Journal of Experimental Psychology: HumanPerception and Performance

SNARC Effects With Numerical and Non-NumericalSymbolic Comparative Judgments: Instructional AndCultural DependenciesSamuel Shaki, William M. Petrusic, and Craig Leth-SteensenOnline First Publication, January 30, 2012. doi: 10.1037/a0026729

CITATIONShaki, S., Petrusic, W. M., & Leth-Steensen, C. (2012, January 30). SNARC Effects WithNumerical and Non-Numerical Symbolic Comparative Judgments: Instructional And CulturalDependencies. Journal of Experimental Psychology: Human Perception and Performance.Advance online publication. doi: 10.1037/a0026729

SNARC Effects With Numerical and Non-Numerical SymbolicComparative Judgments: Instructional And Cultural Dependencies

Samuel ShakiAriel University Center of Samaria

William M. Petrusic and Craig Leth-SteensenCarleton University

With English-language readers in an experiment requiring pairwise comparative judgments of the sizesof animals, the nature of the association between the magnitudes of the animal pairs and the left or rightsides of response (i.e., the SNARC effect) was reversed depending on whether the participants had tochoose either the smaller or the larger member of the pair. In contrast, such a dependence of the directionof the SNARC effect on the form of the comparative instructions was not evident for pairwisecomparisons of numerical magnitude made by a similar group of participants. Furthermore, exactly thesame configuration of findings was obtained for a single group of Israeli-Palestinian right-to-left readingand writing participants, except that the spatial direction of the SNARC effects for both the animal-sizeand number comparisons were completely reversed. In a final experiment with English readers, SNARCeffects paralleling those for the animal-size comparisons were obtained for pairwise comparativejudgments involving the just-learned height relations between 6 imaginary individuals. As will bediscussed, such results serve to extend the generality of the SNARC effect far beyond the current modalview that it simply reflects culturally influenced, long-term learned associations between numericalmagnitudes and the locations on a fixed mental number line. The implications that these results have forboth the Proctor and Cho (2006) polarity correspondence view and the Gevers, Verguts, Reynvoet,Caessens, and Fias (2006) computational model of the SNARC effect will also discussed.

Keywords: mental number line, SNARC effect, spatial representation, cultural influences, readingdirection

Cognitive psychologists have made great strides, to date, withrespect to developing a greater understanding of the nature ofspatial representations in the brain as well as the nature of theassociations that exist between these representations and othermore conceptual, perceptual, and motor representations. One suchtype of association that has received quite a bit of attention is thatbetween numerical magnitudes and spatial codes for left and right.First discovered by Dehaene and colleagues (Dehaene, 1992; De-haene, Bossini, & Giraux, 1993; Dehaene, Dupoux, & Mehler,1990; which Dehaene et al., 1993, called SNARC for the “SpatialNumerical Association of Response Codes”), it is characterized by

a seeming association between smaller numerical magnitudes andleft spatial codes and, similarly, between larger numerical magni-tudes and right spatial codes.

The key empirical phenomenon through which this associationbecomes most evident is the finding that left-hand responses arequicker when responding to smaller numbers whereas right-handresponses are quicker when responding to larger numbers. The factthat this effect can occur even when the task itself does nottechnically require the retrieval of any actual magnitude informa-tion, as in the determination of a number’s even–odd parity(Dehaene et al., 1993), the monitoring of phonemes in the namesof presented numerals (Fias, Brysbaert, Geypens, & d’Ydewalle,1996), or orientation judgments for shapes with embedded irrele-vant digits (Fias, Lauwereyns, & Lammertyn, 2001), has promptedthe notion that the mere presentation of a number is enough for itscorresponding magnitude information to be automatically re-trieved and prime up the associated left or right spatial code. Themajor theoretical importance of such an association is that itspresence strongly implies that the quantitative representation ofnumerical magnitude has a spatial aspect akin to a mental numberline that orients from left to right (Dehaene et al., 1993).

Importantly, extensive work has been done to show that thiseffect does not simply represent a direct association betweennumerical magnitudes and left–right hand-based motor programs(but see both Muller & Schwarz, 2007, and Wood, Nuerk, &Willmes, 2006, for some recent evidence that such associationscan occur), given that it occurs in the same fashion for crossedresponse hands (Dehaene et al., 1993), for left or right pointingresponses using the same hand (Fischer, 2003; Gevers, Lammer-

Samuel Shaki, Department of Behavioral Sciences, Ariel UniversityCenter of Samaria, Ariel, Israel; William M. Petrusic and Craig Leth-Steensen, Department of Psychology, Carleton University, Ottawa, On-tario, Canada.

This work was supported by Natural Sciences and Engineering ResearchCouncil of Canada Individual Discovery Grants to both William M. Petru-sic and Craig Leth-Steensen. Earlier versions of this paper were presentedat the 17th Annual Meeting of the Canadian Society for Brain, Behavior,and Cognitive Science, Victoria, British Columbia, Canada, June 2007; theJoint Meeting of the Experimental Psychology Society and the Psycho-nomic Society, Edinburgh, Scotland, July 2007; the 23rd Annual Meetingof the International Society for Psychophysics, Tokyo, Japan, October2007; and the 31st Annual Meeting of the Cognitive Science Society,Amsterdam, The Netherlands, August, 2009.

Correspondence concerning this article should be addressed to WilliamM. Petrusic, Department of Psychology, Carleton University, Ottawa,Ontario K1S5B6, Canada. E-mail: bill_petrusic@carleton.ca

Journal of Experimental Psychology: © 2012 American Psychological AssociationHuman Perception and Performance2012, Vol. ●●, No. ●, 000–000

0096-1523/12/$12.00 DOI: 10.1037/a0026729

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tyn, Notebaert, Verguts, & Fias, 2006), for left or right occulomo-tor saccadic responses (Schwarz & Keus, 2004), and even for leftand right vocal responses (Gevers et al., 2010), but it does indeedrepresent an association with more centrally represented left–rightspatial location codes. It is also clear that SNARC effects are notexclusive to the visual presentation modality, as Nuerk, Wood, andWillmes (2005) have observed comparable SNARC effects withauditorily presented digits.

Generalizing the SNARC Effect to OrdinalMagnitudes

Another key line of research, however, has served to cast somedoubt on the notion of a mental number line, or at least one that issomehow unique to the representation of number magnitude. Thiswork has demonstrated that SNARC effects can also be obtainedfor stimuli from linear orderings. In this vein, Gevers, Reynvoet,and Fias (2003) found that for both order-relevant and order-irrelevant judgment tasks involving months of the year (i.e., judgewhether a presented month of the year comes before or after Julyor whether it does or does not end with the letter “R,” respec-tively), reaction times (RTs) were indeed faster for the left handthan the right hand when responding to the earlier months in theyear but faster for the right hand than the left hand when respond-ing to the later months. Similar results were also obtained byGevers et al. (2003), for order-relevant and order-irrelevant judg-ment tasks using letters of the alphabet as stimuli (although theSNARC effect was highly attenuated, but still significant, in thelatter case), and Gevers, Reynvoet, and Fias (2004), for judgmentsinvolving the days of the week as stimuli. These researchersconcluded their results provided clear evidence that “the mentalrepresentation of ordinal information is spatially defined and canaffect performance automatically” (Gevers et al., 2003, p. 294).Because ordinality is also a property of number representation (inaddition to cardinality), Gevers et al.’s (2003, 2004) results alsoraised the possibility that the SNARC effects observed for numberstimuli might also simply be ordinal based.

Quite recently, Previtali, de Hevia, and Girelli (2010; see alsoVan Opstal, Fias, Peigneux, & Verguts, 2009) also obtained theSNARC effect for judgments to stimulus items from an ordered listof nine words that their participants had just memorized. Namely,left-hand responses were faster than right-hand responses for itemswith positions earlier in the list and vice versa for later list itemsfor both order-relevant (i.e., before-after) and order-irrelevant (let-ter detection) judgment tasks. As remarked by Previtali et al.(2010), such results suggest “that a left-to-right spatial arrange-ment of information in long-term memory is the preferential wayto organize ordinal learning, at least in western cultures” (p. 604).

Symbolic Comparative Judgments andthe SNARC Effect

The initial focus of the experiments reported here was to deter-mine the extent to which SNARC effects might be found forcomparative judgments of animal sizes, given that such magni-tudes can be regarded as representing a naturally occurring, or-dered attribute continuum in long-term semantic memory. A long-standing question about knowledge of this sort concerns the natureof the mental representation that becomes activated by exposure to

the corresponding symbolic name referents (e.g., Moyer, 1973).Moreover, one key aspect of such an ordering is that, unlike formonths, days of the week, or letters, it is based on a real-lifeordering of animal sizes and, hence, has likely never actually beenrehearsed in any kind of a serial fashion. The presence of SNARCeffects for such judgments would represent a further generalizationof this effect beyond numerical magnitudes and would also implythat the mental representation of animal-size relations might in-deed contain spatial components. Although the presence of suchcomponents has periodically been hypothesized by symbolic com-parison researchers (e.g., Holyoak & Patterson, 1981, who pro-posed that such attributes might be represented along a mentalspatial array; although see also a further discussion of this proposalby Shoben, Eech, Schwanenflugel, & Sailor, 1989), no directevidence for them has really ever been provided.

To foreshadow that first set of results, SNARC-like effects canindeed be obtained when paired comparisons of animal sizes aremade. Interestingly, however, it was also the case that the left–right orientation of these effects depended on the direction of thecomparative instruction (i.e., to choose the smaller animal or tochoose the larger animal), indicating that the association of smalland large animal sizes with left and right spatial codes is not fixedbut, rather, is tied to the instructional context under which thecomparison is being made. Such flexibility in the nature of theassociation between small–large animal-size magnitudes and left–right spatial codes is rather inconsistent with the quite commonlyaccepted view of the underlying basis for the numerical SNARCeffects, namely, that they arise due to the presence of learnedenvironmental associations between small and large numbers (re-spectively) and left and right spatial locations (respectively; Chen& Verguts, 2010; Dehaene et al., 1993).

Nonetheless, although the comparison of pairs of presentedstimulus items is quite ubiquitous within the domains of bothpsychophysics and decision making, it is somewhat of an atypicalparadigm with respect to those generally used to examine SNARCeffects. Such paradigms have almost exclusively involved judg-ments made about single stimuli (e.g., is a presented digit eithersmaller or larger than 5?). Hence, our next focus was to determinethe extent to which those initial findings might have been depen-dent not upon the particular stimuli being compared (i.e., animalsizes) but upon the paired comparison task we used, by examiningthe nature of the SNARC effects obtained for comparisons of pairsof single-digit numbers.

Importantly, previous work by Shaki and Petrusic (2005), in-volving paired comparisons of both positive and negative single-digit numbers, suggests that SNARC effects obtained for pairednumerical magnitude comparisons should not, in fact, differ acrossthe two forms of the comparative instructions. For comparisonsinvolving pairs of positive numbers, SNARC-like effects involvingfaster left-hand responses to small number pairs and faster right-hand responses to larger number pairs were obtained by Shaki andPetrusic (2005) that were evident when participants had to choosethe smaller digit in a pair and also when they had to choose thelarger digit. For comparisons involving pairs of negative numbers,analogous SNARC-like effects were also found that were similarfor both forms of the comparative instruction but reversed indirection when the negative digits were presented in a blockedfashion compared with when they were intermixed with the pos-itive digits within blocks (note that Shaki & Petrusic, 2005, took

2 SHAKI, PETRUSIC, AND LETH-STEENSEN

that finding to indicate that number polarity was not processed inthe blocked condition).

The Influence of Cultural Conventions on theSNARC Effect

Another focus of the current experimental work was to deter-mine the extent to which the SNARC effects we obtained might bemediated by cultural factors, particularly with respect to readingand writing habits. Note that whereas the preferred direction ofreading and writing for North Americans and Europeans is fromleft to right, this preference is not the same for some other cultures.For example, in Arabic societies, reading and writing proceedsfrom right to left, and there is some evidence that the SNARCeffect is either attenuated or its direction reversed accordingly forsuch participants. For example, Dehaene et al. (1993, Experiment7) examined the SNARC effect in parity judgments for Iranianswho had lived in France as immigrants for varying amounts oftime. Although they did not find a significant SNARC (or reverseSNARC) effect in their data, a subsequent regression analysis didreveal that the size of the SNARC effect was larger for participantswho been away from Iran for a longer time, indicating that themore time the Iranians spent in France, presumably reading fromleft to right, the more likely they would show the typical SNARCeffect.

Zebian (2005) attempted to examine this issue using a numberof different groups of participants, one of which was made up ofArab monoliterate speakers residing in Lebanon. The task used byZebian (2005) was a modified version of one previously used toinvestigate the SNARC effect by Dehaene and Akhavein (1995)and involved determining whether a pair of numerals presentedvisually side by side were the same or different by providing “yes”or “no” vocal responses. The key result of interest was the direc-tion of difference in reaction time between the responses to thepairs (9 2) and (2 9). For the group of Arab monoliterates, re-sponding was faster for the pair (9 2) than for the pair (2 9),suggesting that the larger/left and smaller/right orientation of thenumbers in the (9 2) pair was indeed more consistent with themanner in which those numbers are represented spatially by thoseparticipants (note, as well, that a similar—but much smaller andnonsignificant—effect was also found in this study for a group ofArabic-English biliterates). Zebian (2005) referred this finding asa “Reverse SNARC” effect. One problem with this work, though,is that Zebian (2005) failed to find a significant standard SNARCeffect in this task for her group of undergraduate English monlit-erates. She attributed this null result possibly to the fact that theseparticipants might have easily discerned that the task could beperformed on the basis of perceptual similarity alone.

More recently, Shaki, Fischer, and Petrusic (2009) have found areversal of the SNARC effect for a group of Arabic-speakingPalestinian participants. In that study, three groups of partici-pants—Canadians, Palestinians, and Israelis—performed a paritytask. For the Canadians, who habitually read and write bothEnglish words and Arabic numbers from left to right, the standardSNARC effect was found. For the Palestinians, who read and writeboth Arabic text and Arabic-Indic numbers (also called EasternArabic numerals) from right to left, a reverse SNARC effect wasfound (i.e., faster right-hand responding to smaller numbers andfaster left-hand responding to larger numbers). Interestingly, for

the Israelis, who habitually read and write Hebrew words fromright to left but Arabic numbers from left to right, only quite smalland inconsistent SNARC effects were found, indicating that in-consistent directional habits associated with reading both text andnumbers might have served to dilute the SNARC effect for thoseparticipants.

Relatedly, Hung, Hung, Tzeng, and Wu (2008) obtained bothhorizontal and vertical SNARC effects for parity judgments madeby Taiwanese participants. Interestingly, these effects were nota-tion dependent in that the horizontal SNARC effect was onlyfound for Arabic digits (which are typically printed in a left-to-right horizontal fashion in Chinese text), whereas the verticalSNARC effect was found only for Chinese numerical words(which typically appear in top-to-bottom aligned vertical text).Moreover, the direction of the vertical SNARC effects that werefound were indeed consistent with the direction of Chinese readingand writing habit (i.e., faster responding with the top key forsmaller numbers and faster responding with the bottom key forlarger numbers). Hung et al. (2008) concluded that these resultssuggest that number-space mappings can indeed be quite flexibleand that the manner in which such mappings become orientatedmentally can be determined both by previous reading and writingexperiences as well as by the specific context in which the num-bers are encountered.

If cultural conventions are indeed a determining factor withrespect to the directionality of spatial-magnitude associations, thenthe direction of the SNARC effects obtained for a set of partici-pants who read and write from right to left should be completelyreversed from those observed for North American left-to-rightreading and writing participants. Importantly, a full reversal of thedirection of any instruction-dependent SNARC effects for animal-size comparisons would indicate that cultural conventions mightnot only affect spatial-magnitude associations that are specificallylearned (as is typically assumed to be the case for numbers) but,perhaps, also affect spatial thinking more generally.

Symbolic Comparative Judgments of Items From aRecently Learned Linear Ordering and the

SNARC Effect

In order to establish the generality of the instructional depen-dency of the SNARC-like effects obtained for the animal-sizecomparisons, the final focus of experimental work reported herewas to determine the extent to which such effects might be ob-tained for comparisons of items from an alternative type of sym-bolic magnitude ordering, namely, an artificially induced linearordering that is learned within the experimental setting itself. Forthis extension, the Leth-Steensen and Marley (2000) paradigm wasused whereby participants first learned the relative heights of siximaginary individuals in an initial training phase involving pre-sentation of only the pairs of stimuli that are adjacent within theordering. In a subsequent test phase, comparisons involving allpossible pairs of stimuli are performed.

Two important aspects of these comparison stimuli make theminteresting ones to study. First, because their ordering is notderived with respect to any actual perceptual referents, the mag-nitude information associated with them could be regarded asbeing almost exclusively ordinal. Second, like the serially learnedword-list stimuli used by Previtali et al. (2010), their ordering

3EXTENDING THE SNARC EFFECT

could not, in any way, be regarded as being overlearned. Hence, itcould be expected that any SNARC-like effects obtained for pairedcomparison of such stimuli might be highly susceptible to theinfluence of contextual factors such as the nature of the compar-ative instructions.

The Present Experiments

In summary, in our first experiment, we demonstrate that forpaired comparisons of animal sizes, the SNARC effects that arepresent actually manifest themselves quite differently over the twoforms of the comparative instructions. In contrast, in our secondexperiment, we show that for paired comparisons of numericalmagnitudes, the SNARC effects that occur are indeed quite similarover the two forms of the comparative instructions. In our thirdexperiment, we show that the pattern of SNARC effects obtainedin the first two experiments are, in fact, reversed for a group ofright-to-left reading and writing participants. In our fourth exper-iment, we demonstrate that the SNARC effects obtained for pairedcomparisons of recently learned, linearly ordered items are anal-ogous to those obtained in our first experiment for paired compar-isons of animal sizes. Finally, in the General Discussion section,we further discuss the implications that our present findings havewith respect to current theorizing about the SNARC effect, itscultural dependence, and the representation of numeric and non-numeric magnitude information. We also discuss the ramificationsthat these experimental results have for two of the more explicitlydeveloped available theories for the SNARC effect, namely, theGevers, Verguts, et al. (2006) computational model and the Proctorand Cho (2006) polarity correspondence view.

Experiment 1: Comparisons of the Remembered Sizesof Animals

The first experiment was conducted in order to determinewhether SNARC effects occur when participants make symboliccomparative judgments of animal size. As is standard for practi-cally all symbolic comparison studies, we employed the method-ology of paired comparisons here. Unlike any of those previousstudies, however, we also examined the differences between right-and left-hand RTs and the relation of those differences to pairmagnitudes when participants have selected the name correspond-ing to the smaller animal in the pair on some trials and the largeranimal on other trials.

Method

Participants. Twelve Carleton University students partici-pated in one 40-min session to satisfy course requirements. Allsubjects reported normal or corrected-to-normal vision.

Stimuli and design. Eight animal names, all five-letter wordsin English, printed in Times New Roman font (25, bold) definedthe stimulus set. Four of the animals were relatively small (snail,mouse, snake, goose) and four were relatively large (tiger, zebra,moose, whale), as determined from the size norms provided inPaivio (1975). Three pairs of relatively small animals were formed(snail-mouse, mouse-snake, snake-goose) and three pairs of rela-tively large animals (tiger-zebra, zebra-moose, moose-whale) werealso formed. Each pair in the design was presented in each of the

two possible left–right position orders, yielding 12 animal-namepairs.

The form of the comparative instruction (i.e., choose the smalleror choose the larger) was held constant within blocks, and thefactorial combination of the 12 stimulus pairs by two instructionswas replicated 10 times, preceded by three replications of practicetrials. Precisely, the same sequence of blocks of trials was used forthe practice trials as for the experimental trials for each participant.The participants were not aware of the partition into practice andexperimental trials. The order of presentation of the stimulus pairswithin blocks was random and different for each participant.

Procedure. Participants were tested individually in a dimly litroom, seated approximately 80 cm from the center of the videomonitor. Participants were told that the presentation of either theword “SMALLER” or “LARGER” served as a warning for thenext trial and was an instruction that indicated whether they wereto choose either the larger or the smaller animal in the presentedpair. After an additional 750 ms, the pair of animal names ap-peared while the comparative instruction remained on the screen.The participant’s task was to press the marked keyboard key (“A”on the left and “L” on the right) on the same side of the smaller (orlarger, respectively) member of the pair. The presentation of thestimuli and the comparative instruction were response terminated.The next trial began 1000 ms later. Participants were encouragedto respond quickly but accurately. The session included severalplanned breaks, which ended with the participants’ decision tocontinue.

The pairs of stimuli appeared at the respective centers of the leftand right hemifields on the white background of a 17-in (43-cm)View Sonic video monitor and the instructions, printed in Davidfont (30, bold), appeared at the center of the upper third of thescreen. Event sequencing, randomization of trials and instructions,and recording of responses and response times was under thecontrol of SuperLab software run on a Pentium III microprocessor.

Results

The findings for this experiment and the subsequent experi-ments are presented in three sections. The first two present RTanalyses and the third presents analyses of error rates. For eachparticipant, the dependent variable was either the mean RTs forcorrect responses or the percent errors. For both dependent vari-ables, ANOVAs were conducted with the two instructions, the sixdigit pairs, and hand of response (which covaries exactly withleft–right pair presentation order) as within-participant factors. Inthis experiment and the others, we focus on the outcomes of theANOVAs with RTs, since error rates were generally low and theeffects evident with RTs were, for the most part, also present withthe error data. We do provide the mean overall error rates and adetermination of whether speed–accuracy trade-offs occurred. Forthis experiment and the subsequent experiments, Huynh-Feldtepsilon adjustment of degrees of freedom is used, although thedegrees of freedom and mean standard errors (MSEs) indicated inthe text are those defined by the design. Level of significance forall tests here, and in the following three experiments, is set at 0.05.

RT analyses. The ANOVA with the two instructions, the sixstimulus pairs, and hand of response serving as within-participantfactors revealed a significant main effect of pair. The main effectof pair was reliable, F(5, 115) � 10.39, MSE � 161796; the pairs

4 SHAKI, PETRUSIC, AND LETH-STEENSEN

involving the name of the smallest and the largest animals had thefastest RTs (i.e., an endpoint effect; Shoben et al., 1989). RTs werefaster with the instruction to select the name of the smaller of a pairof small animals than the larger, and conversely with the instruc-tion to select the name corresponding to the larger of the twoanimals, F(5, 115) � 8.39, MSE � 78301 (i.e., a semantic con-gruity effect; Shaki, Leth-Steensen, & Petrusic, 2006; Petrusic,Shaki, & Leth-Steensen, 2008).

The overall interaction between stimulus pair and hand of re-sponse, which is closely associated with the standard SNARCeffect, was not statistically reliable, F(5, 115) � 2.02, MSE �71657. Rather, it was the linear component of the three-wayinteraction involving stimulus pair, hand of response, and instruc-tion that was reliable, F(1, 115) � 33.82, MSE � 18587. Indeed,as is evident in the plots in Figure 1, SNARC-like effects werepresent with the smaller instruction. However, with the largerinstruction, reverse SNARC-like effects occurred.

Individual participant linear regression analyses. We con-ducted repeated measures regression analyses as outlined in Lorchand Myers (1990), separately for each instruction. In each case, wefirst obtained standardized beta regression coefficients for eachparticipant with the SNARC index, RT(Right) � RT(Left), as thedependent variable and ordinal pair magnitude as the predictor. Wethen tested the two-tailed hypothesis that the mean of theseweights differed from zero using the t-distribution.

With the smaller instruction, the mean of the standardizedregression coefficients (M � �0.50, SD � 0.27) differed reliablyfrom zero, t(11) � �6.50, p � .0001. Indeed, for 12 of the 12participants, the slope of the regression line was negative (indicat-ing that the right minus left RT difference decreases, eventuallybecoming negative, as the pairs increase in magnitude). On theother hand, with the larger instruction, the slope was positive for 7of the 12 participants, and although the mean of the standardizedregression coefficients (M � 0.20, SD � 0.39) was positive, thismean was only marginally significantly different from zero, t(1) �1.82, p � .097.

Error analyses. The overall error rate was 3.96%, and thecorrelation between error rate and mean RT over the 24 cells of the

design, defined by the factorial combination of instruction, stim-ulus pair, and hand, was r � .358, F(1, 22) � 3.31, p � .097. Thus,there was no speed–accuracy trade-off.

Discussion

This experiment demonstrates that when making relative sizejudgments between the members of pairs of animal names,SNARC-like effects that reflect the presence of an associationbetween the relative magnitude of the whole pair on the continuumand left and right side responses can indeed occur. However, theorientational nature of this association differed across the twoforms of the comparative instruction, such that left-hand responseswere significantly facilitated when choosing the smaller of a pairof small animals but right-hand responses were significantly facil-itated when choosing the smaller of a pair of large animals. Incontrast, when choosing the larger of a pair of animals, thesesmall–large and left–right associations tended to reverse (note thatalthough this latter effect did not reach conventional levels ofsignificance in the standardized regression analyses, it is quiteclearly and systematically evident in the right minus left mean RTdifferences across the first five pairs in Figure 1).

Hence, such results provide evidence for the fact that long-termsemantic knowledge of the continuum of animal sizes could in-volve some form of spatial organization. Moreover, they alsosuggest that the retrieval of magnitude information regarding thesizes of specific pairs of animals could occur in the form of aspatially based mental representation whose left–right directionalorientation dynamically depends on the direction of the compari-son. Namely, for the instruction to choose the smaller animal, theretrieved representation of this continuum seems to entail a mentalprojection of the smaller pairs of animals on the left and the largeranimals on the right, whereas for the instruction to choose thelarger animal, for most individuals, the retrieved representation ofthis continuum seems to involve a mental projection of the largerpairs of animals on the left and the smaller animals on the right.Note that such spatial projections would arise naturally from thenotion that the participants tend to demark this spatial representa-tion by regarding the very left-hand side of it as a point ofreference that is defined by the form of the comparative instruc-tion.

Such representational flexibility is indeed quite reminiscent ofthat found in a study performed by Bachtold, Baumuller, andBrugger (1998) that has often been cited in the SNARC-basedliterature. In this study, participants were instructed to imagineeither an actual 12-unit ruler or an actual clock face while theywere performing a speeded decision task. When imagining theruler, this task involved deciding whether the distance representedby a presented number was shorter or longer than 6 units and,indeed, a SNARC effect was found in the RTs. In contrast, whenimagining the clock face, this task involved deciding whether thetime represented by a presented number was earlier or later than 6o’clock and, now, a reverse SNARC effect was obtained (i.e.,faster right-hand than left-hand responses to the smaller numbersand faster left-hand than right-hand responses to the larger num-bers). In the current work, however, note that such representationalflexibility was implicitly induced upon the exact same attributecontinuum simply by changing the form of the comparative in-struction (as opposed to being explicitly induced in Bachtold et al.,

Figure 1. Mean RTs with the left hand subtracted from mean RTs withthe right hand (SNARC index), plotted as a function of stimulus pair witheach instruction for the animal-size symbolic comparisons of Experiment1. In-laid regression equations refer to regressions ran directly on the groupmean RT difference data points shown in this plot.

5EXTENDING THE SNARC EFFECT

1998, by instructing participants to make use of quite dissimilarimagery representations).

Note, as well, that it was the nature of the paired comparisonmethodology used here that allowed us to observe this represen-tational flexibility. Namely, the types of magnitude- or order-relevant comparison tasks that are typically used to examine theSNARC effect involve the presentation of a single stimulus, whichmust then be compared to some other fixed standard within therange of possible stimuli (invariably the middle stimulus) byproviding either explicit smaller–larger or earlier–later responses.For these cases, the directional orientation of any underlyingspatially based mental representation of the corresponding magni-tude information that might then be retrieved would presumablyrepresent the preferred default orientation with respect to thepositioning of smaller/earlier and larger/later stimuli to either theleft or right sides.

Experiment 2: Comparisons of Numerical Magnitude

The previous experiment was clear in demonstrating a novelinstruction-dependent SNARC-like effect in the comparative judg-ment of animal sizes. However, the use of both the paired com-parison methodology and animal magnitudes as the relevant stim-ulus dimension is somewhat unusual with respect to practically allprevious investigations of the SNARC effect. Hence, in this sec-ond experiment, it is important to determine whether or not similarresults might be obtained using this same method for symboliccomparisons of numerical magnitude. In line with some previouswork performed by the first two authors (Shaki & Petrusic, 2005),we did not expect to find a dependency here of any SNARC effectson the direction of the comparative instruction. A further purposefor this study, though, was also to determine how the manner inwhich the comparative instructions are presented might influencethe SNARC effect. In particular, using a within-participants de-sign, in one condition, the instructions were randomly varied fromtrial to trial (i.e., the mixed instruction condition), and in the othercondition, they remained constant over a block of trials (i.e., theblocked instruction condition).

Method

Participants. Twelve Carleton University students partici-pated in a 50-min session to satisfy course requirements. Allsubjects reported normal or corrected-to-normal vision.

Stimuli and design. Eight digits, printed in Times NewRoman font (25, bold) defined the stimulus set. Four digits wererelatively small (0, 1, 2, 3), whereas the other four digits wererelatively large (6, 7, 8, 9). The digits were paired within catego-ries. This arrangement produces three relatively small digit pairs(0–1, 1–2, 2–3) and three relatively large digit pairs (6–7, 7–8,8–9). Each pair in the design was presented in each of the twopossible left–right position orders, yielding 12 digit pairs.

The two forms of the comparative instructions (i.e., choose thesmaller or choose the larger) occurred equally often and wereconstant over a block in one condition (i.e., blocked), and wereintermixed, occurring equally often and in random order, in asecond condition (i.e., mixed). This factorial combination of the 12stimulus pairs, two instructions and two instruction presentationconditions was replicated 10 times, preceded by three replications

of practice trials. Both the order in which the conditions werepresented (blocked first or mixed first) and the order in which thetwo instructions were used in the blocked condition (smaller first,then larger; or larger first, then smaller) were counterbalanced. Allother aspects of the stimuli and design were the same as forExperiment 1.

Procedure. The procedure was the same as that reported forExperiment 1.

Results

For each participant, the dependent variable was either the meanRTs for correct responses or the percent errors. For both dependentvariables, ANOVAs were conducted with condition (blocked vs.intermixed), the two instructions, the six digit pairs, and hand ofresponse as within-participant factors.

RT analyses. The ANOVA revealed that the stimulus pairsdiffered reliably, F(5, 55) � 16.39, MSE � 2777966, with RTsgenerally increasing as the pairs increased in magnitude, reflectingthe fact that numerical magnitude comparisons are based on rela-tive magnitudes (analogous to Weber’s Law). The Pair x Instruc-tion interaction was also reliable, F(5, 55) � 5.98, MSE � 5127,as a consequence of the robust semantic congruity effects that arealso typically obtained with numerical magnitude comparisons.RTs were faster with the instruction to select the smaller digit thanthe larger when the digits were relatively small, and converselywhen the digits were relatively large (cf., Banks, Fujii, & Kayra-Stuart, 1976).

More importantly, turning now to the effects involving the handof the response, as the plots in Figure 2 show, it is clear that RTsare generally faster with left-hand responses than with right-handresponses for the small number pairs, and generally faster with theright hand than with the left hand for the relatively large numberpairs. Hence, in contrast to the SNARC-like effects found previ-ously for the symbolic animal size comparisons, the interactioninvolving stimulus pair and hand is now statistically reliable, F(5,55) � 7.69, MSE � 2980. Importantly, as is also evident in theplots in Figure 2, the obtained SNARC effects did not depend oninstruction, F(5, 55) � 2.08, MSE � 5478, p � .125, nor whetherthe instructions were blocked or randomly mixed, F(5, 55) � .70,MSE � 2150, p � .529.

Individual participant analyses. As in Experiment 1, stan-dardized regression coefficients were obtained for each participant,separately for each instruction and for each instruction presenta-tion condition (i.e., blocked and mixed). With the instruction toselect the smaller number (after combining the data over instruc-tion presentation conditions), the mean standardized beta weight,M � �0.68, with standard deviation, SD � 0.34, differed reliablyfrom zero, t(11) � �3.72, p � .0003, affirming the clear presenceof a SNARC effect with this instruction. Similarly, comparableSNARC effects were also obtained with the instruction to selectthe larger number: M � �0.52, SD � 0.23 and t(11) � �7.79, p �.00001. When the instructions were blocked (after combining thedata over instructions), reliable SNARC effects were obtained:M � �0.51, SD � 0.36, t(11) � �4.90, p � .0001. ComparableSNARC effects were obtained when the two instructions wererandomly intermixed: M � �0.47, SD � 0.28, t(11) � �5.79, p �.0001.

6 SHAKI, PETRUSIC, AND LETH-STEENSEN

Error analyses. The overall error rate was 2.49%, and thecorrelation between error rate and mean RT over the 48 cells of thedesign defined by the factorial combination of condition, instruc-tion, stimulus pair, and hand was r � .302, F(1, 46) � 4.62, p �.023. Thus, there was no speed–accuracy trade-off.

Discussion

In stark contrast to the results of Experiment 1, but analogous tothose of Shaki and Petrusic (2005), SNARC-like effects that wereconsistent with the standard directional orientation of such effects(i.e., faster left-hand responses for small stimulus pairs and fasterright-hand responses for large stimulus pairs) were obtained inExperiment 2 for size comparisons of positive digit pairs thatdepended neither on the direction of the comparative instructionnor on how the instructions were presented (i.e., either varyingrandomly for trial or fixed over a block of trials). As such, theseresults indicate that for number magnitudes, unlike for animalsizes, the association of small and large magnitudes with left andright response codes, respectively, indeed seems to be a fairly rigidproperty of the mental representation of numerical magnitudeinformation. Importantly, such results also clearly indicate that thepresence of the instruction-dependent SNARC-like effects for theanimal-size comparisons in Experiment 1 was not simply a con-sequence of the use of the paired comparison methodology.

Experiment 3: Hebrew and Arabic Language Readers

The results of the first two experiments suggest (a) that semanticrepresentations of the magnitudes of both numerical and non-numerical continua have spatial components, and (b) that thedirectional nature of the association of small and large magnitudeswith left and right spatial locations is much more ingrained fornumerical magnitude. The pervasiveness of the small/left andlarge/right associations for numbers is indeed highly consistent

with the view that they may be highly overlearned on the basis ofboth mathematical conventions and culturally determined readingand writing habits (Dehaene et al., 1993). In contrast, the depen-dence of these associations on the direction of the comparativeinstruction for the animal-size comparisons implies a degree ofrepresentational flexibility that is consistent with the notion thatsuch representations are derived in a much more ad hoc manner inorder to help “problem solve” the task of determining the relativesizes of a given pair of animals. Even so, the directionality of thespatial reference frames that might be induced by such compari-sons still seem to flow rightward from a left-sided point of refer-ence that is determined by the form of the comparative instruction(i.e., from left-to-right). In this sense, such directionality is stillconsistent with the culturally determined reading and writing hab-its of the participants used in Experiment 1.

In order to determine whether cultural factors are indeed influ-encing the directionality of any spatial representations being in-duced by each of these comparison tasks, in this third experimentwe had a group of Hebrew and Arabic readers (who have not readEnglish or French text) perform paired magnitude comparisons ofboth single-digit numbers and animal sizes. Because the directionof reading and writing for these participants is from right to left,we expected to find SNARC-like effects orientated in the oppositedirection as those obtained for the Canadian participants in ourfirst two experiments. Additionally, a further important aspect ofthe design of this study was to extend the generality of the findingsof the first two experiments to conditions in which both tasks areperformed by all participants in a fully within-participants fashion.

Method

Participants. Seven Israelis and 5 Palestinians (19 to 26years old) participated in two 30-min sessions. All participantsread Hebrew or/and Arabic only and reported a minimal exposure

Figure 2. Mean RTs with the left hand subtracted from mean RTs with the right hand (SNARC index) for theblocked and mixed instructional presentation conditions (after combining the data over instruction) in Panel Aand for each instruction in Panel B (after combining the data over instruction presentation condition), plotted asa function of stimulus pair (in terms of the maximum of the two numbers compared) in Experiment 2. In-laidregression equations refer to regressions ran directly on the group mean RT difference data points shown in thisplot.

7EXTENDING THE SNARC EFFECT

to any left-to-right language. In addition, all subjects reportednormal or corrected-to-normal vision.

Stimuli and design. Eight digits and eight animal names, allthree-letter or four-letter words in Hebrew or Arabic, printed inDavid font (25, bold) defined the two stimulus sets. Four digitswere relatively small (0, 1, 2, 3), whereas the other four digits wererelatively large (6, 7, 8, 9). As well, four names were of relativelysmall animals (ant, bee, mouse, rat), and the other four names wereof relatively large animals (dog, pig, cow, elephant), each printedin Hebrew for the Israeli participants and in Arabic for the Pales-tinians. The set of stimulus comparison pairs was comprised ofthree relatively small digit pairs (0–1, 1–2, 2–3) and three rela-tively large digit pairs (6–7, 7–8, 8–9). As well, the animal setincluded three relatively small animal pairs (ant-bee, bee-mouse,mouse-rat), and three relatively large animal pairs (dog-pig, pig-cow, cow-elephant). Each pair in the design was presented in eachof the two possible left–right position orders, resulting in 12 digitpairs and 12 animal names pairs.

The two forms of the comparative instructions (“Smaller” and“Larger”) occurred equally often and were randomly changed fromtrial to trial. This factorial combination (the 12 stimulus pairs, twoinstructions and two stimulus type conditions) was replicated sixtimes, preceded by a single replication of practice trials. Theparticipants were not aware of the partition into practice andexperimental trials. The order of presentation of the stimulus pairswithin blocks was random and different for each participant. Theorder of the two sessions (the numbers session and the animalssession) was counterbalanced, and the second session was per-formed 3 to 5 days after the first one.

Procedure. Participants were tested individually in a dimly litroom, seated approximately 60 cm from the center of the videomonitor. Participants were told that the presentation of eitherthe word “SMALLER” or “LARGER”

served as a warning for the next trial and was aninstruction that indicated whether they were to choose either thesmaller or the larger stimulus (digit or animal) in the pair. After anadditional 750 ms, the pair of digits or animal names appearedwhile the comparative instruction remained on the screen. Theparticipant’s task was to press the key (“A” on the left and “L” onthe right) on the same side of the smaller (or larger, respectively)member of the pair. The presentation of the stimuli and thecomparative instruction were response terminated. The next trialbegan 1000 ms later. Participants were encouraged to respondquickly but accurately. Each 30-min session included a singleplanned break, which ended with the participant’s decision tocontinue.

The pairs of stimuli (either digits or animal names) appeared atthe respective centers of the left and right hemifields on the whitebackground of a 17-in (43-cm) View Sonic video monitor and theinstructions, printed in David font (30, bold), appeared at thecenter of the upper third of the screen. Event sequencing, random-ization of trials and instructions, and recording of responses andresponse times was under the control SuperLab run on a PentiumIII microprocessor.

Results for the Number Comparisons

RT analyses. An ANOVA with pair, instruction, and hand aswithin-participant factors revealed a significant linear component

for the pair factor, with RTs generally increasing as the digitsbecame larger, F(1, 11) � 5.59, MSE � 52553. The linear com-ponent of the Hand x Pair interaction was reliable, F(1, 11) �10.27, MSE � 23711, affirming the presence of a reliable SNARCeffect. As is evident from the plots in Figure 3, the SNARC effectwas indeed reversed for these participants. Moreover, as for theEnglish participants in Experiment 1, the SNARC effect here wasnot instruction dependent, and the three-way interaction involvingpair, hand, and instruction did not attain statistical significance,F(5, 55) � 0.59, MSE � 70332.

Individual participant analyses. In accord with theANOVA results for the Hand x Pair interaction, individual partic-ipant regression analyses with the smaller instruction revealed thatthe mean of the standardized regression coefficients (M � 0.245,SD � 0.394) differed from zero in a marginally significant way,t(11) � 2.16, p � .054. With the larger instruction, the meanstandardized regression coefficient (M � 0.300, SD � 0.391) wassignificantly different from zero, t(11) � 2.31, p � .041. Indeed,10 of 12 standardized regression coefficients were positive witheach instruction.

Error analyses. The mean error rate was 3.98%, and thecorrelation between mean RT and error rate was r � .574, F(1,22) � 10.84, p � .003. Thus, as in the earlier experiments, therewas no speed–accuracy trade-off.

Results for the Animal-Size Comparisons

RT analyses. An ANOVA with the same within-participantfactors revealed a significant linear component of the pair by handby instruction three-way interaction, F(1, 11) � 13.19, MSE �77857. As is clear from the plots in Figure 4, an instruction-dependent SNARC effect was obtained which was the completereverse of that found in Experiment 1 for the English-languageparticipants. As well, the main effect of pair was significant, F(5,55) � 4.57, MSE � 31621, although it was not readily interpre-

Figure 3. Mean RTs with the left hand subtracted from mean RTs withright hand (SNARC index), plotted as a function of stimulus pair (in termsof the maximum of the two numbers compared), with each instruction forthe numerical digit comparisons of Experiment 3. In-laid regression equa-tions refer to regressions ran directly on the group mean RT difference datapoints shown in this plot.

8 SHAKI, PETRUSIC, AND LETH-STEENSEN

table. As expected, the interaction between pair and instructionwas also significant, F(1, 55) � 3.93, MSE � 548940, reflectingthe presence of the semantic congruity effect.

Individual participant analyses. With the smaller instruc-tion, the mean standardized regression coefficient was M � 0.254(SD � 0.279) which was significantly different from zero, t(11) �3.16, p � .009. On the other hand, with the instruction to choosethe name of the larger animal, the direction of the SNARC effectreversed. The mean standardized regression coefficient was M ��0.300 (SD � 0.391) which was also significantly different fromzero, t(11) � �2.66, p � .022.

Error analyses. The overall error rate for these animal-sizecomparisons was 3.99%. In contrast with the earlier experiments,longer RTs did not accompany higher error rates. Rather, there wasno reliable relationship between mean RT and mean error rate andthe correlation between these two measures was negligible (r �.128, F � 1.00). Nevertheless, because this correlation was notnegative, there was still no speed–accuracy trade-off.

Discussion

In accordance with the findings of Experiments 1 and 2,SNARC-like effects were indeed found in this study. Also inaccord with those previous two experiments, the directions of theseeffects were dependent on the smaller and larger forms of thecomparative instruction for the animal-size comparisons but notfor the number comparisons. Hence, this study clearly indicatesthat such results can still be obtained under conditions in which allparticipants have performed both types of comparison tasks.

Most importantly, with respect to the main purpose for runningthis third study, the directional nature of these effects was com-pletely reversed for the present group of Israeli-Palestinian partic-ipants who read and write from right to left. Hence, such resultsprovide further evidence for the fact that cultural factors do indeedseem to have role to play in determining the directional nature inwhich SNARC effects become manifested for decision tasks in-

volving both numerical magnitudes and, now (for the first time),non-numerical magnitudes as well.

Experiment 4: Comparisons of Items From anArtificial Linear Ordering

In terms of the body of available literature on the SNARC effect,the instruction-dependent SNARC-like effects obtained for theanimal-size comparisons in our Experiment 1 are extremely novel.Hence, it is important to replicate this instructional dependency forcomparisons of items from another type of non-numerical order-ing. In this vein, note that one reason for the presence ofinstruction-dependent SNARC effects for remembered animalmagnitudes, but not numerical ones, could be that the ordering ofanimal sizes is much less well learned than is the ordering ofnumber magnitudes, If so, similar instruction-dependent SNARC-like effects should indeed be expected to occur for comparisons ofother types of ordered symbolic magnitudes, as long as theirordering is not overlearned. Hence, in this final study, we exam-ined the pattern of SNARC effects obtained for size comparisonsof symbolic items taken from an artificially induced, six-termlinear ordering that has just been learned by the participants (i.e.,the same paradigm used by Leth-Steensen & Marley, 2000).

Method

Participants. Forty-five introductory psychology studentsfrom the University of Illinois with normal or corrected-to-normalvision participated (individually) in a single 90-min session forcourse credit.

Stimuli and apparatus. The experiment was programmedand run using MEL v2.0 on a 486 computer. During each trial, theinstruction for comparison (i.e., “Taller?” or “Shorter?”) was firstpresented at the top of the screen, after which a pair of three-letternames was presented side by side in the center of the computerscreen (in MEL System48 font size). Responses were made bypressing either the “Z” or “/” response keys on each side of thebottom row of the computer keyboard (marked in yellow).

Each name was a label that stood for an imaginary person. Six“people” were used, all of whom were assumed to differ in height.Four different orderings of these names were derived a priori.From tallest to shortest, the four orderings were (a) Pat, Bob, Ted,Dan, Jim, and Mel, (b) Dan, Ted, Jim, Pat, Mel, and Bob, (c) Ted,Dan, Mel, Bob, Pat, and Jim, and (d) Bob, Mel, Dan, Jim, Ted, andPat. These orderings were assigned randomly to participants.

Procedure. The first part of the experiment was a learningphase, in which the participants were presented with each of thefive comparison pairs consisting of the stimuli that were adjacentto each other in the relevant ordering (i.e., the Split 1 pairs). Eachcomparison trial began with a blank screen for 1000 ms. Before apair of names appeared, the relevant comparative instruction(“Taller?” or “Shorter?”) was displayed for 1000 ms just above aplus sign, which acted as a temporary fixation point for thelocation of the name stimuli. On each comparison trial, the par-ticipants were presented with two of the six names and had tochoose which person (i.e., the name presented on the left or thename presented on the right) was either the shorter or, respectively,the taller of the pair. They were asked to use the index fingers ontheir left and right hands to make their responses.

Figure 4. Mean RTs with the left hand subtracted from mean RTs withthe right hand (SNARC index), plotted as a function of stimulus pair, witheach instruction for the animal-size comparisons in Experiment 3. In-laidregression equations refer to regressions ran directly on the group mean RTdifference data points shown in this plot.

9EXTENDING THE SNARC EFFECT

The participants were not expected to know the relative heightsof the stimuli at the very start of the experiment and, hence, wouldinitially be guessing. After each response in the learning phase,though, feedback was immediately provided on the computerscreen that indicated whether the response had been correct orincorrect and that also showed the correct name for that compar-ison trial. This feedback helped the participants eventually learnwhich person was the taller and which was the shorter in each pair.They were able to examine this feedback for as long as theywanted and could initiate the next trial with a press of the spacebar. Both the comparative instruction and the pair of names re-mained on the screen throughout the trial (including during thepresentation of the feedback).

Learning trials were presented in blocks of 20 trials (i.e.), fivepairs with each of the two instructions in each of the two left–rightspatial presentation of the pairs, with breaks after the first twolearning blocks only. In the first two blocks, the pairs werepresented in an ordered fashion and then presented randomlywithin the remaining blocks. The learning phase took anywherefrom 15 to 35 min to perform and was completed when theparticipant had been correct for a full block of 20 learning trials.Two participants who did not reach this learning criterion within10 blocks of learning trials were given a shorter version of theexperiment by the experimental program, and their results were notincluded in the following analysis.

The second part of each experiment was the test phase, and theprocedure for it was essentially the same as that of the learningphase except for the fact that (a) all of the 15 possible pairs ofnames were now included in the stimulus set, and (b) no feedbackwas provided. Each block of the test phase contained 120 random-ized comparison trials (made up of the 15 pairs, presented twice,with each instruction in each left–right stimulus presentation or-der). The participants were given an optional rest period betweeneach block and they were asked to be accurate with each decisionwithout taking too much time to respond.

It must also be noted that the data used for this study actuallycame from three separate experiments. In each experiment, partic-ipants performed, in a counterbalanced fashion, two blocks of testphase trials in the standard fashion (i.e., exactly as just described)but also two other blocks that manipulated the presentation of theinstruction (e.g., flashing it briefly or presenting it either after orsimultaneously with the stimulus pair).

Results

Only the RT data for correct responses to the Split 1 pairs in thetwo blocks of test phase trials performed in the standard fashionwere analyzed. Unlike our previous three experiments, becausecomparisons of symbolic stimuli from recently learned linearorderings of this nature can be highly susceptible to the presenceof a number of really long outlying RTs, any RTs for a participantthat were more than 3 SDs above their mean for each Split 1 pairwere removed before running the analysis (31 RTs in total). Theindependent variables in the ANOVA were instruction type (twolevels: shorter, taller), pair (five levels), and response side (twolevels: left, right). In the ANOVA results, the main effect of pairwas significant, F(4, 176) � 44.26, MSE � 669045, where theoverall mean correct RTs for each of the increasing pairs (1, 2), (2,3), (3, 4), (4, 5), and (5, 6) were 1494, 2131, 2157, 1836, and 1225ms, respectively. The interaction between instruction type and pairwas also significant, F(4, 176) � 16.28, MSE � 157829, due to thepresence of a robust semantic congruity effect in these data (i.e.,faster RTs for shorter pairs when choosing the shorter individualand for taller pairs when choosing the taller individual).

Finally, and most importantly, the linear trend of the three-wayInstruction Type � Pair � Response Side interaction was signif-icant, F(1, 44) � 4.32, MSE � 144652. This interaction occurredbecause, when the instruction was to choose the shorter, there wasa trend for correct left-hand responses to be faster than correctright-hand responses for relatively short pairs, and correct right-hand responses to be faster than correct left-hand responses forrelatively tall pairs (which is analogous to the standard SNARCeffect found for number comparisons). On the other hand, whenthe instruction was to choose the taller, there was a trend forcorrect left-hand responses to be faster than correct right-handresponses for relatively tall pairs, and correct right-hand responsesto be faster than correct left-hand responses for relatively shortpairs (i.e., a reversal of the SNARC effect). These effects areshown in Figure 5.

Individual participant linear regression analyses. With theshorter instruction, the mean of the standardized regression coef-ficients (M � �0.094, SD � 0.482) did not differ reliably fromzero, t(44) � �1.309, p � .197, where the slope of the regressionline was negative for 25 of the 45 participants. With the tallerinstruction, the slope was positive for 30 of the 45 participants,

Figure 5. Right-hand minus left-hand mean correct RT differences for each of the Split 1 pairs under each formof the comparative instruction in Experiment 4.

10 SHAKI, PETRUSIC, AND LETH-STEENSEN

although the mean of the standardized regression coefficients(M � 0.099, SD � 0.517) was also not significantly different fromzero, t(44) � 1.288, p � .205. Nonetheless, a paired t test didindicate that the standardized betas were significantly differentfrom each other, t(44) � �1.786, p � .081, but only marginallyso. Note, though, that a corresponding analysis of the unstandard-ized regression coefficients indicated that whereas they still did notsignificantly differ from 0 for the shorter instruction, t(44) ��1.567, p � .124 (M � �44.33, SD � 189.76), they now did forthe taller instruction, t(44) � 2.303, p � .026 (M � 68.37 SD �199.17). Moreover, the paired t test was also now significant,t(44) � �2.671, p � .011.

Error Analyses

The overall error rate was 4.80%. The quadratic trend of the pairmain effect was significant, F(1, 44) � 4.81, p � .034, MSE �.133 (where the error rates were 3.4, 5.1, 7.5, 4.9, and 3.0% for theshortest to the tallest increasing pairs, respectively). The correla-tion between error rate and mean RT over the 20 cells of the designdefined by the factorial combination of instruction, stimulus pair,and hand was r � .772, F(1, 18) � 26.58, p � .001, thus indicatingthat there was no speed–accuracy trade-off.

Discussion

In this final study, instruction-dependent SNARC-like effectswere found in comparison responses to pairs of items from anartificially induced six-term linear ordering. Although such a resultonly reached conventional levels of significance for the regression-based analyses involving unstandardized regression coefficients,note that in studies of the SNARC effect, such analyses aretypically only performed on unstandardized coefficients (Fias &Fischer, 2005).

Hence, we have now demonstrated that such paired-comparison-based SNARC effects can occur for comparison tasks involvingtwo quite dissimilar types of ordered symbolic stimuli that couldbe regarded as covering a fairly wide swath of possible longer-versus shorter-term attribute-based semantic memory representa-tions. As we have hypothesized, the commonality between the twotypes of representations seems to be that, unlike for numbers, andeven months or days of the week, the representation of order forboth of these cases is not highly overlearned (particularly in anyspecific spatial, temporal, or sequential fashion). As such, it seemsas if any potential spatial characterization of such orderings mightessentially be constructed “on the fly” during the magnitude com-parison task, rendering them susceptible to the influences of thecontext signaled by form of the comparative instruction (althoughnote that for the latter type of artificially induced ordering, theformation of an explicit spatial characterization for it has some-times been regarded as a key aspect of the manner in which suchan ordering might be learned even when, as in this fourth study,participants are never actually perceptually exposed to the wholesequence of symbolic items ordered horizontally in space; Ho-lyoak & Patterson, 1981; Trabasso & Riley, 1975; Sternberg,1980).

General Discussion

In the present set of experiments, the nature of the SNARC-likeeffects that can occur for paired comparisons of symbolic stimulus

items from both numerical and two different kinds of non-numerical magnitude continua were examined. The first mainresult was that SNARC effects were indeed observed across allfour studies, indicating that during the course of processing all ofthose comparisons, left–right spatial location information was alsolikely being retrieved (or, perhaps, generated). The second mainresult was that specific manner in which the association betweenthe left or right responses and the pair magnitudes became mani-fested in the RT results depended on the form of the comparativeinstruction for comparisons of non-numerical magnitudes but notfor comparisons of numerical magnitudes. This second result in-dicates that the directional nature of such associations seems to bean integral part of the long-term representation of numerical mag-nitude information but not of either the long-term or the moreshorter-term representations of the two types of non-numericalmagnitude information examined here (where in the latter twocases, it seems that the directional nature of such spatial informa-tion arises simply as a consequence of the directional manner inwhich the pair magnitude is being processed at the time). The thirdmain result was that both the instruction-dependent andinstruction-independent SNARC effects observed here were quitedramatically moderated by the conventional direction of readingand writing of the participants. That is, the direction of theseeffects was shown to be completely reversed for right-to-leftreaders in comparison to left-to-right readers. Such a result servesto further establish the presence of a strong cultural dependency onwhat is essentially a spatially based effect.

Implications for the Nature of the Representation ofNumerical and Non-Numerical Symbolic MagnitudeInformation

The results of our first three experiments serve to further iden-tify the nature of both the commonalities and the differencesbetween the mental representation of numbers and the mentalrepresentation of other kinds of symbolic stimuli with underlyingperceptual referents (where the association between symbol andpercept is acquired naturally through experience). For example,because SNARC-like effects are present here for comparisons ofboth numbers and animal sizes, it is now clear that spatial com-ponents are likely associated with both kinds of magnitude infor-mation (and, hence, do not strictly seem to be a unique property ofnumber representation; cf., the mental number line). With respectto the representation of animal-size information in long-term mem-ory, the presence of such components has really only been hypoth-esized (e.g., Holyoak & Patterson, 1981). However, it must also benoted that the mere fact that spatial information is being activatedin association with the activation of magnitude information doesnot, in and of itself, conclusively imply that such spatial informa-tion is then actually being used by the comparison process itself(for a further discussion of this issue, see Dean, Dewhurst, Morris,& Whitaker, 2005, who found that visual–spatial interferencesignificantly slowed animal-size comparisons overall but did notaffect the size of the symbolic distance effects that were present inRT).

Moreover, the SNARC effects found in our final experiment—for comparisons involving a small set of very recently learned,linearly ordered stimulus items—clearly represent a replicationand extension of the results for the comparisons of animal mag-

11EXTENDING THE SNARC EFFECT

nitudes. Hence, those results provide some evidence that the se-mantic representation of linear order in shorter-to-intermediate-term memory also involves spatial components (as has also beenpostulated by a few researchers, such as Holyoak & Patterson,1981, and Sternberg, 1980). In fact, it is important to note thatleft-to-right spatial elements (that reverse over instructions) be-came associated with the representation of this ordering of sym-bolic magnitudes, even though the participants had never actuallybeen exposed to the whole sequence of names ordered horizontallyfrom side to side. Moreover, throughout the course of that study,the names of the individuals always appeared equally on the rightand left sides. Hence, this paradigm provided absolutely no exter-nal basis for the presence of an association between the namesthemselves and space. As well, the learning phase here did notinvolve any actual writing down of the information being learned,suggesting that spatial–motor processing during learning is not anecessary condition for the development of SNARC effects.

Nevertheless, our studies also indicate that the spatial frames ofreference associated with numerical magnitudes seem to be a greatdeal more rigid than those associated with the other two types ofsymbolic magnitudes examined here. Such results are highly sug-gestive of the fact that specific aspects of the manner in whichnumber concepts are spatially processed and learned throughoutthe life span are indeed contributing to the development of thespatial components underlying the representation and processingof numerical magnitude (quite possibly by way of a fairly fixedmental-number-line-like representation) that are not contributingto the formation of the spatial components underlying the repre-sentation and processing of other non-numerical magnitude infor-mation. As we have suggested, in the latter case, it is possible thatspatial frames of reference are strategically generated for thepurpose of making the appropriate comparison response (althoughnote that Fischer, 2006, has recently made a case for the fact thatstrategic factors, albeit “environment-centered” ones, might alsoplay an important role in determining the direction and size ofnumerically based SNARC effects as well). In light of such a view,in future work, it would seem to be quite important to determinethe nature of the instructional dependency that might occur in theSNARC effects obtained for comparisons involving stimuli fromother non-numerical, but still highly overlearned, spatially basedorderings such as the months of the year or the days of the week.

A more extreme view of such results, however, might be thatthey are consistent with the notion that the processing of numericaland non-numerical magnitude information might actually makeuse of distinct neural processing mechanisms (both of which, ofcourse, should still involve spatial components). In fact, such aview has indeed been furthered recently by a few researchers whohave marshaled some evidence for the presence of both experi-mentally based (Dodd, Van der Stigchel, Leghari, Fung, & King-stone, 2008) and neurologically based (Van Opstal et al., 2009;Zorzi, Priftis, Meneghello, Marenzi, & Umilta, 2006) dissociationsinvolving the processing of numerical and non-numerical magni-tudes.

Implications for the Contribution of Cultural Factorsto the SNARC Effect

Importantly, our third study is also quite decisive in providingevidence for the view that the direction of reading and writing

seems to be an important determiner of the effective organizationof the spatial components in the mental representations of bothnumbers and other symbolic magnitudes. With respect to numer-ical magnitudes, the factors just discussed regarding the manner inwhich such concepts are generally learned could also be assumedto be contributing in a similar, but opposite, fashion for right-to-left reading cultures. With respect to the reversal of the instruction-dependent SNARC effects that we observed across cultures forcomparisons of the animal magnitudes, such findings convergenicely with other recent work showing an influence of the directionof reading and writing on spatial reasoning more generally. Forexample, Dobel, Diesendruck, and Bölte (2007) found that whenparticipants were asked to spatially depict the content of verballypresented sentences, left-to-right readers tended to place the agentof an action to the left of the recipient, whereas, on the other hand,right-to-left readers tended to place the agent of the action to theright of the recipient.

In fact, some other recent work involving the first author hasprovided some evidence for the notion that the role of reading andwriting directions might simply only be to provide a spatial set forany subsequent spatial processing of magnitude information, in-cluding that involving numbers. Namely, Fischer, Shaki, andCruise (2009) showed that for bilingual Russian-Hebrew readers,SNARC effects for parity judgments were significantly larger notonly for number-word stimuli presented visually in Russian (com-pared with Hebrew) but also for digits presented on the nextsubsequent trial. Similarly, Shaki and Fischer (2008) have alsoshown, for these same bilingual participants, that such SNARCeffects can be significantly attenuated within a whole block oftrials simply after reading a short passage of text in Hebrew(compared with Russian).

Implications for the Gevers, Verguts, et al. (2006) andChen and Verguts (2010) Computational Models of theSNARC Effect

The notion of long-term semantic associations between smallerand larger numbers and left–right spatial location codes is a keyaspect of some recent computational modeling of the SNARCeffect that has been based on the model of numerical cognitiondeveloped by Verguts, Fias, and Stevens (2005). That originalmodel was used to simulate paired comparisons of numericalmagnitude in addition to number naming and parity judgments. Toperform paired comparisons of two presented digits with thismodel, the magnitudes of each digit in a comparison pair arerepresented as activated units on separate left and right position-specific number-line representations (which they referred to as aplace-coding representational system). All of the left and rightnumber-line units are connected to left and right response units bysets of learned connection weights (one set for each of the smallerand larger form of the comparative instruction), which insure thatthe appropriate response will become relatively more activated foreach possible comparison pair (for a similar model, see Leth-Steensen & Marley, 2000).

Gevers, Verguts, et al. (2006) extended this model to derivesimulations of the SNARC effect for both the parity judgment and(single digit) magnitude comparison tasks. To derive simulationsof the latter task (e.g., is the presented digit smaller or larger than5?), Gevers, Verguts, et al. (2006) assumed that one of the number

12 SHAKI, PETRUSIC, AND LETH-STEENSEN

fields in the Verguts et al. (2005) paired-comparison model couldbe used to represent magnitude of the standard (e.g., 5) and theother used to represent the magnitude of the presented digit stim-ulus. These number field representations were used (with the samesets of comparison weights as in Verguts et al., 2005) to activatean intermediate level of two categorically defined (i.e., small andlarge) magnitude units. These units, in turn, were assumed toactivate left and right response units. To obtain the SNARC effect,a dual-route framework was invoked in which the activations ofthe response units are determined by both an automatic routecontaining hardwired positive connections between the small andlarge categorical-magnitude coding units and the left and rightresponse units, respectively, and a controlled route whereby thenature of the connections between the two categorical-magnitudecoding units and the left and right response units is switcheddepending on the specific small–large/left–right response mappingbeing used. In the Gevers, Verguts, et al. (2006) simulations, thecontribution of the automatic route in determining the responsewas set to be about one fifth the contribution of the controlledroute.

Recently, Chen and Verguts (2010) have extended the architec-ture of this model even further by adding both a symbolic numberlayer and a space layer, each containing localist connectionist unitsrepresenting Arabic number forms and left–right eye-centeredobject locations, respectively. Each of these new layers are as-sumed to be connected (bidirectionally) to left and right humanhomologues of the lateral interparietal area (hLIP), which respondmore strongly to activation on the contralateral side of the spacelayer (e.g., more activation occurs in the right hLIP in response toactivated units in the space layer coding object locations on the leftside, and vice versa). Cultural effects on the mappings of numberto space were instantiated by setting bidirectional connectionsbetween the symbolic number layer and the left and right hLIPs,such that the right hLIP responds more strongly to smaller num-bers and the left hLIP responds more strongly to larger numbers.In fact, such a mapping was regarded as a key assumption of theirmodel, namely, “that an environmental correlation between sym-bolic (e.g., Arabic) numbers and physical space (left or rightpositions) leaves its signature in the brain” (Chen & Verguts, 2010,p. 220). Finally, units in the left and right hLIPs are assumed tohave small positive connections to right and left response units,respectively. This model also aligns with the previous Gevers,Verguts, et al. (2006) model by having connections between thesymbolic number units and the numerical place-field units of thatprevious model, allowing it to model SNARC effects in the samemanner as before (but now also with a noncategorical visual–spatial route through the left and right hLIPs).

The manner in which the Gevers, Verguts, et al. (2006) com-putational model would need to be modified in order to account forthe standard SNARC effects obtained here, for the paired numer-ical comparisons in Experiment 2, is somewhat straightforward.Specifically, all that would be required is the addition of a mag-nitude field (or fields), which could be used in the exact samemanner as in Gevers, Verguts, et al. (2006), to derive a small orlarge categorical-magnitude coding for each of the digits in thepair within an automatic route (or routes) that would then serve toprime the left and right responses, respectively. Processing in thecontrolled route would involve a direct comparison of the digitswithin the pair using the set of connection weights corresponding

to the relevant choose-the-larger or choose-the-smaller form of thecomparative instruction.

Accounting for the instruction-dependent SNARC effects ob-tained here for the paired animal-size comparisons in Experiment1 would, however, be somewhat less straightforward for theGevers, Verguts, et al. (2006) model. Given the same modelarchitecture, and assuming that the initial place-coding represen-tational layer now codes for animal magnitudes, the model couldtechnically then be run in the same manner as described previ-ously. In order to model instruction-dependent SNARC effects,though, the connections between the small and large categorical-magnitude coding units and the left and right response units in theautomatic route would then need to be switched for each form ofthe instruction (i.e., such that the small categorical unit positivelyprimes the left response unit for the smaller instruction, but theright response unit for the larger instruction, and vice versa for thelarge categorical unit). Such a state of affairs, however, does notseem to be very consistent with the assumed automatic nature ofsuch route, which, presumably, is based on long-term memoryassociations between small and large magnitudes and left–rightspatial codes, respectively. In fact, if anything, the current resultsindicate that although the presence of such long-term memoryassociations do indeed seem to be in place for numerical magni-tudes, no such associations seem to exist for animal magnitudes.

On the other hand, we do believe that the presence ofinstruction-dependent SNARC effects are consistent with the no-tion that there might be a more natural, automatic-priming routebetween the units on the left and right sides of the place-codingrepresentational fields in the Verguts et al. (2005) model and theleft and right response codes, respectively. Given this view, it isthe left–right positioning on this place-coding field of the orderingof animal sizes that switches with the direction of the comparativeinstruction. In fact, the addition of both the space layer and the leftand right hLIPs in the Chen and Verguts (2010) version of thismodel might indeed provide just such a structure through whichsuch associations might better be realized. Under this view, re-trieved magnitudes for each animal in a comparison pair wouldfirst be mapped onto its own space-layer representation, but in aflexible manner such that magnitudes that are more consistent withthe form of the instruction activate space units corresponding toleft spatial positions and those that are less consistent activatespace units corresponding to right spatial positions. As describedearlier, activation of units on these space layers would then inducea differential activity in each of the left and right hLIPs, whichwould then automatically prime the left and right response units ina differential fashion, with the result of this process being thatactivation of space-layer units corresponding to the left or rightsides of space serve to prime up their corresponding left or rightresponse units. In order to generate the size comparison responses,it would also have to be assumed that the two space-layer repre-sentations are compared using comparison weights analogous tothose used to compare numbers in the Verguts et al. (2005) model(where categorical coding units such as that proposed by Gevers,Verguts, et al., 2006, could also be assumed to be operative butwould probably need to involve a “more” or “less” type of coding,given that identical activations on the space layer would now havedifferent meanings depending on the form of the comparativeinstruction). Regardless of whether instruction-dependent SNARCeffects within such a framework arise from response interference

13EXTENDING THE SNARC EFFECT

generated by either a categorically or a visual-spatially (i.e., hLIP)based automatic route, it is important to note that we indeedbelieve that the presence of such effects does imply that suchinterference must necessarily be driven by the nature of the spatialorganization that is applied to the representation of the items at themore central representational levels of this model.

Implications for the Proctor and Cho (2006) PolarityCorrespondence View

Proctor and Cho (2006; see also Bae, Choi, Cho, & Proctor,2009) have recently proposed an alternative account of theSNARC effect that involves correspondences between bipolarpropositional representations of the stimulus and response dimen-sions. According to this view, both nonverbal and verbal dimen-sional representations can be coded in terms of � and � polarities(e.g., above and below as � and � on the dimension of verticality,and “yes” and “no” responses as � and � on the dimension ofaffirmation). As demonstrated by Proctor and Cho (2006), a largenumber of results for binary classification tasks, especially thoseinvolving word-picture verifications and stimulus–response com-patibility effects, can be explained on the basis of the degree ofcorrespondence between the polarity codes associated with thestimuli and the responses (i.e., with faster responses when thepolarities of the stimulus and response codes correspond). Mostnotably, they suggested that the SNARC effect in the parity taskcould arise on the basis of a correspondence between a � and �polarity coding of the left and right responses, respectively, anda � and � polarity coding of smaller and larger numerical mag-nitudes, respectively. Note that such a view can also easily accountfor SNARC effects obtained here for the paired numerical com-parisons in our Experiment 2, by assuming that smaller and largerpairs of numbers can become polarity coded as � and � polarity,respectively (given that left and right responses are generallyassumed to have � and � polarity codes, respectively).

For such a view to be able to account for the instruction-dependent SNARC effects obtained in our Experiment 1, though,it would need to be assumed that the polarities assigned to thesmaller and larger animal pairs are reversed across each form ofthe comparative instruction. More specifically, although for thesmaller instruction, small and large could still be polarity codedas � and �, for the larger instruction, small and large would nowhave to be polarity coded as � and � in order to yield a reverseSNARC effect. However, such a notion would be somewhat con-sistent with a reversal of a spatial frame of reference for theanimal-size dimension on the basis of the direction of the com-parison, given that polarities are deemed to be “determined by thereference point for the dimension” (Proctor & Cho, 2006, p. 422,Point 4). If so, pairs whose magnitudes are closer to the referencepoint would receive a � polarity coding, and pairs whose magni-tudes are farther from the reference point would receive a �polarity coding. To then account for the results for the Hebrew-Arabic participants in our Experiment 3, it could simply be as-sumed that, for them, left and right are now polarity coded as �and �, respectively. Interestingly, such a notion would indicatethat the polarity coding of left and right is determined by the frameof reference imposed by the direction of reading and writinghabits.

However, the notion of such an instructionally determinedreference-point-based polarity coding of small and large pair mag-nitudes does not seem that consistent with the nature of the polaritycoding that might have been expected, given the notion thatmagnitudes that are more consistent with form of the instructionshould actually have more salience (e.g., small magnitudes underthe instruction to choose the smaller) and, hence, be given �polarity codes (a point which serves to highlight the often apparentambiguity that is present in the enterprise of assigning polaritycodes). Moreover, if such differential reference frames are indeedbeing used to polarity code small and large magnitudes whileperforming the animal size comparisons, it is not all clear why theywould not also be used to polarity code small and large magnitudeswhile performing the number comparisons. Put another way, asdiscussed previously, a spatial representational account for thepresence of instructional-independent SNARC effects in numbercomparison would almost certainly have to involve the assumptionthat they are due to the presence of long-term learned associationsbetween numerical magnitudes and spatial locations. If that as-sumption is then thrown away and replaced by the notion ofpolarity coding, the presence of long-term learned associationsbetween small and large numerical magnitudes and �and �polarity codes, respectively, would then have to be assumed(which then override any temporary reference-point-based polaritycoding that might have otherwise occurred). Whereas the basis forthe associations espoused in the former case is quite intuitive andecologically valid, the basis for the presence of the associationsespoused in the latter case is not as clear (although perhaps theyare mediated by the fact that because small numbers, e.g., oftenoccur on left of physical displays involving numbers and left ispolarity coded as �, a more permanent association between smallnumbers and � polarity codes might then develop).

Conclusion

The present research adds to a growing body of availablescientific evidence surrounding the SNARC effect that indicatesthat some sort of spatial organization can be regarded as a generalproperty of the representation of both numerical and non-numerical ordinal-based magnitude information. It also adds to agrowing body of evidence that indicates that SNARC effects arenot, in fact, constrained to associations between small magnitudesand left spatial codes, on the one hand, and large magnitudes andright spatial codes, on the other (although such associations indeedseem to be quite pervasive to representations of numerical mag-nitude). It also adds to a growing body of research that indicatesthat cultural factors pertaining to the habitual direction of readingand writing can have a major influence on the expressed direc-tionality of the SNARC effect (that goes beyond learned associa-tions between symbols representing magnitude and space).

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Received October 28, 2009Revision received January 3, 2011

Accepted January 30, 2011 �

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