© 2014 American Psychological Association O278-7393/14/$12.0O DOI: IO.lO37/aOO36378
Journal of Experimental Psychology: Learning. Memory, and Cognition 2014, Vol. 40, No. 4, 976-986
The Impact of Verbal Working Memory on Number-Space Associations Véronique Ginsburg
Jean-Philippe van Dijck
Université Libre de Bruxelles
Ghent University and University of Antwerp
Paola Previtali
Wim Fias
University of Milano-Bicocca
Ghent University
Wim Gevers Université Libre de Bruxelles Spatial-numerical associations are observed when participants perform number categorization tasks. One such observation is the spatial numerical associations of response codes (SNARC) effect, showing an association between small numbers and the left-hand side and between large numbers and the right-hand side. It has long been argued that this spatial association is automatically activated by the long-term representation underlying numbers processing. Instead, van Dijck and Fias (2011) argued that this association is a short-term representation that is constructed during task execution. This argument was based on the observation of an association between the ordinal position of an item in working memory and response side (e.g., the ordinal position effect). Four different experiments were set up to systematically investigate this assumption. Our results indicate that the activation of the canonical order of numbers in working memory (e.g., 1, 2, 3, etc.) is indeed necessary to observe the SNARC effect. The activation of the standard sequence of numbers (e.g., from 1 to 9) can be overruled when a new random sequence is memorized. However, this is only observed when retrieval of the memorized sequence is required during the numbers classification task. Keywords: numbers, space, SNARC effect, working memory, ordinal coding
have to classify target numbers as odd or even by pressing a left or a right response button. The SNARC effect is also obtained when magnitude information has to be accessed more explicitly such as in a magtiitude comparison task (Dehaene, Dupwux, & Mehler, 1990). In this task, participants have to judge whether a target number is smaller or larger than a reference number by pressing a left- or a right-sided response button. The SNARC effect is influenced by cultural factors such as reading and writing experiences (Dehaene et al., 1993; Shaki & Fischer, 2008; Shaki, Fischer, & Petrusic, 2009; Zebian, 2005). For example, Dehaene et al. (1993) observed that Iranian participants, who read from right to left, presented a weak or even a reversed SNARC effect if they had only limited exposure to French. When Iranian participants with a high degree of familiarity with French were tested, a tendency for a regular SNARC effect was observed. In Western cultures, numbers are often presented physically from left to right in a canonical order (i.e., numeral sequence) like on a ruler, with small numbers presented on the left and large numbers on the right. It has been assumed that repeated exposure to this left-to-right orientation of numerical magnitude installs a stronger correlation between small numbers and the left side of space and between large numbers and the right side of space (Chen & Verguts, 2010). The observations of cultural influences on the SNARC effect suggest that the direction of the mapping between numbers and space results from long-term learning mechanisms.
Research in the domain of numerical cognition has highlighted the fact that numerical processing is linked with spatial processing. One observation that is often used to describe this link between numbers and space is the spatial numerical associations of response codes (SNARC) effect (Dehaene, Bossini, & Giraux, 1993). The SNARC effect reveals an association between numerical magnitude and lateralized motor responses: Participants respond faster to small numbers with the left-hand side and to large numbers with theright-handside. The most widely used task to investigate the SNARC effect is the parity judgment task (Dehaene et al., 1993). In this task, participants
This article was published Online First April 7, 2014. Véronique Ginsburg, Center for Research in Cognition and Neurosciences (CRCN), ULB Neurosciences Institute (UNI), Université Libre de Bruxelles (ULB); Jean-Philippe van Dijck, Department of Experimental Psychology, Ghent University, and Collaborative Antwerp Psychiatric Research Institute, University of Antweip; Paola Previtali, Department of Psychology, University of Milano-Bicocca; Wim Fias, Department of Experimental Psychology, Ghent University; Wim Gevers, Center for Research in Cognition and Neurosciences (CRCN), ULB Neurosciences Institute (UNI), Université Libre de Bruxelles (ULB). Véronique Ginsburg is a research fellow at the Belgian Fonds National de la Recherche Scientifique (F.R.S.-FNRS). Correspondence concerning this article should be addressed to Véronique Ginsburg, Université Libre de Bruxelles, Avenue F.D. Roosevelt 50, B-I050 Brussels, Belgium. E-mail: [email protected] 976
VERBAL WORKING MEMORY AND NUMBER-SPACE ASSOCIATIONS At the same time, however, the mapping between numbers and space is highly fiexible. Eariy reports on the SNARC effect demonstrated that relative instead of absolute magnitude information is associated with response side (Dehaene et al, 1993; Fias, Brysbaert, Geypens, & d'Ydewalle, 1996). In these studies, the number 5 was responded to faster with the left hand when it was relatively small within the range (e.g., numbers ranged from 4 to 9), but the same number was responded to faster with the right hand when it was relatively large within the range (e.g., from 1 to 5). Additionally, Bächtold, Baumüller, and Brugger (1998) demonstrated that the SNARC effect could be reversed by means of mental imagery. When subjects were asked to imagine numbers on a clock face, the SNARC effect reversed, because now small numbers occurred on the right side of the clock face and large numbers on the left side. Similarly, Shaki and Fischer (2008) showed that Russian Hebrew bilinguals present a normal SNARC effect when they had to read a Russian text (reading from left to right) just before the SNARC task but that this effect was significantly reduced when they had to read a Hebrew text (reading from right to left) just before. In sum, the association between numbers and space depends on relative number magnitude (Dehaene et al, 1993; Fias et al., 1996). Furthermore, the high fiexibility of the association between numbers and space suggests that the association is generated online during task execution (e.g., Fischer, 2006). Together, these observations led to the hypothesis that working memory has an important role in the creation of number-space associations (e.g.. Fias, van Dijck, & Gevers, 2011). Empirical support for the involvement of working memory in associating numbers with space is accumulating (Herrera, Macizo, & Semenza, 2008; Lindemann, Abolafia, Pratt, & Bekkering, 2008; van Dijck, Abrahamse, Acar, Ketels, & Fias, in press; van Dijck, Abrahamse, Majems, & Fias, 2013; van Dijck & Fias, 2011; van Dijck, Gevers, 6 Fias, 2009). Working memory is generally described as a system that encodes, maintains, and processes a limited amount of information during a brief period of time (Baddeley, 1986, 2000; Baddeley & Hitch, 1974; Cowan, 1995, 1999; Oberauer, 2002). Encoding and maintenance are the processes needed to temporarily keep information for later use. In what follows, we define encoding to comprise both the positioning of an item within a memorized sequence and the maintenance-related processes that act on it. With retrieval, we refer to the act of processing and retrieving the encoded information. Most models on working memory functioning have in common that they make a distinction between encoding and retrieving information from working memory (Baddeley & Hitch, 1974; Oberauer, 2002). Another relevant issue is how information of different modalities is encoded by the system. There is general agreement that different systems exist for encoding verbal information and for encoding visual and spatial information (e.g., Baddeley & Hitch, 1974; Shah & Miyake, 1996; Smith, Jonides, & Koeppe, 1996). Some researchers investigated the influence of encoding information of different modalities (verbal vs. visuospatial) on the association between numbers and space. In these studies, participants had to encode verbal or visuospatial information in working memory while performing a parity judgment task (van Dijck et al., 2009) or a magnitude comparison task (Herrera et al., 2008; van Dijck et al., 2009) during the retention interval. A double dissociation was observed between the type of working memory load
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(verbal or visuospatial) and the type of task (magnitude comparison or parity judgment). When participants performed a magnitude comparison task, the SNARC effect disappeared with a visuospatial load but was unaffected by a verbal load. The distance effect (the observation that reaction times [RTs] speed up when the distance between the numbers increases; Moyer & Landauer, 1967), however, was not affected by the working memory load, suggesting that the visuospatial load effect was specific to the SNARC effect and the spatial associations reflected therein. In contrast, in a parity judgment task, the SNARC effect disappeared with a verbal load but was unaffected by a visuospatial load. Together, these observations indicate that the formation of number-space associations requires availability of working memory resources: The SNARC effect in a parity judgment context needs verbal working memory resources, whereas the SNARC effect in a magnitude comparison needs visuospatial working memory resources (see also van Dijck, Gevers, Lafosse, & Fias, 2012). In line with this, a principal component analysis on parity and magnitude comparison performance tested within the same subjects showed that the SNARC effect in a parity judgment task and in a magnitude comparison task loaded on two independent components (van Dijck et al., 2012). Recent studies more directly investigated the influence of working memory on the creation of number-space associations (van Dijck & Fias, 2011; van Dijck et al., in press). Van Dijck and Fias (2011) asked participants to keep a sequence of five numbers (randomly chosen between 1 and 10) in working memory. Subsequently, all numbers in the range from 1 to 10 were randomly presented as stimuli in a parity judgment task. To ensure that the numbers had to be retrieved form working memory, a go/no-go procedure was included. Participants responded to the parity of the number, but only if the number belonged to the memorized sequence. No SNARC effect was observed: Regardless of the magnitude of the number, responses were equally fast with the left hand as with the right hand. However, spatial associations were observed with the position of the number in the working memory sequence. Numbers from the beginning of the memorized sequence were responded to faster with the left-hand side, whereas numbers at the end of the sequence were responded to faster with the right-hand side (e.g., hereinafter, this observation will be termed the ordinal position effect). A subsequent experiment showed that these spatial-positional associations were not limited to numerical information. Instead of using numbers, participants had to classify words as being fruits or vegetables. Again, the ordinal position effect was observed, with words early in the sequence responded to faster with the left-hand side and words late in the sequence responded to faster with the right-hand side. Furthermore, the ordinal position effect obtained with words correlated with the SNARC effect observed in a separate regular parity judgment task. On the basis of this correlation, the authors suggested that the position of an item in working memory, not the magnitude of the number, drives the SNARC effect (van Dijck & Fias, 2011). A number of altemative possibilities require investigation before we can accept the conclusion that the absence of the SNARC effect is truly due to the presence of the ordinal position effect. One possibility is that the SNARC effect was not observed, simply because the setup of the study of van Dijck and Fias (2011) was not optimal to observe a SNARC effect. In their task, the response
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mapping on the numbers was counterbalanced between participants such that half of the participants responded to the odd numbers with the left- hand side and the other half of the participants responded to the even numbers with the left-hand side, and vice versa. Optimal sensitivity for the SNARC effect might only be obtained if all numbers are responded to, both with the left hand and with the right hand side, within the same experimental session (e.g.. Fias et al, 1996). For this reason, in Experiment 1, we repeat the experiment of van Dijck and Fias (2011), with the exception that the response mapping is switched within participants. As such, every position and every number is responded to with both response sides. This switched response mapping can be expected to enhance the likelihood of observing a SNARC effect. Another possible reason for the absence of the SNARC effect may have been that the cognitive functions underlying the maintenance of verbal information in working memory and the spatial associations responsible for the SNARC effect compete for the same resources. That is, participants performed a parity judgment task while encoding a verbal working memory load (e.g., a sequence of numbers). As outlined above, the maintenance of verbal information in working memory and the SNARC effect in a parity judgment task use the same working memory resources resulting in the elimination of the SNARC effect. At the same time, the SNARC effect was unaffected when a verbal load was combined with the magnitude comparison task (van Dijck et al., 2009), indicating that the SNARC effect in a magnitude comparison task does not depend on verbal resources. For this reason, in Experiment 2, we use a magnitude comparison task instead of a parity judgment task. If the absence of the SNARC effect was due to the fact that a verbal load was added to a parity judgment task, we expect to observe a SNARC effect in the magnitude comparison task. Another reason for using the magnitude comparison task is that it enables us to evaluate whether the ordinal position effect generalizes to tasks other than the parity judgment task. A magnitude comparison task requires explicit access to the magnitude of the number. Such explicit access may favor the activation of associations between response side and the magnitude of the number (e.g., the SNARC effect) and not with the position in working memory. Furthermore, a magnitude comparison task allows the calculation of the distance effect, which provides us with an indication of whether numbers are effectively processed up to the semantic level. In Experiments 3 and 4, we more specifically investigate whether and how the mapping between numbers and space is influenced by the type of processing required in the memorized sequence. The first two experiments used the same go/no-go procedure as used in the original design (van Dijck & Fias, 2011). Participants responded to a presented target number only if this number belonged to the memorized sequence. This forced participants to explicitly retrieve the numbers encoded in working memory. In Experiment 3 (magnitude comparison) and Experiment 4 (parity judgment), we remove the go/no-go procedure from the design. Participants responded to all numbers, regardless of whether the numbers belonged to the memorized sequence. As such, the memorized sequence only needed to be maintained throughout the categorization phase, while no explicit retrieval from the memory sequence is required. An ordinal position effect is expected if maintenance is sufficient to create spatial associations with ordinal position in working memory. However, it is
possible that the ordinal position effect is created at the moment when information is retrieved from working memory. If this is the case, no ordinal position effect is expected when the go/no-go procedure (e.g., retrieval) is removed from the design.
Experiment 1 The study of van Dijck and Fias (2011) demonstrated an ordinal position effect in the absence of a SNARC effect. Here, we investigate whether the absence of the SNARC effect was related to the specifics of the design used in that study. In van Dijck and Fias (2011), participants only performed one response mapping (e.g., only odd-left and even-right or only odd-right and even-left). In the present experiment, the response mapping was switched within participants, as it was the case in earher SNARC experiments (e.g.. Fias et al., 1996). In doing so, we ensure that each position in working memory as well as each number is responded to with both the left- and the right-hand side. This enhances the sensitivity to detect a SNARC effect. Note that van Dijck et al. (2009) demonstrated that the SNARC effect is eliminated when a verbal load is added to a parity judgment task. However, in their study, a sequence of letters had to be maintained while performing a parity judgment task on numbers. This constitutes an important difference with the current experiment, where both the working memory task and the parity judgment task have to be performed on exactly the same sequence of numbers.
Method Participants. In total, 29 paid volunteers (M = 21.21 years, SD = 2.09; 20 women [two left-handed] and nine men [one left-handed]) participated in the experiment. All participants were undergraduate students recmited via an announcement on Facebook and assigned randomly to one of the four experiments. Participants received €8 as compensation for their participation. The ethical committee approved this study and participants were debriefed after completing a single 40-min session. All participants were naive with respect to the purpose of the experiment. Stimuli and procedure. The experiment was performed using E-Prime 2 Professional Software (Psychology Software Tools). Participants were seated in a quiet room approximately 50 cm from a 17-in. LCD computer screen with a resolution of 1,280 X 1,024 pixels. The motor responses were collected via button presses on a response box. Each digit (approximately 1.37°) was presented on the computer screen in black on a white background. Each block consisted of three subsequent phases; an encoding phase, a classification phase, and a control phase. In total, the experiment consisted of 20 different blocks. During the encoding phase, five digits (randomly chosen in the range from 1 to 10) were successively presented at the center of the screen. Participants were instmcted to memorize this sequence of numbers in the correct order. To enable encoding at their own pace, we had the participants press the space bar to proceed from one digit to the next. A blank screen followed the final digit (2,500 ms), allowing for rehearsal, after which the classification phase began. During this phase, participants continued to keep the memorized sequence in mind while they performed a parity judgment task. For this, all numbers ranging from 1 to 10 were randomly presented twice with the restriction that the same number could not be repeated on
VERBAL WORKING MEMORY AND NUMBER-SPACE ASSOCIATIONS consecutive trials. The task was to respond only to those numbers that were part of the memorized sequence (go/no-go paradigm). The experiment consisted of 10 blocks (for each response mapping), resulting in a total of 200 classification trials that consisted of 100 go trails and 100 no-go trials. A trial consisted of a fixation point (500 ms) followed by a target number presented in black on a white background. Participants pressed the left or the right button on a response box as a function of the parity status. The response mapping was counterbalanced within subjects. In the flrst half of the experiment (consisting of 10 blocks), participants had to press the left button for odd numbers and the right button for even numbers, whereas for the other half of the experiment (consisting of 10 blocks), this response mapping was reversed. The order of these conditions was counterbalanced across participants. The response deadline was set to 1,500 ms. After this deadline or after a response, the next trial was initiated, following an intertrial interval of 1,000 ms. During the last phase, the control phase, participants had to judge whether a new sequence of five digits (sequentially presented in the center of the screen over 1,000 ms with an interstimulus interval of 200 ms) was the same sequence as the one kept in memory. The nonconresponding sequences were composed of the same five numbers of the memorized sequence but, at a random location, the order between two adjacent numbers was changed. The entire block was introduced again at the end of the experiment if the participant responded erroneously to the control sequence. Data analysis. Across experiments, we used repeatedmeasures analyses of variance (ANOVAs) with numerical magnitude (2: small, 1-5; large, 6-10), ordinal position (5: from 1 to 5), and response side (2: left, right) as within-subjects factors and response mapping as the between-subjects factor. Response mapping never interacted significantly with our effects of interest. For this reason, we removed this factor from the following analyses. As such, the repeated-measures ANOVA was limited to the within-subject factors magnitude, response side, and ordinal position. On the basis of these factors, we could investigate the interaction between ordinal position and response side (ordinal position effect), the interaction between numerical magnitude and response side (the SNARC effect), and the main effect of position (serial search effect). These analyses were complemented with a regression approach described by Lorch and Myers (1990; see also Fias et al., 1996). This method consists of computing the difference in RTs (dRT; RT right hand minus RT left hand) for each number (from 1 to 10) or position (from 1 to 5) separately. Per subjects, these values were entered in a regression analysis with number or position in working memory as predictor. A t test was performed to evaluate whether the regression weights of the group deviated significantly from zero. Because of the characteristics of the SNARC effect (faster left-hand responses for small numbers and faster right-hand responses for large numbers) and the ordinal position effect (faster left-hand responses for early positions and faster right-hand responses for later positions in working memory), negative RT difference (dRT) values are expected with increasing magnitude or the further the ordinal position.
Results and Discussion Two participants were excluded from the analysis because they made too many errors (more than 2 standard deviations above the
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mean of errors). We only took into account blocks in which the control phase was responded correctly and only correct go/no-go trials with RTs larger than 250 ms. We discarded only two data points with this RT cutoff. It took, on average, 10.82 blocks {SD = 1.04) before all 10 blocks (for both conditions: odd-left/even-right and odd-right/even-left) were correctly performed. During the parity judgment task, average RT was 844.28 ms {SD = 113.66 ms) and the average number of errors was 7.85% (SD = 8.14%). A main effect of ordinal position, F(4, 104) = 18.06, p < .001, Ti^ = .41, was observed. Average RTs per position increased gradually (810, 827, 858, 854, and 876 ms for each position, respectively). A polynomial contrast confirmed the linear trend of these RTs, F(l, 26) = 57.63, p < .001,115 = -69, suggesting a serial search strategy. No other main effects reached significance. Replicating the ordinal position effect, a significant interaction was observed between ordinal position and response side, F(4, 104) = 6.75, p < .001, TIJ = .21, indicating that early positions in the memorized sequence were responded to faster with the left hand (Positions 1 and 2 together: 808.18 ms with the left hand and 829.34 ms with the right hand), whereas later positions were responded to faster with the right hand (Positions 4 and 5 together: 876.38 ms with the left hand and 854.38 ms with the right hand). The interaction between numerical magnitude and response side (e.g., the SNARC effect) was not significant, F(l, 26) = 1.87, p = .18, Tip = .07. The triple interaction between numerical magnitude, ordinal position, and response side was not significant, F(4, 104) = 1.06, p = .38, y]l = .04. In a final step, we reanalyzed the data using a regression analysis. The dRTs deceased 18.09 ms per position, t(26) = -3.63, p < .005 (see Figure lA). This was not the case for the SNARC effect, where the slope did not differ from zero, i(26) = -1.58, p = .13 (see Figure IB). Both the ANOVA and the regression analysis reveal the same pattem as in van Dijck and Fias (2011): the presence of an ordinal position effect and the absence of the SNARC effect. Although the experimental design was optimized to have equal sensitivity to detect eitiier the ordinal position effect or the SNARC effect, only the ordinal position effect was observed.
Experiment 2 In Experiment 2, we investigated whether the ordinal position effect and/or the SNARC effect are present when the working memory load added to the classification task did not affect the number-space associations. Earlier work showed that imposing a verbal working memory load during a parity judgment task prevented the activation of spatial components associated with numbers (van Dijck, Gevers, & Fias, 2009), possibly explaining the absence of the SNARC effect in the previous experiment. The SNARC effect in a magnitude comparison task is not eliminated by a verbal working memory load (Herrera et al., 2008; van Dijck et al., 2009). Therefore, changing the parity judgment task into a magnitude comparison task could result in both a SNARC effect and an ordinal position effect. If, however, the absence of the SNARC effect was due to the presence of the ordinal position effect, again, no SNARC effect is expected.
GINSBURG, VAN DUCK, PREVITALI, FL\S, AND GEVERS
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Figure 1. Observed data and regression line of Experiment 1, representing reaction time differences (dRT) between right- and left-hand responses as a function of their position in the working memory sequence (A) and as a function of the numerical magnitude for numbers inside working memory (B). Positive values reflect faster left than right responses. SNARC effect = spatial numerical associations of response codes effect.
Method Participants. In total, 36 paid volunteers (M = 20.44 years, SD = 2.78; 28 women [all right-handed] and eight men [one left-handed]) participated in this experiment. All participants were undergraduate students recruited via an announcement on Facebook and assigned randomly to one of the four experiments. They received €8 as compensation for their participation. The ethical committee approved this study and participants were debriefed after completing a single 40-min session. All participants were naive with respect to the purpose of the experiment. Stimuli and procedure. In Experiment 2, we used exactly the same stimuli and the same procedure as in Experiment 1 with the exception that during the classification phase, participants performed a magnitude comparison task instead of a parity judgment task. Participants had to indicate whether the presented target number was small (range: 1 - 5) or large (range: 6 - 10). As such, there was no central referent to which the presented numbers had to be compared, as is the case in a regular magnitude comparison task with numbers ranging from 1 to 9 (e.g., "Is the number smaller or larger than 5?"; Gevers, Verguts, Reynvoet, Caessens, & Eias, 2006). This slightly adapted design was chosen to make the design as similar as possible to the parity judgment task of Experiment I. Another reason is that if we want working memory position and numerical magnitude to be fully orthogonal, sequences of 10 numbers are needed when participants have to maintain sequences of five numbers and every number has to be presented in each working memory position an equal amount of times. Each participant performed two conditions. In the first, they had to press the left button for smaller numbers and the right button for larger numbers. In the second, they performed the opposite mapping. The order of conditions was counterbalanced across participants.
Results and Discussion Two participants were removed from the analysis. One of them made too many errors (more than 2 standard deviations above the mean of the errors) and one other responded too slowly (more than 2 standard deviations above the mean of the RTs). As in Experiment 1, we took into account only blocks with correct control phase and correct go/no-go trials with RTs above 250 ms. We discarded only three data points with this RT cutoff. It took, on average, 11.25 blocks (SD = 1.75) before all 10 blocks (for both
conditions: odd-left/even-right and odd-right/even-left) were correctly performed. During the magnitude comparison task, average RT was 748.14 ms (SD = 108.04 ms) and the average number of errors was 6.93% (SD = 4.48%). A sharp drop in performance was observed for the numbers 5 and 6 compared with other numbers: in terms of RTs (804.41 ms vs. 734.67 ms) and in terms of errors (11.2% vs. 5.3%). Apparently, classifying the numbers 5 and 6 as small or large is particularly difficult because these numbers lie at the boundary of small and large categorizations. For this reason, we decided to remove these numbers from the ANOVA. Note that a separate analysis with the numbers 5 and 6 included resulted in exactly the same pattern of results. As in Experiment 1, the repeated-measures ANOVA with ordinal position, numerical magnitude, and response side showed a main effect of ordinal position, f(4, 132) = 10.28,/) < .001, -q^ = .24. Average RTs per position were 703, 720, 742, 757, and 762 ms. A linear trend of these RTs, F(l, 33) = 45.13,p < .001, TI^ = .58, was highlighted by a polynomial contrast, again suggesting a serial search strategy. An ordinal position effect was observed, indicated by a significant interaction between ordinal position and response side, F(4, 132) = 5.45, p < .001, •(]j = .14. This analysis confirmed that numbers at the beginning of the sequence were responded to faster with the left hand (Positions 1 and 2 together: 714.19 ms with the left hand and 732.75 ms with the right hand), whereas the reversed pattern was observed for numbers at the end ofthe sequence (Positions 4 and 5 together: 783.96 ms with the left hand and 761.59 ms with the right hand). No SNARC effect was observed: Numerical magnitude and response side did not interact (p = .63). Because this experiment involves a magnitude comparison task, we are able to analyze the presence of the distance effect (Moyer & Landauer, 1967). This effect reflects the finding that RTs speed up when the numerical distance between the numbers increases (e.g., it is easier to indicate that 1 < 4 than 3 < 4). In this case, however, the distance effect we refer to is slightly different because it refers to the ease with which a number is categorized as being small or large. A significant distance effect was observed with slower responses for numbers close to the middle of the range (752.31 ms) than for numbers far from the middle of the range (716.45 ms), F(l, 33) = 34.59, p < .001. The results of the regression analysis were in accord with the ANOVA. The ordinal position effect is significantly present,
VERBAL WORKING MEMORY AND NUMBER-SPACE ASSOCIATIONS
dRT = -15.61 ms, i(33) = -3.9, p < .005 (see Figure 2A), and the slope reflecting the SNARC effect was not different from zero, i(33) = -0.69, p = .50 (see Figure 2B). In sum, a similar pattern of results was found as in Experiment 1 (i.e., the presence of an ordinal position effect and the absence of a SNARC effect), meaning that this pattern is observed irrespective of whether the classification task and the memory task use the same resources. Furthermore, a distance effect was observed, suggesting that participants effectively accessed magnitude information during the classification task.
Experiment 3 In Experiments 1 and 2, an association was observed between lateralized responses and ordinal position in working memory. At the same time, no association between magnitude and response side was observed. In the next experiments, we attempt to further specifying the nature of the memory processes involved. In this third experiment, we investigated whether memorized items need to be actively retrieved or whether encoding is sufficient to obtain the ordinal position effect. For this purpose, we removed the go/no-go component from the classification task and asked the participants to respond to all items. If encoding is sufficient, the ordinal position effect should be obtained when participants respond to all numbers during the classification task. If retrieval from working memory is required, no ordinal position effect is expected.
Method Participants. In total, 21 paid volunteers (M = 21.9 years, SD = 2.81; 17 women [all right-handed] and four men [all righthanded]) participated. All participants were undergraduate students recruited via an announcement on Facebook and assigned randomly to one of the four experiments. They received €8 as compensation for their participation. The ethical committee approved this study and participants were debriefed after completing a single 40-min session. All participants were naive with respect to the purpose of the experiment. Stimuli and procedure. Experiment 3 used exactly the same stimuli and followed the same procedure as Experiment 2 except
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that during the classification phase, the go/no-go procedure was dropped such that participants had to perform a magnitude comparison task on every presented number. In doing so, even when participants respond to numbers belonging to the memorized sequence (e.g., if the number 3 is part of the sequence, it still requires a response during the classification task), they do not need to retrieve it (because presence inside working memory is no longer decisive to initiate a response). Responses are collected for numbers both inside and outside the memorized sequence, allowing us to test the presence and compare the size of the SNARC effect both inside and outside the memorized sequence.
Results Three participants were removed from the analysis: One made too many errors (more than 2 standard deviations above the mean of the errors) and the two others responded too slowly (more than 2 standard deviations above the mean of the RTs). It took, on average, 10.34 blocks (SD = 0.53) before all 10 blocks (for both conditions: odd-left/even-right and odd-right/even-left) were correctly performed. During the magnitude comparison task, for the items inside the memorized sequence, RT was 498.99 ms (SD = 62.85 ms) and the average number of errors was 4.52% (SD = 3.15%). For the items outside the memorized sequence, RT was 493.97 ms (SD = 57.42 ms) and the average number of errors was 5.59% (SD = 3.94%). For the same reasons as in the previous expedment, analyses were performed on all numbers except the numbers 5 and 6. Again, as in the previous experiment, separate analyses on the entire range of numbers showed the same results. The repeated-measures ANOVA with ordinal position, numerical magnitude, and response side as within-subjects factors showed an interaction between numerical magnitude and response, indicating the presence of a SNARC effect, F(l, 17) = 18.84, p < .001, Tip = .53. In fact, participants responded faster to small digits with the left-hand side (mean RT = 469.57 ms, SD = 15.77) than with the right-hand side (mean RT = 489.86 ms, SD = 16.76). Further, they responded faster to large digits with the right-hand side (mean RT = 459.95 ms, SD = U.I4) than with the left-hand side (mean RT = 502.78 ms, SD = 14.82). No ordinal position effect was observed (p = .66). We conducted a separate analysis for numbers that were responded to but that were not part of the
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Figure 2. Observed data and regression line of Experiment 2, representing reaction time differences (dRT) between right- and left-hand responses as a function of their position in the working memory sequence (A) and as a function of the numerical magnitude for numbers inside working memory (B). Positive values reflect faster left than right responses. SNARC effect = spatial numerical associations of response codes effect.
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memorized sequence. Also, for these targets, a significant SNARC effect was present, F(\, 17) = 10.67, p < .01,% = .39. A direct comparison for numbers inside and outside the memory sequence showed no difference in the size of SNARC (p = .23). The regression analysis confirmed the presence of the SNARC effect, dRT = -11.32 ms, i(17) = -4.02, p < .005 (see Figure 3B). This effect is observed for numbers both inside, dRT = -12.87 ms, i(17) = -4.38, p < .005 (see Figure 3C), and outside, dRT = -9.57 ms, /(17) = -3.09, p < .01 (see Figure 3D), the working memory sequence. The slopes of these regressions were not significantly different from each other, r(17) = -1.25,p = .23, and were strongly correlated (r = .69, p = .002). Participants with a strong SNARC effect inside the memorized sequence also had a strong SNARC effect for targets outside the memorized sequence. Confirming the results of the repeatedmeasures ANOVA, no evidence was found for the ordinal position effect, i(17) = 0.61, p = .552 (see Figure 3A). In agreement with the idea that the items in working memory were encoded but not retrieved during the classification task, no serial position effect was observed, i(17) = 0.984, p = .34. Finally, a distance effect was observed for both numbers inside, F(l, 17) = 8.81,/) < .01, •ï\l = .34, and outside, F(l, 17) = 28.11, p < .001, -^j = .62, the memorized sequence. The size of the distance effect was not different for numbers inside and outside the memorized sequence (p = .82). In sum, for the magnitude comparison task, when information in working memory is encoded but not retrieved, the ordinal position effect is not observed while at the same time a SNARC effect is present.
Experiment 4 The aim of the Experiment 4 is to validate, within the same experiment, the findings of the previous experiments and to integrate them with the existing literature. The go/no-go procedure used in Experiments 1 and 2 forced participants to retrieve the information maintained in working memory during the classification. Retrieval was not needed in Experiment 3, in which participants classified the magnitude of all numbers. An ordinal position effect was observed only when retrieval was required during the classification task. A SNARC effect was observed only when retrieval was not needed. Like in Experiment 3, in Experiment 4, participants again have to respond to all numbers (no retrieval required), but this time numbers have to be classified according to their parity. Validating the crucial role of retrieval for the ordinal position effect and its infiuence on the SNARC effect, we expect to observe a SNARC effect but no ordinal position effect. Besides this, the use of the parity judgment task makes it possible to investigate a final outstanding question: Is the maintenance of a numerical sequence involved in the creation of spatial associations between these numbers and lateralized responses? In Experiment 3, it seemed that the maintenance of information had no influence on the SNARC effect. Indeed, a SNARC effect was observed for numbers both inside and outside the memorized sequence. However, in a magnitude comparison task, it has been demonstrated that a verbal load has no infiuence on the SNARC effect (Herrera et al., 2008; van Dijck et al., 2009). A verbal load
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Journal of Experimental Psychology: Learning. Memory, and Cognition 2014, Vol. 40, No. 4, 976-986
The Impact of Verbal Working Memory on Number-Space Associations Véronique Ginsburg
Jean-Philippe van Dijck
Université Libre de Bruxelles
Ghent University and University of Antwerp
Paola Previtali
Wim Fias
University of Milano-Bicocca
Ghent University
Wim Gevers Université Libre de Bruxelles Spatial-numerical associations are observed when participants perform number categorization tasks. One such observation is the spatial numerical associations of response codes (SNARC) effect, showing an association between small numbers and the left-hand side and between large numbers and the right-hand side. It has long been argued that this spatial association is automatically activated by the long-term representation underlying numbers processing. Instead, van Dijck and Fias (2011) argued that this association is a short-term representation that is constructed during task execution. This argument was based on the observation of an association between the ordinal position of an item in working memory and response side (e.g., the ordinal position effect). Four different experiments were set up to systematically investigate this assumption. Our results indicate that the activation of the canonical order of numbers in working memory (e.g., 1, 2, 3, etc.) is indeed necessary to observe the SNARC effect. The activation of the standard sequence of numbers (e.g., from 1 to 9) can be overruled when a new random sequence is memorized. However, this is only observed when retrieval of the memorized sequence is required during the numbers classification task. Keywords: numbers, space, SNARC effect, working memory, ordinal coding
have to classify target numbers as odd or even by pressing a left or a right response button. The SNARC effect is also obtained when magnitude information has to be accessed more explicitly such as in a magtiitude comparison task (Dehaene, Dupwux, & Mehler, 1990). In this task, participants have to judge whether a target number is smaller or larger than a reference number by pressing a left- or a right-sided response button. The SNARC effect is influenced by cultural factors such as reading and writing experiences (Dehaene et al., 1993; Shaki & Fischer, 2008; Shaki, Fischer, & Petrusic, 2009; Zebian, 2005). For example, Dehaene et al. (1993) observed that Iranian participants, who read from right to left, presented a weak or even a reversed SNARC effect if they had only limited exposure to French. When Iranian participants with a high degree of familiarity with French were tested, a tendency for a regular SNARC effect was observed. In Western cultures, numbers are often presented physically from left to right in a canonical order (i.e., numeral sequence) like on a ruler, with small numbers presented on the left and large numbers on the right. It has been assumed that repeated exposure to this left-to-right orientation of numerical magnitude installs a stronger correlation between small numbers and the left side of space and between large numbers and the right side of space (Chen & Verguts, 2010). The observations of cultural influences on the SNARC effect suggest that the direction of the mapping between numbers and space results from long-term learning mechanisms.
Research in the domain of numerical cognition has highlighted the fact that numerical processing is linked with spatial processing. One observation that is often used to describe this link between numbers and space is the spatial numerical associations of response codes (SNARC) effect (Dehaene, Bossini, & Giraux, 1993). The SNARC effect reveals an association between numerical magnitude and lateralized motor responses: Participants respond faster to small numbers with the left-hand side and to large numbers with theright-handside. The most widely used task to investigate the SNARC effect is the parity judgment task (Dehaene et al., 1993). In this task, participants
This article was published Online First April 7, 2014. Véronique Ginsburg, Center for Research in Cognition and Neurosciences (CRCN), ULB Neurosciences Institute (UNI), Université Libre de Bruxelles (ULB); Jean-Philippe van Dijck, Department of Experimental Psychology, Ghent University, and Collaborative Antwerp Psychiatric Research Institute, University of Antweip; Paola Previtali, Department of Psychology, University of Milano-Bicocca; Wim Fias, Department of Experimental Psychology, Ghent University; Wim Gevers, Center for Research in Cognition and Neurosciences (CRCN), ULB Neurosciences Institute (UNI), Université Libre de Bruxelles (ULB). Véronique Ginsburg is a research fellow at the Belgian Fonds National de la Recherche Scientifique (F.R.S.-FNRS). Correspondence concerning this article should be addressed to Véronique Ginsburg, Université Libre de Bruxelles, Avenue F.D. Roosevelt 50, B-I050 Brussels, Belgium. E-mail: [email protected] 976
VERBAL WORKING MEMORY AND NUMBER-SPACE ASSOCIATIONS At the same time, however, the mapping between numbers and space is highly fiexible. Eariy reports on the SNARC effect demonstrated that relative instead of absolute magnitude information is associated with response side (Dehaene et al, 1993; Fias, Brysbaert, Geypens, & d'Ydewalle, 1996). In these studies, the number 5 was responded to faster with the left hand when it was relatively small within the range (e.g., numbers ranged from 4 to 9), but the same number was responded to faster with the right hand when it was relatively large within the range (e.g., from 1 to 5). Additionally, Bächtold, Baumüller, and Brugger (1998) demonstrated that the SNARC effect could be reversed by means of mental imagery. When subjects were asked to imagine numbers on a clock face, the SNARC effect reversed, because now small numbers occurred on the right side of the clock face and large numbers on the left side. Similarly, Shaki and Fischer (2008) showed that Russian Hebrew bilinguals present a normal SNARC effect when they had to read a Russian text (reading from left to right) just before the SNARC task but that this effect was significantly reduced when they had to read a Hebrew text (reading from right to left) just before. In sum, the association between numbers and space depends on relative number magnitude (Dehaene et al, 1993; Fias et al., 1996). Furthermore, the high fiexibility of the association between numbers and space suggests that the association is generated online during task execution (e.g., Fischer, 2006). Together, these observations led to the hypothesis that working memory has an important role in the creation of number-space associations (e.g.. Fias, van Dijck, & Gevers, 2011). Empirical support for the involvement of working memory in associating numbers with space is accumulating (Herrera, Macizo, & Semenza, 2008; Lindemann, Abolafia, Pratt, & Bekkering, 2008; van Dijck, Abrahamse, Acar, Ketels, & Fias, in press; van Dijck, Abrahamse, Majems, & Fias, 2013; van Dijck & Fias, 2011; van Dijck, Gevers, 6 Fias, 2009). Working memory is generally described as a system that encodes, maintains, and processes a limited amount of information during a brief period of time (Baddeley, 1986, 2000; Baddeley & Hitch, 1974; Cowan, 1995, 1999; Oberauer, 2002). Encoding and maintenance are the processes needed to temporarily keep information for later use. In what follows, we define encoding to comprise both the positioning of an item within a memorized sequence and the maintenance-related processes that act on it. With retrieval, we refer to the act of processing and retrieving the encoded information. Most models on working memory functioning have in common that they make a distinction between encoding and retrieving information from working memory (Baddeley & Hitch, 1974; Oberauer, 2002). Another relevant issue is how information of different modalities is encoded by the system. There is general agreement that different systems exist for encoding verbal information and for encoding visual and spatial information (e.g., Baddeley & Hitch, 1974; Shah & Miyake, 1996; Smith, Jonides, & Koeppe, 1996). Some researchers investigated the influence of encoding information of different modalities (verbal vs. visuospatial) on the association between numbers and space. In these studies, participants had to encode verbal or visuospatial information in working memory while performing a parity judgment task (van Dijck et al., 2009) or a magnitude comparison task (Herrera et al., 2008; van Dijck et al., 2009) during the retention interval. A double dissociation was observed between the type of working memory load
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(verbal or visuospatial) and the type of task (magnitude comparison or parity judgment). When participants performed a magnitude comparison task, the SNARC effect disappeared with a visuospatial load but was unaffected by a verbal load. The distance effect (the observation that reaction times [RTs] speed up when the distance between the numbers increases; Moyer & Landauer, 1967), however, was not affected by the working memory load, suggesting that the visuospatial load effect was specific to the SNARC effect and the spatial associations reflected therein. In contrast, in a parity judgment task, the SNARC effect disappeared with a verbal load but was unaffected by a visuospatial load. Together, these observations indicate that the formation of number-space associations requires availability of working memory resources: The SNARC effect in a parity judgment context needs verbal working memory resources, whereas the SNARC effect in a magnitude comparison needs visuospatial working memory resources (see also van Dijck, Gevers, Lafosse, & Fias, 2012). In line with this, a principal component analysis on parity and magnitude comparison performance tested within the same subjects showed that the SNARC effect in a parity judgment task and in a magnitude comparison task loaded on two independent components (van Dijck et al., 2012). Recent studies more directly investigated the influence of working memory on the creation of number-space associations (van Dijck & Fias, 2011; van Dijck et al., in press). Van Dijck and Fias (2011) asked participants to keep a sequence of five numbers (randomly chosen between 1 and 10) in working memory. Subsequently, all numbers in the range from 1 to 10 were randomly presented as stimuli in a parity judgment task. To ensure that the numbers had to be retrieved form working memory, a go/no-go procedure was included. Participants responded to the parity of the number, but only if the number belonged to the memorized sequence. No SNARC effect was observed: Regardless of the magnitude of the number, responses were equally fast with the left hand as with the right hand. However, spatial associations were observed with the position of the number in the working memory sequence. Numbers from the beginning of the memorized sequence were responded to faster with the left-hand side, whereas numbers at the end of the sequence were responded to faster with the right-hand side (e.g., hereinafter, this observation will be termed the ordinal position effect). A subsequent experiment showed that these spatial-positional associations were not limited to numerical information. Instead of using numbers, participants had to classify words as being fruits or vegetables. Again, the ordinal position effect was observed, with words early in the sequence responded to faster with the left-hand side and words late in the sequence responded to faster with the right-hand side. Furthermore, the ordinal position effect obtained with words correlated with the SNARC effect observed in a separate regular parity judgment task. On the basis of this correlation, the authors suggested that the position of an item in working memory, not the magnitude of the number, drives the SNARC effect (van Dijck & Fias, 2011). A number of altemative possibilities require investigation before we can accept the conclusion that the absence of the SNARC effect is truly due to the presence of the ordinal position effect. One possibility is that the SNARC effect was not observed, simply because the setup of the study of van Dijck and Fias (2011) was not optimal to observe a SNARC effect. In their task, the response
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mapping on the numbers was counterbalanced between participants such that half of the participants responded to the odd numbers with the left- hand side and the other half of the participants responded to the even numbers with the left-hand side, and vice versa. Optimal sensitivity for the SNARC effect might only be obtained if all numbers are responded to, both with the left hand and with the right hand side, within the same experimental session (e.g.. Fias et al, 1996). For this reason, in Experiment 1, we repeat the experiment of van Dijck and Fias (2011), with the exception that the response mapping is switched within participants. As such, every position and every number is responded to with both response sides. This switched response mapping can be expected to enhance the likelihood of observing a SNARC effect. Another possible reason for the absence of the SNARC effect may have been that the cognitive functions underlying the maintenance of verbal information in working memory and the spatial associations responsible for the SNARC effect compete for the same resources. That is, participants performed a parity judgment task while encoding a verbal working memory load (e.g., a sequence of numbers). As outlined above, the maintenance of verbal information in working memory and the SNARC effect in a parity judgment task use the same working memory resources resulting in the elimination of the SNARC effect. At the same time, the SNARC effect was unaffected when a verbal load was combined with the magnitude comparison task (van Dijck et al., 2009), indicating that the SNARC effect in a magnitude comparison task does not depend on verbal resources. For this reason, in Experiment 2, we use a magnitude comparison task instead of a parity judgment task. If the absence of the SNARC effect was due to the fact that a verbal load was added to a parity judgment task, we expect to observe a SNARC effect in the magnitude comparison task. Another reason for using the magnitude comparison task is that it enables us to evaluate whether the ordinal position effect generalizes to tasks other than the parity judgment task. A magnitude comparison task requires explicit access to the magnitude of the number. Such explicit access may favor the activation of associations between response side and the magnitude of the number (e.g., the SNARC effect) and not with the position in working memory. Furthermore, a magnitude comparison task allows the calculation of the distance effect, which provides us with an indication of whether numbers are effectively processed up to the semantic level. In Experiments 3 and 4, we more specifically investigate whether and how the mapping between numbers and space is influenced by the type of processing required in the memorized sequence. The first two experiments used the same go/no-go procedure as used in the original design (van Dijck & Fias, 2011). Participants responded to a presented target number only if this number belonged to the memorized sequence. This forced participants to explicitly retrieve the numbers encoded in working memory. In Experiment 3 (magnitude comparison) and Experiment 4 (parity judgment), we remove the go/no-go procedure from the design. Participants responded to all numbers, regardless of whether the numbers belonged to the memorized sequence. As such, the memorized sequence only needed to be maintained throughout the categorization phase, while no explicit retrieval from the memory sequence is required. An ordinal position effect is expected if maintenance is sufficient to create spatial associations with ordinal position in working memory. However, it is
possible that the ordinal position effect is created at the moment when information is retrieved from working memory. If this is the case, no ordinal position effect is expected when the go/no-go procedure (e.g., retrieval) is removed from the design.
Experiment 1 The study of van Dijck and Fias (2011) demonstrated an ordinal position effect in the absence of a SNARC effect. Here, we investigate whether the absence of the SNARC effect was related to the specifics of the design used in that study. In van Dijck and Fias (2011), participants only performed one response mapping (e.g., only odd-left and even-right or only odd-right and even-left). In the present experiment, the response mapping was switched within participants, as it was the case in earher SNARC experiments (e.g.. Fias et al., 1996). In doing so, we ensure that each position in working memory as well as each number is responded to with both the left- and the right-hand side. This enhances the sensitivity to detect a SNARC effect. Note that van Dijck et al. (2009) demonstrated that the SNARC effect is eliminated when a verbal load is added to a parity judgment task. However, in their study, a sequence of letters had to be maintained while performing a parity judgment task on numbers. This constitutes an important difference with the current experiment, where both the working memory task and the parity judgment task have to be performed on exactly the same sequence of numbers.
Method Participants. In total, 29 paid volunteers (M = 21.21 years, SD = 2.09; 20 women [two left-handed] and nine men [one left-handed]) participated in the experiment. All participants were undergraduate students recmited via an announcement on Facebook and assigned randomly to one of the four experiments. Participants received €8 as compensation for their participation. The ethical committee approved this study and participants were debriefed after completing a single 40-min session. All participants were naive with respect to the purpose of the experiment. Stimuli and procedure. The experiment was performed using E-Prime 2 Professional Software (Psychology Software Tools). Participants were seated in a quiet room approximately 50 cm from a 17-in. LCD computer screen with a resolution of 1,280 X 1,024 pixels. The motor responses were collected via button presses on a response box. Each digit (approximately 1.37°) was presented on the computer screen in black on a white background. Each block consisted of three subsequent phases; an encoding phase, a classification phase, and a control phase. In total, the experiment consisted of 20 different blocks. During the encoding phase, five digits (randomly chosen in the range from 1 to 10) were successively presented at the center of the screen. Participants were instmcted to memorize this sequence of numbers in the correct order. To enable encoding at their own pace, we had the participants press the space bar to proceed from one digit to the next. A blank screen followed the final digit (2,500 ms), allowing for rehearsal, after which the classification phase began. During this phase, participants continued to keep the memorized sequence in mind while they performed a parity judgment task. For this, all numbers ranging from 1 to 10 were randomly presented twice with the restriction that the same number could not be repeated on
VERBAL WORKING MEMORY AND NUMBER-SPACE ASSOCIATIONS consecutive trials. The task was to respond only to those numbers that were part of the memorized sequence (go/no-go paradigm). The experiment consisted of 10 blocks (for each response mapping), resulting in a total of 200 classification trials that consisted of 100 go trails and 100 no-go trials. A trial consisted of a fixation point (500 ms) followed by a target number presented in black on a white background. Participants pressed the left or the right button on a response box as a function of the parity status. The response mapping was counterbalanced within subjects. In the flrst half of the experiment (consisting of 10 blocks), participants had to press the left button for odd numbers and the right button for even numbers, whereas for the other half of the experiment (consisting of 10 blocks), this response mapping was reversed. The order of these conditions was counterbalanced across participants. The response deadline was set to 1,500 ms. After this deadline or after a response, the next trial was initiated, following an intertrial interval of 1,000 ms. During the last phase, the control phase, participants had to judge whether a new sequence of five digits (sequentially presented in the center of the screen over 1,000 ms with an interstimulus interval of 200 ms) was the same sequence as the one kept in memory. The nonconresponding sequences were composed of the same five numbers of the memorized sequence but, at a random location, the order between two adjacent numbers was changed. The entire block was introduced again at the end of the experiment if the participant responded erroneously to the control sequence. Data analysis. Across experiments, we used repeatedmeasures analyses of variance (ANOVAs) with numerical magnitude (2: small, 1-5; large, 6-10), ordinal position (5: from 1 to 5), and response side (2: left, right) as within-subjects factors and response mapping as the between-subjects factor. Response mapping never interacted significantly with our effects of interest. For this reason, we removed this factor from the following analyses. As such, the repeated-measures ANOVA was limited to the within-subject factors magnitude, response side, and ordinal position. On the basis of these factors, we could investigate the interaction between ordinal position and response side (ordinal position effect), the interaction between numerical magnitude and response side (the SNARC effect), and the main effect of position (serial search effect). These analyses were complemented with a regression approach described by Lorch and Myers (1990; see also Fias et al., 1996). This method consists of computing the difference in RTs (dRT; RT right hand minus RT left hand) for each number (from 1 to 10) or position (from 1 to 5) separately. Per subjects, these values were entered in a regression analysis with number or position in working memory as predictor. A t test was performed to evaluate whether the regression weights of the group deviated significantly from zero. Because of the characteristics of the SNARC effect (faster left-hand responses for small numbers and faster right-hand responses for large numbers) and the ordinal position effect (faster left-hand responses for early positions and faster right-hand responses for later positions in working memory), negative RT difference (dRT) values are expected with increasing magnitude or the further the ordinal position.
Results and Discussion Two participants were excluded from the analysis because they made too many errors (more than 2 standard deviations above the
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mean of errors). We only took into account blocks in which the control phase was responded correctly and only correct go/no-go trials with RTs larger than 250 ms. We discarded only two data points with this RT cutoff. It took, on average, 10.82 blocks {SD = 1.04) before all 10 blocks (for both conditions: odd-left/even-right and odd-right/even-left) were correctly performed. During the parity judgment task, average RT was 844.28 ms {SD = 113.66 ms) and the average number of errors was 7.85% (SD = 8.14%). A main effect of ordinal position, F(4, 104) = 18.06, p < .001, Ti^ = .41, was observed. Average RTs per position increased gradually (810, 827, 858, 854, and 876 ms for each position, respectively). A polynomial contrast confirmed the linear trend of these RTs, F(l, 26) = 57.63, p < .001,115 = -69, suggesting a serial search strategy. No other main effects reached significance. Replicating the ordinal position effect, a significant interaction was observed between ordinal position and response side, F(4, 104) = 6.75, p < .001, TIJ = .21, indicating that early positions in the memorized sequence were responded to faster with the left hand (Positions 1 and 2 together: 808.18 ms with the left hand and 829.34 ms with the right hand), whereas later positions were responded to faster with the right hand (Positions 4 and 5 together: 876.38 ms with the left hand and 854.38 ms with the right hand). The interaction between numerical magnitude and response side (e.g., the SNARC effect) was not significant, F(l, 26) = 1.87, p = .18, Tip = .07. The triple interaction between numerical magnitude, ordinal position, and response side was not significant, F(4, 104) = 1.06, p = .38, y]l = .04. In a final step, we reanalyzed the data using a regression analysis. The dRTs deceased 18.09 ms per position, t(26) = -3.63, p < .005 (see Figure lA). This was not the case for the SNARC effect, where the slope did not differ from zero, i(26) = -1.58, p = .13 (see Figure IB). Both the ANOVA and the regression analysis reveal the same pattem as in van Dijck and Fias (2011): the presence of an ordinal position effect and the absence of the SNARC effect. Although the experimental design was optimized to have equal sensitivity to detect eitiier the ordinal position effect or the SNARC effect, only the ordinal position effect was observed.
Experiment 2 In Experiment 2, we investigated whether the ordinal position effect and/or the SNARC effect are present when the working memory load added to the classification task did not affect the number-space associations. Earlier work showed that imposing a verbal working memory load during a parity judgment task prevented the activation of spatial components associated with numbers (van Dijck, Gevers, & Fias, 2009), possibly explaining the absence of the SNARC effect in the previous experiment. The SNARC effect in a magnitude comparison task is not eliminated by a verbal working memory load (Herrera et al., 2008; van Dijck et al., 2009). Therefore, changing the parity judgment task into a magnitude comparison task could result in both a SNARC effect and an ordinal position effect. If, however, the absence of the SNARC effect was due to the presence of the ordinal position effect, again, no SNARC effect is expected.
GINSBURG, VAN DUCK, PREVITALI, FL\S, AND GEVERS
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Figure 1. Observed data and regression line of Experiment 1, representing reaction time differences (dRT) between right- and left-hand responses as a function of their position in the working memory sequence (A) and as a function of the numerical magnitude for numbers inside working memory (B). Positive values reflect faster left than right responses. SNARC effect = spatial numerical associations of response codes effect.
Method Participants. In total, 36 paid volunteers (M = 20.44 years, SD = 2.78; 28 women [all right-handed] and eight men [one left-handed]) participated in this experiment. All participants were undergraduate students recruited via an announcement on Facebook and assigned randomly to one of the four experiments. They received €8 as compensation for their participation. The ethical committee approved this study and participants were debriefed after completing a single 40-min session. All participants were naive with respect to the purpose of the experiment. Stimuli and procedure. In Experiment 2, we used exactly the same stimuli and the same procedure as in Experiment 1 with the exception that during the classification phase, participants performed a magnitude comparison task instead of a parity judgment task. Participants had to indicate whether the presented target number was small (range: 1 - 5) or large (range: 6 - 10). As such, there was no central referent to which the presented numbers had to be compared, as is the case in a regular magnitude comparison task with numbers ranging from 1 to 9 (e.g., "Is the number smaller or larger than 5?"; Gevers, Verguts, Reynvoet, Caessens, & Eias, 2006). This slightly adapted design was chosen to make the design as similar as possible to the parity judgment task of Experiment I. Another reason is that if we want working memory position and numerical magnitude to be fully orthogonal, sequences of 10 numbers are needed when participants have to maintain sequences of five numbers and every number has to be presented in each working memory position an equal amount of times. Each participant performed two conditions. In the first, they had to press the left button for smaller numbers and the right button for larger numbers. In the second, they performed the opposite mapping. The order of conditions was counterbalanced across participants.
Results and Discussion Two participants were removed from the analysis. One of them made too many errors (more than 2 standard deviations above the mean of the errors) and one other responded too slowly (more than 2 standard deviations above the mean of the RTs). As in Experiment 1, we took into account only blocks with correct control phase and correct go/no-go trials with RTs above 250 ms. We discarded only three data points with this RT cutoff. It took, on average, 11.25 blocks (SD = 1.75) before all 10 blocks (for both
conditions: odd-left/even-right and odd-right/even-left) were correctly performed. During the magnitude comparison task, average RT was 748.14 ms (SD = 108.04 ms) and the average number of errors was 6.93% (SD = 4.48%). A sharp drop in performance was observed for the numbers 5 and 6 compared with other numbers: in terms of RTs (804.41 ms vs. 734.67 ms) and in terms of errors (11.2% vs. 5.3%). Apparently, classifying the numbers 5 and 6 as small or large is particularly difficult because these numbers lie at the boundary of small and large categorizations. For this reason, we decided to remove these numbers from the ANOVA. Note that a separate analysis with the numbers 5 and 6 included resulted in exactly the same pattern of results. As in Experiment 1, the repeated-measures ANOVA with ordinal position, numerical magnitude, and response side showed a main effect of ordinal position, f(4, 132) = 10.28,/) < .001, -q^ = .24. Average RTs per position were 703, 720, 742, 757, and 762 ms. A linear trend of these RTs, F(l, 33) = 45.13,p < .001, TI^ = .58, was highlighted by a polynomial contrast, again suggesting a serial search strategy. An ordinal position effect was observed, indicated by a significant interaction between ordinal position and response side, F(4, 132) = 5.45, p < .001, •(]j = .14. This analysis confirmed that numbers at the beginning of the sequence were responded to faster with the left hand (Positions 1 and 2 together: 714.19 ms with the left hand and 732.75 ms with the right hand), whereas the reversed pattern was observed for numbers at the end ofthe sequence (Positions 4 and 5 together: 783.96 ms with the left hand and 761.59 ms with the right hand). No SNARC effect was observed: Numerical magnitude and response side did not interact (p = .63). Because this experiment involves a magnitude comparison task, we are able to analyze the presence of the distance effect (Moyer & Landauer, 1967). This effect reflects the finding that RTs speed up when the numerical distance between the numbers increases (e.g., it is easier to indicate that 1 < 4 than 3 < 4). In this case, however, the distance effect we refer to is slightly different because it refers to the ease with which a number is categorized as being small or large. A significant distance effect was observed with slower responses for numbers close to the middle of the range (752.31 ms) than for numbers far from the middle of the range (716.45 ms), F(l, 33) = 34.59, p < .001. The results of the regression analysis were in accord with the ANOVA. The ordinal position effect is significantly present,
VERBAL WORKING MEMORY AND NUMBER-SPACE ASSOCIATIONS
dRT = -15.61 ms, i(33) = -3.9, p < .005 (see Figure 2A), and the slope reflecting the SNARC effect was not different from zero, i(33) = -0.69, p = .50 (see Figure 2B). In sum, a similar pattern of results was found as in Experiment 1 (i.e., the presence of an ordinal position effect and the absence of a SNARC effect), meaning that this pattern is observed irrespective of whether the classification task and the memory task use the same resources. Furthermore, a distance effect was observed, suggesting that participants effectively accessed magnitude information during the classification task.
Experiment 3 In Experiments 1 and 2, an association was observed between lateralized responses and ordinal position in working memory. At the same time, no association between magnitude and response side was observed. In the next experiments, we attempt to further specifying the nature of the memory processes involved. In this third experiment, we investigated whether memorized items need to be actively retrieved or whether encoding is sufficient to obtain the ordinal position effect. For this purpose, we removed the go/no-go component from the classification task and asked the participants to respond to all items. If encoding is sufficient, the ordinal position effect should be obtained when participants respond to all numbers during the classification task. If retrieval from working memory is required, no ordinal position effect is expected.
Method Participants. In total, 21 paid volunteers (M = 21.9 years, SD = 2.81; 17 women [all right-handed] and four men [all righthanded]) participated. All participants were undergraduate students recruited via an announcement on Facebook and assigned randomly to one of the four experiments. They received €8 as compensation for their participation. The ethical committee approved this study and participants were debriefed after completing a single 40-min session. All participants were naive with respect to the purpose of the experiment. Stimuli and procedure. Experiment 3 used exactly the same stimuli and followed the same procedure as Experiment 2 except
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that during the classification phase, the go/no-go procedure was dropped such that participants had to perform a magnitude comparison task on every presented number. In doing so, even when participants respond to numbers belonging to the memorized sequence (e.g., if the number 3 is part of the sequence, it still requires a response during the classification task), they do not need to retrieve it (because presence inside working memory is no longer decisive to initiate a response). Responses are collected for numbers both inside and outside the memorized sequence, allowing us to test the presence and compare the size of the SNARC effect both inside and outside the memorized sequence.
Results Three participants were removed from the analysis: One made too many errors (more than 2 standard deviations above the mean of the errors) and the two others responded too slowly (more than 2 standard deviations above the mean of the RTs). It took, on average, 10.34 blocks (SD = 0.53) before all 10 blocks (for both conditions: odd-left/even-right and odd-right/even-left) were correctly performed. During the magnitude comparison task, for the items inside the memorized sequence, RT was 498.99 ms (SD = 62.85 ms) and the average number of errors was 4.52% (SD = 3.15%). For the items outside the memorized sequence, RT was 493.97 ms (SD = 57.42 ms) and the average number of errors was 5.59% (SD = 3.94%). For the same reasons as in the previous expedment, analyses were performed on all numbers except the numbers 5 and 6. Again, as in the previous experiment, separate analyses on the entire range of numbers showed the same results. The repeated-measures ANOVA with ordinal position, numerical magnitude, and response side as within-subjects factors showed an interaction between numerical magnitude and response, indicating the presence of a SNARC effect, F(l, 17) = 18.84, p < .001, Tip = .53. In fact, participants responded faster to small digits with the left-hand side (mean RT = 469.57 ms, SD = 15.77) than with the right-hand side (mean RT = 489.86 ms, SD = 16.76). Further, they responded faster to large digits with the right-hand side (mean RT = 459.95 ms, SD = U.I4) than with the left-hand side (mean RT = 502.78 ms, SD = 14.82). No ordinal position effect was observed (p = .66). We conducted a separate analysis for numbers that were responded to but that were not part of the
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Figure 2. Observed data and regression line of Experiment 2, representing reaction time differences (dRT) between right- and left-hand responses as a function of their position in the working memory sequence (A) and as a function of the numerical magnitude for numbers inside working memory (B). Positive values reflect faster left than right responses. SNARC effect = spatial numerical associations of response codes effect.
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GINSBURG, VAN DIJCK. PREVITALI, FIAS, AND GEVERS
memorized sequence. Also, for these targets, a significant SNARC effect was present, F(\, 17) = 10.67, p < .01,% = .39. A direct comparison for numbers inside and outside the memory sequence showed no difference in the size of SNARC (p = .23). The regression analysis confirmed the presence of the SNARC effect, dRT = -11.32 ms, i(17) = -4.02, p < .005 (see Figure 3B). This effect is observed for numbers both inside, dRT = -12.87 ms, i(17) = -4.38, p < .005 (see Figure 3C), and outside, dRT = -9.57 ms, /(17) = -3.09, p < .01 (see Figure 3D), the working memory sequence. The slopes of these regressions were not significantly different from each other, r(17) = -1.25,p = .23, and were strongly correlated (r = .69, p = .002). Participants with a strong SNARC effect inside the memorized sequence also had a strong SNARC effect for targets outside the memorized sequence. Confirming the results of the repeatedmeasures ANOVA, no evidence was found for the ordinal position effect, i(17) = 0.61, p = .552 (see Figure 3A). In agreement with the idea that the items in working memory were encoded but not retrieved during the classification task, no serial position effect was observed, i(17) = 0.984, p = .34. Finally, a distance effect was observed for both numbers inside, F(l, 17) = 8.81,/) < .01, •ï\l = .34, and outside, F(l, 17) = 28.11, p < .001, -^j = .62, the memorized sequence. The size of the distance effect was not different for numbers inside and outside the memorized sequence (p = .82). In sum, for the magnitude comparison task, when information in working memory is encoded but not retrieved, the ordinal position effect is not observed while at the same time a SNARC effect is present.
Experiment 4 The aim of the Experiment 4 is to validate, within the same experiment, the findings of the previous experiments and to integrate them with the existing literature. The go/no-go procedure used in Experiments 1 and 2 forced participants to retrieve the information maintained in working memory during the classification. Retrieval was not needed in Experiment 3, in which participants classified the magnitude of all numbers. An ordinal position effect was observed only when retrieval was required during the classification task. A SNARC effect was observed only when retrieval was not needed. Like in Experiment 3, in Experiment 4, participants again have to respond to all numbers (no retrieval required), but this time numbers have to be classified according to their parity. Validating the crucial role of retrieval for the ordinal position effect and its infiuence on the SNARC effect, we expect to observe a SNARC effect but no ordinal position effect. Besides this, the use of the parity judgment task makes it possible to investigate a final outstanding question: Is the maintenance of a numerical sequence involved in the creation of spatial associations between these numbers and lateralized responses? In Experiment 3, it seemed that the maintenance of information had no influence on the SNARC effect. Indeed, a SNARC effect was observed for numbers both inside and outside the memorized sequence. However, in a magnitude comparison task, it has been demonstrated that a verbal load has no infiuence on the SNARC effect (Herrera et al., 2008; van Dijck et al., 2009). A verbal load
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