size congruency paradigm: An ERP study

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a v a i l a b l e a t w w w. s c i e n c e d i r e c t . c o m

w w w. e l s e v i e r. c o m / l o c a t e / b r a i n r e s

Research Report

The interaction of task-relevant and task-irrelevant stimulus features in the number/size congruency paradigm: An ERP study Dénes Szűcs a,b,⁎, Fruzsina Soltész a a

University of Cambridge, Centre for Neuroscience, Faculty of Education, 184 Hills Road, Cambridge, CB2 2PQ, UK Research Institute for Psychology of the Hungarian Academy of Sciences, Department of Psychophysiology, Budapest, Hungary

b

A R T I C LE I N FO

AB S T R A C T

Article history:

We studied whether task-relevant numerical information and task-irrelevant physical size

Accepted 3 November 2007

information interact during perceptual and/or response processing in the number/size

Available online 12 November 2007

congruency paradigm (NSCP). Participants decided which of two simultaneously presented numbers was larger numerically. The physical size of numbers delivered neutral, congruent,

Keywords:

or incongruent information with numerical magnitude. Both stimulus- and response-locked

Facilitation

event-related brain potentials (ERPs) were analyzed. The lateralized readiness potential (LRP)

Interference

was used for indexing motor preparation. Similar early facilitation and interference effects

Perceptual interaction

appeared in the amplitude of ERPs between 150 and 250 ms after stimulus presentation,

Response competition

focused over parieto-occipital electrode-sites. We conclude that these effects reflected a

Numerical cognition

similar process in both facilitation and interference, related to a general increase of processing

Number representation

load and/or conflict detection. Further, we have replicated our former findings demonstrating

Distance effect

late facilitation and interference effects between 300 and 430 ms. These effects may be related

Comparison

to the conflict monitoring and response-selection activity of the anterior cingulate cortex, or may be related to higher level contextual analysis. Our findings suggest that facilitation and interference effects appear at multiple levels of stimulus and response processing. We have also demonstrated ERP amplitude effects as a function of numerical difference between the to-be-compared numbers both in stimulus- and response-locked ERPs. © 2007 Elsevier B.V. All rights reserved.

1.

Introduction

It is a major question how perceptual and response processes initiated by parallel processed task-relevant and task-irrelevant stimulus features interact with each other during cognitive processing. The number/size congruency paradigm (NSCP) pro-

vides a means to investigate this question. In the NSCP participants decide which one of two simultaneously presented Arabic digits is larger than the other one either in numerical magnitude or in physical size (Henik and Tzelgov, 1982; Duncan and McFarland, 1980). The relationship of numerical and physical size features of the digits may be neutral, congruent, or

⁎ Corresponding author. University of Cambridge, Centre for Neuroscience, Faculty of Education, 184 Hills Road, Cambridge, CB2 2PQ, UK. Fax: +44 01223 767602. E-mail address: [email protected] (D. Szűcs). Abbreviations: ACC, Anterior cingulate cortex; ANOVA, Analysis of variance; ERP, Event-related potential; fMRI, Functional magnetic resonance imaging; IPS, Horizontal intraparietal sulci; LRP, Lateralized readiness potential; NSCP, Number/size congruency paradigm; SNARC, Spatial–numerical association of response codes 0006-8993/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.brainres.2007.11.010

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incongruent. In the congruent condition the numerically larger digit is physically larger than the other digit (e.g. which is larger numerically? 2 or 9?). In the incongruent condition the numerically larger digit is physically smaller than the other one (e.g. which is larger numerically? 2 or 9?). In the neutral condition the digits do not differ on the task-irrelevant stimulus dimension (e.g. which is larger numerically? 2 or 9?). The RT is faster in the congruent condition than in the neutral condition, and the RT is slower in the incongruent condition than in the neutral condition. The speed-up of RT in the congruent condition relative to the neutral condition is called facilitation. The slowing of the RT in the incongruent condition relative to the neutral condition is called interference. The phenomena of facilitation and interference attest that the task-irrelevant stimulus feature is processed automatically and in parallel with the task-relevant feature (Henik and Tzelgov, 1982). However, it is an open question whether task-relevant and task-irrelevant features interact during perceptual and/or response processing. In order to examine this issue we have investigated the timing of facilitation and interference effects in the NSCP. According to the continuous flow model of Eriksen and Schultz (1979) stimulus processing can be roughly subdivided into temporally overlapping perceptual and response organization phases. These processing phases do not follow each other in a perfectly serial fashion (Sternerg, 1969). Rather, perceptual processes influence response activity in a continuous fashion even before the final completion of stimulus analysis: According to the continuous flow model information about the stimuli accumulates gradually during perceptual processing. As soon as the gradual perceptual processing of the stimuli reaches a certain degree, perceptual processes begin to influence response activity. Therefore even partially processed stimulus information can affect response activity. The more advanced the perceptual processing of stimulus features, the more they will influence response activity. An overt behavioural response is produced when the activation level of a certain response exceeds a criterion (Eriksen and Schultz, 1979; Smid et al., 1990; Eriksen et al., 1985; Coles et al., 1985; Gratton et al., 1988). Within the context of the continuous flow model stimulus features can interact with each other during the course of either perceptual or response processing. Considering the above model, numerical and size information can be thought to interact with each other during the perceptual and/or the response phase of the NSCP. Facilitation and interference effects result from these interactions. On the one hand, perceptual level interactions would suggest that stimulus features interact with each other at the level of stimulus representations (Hock and Egeth, 1970). On the other hand, interactions may also happen during the response phase. One possible explanation of interference during the response phase is that interactions are related to motor processes. This explanation assumes that the parallel processed numerical and physical size information compete with each other in order to dominate response activity (Morton and Chambers, 1973; Posner and Snyder, 1975). Facilitation and interference processes then result from motor facilitation/competition between the response processes initiated by task-relevant and task-irrelevant information. Another possibility is that response-phase facilitation/interference result from the interaction of complex and slow stimulus analysis processes (e.g. decisions about stimulus categories).

The high temporal resolution of event-related brain potentials (ERPs) offers a chance to determine whether facilitation and interference effects happen during perceptual or response processing. First, facilitation and interference effects in the amplitude of ERPs can reveal the onset and duration of facilitation and interference effects. Second, the so-called lateralized readiness potential (LRP) is able to track the onset of motor preparation. The LRP is a measure of motor cortex activation, and it indicates selective motor preparation and response initiation before an overt response is given (Gratton et al., 1988; De Jong et al., 1988). According to the conventional computation of the LRP a significant negative LRP deflection reflects a correct response tendency whereas a significant positive LRP deflection reflects an incorrect response tendency. A significant deviation of the LRP from the baseline suggests that motor preparation has begun. Therefore in the context of the continuous flow model (Eriksen and Schultz, 1979) the LRP can be used to determine the time point when enough perceptual information has been accumulated and the influencing of motor processing has begun. This, in turn, allows for the dissociation of cognitive processes happening during the perceptual and response phases. Using the above approach, in a recent ERP study of the NSCP (Szűcs and Soltész, 2007) we analyzed the timing of facilitation and interference effects in the amplitude of ERPs, and we have also monitored LRP effects. Contrasting the congruent and neutral conditions we found that numerical decisions were facilitated by task-irrelevant physical size information. Contrasting the incongruent and neutral conditions we found that numerical decisions interfered with task-irrelevant physical size information. One facilitation effect appeared in the amplitude of ERPs before the onset of motor preparation between 140 and 240 ms, another facilitation effect appeared after the onset of motor preparation between 280 and 320 ms. In contrast, ERP interference effects appeared only after the onset of motor preparation between 330–460 and 550–660 ms. Therefore we concluded that facilitation appeared during both the perceptual (early) and response processing (late) phases, whereas interference appeared solely during the response processing phase. Late facilitation and interference effects in the amplitude of ERPs in our previous data were in agreement with the first study of the NSCP (Schwarz and Heinze, 1998) and with a recent study published after the initial submission of the current article (Cohen-Kadosh et al., 2007). The study of Schwarz and Heinze (1998) used 6 recording electrodes, reported data on 2 electrodes, and contrasted the congruent and incongruent conditions (congruency effect) of the NSCP (Schwarz and Heinze, 1998). This study reported a congruency effect beginning from 368 ms post-stimulus in the numerical comparison task. This congruency effect appeared after the LRP had deviated from baseline (at 240 ms). Schwarz and Heinze (1998) wished to decide between the early and late interaction explanations by expecting that late interaction would be suggested especially by the following observations (bottom of page 1170): (1) There are no congruity effects in early difference potentials (their point b.i.). (2) The faster processed irrelevant stimulus dimension causes initial incorrect response activation measured by the LRP (their point b.ii). No early congruity effects were observed in the amplitude of ERPs (observing such

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effects would suggest early interaction), and no initial incorrect response activation was detected in the LRP. On the basis of the second observation it was concluded that response competition did not play a serious role in task-execution, and the observations were interpreted as demonstrating an interaction during perceptual, rather than during response processing. However, the study failed to directly demonstrate early congruency effects in the amplitude of ERPs during perceptual processing, and the interpretation of the LRP results is questionable. Most importantly, the lack of observing initial incorrect response activation was considered to support the early perceptual interaction hypothesis and reject the response competition hypothesis. However, “initial incorrect response activation” and “response competition” do not refer to the same phenomena. Detecting initial incorrect response activation would suggest that some dimension of the stimulus (e.g. physical size) was able to initiate a response before the other dimension (e.g. numerical information) did (Gratton et al., 1988; De Jong et al., 1988). This would indeed suggest that response competition plays a role in task execution. However, the lack of initial incorrect response activation is not sufficient proof for accepting that response competition does not play a role in task-execution. It simply suggests that none of the stimulus dimensions able to elicit a response were processed considerably faster than other dimensions. In such a case the task-relevant and task-irrelevant information initiates responses nearly at the same time, and it is unlikely that initial incorrect response activation will be detectable in the LRP. In contrast, if there is no substantial processing speed difference between the stimulus dimensions, response competition will have consequences during the part of the LRP going into the correct (negative) direction (this is acknowledged in point b.iii in Schwarz and Heinze, 1998): The LRP will deviate into the correct direction and there will be an LRP amplitude difference between the congruent and incongruent conditions. This is exactly what Schwarz and Heinze (1998) found. Considering that in their experiment there was only 21 ms difference between the RT in the numerical and physical comparison tasks, it seems that the processing speed of the numerical and size information was indeed nearly the same. Taken together with the fact that Schwarz and Heinze (1998) found only late (after the LRP has deviated from baseline) congruency effects in the amplitude of ERPs, and that they could not directly demonstrate early congruency effects in the amplitude of ERPs, we conclude that Schwarz and Heinze (1998) could not present sufficient evidence for supporting the early interaction account. The study of Cohen-Kadosh et al. (2007) contrasted the average of ERPs recorded in the neutral and congruent conditions with ERPs in the incongruent condition. The data was recorded on 128 electrodes, but only one electrode (Pz) and the LRP was presented. There were two main ERP findings. First, similarly to other studies (Schwarz and Heinze, 1998; Szűcs and Soltész, 2007) the study found a congruency effect over electrode Pz between 300 and 500 ms which suggests late interaction. Second, the study also showed a response-locked LRP difference (average of [neutral and congruent] vs. incongruent) at 200 ms before the response when numerical distance was 5, but not when distance was 1. This was considered to suggest that response-related processing is relevant when numerical

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distance is large, but not when distance is small. The lack of the response-locked effect was considered to suggest that the interaction happens during perceptual processing when numerical distance is small (stimulus-locked effects were not reported). However, similarly to the study of Schwarz and Heinze (1998), no early congruency effects in the amplitude of ERPs were demonstrated by Cohen-Kadosh et al. (2007). Therefore their conclusion about early perceptual processing, building on the lack of a response-locked effect, is questionable. A further issue is that both Schwarz and Heinze (1998) and Cohen-Kadosh et al. (2007) detected congruency effects on top of the P300 ERP component. First of all, it may be argued that P300 amplitude effects reflect “early” perceptual processing effects (Cohen-Kadosh et al., 2007, p. 965). This argument is problematic because the P300 amplitude is related to stimulus categorization decisions which happen relatively late, well after initial perceptual processing (Donchin, 1981). Therefore no firm conclusions can be drawn about perceptual processes by observing the P300 amplitude. Second, the P300 is not one component but rather, a complex of several components (e.g. Dien et al., 2004), it may even include response-related ERP effects (Verleger, 1997), and it may also be affected by ERP effects unrelated to the usual constituents of the P300 (e.g. response-interference effects). Therefore it is impossible to interpret ERP effects in the P300 time-range on electrode Pz without examining the topography of effects (Dien et al., 2004). The studies of Schwarz and Heinze (1998) and Cohen-Kadosh et al. (2007) failed to examine the topography of the P300-range effects. All in all, considering all available results, previous studies have demonstrated late amplitude effects which can suggest that late interactions play a major role in the NSCP (Schwarz and Heinze, 1998; Cohen-Kadosh et al., 2007; Szűcs and Soltész, 2007). However, previous studies could not convincingly demonstrate early interference effects, related to perceptual processing (only an early facilitation effect was detected in Szűcs and Soltész, 2007). This is surprising in the light of current numerical cognition research. Several functional magnetic resonance imaging (fMRI) studies have shown that there is a representation of numerical magnitude in the bilateral horizontal intraparietal sulci (IPS; for a review see Dehaene et al., 2004). In studies where subjects compared Arabic digits it has been demonstrated that the activity of the intraparietal sulci changes in function of the numerical difference between the compared numbers (Pinel et al., 2001, 2004; Kaufmann et al., 2005). Other studies suggest that the intraparietal sulci code not only symbolic but non-symbolic numerosities and physical quantities as well. These studies have shown that the activity of the intraparietal sulci changes in function of the difference between non-symbolically presented numerosities (e.g. when the number of dots in a display changes), and in function of the physical difference between to-be-compared physical quantities (e.g. when comparing line angles; Fias et al., 2001). This is the brain imaging correlate of the behavioural numerical distance effect (reaction time is slower when comparing closer than further away quantities; Moyer and Landauer, 1967). The imaging results are explained by assuming that numerical and physical magnitude is coded by a common magnitude representation in the brain. Strong support for this view stems from an fMRI study

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Fig. 1 – The 65-channel Geodesic Sensor Net. Electrodes 17 and 54 are marked by squares. These electrodes were used for the computation of the LRP. Other electrode positions are marked by dots. Numbered and circled dots denote the positions and numerical labels of electrodes shown in further figures. where participants saw two simultaneously presented Arabic digits and decided whether one of them was larger numerically or physically, or whether one of them was brighter than the other one (Pinel et al., 2004). The numerical, physical and luminance difference between the digits was manipulated. It was found that partially overlapping brain areas reacted to the

change in numerical and physical size difference, especially in the intraparietal sulci. This study provides direct evidence that partially identical neural networks participate in representing both numerical and physical magnitude (Dehaene et al., 2004). The above research suggests that a perceptual level interaction of numerical and physical magnitude information can be expected in the NSCP: It can be predicted that physical size and numerical magnitude will interact with each other during perceptual processing, at the level of the common intraparietal magnitude representation. Therefore it is remarkable, and merits further investigation that no perceptual level interference effect could be reliably demonstrated in earlier studies. As summarized above, the best established model of the magnitude representation predicts perceptual level interaction between numerical and physical magnitude information. Therefore our main objective was to investigate whether facilitation and interference effects can be detected during the perceptual phase of task-execution. Importantly, we aimed at the direct demonstration of such effects in the amplitude of ERPs, overcoming the shortcomings of indirect conclusions of former studies (Schwarz and Heinze, 1998; Cohen-Kadosh et al., 2007). A direct demonstration of congruency effects would clearly suggest that early perceptual processes play a role in the NSCP. There is a chance that in our previous study (Szűcs and Soltész, 2007) we failed to identify interference effects during perceptual processing because the ERP amplitude effects were too small to get detected. Therefore, here we have increased the number of trials twofold relative to our earlier experiment. In our previous study we have demonstrated that facilitation and interference involve different cognitive processes (Szűcs and Soltész, 2007). Therefore,

Fig. 2 – Group average stimulus-locked ERPs. Electrode positions are shown in Fig. 1.

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similarly to our previous study (Szűcs and Soltész, 2007), but unlike other studies (Schwarz and Heinze, 1998; Cohen-Kadosh et al., 2007) we have distinguished between facilitation (neutral vs. congruent) and interference (neutral vs. incongruent) effects. Specifically, our primary question was whether facilitation and interference effects can be demonstrated before motor-preparation begins, that is, before the LRP significantly deviates from baseline. The topography of such early effects could be expected to be similar to that of the ERP distance effect usually detected 200 ms after stimulus presentation (e.g. Dehaene, 1996; Pinel et al., 2001; Szűcs and Csépe, 2004, 2005; Szűcs et al., 2007). Second, we aimed to replicate our earlier findings, that is, to demonstrate facilitation and interference effects during the response phase of task-execution. In order to help to distinguish stimulus and response-related processing, both stimulus- and response-locked ERP effects were analyzed.

2.

Results

2.1.

Behavioural data

Accuracy was 100% with right hand and 98.3 ± 3% with left hand (left vs. right hand difference according to sign test: Z = 3.01; p b 0.0025). Responses given with the left hand were entered into a Congruency × Distance ANOVA. There was a Congruency effect (F(2,26) = 10.71; ε = 0.526; p = 0.0052). The interference effect was significant (Tukey p for the neutral vs. incongruent difference from Congruency contrasts = 0.0016). There were more correct responses in condition Distance 7 than in Dis-

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tance 1 (99.7 ± 2% vs. 97 ± 1%; F(1,13) = 11.34; p = 0.005). There was also a Congruency × Distance interaction (F(2,26) = 7.68; ε = 0.537; p = 0.0137). The interaction appeared because the Distance effect was present only in the incongruent condition (Distance 1: 92.1 ± 5%; Distance 7: 99.1 ± 1%. Tukey p for Distance 1 vs. 7 = 0.0004; from Congruency × Distance contrasts). The RT (mean ± S.D.) was 542 ± 69, 504 ± 56 and 592 ± 77 ms in the neutral, congruent and incongruent conditions, subsequently. There was a congruency effect (F(2,26) = 73.34; ε = 0.713; p b 0.0001). Both the facilitation (Tukey p for the neutral vs. congruent difference = 0.0002) and the interference effects (neutral vs. incongruent: p = 0.0001) were significant. There was a numerical distance effect (F(1,13) = 73.86; p b 0.0001. Distance 1: 573 ± 78; Distance 7: 518 ± 54 ms.). The Response Hand factor (p = 0.8) and interactions with it were not significant.

2.2.

ERP data

2.2.1.

Stimulus-locked effects

The electrode net used for data acquisition is schematically represented in Fig. 1. Grand average stimulus-locked ERPs on representative electrodes are shown in Fig. 2. Congruent minus neutral (facilitation) and incongruent minus neutral (interference) difference potentials are shown in Fig. 3. Significant facilitation effects were identified between 150–250 ms, 300– 350 ms and 590–630 ms. Significant interference effects were identified between 150–250 ms, 340–430 ms and 520–710 ms. Overall statistics for facilitation and interference effects are provided in Table 1.

Fig. 3 – Stimulus-locked congruent minus neutral (facilitation), and incongruent minus neutral (interference) difference potentials. The difference between interference and facilitation is also shown. Electrode positions are given in Fig. 1.

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Table 1 – Facilitation and interference effects in the amplitude of stimulus-locked ERPs in given time intervals (A–D) Facilitation

Interval (ms) Positive Negative

F(1,13) pb F(1,13) pb

Interference

A

B

C

D

A

B

C

D

150–190

190–250

300–350

590–630

150–190

190–250

340–430

520–710

10.76 0.0060 10.77 0.0059

17.04 0.0012 22.15 0.0004

12.39 0.0038 25.24 0.0002

19.14 0.0008 21.56 0.0005

21.33 0.0005 18.18 0.0009

22.02 0.0004 25.06 0.0002

33.79 0.0001 38.36 0.0000

12.61 0.0036 21.43 0.0005

Letters (A–D) refer to topographic maps in Fig. 5. Positive: Overall effects for electrodes where the group average in/congruent minus neutral difference potentials had positive amplitude. Negative: Overall effects for electrodes where the group average in/congruent minus neutral difference potentials had negative amplitude.

The global field power (GFP) served to visualize facilitation and interference effects in a compact way. The GFP is computed as the mean potential deviation of all recording electrodes, and

it reflects the spatial standard deviation of the data (Lehmann and Skrandies, 1980; Skrandies, 1995). ERPs (on all channels) with high peaks and troughs and steep potential gradients are

Fig. 4 – (A) Global field power (GFP) computed from stimulus-locked congruent minus neutral (facilitation), incongruent minus neutral (interference), and distance 1 minus distance 7 difference potentials. The arrows mark GFP peaks. Arrow labels refer to topographic maps in Fig. 5. The range of mean reaction times in the three conditions is marked at the X axis (RT). (B) The stimulus-locked lateralized readiness potential (LRP). Labelled arrows mark GFP peaks in panel “A”. Rhombi on LRP curves mark the onsets and offsets of significant LRP deviations from baseline. Horizontal markers stand for differences between the neutral vs. incongruent (N vs. InC) and neutral vs. congruent (N vs. Co) conditions (p b 0.025). (C) GFPs computed from response-locked difference potentials. The arrows mark GFP peaks. Arrow labels refer to topographic maps in Fig. 8. The baseline extended from −100 to 0 ms relative to stimulus presentation, and it is marked by “BL”. (D) The response-locked LRP. Labelled arrows mark GFP peaks in panel “C”. Horizontal markers stand for differences between the incongruent vs. neutral conditions (p b 0.05).

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Fig. 5 – Topographic maps depicting significant stimulus-locked facilitation and interference effects. Small dots denote electrodes. Large dots denote electrodes demonstrating significant effects (p b 0.025; statistics were done on microvolt values).

accompanied by high GFP, while flat ERPs, or minor effects present only at a few electrode sites are associated with small GFP. Therefore the GFP is an excellent tool for summarizing large and robust ERP effects at many electrodes in the form of a single curve. Importantly, the GFP characterizes the latency of robust ERP effects by an overall single latency value, thereby avoiding subjective bias in selecting electrodes for latency analysis. The stimulus-locked GFP is shown in Fig. 4A. The latencies of the peaks of the GFP were in perfect agreement with the timing of significant facilitation and interference effects. The GFP demonstrated definitive peaks for both facilitation and interference. For facilitation the GFP first peaked at 224 ms, than at 314 ms and at 626 ms. For interference the GFP peaked at 230 ms, 376 ms and at 614 ms. (There was a GFP peak at 740 ms for interference which was not accompanied by significant interference effects.) The topographies of facilitation and interference effects (represented by in/congruent minus neutral difference potentials) are shown in Fig. 5. Because of our special interest in the earliest facilitation and interference effects, the effects between 150 and 250 ms are illustrated in two maps in Fig. 5 (150– 190 and 190–250 ms) and statistics are provided for both early intervals in Table 1. This is to demonstrate the continuity of these early effects: the basic topography of the effects remains unchanged from 150–190 to 190–250 ms, only the extent and

the amplitude of the effects is developing. The direct comparison of facilitation and interference effects identified no Distance effects and no Congruency effect × Distance interactions. The amplitude of facilitation and interference curves was robustly different between 320 and 420 ms (p b 0.025 on 42 electrodes), and between 720 and 780 ms (p b 0.025 on 9 electrodes). The stimulus-locked LRP is shown in Fig. 4B. Intervals where the LPR significantly deviated from the baseline are given in Table 2 (Overall, Stimulus-locked). The LRP peaked later in the incongruent condition than in the neutral and in the congruent conditions (Latencies: neutral: 364 ms; congruent: 358 ms; incongruent: 436 ms. Congruency effect: F(2,28) = 13.09; ε = 0.8789; p b 0.0001. Tukey contrasts: neutral vs. congruent: p = 0.0051; neutral vs. incongruent: p = 0.0002). The amplitude of the LRP was significantly different in the neutral and congruent conditions between 464 and 532 ms, and in the neutral and incongruent conditions between 220 and 370 ms (see horizontal markers in Fig. 4B). In order to be able to compare our data to Cohen-Kadosh et al. (2007) we analyzed the LRP separately for both numerical distances (Figs. 6A–B). The intervals where the LRP significantly deviated from baseline are given in Table 2 (Distance 1 and 7; Stimulus-locked). In the Distance 1 condition the LRP amplitude differed between the neutral vs. incongruent conditions

Table 2 – Intervals where the Lateralized Readiness Potential (LRP) significantly deviated from the baseline in stimuluslocked (Stim. Locked) and response-locked (Resp. Locked) data Overall

Stim. Locked Resp. Locked

Distance 1

Distance 7

Neutral

Congruent

Incongruent

Neutral

Congruent

Incongruent

Neutral

Congruent

Incongruent

220:528 − 296:−10

226:458 −294:−22

312:636 −250:44

240:534 −294:52

246:458 −278:−18

388:646 − 258:42

232:472 −260:− 22

218:446 − 244:− 30

300:570 −220:−16

Overall: Average of Distance 1 and Distance 7 conditions. Time intervals are indicated by the “:” sign, i.e. 220:528 means from 220 to 528 ms.

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Fig. 6 – The lateralized readiness potential in distance 1 and distance 7 conditions. Rhombi on LRP curves mark the onsets and offsets of significant LRP deviations from baseline. Horizontal markers stand for differences between the neutral vs. incongruent (N vs. InC) and neutral vs. congruent (N vs. Co) conditions (p b 0.05).

between 222 and 374 ms, and it differed between the neutral vs. congruent conditions between 562 and 650 ms (see horizontal markers in Fig. 6A). In the Distance 7 condition the LRP amplitude differed between the neutral vs. incongruent conditions between 256–286 ms and 436–638 ms, and it did not significantly differ between the neutral vs. congruent conditions (see horizontal markers in Fig. 6B). Distance effects were found in both facilitation and interference contrasts between 180–220 and 300–500 ms. Electrodes showing distance effects in both facilitation and interference are shown in Fig. 7. In facilitation there were distance effects between 180 and 220 ms (Overall statistics for positive amplitude effects: F(1,13) = 7.69, p = 0.0157; Negative amplitude effects: F(1,13) = 3.56, p = 0.0814), and between 300 and 500 ms (Positive: F(1,13) = 21.53, p = 0.0004; Negative: F(1,13) = 25.76; p = 0.0002). In interference there were distance effects between 180 and 220 ms (Positive: F(1,13) = 13.24, p = 0.0029; Negative: F(1,13)= 16.42, p = 0.0013), and between 300 and 500 ms (Positive: F(1,13)= 16.08, p = 0.0014; Negative: F(1,13) = 24.24, p = 0.0003).

locked facilitation and interference effects (represented by in/ congruent minus neutral difference potentials) are shown in Fig. 8.

2.2.2.

Fig. 7 – The topography of the stimulus-locked distance effect. Small dots denote electrodes. Large dots denote electrodes demonstrating significant distance effects in both facilitation and interference (p b 0.025; statistics were done on microvolt values).

Response-locked effects

The response-locked GFP is shown in Fig. 4C. The GFP showed peaks between −290 and − 220 ms for facilitation (relative to response). The GFP peaked at −125 ms for interference and −94 ms for the distance effect. The topographies of response-

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Fig. 8 – Topographic maps depicting significant response-locked facilitation, interference, and distance effects. Small dots denote electrodes. Large dots denote electrodes demonstrating significant effects (p b 0.025; statistics were done on microvolt values).

Facilitation effects were detected between −300 to −200 and − 100 to −50 ms (Figs. 8A–B.). Interference effects were detected between −300 to −250 and −150 to −60 ms (Figs. 8C–D). Overall statistics are provided in Table 3. The topography of distance effects is given in Fig. 8 (lower row). Statistics for the distance effect are also provided in Table 3. The topography of the distance effect is shown separately for facilitation and interference in order to help judgements about the temporal relationship of stimulus- and response-locked facilitation and interference effects. Note that the second response-locked distance effect in both facilitation (−100 to −50 ms) and interference (−150 to −60 ms) has similar topography to the second stimulus-locked distance effect (300–500 ms post-stimulus). This suggests that coincident stimulus- and responselocked facilitation and interference effects were temporally overlapping. The direct comparison of facilitation and interference effects identified no Distance effects and no Congruency effect × Distance interactions. The amplitude of facilitation and

interference curves was robustly different between −300 to −200 ms (p b 0.025 on 14 electrodes) and −140 to −40 ms (p b 0.025 on 27 electrodes). The response-locked LRP is shown in Fig. 4D. There was no difference between the timing of LRP peaks in different congruency conditions (this can be expected for the LRP if it is aligned with the response). Intervals where the LPR significantly deviated from the baseline are given in Table 2 (Overall, Response-locked). There were no differences between congruency conditions at the p b 0.025 significance level. At the p b 0.05 level the LRP differed between the neutral vs. incongruent conditions from −158 to −132 ms and from −86 to −46 ms. The response-locked LRP was analyzed separately for both numerical distances (Figs. 6C–D). There was no difference between the timing of LRP peaks in different congruency conditions. Intervals where the LPR significantly deviated from the baseline are given in Table 2 (Distance 1 and Distance 7, Response-locked). There were no LRP amplitude differences between conditions at the p b 0.025 significance level. At the

Table 3 – Facilitation and interference effects in the amplitude of response-locked ERPs in given time intervals (A–D) Congruent vs. Neutral Facilitation

Interval (ms) Positive Negative

F(1,13) pb F(1,13) pb

Incongruent vs. Neutral

Distance

Interference

Distance

A

B

A

B

C

D

C

D

300–200

100–50

300–200

100–50

300–250

150–60

300–250

150–60

32.68 0.0001 12.82 0.0034

12.10 0.0041 9.69 0.0082

16.13 0.0015 8.34 0.0127

28.54 0.0001 25.74 0.0002

11.13 0.0054 14.20 0.0023

32.38 0.0001 39.73 0.0000

24.26 0.0003 32.46 0.0001

23.51 0.0003 36.54 0.0000

Letters (A–D) refer to topographic maps in Fig. 8. Positive: Overall effects for electrodes where the grand average in/congruent minus neutral difference potentials had positive amplitude. Negative: Overall effects for electrodes where the group average in/congruent minus neutral difference potentials had negative amplitude.

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p b 0.05 level, the LRPs in the neutral vs. incongruent conditions differed from −174 to − 150 ms in the Distance 1 condition. There were no significant LRP differences in the Distance 7 condition.

3.

Discussion

For the first time we provide direct evidence suggesting that facilitation and interference effects happen during perceptual processing in the NSCP. Further, we have replicated our former findings demonstrating facilitation and interference effects during the post-perceptual phase of the NSCP. Post-perceptual effects may be related to response-selection, and/or to high level semantic/contextual stimulus analysis and categorization processes (Szűcs and Soltész, 2007).

3.1.

Processing speed in the neutral condition

In the neutral condition task-irrelevant physical size information provided neither congruent nor incongruent information relative to numerical information. Therefore the onset of motor preparation in the neutral condition can serve as an index of the speed of motor response initiation in the absence of distracting size information. According to statistical results the stimulus-locked LRP significantly deviated from the baseline between 208 and 526 ms after stimulus presentation in the neutral condition. Even by purely subjective visual observation no tendency of LRP deviation could be seen before 200 ms. This suggests that in the absence of congruent/incongruent size information numerical information needed about 200 ms to reach a level of processing where it could begin to influence response activity. Hence, effects appearing before 208 ms after stimulus presentation happened during the perceptual processing phase of the NSCP, while effects appearing later happened during the response processing phase of the NSCP.

3.2.

Facilitation

The earliest stimulus-locked ERP facilitation effects appeared between 150 and 250 ms. Effects appeared with very circumscribed bilateral occipito-parietal and frontal topography. Facilitation effects onset 58 ms earlier than the onset of motor preparation in the neutral condition and 70 ms earlier than the onset of motor preparation in the congruent condition. The earliest response-locked facilitation effects appeared at occipito-parietal electrodes between −300 and −200 ms relative to responding. Both the stimulus and response-locked effects appeared at about the time when the LRP (stimulus- and responselocked LRP, respectively) deviated from the baseline. This suggests that the stimulus- and response-locked effects were temporally close to each other. It is to note that the presence of response-locked ERP effects does not necessarily indicate that a processing phase is exclusively related to response processing. Response-locked effects simply suggest that there is a good temporal coincidence between the particular effect and responding. For example, the continuous flow model assumes that there is a good temporal coincidence between early perceptual stimulus processing and the start of response activity. Therefore, within the framework of the continuous flow model

purely perceptual processes can also result in response-locked ERP effects. In fact, there are two reasons to believe that early stimuluslocked facilitation effects were more related to perceptual than to response-processing. First, response-locked effects were present at fewer electrodes, and their topography was less focused than that of stimulus-locked effects. This suggests that latency jitter affected response-locked effects more than stimulus-locked effects. Second, the stimulus-locked ERP facilitation effect not only preceded the onset of motor preparation in the congruent condition, but it also well preceded the onset of motor preparation in the neutral condition. This suggests that the ERP facilitation effect happened earlier than it was possible to initiate a response even when no distracting size information was present. This, in turn, suggests that the early facilitation effect was not related to enhanced response processing. Naturally, it is possible that a part of the early facilitation effect was related to response preparation. For example, the LRP may not have been able to pick up very early and small response-preparation effects. Nevertheless, the previous points suggest that the early stimulus-locked ERP facilitation effect was strongly related to perceptual processing. The stimulus-locked LRP began to deviate from baseline during the manifestation of the early facilitation effect. Importantly, the topography of parietal facilitation effects remains basically the same from 150–190 to 190–250 ms, and only the amplitude and the extent of the effects become enhanced. This suggests that the neural mechanism of facilitation was essentially the same between 150–190 and 190–250 ms (Rugg and Coles, 1995). Hence, ERP effects in these time intervals are the correlates of the same early facilitation effect. The enhancement of the amplitude and the extent of the ERP facilitation effect probably correlate with the advance of perceptual processing (Eriksen and Schultz, 1979). The early stimulus-locked facilitation effect between 150 and 250 ms was closely followed by a later stimulus-locked ERP facilitation effect appearing over centro-parietal electrode sites between 300 and 350 ms. This closely replicates our earlier findings (Szűcs and Soltész, 2007). The topography of this later facilitation effect was considerably different from the topography of the early parietal facilitation effect. This suggests that the neural mechanisms of the early and late facilitation effects were different. The timing of the late ERP facilitation effect coincided with the early portion of the peak of the LRP in the neutral condition. This suggests that the facilitation effect appeared when motor preparation processes were already active. The temporal coincidence between the ERP facilitation effect and the early portion of the LRP peak suggests that there may be a relationship between these phenomena. Indeed, response-locked facilitation effects were detected between −100 and − 50 ms relative to responding, right at the peak of the response-locked LRP. These response-locked effects were less expressed than stimulus-locked effects. These observations confirm our former hypothesis of assuming that late ERP facilitation effects in number comparison mostly reflect the facilitation of response-initiation (Szűcs and Soltész, 2007), a phase just following perceptual processing. In addition to the previously described effects, a late ERP facilitation effect appeared between 590 and 630 ms. This effect was restricted to parietal

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electrodes sites, and it followed the timing of the mean RT. Currently no clear explanation can be provided for this effect.

3.3.

Interference

Early stimulus-locked ERP interference effects (150–250 ms) had a similar topography to early facilitation effects, and they onset 58 ms earlier than the onset of motor preparation in the neutral condition, and 160 ms earlier than the onset of motor preparation in the incongruent condition. Early responselocked interference effects (− 300 to −250 ms relative to response) had a similar topography to the early stimulus-locked interference effects. Further, both stimulus and responselocked effects happened right before the LRP deviated from baseline. Similarly to the above argument regarding early facilitation effects we conclude that the early ERP interference effect was most related to the modulation of perceptual processing. The temporal relationship of the early ERP interference/ facilitation effect and the LRP deviation differed in the incongruent and congruent conditions. In the congruent condition the stimulus-locked LRP began to deviate from baseline during the time course of the early facilitation effect. In contrast, in the incongruent condition the stimulus-locked LRP remained at baseline for another 60 ms after the offset of the early ERP interference effect. The most probable explanation for the above phenomenon is that that there was “latent” response competition during perceptual processing and during the 60 ms interval immediately following the perceptually based interference effect: The opposing response tendencies initiated by numerical and physical size information competed to dominate response activity (Morton and Chambers, 1973; Posner and Snyder, 1975), and for a while, this response competition prevented motor processes from reaching the critical threshold where the LRP could have significantly deviated from baseline. It is important to point out that the latency of early ERP waves (N1, P1, N2) did not differ across congruency conditions. In fact, the N1–P1–N2 waves were completely overlapping in different congruency conditions. Therefore latency differences between early ERP waves can explain neither the LRP onset differences, nor late amplitude ERP effects in our data. Rather, LRP onset differences were due to genuine amplitude differences (appearing only after 200 ms) between conditions, reflecting the differential onset of motor processes in different congruency conditions. Similarly, late ERP amplitude differences between conditions reflect relatively late-onsetting congruency effects. 30 ms after the LRP significantly deviated from the baseline a late stimulus-locked ERP interference effect appeared between 340 and 430 ms. This effect took the form of an extended negativity over centro-parietal electrode sites, and a positivity over frontal electrode sites. The topography of late facilitation and interference effects markedly differed which suggests that different neural processes contributed to their appearance. However, the temporal relationship of the interference effect to the peak of the LRP curve in the incongruent condition was very similar to the temporal relationship of the late facilitation effect (300–350 ms) and the peak of the LRP curve in the congruent condition: Both the interference effect

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and the facilitation effect just preceded the peak of the LRP curve. Similarly, a late interference effect appeared in response-locked ERPs over occipito-parietal electrode sites (− 150 to −60 ms) just preceding the peak of the responselocked LRP. Their similar relationship to the LRP peak suggests that stimulus- and response-locked interference effects reflect temporally partially overlapping processes (the responselocked effect was shorter than the stimulus-locked effect). The difference between stimulus- and response-locked topographies suggests that both a midline negativity (stimuluslocked) and bilateral parieto-occitiptal negativities (both stimulus- and response-locked) contributed to the topography of the stimulus-locked interference effect. Previously we have argued that there may be at least two, not mutually exclusive, explanations for the late interference effect (Szűcs and Soltész, 2007). First, the effect may be the expression of the conflict monitoring and action selection activity of the anterior cingulate cortex (ACC), which has been shown to play a role in both the classical colour–word Stroop task (Liotti et al., 2000; Peterson et al., 1999; Carter et al., 2000; Kerns et al., 2004) and in the NSCP (Pinel et al., 2004; Kaufmann et al., 2005). Most importantly, the ACC has been very consistently implied in response conflict monitoring in Stroop-like situations (van Veen et al., 2001; Milham et al., 2001). CohenKadosh et al. (2007) provide further support for the responseselection hypothesis as they demonstrated interference effects in the motor cortex in the NSCP. Second, the late interference effect may be a correlate of higher-level contextual analysis. This account relies on previous arithmetic verification studies, which have found similarly timed amplitude effects in response to unexpected results in mental multiplication (Niedeggen et al., 1999) and mental addition (Szűcs and Csépe, 2004, 2005). These effects were interpreted as arithmetic N400 and P300 (or Late positive component) effects, related to semantic contextual integration processes (Kutas and Federmeier, 2000) and categorization decisions (Donchin, 1981). Most probably, both ACC function and semantic integration processes play a role in shaping the topography of late interference effects (Szűcs and Soltész, 2007).

3.4.

Early facilitation and interference effects

Early facilitation and interference effects are predicted at the level of the common amodal magnitude representation in the intraparietal sulci by the currently dominant neural model of human numerical abilities (Dehaene et al., 2004). Above we concluded that early stimulus-locked ERP facilitation and interference effects (150–250 ms) were most related to perceptual processing. This is in-line with the early interaction prediction of the number processing model. However, it is a further question whether ERP facilitation/interference effects occurred at the level of the magnitude representation? In our study facilitation and interference effects had similar scalp topography, focusing over left and right parieto-occipital electrode sites. ERPs lack precise anatomical information. Therefore we cannot directly tell whether effects originated in the horizontal IPS. However, there are some indications suggesting that early facilitation and interference effects reflect general processing load increase, and/or general conflict detection, rather than magnitude processing in the IPS.

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First, the magnitude representation is sensitive to the magnitude relations of stimuli. In the incongruent condition numerical and physical size delivered different magnitude information. In the congruent condition numerical and physical size delivered similar magnitude information. Hence, overall magnitude relations differed in the congruent and incongruent conditions. Therefore, it is reasonable to assume that the difference in overall magnitude relations between conditions would result in at least amplitude differences between the congruent and incongruent conditions (i.e. between facilitation and interference). However, in our data early ERP facilitation and interference effects had virtually identically topography, polarity, and amplitude. This observation is in contrast with the magnitude representation explanation. Second, the topography of early facilitation/interference effects was very different from the topography of the ERP distance effect. This makes it likely that the generators of the facilitation/interference effect differed from the generators of the distance effect, that is, from the magnitude representation. In line with the above observation, existing fMRI studies of the NSCP contrasting the congruent and incongruent conditions have demonstrated parietal congruency effects with comparable localization to our ERP effects (Pinel et al., 2004; Kaufmann et al., 2005). However, similarly to ERP effects, the only NSCP fMRI study carefully testing for both distance and congruency effects found these effects to be non-identically localized in the brain (Pinel et al., 2004). Third, the ERP topography of the early distance effect is usually very diffuse, not focused. This is inline with several fMRI studies demonstrating that various brain areas contribute to the distance effect (for a review see Szűcs et al., 2007). In contrast, the topography of the early facilitation/interference effects was very focused. Again, this makes it likely that these effects were generated in different parts of the cortex than the distance effect. We conclude that the early facilitation and interference effects were not related to the activity of the magnitude representation. It is also unlikely that effects simply reflect taskdifficulty as the congruent condition was less difficult than the incongruent condition. Similarly, effects cannot reflect differences in stimulus identity, as exactly the same numbers were shown in all conditions. One likely possibility is that effects reflect general processing load increase in the (in)congruent conditions relative to the neutral condition. This may be the case because only one stimulus dimension provided comparative magnitude information in the neutral condition, whereas such information was provided on two dimensions in the (in)congruent conditions. The increased processing load in the (in)congruent conditions may have resulted in the early facilitation/interference ERP effects. Another possibility is that effects were related to general conflict detection. This explanation draws on the fact that stimulus-conflict effects were localized in the posterior parietal cortex by recent fMRI studies of the Stroop effect (Liston et al., 2006; Egner et al., 2007). This location fits very well with the focal topography of our early facilitation/interference effects. Conflict could have arisen because physical size information carried somewhat different magnitude information relative to numerical information in both the congruent and incongruent conditions, while there was no such conflict in the neutral condition.

In summary, we suggest that early facilitation/interference effects reflect the same common processing component both in the congruent and incongruent conditions. There may be at least two alternative hypotheses regarding the mechanism of this processing component. Both the increased processing load and the conflict detection hypothesis fits well with our previous conclusion that early facilitation/interference effects were related to perceptual processing. Naturally, our interpretation does not exclude that differential facilitation/interference effects may happen at the level of the magnitude representation. However, it is more likely that the early ERP facilitation/interference effects identified here reflect more general processes.

3.5.

Distance effects

Replicating earlier findings we have demonstrated both early (e.g. Dehaene, 1996; Pinel et al., 2001; Szûcs and Csépe, 2004, 2005; Szűcs et al., 2007) and late (Grune et al., 1993; Schwarz and Heinze, 1998; Soltész et al., 2007) ERP distance effects. Early effects had a diffuse topography and appeared at around 200 ms after stimulus presentation. Late effects appeared parieto-occipitally between 300 and 500 ms, on top of the P300 ERP wave (Grune et al., 1993). For the first time, we have also demonstrated strong response-locked ERP distance effects. The topography of late stimulus- (300–500 ms post-stimulus) and late response-locked (−150 to −50 pre-response) distance effects was very similar to each other. It is up to further research to determine whether these effects reflect stimulus- or response-related processing (e.g. Göbel et al., 2004; Ansari et al., 2006). In order to be able to compare our data to Cohen-Kadosh et al. (2007) we have analyzed facilitation and interference effects in the LRP and ERPs separately for both numerical distances. Cohen-Kadosh et al. (2007) found response-locked congruency effects in the LRP when distance was large, but not when distance was small. Based on the lack of the responselocked effect in the small distance condition, it was concluded that the number/size conflict was fully resolved at the perceptual level when distance was small. However, they did not directly test this hypothesis by checking for stimulus-locked effects in the LRP and in ERPs. Here we have tested both stimulus- and response-locked effects both in the LRP and in ERPs. Stimulus-locked LRP effects were considerably stronger (p b 0.025 vs. p b 0.05) and longer than response-locked effects. Further, the difference between the neutral and incongruent conditions was larger in the distance 1 than in the distance 7 condition during the early portion of the stimulus-locked LRP (220–370 ms). This observation is in-line with the above conclusion of Cohen-Kadosh et al. (2007). However, in contrast to Cohen-Kadosh et al. (2007) we found weak response-locked effects in the LRP when distance was small but not when distance was large. Moreover, we have demonstrated strong stimulus-locked response-phase facilitation/interference effects, as well as response-locked facilitation/interference effects in the amplitude of ERPs right before pressing the response button. Importantly, there were no congruency effect × distance interactions, that is, response-phase and response-locked effects did not differ across distance conditions. These observations do not support the conclusion of Cohen-Kadosh et al.

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Rather, it seems that both perceptual and response-phase interaction played a similar role in both distance conditions. It is important to note that data processing differed between Cohen-Kadosh et al.'s (2007) and our study. First, Cohen-Kadosh et al. (2007) collapsed the neutral and congruent conditions and contrasted their average with the incongruent condition. However, as demonstrated here and previously (Szűcs and Soltész, 2007) the neutral and congruent conditions involve different cognitive processes, i.e. these conditions should be treated separately. Furthermore, above we concluded that stimulus conflict may have been detected in the congruent condition. Therefore the congruent condition cannot be considered a “no conflict” condition with certainty. Second, Cohen-Kadosh et al. (2007) used the interval just preceding individual responselocked epochs as baseline. Therefore the baseline was changing from trial to trial, and from condition to condition (there were significant RT differences between conditions). This way conditions were not comparable to each other reliably. In contrast, here were used the same baseline interval for all congruency conditions, and for both stimulus- and response-locked analysis, which is a more optimal solution. Third, Cohen-Kadosh et al. (2007) did not test for the significance of deviation from the LRP baseline, only for significant congruity effects. That is, the claim to have found a sign of initial incorrect response activation in response-locked LRPs (effect size: −0.42 μV; Fig. 7 in CohenKadosh et al., 2007) is not justified.

3.6.

Response hand effects

It is worth briefly discussing the unexpected response hand effects. Participants' performance was perfect when they had to respond with their right hand. In contrast, there was a congruency effect and a numerical distance effect in accuracy scores only when participants responded with their left hand. Moreover, nearly all the errors were committed when numerical distance was 1 in the incongruent condition. There was no similar effect in RT. One possible explanation of the accuracy effect is that our subjects could control their right hand more effectively than their left-hand (all subjects were right-handed). As demonstrated, response competition probably played an important role in the appearance of interference. Therefore it is possible that response-competition resulted in more errors when subjects used their less-well controlled hand for responding, especially when task-difficulty was high (i.e. when distance was 1 in the incongruent condition). Another possible explanation of the response-hand effect relies on the numerical cognition literature. According to the SNARC (Spatial–Numerical Association of Response Codes) effect in a given range of numbers responses to small numbers are faster with the left hand, whereas responses to large numbers are faster with the right hand (for a review see Fias and Fischer, 2004). The SNARC effect is explained by assuming that there is an association between space and magnitude: smaller numbers are associated with the left side of space while larger numbers are associated with the right side of space. Our participants always had to select the larger number as usual in the NSCP. Because of the association of larger numbers with the right side of space it may be that from the point of view of accuracy it was more advantageous to select the larger number with the right hand than selecting it with the left hand. The explanation based on the SNARC effect is that it

155

was a more natural assignment to select large numbers with the right than with the left hand, and this resulted in the observed response-hand effect. However, there was no effect in RT in our experiment which has been demonstrated in experiments studying the SNARC effect. This leaves the earlier described “handedness account” as the more probable explanation for the response-hand effect in accuracy. The lack of the response hand effect in RT suggests that accuracy and RT were sensitive to different aspects of cognitive processing.

3.7.

Conclusion

Both facilitation and interference effects have been demonstrated during early perceptual processing. We conclude that these effects reflected a similar process in both facilitation and interference, related to a general increase of processing load and/or conflict detection. Further, we have replicated our former findings showing late facilitation and interference effects during the response phase of the NSCP. These effects may be related to the conflict monitoring and response-selection activity of the anterior cingulate cortex, or may be related to higher level contextual analysis. Our findings suggest that facilitation and interference effects may appear at multiple levels of stimulus and response processing. An unexpected response-hand effect may have been a consequence of the better control of the right hand, or that of the association between space and numerical magnitude. The ERP distance effect was demonstrated in both stimulus- and response-locked ERPs.

4.

Experimental procedures

4.1.

Experimental subjects

14 right-handed adult subjects' data was analyzed (mean: 27 years, range: 23–38 years; 9 women; undergraduate and graduate students at the University of Cambridge). Originally 16 adults participated in the experiment; the data of 2 subjects was excluded because of EEG artefacts. Participants gave informed written consent and were paid for participation. The study received ethical approval from the Psychology Research Ethics Committee of the University of Cambridge.

4.2.

Stimuli and tasks

Stimuli were pairs of Arabic digits shown simultaneously in the middle of a 17-in. computer screen. Stimuli were white on black background. Eight pairs of digits (1–8, 2–9, 8–1, 9–2, 1–2, 8–9, 2–1, 9–8) were used in equal proportions. Subjects were instructed to decide which item of the pair was numerically larger than the other one. Subjects pressed a response button on the side (left or right: Response Hand factor) where they detected the numerically larger stimulus. The correct response had to be given with the right hand in 50% of the cases, and with the left hand in the other 50%. Numerical and physical size information could be neutral, congruent or incongruent (Congruency factor) with each other in equal proportions. In the congruent condition the numerically larger (smaller) digit was also physically larger (smaller) than the

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other one. In the incongruent condition the numerically larger (smaller) digit was physically smaller (larger) than the other one. In the neutral condition both digits were of the same physical size. The numerical distance between digits was 1 or 7 (Distance factor) in equal proportions in each Congruency × Response Hand cell. Each trial began with a fixation sign (a drawing of an eye) shown for 500 ms. Subjects were instructed to blink if necessary when they saw the fixation sign. After a 500 ms pause, a pair of stimuli were shown for maximum 3 s, or until the subject gave a response. The stimuli were followed by a pause of 500 ms. The viewing distance was approximately 80 cm. Physically small stimuli had a font-size of 40, physically large stimuli had a fontsize of 50. Stimulus pairs with one small and one large-sized stimulus subtended a view angle of 2.4° horizontally, and 1° vertically. In half of the neutral trials both digits had a font size of 40 (horizontal view angle: 1.9°; vertical view angle: 0.7°), in the other half both digits had a font size of 50 (horizontal view angle: 2.4°; vertical view angle: 1°). 576 trials were presented in 8 blocks. The experiment was preceded by 24 practice trials. Subjects could have a short break between blocks.

4.3.

Behavioural analysis

RT and accuracy were examined by Congruency (neutral, congruent, and incongruent)×Numerical Distance (1 vs. 7)×Response Hand (Left vs. Right) repeated measures ANOVAs. Tukey tests from Congruency contrasts were used to determine facilitation (neutral vs. congruent) and interference (neutral vs. incongruent) effects. Behavioural data was analyzed in Statistica 7.0.

4.4.

EEG recording and analysis

EEG was recorded by an Electrical Geodesics system with a 65 channel Geodesic Sensor Net. Electrode positions are shown in Fig. 1. The sampling rate was 500 Hz, an on-line bandpass filter of 0.01–70 Hz was used. The data was bandpass filtered between 0.01 and 30 Hz offline, and was recomputed to average reference. Stimulus-locked epochs extended from −100 to 1000 ms relative to stimulus presentation. Response-locked epochs extended from −300 to 200 ms relative to pressing the response button. Data was baseline corrected. The same, −100 to 0 ms relative to stimulus presentation, baseline was used for both stimulus and response-locked averaging. Epochs containing ocular artefacts (monitored at electrodes below, above and next to the eyes), and epochs containing voltage deviations exceeding ±100 μV relative to baseline at any of the recording electrodes were rejected. The LRP was computed as proposed by Coles (1989): ½ðER  ELÞLEFT HAND response þ ðEL  ERÞRIGHT HAND response =2; where ER denotes the amplitude of the ERP at an electrode placed over the right motor cortex, and EL denotes the amplitude of the ERP at an electrode placed over the left motor cortex. Electrode 54 was used as the electrode above the right motor cortex, and electrode 17 was used as the electrode above the left motor cortex (see Fig. 1). According to convention a negative LRP indicates a correct response tendency, and a positive LRP indicates an incorrect response tendency. The deviation of the LRP form baseline was tested by point-by-point two-tailed one-sample t-tests (p b 0.025). The amplitude of the

LRP was compared between the neutral vs. congruent and the neutral vs. incongruent conditions by point-by-point twotailed matched t-tests (p b 0.025). In response-locked LRPs no LRP differences were found at the p b 0.025 significance level. Therefore we checked effects at the p b 0.05 level. This is noted in the Results section. The peak latency of the stimulus-locked LRP was measured as the most negative peak between 200 and 700 ms (relative to stimulus presentation). Peak latencies were compared across conditions by a repeated-measures ANOVA with a Congruency (neutral, congruent and incongruent) factor. Facilitation effects were visualized as congruent minus neutral difference potentials, interference effects were visualized as incongruent minus neutral difference potentials. Facilitation and interference effects were identified by point-by-point Congruency (neutral vs. congruent for facilitation, and neutral vs. incongruent for interference) ×Distance (1 vs. 7) repeatedmeasures ANOVAs. Time intervals where Congruency effects reached significance (p b 0.025) over a minimum of 15 consecutive sampling points at least at 6 electrode channels were considered to demonstrate significant facilitation and interference effects. The results of point-by-point ANOVAs were confirmed by Congruency× Distance × Electrode ANOVAs. These ANOVAs were run on the mean amplitude of ERPs in the intervals found to show significant effects by point-by-point testing. Facilitation and interference effects were directly compared by a Congruency effect (facilitation vs. interference) × Distance (1 vs. 7) ANOVA run on (in)congruent minus neutral difference potentials (p b 0.025; at least 15 consecutive points must have shown significant effects). The global field power (GFP) served to visualize facilitation and interference effects in a compact way. The GFP is computed as the mean potential deviation of all recording electrodes, and it reflects the spatial standard deviation of the data (Lehmann and Skrandies, 1980; Skrandies, 1995). The GFP was computed from congruent minus neutral difference potentials for facilitation effects, from incongruent minus neutral difference potentials for interference effects, and from Distance 1 minus Distance 7 difference potentials for the distance effect. EEG data was analyzed in Matlab 7.1 and Statistica 7.0. Topographic maps were created in EEGLab (Delorme and Makeig, 2004).

Acknowledgments Supported by a grant from the Faculty of Education, University of Cambridge. The authors thank the Reviewers' advice, especially those of Reviewer 1. REFERENCES

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