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Running head: CODING STRATEGIES IN NUMBER SPACE
Coding Strategies in Number Space: Memory Requirements
Influence Spatial-Numerical Associations
Oliver Lindemann
1, 2
, Juan M. Abolafia
1,3
, Jay Pratt
4
& Harold Bekkering
1
1
Nijmegen Institute for Cognition and Information,
University of Nijmegen, The Netherlands
2
School of Behavioral and Cognitive Neuroscience,
University of Groningen, The Netherlands
3
Instituto de Neurociencias de Alicante,
Universidad Miguel Hernández-CSIC, Spain
4
Department of Psychology,
University of Toronto, Canada
Correspondence:
Oliver Lindemann,
Nijmegen Institute for Cognition and Information,
University of Nijmegen,
P.O. Box 9104,
6500 HE Nijmegen,
The Netherlands,
Phone: +31 24 36 12615
E-mail: o.lindemann@nici.ru.nl
Coding Strategies in Number Space 2
ABSTARCT
The tendency to respond faster with the left hand to relatively small numbers
and faster with the right hand to relatively large numbers (SNARC effect) has been
interpreted as an automatic association of spatial and numerical information. We
investigated in two experiments the impact of task-irrelevant memory representations
on this effect. Participants memorized three Arabic digits describing a left-to-right
ascending number sequence (e.g., 3-4-5), a descending sequence (e.g., 5-4-3) or a
disordered sequence (e.g., 5-3-4) and indicated afterwards the parity status of a centrally
presented digit (i.e., 1, 2, 8, or 9) with a left/right keypress response. As indicated by the
reaction times, the SNARC effect in the parity task was mediated by the coding
requirements of the memory tasks. That is, a SNARC effect was only present after
memorizing ascending or disordered number sequences but disappeared after processing
descending sequences. Interestingly, the effects of the second task were only present if
all sequences within one experimental block had the same type of order. Taken together,
our findings are inconsistent with the idea that spatial-numerical associations are the
result of an automatic and obligatory cognitive process but do suggest that coding
strategies might be responsible for the cognitive link between numbers and space.
Coding Strategies in Number Space 3
Research in the field of mathematical cognition has accumulated evidence
indicating that cognitive representations of numerical magnitudes are closely linked
with representations of space. A striking demonstration of this connection is the so
called effect of the spatial numerical association of response codes (SNARC effect),
which reflects the tendency of participants to respond faster with the left hand toward
relatively small numbers and to respond faster with the right hand toward relatively
large numbers (Dehaene, Bossini, & Giraux, 1993). This interaction between number
size and spatial response features has been consistently interpreted as evidence that
numerical magnitude information is spatially coded and associated with a mental
continuum (“mental number line”) on which numbers are consecutively arranged in an
ascending order from the left side to the right (for recent reviews see, e.g., Hubbard,
Piazza, Pinel, & Dehaene, 2005; Fias & Fischer, 2005).
Several authors have proposed that the spatial representation of numbers along
the mental number line can be described as an automatic and obligatory process. In this
context, automatic coding of numerical magnitude is understood as a process that occurs
without the intentional setting of the goal of the behaviour and does not require any
conscious monitoring (see, e.g., Ganor-Stern, Tzelgov, & Ellenbogen, 2007). The idea
of an automatic coding of numerical magnitude is supported by the findings showing
that number magnitude effects on lateralized motor responses emerge even when the
processing of a presented numeral is not required and irrelevant for solving the task
(Fias, Lauwereyns & Lammertyn, 2001; Gevers, Lammertyn, Notebaert, Verguts, &
Fias, 2006). Fias et al. (2001), for instance, reported a SNARC effect caused by
numerals presented as background stimuli while participants were required to
Coding Strategies in Number Space 4
discriminate the orientation of lines and interpreted that both the activation of number
meaning and the association of magnitude with space are obligatory cognitive
processes. Further support for the idea that merely looking at numbers evokes an
activation of spatial cognitive codes is coming from a study on visual-spatial attention
reported by Fischer, Castel, Dodd, and Pratt (2003). The authors presented Arabic digits
in the centre of the screen while participants preformed a simple detection task and
found a shift in covert attention to the left or right side according to the relative size of
the number. Although the cueing of visuospatial attention by numerals has often been
assessed as important evidence for an automatic activation of the mental number line
(Hubbard et al., 2005; Fias & Fischer, 2005), it is important to notice that attentional
effects of numbers emerge far slower than effects of other symbolic cues with
directional meaning (e.g., the words “left” and “right”; Hommel, Pratt, Colzato, &
Godijn, 2001).
There is also a growing body of evidence suggesting that SNARC effects are
influenced by top-down factors and that the associations between numbers and space
are rather flexible. Since the first report of SNARC effects by Dehaene et al. (1993), it
is known that the same number can be linked with either the left or the right side of
space, depending on whether it is the smallest or the largest in the used range of
numbers. Moreover, it has been shown that the same set of numerals evoke reversed
SNARC effects if numbers are intentionally mapped with locations using a different
spatial frame of reference (Bächthold, Baumüller, & Brugger, 1998; Vuilleumier,
Ortigue, & Brugger, 2004; Ristic, Wright, Kingstone, 2006; Galfano, Rusconi, Umilta,
2006). For example, Bächthold et al. (1998) asked participants to make speeded
responses toward numbers ranging from 1 to 11 and instructed to conceive them either
as distances on a ruler or as hours on an analogue clock face. Participants in the ruler
Coding Strategies in Number Space 5
condition showed a regular SNARC effect. Interestingly, in the clock face condition,
where smaller numbers had to be associated with the right side of space (e.g., 3 o’clock)
and large numbers with the left side (e.g., 9 o’clock), the SNARC effect reversed. This
strong impact of the task instruction on the effects of number reading seems to suggest
that the spatial coding of numerical magnitude can be dynamically adapted according to
current task demands. Further support for the notion that SNARC effects are flexible
and not restricted to a left-to-right oriented continuum can also be derived from the
observation of large interindividual variability in the preferred default mapping of
numbers and space. For example, we know from studies with English, Arabic, and
Japanese participants that the spatial associations with numbers are strongly mediated
by culturally acquired reading or scanning habits (Dehaene et al., 1993; Zebian, 2005;
Ito & Hatta, 2004) as well as by learned finger-counting strategies (Di Luca, Granà,
Semenza, Seron, & Pesenti, 2006). Taken together, there is accumulating evidence that
spatial-numerical associations vary across different situations and across different
groups of subjects. Thus, the SNARC effect may depend on the spatial frame of
reference which is intentionally used or required by the task.
In the same vein, Fischer (2006) recently proposed that the spatial representation
of numbers might be the result of an individual’s strategic decision in the light of
current task demands and not the consequence of an automatic activation of the mental
number line. Although there is evidence showing that the selection of a spatial-
numerical reference frame for magnitude representation depends on task demands as
well as on cultural factors, the literature does not provide consistent evidence whether
the activation of spatial codes in number cognition is an automatic obligatory process
or, conversely, whether it is the result of a volitionally controlled cognitive strategy to
deal with magnitude information.
Coding Strategies in Number Space 6
Importantly, a crucial criterion for describing a cognitive process as being
automatic is the absence of any dual task interference (see e.g., Palmeri, 2002).
Consequently, if the association between numbers and space can be described as an
automatic process, the presence of a SNARC effect should not be affected by
requirements of a second unrelated task and should not interfere with spatial-numerical
cognitive codes activated at the same time. To our knowledge, there is no definitive
empirical evidence showing that the SNARC effect is either sensitive, or insensitive, to
interference from an unrelated number task. Given this dearth in the literature, the goal
of the present study was to test whether the spatial representations of numbers in one
task are modulated by the coding requirements of a second simultaneously performed
memory task. If number processing results automatically in an activation of the mental
number line, the presence of the SNARC effect should not be influenced by the
demands of the second task. If the mental number line represents, however, the current
cognitive coding strategy of a person, the SNARC effect should be affected by the
sequential order of an activated memory representation and by an activation of spatial
mnemonic strategies for the second task.
EXPERIMENT 1
Participants were required to judge the parity status of Arabic numerals (parity
task) after they had memorized a short sequence of three digits for later recall (memory
task). The digits were arranged so that they formed a left-to-right ascending number
sequence (e.g., 3-4-5), a descending sequence (e.g., 5-4-3) or a disordered sequence
(e.g., 5-3-4). The type of digit sequence was varied between three experimental blocks.
Assuming that the mapping of numbers onto space is the result of a cognitive coding
strategy (Fischer, 2006), the SNARC effect in the parity task should be affected by the
Coding Strategies in Number Space 7
ordering of the digits in the memory task. Specifically, we expect the SNARC effect to
be diminished or even reversed in the experimental block of descending number
sequences.
Method
Participants
22 students of the Radboud University Nijmegen (2 males; average age: 21.2)
participated in the experiment in return for course credits.
Apparatus and Stimuli
Participants faced three horizontally aligned square outlines, which served as
placeholder boxes for the presentation of the number stimuli. From viewing distance of
about 70 cm, each of these frames measured 3.8° of visual angle. All numbers were
printed in black sans serif fonts on light grey background and subtended a horizontal
visual angle of about 1.3°. Reaction times were measured with using a custom-built
external response box with three horizontally aligned buttons.
Please insert Figure 1 about here
The to-be-memorized number sequences were composed of three consecutive
Arabic digits between 3 and 7. They could be subdivided in three categories: sequences
with a left-to-right ascending order (e.g., 3-4-5), sequences with a left-to-right
descending order (e.g.: 5-4-3), and sequences with no monotone order (no order; e.g.,
5-3-4 or 4-5-3). Only number sequences with no order that did not share any digit
location with the corresponding ascending sequence were selected (i.e., sequences like,
e.g., 3-5-4 or 4-3-5 were excluded). As target stimuli for the parity task, we used a
different set of Arabic digits, namely, the numbers 1, 2, 8, and 9. Thus, half of the target
Coding Strategies in Number Space 8
digits in the parity task were smaller than the digits of the memory task and the other
half of the targets were larger.
Procedure
Figure 1 illustrates the sequence of events in one trial. All trials started with the
presentation of a number sequence, where each digit was displayed in the centre of
another placeholder box. Participants were required to memorize all digits and their
relative locations (left, central, and right location) for later recall. After a presentation
time of 2,500 ms, each digit was replaced by a sharp symbol (‘#’) that remained visible
for 50 ms. 500 ms later, a fixation cross appeared in the central placeholder box and was
replaced after 1000 ms by a single digit. Participants’ task was to indicate as soon as
possible the parity status (odd or even) of this number by means of a left or right hand
keypress response (i.e., pressing the left or right button of the response box). The
assignment of response keys to odd and even digits was balanced across participants.
The digit disappeared after responding or if no response was given after 1000 ms
(missing response). Afterwards, one digit of the previously presented number sequence
was randomly chosen and displayed in each of the three placeholder boxes. Participants
were required to recall the former location of this digit in the sequence and indicate their
answer by pressing the corresponding button of the response box (i.e., left, central, or
right button). There was no time limit for the location recall. The inter-trial-interval was
2000 ms. In the case of an incorrect response in the parity or memory task, a 4400 Hz
beep sound (lasting 200 ms) was presented as acoustic error feedback.
Design
The digit sequence types (ascending order, descending order, and no order) were
systematically varied between three experimental blocks. Thus, for all sequences within
Coding Strategies in Number Space 9
one block the digits were arranged in the same order. Each block comprised 72 trials
presented in random order. They were composed of all possible combinations of the
four target numbers and the digit sequences of this particular experimental block. The
order of blocks was permutated across participants. Before the actual experiment
started, participants performed 38 randomly chosen training trials.
Data analysis
Trials with incorrect parity judgments or incorrect position recalls were
identified and removed from the reaction times (RT) analyses. We calculated the mean
RT and error rate in the parity task for each participant and each possible combination
of the factors Number Magnitude (small: 1 and 2; large: 8 and 9), Response Side (left,
right), and Sequence Type (ascending order, descending order, no order) and analyzed
the data using repeated measures analysis of variance (ANOVA). A one-factorial
ANOVA was performed on the error rates in the position recall task to test for effects of
the sequence type. In all statistical tests reported here, a Type I error rate of
α = .05 was
used.
The SNARC effect in the present paradigm was represented by an interaction
between the factors Number Magnitude and Response Side. In order to obtain in this
type of ANOVA design a standardized estimate of the size of the observed SNARC
effect, we calculated the effect size parameter
2
η
of this interaction and its 95 %
confidences interval CI (see Smithson, 2001).
Since the parameter
2
η
provides an
estimation of the proportion of variance accounted by the effect, it represents a
generalization of the correlation coefficient r
2
. The SNARC effect size
2
SNARC
η
allows
therefore a direct comparison with studies employing regression analyses (e.g., Fias,
Brysbaert, Geypens, & d’Ydewalle, 1996), in which the SNARC effect is quantified by
Coding Strategies in Number Space 10
the correlation of the number magnitudes with the reaction time differences between left
and right hand responses.
Results
The analyses of the error rates in the parity judgment task and the position recall
task (see Table 1 for means) did not reveal any effect of the factor Sequence Type, both
Fs(2, 42)<1. Also none of the other effects in the ANOVA of judgment errors reached
significance, all Fs<1.8.
Please insert Figure 2 and Table 1 about here
The mean RTs in the parity judgment task are depicted in Figure 2. The
ANOVA revealed two significant effects: The two-way interaction between the factors
Number Magnitude and Response Side, F(1, 21)=6.90, MSE=3,475, p<.05, indicated
the presence of an overall SNARC effect across all sequence types. That is, left hand
responses were faster to small digits (523 ms) than to large digits (547 ms), t(21)=2.23,
p<.05. This effect tended to be reversed for right hand response (535 ms vs. 520 ms;
t(21)=-1.67, p=.11). Most importantly, however, the analysis revealed a significant
three-way interaction, F(2, 42)=7.36, MSE=935, p<.01,
2
ˆ
η
=.26, which indicates that
SNARC effects were affect by the factor Sequence Type. None of the main effects
reached significance, all Fs< 1.3.
To explore the pattern of the high-order interaction, we tested the interactions
between Number Magnitude and Response Side separately for each experimental block.
Interestingly, SNARC effects were present in the blocks with Ascending Order,
F(1,21)=25.36, MSE=850, p<.001,
2
ˆ
SNARC
η
=.55 (CI=[.22 .71]), and No Order,
Coding Strategies in Number Space 11
F(1,21)=9.45, MSE=1709, p<.01,
2
ˆ
SNARC
η
=.31 (CI=[.03 .54]), but not the block with
Descending Order, F(1,21)<1,
2
ˆ
SNARC
η
<.001.
Discussion
A SNARC effect was present if participants memorized an ascending number
sequence but vanished completely in the block where the order of descending number
sequences had to be recalled. Since a SNARC effect was also found for sequences of no
monotonic order, we can exclude that the dissociation of the effect was merely the result
of a higher task difficulty in the descending block or a general cognitive effect of the
increased memory load. Moreover, the lack of a SNARC effect did not reflect any
speed-accuracy trade-off because the analysis of error rates in the parity judgment and
position recall task did not reveal any effect of the sequence type. Thus, the results of
Experiment 1 clearly show that the SNARC effect is modulated by the cognitive coding
of short descending number sequences. More specifically, the spatial representations of
numbers in the parity task were affected by the specific spatial coding requirements and
the resulting memory traces of the second task.
Since the manipulation of the sequence type was varied only between the three
experimental blocks, the internal ordering of the digits was known before the trial
started. It is therefore likely that the knowledge about the ordering of the upcoming
sequence has been used to simplify the coding and recall of the number locations. That
is, participants may have used in the block of descending sequences the concept of
right-to-left orientated number line as strategy to code the digit location. This mnemonic
strategy of a reversed number line, however, is in conflict with the spatial-numerical
coding in the parity task and may therefore explain the vanishing of the SNARC effect.
Alternatively, it might be also possible that the mere coding of three digits in a
Coding Strategies in Number Space 12
descending order automatically activates a spatially reversed mental number line and
interferes therefore with the subsequent spatial coding of numbers. In order to
distinguish between these two accounts—automatic activation of opposite number lines
versus selected memory strategy—we performed a second experiment.
EXPERIMENT 2
Experiment 1 has demonstrated that the SNARC effect vanishes if the actual
memory task required a coding of numbers arranged in descending order. Experiment 2
tests whether the same interference can be observed if the type of ordering is
randomized on trial-by-trial basis. If the sequence type is not predictable, participants
cannot use their prior knowledge about the sequence ordering to code the digit
locations. Consequently, we should expect the SNARC effect to be unaffected by the
sequence type in the memory task, if a coding strategy of oriented number lines was
responsible for the inhibition of spatial-numerical associations. If, however, the mere
representation of three numbers in a descending order results automatically in an
activation of a reversed number line, we expect the SNARC effect to be modulated by
the sequence coding as it was the case in Experiment 1.
Method
Participants
22 students of the Radboud University Nijmegen (4 males; average age: 22.2;
participated in Experiment 2 in return for course credits. None of them took part in the
previous experiment.
Coding Strategies in Number Space 13
Apparatus, stimuli, procedure, design and data analysis
The experimental setup, stimuli, procedure and data analysis were identical to
Experiment 1. The only modification was related to the order of trial presentation.
Again, participants ran through three experimental blocks of 72 trials. However, instead
of varying the factor Sequence Type between blocks, all trials were this time fully
randomized. Thus, each experimental block comprised trials with all three types of digit
ordering.
Results
As found before, there were no effects of the Sequence Type in the error rates of
the parity judgment task and position recall task, F(2, 42)<1 and F(2, 42)=1.52,
respectively (see Table 1 for means). The ANOVA of the judgment errors revealed an
interaction between Response Side and Number Magnitude, F(1, 21)=15.15,
MSE=1,464, p<.001,
2
ˆ
η
=.42, reflecting a SNARC effect in the accuracy data. That is,
participants made fewer judgment errors if the parity of small numbers had to be
indicated with the left hand (1.64%) than with the right hand (6.27%), t(21)=-3.06,
p<.01, while this effect reversed for large numbers, (6.64% vs. 1.86%), t(21)=3.59,
p<.01.
The ANOVA of the RT data (see Figure 3 for means) yielded a main effect for
the factor Response Side, F(1,21)=6.27, MSE=2,468, p<.05, indicating that right hand
responses (546 ms) were faster than left hand responses (562 ms). Also the interaction
between the Response Side and Number Magnitude reached significance,
F(1,21)=39.60, MSE=2,791, p<.001. That is, left side responses were faster in response
to small numbers (541 ms) than to large numbers (582 ms), t(21)=5.01, p<.001, while
right side responses were slower to small (567 ms) than to large numbers (526 ms),
Coding Strategies in Number Space 14
t(21)=-4.56, p<.001. Most important, however, the three-way interaction between the
factors Response Side, Number Magnitude and Number Sequence failed to reach
significance, F(2, 30)<1. Since the statistical power
1
was sufficient to detect a three-way
interaction effect as observed in Experiment 1, (1-β)=.80, the analysis indicates that the
SNARC effect was not mediated by the type of number sequence.
Please insert Figure 3 about here
As shown by separate tests for interaction between Number Magnitude and
Response Side, SNARC effect size did not differ for all sequence type conditions:
Ascending Order, F(1, 21)=20.98, MSE=2,172, p<.001,
2
ˆ
snarc
η
=.50 (CI=[.17, .68]),
Descending Order, F(1, 21)=26.27, MSE=801, p<.001,
2
ˆ
snarc
η
=.56 (CI=[.23, .71]) and
No Order, F(1, 21)=22.23, MSE=2,123, p<.001,
2
ˆ
snarc
η
=.51 (CI=[.18, .69]).
Discussion
Experiment 2 revealed that if digit ordering varied randomly, the SNARC effect
was not affected by the coding of number locations between trials and was now also
present when participants memorized digits in a descending order. It can be therefore
concluded that the mere coding of a digit sequence in the memory task was not
sufficient to affect the spatial representation of numbers in the parity task. This argues
against the explanation that the findings in Experiment 1 were the result of an automatic
activation of two oppositely oriented mental number lines. Rather, Experiment 2
suggests that participants were unable to adopt a strong spatial coding strategy for
sequences. Apparently, participants represent the sequences under these circumstances
as three independent numbers without their inner structure and did not activate the
concept of a mental number line. Thus, the results of Experiment 2 support the account
Coding Strategies in Number Space 15
that it was the cognitive strategy in the memory task of Experiment 1 that influenced the
spatial representation of numbers in the parity task.
GENERAL DISCUSSION
The present study demonstrates that the cognitive association of numbers and
space is influenced by current task demands. We observed that the SNARC effect in a
parity task is mediated by the specific sequential order involved in a simultaneously
performed unrelated numerical task. This finding is inconsistent with the assumption of
an automatic obligatory spatial representation of numbers along the mental number line.
Since a SNARC effect was found under dual task conditions when the memorized
number sequences had no internal monotonic order (Experiment 1), as well as when the
number ordering was unpredictable (Experiment 2), the observed interference with the
descending sequences in the first experiment cannot be due to an increased task
difficulty or a higher cognitive load in general. Moreover, this mediation of the SNARC
effect was not due to any sequence-specific speed-accuracy trade-off. We argue
consequently that the specific requirement to maintain a short-term memory
representation of numbers in a descending order was responsible for the lack of spatial-
numerical associations in the parity judgment task.
Interestingly, the SNARC effect was only sensitive to the sequential order of the
memory representations if all number sequences within one experimental block were
identically ordered (Experiment 1), but not if the sequence type was fully randomized
(Experiment 2). This dissociation in the SNARC effect can be explained by the use of
different coding strategies when sequences types were blocked or completely
randomized. That is, if numbers are repetitively arranged in a descending order,
participants seem to use the information about the right-to-left digit ordering to simplify
Coding Strategies in Number Space 16
the processing of the number locations. This activated spatial-numerical frame of
reference, however, is in conflict with the representation of magnitude along a left-to-
right oriented mental number line and seems to result in an absence of spatial-numerical
associations. In other words, we interpret that the use of spatial strategies in the memory
task modulated the spatial coding of numbers for parity judgments. The outcome of the
present study is therefore consistent with the notion that the SNARC effect is driven by
top-down processes and provides direct empirical support for the idea of a strategic
origin of the mental number line (Fischer, 2006).
In contrast to our interpretation that the SNARC effect depends on the
concurrent task requirements, several authors have argued that spatial numerical
associations are driven by an automatic activation of the mental number line. This idea
received so far support from studies showing that numerical magnitude information
activates spatial codes even under conditions in which number processing is irrelevant
for the task performance (Fias et al., 2001; Gevers et al., 2006). However, the notion of
an automatic SNARC effect implies not only that spatial codes are evoked by task
irrelevant magnitude information. It is also important to notice that the assumption of
automaticity entails by definition the presence of an obligatory cognitive process, which
is immune against the influence of any other task concurrently executed (Palmeri,
2002). With the present paradigm, we now provide a direct behavioural test of this
prediction and demonstrate for the first time that SNARC effects are strongly affected
under certain dual task conditions. This outcome clearly argues against the idea that
spatial-numerical associations are the result of an automatic and obligatory cognitive
process.
An interesting aspect of the current data is that the SNARC effect disappeared,
but did not reverse, when descending number sequences were memorized. A reason for
Coding Strategies in Number Space 17
this might be that the two tasks were functionally unrelated and independent from each
other. Apparently, participants do not employ a pre-existing spatial structure that has
been activated for one task to process numbers for another task. Instead, they seem to
refrain from spatial number processing if it is under dual-task conditions in conflict with
concurrently activated and to-be-maintained memory representations. Thus, together
with the finding of a SNARC effect for disordered sequences, which demonstrate the
participants’ preference for a left-to-right mapping of numbers with space, our data
indicate that this highly overlearned spatial coding strategy can be ignored in certain
situations. The lack of a reversed SNARC effect further suggests that the coding of
numbers along a mental continuum oriented differently than the default mental number
line is a more effortful process that will not be performed if it is not required or
beneficial for solving the task (see Bächthold et al., 1998).
Our report that the spatial coding of numbers is affected by the memory
requirements of a second unrelated task substantially extends previous research
demonstrating that the SNARC effect is sensitive to contextual task-related information
(Dehaene at al., 1993) and affected if participants are explicitly instructed to use a
different frame of reference for the spatial mapping of numbers (Bächthold et al., 1998;
Vuilleumier et al., 2004; Ristic et al., 2006; Galfano, et al., 2006). In line with these
studies, we demonstrate that left-to-right orientation of the mental number line is not
obligatory and can be easily adapted or inhibited if the current task requires conceiving
numbers differently. Moreover, our findings demonstrate that the SNARC effect is
modulated by the sequential order of task-irrelevant memory representations and by the
activation of spatial-numerical reference frames in another simultaneously performed
task.
Coding Strategies in Number Space 18
Taken together, the present study provides support for the idea that the spatial
coding of numbers is the result of a cognitive coding strategy of how to deal with
numerical magnitude information.
Coding Strategies in Number Space 19
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Coding Strategies in Number Space 22
AUTHOR NOTES
Correspondence concerning this article should be addressed to Oliver
Lindemann, Nijmegen Institute for Cognition and Information, Radboud University
Nijmegen, P.O. Box 9104, 6500 HE Nijmegen, the Netherlands. E-mail:
o.lindemann@nici.ru.nl
Coding Strategies in Number Space 23
FOOTNOTES
1. The statistical power analysis was based upon the effect size for the three-way
interaction and the correlation between the measures of Experiment 1. The power
calculations were performed using the program G*Power 3 (Faul, Erdfelder, Lang, &
Buchner, 2007).
TABLES
Table 1
Percentages of Errors in Experiment 1 and 2. Error Rates in Parity Judgment Task are Presented as a Function of the Factors Sequence Type,
Response Side, and Number Magnitude. Errors Rates in the Position Recall Task are Presented as a Function for the Factor Sequence Type.
Experiment 1 Experiment 2
Ascending
Order
Descending
Order
No
Order
Ascending
Order
Descending
Order
No
Order
Parity Judgment Task
Left Hand – Small Number
1.28 2.90 1.26 1.83 1.80 1.29
Left Hand – Large Number
1.81 2.55 2.04 7.07 6.86 6.00
Right Hand – Small Number
3.57 1.80 2.27 6.47 5.56 6.80
Right Hand – Large Number
0.52 2.78 1.81 1.91 3.10 0.56
Position Recall Task
1.41 1.18 1.14
3.64 2.46 3.59
FIGURE CAPTIONS
Figure 1: Illustration of the sequence of events in Experiment 1 and 2. (a)
Participants memorized the locations of three digits before (b) judging the parity status
of the centrally presented digit. (c) Each trial ended with a recall of the location of one
of the three digits. See text for detailed descriptions.
Figure 2: Mean reaction times in the parity judgment task of Experiment 1 as a
function of the factors Number Magnitude, Response Side, and Sequence Type.
Figure 3: Mean reaction times in the parity judgment task of Experiment 2 as a
function of the factors Number Magnitude, Response Side, and Sequence Type.
Figure 1
(c)
(b)
(a)
Figure 2
Small Large Small Large Small Large
Number Magnitude
500
510
520
530
540
550
560
Reaction time (msec)
Left Hand
Right Hand
Ascending Order Descending Order
No Order
Figure 3
Small Large Small Large Small Large
Number Magnitude
510
520
530
540
550
560
570
580
590
Reaction time (msec)
Left Hand
Right Hand
Ascending Order Descending Order
No Order
