The Instructional Dependency of SNARC Effects Reveals Flexibility of the Space-Magnitude Association of Nonsymbolic and Symbolic Magnitudes

Abstract

The Spatial-Numerical Association of Response Codes (SNARC) effect refers to the phenomenon that small versus large numbers are responded to faster in the left versus right side of space, respectively. Using a pairwise comparison task, Shaki et al. found that task instruction influences the pattern of SNARC effects of certain types of magnitudes which are less rigid in their space-magnitude association .The present study examined the generalizability of this instruction effect using pairwise comparison of nonsymbolic and symbolic stimuli within a wide range of magnitudes. We contrasted performance between trials in which subjects were instructed to select the stimulus representing the smaller versus larger magnitude within each pair. We found an instruction-dependent pattern of SNARC effects for both nonsymbolic and symbolic magnitudes. Specifically, we observed a SNARC effect for the “Select Smaller” instruction, but a reverse SNARC effect for the “Select Larger” instruction. Considered together with previous studies, our findings suggest that nonsymbolic magnitudes and relatively large symbolic magnitudes have greater flexibility in their space-magnitude association.

Keywords

space-magnitude association SNARC effect reverse SNARC effect symbolic numbers nonsymbolic numbers instruction magnitude

Introduction

The Spatial-Numerical Association of Response Codes (SNARC) effect refers to the phenomenon that left hand responses are faster when responding to smaller numbers while right hand responses are faster when responding to larger numbers, suggesting that the mental representations of numbers are spatially organized in a left-to-right orientation (Dehaene, Bossini, & Giraux, 1993; Hubbard, Piazza, Pinel, & Dehaene, 2005; Wood, Willmes, Nuerk, & Fischer, 2008). The SNARC effect has been found even when the semantic meaning (i.e., magnitude) of numbers was irrelevant to task performance (e.g., phonemic judgment). This effect has been interpreted as implying that the magnitude of numbers is accessed automatically (Dehaene et al., 1993). The SNARC effect has been found for both symbolic (Berch, Foley, Hill, & Ryan, 1999; Bull, Marschark, & Blatto-Vallee, 2005; Dehaene et al, 1993; Fischer, 2003a; Fischer, Warlop, Hill, & Fias, 2004; Keus, Jenks, & Schwarz, 2005; Keus & Schwarz, 2005; Reynvoet & Brysbaert, 1999) and nonsymbolic (Bulf, Cassia, & de Hevia, 2014; Ebersbach, Luwel, & Verschaffel, 2014; Luccio, Fumarola, Tamburini, & Agostini, 2012; Mitchell, Bull, & Cleland, 2012; Nuerk, Wood, & Willmes, 2005) magnitudes. The SNARC effect has been commonly observed from tasks presenting a single stimulus to be compared with a reference number (e.g., “Is the presented digit smaller or larger than 5?”). In these tasks, numbers that were larger than the reference number were responded to faster with the right hand, while numbers that were smaller than the reference number were responded to faster with the left hand. In addition, a few studies using a pairwise comparison task also found a SNARC or SNARC-related effect for symbolic (Brysbaert, 1995; Turconi, Campbell, & Seron, 2006; but see Fischer, 2003b) and nonsymbolic (Patro & Haman, 2012) magnitudes. In studies using pairwise comparison of digits, performance was better when the larger number was presented on the right (e.g., 2 5) compared to the left side of space (e.g., 5 2). Using a nonsymbolic number comparison task, Patro and Haman (2012) reported that preschoolers performed better when the less numerous array was presented on the left while the more numerous array was presented on the right (Patro & Haman, 2012). Taken together, these results imply that there is a robust SNARC or SNARC-related effect for both symbolic and nonsymbolic numbers regardless of task format (i.e., single stimulus or pairwise comparison).

However, Shaki, Petrusic, and Leth-Steensen. (2012) raised the possibility that tasks using a single stimulus and tasks using pairwise comparison may elicit different degrees of flexibility in the mental representation of certain types of magnitudes which are less rigid in their space-magnitude association. In their experiment, they asked Canadian subjects to compare the size of larger versus smaller animal pairs (e.g., smaller pair: snail vs. mouse; larger pair: tiger vs. zebra). They found a SNARC-like effect (left-hand advantage for the comparison of smaller animal pairs and right-hand advantage for the comparison of larger animal pairs) when subjects were instructed to “select the smaller animal,” but a reverse SNARC-like effect (right-hand advantage for the comparison of smaller animal pairs and left-hand advantage for comparison of larger animal pairs) when subjects were instructed to “select the larger animal.” The authors suggest that in a task using a single stimulus, a fixed standard (typically located around the middle of all possible magnitudes presented throughout the experiment) is likely to play a role as a central standard so that magnitudes smaller (vs. larger) than the standard becomes associated with the left (vs. right) side of space, respectively. Thus, the task tends to evoke the default, left-to-right ordered mental representation of magnitudes (“small-left” and “large-right” association). On the other hand, a pairwise comparison task does not entail a central standard and thus allows for a more flexible reconstruction of mental representations according to task instruction, that is, regarding the left side of space as the point of reference, participants associate the smaller magnitude with left side (ascending order) for the “Select Smaller” instruction and the larger magnitude with left side (descending order) for the “Select Larger” instruction (Shaki et al., 2012).

As such, Shaki et al. (2012) emphasize that the nature of the paired comparison method is a critical factor contributing to this representational flexibility. Critically, the authors found that this instructional dependency was manifest only for the comparison of animal size but not for the comparison of symbolic numerical magnitudes tested (i.e., Arabic numbers from one to nine). Given that repeated exposure to an ordinal sequence of magnitudes (e.g., counting sequence, rulers, calendars, etc.) is believed to be one of the main sources of magnitude-space association (Gevers, Reynvoet, & Fias, 2003; Previtali, de Hevia, & Grirelli, 2010), single-digit symbolic numbers’ spatial representation is likely to be rigidly formed in a left-to-right orientation, while that of animal sizes are not. Thus, pairwise comparison of magnitudes may reveal differences in the flexibility of space-magnitude association, manifest as an instruction effect on SNARC-like effects, depending on the nature of the magnitude representations.

We believe that Shaki et al.’s demonstration of the representational flexibility in certain magnitude representations is an interesting phenomenon that should be examined further. The instruction effect has only been investigated for symbolic magnitudes such as Arabic digits and animal size represented by animal names (Shaki et al., 2012). Our study is the first to examine the instruction effect using nonsymbolic magnitudes. In addition, we tested magnitudes within a wide range of magnitudes that are larger than those previously examined (cf., the instruction effect of symbolic numerical magnitudes was tested from one to nine in Shaki et al.’s study). Secondly, we aimed to verify whether there would be an instruction effect (representational flexibility) even for symbolic numerical magnitudes if examined within relatively larger magnitude ranges, because the space-magnitude association is thought to be weaker for larger numerical magnitude ranges; for example, the SNARC effect is observed in relatively smaller number ranges (1–9) but is weakened or absent in relatively larger number ranges (10–19) (Dehaene et al., 1993).

We expected to see an instruction effect for nonsymbolic magnitudes, because nonsymbolic magnitudes are not repeatedly mapped to a left–right ordinal sequence (unlike symbolic magnitudes). However, because we chose to include relatively larger magnitude ranges, we were open to the possibility that even symbolic magnitudes may show instruction effects. More specifically, based on the results of Shaki et al. (2012)’s animal size comparison task, when relatively smaller magnitude pairs are presented, we predicted that a “Select Larger” instruction would lead to faster responses with the right hand, whereas a “Select Smaller” instruction would lead to faster responses with the left hand. On the other hand, when relatively larger magnitude pairs are presented, we predicted that a “Select Larger” instruction would lead to faster responses with the left hand, whereas a “Select Smaller” instruction would lead to faster responses with the right hand.

In sum, the present study aimed to investigate the instruction-dependency of SNARC effects using a pairwise comparison task for both nonsymbolic and symbolic magnitudes across an expanded range including relatively larger magnitudes compared to previous studies. We tested for performance differences between the Hand of Response as a measure of the SNARC effect. In order to examine the effect of task instruction, subjects were instructed to “Select Larger” in Experiment 1 and “Select Smaller” in Experiment 2.

Methods

Participants

Sixty five adults (36 females, two left-handed, mean age = 23.8) participated in both Experiments 1 and 2. All participants were native Korean speakers (accustomed to left-to-right reading direction). All participants had normal or corrected-to-normal vision and provided written, informed consent prior to participation.

Tasks and Procedure

Experiment 1: “Select Larger” instruction

We conducted two tasks: (a) nonsymbolic and (b) symbolic number comparison to examine the effect of instruction on SNARC effects. In Experiment 1, participants were instructed to indicate the location of the stimulus representing the larger numerosity/number via left or right button press.

Nonsymbolic numerosity comparison task. Two arrays of black dots were presented side by side for 1,000 ms. Subjects were instructed to indicate the location (left vs. right) of the array with more dots with a keyboard press (“3” for left and “8” for right). Participants pressed the “3” key with their left hand and the “8” key with their right hand. On half of the trials, the array with more dots was presented on the right side of the screen while on the other half, the array with more dots was presented on the left. Numerosities were selected from a wide range of magnitudes from 6 to 50, excluding the subitizing range (Mitchell et al., 2012; Trick & Pylyshyn, 1994) while including magnitudes larger than those investigated in previous studies that examined the instruction effect. Trials were classified into relatively Small (hereafter Small) or relatively Large (hereafter Large) magnitude conditions depending on the mean of the two numerosities within a pair (Small magnitude range: 6–24; Large magnitude range: 25–50; see Table S1 for the entire list of pairs classified into Small vs. Large magnitude conditions). This Large versus Small classification is based on a previous study reporting that the SNARC effect depends not on the absolute but the relative magnitude of numbers within the experimental context (Dehaene et al., 1993). Given that the difficulty of comparison is known to depend on the ratio of the two magnitudes, the ratio of the two numerosities was matched between Large and Small magnitude pairs from 5:6 to 10:11 (5:6, 6:7, 7:8, 8:9, 9:10, and 10:11).

Although it is not possible to perfectly control for the influence of all continuous visual properties associated with dot arrays on a trial by trial basis (Gebuis & Reynvoet, 2011; Leibovich & Henik, 2013; Maloney, Risko, Ansari, & Fugelsang, 2010), we used control conditions and random variation of continuous visual properties so that subjects could not consistently rely on non-numerical continuous visual cues to guess numerosity (Cordes & Brannon, 2008, 2009; Halberda, Mazzocco, & Feigenson, 2008; Maloney et al., 2010; Mussolin, Mejias, & Noël, 2010; Nys & Content, 2012). Trials were evenly divided into two conditions. In the Area controlled condition (hereafter AR condition), the cumulative area of dots (the aggregate of all of the dot surfaces) was equated between arrays (i.e., average dot size was inversely proportional to numerical magnitude). The average size (diameter) of dots ranged from 8 to 23 pixels and the cumulative area of dots was about 630π pixels. In the Size controlled (SZ) condition (hereafter SZ condition), average size (diameter) of dots was equivalent between arrays (i.e., the cumulative area of the dot arrays increased with numerical magnitude). The diameter of each dot varied from 80% to 120% of the average diameter (8 pixels) and the cumulative area of dots ranged from 96 to 800π pixels. Dot density and convex hull were controlled by random spatial placement of each dot within a fixed rectangular frame for each array (Halberda & Feigenson, 2008). The order of these conditions was randomly intermixed and randomized. The total number of trials was 120 (10 trials per each ratio by control condition [AR, SZ]). For each trial, two arrays of dots were presented side by side on a 1366 × 768 pixel screen. Each array of dots was arranged within a 290 × 217 virtual rectangle and the distance between centers of each array was fixed at 355 pixels. Trials from each condition/ratio were of equal number and were intermixed in random order. Five practice trials with feedback were given before the main experiment.

Symbolic number comparison task. Two Arabic numerals were presented side by side for 200 ms. Subjects were instructed to indicate the location (left vs. right) of the (semantically) larger number with a keyboard press (“3” for left and “8” for right). Participants pressed the “3” key with their left hand and the “8” key with their right hand. On half of the trials, the larger numeral was presented on the right side of the screen while on the other half, the larger numeral was presented on the left. The range of magnitudes, ratios, and task procedure were exactly the same as in the nonsymbolic number comparison task. For each trial, two digits were presented side by side on a 1366 × 768 pixel screen. The font size was fixed at 60. The total number of trials was 60 (10 trials per each ratio). Trials from each condition/ratio were of equal number and randomly intermixed. Eight practice trials with feedback were administered before the main experiment. E-prime software was used for stimuli presentation and data collection (Schneider, Eschman, & Zuccolotto, 2002).

Experiment 2: “Select Smaller” instruction

The same subjects from Experiment 1 participated in Experiment 2. Tasks and procedure were exactly the same as in Experiment 1 except for the instruction. In Experiment 2, participants were instructed to indicate the location of the smaller numerosity/number via left or right button press.

Data Analysis

For quality control, trials with reaction times (RT) beyond ±3 SD from the mean were excluded. Data from the two control (SZ and AR) conditions of the nonsymbolic comparison task were pooled after verification of identical pattern of results from separate analyses (see Table S2 of Supplementary Information). Descriptive statistics for each condition of the nonsymbolic numerosity comparison performance are provided in Tables S3 and S4.

In order to measure the degree of the SNARC effect, we calculated the difference in response times (RTs) and accuracy between the hand of response (Right-Hand RT/accuracy—Left-Hand RT/accuracy). RT/Accuracy Difference was then regressed on mean Magnitude (the mean of the two numerosities/numbers within a pair, hereafter Magnitude). The sign of the regression coefficient represents the direction of the SNARC effect. For RT differences, a negative slope indicates the presence of a SNARC effect, while a positive slope indicates a reverse SNARC effect. The converse is true for Accuracy Differences. Secondly, as a post-hoc analysis, we conducted a three-way repeated measures analysis of variance (i.e., Format [Symbolic, Nonsymbolic] × Magnitude [Small, Large] × Instruction [Select Larger, Select Smaller] on RT/Accuracy Difference.

Results

Instruction-Dependent SNARC Effect

Nonsymbolic magnitudes

First, in a regression analysis, Magnitude significantly predicted RT Difference (Right-Hand RT—Left-Hand RT) for the “Select Smaller” but not “Select Larger” Instruction (Select Larger: r²(27) = .099, F(27) = 2.96, p = .097; Select Smaller: r²(27) = .421, F(1, 27) = 19.61, p < .001; Figure 1(a)). The standardized regression coefficient of Magnitude was negative (and significant) for the “Select Smaller” Instruction (β = −.65, t(27) = −4.43, p < .001), manifesting a SNARC effect; that is, as seen in Figure 2(a), Left-Hand (hereafter LH) responses were faster compared to Right-Hand (hereafter RH) responses for smaller magnitudes and the opposite was true for larger magnitudes. The same regression analyses were also conducted on Accuracy Difference (RH Accuracy–LH Accuracy). Magnitude significantly predicted Accuracy Difference for both the “Select Larger” and “Select Smaller” Instructions (Select Larger: r²(27) = .472, F(1, 27) = 24.14, p < .001; Select Smaller: r²(27) = .293, F(1, 27) = 11.22, p < .01; Figure 1(b)). The standardized regression coefficient of Magnitude was negative (and significant) for the “Select Larger” Instruction (β = −.69, t(27) = −4.91, p < .001) but positive (and significant) for the “Select Smaller” Instruction (β = .54, t(27) = 3.34, p < .01), revealing a SNARC effect for the “Select Smaller” but a reverse SNARC effect for the “Select Larger” Instruction. There was no negative correlation between RT and error rates indicating an absence of speed–accuracy trade-off (Select Larger Instruction: r(64) = + .43, p < .05; Select Smaller Instruction: r(64) = + .27, p < .05).

Figure 1.

RT (a, c) and accuracy (b, d) differences between the hand of response as a function of mean magnitude for the “Select Larger” (solid lines) and “Select Smaller” (dashed lines) Instructions. RH = right-hand; LH = left-hand; ACC = accuracy; RT = response time.

Figure 2.

RT (a, c) and accuracy (b, d) differences between the hand of response for each format and instruction. Error bars represent standard errors of the mean (SEM). RH = right-hand; LH = left-hand; ACC = accuracy; RT = response time.

Symbolic magnitudes

Magnitude significantly predicted RT Difference for both the “Select Larger” and “Select Smaller” Instructions (Select Larger: r²(27) = .404, F(1, 27) = 18.30, p < .001; Select Smaller: r²(27) = .498, F(1, 27) = 26.82, p < .001; Figure 1(c)). The standardized regression coefficient of Magnitude was positive (and significant) for the “Select Larger” Instruction (β = .64, t(27) = 4.28, p < .001) but negative (and significant) for the “Select Smaller” Instruction (β = −.71, t(27) = −5.18, p < .0001), indicating a SNARC effect for the “Select Smaller” but a reverse SNARC effect for the “Select Larger” Instruction. The same regression analyses were also conducted on Accuracy Difference. Magnitude significantly predicted Accuracy Difference only in the “Select Larger” Instruction (Select Larger: r²(27) = .342, F(1, 27) = 14.00, p < .01; Select Smaller: r²(27) = .009, F(1, 27) = .24, p > .05; Figure 1(d)). The standardized regression coefficient of Magnitude was negative (and significant) for the “Select Larger” Instruction (β = −.58, t(27) = −3.74, p < .01), manifesting a reverse SNARC effect. There was no negative correlation between RT and error rates indicating an absence of speed–accuracy trade-off (“Select Larger”: r(64) = + .27, p < .05; “Select Smaller”: r(64) = + .10, p > .05).

Overall summary of results

Taken together, the results from either RT or accuracy demonstrate a SNARC effect for the “Select Smaller” Instruction but a reverse SNARC effect for the “Select Larger” Instruction. The opposite pattern of results for the “Select Larger” versus “Select Smaller” Instruction shows an instruction-dependent SNARC effect for both nonsymbolic and symbolic magnitudes.

Testing for the Interaction Among Format x Magnitude x Instruction

We next conducted post-hoc analyses in order to test the interaction among Format, Magnitude, and Instruction. A three-way repeated measures analysis of variance testing for the effect of Format (Symbolic, Nonsymbolic) × Magnitude (Small, Large) × Instruction (Select Larger, Select Smaller) on RT Difference revealed a significant Instruction × Magnitude interaction (F(1, 64) = 37.09, p < .001, η²= .37; Figure 2). In the “Select Larger” Instruction, RTs from the RH were faster than the LH on Small Magnitude trials while RTs from the LH were faster than the RH on Large Magnitude trials (F(1, 64) = 14.73, p < .001, η²= .19). The opposite pattern of results was found in the “Select Smaller” Instruction (F(1, 64) = 27.79, p < .001, η²= .30). All other main effects and interaction effects were not significant (ps > .05), suggesting that the Instruction × Magnitude interaction effect was similar between Nonsymbolic (Figure 2(a)) and Symbolic (Figure 2(c)) magnitude comparison tasks.

The same analysis on Accuracy Difference also showed a significant two-way interaction between Instruction and Magnitude (F(1, 64) = 23.43, p < .001, η²= .27). In addition, the three-way interaction between Magnitude, Instruction, and Format was significant (F(1, 64) = 10.94, p < .05, η²= .15); that is, the SNARC effect was reversed depending on Instruction for the Nonsymbolic (F(1, 64) = 24.28, p < .001, η²= .28; Figure 2(b)) but not for the Symbolic task (F(1, 64) = 2.55, p > .05; Figure 2(d)). Although this three-way interaction may seem to indicate a difference in the pattern of the Instruction × Magnitude interaction between Nonsymbolic and Symbolic magnitudes, it should be noted that accuracy on Small magnitude trials of the Symbolic task was relatively higher compared to all other conditions (Tables 1 and 2). Specifically, for the Symbolic task, Accuracy Difference on Large magnitude trials was significantly different between Instructions (p < .01), while Accuracy Difference on Small magnitude trials was similar between Instructions (p > .05). In other words, performance on Small magnitude trials of the Symbolic task was equivalently high regardless of the Hand of Response or Instruction. Thus, it seems more reasonable to conclude that the observed three-way interaction effect is a byproduct of the null (or semi-ceiling) effect from the Small magnitude trials of the Symbolic task rather than a manifestation of a meaningful difference in the Instruction × Magnitude interaction between Nonsymbolic and Symbolic magnitude comparison tasks. All other main effects were not significant (ps > .05).

Table 1.

Descriptive Statistics for Experiment 1.

Stimuli	Small magnitude		Large magnitude
Stimuli	LH	RH	LH	RH
Symbolic
ACC	.92 ± .09	.93 ± .08	.92 ± .09	.87 ± .12
RT(ms)	525 ± 67	510 ± 73	546 ± 79	558 ± 76
Nonsymbolic
ACC	.77 ± .13	.82 ± .10	.78 ± .11	.72 ± .15
RT(ms)	1145 ± 297	1120 ± 315	1114 ± 306	1127 ± 300

RH = right-hand; LH = left-hand; ACC = accuracy; RT = response time.

Values indicate the mean (M) ± standard deviation (SD).

Table 2.

Descriptive Statistics for Experiment 2.

Stimuli	Small magnitude		Large magnitude
Stimuli	LH	RH	LH	RH
Symbolic
ACC	.93 ± .10	.94 ± .09	.90 ± .11	.91 ± .09
RT(ms)	531 ± 78	542 ± 73	611 ± 82	578 ± 85
Nonsymbolic
ACC	.79 ± .11	.74 ± .14	.71 ± .13	.75 ± .14
RT(ms)	1129 ± 325	1161 ± 300	1136 ± 324	1115 ± 310

RH = right-hand; LH = left-hand; ACC = accuracy; RT = response time.

Values indicate the mean (M) ± standard deviation (SD).

Taken together, the overall pattern of results points to a similarity in the pattern and strength of the Instruction × Magnitude interaction effect between Nonsymbolic versus Symbolic magnitude comparison tasks.

Discussion

In the present study, we examined the effect of instruction on SNARC effects from Nonsymbolic and Symbolic numerical magnitude comparison task performance. We found a SNARC effect (left-hand advantage for the comparison of relatively smaller magnitudes and right-hand advantage for the comparison of relatively larger magnitudes) for the “Select Smaller” Instruction but a reverse SNARC effect (right-hand advantage for the comparison of relatively smaller magnitudes and left-hand advantage for the comparison of relatively larger magnitudes) for the “Select Larger” Instruction. Taken together, the overall pattern of results manifests instructional dependency of space-magnitude association for both Nonsymbolic and Symbolic numerical magnitudes.

Space-Magnitude Association Is Flexibly Reconstructed for Larger Magnitudes

Shaki et al. (2012) found an instruction-dependent SNARC-like effect for the comparison of non-numerical symbolic magnitude (e.g., comparing animal names) but not symbolic numbers. Given that the left-to-right ordering of numbers is much overlearned while that of animal sizes are not, the space-magnitude association of numbers is believed to be rigid and thus less susceptible to the influence of experimental context or task instruction (Gevers et al., 2003; Previtali et al., 2010). Shaki et al. interpreted their finding as reflecting a difference in the strength of space-magnitude association (“small-left” and “large-right”) between non-numerical versus numerical symbolic magnitudes.

While Shaki et al. (2012) contrasted between non-numerical versus numerical symbolic magnitudes, the present study examined the space-magnitude association of Nonsymbolic and Symbolic numbers within a wide range including magnitudes larger than those used in Shaki et al.s’ study (2012). Our results demonstrated that the spatial representation associated with nonsymbolic magnitudes and even symbolic magnitudes in relatively larger magnitude ranges can be flexibly reconstructed depending on task instruction. The spatial representation of nonsymbolic magnitudes and relatively larger symbolic magnitudes is likely to be less rigid since they both are not repeatedly mapped to a left–right spatial sequence (unlike small symbolic magnitudes). This interpretation is consistent with the previous finding that the SNARC effect is observed in relatively smaller number ranges (1–9) but is weakened or absent in relatively larger number ranges (10–19) (Dehaene et al., 1993). Similarly, Mitchell et al. (2012) had also reported that the SNARC effect for nonsymbolic numerosity was weaker in relatively larger magnitudes (6–9) than smaller ones (1–4). Note, that Dehaene et al. (1993) and Mitchell et al. (2012)’s study both used a single stimulus paradigm and relatively smaller number ranges. As stated by Shaki et al. (2012), tasks using a single stimulus are more likely to evoke the default, left-to-right mapping of the smaller versus larger stimuli, while in a pairwise comparison task, participants tend to reconstruct the spatial representation regarding the left side of space as the point of reference (Shaki et al., 2012). Thus, the use of a pairwise comparison task in the present study seems to have allowed for greater representational flexibility depending on task instruction leading to a SNARC effect for the “Select Smaller” Instruction but a reverse SNARC effect for the “Select Larger” Instruction.

Alternative Explanation Based on the Framework of “Space Order Error”

Note that our results can be understood alternatively using the framework of Space Order Error (Hellström, 2003; Masin & Agostini, 1991; Patching, Englund, & Hellström, 2012). Space Order Error (hereafter SOE) refers to the phenomenon that the perceived magnitude of the left-side stimulus tends to be under- or over-estimated during paired comparison depending on task context such as magnitude range (Charles, Sahraie, & McGeorge, 2007; Hellström, 2003; Masin & Agostini, 1991). For example, when comparing two side by side lines, participants overestimated the left line of longer pairs but underestimated the left line of shorter pairs (Masin & Agostini, 1991). This kind of bias is thought to be caused by greater specialization of the right hemisphere in visuospatial processing which facilitates the processing of the stimulus in the left visual field (Luh, 1995; Mattingley, Bradshaw, Nettleton, & Bradshaw, 1994; but for an account of sensation-weighting model, see Hellström, 1985, 2003, Patching et al., 2012). In addition, the left-to-right scanning habit (in left-to-right reading cultures) causes the left-side stimulus to be attended to first, possibly cutting down time to encode the right-side stimulus when given limited time for judgment (Klein & Farrell, 1989; Masin & Agostini, 1991). Thus, there is greater probability that the comparative judgment is made mainly on the basis of the left-side stimulus; that is, the left-side stimulus of larger pairs is overestimated more than the right-side stimulus, while the left-side stimulus of smaller pairs is underestimated more than the right-side stimulus (Masin & Agostini, 1991).

The present results also show the same pattern of results when we divide trials into Ascending and Descending Order conditions depending on whether the larger numeral was presented on the right (Ascending) or left (Descending). Since Order, Hand of Response and Instruction covary with one another; that is, better Left-Hand compared to Right-Hand response corresponds to better performance on Ascending Order trials under the “Select Smaller” instruction, but better performance on Descending Order trials under the “Select Larger” instruction. Using difference in performance between the Hand of Response as dependent variable, the present results manifest an interaction between Order and Magnitude. Under the “Select Smaller” instruction, participants showed better performance for the Ascending Order (Left-Hand advantage) on Small magnitude trials but better performance for Descending Order (Right-Hand advantage) on Large magnitude trials. Reversely, under the “Select Larger” instruction, participants showed better performance for the Ascending Order (Right-Hand advantage) on Small magnitude trials and better performance for the Descending Order (Left-Hand advantage) on Large magnitude trials. Thus, performance on Small magnitudes was better for the Ascending Order while performance on Large magnitudes was better for the Descending Order, regardless of task instruction. This pattern of results can be interpreted as follows. As suggested by Masin and Agostini (1991), if participants overestimate the perceived magnitude of the left-side stimulus on Ascending Large Magnitude trials, the perceived distance between the two numbers would become smaller (i.e., harder to discriminate). On the other hand, performance would be facilitated in the Descending Large Magnitude condition, because the perceived distance between the two numbers would become larger (i.e., easier to discriminate). In contrast, underestimation of the left-side stimulus for Small Magnitude trials will lead to the opposite pattern. Although the effect of SOE had rarely been reported for side-by-side presentation of numerical stimuli (Nicholls, Bradshaw, & Mattingley, 1999), given that numerical magnitudes are also dominantly processed by the right hemisphere (Chassy & Grodd, 2012; Chochon, Cohen, van de Moortele, & Dehaene, 1999; Dehaene, 1996; Dormal & Pesenti, 2009; Holloway, Price, & Ansari, 2010; Le Clec et al., 2000), the activation of which is thought to cause SOE, it is possible that the same explanation can be applied to the results of the present study (Luh, 1995; Mattingley et al., 1994).

Symbolic Versus Nonsymbolic Magnitude Representations

The same pattern of instruction effects for both nonsymbolic and symbolic magnitudes suggests that the spatial representation of nonsymbolic and symbolic magnitudes is flexibly reconstructed in a similar manner. These findings are in line with previous studies reporting that symbolic and nonsymbolic magnitudes have similar spatial representational characteristics; for example, symbolic and nonsymbolic magnitudes show the same pattern of space-magnitude association (Brysbaert, 1995; Bulf et al., 2014; Dehaene et al., 1993; Ebersbach et al., 2014; Luccio et al., 2012; Mitchell et al., 2012; Nuerk, Wood, & Willmes, 2005) and bias on a bisection task (de Hevia, Girelli, & Vallar, 2006; de Hevia & Spelke, 2009). On the other hand, it may be expected that the degree of flexibility in space-magnitude association of symbolic versus nonsymbolic magnitudes differ because the left-to-right ordering of symbolic magnitudes are explicitly (over) learned while that of nonsymbolic magnitudes are not. Our results showing that symbolic and nonsymbolic magnitudes show a similar pattern of representational flexibility support the idea that symbolic and nonsymbolic magnitude representations have similar spatial characteristics within relatively larger magnitude ranges. Thus, the range of magnitude (rather than the format) seems to be a more critical factor influencing the spatial characteristics of numerical magnitude representations. However, it should be emphasized that similarities in spatial characteristics of numerical magnitude representations do not necessarily indicate the presence of a common internal representation between symbolic and nonsymbolic magnitudes (Koechlin, Naccache, Block, & Dehaene, 1999). It is beyond the scope of this study to further discuss this issue which is being pursued by a large body of research, but refer to the following papers for an in-depth discussion on this topic (Herrera & Macizo, 2008; Lyons, Ansari, & Beilock, 2012, 2015; Piazza, Pinel, Bihan, & Dehaene, 2006).

The Origin of the SNARC Effect

There have been conflicting perspectives on the origin of the SNARC effect. Previous studies have found an early predisposition or preference to associate numerical order with a left-to-right spatial orientation in infants, preschoolers, and birds (de Hevia, Girelli, Addabbo, & Cassia, 2014; Patro & Haman, 2012; Rugani, Kelly, Szelest, Regolin, & Vallortigara, 2010). These results suggest that the orientation of this default space-magnitude association is not likely to be cultivated through learning or experience. Early preference for left-to-right ordering (i.e., ascending order) of magnitudes has been attributed to dominance of the right hemisphere in visuospatial processing which accompanies greater attentional allocation to the left visual field (Diekamp, Regolin, Güntürkün, & Vallortigara, 2005; Regolin, 2006; Rugani et al., 2010; Vallortigara & Rogers, 2005). For example, neuroimaging studies of infants found that numerical quantity processing is lateralized to the right hemisphere (Hyde, Boas, Blair, & Carey, 2010; Izard, Dehaene-Lambertz, & Dehaene, 2008). Taken together, these studies suggest that innate leftward bias might be at the root of the left-to-right orientation of the mental number line (Rugani et al., 2010). On the other hand, cultural factors such as reading/writing direction are also thought to influence space-magnitude association. In left-to-right reading western cultures, small (vs. large) numbers are associated with the left (vs. right) side of space, whereas in right-to-left reading Arabic cultures, the reverse pattern is observed (Dehaene et al., 1993; Zebian, 2005). In addition, Shaki et al. (2012) found that in the comparison of animal size, the spatial ordering of magnitudes was strategically reconstructed in a left-to-right or right-to-left orientation depending on task instruction. The orientation in which spatial representations were reconstructed depended on participants’ reading and writing habits; that is, adults in Western cultures reconstructed the spatial representation considering the left side of space as the point of reference, while Hebrew and Arabic readers showed the opposite pattern (Shaki et al., 2012).

Altogether, there seems to exist innate preference for left-to-right spatial ordering of magnitudes. But through development, humans learn to reconstruct the spatial representation of certain kinds of magnitudes in a flexible, strategic manner depending on cultural convention or task context. This developmental change is influenced by cultural experience such as reading and writing habits as demonstrated by Shaki et al. (2012). The present results and that of Shaki et al. (2012) together demonstrate a difference in the space-magnitude association of relatively larger versus smaller magnitudes which is also consistent with the idea that learning and experience can influence the spatial characteristics of magnitude representations. In other words, smaller numbers that are overly exposed to left-to-right sequences have more fixed, rigid spatial mapping while relatively larger numbers and nonsymbolic magnitudes are more flexible in their spatial characteristics.

Conclusion

The present study found a similar pattern of instructional dependency of space-magnitude association for both nonsymbolic and symbolic magnitudes, that is, we observed a SNARC effect for the “Select Smaller” instruction, but a reverse SNARC effect for the “Select Larger” instruction. These findings imply that the space-magnitude association of relatively larger magnitudes is more flexible and susceptible to task context compared to smaller magnitudes which were found to be rigid in its left-to-right spatial mapping. Interestingly, in contrast to previous studies, relatively large symbolic magnitudes tested in the present study showed spatial characteristics and representational flexibility similar to nonsymbolic magnitudes. We believe that nonsymbolic magnitudes and relatively large symbolic magnitudes may have greater representational flexibility, because (unlike smaller symbolic magnitudes), they both are not repeatedly mapped to a left-to-right ordered sequence. As Shaki et al. (2012) had proposed, this representational flexibility of magnitudes may have been amplified by the use of a pairwise comparison task format in the present study. We look forward to future studies to unravel the influence of various factors such as task format and type of magnitude on representational flexibility and how space-magnitude association is affected by learning and culture throughout development.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by grants from the National Research Foundation of Korea funded by the Korean Government (NRF-2012R1A1A1011872, NRF-2014R1A1A3051034, BK 21 PLUS 22B20130012738).

References

Berch

D. B.

Foley

E. J.

Hill

R. J.

Ryan

P. M.

(1999) Extracting parity and magnitude from Arabic numerals: Developmental changes in number processing and mental representation. Journal of Experimental Child Psychology 74: 286–308.

Brysbaert

(1995) Arabic number reading: On the nature of the numerical scale and the origin of phonological recoding. Journal of Experimental Psychology: General 124: 434.

Bulf

Cassia

V. M.

de Hevia

M. D.

(2014) Are numbers, size and brightness equally efficient in orienting visual attention? Evidence from an eye-tracking study. PLoS ONE 9: e99499.

Bull

Marschark

Blatto-Vallee

(2005) SNARC hunting: Examining number representation in deaf students. Learning and Individual Differences 15: 223–236.

Charles

Sahraie

McGeorge

(2007) Hemispatial asymmetries in judgment of stimulus size. Perception & Psychophysics 69: 687–698.

Chassy

Grodd

(2012) Comparison of quantities: Core and format-dependent regions as revealed by fMRI. Cerebral Cortex 22: 1420–1430.

Chochon

Cohen

Van De Moortele

Dehaene

(1999) Differential contributions of the left and right inferior parietal lobules to number processing. Journal of Cognitive Neuroscience 11: 617–630.

Cordes

Brannon

E. M.

(2008) The difficulties of representing continuous extent in infancy: Using number is just easier. Child Development 79: 476–489.

Cordes

Brannon

E. M.

(2009) The relative salience of discrete and continuous quantity in young infants. Developmental Science 12: 453–463.

10.

de Hevia

M. D.

Girelli

Addabbo

Cassia

V. M.

(2014) Human infants' preference for left-to-right oriented increasing numerical sequences. PLoS ONE 9: e96412.

11.

de Hevia

M. D.

Girelli

Vallar

(2006) Numbers and space: A cognitive illusion? Experimental Brain Research 168: 254–264.

12.

de Hevia

M. D.

Spelke

E. S.

(2009) Spontaneous mapping of number and space in adults and young children. Cognition 110: 198–207.

13.

Dehaene

(1996) The organization of brain activations in number comparison: Event-related potentials and the additive-factors method. Journal of Cognitive Neuroscience 8: 47–68.

14.

Dehaene

Bossini

Giraux

(1993) The mental representation of parity and number magnitude. Journal of Experimental Psychology: General 122: 371–396.

15.

Diekamp

Regolin

Güntürkün

Vallortigara

(2005) A left-sided visuospatial bias in birds. Current Biology 15: R372–R373.

16.

Dormal

Pesenti

(2009) Common and specific contributions of the intraparietal sulci to numerosity and length processing. Human Brain Mapping 30: 2466–2476.

17.

Ebersbach

Luwel

Verschaffel

(2014) Further evidence for a spatial-numerical association in children before formal schooling. Experimental Psychology 61: 323–329.

18.

Fischer

M. H.

(2003a) Spatial representations in number processing-evidence from a pointing task. Visual Cognition 10: 493–508.

19.

Fischer

M. H.

(2003b) Cognitive representation of negative numbers. Psychological Science 14: 278–282.

20.

Fischer

M. H.

Warlop

Hill

R. L.

Fias

(2004) Oculomotor bias induced by number perception. Experimental Psychology 51: 91–97.

21.

Gebuis

Reynvoet

(2011) Generating nonsymbolic number stimuli. Behavior Research Methods 43: 981–986.

22.

Gevers

Reynvoet

Fias

(2003) The mental representation of ordinal sequences is spatially organized. Cognition 87: B87–B95.

23.

Halberda

Feigenson

(2008) Developmental change in the acuity of the “Number Sense”: The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology 44: 1457.

24.

Halberda

Mazzocco

M. M.

Feigenson

(2008) Individual differences in non-verbal number acuity correlate with maths achievement. Nature 455: 665–668.

25.

Hellström

Å.

(1985) The time-order error and its relatives: Mirrors of cognitive processes in comparing. Psychological Bulletin 97: 35.

26.

Hellström

Å.

(2003) Comparison is not just subtraction: Effects of time-and space-order on subjective stimulus difference. Perception & Psychophysics 65: 1161–1177.

27.

Herrera

Macizo

(2008) Cross-notational semantic priming between symbolic and nonsymbolic numerosity. The Quarterly Journal of Experimental Psychology 61: 1538–1552.

28.

Holloway

I. D.

Price

G. R.

Ansari

(2010) Common and segregated neural pathways for the processing of symbolic and nonsymbolic numerical magnitude: An fMRI study. Neuroimage 49: 1006–1017.

29.

Hubbard

E. M.

Piazza

Pinel

Dehaene

(2005) Interactions between number and space in parietal cortex. Nature Reviews Neuroscience 6: 435–448.

30.

Hyde

D. C.

Boas

D. A.

Blair

Carey

(2010) Near-infrared spectroscopy shows right parietal specialization for number in pre-verbal infants. Neuroimage 53: 647–652.

31.

Izard

Dehaene-Lambertz

Dehaene

(2008) Distinct cerebral pathways for object identity and number in human infants. PLoS Biology 6: e11.

32.

Keus

I. M.

Jenks

K. M.

Schwarz

(2005) Psychophysiological evidence that the SNARC effect has its functional locus in a response selection stage. Cognitive Brain Research 24: 48–56.

33.

Keus

I. M.

Schwarz

(2005) Searching for the functional locus of the SNARC effect: Evidence for a response-related origin. Memory & Cognition 33: 681–695.

34.

Klein

Farrell

(1989) Search performance without eye movements. Perception & Psychophysics 46: 476–482.

35.

Koechlin

Naccache

Block

Dehaene

(1999) Primed numbers: Exploring the modularity of numerical representations with masked and unmasked semantic priming. Journal of Experimental Psychology: Human Perception and Performance 25: 1882.

36.

Le Clec

H. G.

Dehaene

Cohen

Mehler

Dupoux

Poline

J. B.

Le Bihan (2000) Distinct cortical areas for names of numbers and body parts independent of language and input modality. Neuroimage 12: 381–391.

37.

Leibovich

Henik

(2013) Magnitude processing in non-symbolic stimuli. Frontiers in Psychology 4: 375.

38.

Luccio

Fumarola

Tamburini

Agostini

(2012) The spatial representation of non-symbolic numerical quantities. Proceedings of Fechner Day 28: 321–327.

39.

Luh

K. E.

(1995) Line bisection and perceptual asymmetries in normal individuals: What you see is not what you get. Neuropsychology 9: 435.

40.

Lyons

I. M.

Ansari

Beilock

S. L.

(2012) Symbolic estrangement: Evidence against a strong association between numerical symbols and the quantities they represent. Journal of Experimental Psychology: General 141: 635.

41.

Lyons

I. M.

Ansari

Beilock

S. L.

(2015) Qualitatively different coding of symbolic and nonsymbolic numbers in the human brain. Human Brain Mapping 36: 475–488.

42.

Maloney

E. A.

Risko

E. F.

Ansari

Fugelsang

(2010) Mathematics anxiety affects counting but not subitizing during visual enumeration. Cognition 114: 293–297.

43.

Masin

S. C.

Agostini

(1991) Attentional scanning and space errors. Perception & Psychophysics 50: 285–289.

44.

Mattingley

J. B.

Bradshaw

J. L.

Nettleton

N. C.

Bradshaw

J. A.

(1994) Can task specific perceptual bias be distinguished from unilateral neglect? Neuropsychologia 32: 805–817.

45.

Mitchell

Bull

Cleland

A. A.

(2012) Implicit response-irrelevant number information triggers the SNARC effect: Evidence using a neural overlap paradigm. The Quarterly Journal of Experimental Psychology 65: 1945–1961.

46.

Mussolin

Mejias

Noël

M.-P.

(2010) Symbolic and nonsymbolic number comparison in children with and without dyscalculia. Cognition 115: 10–25.

47.

Nicholls

M. E.

Bradshaw

J. L.

Mattingley

J. B.

(1999) Free-viewing perceptual asymmetries for the judgement of brightness, numerosity and size. Neuropsychologia 37: 307–314.

48.

Nuerk

H.-C.

Wood

Willmes

(2005) The universal SNARC effect: The association between number magnitude and space is amodal. Experimental Psychology 52: 187–194.

49.

Nys

Content

(2012) Judgement of discrete and continuous quantity in adults: Number counts!. The Quarterly Journal of Experimental Psychology 65: 675–690.

50.

Patching

G. R.

Englund

M. P.

Hellström

Å.

(2012) Time-and space-order effects in timed discrimination of brightness and size of paired visual stimuli. Journal of Experimental Psychology: Human Perception and Performance 38: 915.

51.

Patro

Haman

(2012) The spatial–numerical congruity effect in preschoolers. Journal of Experimental Child Psychology 111: 534–542.

52.

Piazza

Pinel

Le Bihan

Dehaene

(2006) A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron 53: 293–305.

53.

Previtali

de Hevia

M. D.

Girelli

(2010) Placing order in space: The SNARC effect in serial learning. Experimental Brain Research 201: 599–605.

54.

Regolin

(2006) The case of the line-bisection: When both humans and chickens wander left. Cortex 42: 101–103.

55.

Reynvoet

Brysbaert

(1999) Single-digit and two-digit Arabic numerals address the same semantic number line. Cognition 72: 191–201.

56.

Rugani

Kelly

D. M.

Szelest

Regolin

Vallortigara

(2010) Is it only humans that count from left to right? Biology Letters 6: 290–292.

57.

Schneider

Eschman

Zuccolotto

(2002) E-Prime user’s guide, Pittsburgh, PA: Psychology Software Tools.

58.

Shaki

Petrusic

W. M.

Leth-Steensen

(2012) SNARC effects with numerical and non-numerical symbolic comparative judgments: Instructional and cultural dependencies. Journal of Experimental Psychology: Human Perception and Performance 38: 515.

59.

Trick

L. M.

Pylyshyn

Z. W.

(1994) Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision. Psychological Review 101: 80.

60.

Turconi

Campbell

J. I.

Seron

(2006) Numerical order and quantity processing in number comparison. Cognition 98: 273–285.

61.

Vallortigara

Rogers

L. J.

(2005) Survival with an asymmetrical brain: Advantages and disadvantages of cerebral lateralization. Behavioral and Brain Sciences 28: 575–588.

62.

Wood

Willmes

Nuerk

H.-C.

Fischer

M. H.

(2008) On the cognitive link between space and number: A meta-analysis of the SNARC effect. Psychology Science Quarterly 50: 489.

63.

Zebian

(2005) Linkages between number concepts, spatial thinking, and directionality of writing: The SNARC effect and the reverse SNARC effect in English and Arabic monoliterates, biliterates, and illiterate Arabic speakers. Journal of Cognition and Culture 5: 165–190.