Numerical Stimuli Research Articles

Automatic Experimental Numerosity Generation and Numerical Training for Rodents.

Non-symbolic stimuli representing numerosities are invariably associated with continuous magnitudes, complicating the interpretation of experimental studies on numerosity perception. Although various algorithms for experimental numerosity generation have been proposed, they do not consider the quantifiable distribution of values of continuous magnitudes and the degree of numerosity-magnitudes association. Consequently, they cannot thoroughly exclude the possibility of magnitudes integration or strategy switch between different magnitudes in numerical stimulus perception. Here, we introduce a protocol for numerosity generation, animal training, and behavior outcomes analysis that takes the aforementioned issues into consideration. This protocol has been applied to rodents and is applicable to other animals in numerosity studies. © 2024 Wiley Periodicals LLC. Basic Protocol 1: Algorithm for generating non-symbolic numerical stimuli Alternate Protocol: General algorithm for generating non-symbolic numerical stimuli Basic Protocol 2: Numerical training and testing for rodents.

Eye-Tracking Evidence for the SNARC Effect: Unveiling Attentional Stages

The Spatial Numerical Association of Response Codes (SNARC) effect, which involves the conjunction of spatial and numerical response coding, was initially identified through reaction time experiments involving numerical stimuli. Research has revealed a common tendency among individuals to associate smaller numbers with the left side and larger numbers with the right side. Furthermore, scholars have identified additional dimensions, such as the “up-down” and “near-far” associations, that contribute to the complexity of the SNARC effect. However, the universality of the SNARC effect and the underlying psychological and physiological mechanisms continue to be a topic of debate within the academic community. Various studies have proposed a range of interpretations and understandings of this effect. The present study delves into the cognitive mechanisms of the SNARC effect, employing eye-tracking technology to objectively quantify participants’ responses. Utilizing the parity judgment task, a method frequently employed in SNARC effect research, in conjunction with eye-tracking, participants were instructed to judge the parity of numerical stimuli while directing their gaze to the left or right, and above or below the numbers as per the experimental requirements. Colored blocks were positioned around the numbers to serve as visual anchors, indicating the spatial directions of left/right and top/down. Data analysis revealed that when smaller numbers (1-4) were presented, participants exhibited a tendency to focus on the left color block adjacent to the number, characterized by a higher Total Fixation Duration (TFD) and a shorter Time to First Fixation (TFF). In contrast, when larger numbers (6-9) appeared, participants were more likely to focus on the right color block, indicating the presence of a SNARC effect in the horizontal dimension. However, no significant effect was observed in the vertical dimension. Additionally, this study innovatively employed a blank page in conjunction with a test page to differentiate between the early and late stages of participants’ attentional processing. The examination of TFF and TFD data uncovered a two-stage processing mechanism associated with the SNARC effect. This experimental approach and methodological framework offer novel perspectives that contribute to the advancement of research in this domain.

Perceived Quality of Binaural Rendering from Baffled Microphone Arrays Evaluated Without an Explicit Reference

The authors present a perceptual evaluation of the binaural rendering quality of signals from several types of baffled microphone arrays. They employ the multi-stimulus category rating (MuSCR) paradigm that does not require a reference stimulus. The tested conditions also comprise a very high numerical accuracy stimulus, given the highest quality rating in approximately half of the multi-stimulus trials. A comparison with the literature on spherical microphone arrays (SMAs) shows that MuSCR allows for drawing representative conclusions regarding the dependency of the perceived quality on the array and rendering parameters as in previous experiments with an explicit high-fidelity reference. The authors applied the MuSCR paradigm to evaluate the perceived reproduction quality of equatorial microphone arrays (EMAs) with microphones only along the equator of the spherical baffle and of equatorial arrays with a nonspherical baffle (XMAs). The results endorse the observations from SMAs that an increasing spherical harmonic order leads to improved perceived quality. The authors also confirm that EMAs lead to the same perceived quality as SMAs despite the substantial difference in the number of microphones. Magnitude equalization of artifacts from spatial undersampling can be very effective for XMAs the raw solution deviates significantly from the other array types at high frequencies.

Number and domain both affect the relation between executive function and mathematics achievement: A study of children's executive function with and without numbers.

Magnitude processing and executive functions (EFs) have emerged as robust predictors of mathematics achievement. However, the nature of these associations is still unclear. For example, it is uncertain if EFs applied in the context of domain-specific mathematical cognition (i.e., EFs applied while processing numbers) are more closely related to mathematics achievement than EFs applied in nonnumerical, domain-general contexts. Also, how distinct EF domains-that is, working memory, inhibitory control, and cognitive flexibility-and contents-that is, numerical versus nonnumerical-moderate the association between magnitude processing and mathematics achievement has not been fully understood. To address these issues, we investigated how magnitude processing, EFs applied to nonnumerical and numerical task stimuli, and their interactions were associated with mathematics achievement. Three hundred fifty-nine Brazilian third- to fifth-grade (8-10 years old) students completed measures of working memory, inhibitory control, and cognitive flexibility with numerical and nonnumerical task versions, nonsymbolic and symbolic magnitude comparison, and mathematics achievement. A series of regression models indicated that nonsymbolic and symbolic magnitude processing are consistently associated with mathematics achievement, even when controlling for working memory, inhibitory control, and cognitive flexibility measured with both numerical and nonnumerical contents. All EF measures were associated with mathematics achievement. However, cognitive flexibility measured with numerical content showed the strongest association. Results support the hypothesis that magnitude processing and EFs are uniquely associated with mathematics achievement. Furthermore, EFs measured with nonnumerical and numerical contents related differently to mathematics achievement, even when controlling for symbolic and nonsymbolic magnitude processing, suggesting they encompass somewhat distinct cognitive processes. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Measuring temporal bias in sequential numerosity comparison

While several methods have been proposed to assess the influence of continuous visual cues in parallel numerosity estimation, the impact of temporal magnitudes on sequential numerosity judgments has been largely ignored. To overcome this issue, we extend a recently proposed framework that makes it possible to separate the contribution of numerical and non-numerical information in numerosity comparison by introducing a novel stimulus space designed for sequential tasks. Our method systematically varies the temporal magnitudes embedded into event sequences through the orthogonal manipulation of numerosity and two latent factors, which we designate as “duration” and “temporal spacing”. This allows us to measure the contribution of finer-grained temporal features on numerosity judgments in several sensory modalities. We validate the proposed method on two different experiments in both visual and auditory modalities: results show that adult participants discriminated sequences primarily by relying on numerosity, with similar acuity in the visual and auditory modality. However, participants were similarly influenced by non-numerical cues, such as the total duration of the stimuli, suggesting that temporal cues can significantly bias numerical processing. Our findings highlight the need to carefully consider the continuous properties of numerical stimuli in a sequential mode of presentation as well, with particular relevance in multimodal and cross-modal investigations. We provide the complete code for creating sequential stimuli and analyzing participants’ responses.

A neural network model of mathematics anxiety: The role of attention

Anxiety about performing numerical calculations is becoming an increasingly important issue. Termed mathematics anxiety, this condition negatively impacts performance in numerical tasks which can affect education outcomes and future employment. The disruption account proposes poor performance is due to anxiety disrupting limited attentional and inhibitory resources leaving fewer cognitive resources for the current task. This study provides the first neural network model of math anxiety. The model simulates performance in two commonly-used tasks related to math anxiety: the numerical Stroop and symbolic number comparison. Different model modifications were used to simulate high and low math-anxious conditions by modifying attentional processes and learning; these model modifications address different theories of math anxiety. The model simulations suggest that math anxiety is associated with reduced attention to numerical stimuli. These results are consistent with the disruption account and the attentional control theory where anxiety decreases goal-directed attention and increases stimulus-driven attention.

Collective nouns are conceptually plural: Evidence from the grammatical SNARC effect.

To develop theories of how comprehenders extract the message from a linguistic stream, it is critical to understand how they conceptually represent referents. The experiments reported here focus on singular collective nouns (e.g., committee, team), which introduce a single group into the discourse and test whether they nonetheless are conceptually plural (i.e., construed as consisting of multiple entities) by using the spatial-numerical association of response codes (SNARC) paradigm (Dehaene & Changeux, 1993). In this paradigm, participants are typically faster to respond to smaller numbers or numerical stimuli when making a response on their left and faster to respond to larger numbers or numerical stimuli when making a response on their right. In three experiments, participants saw German words on a computer screen and decided whether each one described a single entity or something that could be subdivided into multiple entities (Experiment 1) or whether they would use "ist" or "sind" ("is" or "are") in combination with the word if it were the subject of a sentence (Experiments 2 and 3). The mapping of responses to participants' left and right hands was counterbalanced. Experiment 1 failed to show a grammatical SNARC effect. Experiments 2 and 3 showed a grammatical SNARC effect that extended to collective noun phrases. The results of these experiments suggest that collective noun phrases are instantiated as conceptually plural in comprehenders' minds. We discuss the differential task effects and the implications of these data on theories of language comprehension. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Intuitive mapping between nonsymbolic quantity and observed action across development

Adults’ concurrent processing of numerical and action information yields bidirectional interference effects consistent with a cognitive link between these two systems of representation. This link is in place early in life: infants create expectations of congruency across numerical and action-related stimuli (i.e., a small [large] hand aperture associated with a smaller [larger] numerosity). Although these studies point to a developmental continuity of this mapping, little is known about the later development and thus how experience shapes such relationships. We explored how number–action intuitions develop across early and later childhood using the same methodology as in adults. We asked 3-, 6-, and 8-year-old children, as well as adults, to relate the magnitude of an observed action (a static hand shape, open vs. closed, in Experiment 1; a dynamic hand movement, opening vs. closing, in Experiment 2) to either a small or large nonsymbolic quantity (numerosity in Experiment 1 and numerosity and/or object size in Experiment 2). From 6 years of age, children started performing in a systematic congruent way in some conditions, but only 8-year-olds (added in Experiment 2) and adults performed reliably above chance in this task. We provide initial evidence that early intuitions guiding infants’ mapping between magnitude across nonsymbolic number and observed action are used in an explicit way only from late childhood, with a mapping between action and size possibly being the most intuitive. An initial coarse mapping between number and action is likely modulated with extensive experience with grasping and related actions directed to both arrays and individual objects.

Spatial-numerical associations of manual response codes are strongly asymmetrical

The spatial-numerical association of response codes (SNARC) effect denotes the observation that humans respond faster and more accurately with a left-side response to smaller numbers and a right-side response to larger numbers, as compared to the opposite mapping. Existing accounts, such as the mental number line hypothesis or the polarity correspondence principle, differ in whether they assume symmetrical associations between numerical and spatial stimulus and response codes or not. In two experiments, we investigated the reciprocity of the SNARC effect in manual choice-response tasks with two conditions. In the number-location task, participants pressed a left or right key to a number stimulus (dots in Experiment 1, digits in Experiment 2). In the location-number task, participants made one or two consecutive keypresses with one hand to a left- or right-side stimulus. Both tasks were performed with a compatible (one-left, two-right; left-one, right-two) and an incompatible (one-right, two-left; left-two, right-one) mapping. In both experiments, results showed a strong compatibility effect in the number-location task, reflecting the typical SNARC effect. In contrast, in both experiments, there was no mapping effect in the location-number task when outliers were excluded. However, when outliers were not excluded, small reciprocal SNARC effects occurred in Experiment 2. Together, the findings suggest that priming of spatial responses by numerical stimuli is much stronger than priming of numerical responses by spatial stimuli. The results are consistent with some accounts of the SNARC effect (e.g., the mental number line hypothesis), but not with others (e.g., the polarity correspondence principle).

Electrophysiological Correlates of the Interaction of Physical and Numerical Size in Symbolic Number Processing: Insights from a Novel Go/Nogo Numerical Stroop Task.

The interaction of physical and numerical size has been investigated and repeatedly demonstrated in the numerical Stroop task, in which participants compare digits of different physical sizes. It is, however, not entirely clear yet what psychological processes contribute to this interaction. The aim of the present study is to investigate the role of inhibition in the interaction of physical and numerical size, by introducing a novel paradigm that is suitable to elicit inhibition-related event-related potential components. To this end, we combined the go/nogo paradigm with the numerical Stroop task while measuring EEG and reaction times. Participants were presented with Arabic number pairs and had to press a button if the number on one side was numerically larger and they had to refrain from responding if the number on the other side was numerically larger. The physical size of the number pairs was also manipulated, in order to create congruent, neutral, and incongruent trials. Behavioural results confirmed the well-established numerical distance and numerical Stroop effects. Analysis of electrophysiological data revealed the classical go/nogo electrophysiological effects with numerical stimuli, and showed that peak amplitudes were larger for nogo than for go trials on the N2, as well as on the P3 component, on frontal and midline electrodes. When analysing the congruency effects, the peak amplitude of N2 was larger in incongruent trials than in neutral and congruent trials, while there was no evidence of a congruency effect on the P3 component peaks. Further analysis of the electrophysiological data revealed an additional facilitatory effect in the go trials, as well as an additional interference effect in the nogo trials. Taken together, it seems that interference effects are probably resolved by inhibitory processes and that facilitatory effects are affected by different cognitive control processes required by go versus nogo trials.

The role of inhibition and speed of processing in mathematics

AbstractThe current study highlights the importance of inhibitory ability in facilitating performance in mathematics. To understand the role of inhibition in mathematical knowledge, this study tested 102 college students on a series of standardized complex math exercises. Inhibition tasks varied by task and stimuli (letters, numbers, and arrows). The result showed stronger associations between math abilities and strength of inhibition with more inhibition found for the flanker task (involving inhibition of peripheral stimuli) than for the Navon task (requiring inhibition of a potential response). The results supported the view that Inhibition in general (which is not unique to numerical stimuli) is associated with math abilities. General, rather than specific inhibition was associated with math abilities and finally, speed of processing masked the relationship between math and inhibition. These results confirm the assumption that the relation between inhibition and math performance is modulated by the task that measures the inhibition, and by additional predictors such as processing speed.

Laterality in simple multiplication: Assessing hemispheric specialization of arithmetic fact retrieval in a visual hemifield paradigm.

The prominent view in numerical cognition is that highly overlearned arithmetic facts are verbally mediated and unilaterally processed in a left-hemispheric network, including language areas. However, this view has recently been challenged. Here, we evaluated the hemispheric specialization of verbal arithmetic fact retrieval and number magnitude processing using two verification tasks (i.e., multiplication and number magnitude comparison) in a divided hemifield paradigm in healthy participants (n = 35). In the number comparison task, we replicated bilateral processing advantages for the unit-decade compatibility effect. Magnitude processing was facilitated after bilateral compared with a unilateral presentation. In the multiplication task, lateralized presentation to the left hemisphere yielded processing advantages in arithmetic fact retrieval when the required interhemispheric transitions from the input, processing, and output stages were considered. Crucially, we observed a systematic processing advantage in left visual hemifield stimuli presentation (i.e., initial right-hemisphere processing). Our findings corroborate the assumption that arithmetic fact retrieval is subserved by left-lateralized verbal/linguistic processing. Thereby, they suggest a distinction between unilateral left-hemispheric linguistic processing of arithmetic fact retrieval and bilateral number magnitude processing. Interestingly, however, our data present right-hemispheric processing advantages in identifying early processed visual symbolic numerical stimuli. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

The impact of stimulus format on task inhibition during task switching.

Switching between competing tasks is supported by active inhibition of the preceding task. The level of task stimulus processing at which interference between competing tasks must occur for inhibition to be recruited is still unclear. Here, we investigated whether inhibition is recruited by task conflict occurring at an early or late (semantic) stage of task stimulus processing by dissociating the task stimulus format from its meaning. In two experiments, participants performed three different numerical judgment tasks on numerical stimuli that could be presented as digits or number words (e.g., "6" or "six") in a cued task-switching procedure. The effects of the change of stimulus format for the inhibition of the previous task were investigated and assessed by the N-2 task repetition cost, an index of the extent to which task representations are inhibited. The N-2 task repetition cost observed in the same stimulus format condition disappeared when target stimuli on task N-1 were presented in a different format from stimuli of task N-2 and N. This occurred both when the format changed from digits to number words stimuli (Experiment 1) as well as when it changed from number words to digits stimuli (Experiment 2). Results indicated that task set inhibition is recruited very early during the stimulus processing stage. They also provided evidence that task inhibition is not tied to task preparation processes but operates as a reactive, rather than proactive mechanism of conflict resolution.

Making sense of the relation between number sense and math

While several studies have shown that the performance on numerosity comparison tasks is related to individual differences in math abilities, others have failed to find such a link. These inconsistencies could be due to variations in which math was assessed, different stimulus generation protocols for the numerosity comparison task, or differences in inhibitory control. This within-subject study is a conceptual replication tapping into the relation between numerosity comparison, math, and inhibition in adults (N = 122). Three aspects of math ability were measured using standardized assessments: Arithmetic fluency, calculation, and applied problem solving skills. Participants’ inhibitory skills were measured using Stroop and Go/No-Go tasks with numerical and non-numerical stimuli. Finally, non-symbolic number sense was measured using two different versions of a numerosity comparison task that differed in the stimulus generation protocols (Panamath; Halberda, Mazzocco & Feigenson, 2008, https://doi.org/10.1038/nature07246; G&R, Gebuis & Reynvoet, 2011, https://doi.org/10.3758/s13428-011-0097-5). We find that performance on the Panamath task, but not the G&R task, related to measures of calculation and applied problem solving but not arithmetic fluency, even when controlling for inhibitory control. One possible explanation is that depending on the characteristics of the stimuli in the numerosity comparison task, the reliance on numerical and non-numerical information may vary and only when performance relies more on numerical representations, a relation with math achievement is found. Our findings help to explain prior mixed findings regarding the link between non-symbolic number sense and math and highlight the need to carefully consider variations in numerosity comparison tasks and math measures.

Resources Underlying Visuo-Spatial Working Memory Enable Veridical Large Numerosity Perception.

Humans can quickly approximate how many objects are in a visual image, but no clear consensus has been achieved on the cognitive resources underlying this ability. Previous work has lent support to the notion that mechanisms which explicitly represent the locations of multiple objects in the visual scene within a mental map are critical for both visuo-spatial working memory and enumeration (at least for relatively small numbers of items). Regarding the cognitive underpinnings of large numerosity perception, an issue currently subject to much controversy is why numerosity estimates are often non-veridical (i.e., susceptible to biases from non-numerical quantities). Such biases have been found to be particularly pronounced in individuals with developmental dyscalculia (DD), a learning disability affecting the acquisition of arithmetic skills. Motivated by findings showing that DD individuals are also often impaired in visuo-spatial working memory, we hypothesized that resources supporting this type of working memory, which allow for the simultaneous identification of multiple objects, might also be critical for precise and unbiased perception of larger numerosities. We therefore tested whether loading working memory of healthy adult participants during discrimination of large numerosities would lead to increased interference from non-numerical quantities. Participants performed a numerosity discrimination task on multi-item arrays in which numerical and non-numerical stimulus dimensions varied congruently or incongruently relative to each other, either in isolation or in the context of a concurrent visuo-spatial or verbal working memory task. During performance of the visuo-spatial, but not verbal, working memory task, precision in numerosity discrimination decreased, participants’ choices became strongly biased by item size, and the strength of this bias correlated with measures of arithmetical skills. Moreover, the interference between numerosity and working memory tasks was bidirectional, with number discrimination impacting visuo-spatial (but not verbal) performance. Overall, these results suggest that representing visual numerosity in a way that is unbiased by non-numerical quantities relies on processes which explicitly segregate/identify the locations of multiple objects that are shared with visuo-spatial (but not verbal) working memory. This shared resource may potentially be impaired in DD, explaining the observed co-occurrence of working memory and numerosity discrimination deficits in this clinical population.

Numbers (but not words) make math anxious individuals sweat: Physiological evidence

The study aimed to determine the specificity of math anxiety by measuring physiological arousal to the presentation of numerical and non-numerical stimuli. It also investigated whether math and trait anxieties share similar behavioral and physiological manifestations. Fifty-two female university students performed an experimental task including simple or complex arithmetical equations and math-related or neutral words. Participants’ electrodermal activity (skin conductance response) was monitored during the task. Math and trait anxieties were measured using common explicit questionnaires. Results showed math anxiety levels were significantly related to physiological arousal during the performance of complex numerical tasks. Importantly, math anxiety significantly mediated the links between trait anxiety and physiological arousal in complex numerical tasks. The findings support previous work finding relations between math and trait anxieties, but also show math anxiety is a unique phenomenon with specific behavioral and physiological manifestations, especially during the processing of complex numerical information.

Implicit visuospatial attention shapes numerosity adaptation and perception

The perception of numerical quantities is susceptible to adaptation: after inspecting a numerous dot array for a few seconds a subsequent dot array is grossly underestimated. In a recent work we showed that the mere appearance of an additional numerically neutral stimulus significantly reduces the adaptation magnitude. Here we demonstrate that this reduction is likely due to a numerosity underestimation of the adaptor caused by a change of numerosity-related attentional resources deployed on the adapting stimulus. In Experiment 1 we replicated previous findings revealing a robust reduction of numerosity adaptation when an additional adaptor (even if neutral) was displayed. In Experiment 2 we used the method of magnitude estimation to demonstrate that numerosity is underestimated whenever a second task-irrelevant numerical stimulus appears on screen. Furthermore we demonstrated that the same experimental manipulations were not effective in modulating orientation adaptation magnitude as well as orientation estimation accuracy. Our results support the hypothesis of a tight relationship between numerosity perception and implicit visuospatial attention and corroborate the notion that numerosity adaptation depends on perceived rather than physical numerosity. However the lack of an effect of visuospatial attentional deployment for orientation perception suggests that attention might differently shape adaptation aftereffects for different features along the visual hierarchy.

Order processing of number symbols is influenced by direction, but not format.

This study probed the cognitive mechanisms that underlie order processing for number symbols, specifically the extent to which the direction and format in which number symbols are presented influence the processing of numerical order, as well as the extent to which the relationship between numerical order processing and mathematical achievement is specific to Arabic numerals or generalisable to other notational formats. Seventy adults who were bilingual in English and Chinese completed a Numerical Ordinality Task, using number sequences of various directional conditions (i.e., ascending, descending, mixed) and notational formats (i.e., Arabic numerals, English number words, and Chinese number words). Order processing was found to occur for ascending and descending number sequences (i.e., ordered but not non-ordered trials), with the overall pattern of data supporting the theoretical perspective that the strength and closeness of associations between items in the number sequence could underlie numerical order processing. However, order processing was found to be independent of the notational format in which the numerical stimuli were presented, suggesting that the psychological representations and processes associated with numerical order are abstract across different formats of number symbols. In addition, a relationship between the processing speed for numerical order judgements and mathematical achievement was observed for Arabic numerals and Chinese number words, and to a weaker extent, English number words. Together, our findings have started to uncover the cognitive mechanisms that could underlie order processing for different formats of number symbols, and raise new questions about the generalisability of these findings to other notational formats.

Judging Numbers: Global and Local Contextual Effects in Individual and Group Data

This study examined the generality of the result that linear or logarithmic functions best describe the relationship between numerical stimuli and people’s judgments about those stimuli. In Experiment 1, one group of participants was told that 2 was a perfect example of category x and 6 was a perfect example of category y; another group was told the same about 6 and 18. The participants then rated how well logarithmically spaced numbers matched the category x number. Exponential and logarithmic functions best fit the data of individual participants who did the “2 vs. 6” task; power functions did the same in the “6 vs. 18” task. When participants’ data were averaged, a logarithmic function was the best fit for the ratings produced by the “2 vs. 6” task; power and exponential functions were the best fits for the ratings produced by the “6 vs. 18” task. In Experiment 2, two groups of participants were given similar rules about two numbers (2 vs. 4 or 4 vs. 6) and then rated how well linearly spaced numbers matched the category x number. For both tasks, most individuals’ ratings best fit a linear function. When the data were averaged, though, a logarithmic function was the best fit for the ratings produced by both tasks. The results highlight the importance of presenting individuals’ data and suggest that global and local numerical contexts influence people’s judgments about the numbers. Stimulus generalization may be a mechanism by which the local influence occurs.

What Stimuli Are Necessary for Anchoring Effects to Occur?

The anchoring effect is a form of cognitive bias in which exposure to some piece of information affects its subsequent numerical estimation. Previous studies have discussed which stimuli, such as numbers or semantic priming stimuli, are most likely to induce anchoring effects. However, it has not been determined whether anchoring effects will occur when a number is presented alone or when the semantic priming stimuli have an equivalent dimension between a target and the stimuli without a number. We conducted five experimental studies (N = 493) using stimuli to induce anchoring effects. We found that anchoring effects did not occur when a number was presented alone or when phrases to induce semantic priming were used without presenting a number. These results indicate that both numerical and semantic priming stimuli must be presented for anchoring effects to occur. Our findings represent a substantial contribution to the literature on anchoring effects by offering insights into how these effects are generated.