Spatial-numerical Association Of Response Codes Research Articles

The SNARC effect: a preregistered study on the interaction of horizontal, vertical, and sagittal spatial–numerical associations

Small numbers are processed faster through left-sided than right-sided responses, whereas large numbers are processed faster through right-sided than left-sided responses [i.e., the Spatial–Numerical Association of Response Codes (SNARC) effect]. This effect suggests that small numbers are mentally represented on the left side of space, whereas large numbers are mentally represented on the right side of space, along a mental number line. The SNARC effect has been widely investigated along the horizontal Cartesian axis (i.e., left–right). Aleotti et al. (Cognition 195:104111, 2020), however, have shown that the SNARC effect could also be observed along the vertical (i.e., small numbers-down side vs. large numbers-up side) and the sagittal axis (i.e., small numbers-near side vs. large numbers-far side). Here, we investigated whether the three Cartesian axes could interact to elicit the SNARC effect. Participants were asked to decide whether a centrally presented Arabic digit was odd or even. Responses were collected through an ad hoc-made response box on which the SNARC effect could be compatible for one, two, or three Cartesian axes. The results showed that the higher the number of SNARC-compatible Cartesian axes, the stronger the SNARC effect. We suggest that numbers are represented in a three-dimensional number space defined by interacting Cartesian axes.

Separate processing mechanisms for spatial-numerical compatibility and numerical-size congruity.

Across two experiments, the numerical magnitude and the physical size of single digits presented in either two (Experiment 1) or four (Experiment 2) different font sizes were judged using either horizontally and vertically (Experiment 1) or just horizontally (Experiment 2) aligned manual responses. Such a design allowed for the simultaneous examination of the size congruity effect (SiCE), the spatial-numerical association of response codes (SNARC) effect, and the more novel spatial-size association of response codes (SSARC) effect. In Experiment 1, SiCEs and SNARC effects were found that operated independently of one another but no SSARC effect occurred. In Experiment 2, separate SiCEs and SNARC effects were found when judging numerical magnitude whereas separate SiCEs and SSARC effects were found when judging physical size. As will be discussed, such findings provide important constraints on the manner in which the full set of congruency and compatibility effects between stimulus and response dimensions in such tasks may be modeled. To illustrate this point, four different versions of a general computational processing model of these effects are considered. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

The Effect of Verbal Task Instruction on Spatial-Numerical Associations of Response Codes Effect Coding of Spatial-Numerical Associations: Evidence From Event-Related Potential.

The spatial-numerical associations of response codes (SNARC) effect reveals that individuals can represent numbers spatially. In this study, event-related potential (ERP) technology was used to probe the effect of verbal-spatial task instructions on spatial-numerical association coding by using digit parity and magnitude judgment tasks, with the numbers 1–9 (except 5) and Chinese word labels (“left” and “right”) as experimental materials. The behavioral results of Experiment 1 showed that the SNARC effect was mainly based on verbal-spatial coding and appeared when the stimulus onset asynchrony (SOA) between the presentation of the verbal labels and the target digit was 0 ms. ERP results did not reveal any significant SNARC-related effects in either the N1 or P3 components. The behavioral results of Experiment 2 again showed that the SNARC effect was dominated by verbal-spatial coding. ERP results showed that significant effects related to verbal-spatial coding were found in both the early positive deflection of the stimulus-locked lateralized readiness potential (S-LRP) and the latency of the response-locked LRP (R-LRP). Hence, in this study, the nature of the spatial coding of the digit magnitudes was influenced by the processing of the word labels and affected both the response selection and response preparation stages.

Cultural factors weaken but do not reverse left-to-right spatial biases in numerosity processing: Data from Arabic and English monoliterates and Arabic-English biliterates.

Directional response biases due to a conceptual link between space and number, such as a left-to-right hand bias for increasing numerical magnitude, are known as the SNARC (Spatial-Numerical Association of Response Codes) effect. We investigated how the SNARC effect for numerosities would be influenced by reading-writing direction, task instructions, and ambient visual environment in four literate populations exemplifying opposite reading-writing cultures—namely, Arabic (right-to-left script) and English (left-to-right script). Monoliterates and biliterates in Jordan and the U.S. completed a speeded numerosity comparison task to assess the directionality and magnitude of a SNARC effect in their numerosity processing. Monoliterates’ results replicated previously documented effects of reading-writing direction and task instructions: the SNARC effect found in left-to-right readers was weakened in right-to-left readers, and the left-to-right group exhibited a task-dependency effect (SNARC effect in the smaller condition, reverse SNARC effect in the larger condition). Biliterates’ results did not show a clear effect of environment; instead, both biliterate groups resembled English monoliterates in showing a left-to-right, task-dependent SNARC effect, albeit weaker than English monoliterates’. The absence of significant biases in all Arabic-reading groups (biliterates and Arabic monoliterates) points to a potential conflict between distinct spatial-numerical mapping codes. This view is explained in terms of the proposed Multiple Competing Codes Theory (MCCT), which posits three distinct spatial-numerical mapping codes (innate, cardinal, ordinal) during numerical processing—each involved at varying levels depending on individual and task factors.

The mental representation of nonnumerical quantifiers: The Spatial-Linguistic Association of Response Codes (SLARC) effect.

How quantifiers are represented in the human mind is still a topic of intense debate. Seminal studies have addressed the issue of how a subclass of quantifiers, that is, number words, is spatially coded displaying the Spatial-Numerical Association of Response Codes (SNARC) effect; yet, none of these studies have explored the spatial representation of nonnumerical quantifiers such as "some" or "many." The aim of the present study is to investigate whether nonnumerical quantifiers are spatially coded in the human mind. We administered two typical comparison tasks to 52 participants: the first task involved nonnumerical quantifiers; the second task involved number words. Results showed a response-side compatibility effect for both number words and nonnumerical quantifiers, suggesting that both types of quantifiers are encoded in a spatial format; quantifiers referring to "small" quantities are responded to faster with the left hand and quantifiers referring to "large" quantities are responded to faster with the right hand. We labeled this effect for nonnumerical quantifiers as the Spatial-Linguistic Association of Response Codes (SLARC) effect. Notably, we found that the SNARC and the SLARC effects were strictly related to each other, namely the more a participant was sensitive to the SNARC effect in the number-word task, the more a SLARC effect was detectable in the nonnumerical quantifier task. These findings add evidence to the tendency of humans to align magnitude information on a mental line that is coded from left to right. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Snarcing with a phone: The role of order in spatial-numerical associations is revealed by context and task demands.

Previous literature on the spatial-numerical association of response codes (SNARC) effect examined which factors modulate spatial-numerical associations. Recently, the role of order in the SNARC effect has been debated, and further research is necessary to better understand its contribution. The present study investigated how the order elicited by the context of the stimuli and by task demands interact. Across three experiments, we presented numbers in the context of a mobile phone keypad, an overlearned numerical display in which the ordinal position of numbers differs from the mental number line. The experiments employed three tasks with different levels of consistency with the order elicited by the context. In Experiment 1, participants judged numbers based on their spatial position on the keypad, and we found a spatial association consistent with the keypad configuration, indicating that the spatial association is driven both by the context and by the task when they consistently elicit the same order. In Experiment 2a, participants performed a magnitude classification task, and results revealed a lack of spatial associations, suggesting a conflict between the orders elicited by the context and by the task. In Experiment 2b, participants performed a parity judgment task, and the results revealed a SNARC effect, suggesting that the order elicited by the context did not modulate the spatial association. Overall, three different tasks gave rise to three different results. This shows that the context alone is not sufficient in modulating spatial-numerical associations but that the consistency between the orders elicited by context and task demands is a key factor. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Is the attentional SNARC effect truly attentional? Using temporal order judgements to differentiate attention from response.

The spatial–numerical association of response codes (SNARC) effect reflects the phenomenon that low digits are responded to faster with the left hand and high digits with the right. Recently, a particular variant of the SNARC effect known as the attentional SNARC (which reflects that attention can be shifted in a similar manner) has had notable replicability issues. However, a potentially useful method for measuring it was revealed by Casarotti et al. using a temporal order judgement (TOJ) task. Accordingly, the present study evaluated whether Casarotti et al.’s results were reproducible by presenting a low (1) or high (9) digit prior to a TOJ task where participants had to indicate which of two peripherally presented targets appeared first (Experiment 1) or second (Experiment 2). In Experiment 1, it was revealed that the findings of Casarotti et al.’s were indeed observable upon replication. In Experiment 2, when attention and response dimensions were put in opposition, the SNARC effect corresponded to the side of response rather than attention. Taken together, the present study confirms the robustness of the attentional SNARC in TOJ tasks, but that it is not likely due to shifts in attention.

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.

Two processing stages of the SNARC effect.

The spatial-numerical association of response codes (SNARC) effect showed that small/large numbers represented in the left/right space facilitated left/right responses, respectively. However, the processing stage (semantic representation or response selection) of the SNARC effect is still controversial. To investigate this issue, we adopted a modified magnitude comparison task in which the effects of SNARC, Stroop (semantic-representation stage), and Simon (response-selection stage) could be simultaneously induced. The processing stages of the SNARC effect were investigated by examining the interactions among these effects. According to the additive factor logic, if two effects are interactive, then they occur in the same stage; if two effects are additive, then they occur in different stages. Across two experiments, the SNARC effect interacted with the Stroop effect and with the Simon effect. These results suggested that the SNARC effect occurred in both the semantic-representation and response-selection stages and provided insight into that the SNARC effect might have two originating sources.

Turn the beat around: Commentary on \u201cSlow and fast beat sequences are represented differently through space" (De Tommaso & Prpic, 2020, in Attention, Perception, & Psychophysics)

There has been increasing interest in the spatial mapping of various perceptual and cognitive magnitudes, such as expanding the spatial-numerical association of response codes (SNARC) effect into domains outside of numerical cognition. Recently, De Tommaso and Prpic (Attention, Perception, & Psychophysics, 82, 2765–2773, 2020) reported in this journal that only fast tempos over 104 beats per minute have spatial associations, with more right-sided associations and faster responses for faster tempos. After discussing the role of perceived loudness and possible response strategies, we propose and recommend methodological improvements for further research.

The Spatial-Numerical Association of Response Codes (SNARC) effect in highly math-anxious individuals: An ERP study

The Spatial-Numerical Association of Response Codes (SNARC) effect was examined in highly (HMA) and low math-anxious (LMA) individuals performing a number comparison in an ERP study. The SNARC effect consists of faster latencies when the response side is congruent with number location in the mental number line (MNL). Despite the stronger SNARC effect in the HMA group, their responses in incongruent trials were slower than in congruent trials only for the largest numerical magnitudes. Moreover, HMAs showed a less positive centroparietal P3b component in incongruent trials than in congruent ones, but only for the largest magnitudes. Since the SNARC effect arises during response selection and P3b positivity decreases with the difficulty of decision, this result suggests that HMA individuals might find it more difficult than LMAs to control the conflict between the automatically activated location of numbers in the MNL and the response side, especially in more cognitively demanding trials.

Brain activity underlying response induced by SNARC-congruent and SNARC-incongruent stimuli

At least three well-documented phenomena indicate a relationship between numbers and the internal representation of space. They are shifting attention in accordance with the localization of numbers on the mental number line (MNL); the spatial‑numerical association of response codes (SNARC) effect, which manifests as faster responses to high numbers with the right hand than with the left, and vice versa for low numbers; and the processing of both numbers and space primarily in the parietal cortex. Some EEG studies have pointed to the response selection stage as a locus of this effect. However, this explanation has yet to be corroborated by the fMRI experiments. The goal of this study was to investigate the functional anatomy underlying response selection induced by SNARC‑congruent and SNARC‑incongruent stimuli in a spatial visual cueing task. Healthy adult volunteers responded to a pair of target stimuli consisting of digits, non‑digit symbols, or a mix of both. In each trial, the stimuli were preceded by a centrally presented numerical or non‑numerical cue stimulus which was required to be memorized. One of the target stimuli that then appeared would be identical to the cue; the task was to determine which side it was presented on, within the pair. In the case of numerical stimuli, the side was congruent with its localization on the MNL in one‑half of the trials. In the other half of the trials, it was incongruent. The behavioral results revealed the SNARC effect, as well as a faster reaction to low numbers than to high numbers. The fMRI responses to the target stimuli showed engagement of regions implicated in number processing but also in sensory‑motor areas. This suggests that the motor response selection or execution stage may be the locus of the SNARC effect. Yet, the activation pattern obtained in the congruent and incongruent conditions did not allow us to determine, indisputably, the neural correlates of the mechanisms involved in the SNARC effect. Moreover, we did not observe any stimulus-specific responses to cues.

SNARC compatibility triggers positive affect

ABSTRACT Previous research on the spatial-numerical association of response codes (SNARC) has demonstrated that SNARC-compatible digit arrangements are processed faster and more accurately than SNARC-incompatible arrangements. Concurrently, processing speed and accuracy have been conceptualised as indicating processing fluency – the ease of information processing – which has been shown to entail affective downstream consequences. Bridging these two research lines for the first time, we investigated whether digit arrangements that are compatible to this association are affectively preferred to association-incompatible digit arrangements. In a line of four experiments (total N = 786), German participants were asked to indicate how much they like the overall appearance of two digits that appear at the right and at the left side of the screen. Results from three of the four experiments suggest that digit arrangements that are compatible with this spatial-numerical association indeed trigger positive feelings. These preference patterns were not moderated by the horizontal distance between the two digits, pointing towards a stable phenomenon that is insensitive to contextual spatial cues.

SNARC effect modulated by central executive control: revealed in a cue-based trisection task.

People respond to small numbers faster with the left hand and respond to large numbers faster with the right hand, a phenomenon known as the Spatial-Numerical Association of Response Codes (SNARC) effect. Whether the SNARC effect originates from culturally determined long-term experience or the task-set-influenced temporary associations among spaces, locations, and numerical magnitudes in working memory (WM) is still controversial. In the present study, we used a trisection paradigm in which numbers were divided into three categories (small: 1, 2; middle: 4, 5, 6; and large: 8, 9) to explore whether the central executive control can modulate the SNARC effect. Participants were serially presented with a cue and a target number. The cue denoted a task rule, which informed participants to compare the target number with either 3 or 7. The cue was either switched or repeated across trials. We found that the SNARC effects were observed in the cue-switching condition. In the cue-repeat condition, the SNARC effect disappeared. These findings suggest that the SNARC effect is modulated by set-shifting-related central executive control in WM, supporting the view that the SNARC effect is WM-dependent.

Reading direction and spatial effects in parity and arithmetic tasks.

This study investigated the relationship between numerical and spatial processing and reading direction, conducting conceptual replications of the Shaki et al. (Psychonomic Bulletin & Review 16(2): 328-331, 2009) parity task and the Mathieu et al. (Cognition 146: 229-239, 2016, Experiment 1) simple addition (e.g., 3 + 2) and subtraction (e.g., 3 - 2) task. Twenty-four left-to-right readers (LTR) and 24 right-to-left readers (RTL) were tested. The response time (RT) analysis of the parity task presented a robust spatial-numerical association of response codes (SNARC) effect (left-side response advantage for smaller numbers and right-side advantage for larger numbers) for LTR but not RTL readers. In the arithmetic task, the three problem elements (e.g., 3 + 4) were presented sequentially with the second operand displaced slightly to the left or right of fixation. RTL but not LTR readers presented a RT advantage for subtraction relative to addition with a right-shifted second operand compared to it being left-shifted. This is consistent with a spatial bias linked to native reading direction. For both reading-direction groups, effects of the left vs. right side manipulation in the arithmetic or parity task did not correspond to parallel effects in the other task. The results imply that the parity-based SNARC effects and side-related effects in cognitive arithmetic are not equivalent measures of space-related processes in cognitive number processing and likely reflect distinct mechanisms.

A SNARC-like effect for music notation: The role of expertise and musical instrument

The Spatial-Numerical Association of Response Codes (SNARC) suggests the existence of an association between number magnitude and response location, with faster left key-press responses to small numbers and faster right key-press responses to large numbers. We investigated whether a similar association exists between musical notes on the stave and the space of response execution, involving amateur and expert musicians (Experiment 1). Moreover, in Experiment 2 we further investigated such association in two groups of expert musicians (piano and transverse flute players) who differ in the note mapping on their instruments. Results indicate a clear association between musical notes and the space of response execution only for musicians with formal education. Furthermore, this association seems not to be influenced by the specific instrument played, as both piano and transverse flute players showed the same effect direction (left key-press advantage for low notes, and vice versa).

Emotional SNARC: emotional faces affect the impact of number magnitude on gaze patterns.

The Spatial-Numerical Association of Response Codes (SNARC) effect is characterised by a spatial cognitive representation of low numbers to the left side of space and high numbers to the right side of space. This effect has been found using a diversity of stimuli and experimental paradigms. However, the influence of emotional stimuli on this effect remains unclear. In this study, the SNARC effect is analysed in relation to pairs of emotional facial stimuli (happy-neutral, sad-neutral and happy-sad pairs). Gaze patterns of 151 participants were analysed when exposed to a free-viewing eye-tracking paradigm consisting of pairs of emotional faces preceded by small and large numbers. Replicating previous results, a standard SNARC effect was found independently of the emotional expressions of the faces (i.e., there was a significant linear trend of number magnitude in the frequency of first fixations of the gaze to the left side space). However, specific slope analyses revealed that the SNARC effect was influenced by the spatial position of each emotion presented in the emotional pairs. Specifically, the effect disappeared in happy-neutral trials, when the happy faces were allocated in the right position and also in happy-sad trials when two emotional stimuli were simultaneously displayed. The study revealed that the SNARC effect is sensitive to the spatial position of emotional stimuli which further adds to other known limits of the phenomenon. The limitations of the study and its implications in the area of cognition and emotion are also discussed.

Registered Replication Report on Fischer, Castel, Dodd, and Pratt (2003)

The attentional spatial-numerical association of response codes (Att-SNARC) effect (Fischer, Castel, Dodd, & Pratt, 2003)—the finding that participants are quicker to detect left-side targets when the targets are preceded by small numbers and quicker to detect right-side targets when they are preceded by large numbers—has been used as evidence for embodied number representations and to support strong claims about the link between number and space (e.g., a mental number line). We attempted to replicate Experiment 2 of Fischer et al. by collecting data from 1,105 participants at 17 labs. Across all 1,105 participants and four interstimulus-interval conditions, the proportion of times the effect we observed was positive (i.e., directionally consistent with the original effect) was .50. Further, the effects we observed both within and across labs were minuscule and incompatible with those observed by Fischer et al. Given this, we conclude that we failed to replicate the effect reported by Fischer et al. In addition, our analysis of several participant-level moderators (finger-counting habits, reading and writing direction, handedness, and mathematics fluency and mathematics anxiety) revealed no substantial moderating effects. Our results indicate that the Att-SNARC effect cannot be used as evidence to support strong claims about the link between number and space.

A gifted SNARC? Directional spatial\u2013numerical associations in gifted children with high-level math skills do not differ from controls

The SNARC (Spatial-Numerical Association of Response Codes) effect (i.e., a tendency to associate small/large magnitude numbers with the left/right hand side) is prevalent across the whole lifespan. Because the ability to relate numbers to space has been viewed as a cornerstone in the development of mathematical skills, the relationship between the SNARC effect and math skills has been frequently examined. The results remain largely inconsistent. Studies testing groups of people with very low or very high skill levels in math sometimes found relationships between SNARC and math skills. So far, however, studies testing such extreme math skills level groups were mostly investigating the SNARC effect in individuals revealing math difficulties. Groups with above average math skills remain understudied, especially in regard to children. Here, we investigate the SNARC effect in gifted children, as compared to normally developing children (overall n = 165). Frequentist and Bayesian analysis suggested that the groups did not differ from each other in the SNARC effect. These results are the first to provide evidence for the SNARC effect in a relatively large sample of gifted (and mathematically highly skilled) children. In sum, our study provides another piece of evidence for no direct link between the SNARC effect and mathematical ability in childhood.

Spatializing Emotions Besides Magnitudes: Is There a Left-to-Right Valence or Intensity Mapping?

The Spatial–Numerical Association of Response Codes (SNARC), namely the automatic association between smaller numbers and left space and between larger numbers and right space, is often attributed to a Mental Number Line (MNL), in which magnitudes would be placed left-to-right. Previous studies have suggested that the MNL could be extended to emotional processing. In this study, participants were asked to carry out a parity judgment task (categorizing one to five digits as even or odd) and an emotional judgment task, in which emotional smilies were presented with four emotional expressions (very sad, sad, happy, very happy). Half of the sample was asked to categorize the emotional valence (positive or negative valence), the other half was asked to categorize the emotional intensity (lower or higher intensity). The results of the parity judgment task confirmed the expected SNARC effect. In the emotional judgment task, the performance of both subgroups was better for happy than for sad expressions. Importantly, a better performance was found only in the valence task for lower intensity stimuli categorized with the left hand and for higher intensity stimuli categorized with the right hand, but only for happy smilies. The present results show that neither emotional valence nor emotional intensity alone are spatialized left-to-right, suggesting that magnitudes and emotions are processed independently from one another, and that the mental representation of emotions could be more complex than the bi-dimentional left-to-right spatialization found for numbers.