabic digits (Experiment 1). There was a SNARC effect for color decision to digits when participants recognized the stimulus as a digit before responding (Experiment 2), participants viewed the digit for sufficient time before color onset (Experiments 3 and 5), or there was temporal uncertainty regarding color onset (Experiment 3). There was no SNARC effect for color decision to arrays of circles (Experiment 4), regardless of viewing time or temporal uncertainty. Overall, our results suggest that, while access to magnitude and its spatial associations is not automatic in an "all-or-none" sense, it is certainly at the strong end of automaticity, and that this automatic activation is modality dependent. Our findings are most supportive of conceptual coding accounts of the SNARC effect. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Spatial Presentations, but Not Response Formats Influence Spatial-Numerical Associations in Adults.

According to theories of embodied numerosity, processing of numerical magnitude is anchored in bodily experiences. In particular, spatial representations of number interact with movement in physical space, but it is still unclear whether the extent of the movement is relevant for this interaction. In this study, we compared spatial-numerical associations over response movements of differing spatial expansion. We expected spatial-numerical effects to increase with the extent of physical response movements. In addition, we hypothesized that these effects should be influenced by whether or not a spatial representation of numbers was presented. Adult participants performed two tasks: a magnitude classification (comparing numbers to the fixed standard 5), from which we calculated the Spatial Numerical Association of Response Codes (SNARC) effect; and a magnitude comparison task (comparing two numbers against each other), from which we calculated a relative numerical congruity effect (NCE), which describes that when two relatively small numbers are compared, responses to the smaller number are faster than responses to the larger number; and vice versa for large numbers. A SNARC effect was observed across all conditions and was not influenced by response movement extent but increased when a number line was presented. In contrast, an NCE was only observed when no number line was presented. This suggests that the SNARC effect and the NCE reflect two different processes. The SNARC effect seems to represent a highly automated classification of numbers as large or small, which is further emphasized by the presentation of a number line. In contrast, the NCE likely results from participants not only classifying numbers as small or large, but also processing their relative size within the relevant section of their mental number line representation. An additional external presentation of a number line might interfere with this process, resulting in overall slower responses. This study follows up on previous spatial-numerical training studies and has implications for future spatial-numerical trainings. Specifically, similar studies with children showed contrasting results, in that response format but not number line presentation influenced spatial-numerical associations. Accordingly, during development, the relative relevance of physical experiences and presentation format for spatial-numerical associations might change.

There's a SNARC in the Size Congruity Task.

The size congruity effect involves interference between numerical magnitude and physical size of visually presented numbers: congruent numbers (either both small or both large in numerical magnitude and physical size) are responded to faster than incongruent ones (small numerical magnitude/large physical size or vice versa). Besides, numerical magnitude is associated with lateralized response codes, leading to the Spatial Numerical Association of Response Codes (SNARC) effect: small numerical magnitudes are preferably responded to on the left side and large ones on the right side. Whereas size congruity effects are ascribed to interference between stimulus dimensions in the decision stage, SNARC effects are understood as (in)compatibilities in stimulus-response combinations. Accordingly, size congruity and SNARC effects were previously found to be independent in parity and in physical size judgment tasks. We investigated their dependency in numerical magnitude judgment tasks. We obtained independent size congruity and SNARC effects in these tasks and replicated this observation for the parity judgment task. The results confirm and extend the notion that size congruity and SNARC effects operate in different representational spaces. We discuss possible implications for number representation.

The Association of Number and Space Under Different Tasks: Insight From a Process Perspective.

We investigated the Spatial Numerical Association of Response Codes (SNARC) effect in 240 adults using a parity judgment and a magnitude classification task. Eight numbers from 1 to 9 except 5 were randomly presented one at a time, half of the participants were asked to compare these number with the target number 5 in the magnitude classification task; the other half of the participants were asked to judge whether these numbers were even or odd. It was called a phase when all eight numbers were tested; there were in total 16 phases. Detailed analyses of the changes in response times across the range of numbers and the chronological trend of the SNARC effect size over 16 phases estimated by a curvilinear regression model were reported. This phase-to-phase design and analyses provide an insight into the process of the SNARC effect in different tasks. We found that the SNARC effect emerged earlier and stayed more stable in magnitude classification task than in the parity task during the time course. Furthermore, the size of SNARC effect increased with time in the magnitude classification task, whereas it fluctuated up and down over time in the parity task. These findings indicate that the association of the number and space is dynamic and the process of the SNARC effect varies across tasks.

Time dependency of the SNARC effect for different number formats: evidence from saccadic responses.

In line with the suggestion that the strength of the spatial numerical association of response codes (SNARC) effect was time dependent, the aim of the present study was to assess whether the association strength depends on the processing time of numerical quantity and/or of the time to initiate responses. More specifically, we examined whether and how the SNARC effect could be modulated by number format and effector type. Experiment 1 compared the effect induced by Arabic numbers and number words on the basis of saccadic responses in a parity judgment task. Indeed, previous studies have shown that Arabic numbers lead to faster processing than number words. The results replicated the SNARC effect with Arabic numbers, but not with number words. Experiment 2 was similar to Experiment 1, but this time manual responses (i.e., responses far slower than saccadic ones) were recorded. A strong SNARC effect was observed for both number formats. Further analyses revealed a correlation between mean individual response times and the strength of the SNARC effect. We proposed that the initiation times for saccadic responses may be too short for the SNARC effect to appear, in particular with the written number format for which activation of magnitude takes time. We conclude in terms of time variations resulting from processing specificities related with number format, effector type and also individual reaction and processing speed.

On pacing trials while scanning brain hemodynamics: The case of the SNARC effect.

Experimental designs used to describe psychological effects on overt human behavior are seldom suited to localize their corresponding neural substrates based on the analysis of stimulus-evoked brain hemodynamic responses. This is because stimuli in behavioral studies are usually separated by intertrial intervals (ITIs) in the order of 1 second or so following a behavioral response, which is notoriously too brief a time to detect a corresponding hemodynamic response. In fact, a solution commonly adopted in neuroimaging studies is to prolong the ITI up to several seconds. In doing so, the consequences of ITI variations between behavioral and neuroimaging design variants are either benignly neglected or explicitly assumed to be negligible. Here, we provide a systematic investigation of the consequence of manipulating ITI in a design optimized to study a well-established and highly replicable psychological phenomenon-the spatial numerical association of response codes (SNARC). The present exploration encompassed standard estimates of the SNARC effect (i.e., on reaction times and accuracy), estimates of ITI effects on the emotional state of participants before and after performing the SNARC task, as well as the degree of perceived task difficulty. The results showed that, in striking contrast to the common wisdom about the nil role of ITI, the substantial number of parametric differences observed between the two ITI conditions suggests that ITI plays a critical role in shaping the meaning of hemodynamic correlate of a psychological, at least the SNARC, effect.

“Sex differences in the spatial representation of number”: Correction to Bull et al. (2013).

Reports an error in "Sex differences in the spatial representation of number" by Rebecca Bull, Alexandra A. Cleland and Thomas Mitchell (Journal of Experimental Psychology: General, 2013[Feb], Vol 142[1], 181-192). In the article, there was an error in the Results section of Experiment 2. The t value incorrectly repeated the beta weight ( .25). The correct value is t(39) = 3.38, p = .002. There was also an error in the Discussion section of Experiment 2. The reported result of F(1, 94) = 4.27, should read F(1, 94) = 4.72, p = .032. Finally, there was an error in the Results section of Experiment 4. The t value for was incorrectly reported as t(50) = 1.56, p = .05. It should be t(50) = 1.98. These typographical errors do not change the overall pattern of results or interpretation of the findings. (The following abstract of the original article appeared in record 2012-10822-001.) There is a large body of accumulated evidence from behavioral and neuroimaging studies regarding how and where in the brain we represent basic numerical information. A number of these studies have considered how numerical representations may differ between individuals according to their age or level of mathematical ability, but one issue rarely considered is whether the representational acuity or automaticity of using numerical representations differs between the sexes. We report 4 studies that suggest that male participants show a stronger influence of the spatial representation of number as revealed through the spatial numerical association of response codes (SNARC) effect, through the numerical distance effect (NDE), and through number-line estimations. Evidence for a sex difference in processing number was present for parity decisions (Experiment 1), color decisions (Experiment 2), number-line estimations (Experiment 3), and magnitude decisions (Experiment 4). We argue that this pattern of results reflects a sex difference in either the acuity of representation or reliance upon spatial representations of number, and that this difference may arise due to differences in the parietal lobes of men and women. (PsycINFO Database Record

Hemispheric Asymmetries in Price Estimation: Do Brain Hemispheres Attribute Different Monetary Values?

The Spatial Numerical Association of Response Codes (SNARC) effect has been associated with a wide range of magnitude processing. This effect is due to an implicit relationship between numbers and horizontal space, according to which weaker magnitudes and smaller numbers are represented on the left, whereas stronger magnitudes and larger numbers are represented on the right. However, for some particular type of magnitudes such as price, judgments may be also influenced by perceived quality and thus involving valence attribution biases driven by brain asymmetries. In the present study, a lateralized tachistoscopic presentation was used in a price estimation task, using a weight estimation task as a control, to assess differences in asymmetries between these two attributes. Results show a side bias in the former condition but not in the latter, thus indicating that other non-numerical mechanisms are involved in price estimation. Specifically, prices were estimated lower in the left visual field than in the right visual field. The proposed explanation is that price appraisal might involve a valence attribution mechanism leading to a better perceived quality (related to higher prices) when objects are processed primarily in the left hemisphere, and to a lower perceived quality (related to lower prices) when objects are processed primarily in the right hemisphere.

Finding the SNARC Instead of Hunting It: A 20∗20 Monte Carlo Investigation

The Spatial Numerical Association of Response Codes (SNARC) effect describes a stimulus-response association of left with small magnitude and right with large magnitude. Usually, it is estimated by means of regression slopes, where the independent variable only has a limited number of levels. Inspection of the literature reveals that it is not difficult to detect a SNARC effect within a group, but it has been quite unusual to find group differences. Is the SNARC effect as it is usually estimated using regression slopes largely insensitive to group differences, and are there design parameters necessary to increase sensitivity in group comparison analyses? Using numerical simulations, we provide evidence that both sample size and the number of stimulus repetitions, as well as intra-individual variability, contribute in a substantial way to the probability of detecting an existing SNARC effect. Our results show that the adequate choice of either sample size or number of repetitions per experimental cell does not fully compensate for a poor choice of the other parameter. Moreover, repeated failures to find significant group differences in the SNARC effect can be explained by insufficient power. Fortunately, increasing the number of repetitions to about 20 and testing at least 20 participants provides in most cases sufficient sensitivity to reliably detect the SNARC effect as well as group differences. Power plots are provided, which may help to improve both the economy and sensitivity of experimental design in future SNARC experiments, or, more generally when regression slopes are estimated intra-individually.

Transcranial direct current stimulation (tDCS) reveals a dissociation between SNARC and MARC effects: Implication for the polarity correspondence account

The concept of stimulus response compatibility (SRC) refers to the existence of a privileged association between a specific stimulus feature and a specific response feature. Two examples of SRC are the Spatial Numerical Association of Response Codes (SNARC) and the Markedness Association of Response Codes (MARC) effects. According to the polarity correspondence principle, these two SRC effects occur because of a match between the most salient dimensions of stimulus and response. Specifically, the SNARC effect would be caused by a match between right-sided responses and large numbers, while a match between right-sided responses and even numbers would give rise to the MARC effect. The aim of the present study was to test the validity of the polarity correspondence principle in explaining these two SRC effects. To this end, we applied transcranial direct current stimulation (tDCS) over left and right posterior parietal cortex (PPC), which is thought to be the neural basis of salience processing, during a parity judgement task. Results showed that cathodal tDCS over the PPC significantly reduced the MARC effect but did not affect the SNARC effect, suggesting a dissociation between the two effects. That is, the MARC would rely on a salience processing mechanism, whereas the SNARC would not. Despite this interpretation is in need of further experimental confirmations (i.e., testing different tasks or using different tDCS montages), our results suggest that the polarity correspondence principle can be a plausible explanation only for the MARC effect but not for the SNARC effect.