Perceiving numbers does not cause automatic shifts of spatial attention

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Perceiving numbers does not cause automatic shifts of spatial attention Enrico Fattorini a,b, Mario Pinto a,b, Francesca Rotondaro a,b and Fabrizio Doricchi a,b,* a b

 degli Studi di Roma “La Sapienza”, Roma, Italy Dipartimento di Psicologia 39, Universita Fondazione Santa Lucia IRCCS, Roma, Italy

article info

abstract

Article history:

It is frequently assumed that the brain codes number magnitudes according to an inherent

Received 10 February 2015

left-to-right spatial organization. In support of this hypothesis it has been reported that in

Reviewed 6 May 2015

humans, perceiving small numbers induces automatic shifts of attention toward the left

Revised 26 May 2015

side of space whereas perceiving large numbers automatically shifts attention to the right

Accepted 14 September 2015

side of space (i.e., Attentional SNARC: Att-SNARC; Fischer, Castel, Dodd, & Pratt, 2003).

Action editor Yves Rossetti

Nonetheless, the Att-SNARC has been often not replicated and its reliability never tested.

Published online 28 September 2015

To ascertain whether the mere perception of numbers causes shifts of spatial attention or whether numberespace interaction takes place at a different stage of cognitive processing,

Keywords:

we re-assessed the consistency and reliability of the Att-SNARC and investigated its role in

Numbers

the production of SNARC effects in Parity Judgement (PJ) and Magnitude Comparison (MC)

Attention

tasks. In a first study in 60 participants, we found no Att-SNARC, despite finding strong PJ-

SNARC

and MC-SNARC effects. No correlation was present between the Att-SNARC and the

Mental Number Line

SNARC. Split-half tests showed no reliability of the Att-SNARC and high reliability of the PJ-

Individual differences

and MC-SNARC. In a second study, we re-assessed the Att-SNARC and tested its direct influence on a MC-SNARC task with laterally presented targets. No Att-SNARC and no influence of the Att-SNARC on the MC-SNARC were found. Also in this case, the SNARC was reliable whereas the Att-SNARC task was not. Finally, in a third study we observed a significant Att-SNARC when participants were asked to recall the position occupied on a ruler by the numbers presented in each trial: however the Att-SNARC task was not reliable. These results show that perceiving numbers does not cause automatic shifts of spatial attention and that whenever present, these shifts do not modulate the SNARC. The same results suggest that numbers have no inherent mental left-to-right organization and that, whenever present, this organization can have both response-related and strategically driven memory-related origins. Nonetheless, response-related factors generate more reliable and stable spatial representations of numbers. © 2015 Elsevier Ltd. All rights reserved.

 degli Studi di Roma “La Sapienza”, Via dei Marsi 78, 00185 Roma, Italy. * Corresponding author. Dipartimento di Psicologia 39, Universita E-mail address: [email protected] (F. Doricchi). http://dx.doi.org/10.1016/j.cortex.2015.09.007 0010-9452/© 2015 Elsevier Ltd. All rights reserved.

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1.

Introduction

One of the most valid and reliable examples of the functional interaction between space and number processing is the SNARC effect (Spatial-Numerical Association of Response Codes, Dehaene, Bossini, & Giraux, 1993). The SNARC reflects the observation that when healthy humans are asked to provide judgements of number magnitude (e.g., higher or lower than 5?) or number parity (e.g., odd or even?) by choosing between a response key on the left-hand side and a response key on the right-hand side, they provide faster responses to small magnitudes with the key on the left side and faster responses to large magnitudes with the key on the right side (Dehaene, Dupoux, & Mehler, 1990). Different interpretations of the SNARC were advanced to date (for reviews see Cohen Kadosh, Lammertyn, & Izard, 2008; Wood, Nuerk, Willmes, & Fischer, 2008). Some authors claim that the SNARC depends on the correspondence between the inherent spatial position that numbers occupy on the mental equivalent of a left-to-right organised ruler, i.e., the Mental Number Line (MNL; Restle, 1970), and the position of response keys (Hubbard, Piazza, Pinel, & Dehaene, 2005). Other authors emphasise that the SNARC depends on a culturally based association between “left/right” and “small/large” semantic codes (Gevers et al., 2010; Proctor & Cho, 2006; Santens & Gevers, 2008). Some other authors have proposed that during the performance of the SNARC task, the mental left-to-right organization of number magnitudes is generated by the left/right spatial codes that are used for the selection of the motor response (Ishihara et al., 2006; Mu¨ller & Schwarz, 2007). This “responserelated” interpretation of the SNARC effect is supported by investigations with Event Related Potentials (ERPs) showing that the SNARC arises at the response-related stage, i.e., during the selection of the left versus right response key, rather than at an early stage of perceptual or visual imagery processing (Gevers, Verguts, Reynvoet, Caessens, & Fias, 2006; Keus & Scwarz, 2005). In summary, no univocal explanation of the SNARC effect has yet been established and no consensus has yet been reached on the stage of cognitive processing in which the association between left/right spatial codes and the coding of number magnitude takes place. In a relatively recent and frequently quoted study, Fischer, Castel, Dodd, and Pratt, (2003) have documented a behavioural effect that seems pointing at the inherent and responseindependent left-to-right spatial organization of number magnitudes. In two experiments run in relatively small samples of fifteen (Experiment 1) and ten participants (Experiment 2), these authors used a modification of the typical attentioncuing paradigm proposed by Posner (1980). At the beginning of each trial a digit cue (i.e., 1, 2, 8 or 9) was presented at central fixation. Following a varying Cue-Target Interval (CTI), a dottarget was randomly presented in the left or the right visual field. Participants were required to press a central key in response to target appearance. They were also informed that digit cues were irrelevant to target detection and did not predict target location. At 500 msec and 750 msec CTIs, Fischer et al. (2003) observed relatively faster RTs to left side targets when these were preceded by small digit cues, i.e., 1 or 2, and relatively faster RTs to right side targets when these were

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preceded by large digit cues, i.e., 8 or 9. The authors concluded that the perception of small number magnitudes induces automatic leftward shifts of attention whereas the perception of large numbers induces rightward shifts of attention. This effect, which is based on simple unimanual RTs has been called Attentional SNARC (Att-SNARC; van Dijck, Abrahamse, Acar, Ketels, & Fias, 2014; Dodd, Van der Stigchel, Leghari, Fung, & Kingstone, 2008) to differentiate it from the classical SNARC effect that is observed when motor responses in the left and right side of space must be reciprocally contrasted and associated to number magnitude or number parity. Results from ensuing studies have provided important qualifications of the Att-SNARC and suggest that, at variance with the SNARC effect, the Att-SNARC is elusive (see Rossetti et al., 2011; for a review). Some authors (Galfano, Rusconi, &  , 2006; Ristic, Wright, & Kingstone, 2006) have repliUmilta cated the Att-SNARC but have also pointed out that this is driven by strategic top-down factors rather than being a truly automatic effect [see Fischer (2006) for a similar proposal on the SNARC effect and the review by Price and Mattingley (2013) showing no strong evidence for automatic Att-SNARC among people with sequence-space synaesthesia]. This was especially demonstrated by the possibility of reversing the direction of the Att-SNARC, just by changing task instructions and asking participants to imagine a MNL running in the right-toleft rather than left-to-right direction (Ristic et al., 2006). In the same way Galfano et al. (2006) observed an inversion of the Att-SNARC when participants were asked to shift attention leftward in response to large numbers and rightward in response to small numbers. To maximize the activation of the left-right coding of the MNL, Galfano and co-workers also included the digit “5” among cue numbers, to implicitly provide participants with a landmark of the midpoint separating small, i.e., 1 and 2, from large, i.e., 8 and 9, cue numbers. Finally, in another study Dodd et al. (2008, Exp. 1) found the Att-SNARC only at one (500 msec) out of the two CTIs (500 msec and 750 msec) at which the effect was originally observed by Fischer et al. (2003). Others authors have failed to replicate the Att-SNARC both using simple RTs (Bonato, Priftis, Marenzi, & Zorzi, 2009; van Dijck et al., 2014; Hubbard, Ranzini, Piazza, & Dehaene, 2009; Jarick, Dixon, Maxwell, Nicholls, & Smilek, 2009; Ranzini, Dehaene, Piazza, & Hubbard, 2009) and temporal order  , 2007). judgements (Casarotti, Michielin, Zorzi, & Umilta Among these studies the investigation by van Dijck et al., (2014) and the series of experiments by Zanolie and Pecher (2014) are particularly relevant. Both of these studies adopted the same procedure employed by Fischer et al. (2003; Exp. 2). van Dijck et al. (2014) did not replicate the Att-SNARC in a large sample of 43 participants, a number of participants that was well above the estimated number of participants, i.e., 31, needed to obtain a power of .90 based on the effect sizes reported in Fischer et al. (2003) and Dodd et al. (2008). In two repetitions of the original Exp. 2 by Fischer et al. (2003), Zanolie and Pecher also (2014; Exp. 1 and 4) found no Att-SNARC. In another experiment from the same study (Exp. 3), some evidence for the Att-SNARC was provided when participants were asked to judge the magnitude of numerical cues (i.e., higher or lower than 5). However, this finding was not replicated in a control re-test experiment (Exp. 6). Finally, in two

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identical experiments (Exp. 2 and 5) no Att-SNARC was observed when participants were required to judge the parity of numerical cues. In line with the above summarised set of heterogeneous findings, a recent fMRI study investigating the neural correlates of the Att-SNARC task (Goffaux, Martin, Dormal, Goebel, & Schiltz, 2012) reported no Att-SNARC and found that small and large numerical digit cues produced lateralised activations in occipital areas but no corresponding lateralized activations in parietal areas that are typically involved in leftward (i.e., right hemisphere) and rightward (i.e., left hemisphere) shifts of spatial attention. In agreement with this dissociation, another recent fMRI study demonstrated that topographically organised number-sensitive neurons in the superior parietal cortex display no consistent relationship between numerosity coding and the direction of visuospatial responses (Harvey, Klein, Petridou, & Dumoulin, 2013). In the light of the mixed results reported in previous investigations, in the present series of studies we wished to address two main issues. First, we wished to explore in an adequately large sample of healthy participants whether the Att-SNARC is susceptible to important inter-individual variations and whether the strength and direction of the AttSNARC are correlated with the strength and direction of the SNARC or can directly influence the SNARC. This should allow testing accurately whether number-related shifts of spatial attention play a role in the genesis of the SNARC. As a matter of fact, both the Att-SNARC and the SNARC task are based on the presentation of Arabic digits at central fixation: nonetheless, to our knowledge it remains to be investigated whether lateral shifts of attention revealed by the Att-SNARC play a role in the SNARC. Second, we wished to investigate whether task-related factors have a relevant influence in determining the presence and strength of the Att-SNARC. Addressing these issues should help defining more precisely both the cognitive stage at which the interaction between number and space processing takes place and the functional origin of the SNARC.

third session. The order of administration of the PJ and the MC task/session was counterbalanced between participants. Sessions were run on different days and were separated by an interval of two-three days.

2.1.3.

Apparatus

All experiments were run in a sound attenuated room with dim illumination. Stimuli were presented on a 15-inch color 6546 IBM monitor. An Intel Pentium 4 PC running E-Prime software (Schneider, Eschman, & Zuccolotto, 2002) controlled the presentation of stimuli and the recording of responses. Participants had their head positioned on a chin rest at a viewing distance of 57.7 cm from the screen.

2.1.4.

Attentional-SNARC task

2. Study 1: investigating the link between the Att-SNARC and the SNARC through the study of individual differences

The presentation of trial events was organised as in the original task proposed by Fischer et al. (2003). At the beginning of each trial a central fixation cross (.4  .4 ) was presented for 500 msec together with two lateral boxes (1  1 ). One box was centred 5 to the left of central fixation and the other box 5 to the right of fixation. At the end of this 500 msec period, one out of four digit-cues (1, 2, 8 or 9; size ¼ .8  .6 ) replaced the central fixation cross for 300 msec. Following cue presentation, the central fixation cross was showed again during a CTI that varied randomly between 500 or 750 msec. These two CTIs are those at which Fischer et al. (2003) found the original Att-SNARC effect. At the end of the CTI, a white asterisk-target (.5  .5 ) was presented inside the left or the right box for 300 msec. Participants were asked to press the space bar with their right index finger as quick as possible in response to the target. An Inter-Trial Interval (ITI) of 2200 msec was interposed between the response and the start of the ensuing trial. Before testing, participants were instructed that digits presented at fixation were irrelevant to target detection. Participants were also required to maintain gaze on central fixation during task performance. The task consisted of 384 experimental trials (96 repetitions for each digit-cue) and 96 catch trials with no target presentation. Trials were administered in four consecutive blocks, separated by a 4 min pause. A training session consisting of 24 experimental trials (3 trials  digit  target side) was administered before experimental blocks.

2.1.

2.1.5.

2.1.1.

Method Participants

Sixty healthy right-handed undergraduate students (39 females, 21 males; age range: 20e28 years, mean age ¼ 21.9 years, SD ¼ 1.5 years) from the Faculty of Psychology of La Sapienza University in Rome participated in the experiment for course credit. All participants had normal or corrected-tonormal vision and were unaware of the purpose of the study. Participants completed all the tasks included in the study.

2.1.2.

Experimental design and tasks

Tasks were administered during three different experimental sessions. All participants performed the Att-SNARC task (Fischer et al., 2003) in the first session. Parity Judgement (PJ) and Magnitude Comparison (MC) SNARC tasks (Dehaene et al., 1990, 1993) were separately administered in the second and

Parity Judgement task (PJ)

Each trial started with the presentation of a central fixation cross (.4  .4 ) that lasted for 2000 msec. At the end of this delay an Arabic digit (1, 2, 3, 4, 6, 7, 8 or 9; size ¼ .8  .6 ) replaced the central fixation cross. Participants were asked to judge as quick as possible whether the digit was “odd” or “even” by pressing one of two lateral keys positioned one to the left and one to the right of the central fixation reference (i.e., “S” and “@” keys on the computer keyboard). The left index finger was used for the left key and the right index finger for the right one. The key press ended the presentation of the digit, that had a maximal duration of 2000 msec, and the trial. The ITI was 500 msec. Participants performed the task in two different stimulus-response conditions. In the first condition the “odd” response was associated with the left key and the “even” response with the right key. In the second condition, the association between “odd” and “even” responses and the

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Types of trials, number trials and procedures for presentation of stimuli and response recording were as in the PJ task. Participants were required to judge as fast as possible whether the Arabic digit was lower or higher than “5”. Each participant performed the task in two different stimulus-response conditions. In the first “congruent” condition, “lower” responses were associated with the left key and “higher” responses with the right one. In the second “incongruent” condition “lower” responses were associated with the right key and “higher” responses to the left one. The order of stimulus-response conditions was counterbalanced between participants.

regression slope analyses (Lorch & Myers, 1990; see Supplementary Analyses and Results, paragraph 1.1.1). In a final analysis, we assessed the reliability of the AttSNARC task using the split-half method with SpearmanBrown correction. First, individual mean RTs at 500 msecCTI, at 750 msec-CTI, and at collapsed CTIs were calculated separately for the first and second half of the task (it is worth noting that the absence of any influence of Task-Part revealed in the previous series of ANOVAs, suggests that this split is not affected by effects of time on task). Second, individual dRTs between right and left targets were computed and corresponding linear regression slopes were calculated using digitcue as predictor variable. Third, corrected SpearmaneBrown correlation between individual dRTs slopes in the first and second half of the task was computed. No significant correlation was found (CTIs-Collapsed: r1,2 ¼ .19, SpearmaneBrown correction ¼ .47, p ¼ .14; CTI-500 msec: r1,2 ¼ .12, SpearmaneBrown correction ¼ .22, p ¼ .34; CTI-750 msec: r1,2 ¼ .09, SpearmaneBrown correction ¼ .21, p ¼ .48). In line with the absence of the Att-SNARC, these results show that the Att-SNARC task is not reliable, i.e., that participants have no stable and homogeneous performance during the task.

2.2.

2.2.2.

side of response was reversed. The order of stimulus-response conditions was counterbalanced between participants. Each stimulus-response condition consisted of 320 trials (40 repetitions for each digit) subdivided in four blocks of 80 trials each. A 2 min pause was interposed between blocks performed in each stimulus-response condition and a 15 min pause was interposed between the two stimulus-response conditions. Before running the experiment participants performed a short training session composed of 24 trials (i.e., 3 trials per digit).

2.1.6.

Magnitude Comparison task (MC)

Results

In all tasks, responses to catch trials (false alarms), trials in which no response was made (misses), and trials in which RTs were above or below two standard deviations from the individual mean of the corresponding experimental condition were considered outliers and not included in the analyses. This procedure was applied to all the experiments summarised in the present report.

2.2.1.

Att-SNARC task

4.8% of trials were discarded from the analyses. Individual mean RTs were first entered in a Digit-Cue (1, 2, 8, 9)  TargetSide (left, right)  CTI (500, 750 msec) ANOVA. No significant main effect or interaction was found. Crucially, neither the Digit-Cue  Target-Side [F (3,177) ¼ .56, p ¼ .64, h2 ¼ .01] nor the Digit-Cue  Target-Side  CTI [F (3,177) ¼ .39, p ¼ .76, h2 ¼ .007] interaction were significant. This showed the absence of the Att-SNARC (Fig. 1a). No Att-SNARC was also evident in a CueMagnitude (low, high)  Target-Side (left, right)  CTI (500, 750 msec) ANOVA, in which RTs were collapsed across trials with low (1, 2) and high (8, 9) cue digits [Digit-Cue  TargetSide: F (1,59) ¼ 1.69, p ¼ .20, h2 ¼ .03 and Digit-Cue  TargetSide  CTI: F (1,59) ¼ .72, p ¼ .40, h2 ¼ .01]. To further explore the presence of the Att-SNARC and its possible variation during the performance of the task, we repeated the two preceding ANOVAs taking into account the First versus Second Half of the task, i.e., Cue-Magnitude  TargetSide  CTI  Task-Part (First Half, Second Half) ANOVAs. Also in this case, no main effect or interaction approached statistical significance (all p > .13). No Att-SNARC was found both in the First and the Second Half of the task [CueMagnitude  Target-Side  Task-Part interaction: F (1,59) ¼ .1, p ¼ .73, h2 ¼ .002; Cue-Magnitude  Target-Side  CTI  TaskPart interaction: F (1,59) ¼ .4, p ¼ .54, h2 ¼ .006]. The results of these standard factorial ANOVAs were confirmed by

Parity Judgement task

8.2% of trials were discarded from the analyses. The presence of the SNARC was first investigated by entering individual mean RTs in a Task-Order (Magnitude-First/Parity-Second, Parity-First/Magnitude-Second)  Stimulus-Response association order (left-odd/right-even-First & left-even/rightodd-Second, left-even/right-odd-First & left-odd/right-evenSecond)  Target-Magnitude (lower, higher)  Response-Key (left, right) ANOVA. The Task-Order and Stimulus-Response association order effects were not significant [F (1,56) ¼ 1.5, p ¼ .22, h2 ¼ .03 and F (1,56) ¼ .2, p ¼ .64, h2 ¼ .004, respectively] and showed no interaction with other factors (all p > .34). The Target-Magnitude  Response-Key interaction was significant [F (1,56) ¼ 53.7, p < .001, h2 ¼ .49] showing the presence of the SNARC (Fig. 2a). Post-hoc tests showed that the SNARC was significant both for digits lower than 5 (leftside response 571 msec vs right-side response 585 msec: p < .01) and for digits higher than 5 (right-side response 565 msec vs left-side response 595 msec: p < .001). Since no influence of Task-Order or Stimulus-Response association order on the SNARC was present in this first ANOVA, in a second ANOVA we tried to better qualify the SNARC through a Digit-Target (1, 2, 3, 4, 6, 7, 8, 9)  Response-Key (left, right) ANOVA. The Digit-Target  Response-Key interaction resulted again significant [F (7,413) ¼ 13.2, p < .001, h2 ¼ .18] confirming the presence of the SNARC (Fig. 2a). Post-hoc tests revealed a significant SNARC for digits 1, 6, 8 and 9 (p < .001, p < .01, p < .05 and p < .01, respectively), suggesting larger SNARC for higher digits. These results were confirmed by regression slope analyses (see Supplementary Analyses and Results, paragraph 1.1.2). These analyses also documented no influence of Task-Part (First Half, Second Half) on the SNARC. Finally, the split-half method with Spearman-Brown correction demonstrated the reliability of the PJ-SNARC effect (r1,2 ¼ .60, SpearmaneBrown correction ¼ .75, p < .001).

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Fig. 1 e Attentional-SNARC task. (A) Average RTs (with SE) to targets in the left and right side of space as a function of the magnitude of central digit-cues. In this panel RTs scale on the Y-axis is equivalent to that by Fischer et al. (2003) (B) Average RTs (with SE) to targets in the left and right side of space as a function of the magnitude of central digit-cues. In this panel RTs range-scale on the Y-axis is equivalent to that of Figs. 2 and 3 from the present study, to allow comparison between the strength of Att-SNARC and SNARC effects. (C) Slope describing the difference between RTs to targets in the right side of space minus targets in the left side of space (dRT in msec), plotted as a function of the magnitude of central digit-cues. (D) Individual regression slopes ordered by size: negative slopes indicate a conventional Attentional-SNARC effect, positive slopes a reversed Attentional-SNARC effect.

2.2.3.

Magnitude Comparison task

7.6% of trials were discarded from the analyses. Individual mean RTs were first entered in a Task-Order (Magnitude-First/ Parity-Second, Parity-First/Magnitude-Second)  StimulusResponse association order (left-lower/right-higher-First & left-higher/right-lower-Second, left-higher/right-lower-First & left-lower/right-higher-Second)  Target-Magnitude (lower, higher)  Response-Key (left, right) ANOVA. The Task-Order and Stimulus-Response association order effects were not significant [F (1,56) ¼ .4, p ¼ .51, h2 ¼ .008 and F (1,56) ¼ 1.8, p ¼ .18, h2 ¼ .03, respectively]. The main effect of TargetMagnitude was significant [F (1,56) ¼ 13.7, p < .001, h2 ¼ .21] and showed faster RTs to digits lower than 5 (lower ¼ 512 msec vs higher ¼ 522 msec). The Target-Magnitude  Response-Key interaction was significant [F (1,56) ¼ 26.0, p < .001, h2 ¼ .32] revealing the presence of the SNARC. Post-hoc tests showed that the SNARC was significant both for digits lower and higher than 5: RTs to lower digits were faster with left-side than with the right-side key (504 vs 522 msec, p < .01) and RTs to higher digits were faster with the right-side than with the left-side key (511 vs 534 msec, p < .001). The TaskOrder  Target-Magnitude  Response-Key interaction was also significant [F (1,56) ¼ 5.7, p < .05, h2 ¼ .09]. This latter interaction was further explored through Target-Magnitude

(lower, higher)  Response-Key (left, right) ANOVAs ran separately in the two Task-Order groups. The TargetMagnitude  Response-Key interaction that qualifies the SNARC was significant both in participants who performed first the MC task [F (1,29) ¼ 24.6, p < .001, h2 ¼ .47] and in those who performed first the PJ task [F (1,29) ¼ 4.5, p < .05, h2 ¼ .13]. Post-hoc tests showed that in participants who performed the MC task first, the SNARC was present both for digits lower and higher than 5 (p < .01 and p < .001, respectively) whereas in participants who performed the PJ task first the same comparisons did not reach significance (p ¼ .22 and p ¼ .09, respectively). This result suggests a weaker SNARC in this latter group. To better qualify the SNARC an additional DigitTarget (1, 2, 3, 4, 6, 7, 8, 9)  Response-Key (left, right) ANOVA was computed. The Digit-Target  Response-Key interaction resulted significant, [F (7,413) ¼ 14.7, p < .001, h2 ¼ .20] reconfirming the presence of the SNARC (Fig. 3a). Post-hoc comparisons revealed a significant SNARC effect for each digit except digit 3 (left-response ¼ 510 msec vs rightresponse ¼ 515 msec, p ¼ .43). These results were confirmed by regression slope analyses (see Supplementary Analyses and Results, paragraph 1.1.3). These analyses also documented no influence of Task-Part (First Half, Second Half) on the SNARC.

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distance between the target-digit and the central numerical reference “5” (i.e., distance 1 ¼ digits 4 and 6; distance 2 ¼ digits 3 and 7; distance 3 ¼ digits 2 and 8; distance 4 ¼ digits 1 and 9). The Numerical Distance effect was significant [F (3,174) ¼ 170.9, p < .001, h2 ¼ .75] and showed that RTs increased progressively as an inverse function of the distance from the central reference. Pair-wise post-hoc tests were all significant (p < .001) except the one between 3- and 4-unit distance (p ¼ .22). These results were confirmed by regression slope analyses (see Supplementary Analyses and Results, paragraph 1.1.4). These analyses also documented no influence of Task-Part (First Half, Second Half) on the SNARC.

Fig. 2 e Parity Judgement task. (A) Average RTs (with SE) to digit-targets as a function of response side, i.e., left, right. (B) Slope describing the difference between RTs provided with right-side minus left-side response keys (dRT in msec) as a function of the magnitude of digit-cues. (C) Individual regression slopes ordered by size: negative slopes indicate a conventional SNARC effect, positive slopes a reversed SNARC effect.

Split-half testing with Spearman-Brown correction demonstrated the reliability of the MC-SNARC effect (r1,2 ¼ .32, SpearmaneBrown correction ¼ .49, p < .01).

2.2.3.1. NUMERICAL DISTANCE EFFECT. To investigate the Numerical Distance effect (Libertus, Woldorff, & Brannon, 2007; Maloney, Risko, Preston, Ansari, & Fugelsang, 2010 and Moyer & Landauer, 1967) we computed individual mean RTs for each digit-target separately and tested through a one-way ANOVA whether RTs changed as a function of the numerical

Fig. 3 e Magnitude Comparison task. (A) Average RTs (with SE) to digit-targets as a function of response side, i.e., left, right. (B) Slope describing the difference between RTs performed with right-side minus left-side response keys (dRT in msec) as a function of the magnitude of digit-cues. (C) Individual regression slopes ordered by size: negative slopes indicate a conventional SNARC effect, positive slopes a reversed SNARC effect.

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Split-half testing demonstrated the reliability of the Numerical Distance (r1,2 ¼ .51, SpearmaneBrown correction ¼ .67, p < .001).

2.3.

Inter-individual variability in the Att-SNARC

In the following series of analyses we explored whether interindividual variations in the strength and direction of AttSNARC were related to variations in the strength of the SNARC effect in PJ and MC tasks.

2.3.1. Subgroups of participants with conventional and reversed Att-SNARC We initially defined the two subgroups of participants that, over collapsed 500 msec and 750 msec CTIs, showed a conventional Att-SNARC (Att-SNARC þ group, i.e., participants with a negative linear regression slope) or a reversed AttSNARC (Att-SNARC group, i.e., participants with a positive linear regression slope). The Att-SNARC þ group consisted of 36 participants (individual slopes ranged from 5.0 to .001, Average Slope ¼ 1.4 and SD ¼ 1.2) and the Att-SNARC group of 24 participants (individual slopes ranged from .06 to 4.2, Average Slope ¼ 1.2 and SD ¼ 1.3). A binomial test showed that the distribution of participants in these two subgroups was not different from chance (p ¼ .36). A t-test for independent samples showed that the slope value was different between these two subgroups [t (58) ¼ 7.8, p < .001]. One-sample ttests showed that in each subgroup the slope value was different from zero [Figs. 4b and 5b; Att-SNARCþ: t (35) ¼ 6.6, p < .001; Att-SNARC: t (23) ¼ 4.7, p < .001]. Supplementary analyses documented no influence of Task-Part (First Half, Second Half) on the Att-SNARC in both subgroups of participants (See Supplementary Analyses and Results, paragraph 1.2.1). We reassessed the reliability of the Att-SNARC task in these two subgroups of participants using the split-half method with Spearman-Brown correction. No significant correlation was found in both subgroups (Att-SNARCþ, r1,2 ¼ .29, SpearmaneBrown correction ¼ .81, p ¼ .09; AttSNARC, r1,2 ¼ .31, SpearmaneBrown correction ¼ .91, p ¼ .14). These results suggest that both the conventional and reversed Att-SNARC are not reliable. In order to confirm the difference of the Att-SNARC between the two subgroups we ran a Group (Att-SNARCþ, AttSNARC)  Cue-Magnitude (low, high)  Target-Side (left, right) ANOVA. The Cue-Magnitude  TargeteSide interaction was not significant [F (1,58) ¼ .06, p ¼ .81, h2 ¼ .001], reconfirming the absence of the Att-SNARC. The Group  Cue-Magnitude  TargeteSide interaction was highly significant [F (1,58) ¼ 61, p < .001, h2 ¼ .51]. We explored this interaction through Cue-Magnitude (low, high)  TargeteSide (left, right) ANOVAs ran separately in the Att-SNARCþ and Att-SNARC subgroups. The CueMagnitude  TargeteSide interaction was significant in both subgroups [Figs. 4a and 5a; Att-SNARCþ: F (1,35) ¼ 46.3, p < .001, h2 ¼ .57; Att-SNARC: F (1,23) ¼ 20.1, p < .001, h2 ¼ .47]. Post-hoc tests showed that in the AttSNARC þ subgroup the Att-SNARC for high digit cues was significant (p < .001) while that for low digit cues did not reach statistical significance (p ¼ .13). The same tests

Fig. 4 e Attentional-SNARC task in participants with conventional Attentional-SNARC effect (i.e., Att-SNARC þ subgroup). (A) Average RTs (with SE) to targets in the left and right side of space as a function of the magnitude of central digit-cues. In this panel RTs scale on the Y-axis is equivalent to that by Fischer et al. (2003) (B) Average RTs (with SE) to targets in the left and right side of space as (a function of the magnitude of central digit-cues. In this panel RTs range-scale on the Y-axis is equivalent to that of Fig. 2 and 3 from the present study, to allow comparison between the strength of Att-SNARC and SNARC effects. (C) Slope describing the difference between RTs to targets in the right side of space minus targets in the left side of space (dRT in msec), plotted as a function of the magnitude of central digit-cues.

showed that in the Att-SNARC subgroup there was a significantly reversed Att-SNARC for low digit cues (p < .001) and no reversed Att-SNARC for high digit cues (p ¼ .83).

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we explored whether the strength of the PJ-SNARC effect was different between the Att-SNARCþ and Att-SNARC subgroups. A significant TargeteMagnitude  ResponseeKey interaction confirmed the presence of the SNARC effect [F (1,58) ¼ 54.7, p < .001, h2 ¼ .49]. However, the Group  TargeteMagnitude  ResponseeKey interaction was not significant [F (1,58) ¼ .54, p ¼ .46, h2 ¼ .01]: this shows that the SNARC effect was equivalent between the subgroups of participants with conventional and reversed Att-SNARC. These results were confirmed by regression slope analyses (see Supplementary Analyses and Results, paragraph 1.2.2). These analyses also documented no influence of TaskePart (First Half, Second Half) on the PJ-SNARC. Finally, split-half method with Spearman-Brown correction, demonstrated the reliability of the PJ task in both subgroups (Att-SNARCþ: r1,2 ¼ .61, SpearmaneBrown correction ¼ .75, p < .001; Att-SNARC: r1,2 ¼ .61, SpearmaneBrown correction ¼ .76, p < .01). In summary, we have found that the SNARC effect in the PJ task is reliable and does not vary as a function of the strength and direction of the AttSNARC.

2.4.2.

Fig. 5 e Attentional-SNARC task in participants with reversed Attentional-SNARC effect (i.e., Att-SNARC subgroup). (A) Average RTs (with SE) to targets in the left and right side of space as a function of the magnitude of central digit-cues. In this panel RTs scale on the Y-axis is equivalent to that by Fischer et al. (2003) (B) Average RTs (with SE) to targets in the left and right side of space as a function of the magnitude of central digit-cues. In this panel RTs range-scale on the Yaxis is equivalent to that of Figs. 2 and 3 from the present study, to allow comparison between the strength of AttSNARC and SNARC effects. (C) Slope describing the difference between RTs to targets in the right side of space minus targets in the left side of space (dRT in msec), plotted as a function of the magnitude of central digit-cues.

2.4. SNARC effects in participants with conventional and reversed Att-SNARC effect 2.4.1.

Parity Judgement task

Using a Group (Att-SNARC, Att-SNARCþ)  Targete Magnitude (lower, higher)  ResponseeKey (left, right) ANOVA,

Magnitude Comparison task

As in the case of the PJ task, we used a Group (Att-SNARCþ, Att-SNARC)  TargeteMagnitude (lower, higher)  ResponseeKey (left, right) ANOVA to explore whether the strength of the MC-SNARC effect varied between the Att-SNARCþ and Att-SNARC subgroups. The SNARC effect was significant [TargeteMagnitude  ResponseeKey interaction: F (1,58) ¼ 24.8, p < .001, h2 ¼ .30] and equivalent in the two subgroups [Group  TargeteMagnitude  ResponseeKey interaction: F (1,58) ¼ .78, p ¼ .38, h2 ¼ .01]. These results were confirmed by regression slope analyses (see Supplementary Analyses and Results, paragraph 1.2.3). These analyses also documented no influence of TaskePart (First Half, Second Half) on the MCSNARC. In line with these results, split-half testing showed poor reliability of the MC task in the Att-SNARC þ subgroup (r1,2 ¼ .19, SpearmaneBrown correction ¼ .32, p ¼ .28) and good reliability of the same task in the Att-SNARC subgroup (r1,2 ¼ .42, SpearmaneBrown correction ¼ .59, p < .05).

2.4.2.1. NUMERICAL DISTANCE EFFECT IN ATT-SNARCþ AND ATTSNARC SUBGROUPS. To explore whether the strength of the Numerical Distance effect varied between the two subgroups we ran a Group (Att-SNARC, Att-SNARCþ)  Numerical Distance (1, 2, 3, 4) ANOVA. The Numerical Distance effect resulted significant [F (3, 174) ¼ 161.9, p < .001, h2 ¼ .74] and equivalent in the two subgroups [F (3,174) ¼ .56, p ¼ .64, h2 ¼ .01]. These results were confirmed by regression slope analyses (see Supplementary Analyses and Results, paragraph 1.2.4). These analyses also documented no influence of TaskePart (First Half, Second Half) on the Numerical Distance effect. Split-half testing showed that the Numerical Distance effect was reliable in the Att-SNARC þ subgroup (r1,2 ¼ .62, SpearmaneBrown correction ¼ .76, p < .001) and approached significant reliability in the Att-SNARC subgroup (r1,2 ¼ .38, SpearmaneBrown correction ¼ .55, p ¼ .07). As in the case of the PJ task, we have found that the size of the MC-SNARC and the Numerical Distance effect does not

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vary as a function of the strength and direction of the AttSNARC.

2.5. Correlations among Att-SNARC, PJ-SNARC, MCSNARC and numerical distance effects In these series of analyses, we evaluated Pearson-r correlations among the individual slopes defining the Att-SNARC (collapsed across 500 msec and 750 msec CTIs), the PJSNARC, the MC-SNARC and the Numerical Distance effect. We first assessed these correlations in the whole group of participants (Table 1) and then separately in the Att-SNARCþ and Att-SNARC subgroups (Tables 2 and 3, respectively). No correlation was found between the Att-SNARC and the PJ- or MC-SNARC effects (see Table 1 and Fig. 6). No correlation between the Att-SNARC and the PJ- or MC-SNARC was also observed when, in supplementary control analyses, the slopes defining the strength of the SNARC effects were calculated using only the subset of digits that was shared with AttSNARC task (i.e., 1, 2, 8, 9) (whole sample of participants: PJ: r ¼ .04, p ¼ .79, MC: r ¼ .10, p ¼ .44; Att-SNARC þ subgroup: PJ: r ¼ .15, p ¼ .37, MC: r ¼ .00, p ¼ .99; Att-SNARC subgroup: PJ: r ¼ .30, p ¼ .16, MC: r ¼ .10, p ¼ .65). In the whole sample of participants the correlation between the PJ- and MC-SNARC did not reach statistical significance (r ¼ .18, p ¼ .18). This result suggests that the PJ- and MC-SNARC do not rely on entirely overlapping mechanisms. The correlation between the two SNARC effects was significant in the AttSNARC þ subgroup (r ¼ . 39, p ¼ .017), whereas it was not significant in the Att-SNARC subgroup (r ¼ .01, p ¼ .97). This result might suggest that participants with a conventional Att-SNARC adopt similar cognitive strategies during the performance of the PJ- and MC-SNARC tasks. Though potentially interesting, the significance of this finding should be not overemphasised because in the Att-SNARC þ subgroup the correlation between the two tasks resulted no longer significant after Bonferroni correction for multiple comparisons (see Table 2). In the whole sample of participants, the PJ-SNARC, the MC-SNARC and the Att-SNARC were not correlated with the Numerical Distance effect (PJ: r ¼ .06, p ¼ .62; MC: r ¼ .07, p ¼ .57; Att-SNARC: r ¼ .14, p ¼ .29). In the AttSNARC þ group no correlation was present between the PJor the MC-SNARC and the Numerical Distance effect (PJ: r ¼ .03, p ¼ .83; MC: r ¼ .24, p ¼ .15). In the same group the correlation between the Att-SNARC and the Numerical Distance effect approached but did not reach statistical significance (Att-SNARC: r ¼ .30, p ¼ .08). In the Att-SNARC subgroup no significant correlation with the Numerical Distance effect was found (PJ: r ¼ .12, p ¼ .59; MC: r ¼ .05, p ¼ .82; Att-SNARC: r ¼ .30, p ¼ .16). To summarise, these correlation analyses show three main results: 1) in line with the findings from the previous series of ANOVAs and t-tests, they highlight the absence of a functional relationship between the Att-SNARC and the PJ- or the MC-SNARC; 2) they highlight the absence of a relationship between the strength of the PJ- and MC-SNARC effects with the Numerical Distance effect; 3) they show no significant correlation between the Att-SNARC and the Numerical Distance effect.

3. Study 2: a direct test of the relationship between the Att-SNARC and the SNARC effects In Study 1, no consistent Att-SNARC effect was observed whereas, within the same sample of participants, clear and reliable PJ- and MC-SNARC effects were found. In addition, no correlation was found between the strength of the Att-SNARC and that of the PJ- or MC-SNARC despite supplementary investigations in subsamples of participants showing conventional versus reversed Att-SNARC effects. Here, in a second study we wished to test a number of important factors that might have contributed to these results. First, we wished to verify whether failure in replicating the Att-SNARC was due to the use of only two, i.e., 500 and 750 msec, out of the six (50, 100, 200, 300, 400 and 500 msec, Experiment 1) or the four (250, 500, 750 and 1000 msec, Experiment 2) CTIs employed in the original study by Fischer et al. (2003). Although in Study 1, 500 msec and 750 msec CTIs were selected to maximize the possibility of replicating the Att-SNARC, it is important to test whether the emergence of Att-SNARC requires the use of the full CTIs range adopted by Fischer et al. (2003). Second, although the lack of correlations between the Att-SNARC and the PJ- and MC-SNARC documented in the Study 1 suggests that a functional link between these tasks is unlikely, it could still be argued that failure in highlighting this correlation was linked to specific procedural factors like testing the Att-SNARC and SNARC effects in separate sessions or to the poor reliability of the Att-SNARC. Thus, a reasonable solution to circumvent the possible limitations of the correlational approach adopted in Study 1, would be to: a) repeat, in a first experiment, the measurement of the Att-SNARC and of its reliability using the full range of CTIs employed in the study by Fischer et al. (2003); b) test, in a second experiment run in the same sample of participants, the influence of the Att-SNARC on the SNARC by combining the Att-SNARC and SNARC tasks within a single task. Interestingly, this procedure leaves open the possibility of investigating both the correlation between the strength of the Att-SNARC in the first experiment and those of the Att-SNARC and the SNARC effect in the second experiment and the correlation between the Att-SNARC and SNARC effect observed in the second experiment.

Table 1 e Correlations among the Attentional-SNARC, Parity Judgement SNARC, Magnitude Comparison SNARC and Distance effects (Pearson's r coefficient with lower and upper limits of 95% Confidence Intervals inside parentheses) in the whole sample of participants. All participants

1.

2.

3.

1. Attentional-SNARC e collapsed CTIs 2. Parity Judgement .04 (.29/.22) e 3. Magnitude .10 (.43/.24) .18 (.07/.42) e Comparison .14 (.25/51) .06 (.30/.17) .07 (.18/.40) 4. Numerical Distance Note. Correlations among the Attentional-SNARC, Parity Judgement, Magnitude Comparison SNARC effects and Numerical Distance effect (Pearson's r coefficient) in the whole sample of participants (N ¼ 60).

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Table 2 e Correlations among the Attentional-SNARC, Parity Judgement SNARC, Magnitude Comparison SNARC and Distance effects (Pearson's r coefficient with lower and upper limits of 95% Confidence Intervals inside parentheses) in participants with conventional Attentional-SNARC effect (Att-SNARC þ subgroup). Att-SNARCþ

1.

2.

3.

1. Attentional-SNARC e collapsed CTIs 2. Parity Judgement .15 (.23/48) e e 3. Magnitude .00 (.29/37) .39a (03/.67) Comparison 4. Numerical Distance .30 (.14/58) .03 (.30/.26) .24 (.09/.55) Note. Correlations among the Attentional-SNARC, Parity Judgement, Magnitude Comparison SNARC effects and Numerical Distance effect (Pearson's r coefficient) in participants with conventional Attentional-SNARC effect (i.e., Negative Slope group: Att-SNARCþ; N ¼ 36). a Uncorrected p ¼ .017, not significant after correction for multiple comparison (Bonferroni-corrected p level ¼ .008).

Table 3 e Correlations among the Attentional-SNARC, Parity Judgement SNARC, Magnitude Comparison SNARC and Distance effects (Pearson's r coefficient with lower and upper limits of 95% Confidence Intervals inside paretheses) in participants with reversed AttentionalSNARC effect (Att-SNARC¡ subgroup). Att-SNARC

1.

2.

3.

1. Attentionale SNARC collapsed CTIs 2. Parity Judgement .30 (.72/19) e 3. Magnitude .10 (.71/.55) .01 (.52/.45) e Comparison 4. Numerical .30 (.71/.16) .12 (.60/46) .05 (.40/.70) Distance Note. Correlations among the Attentional-SNARC, Parity Judgement, Magnitude Comparison SNARC effects and Numerical Distance effect (Pearson's r coefficient) in participants with reversed Attentional-SNARC effect (i.e., Positive Slope group: Att-SNARC; N ¼ 24).

3.1.

Methods

3.1.1.

Experimental design and tasks

Fig. 6 e Individual regression slopes in the AttentionalSNARC task (black bars) and corresponding slopes in (A) the Parity Judgement (green bars) and (B) Magnitude Comparison SNARC tasks (red bars).

Two experimental tasks were administered in two different sessions. In the first session, participants performed the AttSNARC task with the same four CTIs used in the Experiment 2 of the original report by Fischer et al. (2003). In the second session, participants performed a modified version of the MCSNARC task, i.e., a Cued MC-SNARC task. In this task the same central digits presented in the Att-SNARC task acted as numerical cues for digit-targets that were presented in one of the two lateral boxes used in the Att-SNARC task. Participants had to judge the magnitude of laterally presented digits, i.e., lower versus higher than “5”, by pressing one out of two response keys. To dissociate left/right spatial attentional effects generated by central numerical cues from the contamination of response-related effects linked to the use of left/right codes in the selection of the response, participants were required to

provide RTs by choosing between the lower or the higher of two vertically arranged response keys, i.e., between response keys that were not horizontally arranged like the lateral boxes where targets were presented. Orthogonal dissociation between lower/higher spatial response codes and the possible left/right attentional shifts induced by central numerical cues, allows to tease apart the influence of response bias and better isolate the attentional advantages produced by these cues (Cairney, 1975; Drew, 1896; Figliozzi, Guariglia, Silvetti, Siegler, & Doricchi (2005); Spence, Shore, & Klein, 2001). This procedure allows exploring the direct interaction between the Att-SNARC and the SNARC effect at different levels of cognitive processing. First, we were interested to assess whether within the context of a MC-SNARC task numerical cues can induce lateral shifts of attention that are directionally congruent with the magnitude of the cue. Second, we wished to explore whether these shifts of attention modulate the SNARC. As an example, speeded or increased SNARC could be observed when lateral numerical targets are presented in the side of space that is spatially congruent with the magnitude of the cue. Participants performed the Att-SNARC task in the first session and the Cued MC-SNARC task with lateral targets in the second session. Sessions were ran on different days and were separated by an interval of three/four days. Before running the Att-SNARC and the Cued MC-SNARC experiments, the modified MC-SNARC task with vertically arranged response keys was validated on a different sample of participants that performed the task without the presentation of central digit cues, i.e., an Uncued MC-SNARC task with lateral targets (see Supplementary Analyses and Results, paragraph 2.1).

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Fig. 7 e Study 2 e Experiment 1: Attentional-SNARC task. Average RTs (with SE) to targets presented in the left and right side of space plotted as a function of the magnitude of central digit cues, i.e., Low (1,2) or High (8,9), and Cue-Target Interval.

Fig. 8 e Study 2 e Experiment 2: Cued Magnitude Comparison SNARC task. Average RTs (with SE) plotted as a function of ResponseeKey position (Low, High) and Target Magnitude (lower than 5, higher than 5), in the following experimental conditions: (A) Low Digit Cue (1,2) eTarget Left Side, (B) Low Digit Cue (1,2) e Target Right Side, (C) High Digit Cue (8,9) eTarget Left Side and (D) High Digit Cue (8,9) e Target Right Side.

3.1.2. Att-SNARC task and Cued MC-SNARC task with lateral targets 3.1.2.1. PARTICIPANTS. Thirty-two healthy right-handed stu-

included in the study. None of them was previously included in Study 1 or in the validation experiment of the Uncued MCSNARC task with lateral targets.

dents (24 females and 8 males; age range: 20e29 years, mean age ¼ 23.2 years, SD ¼ 2.4 years) from the Faculty of Psychology of La Sapienza University in Rome participated in the experiments for course credit. All participants had normal or corrected-to-normal vision and were unaware of the purpose of the study. All participants completed the two tasks

3.1.2.2. EXPERIMENT 1: ATT-SNARC TASK. The Att-SNARC task used in Study 2 was similar to that of Study 1 except that now four cue-target CTIs (i.e., 250, 500, 750 and 1000 msec) were used. These were the same CTIs used in the Experiment 2 of the original study by Fischer et al. (2003). 512 experimental

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“1e9” except number 5; size ¼ .9  .7 ; font ¼ Arial; point size ¼ 20) inside the left or the right box. The presentation of the digit was terminated by the response of the participant. When no response was provided, the digit lasted on the screen for 1200 msec. The ITI was 500 msec. Participants were required to judge as fast as possible whether the Arabic digit was lower or higher than “5” by pressing one out of two keys positioned one above the other at the centre of the computer keyboard (i.e., “b” or “y”). Two experimental conditions were used. In the “Congruent” condition participants had to press the higher key (i.e., “y”) in response to digits higher than “5” and the lower key (i.e., “b”) in response to digits lower than “5”. In the “Incongruent” condition the pairing between keys and digits was reversed. The two experimental conditions were administered in two separate parts of the same session. The order of administration of experimental conditions was counterbalanced between participants. In addition, half of the participants pressed the higher key with the left index finger and the lower key with the right index finger while in the other half the association between hands and keys was reversed. The task was divided into four blocks, two for each experimental condition. Each block consisted of 256 trials (32 repetitions for each digit, 16 in the left box and 16 in the right one). A short break was allowed between blocks. A 10 min break was imposed between the two experimental conditions. Before each experimental condition, participants performed a training session of 32 trials to get acquainted with the digitekey association. In order to reduce visual priming effects between cues and targets, the size and font of lateral numerical targets (size ¼ .9  .7 ; font ¼ Arial; point size ¼ 20) were different from those of central numerical cues (size ¼ .8  .6 ; font ¼ Courier New; point size ¼ 18, Bold). The task of participants, the procedure of response collection, the number of trials and the administration of the different experimental conditions, i.e., Congruent vs Incongruent, were the same as in the Uncued MC-SNARC validation task (see Supplementary Analyses and Results, paragraph 2.1.1). Fig. 9 e Study 3. Attentional-SNARC task with explicit spatial coding of numerical cues. (A) Average RTs (with SE) to targets in the left and right side of space as a function of the magnitude of central digit-cues. (B) Slope describing the difference between RTs to targets in the right side of space minus targets in the left side of space (dRT in msec), plotted as a function of the magnitude of central digit-cues. (C) Individual regression slopes ordered by size: negative slopes indicate a conventional Attentional-SNARC effect, positive slopes a reversed Attentional-SNARC effect.

trials were administered (128 repetitions for each digit-cue) plus 64 catch trials with no target presentation. Trials were administered in two consecutive blocks that were separated by a 5 min pause.

3.1.2.3. EXPERIMENT 2: CUED MC-SNARC TASK WITH LATERAL TARGETS. Each trial started with the sequence of fixation, cue presentation and CTIs events of the Att-SNARC task. These were followed by the presentation of an Arabic digit (range

3.2.

Results

3.2.1.

Experiment 1: Att-SNARC task

5.3% of trials were discarded from the analyses. Individual mean RTs were first entered in a Digit-Cue (1, 2, 8, 9)  TargeteSide (left, right)  CTI (250, 500, 750, 1000 msec) ANOVA. No significant Digit-Cue  TargeteSide interaction [F (3,93) ¼ 1.4, p ¼ .26, h2 ¼ .04] or Digit-Cue  TargeteSide  CTI interaction [F (9,279) ¼ .6, p ¼ .81, h2 ¼ .02] were found. These results highlight the absence of the Att-SNARC. The same null results were also observed when RTs were collapsed across trials with low (1, 2) and high (8, 9) cue magnitude and entered in a Cue-Magnitude (low, high)  TargeteSide (left, right)  CTI (250, 500, 750, 1000 msec) ANOVA. This showed no significant Cue-Magnitude  TargeteSide [F (1, 31) ¼ 1.5, p ¼ .22, h2 ¼ .05] or Cue-Magnitude  TargeteSide  CTI [F (3,93) ¼ .05, p ¼ .99, h2 ¼ .002] interaction. These results were confirmed by regression slope analyses (see Supplementary Analyses and Results, paragraph 2.2.1). These analyses also documented no influence of TaskePart (First Half, Second Half) on the AttSNARC (Fig. 7).

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Split-half testing showed no reliability of the task (r1,2 ¼ .08, SpearmaneBrown correction ¼ .17, p ¼ .69). In summary, these results confirm the absence and the unreliability of the Att-SNARC effect documented in Study 1.

3.2.2. Experiment 2: Cued MC-SNARC task with lateral targets 10.1% of trials were discarded from the analyses. Individual mean RTs were entered in a Hand-Key condition (left handlower key/right hand-higher key, left hand-higher key/right hand-lower key)  Cue-Magnitude (low, high)  TargeteMagnitude (lower, higher)  ResponseeKey (lower, higher)  TargeteSide (left, right)  CTI (250, 500, 750, 1000 msec) mixed ANOVA. Hand-Key condition was not significant [F (1,30) ¼ 1.52, p ¼ .23, h2 ¼ .05] and showed no interaction with other factors (all p > .05). This result shows no influence of hand position on RTs. The CueMagnitude  TargeteSide interaction did not reach significance [F (1,30) ¼ 2.1, p ¼ .12, h2 ¼ .09] and showed no interaction with other factors (all p > .05). This suggests that within a task set requiring the explicit processing of the magnitude of target-digits, the magnitude of central digit-cues does not generate significant spatial shifts of attention (i.e., low cuesleftward shifts, high cues-rightward shifts). The TargeteMagnitude  ResponseeKey interaction was significant, demonstrating the presence of the SNARC [F (1,30) ¼ 6.2, p ¼ .02, h2 ¼ .17; lower targets: lower-key 586 msec vs higherkey 609 msec, p ¼ .08; higher targets: higher-key 590 msec vs lower-key 612 msec, p ¼ .08]. These results were confirmed by regression slope analyses (see Supplementary Analyses and Results, paragraph 2.3.1). These analyses also documented no influence of TaskePart (First Half, Second Half) on the Att-SNARC and the MC-SNARC. The TargeteSide  TargeteMagnitude  ResponseeKey interaction was not significant [F (1,30) ¼ 1.1, p ¼ .29, h2 ¼ .03] showing that the SNARC was equivalent between numerical targets presented in the left and right side of space. The CueMagnitude  TargeteMagnitude  ResponseeKey interaction was not significant [F (1,30) ¼ .05, p ¼ .82, h2 ¼ .001] showing that the strength of the SNARC was equivalent when numerical targets were preceded by low or high numerical cues. The Cue-Magnitude  TargeteMagnitude  ResponseeKey  TargeteSide interaction was also not significant [F (1,30) ¼ .06, p ¼ .46, h2 ¼ .02] pointing out that the SNARC observed after the presentation of low and high numerical cues was equivalent when targets were presented on the side of space that was congruent or incongruent with the numerical magnitude of the cue (i.e., congruent: low cues-left side, high cues-right side; incongruent: low cues-right side, high cues-left side). Finally, the Cue-Magnitude  TargeteMagnitude interaction that qualifies semantic numerical priming, i.e., faster response for magnitude compatible cue-target pairings, did not reach significance [F (1,30) ¼ 3.36, p ¼ .08, h2 ¼ .10]. Inspection of the means showed that following low numerical cues, RTs to targets lower or higher than 5 were identical (597 msec) whereas high numerical cues produced a no significant reversed facilitation for targets lower than 5 (598 msec vs 603 msec). A series of control analyses showed that cuetarget visual priming effect, i.e., the possible facilitation in the processing of numerical targets preceded by numerically

identical cues (e.g., cue “1”- target “1”, cue “9”- target “9”) had no influence on the Att-SNARC and on the SNARC observed in the Cued MC-SNARC task (see Supplementary Analyses and Results, paragraph 2.3.2) (Fig. 8) Split-half testing showed that while the Att-SNARC was not reliable (r1,2 ¼ .008, SpearmaneBrown correction ¼ .01, p ¼ .96) the MC-SNARC was highly reliable (r1,2 ¼ .74, SpearmaneBrown correction ¼ .85, p < .001).

3.3. Correlations among the Att-SNARC in Experiment 1 and the Att-SNARC and MC-SNARC effects in Experiment 2 A series of Pearson-r correlations analyses highlighted no correlation between the Att-SNARC in Exp. 1 and the MCSNARC in Exp. 2 (r ¼ .16, p ¼ .38), between the Att-SNARC in Exp. 1 and the Att-SNARC in Exp. 2 (r ¼ .05, p ¼ .79) and between the Att-SNARC and the MC-SNARC in Exp. 2 (r ¼ .08, p ¼ .64). No correlation between the Att-SNARC of both experiments and the SNARC in Exp. 2 was also found (all p > .38) when the slopes defining the SNARC were calculated using only the subset of digits shared with Att-SNARC task (i.e., 1, 2, 8 and 9).

4. Study 3: testing the influence of the explicit spatial coding of numerical cues on the Att-SNARC effect The Cued MC-SNARC task administered in Study 2 allowed for a direct investigation of the relationship between the AttSNARC and the SNARC effect. The results of the study showed neither a significant nor a reliable Att-SNARC and a clear and reliable MC-SNARC. No interaction or correlation was found between the two tasks. These results confirm those obtained through a correlational approach in Study 1. All together these findings suggest no left-to-right mental organization of ascending number magnitudes in the Att-SNARC task and reconfirm the adoption of a left-to-right organization of number magnitudes in the SNARC task. A salient difference between the SNARC and the Att-SNARC task is that in the former task the selection of motor responses is based on the association between number magnitudes and left/right spatial codes whereas no such association for response selection is present in the latter task. As a consequence, the results of Study 1 and 2 suggest a response-related origin of the spatial coding of numbers. Nonetheless, a number of previous studies have suggested that the Att-SNARC can be elicited when, following speeded target detection, participants are required to determine whether the numerical cue comes before or after the midpoint of the ordinal sequence of cues presented during the task (i.e., midpoint ¼ 5 with cues 1, 2, 8 and 9; Dodd et al., 2008) or when participants are asked to recall the ordinal position occupied by the numerical cue in a random sequence of 4 numbers temporarily stored in working memory (van Dijck & Fias, 2011; van Dijck, Abrahamse, Majerus, & Fias, 2013). These evidences suggest that the use of left/right codes for response selection might not be the only source of the left-to-right mental arrangement of numbers and that, due to the automatic retrieval of culturally acquired left-to-right reading habits, this representation can also be

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evoked when a task requires the analysis of the ordinal position of a numerical item. In addition to these results, Gevers et al. (2010; Experiment 1) showed that a significant PJSNARC can also be produced when participants must associate verbal “left” versus “right” responses to the parity of numbers, showing that the verbal-spatial coding of numbers is sufficient to obtain the SNARC effect. Here, in a third study we wished to expand on these suggestions and test whether a significant Att-SNARC can be elicited when central numerical cues must be processed through the use of left/right spatial codes although the same codes play no role in the selection of the motor response to lateral targets. To this aim we administered the Att-SNARC task to a new sample of participants and asked them to speak out, after speeded manual detection of lateral targets, whether the central numerical cue preceding the target is positioned to the left or to the right of the number “5” on the mental equivalent of a spatial ruler.

4.1.

Method

4.1.1.

Participants

Twenty-four healthy right-handed undergraduate students (19 females, 5 males; age range: 20e30 years, mean age ¼ 23.2 years, SD ¼ 2.5 years) from the Faculty of Psychology of La Sapienza University in Rome participated in the experiment for course credit. All participants had normal or corrected-tonormal vision and were unaware of the purpose of the study. None of the participants was previously included in Study 1 and 2.

4.1.2.

Procedure and design

The Att-SNARC task used in Study 3 was identical to that of Study 1 except that following the primary speeded manual detection of the lateral target, in each trial participants had to speak out whether the central numerical cue preceding the target is positioned to the left or to the right of the number 5 on the mental equivalent of a spatial ruler. Vocal responses were recorded through a microphone for off-line scoring.

4.2.

Results

5.5% of trials were discarded from the analysis. No error was virtually observed in the left/right classification of digit-cues (i.e., < .2%). Individual mean RTs were first entered in a Digit-Cue (1, 2, 8 and 9)  TargeteSide (left, right)  CTI (500, 750 msec) ANOVA. The interaction between Digit-Cues and TargeteSide was significant [F (3, 69) ¼ 21.32, p < .001, h2 ¼ .48] highlighting the presence of the Att-SNARC. Post-hoc tests showed that the Att-SNARC was significant for each digit cue (1: left target ¼ 336 msec vs right target ¼ 354 msec, p < .001; 2: left target ¼ 340 msec vs right target ¼ 351 msec, p ¼ .015; 8: left target ¼ 349 msec vs right target ¼ 334 msec, p < .01; 9: left target ¼ 353 msec vs right target ¼ 331 msec, p < .001). The AttSNARC was further verified collapsing RTs across trials with low (1, 2) and high (8, 9) cue magnitude. A Cue-Magnitude (low, high)  TargeteSide (left, right)  CTI (500, 750 msec) ANOVA highlighted a significant Cue-Magnitude  TargeteSide interaction [F (1, 23) ¼ 41.8, p < .001, h2 ¼ .65], confirming the presence of the Att-SNARC. This was qualified by post-hoc

311

tests (low digit magnitudes: left target ¼ 338 msec vs right target ¼ 352 msec, p < .001; high digit magnitudes: left target ¼ 351 msec vs right target ¼ 333 msec, p < .001). No other interaction resulted significant. These results were confirmed by regression slope analyses (see Supplementary Analyses and Results, paragraph 3.1). These analyses also documented no influence of TaskePart (First Half, Second Half) on the Att-SNARC at both CTIs (Fig. 9) Split-half testing showed that the Att-SNARC task only approached reliability at CTI-750 msec (r1,2 ¼ .36, SpearmaneBrown correction ¼ .53, p ¼ .082), whereas it was not reliable both at CTI-500 msec (r1,2 ¼ .12, SpearmaneBrown correction ¼ .29, p ¼ .55) and when the two CTIs were collapsed (r1,2 ¼ .07, SpearmaneBrown correction ¼ .13, p ¼ .73). These findings suggest that the explicit and direct association between left/right spatial codes and numerical cues can induce the generation of lateral shifts of attention that are directionally congruent with the magnitude of the cues. Nonetheless, it is worth noting that the link between space and number magnitudes revealed by these shifts proved to be not as reliable as the response-related one generated during the performance of SNARC task.

5.

Discussion

The main results of the present series of studies show that the mere perception of Arabic digits presented at central fixation does not produce automatic and reliable magnitude-related shifts of spatial attention, i.e., leftward shifts following small digit magnitudes and rightward shifts following large digit magnitudes. This result was found both in Study 1, when the Att-SNARC was tested using the two CTIs at which the effect was originally reported (i.e., 500 and 750 msec.; Fischer et al., 2003), and in Study 2 when the effect was tested using the full range of CTIs adopted in the original investigation by Fischer and co-workers (i.e., 250, 500, 750 and 1000 msec; Fischer et al., 2003; Experiment 2). In the whole sample of sixty participants tested in Study 1, individual differences in the strength of the Att-SNARC were also not correlated to the strength of the significant and reliable SNARC effects observed in the PJ and MC tasks. The absence of relationship between the strength of the Att-SNARC and that of the SNARC was confirmed in the Experiment 2 of Study 2. This study highlighted no direct influence of the Att-SNARC on the SNARC when the interaction between these two effects was assessed in a task where the numerical cues of the Att-SNARC task acted as cues for the spatially lateralised numerical targets of a MC-SNARC task. The magnitude of these cues produced no influence on the SNARC. Within the same task set, the CueMagnitude  TargeteSide interaction signaling the Att-SNARC was not statistically significant and showed no significant interaction with the SNARC. Nonetheless the Att-SNARC showed a slight trend toward significance, i.e., p ¼ .13. This non-significant tendency could be considered consistent with the set of results reported by Zanolie and Pecher (2014). In a first experiment (Exp. 3), these authors found the Att-SNARC when after speeded detection of lateral targets, participants were asked to judge the magnitude of central digit cues (Exp.

312

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3). Unfortunately, the same authors failed to replicate this finding in an identical control re-test experiment (Exp. 6) included in the same study. Future studies should probably expand on these findings and investigate further whether the instruction of explicitly processing the magnitude of numerical items triggers a stable and reliable left-to-right representation of the same items.

5.1.

Insights from the study of individual differences

All together, these findings suggest that shifts of attention related to mere number perception have no role in the genesis of the SNARC effect. In Study 1, the SNARC effects observed in the PJ and MC tasks were not significantly correlated, a result suggesting that the cognitive mechanisms at the base of these two effects are, at least, not entirely overlapping. To our knowledge this is one of the first direct demonstrations of the functional dissociation between the PJ- and MC-SNARC effects (see also a preliminary communication by Cipora (2014) that was presented during the same meeting in which our results were also presented (Fattorini, Pinto, Aglietti, Rotondaro, & Doricchi, 2014)). Interesting qualifications of the above summarised conclusions were obtained in Study 1, when inter-individual variations in the strength of the Att-SNARC were investigated by separating the whole sample of participants in the subsamples of those showing a conventional and a reversed Att-SNARC. This investigation provided three main results. First, in both of these subsamples no correlation was found between the strength of the Att-SNARC and that of the PJ- and MC-SNARC effects. Second, no difference between the same subsamples of participants was found in the strength of the PJ- and MC-SNARC effects. These two results emphasise further the functional independence of the SNARC from the Att-SNARC. Third, a significant correlation between the SNARC in the PJ and MC tasks was found in the subsample of participants with the conventional Att-SNARC whereas the same correlation was absent in the subsample with reversed Att-SNARC. This last finding is potentially intriguing, as it suggests that participants who tend to perform magnituderelated shifts of attention have similar performance in the PJ and MC task. Nevertheless, this conclusion should be considered with caution and tested further because the correlation between the PJ- and MC-SNARC in AttSNARC þ participants did not resist to correction for multiple comparisons. In agreement with the general dissociation between the PJ- and MC-SNARC effects, investigations by Herrera, Macizo, and Semenza (2008) and van Dijck, Gevers, and Fias (2009) have suggested that the PJ and MC task rely on different cognitive resources. Herrera et al. (2008) showed that the maintenance in working memory of spatial information abolishes the MC-SNARC whereas a phonological working memory load produces no interference. van Dijck et al. (2009) replicated and expanded these findings and showed that a phonological working memory load abolishes the PJ-SNARC but not the MC one. In addition to this, in a principal component analysis run on data gathered from the performance of 17 right brain damage patients in Number Interval Bisection, Line Bisection, PJ-SNARC, MC-SNARC tasks and from the evaluation of the Distance Effect, van Dijck,

Gevers, Lafosse, and Fias (2012) showed that the PJ- and MCSNARC load on different factors.

5.2.

Observations on the “numerical distance effect”

In Study 1, the Numerical Distance effect observed in the MCSNARC task was not correlated with the PJ- and MC-SNARC effects or with the Att-SNARC. On the one hand, these findings are in agreement with previous observations by Herrera et al. (2008) in healthy adults and with those by Schneider, Grabner, and Paetsch (2009) who found weak or no correlation between the SNARC and Numerical Distance effects in large samples of fifth and sixth graders. On the other hand, our findings are not in agreement with the results of a recent study by Viarouge, Hubbard, and McCandliss (2014) who found a significant positive correlation between the PJ-SNARC and the Numerical Distance effect in a relatively large sample of 35 adult participants. Based on this correlation, these authors concluded that the SNARC and the Numerical Distance effect characterise, respectively, the spatial features and the precision with which number magnitudes are mapped on the same mental representation, i.e., the MNL. They also argued that the positive correlation between these two effects points out that the more participants rely on a spatial representation of number magnitudes the less precise is the representation of the same magnitudes, i.e., the more participants are prone to interference between the representations of adjacent magnitudes. Unfortunately, the results of our study do not support these conclusions. It is worth noting that in the study by Viarogue and co-workers, the Numerical Distance effect that was used to test the correlation with the PJ-SNARC was gathered from a MC task in which no SNARC was observed. This latter finding provides direct evidence for the nonnecessary association between the Distance effect and the SNARC and suggests the opportunity of investigating further the relationship between these two effects. Viarogue and coworkers noted that since in their study the PJ task was always performed before the MC task, the absence of the MCSNARC might have been due to contextual-strategic effects linked to the fixed order of task administration. In the present study the order of administration of the PJ and MC task was counter-balanced between participants: nonetheless, in agreement with the finding by Viarogue et al. (2014), we found that the MC-SNARC, though statistically significant, was reduced in the group of participant who performed first the PJ task.

5.3. Response-related components of the spatial coding of number magnitudes: insight from present and past findings on the Att-SNARC and SNARC effects and from investigations in patients with spatial neglect The findings from our study point out that no reliable relationship is present between the magnitude of Arabic digit cues presented at central fixation and the speed of unimanual RTs to ensuing targets appearing to the left or to the right of fixation. On the contrary, within the same participants clear RTs advantages are present when, based on a forced choice between a left- and right-side manual response key, left-side responses must be associated with small digit magnitudes

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and right-side responses with large ones. In our view these results provide support to the response-related interpretation of the SNARC effect (Gevers et al., 2006; Keus & Scwarz, 2005; for a similar interpretation of the Simon-effect see Ansorge & Wu¨hr, 2004) and of the interaction between number and space coding (Aiello et al., 2012). On these grounds, one should conclude that the association between leftward and rightward shifts of attention and, respectively, the coding of small and large number magnitudes is not an inherent and automatic one and that it is rather due to cognitive mechanisms triggered by the task set. We hypothesise that in the case of SNARC tasks, the necessity of making a forced choice between left versus right spatial codes triggers the recourse to the culturally acquired left-to-right organization of ascending number magnitudes and the setting of a temporary link between the representation of these magnitudes and the left-toright coding of space. In this sense, it is the use of spatial codes for the selection of motor actions that “makes the link between numbers and space representation” (Rossetti et al., 2004). A number of studies also pointed out that during the performance of SNARC tasks, the left/right coding of number magnitudes is susceptible to important inter-individual variations. As an example, participants with higher mathematical proficiency, i.e., participants who are likely endowed with more efficient automatic access to “abstract” number representations (Hoffmann, Mussolin, Martin, & Schiltz, 2014), have reduced PJ-SNARC effect compared to those with lower mathematical proficiency (Hoffmann et al., 2014) or literary background (Dehaene et al., 1993). It would be an important matter of future investigation establishing which of the mechanisms involved in the genesis of the SNARC are influenced by mathematical proficiency. It is worth of note that, though reduced, in participants with high mathematical proficiency the SNARC is usually still significant. In our view this result points out that mathematical proficiency can only reduce, though not abolish, the strong influence of spatial response-related factors on the genesis of the SNARC. This conclusion is also compatible with studies that have failed to document variations of the SNARC among participants with different mathematical proficiency (Cipora & Nuerk, 2013). Observations in right brain damaged patients (RBD) with left attentional neglect provide support to the responserelated explanation of numberespace interaction. These studies show no systematic association between spatial neglect and pathological numerical biases in tasks that do not require the left versus right coding of motor responses and significant association between neglect and numerical biases in SNARC tasks requiring the left versus right coding of motor responses. On the one hand, studies using the “number interval bisection task”, which requires stating verbally the number that is halfway between two other numbers (Zorzi,  , 2002), have demonstrated that the pathoPriftis, & Umilta logical bias toward numbers higher than the true interval midpoint, i.e., away from small numbers on the putative left side of the interval, is dissociated both from neglect (Aiello et al., 2012; van Dijck, Gevers, Lafosse, & Doricchi, (2011); Doricchi, Guariglia, Gasparini, & Tomaiuolo, 2005 and Doricchi et al., 2009; Loetscher & Brugger, 2009; Pia et al., 2012; Loetscher, Nicholls, Towse, Bradshaw, & Brugger, 2010; Rossetti et al., 2004 and Rossetti et al., 2011) and neglect

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severity (Aiello, Merola, & Doricchi, 2013; van Dijck et al., 2012; Doricchi et al., 2009). In addition, when RBD patients are required to bisect hour/time intervals, the same numerical bias is paradoxically correlated to a bias toward larger hournumbers on the left side of a visual or mental clock-face (Aiello et al., 2012; Rossetti et al., 2011). This finding suggests that in numerical tasks that do not require the left versus right spatial coding of a motor response, RBD patients suffer a deficit in the representation of small number magnitudes independently from the spatial positioning of these magnitudes on the left or the right side of a mental image. A recent fMRI investigation supports this interpretation by showing in the superior parietal cortex of the right hemisphere a topographically organised representation of small number magnitudes that is functionally and anatomically segregated from neuronal populations that regulate shifts of visual attention (Harvey et al., 2013). In contrast to studies using the verbal number interval bisection task, investigations that have tested the performance of neglect patients in the SNARC task have homogenously highlighted slowed RTs for number magnitudes (i.e., “4”) that are immediately lower than the numerical reference (i.e., adjacent to the left of “5”) as compared with numbers (i.e., “6”) that are immediately higher than the same reference (i.e., adjacent to the right of “5”; van Dijck et al., 2012; Vuilleumier, Ortigue, & Brugger, 2004; Zorzi et al., 2012). By showing a RTs disadvantage for numbers positioned to the “left” of the reference, these findings supports the spatial organization of number magnitudes during the performance of SNARC tasks.

5.4. Non response-related components in spaceenumber interaction: are they stable and reliable as response-related ones? The response-related account of the SNARC effect does not necessarily exclude that other factors can play a role in the production of the SNARC and in setting the interaction between numbers and space. As an example, it was recently found that when short arbitrary sequences of up to 5 digits are used in a PJ SNARC task, the coding of ordinal information in working memory, i.e., the coding of the position occupied by each digit in the sequence, has a determinant influence on the SNARC (van Dijck & Fias, 2011). Moreover, this positional influence is entirely independent from the magnitude of the digit. These findings point at an important role of working memory functions on the SNARC. This might imply that response-related factors are integrated with number representation at an intermediate working memory level. Nonetheless one should note that in conventional SNARC tasks no selected short sequence of digit must be considered, so that, in this case, task performance is probably more linked to the semantic long-term memory representation of number magnitudes. On this ground, we think that in conventional SNARC tasks the primary source of the left-to-right representation of number magnitudes is the left versus right coding of motor responses. Nonetheless, in agreement with the possibility that different mechanism might determine the interaction between space and number processing, the findings of our Study 3 showed that in a variation of the Att-SNARC task that required the explicit left/right coding of numerical cues

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according to spatial information stored in long term memory (i.e., the structure of a ruler), cues were effective in promoting shifts of spatial attention toward their long term memory position. This result suggests that the left-to-right representation of number magnitudes can also be elicited when left/ right codes are associated directly to numbers rather than indirectly through response-selection mechanisms. Nonetheless, it is worth noting that in the variation of the AttSNARC task used in our Study 3, the Att-SNARC effect resulted unreliable at the shorter 500 msec CTI and only approached reliability at the longer 750 msec CTI. This result points at an endogenously driven rather than automatic origin of the Att-SNARC and suggests that the spatial representation of number magnitudes evoked in this task is less reliable and stable than that evoked through response-related mechanisms in the SNARC task.

5.5.

Conclusions

To summarise, our study shows that the investigation of inter-individual differences in large samples of healthy participants can provide important insights on relevant issues in numerical cognition. The results gathered from the study of individual differences on the consistency and reliability of the Att-SNARC (Study 1), were confirmed by testing the direct interaction between the Att-SNARC and the SNARC (Study 2) and the dependency of the Att-SNARC on strategical factors triggered by the task set (Study 3). The joint results of these three studies provide evidence that might help reaching an univocal explanation of the SNARC effect and an improved definition of the behavioural conditions that elicit the interaction between the representation of space and the representation of number magnitudes. This evidence can promote investigations that should expand and complete the findings and conclusions of the present study. In the light of the poor reliability of the AttSNARC that we have spotted in our experiments, new investigations are particularly suitable.

Acknowledgements This research was supported by grants from the University “La Sapienza” of Rome and the Fondazione Santa Lucia IRCCS e Rome to Fabrizio Doricchi. We thank Jacopo Aglietti for help in data collection.

Supplementary data Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.cortex.2015.09.007.

references

Aiello, M., Jacquin-Courtois, S., Merola, S., Ottaviani, T., Tomaiuolo, F., Bueti, D., et al. (2012). No inherent left and right side in human ‘mental number line’: evidence from right

brain damage. Brain, 135, 2492e2505. http://dx.doi.org/10.1093/ brain/aws114 (first published online May 10, 2012). Aiello, M., Merola, S., & Doricchi, F. (2013). Small numbers in the right brain: evidence from patients without and with spatial neglect. Cortex, 49(1), 348e351. http://dx.doi.org/10.1016/ j.cortex.2012.06.002. Ansorge, U., & Wu¨hr, P. (2004). A response-discrimination account of the Simon effect. Journal of Experimental Psychology: Human Perception and Performance, 30(2), 365. http://dx.doi.org/ 10.1037/0096-1523.30.2.365. Bonato, M., Priftis, K., Marenzi, R., & Zorzi, M. (2009). Normal and impaired reflexive orienting of attention after central nonpredictive cues. Journal of Cognitive Neuroscience, 21(4), 745e759. http://dx.doi.org/10.1162/jocn.2009.21. Cairney, P. T. (1975). Bisensory order judgement and the prior entry hypothesis. Acta Psychologica, 39(5), 329e340. http:// dx.doi.org/10.1016/0001-6918(75)90025-6.  , C. (2007). Casarotti, M., Michielin, M., Zorzi, M., & Umilta Temporal order judgement reveals how number magnitude affects visuospatial attention. Cognition, 1, 101e117. http:// dx.doi.org/10.1016/j.cognition.2006.09.001. Cipora, K. (2014). Between task consistency of the SNARC effect. In Abstract presented at the European Workshop Cognitive Neuropsychology, Bressanone Italy, 26the31st January 2014. http://bressanone.dur.ac.uk/searchAbstracts.php? showAbstract¼2113. Cipora, K., & Nuerk, H. C. (2013). Is the SNARC effect related to the level of mathematics? No systematic relationship observed despite more power, more repetitions, and more direct assessment of arithmetic skill. The Quarterly Journal of Experimental Psychology, 66(10), 1974e1991. http://dx.doi.org/ 10.1080/17470218.2013.772215. Cohen Kadosh, R., Lammertyn, J., & Izard, V. (2008). Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation. Progress in Neurobiology, 84, 132e147. http:// dx.doi.org/10.1016/j.pneurobio.2007.11.001. Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371e396. http:// dx.doi.org/10.1037/0096-3445.122.3.371. Dehaene, S., Dupoux, E., & Mehler, J. (1990). Is numerical comparison digital? Analogical and symbolic effects in twodigit number comparison. Journal of Experimental Psychology: Human Perception and Performance, 16, 626e641. http:// dx.doi.org/10.1037/0096-1523.16.3.626. van Dijck, J. P., Abrahamse, E. L., Acar, F., Ketels, B., & Fias, W. (2014). A working memory account of the interaction between numbers and spatial attention. The Quarterly Journal of Experimental Psychology, 67(8), 1500e1513. http://dx.doi.org/ 10.1080/17470218.2014.903984. van Dijck, J. P., Abrahamse, E., Majerus, S., & Fias, W. (2013). Spatial attention interacts with serial order retrieval from verbal working memory. Psychological Science, 24, 1854e1859. http://dx.doi.org/10.1177/0956797613479610. van Dijck, J. P., & Fias, W. (2011). A working memory account for spatialenumerical associations. Cognition, 119(1), 114e119. http://dx.doi.org/10.1016/j.cognition.2010.12.013. van Dijck, J. P., Gevers, W., & Fias, W. (2009). Numbers are associated with different types of spatial information depending on the task. Cognition, 113(2), 248e253. http:// dx.doi.org/10.1016/j.neuropsychologia.2011.05.005. van Dijck, J. P., Gevers, W., Lafosse, C., Doricchi, F., & Fias, W. (2011). Non-spatial neglect for the mental number line. Neuropsychologia, 49(9), 2570e2583. http://dx.doi.org/10.1016/ j.neuropsychologia.2011.05.005. van Dijck, J. P., Gevers, W., Lafosse, C., & Fias, W. (2012). The heterogeneous nature of numberespace interactions. Frontiers

c o r t e x 7 3 ( 2 0 1 5 ) 2 9 8 e3 1 6

in Human Neuroscience, 5. http://dx.doi.org/10.3389/ fnhum.2011.00182. Dodd, M. D., Van der Stigchel, S., Leghari, M. A., Fung, G., & Kingstone, A. (2008). Attentional SNARC: there's something special about numbers (let us count the ways). Cognition, 108, 810e818. http://dx.doi.org/10.1016/j.cognition.2008.04.006. Doricchi, F., Guariglia, P., Gasparini, M., & Tomaiuolo, F. (2005). Dissociation between physical and mental number line bisection in right hemisphere brain damage. Nature Neuroscience, 8(12), 1663e1665. http://dx.doi.org/10.1038/nn1563. Doricchi, F., Merola, S., Aiello, M., Guariglia, P., Bruschini, M., Gevers, W., et al. (2009). Spatial orienting biases in the decimal numeral system. Current Biology, 19(8), 682e687. http:// dx.doi.org/10.1016/j.cub.2009.02.059. Drew, F. (1896). Attention: experimental and critical. The American Journal of Psychology, 7(4), 533e573. http://dx.doi.org/10.2307/ 1411848. Fattorini, E., Pinto, M., Aglietti, J., Rotondaro, F., & Doricchi, F. (2014). No inherent left and right side in the Mental Number Line: dissociation between Numerical Posner and SNARC effects in healthy participants. In Abstract presented at the European Workshop Cognitive Neuropsychology, Bressanone Italy, 26the31st January 2014. http://bressanone.dur.ac.uk/ searchAbstracts.php?showAbstract¼2064. Figliozzi, F., Guariglia, P., Silvetti, M., Siegler, I., & Doricchi, F. (2005). Effects of vestibular rotatory accelerations on covert attentional orienting in vision and touch. Journal of Cognitive Neuroscience, 17(10), 1638e1651. http://dx.doi.org/10.1162/ 089892905774597272. Fischer, M. H. (2006). The future for SNARC could be stark…. Cortex, 42(8), 1066e1068. Fischer, M. H., Castel, A. D., Dodd, M. D., & Pratt, J. (2003). Perceiving numbers causes spatial shifts of attention. Nature Neuroscience, 6, 555e556. http://dx.doi.org/10.1038/nn1066.  , C. (2006). Number magnitude Galfano, G., Rusconi, E., & Umilta orients attention, but not against one's will. Psychonomic Bulletin & Review, 13, 869e874. http://dx.doi.org/10.3758/ BF03194011. Gevers, W., Santens, S., Dhooge, E., Chen, Q., Van den Bossche, L., & Fias, W. (2010). Verbal-spatial and visuo-spatial coding of number-space interactions. Journal of Experimental Psychology: General, 139, 180e190. http://dx.doi.org/10.1037/a0017688. Gevers, W., Verguts, T., Reynvoet, B., Caessens, B., & Fias, W. (2006). Numbers and space: a computational model of the SNARC effect. Journal of Experimental Psychology: Human Perception and Performance, 32, 32e44. http://dx.doi.org/10.1037/ 0096-1523.32.1.32. Goffaux, V., Martin, R., Dormal, G., Goebel, R., & Schiltz, C. (2012). Attentional shifts induced by uninformative number symbols modulate neural activity in human occipital cortex. Neuropsychologia, 50(14), 3419e3428. http://dx.doi.org/10.1016/ j.neuropsychologia.2012.09.046. Harvey, B. M., Klein, B. P., Petridou, N., & Dumoulin, S. O. (2013). Topographic representation of numerosity in the human parietal cortex. Science, 341(6150), 1123e1126. http://dx.doi.org/ 10.1126/science.1239052. Herrera, A., Macizo, P., & Semenza, C. (2008). The role of working memory in the association between number magnitude and space. Acta Psychologica, 128(2), 225e237. http://dx.doi.org/ 10.1016/j.actpsy.2008.01.002. Hoffmann, D., Mussolin, C., Martin, R., & Schiltz, C. (2014). The impact of mathematical proficiency on the number-space association. PLoS One, 9(1), e85048. http://dx.doi.org/10.1371/ journal.pone.0085048. Hubbard, E. M., Piazza, M., Pinel, P., & Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nature Reviews Neuroscience, 6(6), 435e448. http://dx.doi.org/ 10.1038/nrn1684.

315

Hubbard, E. M., Ranzini, M., Piazza, M., & Dehaene, S. (2009). What information is critical to elicit interference in number-form synaesthesia? Cortex, 45(10), 1200e1216. Ishihara, M., Jacquin-Courtois, S., Flory, V., Salemme, R., Imanaka, K., & Rossetti, Y. (2006). Interaction between space and number representations during motor preparation in manual aiming. Neuropsychologia, 44(7), 1009e1016. http:// dx.doi.org/10.1016/j.neuropsychologia.2005.11.008. Jarick, M., Dixon, M. J., Maxwell, E. C., Nicholls, M. E., & Smilek, D. (2009). The ups and downs (and lefts and rights) of synaesthetic number forms: validation from spatial cueing and SNARCtype tasks. Cortex, 45(10), 1190e1199. http:// dx.doi.org/10.1016/j.cortex.2009.04.015. Keus, I. M., & Schwarz, W. (2005). Searching for the functional locus of the SNARC effect: evidence for a response related origin. Memory & Cognition, 33, 681e695. http://dx.doi.org/ 10.3758/BF03195335. Libertus, M., Woldorff, M., & Brannon, E. M. (2007). Electrophysiological evidence for notation independence in numerical processing. Behavioral and Brain Functions, 3, 1. http://dx.doi.org/10.1186/1744-9081-3-1. Loetscher, T., & Brugger, P. (2009). Random number generation in neglect patients reveals enhanced response stereotypy, but no neglect in number space. Neuropsychologia, 47(1), 276e279. http://dx.doi.org/10.1016/j.neuropsychologia.2008.08.005. Loetscher, T., Nicholls, M. E., Towse, J. N., Bradshaw, J. L., & Brugger, P. (2010). Lucky numbers: spatial neglect affects physical, but not representational, choices in a Lotto task. Cortex, 46(5), 685e690. http://dx.doi.org/10.1016/ j.cortex.2009.06.010. Lorch, R. F., Jr., & Myers, J. L. (1990). Regression analyses of repeated measures data in cognition research. Journal of Experimental Psychology: Learning, Memory, & Cognition, 16, 149e157. http://dx.doi.org/10.1037/0278-7393.16.1.149. Maloney, E. A., Risko, E. F., Preston, F., Ansari, D., & Fugelsang, J. (2010). Challenging the reliability and validity of cognitive measures: the case of the numerical distance effect. Acta Psychologica, 134, 154e161. http://dx.doi.org/10.1016/ j.actpsy.2010.01.006. Moyer, R. S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215, 1519e1520. http://dx.doi.org/10.1038/2151519a0. Mu¨ller, D., & Schwarz, W. (2007). Exploring the mental number line: evidence from a dual-task paradigm. Psychological Research, 71(5), 598e613. http://dx.doi.org/10.1007/s00426-006-0070-6.  dona, M., Cremasco, L., Gindri, P., Dal Monte, O., Pia, L., Neppi-Mo & Folegatti, A. (2012). Functional independence between numerical and visual space: evidence from right braindamaged patients. Cortex, 48(10), 1351e1358. http://dx.doi.org/ 10.1016/j.cortex.2012.04.005. Posner, M. I. (1980). Orienting of attention. The Quarterly Journal of Experimental Psychology, 32, 3e25. http://dx.doi.org/10.1080/ 00335558008248231. Price, M. C., & Mattingley, J. B. (2013). Automaticity in sequencespace synaesthesia: a critical appraisal of the evidence. Cortex, 49(5), 1165e1186. Proctor, R. W., & Cho, Y. S. (2006). Polarity correspondence: a general principle for performance of speeded binary classification tasks. Psychological Bulletin, 132, 416e442. http:// dx.doi.org/10.1037/0033-2909.132.3.416. Ranzini, M., Dehaene, S., Piazza, M., & Hubbard, E. M. (2009). Neural mechanisms of attentional shifts due to irrelevant spatial and numerical cues. Neuropsychologia, 47, 2615e2624. http://dx.doi.org/10.1016/ j.neuropsychologia.2009.05.011. Restle, F. (1970). Speed of adding and comparing numbers. Journal of Experimental Psychology, 83, 274e278. http://dx.doi.org/ 10.1037/h0028573.

316

c o r t e x 7 3 ( 2 0 1 5 ) 2 9 8 e3 1 6

Ristic, J., Wright, A., & Kingstone, A. (2006). The number line reflects top-down control. Psychonomic Bulletin & Review, 13, 862e868. http://dx.doi.org/10.3758/BF03194010. Rossetti, Y., Jacquin-Courtois, S., Aiello, M., Ishihara, M., brozzolli, C., & Doricchi, F. (2011). Neglect “around the Clock”: dissociating number and spatial neglect in right brain damage. In S. Dehaene, & E. M. Brannon (Eds.), Space, time and number in the brain: Searching for the foundations of mathematical thought (pp. 149e173). Amsterdam: Elsevier. Retrieved from http://dx.doi.org/10.1016/B978-0-12-385948-8. 00011-6. Rossetti, Y., Jacquin-Courtois, S., Rode, G., Ota, H., Michel, C., & Boisson, D. (2004). Does action make the link between number and space representation? Visuo-manual adaptation improves number bisection in unilateral neglect. Psychological Science, 15(6), 426e430. http://dx.doi.org/10.1111/j.09567976.2004.00696.x. Santens, S., & Gevers, W. (2008). The SNARC effect does not imply a mental number line. Cognition, 108(1), 263e270. http:// dx.doi.org/10.1016/j.cognition.2008.01.002. Schneider, W., Eschman, A., & Zuccolotto, A. (2002). E-Prime user's guide. Pittsburgh, PA: Psychology Software Tools. Schneider, M., Grabner, R. H., & Paetsch, J. (2009). Mental number line, number line estimation, and mathematical achievement: their interrelations in grades 5 and 6. Journal of

Educational Psychology, 101(2), 359. http://dx.doi.org/10.1037/ a0013840. Spence, C., Shore, D. I., & Klein, R. M. (2001). Multisensory prior entry. Journal of Experimental Psychology: General, 130(4), 799. http://dx.doi.org/10.1037/0096-3445.130.4.799. Viarouge, A., Hubbard, E. M., & McCandliss, B. D. (2014). The cognitive mechanisms of the SNARC effect: an individual differences approach. PLoS One, 9(4), e95756. http://dx.doi.org/ 10.1371/journal.pone.0095756. Vuilleumier, P., Ortigue, S., & Brugger, P. (2004). The number space and neglect. Cortex, 40(2), 399e410. http://dx.doi.org/10.1126/ science.1239052. Wood, G., Nuerk, H.-C., Willmes, K., & Fischer, M. H. (2008). On the cognitive link between space and number: a meta-analysis of the SNARC effect. Psychology Science Quarterly, 50(4), 489e525. Zanolie, K., & Pecher, D. (2014). Number-induced shifts in spatial attention: a replication study. Frontiers in Psychology, 5. http:// dx.doi.org/10.3389/fpsyg.2014.00987. Zorzi, M., Bonato, M., Treccani, B., Scalambrin, G., Marenzi, R., & Priftis, K. (2012). Neglect impairs explicit processing of the mental number line. Frontiers in Human Neuroscience, 6. http:// dx.doi.org/10.3389/fnhum.2012.00125.  , C. (2002). Brain damage: neglect Zorzi, M., Priftis, K., & Umilta disrupts the mental number line. Nature, 417(6885), 138e139. http://dx.doi.org/10.1038/417138.