Interaction between numbers and size during visual search

Abstract

The current study investigates an interaction between numbers and physical size (i.e. size congruity) in visual search. In three experiments, participants had to detect a physically large (or small) target item amongst physically small (or large) distractors in a search task comprising single- digit numbers. The relative numerical size of the digits was varied, such that the target item was either among the numerically large or small numbers in the search display and the relation between numerical and physical size was either congruent or incongruent. Perceptual differences of the stimuli were controlled by a condition in which participants had to search for a differently coloured target item with the same physical size and by the usage of LCD-style numbers that were matched in visual similarity by shape transformations. The results of all three experiments consistently revealed that detecting a physically large target item is significantly faster when the numerical size of the target item is large as well (congruent), compared to when it is small (incongruent). This novel finding of a size congruity effect in visual search demonstrates an interaction between numerical and physical size in an experimental setting beyond typically used binary comparison tasks, and provides important new evidence for the notion of shared cognitive codes for numbers and sensorimotor magnitudes. Theoretical consequences for recent models on attention, magnitude representation, and their interactions are discussed.

Full text

ORIGINAL ARTICLE
Interaction between numbers and size during visual search
Florian Krause
1,2,3
•Harold Bekkering
3
•Jay Pratt
4
•Oliver Lindemann
5
Received: 7 December 2015 / Accepted: 8 April 2016 / Published online: 3 May 2016
The Author(s) 2016. This article is published with open access at Springerlink.com
Abstract The current study investigates an interaction
between numbers and physical size (i.e. size congruity) in
visual search. In three experiments, participants had to
detect a physically large (or small) target item among
physically small (or large) distractors in a search task
comprising single-digit numbers. The relative numerical
size of the digits was varied, such that the target item was
either among the numerically large or small numbers in the
search display and the relation between numerical and
physical size was either congruent or incongruent. Per-
ceptual differences of the stimuli were controlled by a
condition in which participants had to search for a differ-
ently coloured target item with the same physical size and
by the usage of LCD-style numbers that were matched in
visual similarity by shape transformations. The results of
all three experiments consistently revealed that detecting a
physically large target item is significantly faster when the
numerical size of the target item is large as well (congru-
ent), compared to when it is small (incongruent). This
novel finding of a size congruity effect in visual search
demonstrates an interaction between numerical and
physical size in an experimental setting beyond typically
used binary comparison tasks, and provides important new
evidence for the notion of shared cognitive codes for
numbers and sensorimotor magnitudes. Theoretical con-
sequences for recent models on attention, magnitude rep-
resentation and their interactions are discussed.
Introduction
In our modern society, dealing with numbers has become an
integral part of our daily life. It is therefore important to
understand how our brains process the numerical informa-
tion that surrounds us. Several authors have recently sug-
gested that the cognitive representation of numbers shares
common codes with representations of size-related infor-
mation from sensorimotor processes (Walsh, 2003,2015;
Andres, Olivier, & Badets, 2008; Lindemann & Fischer,
2015). Evidence supporting this idea of a generalised
magnitude system can be found in a variety of behavioural
studies showing that a magnitude comparison in one
domain is influenced by magnitude information in another,
task-irrelevant domain. For instance, effects of cognitive
interference have been observed between the processing of
numerical size and the perception of physical size (Besner
& Coltheart, 1979; Henik & Tzelgov, 1982), luminance
(Cohen Kadosh & Henik, 2006) as well as perceived
affordances of objects (Badets, Andres, Di Luca, & Pesenti,
2007) or the amount of tactilely stimulated fingers (Krause,
Bekkering, & Lindemann, 2013). In addition, numbers have
been shown to influence motor control, such as the planning
of the finger aperture while grasping (e.g. Lindemann,
Abolafia, Girardi, & Bekkering, 2007; Moretto & di Pel-
legrino, 2008) or the required motor force (Vierck & Kiesel,
2010; Krause, Lindemann, Toni, & Bekkering, 2014).
&Florian Krause
florian.krause@maastrichtuniversity.nl
1
Department of Cognitive Neuroscience, Maastricht
University, Maastricht, The Netherlands
2
Brain Innovation B.V., Research, Maastricht, The
Netherlands
3
Radboud University Nijmegen, Donders Institute for Brain,
Cognition and Behaviour, Nijmegen, The Netherlands
4
Department of Psychology, University of Toronto, Toronto,
Canada
5
Division of Cognitive Science, University of Potsdam,
Potsdam, Germany
123
Psychological Research (2017) 81:664–677
DOI 10.1007/s00426-016-0771-4
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The most often replicated finding suggesting shared
magnitude representations for numbers and visual percep-
tion is the so-called size congruity effect (Henik & Tzel-
gov, 1982). In a typical size congruity study, participants
are presented with two digits that differ in numerical as
well as physical size (e.g. 2 6) and are asked to indicate
which one is physically larger by pressing one of two
buttons. Under these conditions, reaction times are shorter
if the physically larger stimulus is also the numerically
larger one (e.g. 2 6), as compared to the situation in which
the physical and numerical size of the stimuli are incon-
gruent (e.g. 6 2; Besner & Coltheart, 1979; Henik &
Tzelgov, 1982; Pansky & Algom, 1999).
Importantly, at the core of the size congruity paradigm lies
the explicit comparison between two stimuli. Recently,
several authors have argued that the observed apparent
interaction between numerical and physical size relies on
specifics of the experimental set-up of such a binary com-
parison (e.g. Risko, Maloney, & Fugelsang, 2013; Santens &
Verguts, 2011). Risko et al. (2013) reasoned that in the
classical size congruity paradigm with two presented digits,
the physically larger digit automatically captures attention
and is hence processed before the other digit, leading to a
temporal congruity effect: if the first processed digit in a
magnitude comparison task is the numerically larger one,
reaction times are known to be faster than when the first
processed digit is the numerically smaller one (Schwarz &
Stein, 1998). While size congruity effects have also been
reported for a variation on the classical paradigm, in which a
single digit was presented and had to be explicitly compared
to a pre-defined standard (Schwarz & Heinze, 1998; Schwarz
& Ischebeck, 2003), this variation is still based on an explicit
comparison between two entities. Santens and Verguts
(2011) have argued that in such an explicit comparison
between two numbers, where two motor responses can be
given (one corresponding to each number), congruity can be
solely defined relative to the binary comparison at hand: if
one of the numbers is physically larger and also numerically
larger, both the task-relevant physical and the task-irrelevant
numerical magnitude will—due to the instructed mapping of
magnitude and response—activate the same motor response,
leading to a shorter response time than in a situation where
one number is numerically larger but the other one is phys-
ically larger, such that the task-relevant physical and task-
irrelevant numerical magnitude activate opposing motor
responses.
Given these task-specific explanations of size congruity,
the question arises whether an interaction between numer-
ical and physical size can also occur in an experimental
setting beyond binary comparison tasks, where congruity
cannot be defined solely in terms of these specifics. The
demonstration of a size congruity effect in a task that is
experimentally and cognitively different from the previ-
ously used binary comparison tasks would suggest a more
general interaction mechanism and could provide new
evidence for the notion that size-related information from
different domains is represented by a generalised magnitude
system (Walsh, 2003,2015). The present study therefore
investigates whether an interaction of numerical and phys-
ical size in form of a size congruity effect does also emerge
during a visual feature search for a target stimulus among
many simultaneously presented distractor stimuli.
Accumulating evidence for an early impact of number
meaning on visual attention and perception makes a possible
existence of a size congruity effect in visual search plausible.
For instance, Corbett, Oriet and Rensink (2006)demonstrated
that the cognitive system is capable of rapidly extracting
numerical information from briefly presented visual displays
such that the visual comparison of two sets of Arabic digits
could be made more efficiently than the comparison of sets of
letters or meaningless control stimuli. Moreover, effects of
numerical information on visual attention have been reported
by Fischer, Castel, Dodd and Pratt (2003; but see also Ranzini,
Dehaene, Piazza, & Hubbard, 2009; Bonato, Priftis, Marenzi,
& Zorzi, 2009). The authors employed a simple visual
detection task and showed that the mere presentation of digits
has an impact on the likelihood to detect laterally presented
visual targets depending on the numerical size of the digit; that
is, consistent with the spatial arrangement of numbers along a
hypothetical mental number line (Dehaene, Bossini, & Ger-
aux, 1993), small numbers (digits 1 and 2) caused a shift in
visual attention to the left and large numbers (digits 8 and 9) to
the right side of space. This finding shows that the mere per-
ception of Arabic digits results in an activation of analogue
magnitude representations.
Furthermore, Schwarz and Eiselt (2012) recently
demonstrated that the magnitude information of different
simultaneously presented Arabic digits becomes automat-
ically activated and affects the visual search for a target
number in these displays. The authors required their par-
ticipants to find a target digit among distractor digits in
displays in which the average numerical distance between
the target and distractors was systematically varied. Their
analyses of the visual search performance revealed that the
speed and accuracy under these conditions increased lin-
early with the numerical distance. The authors interpret this
as evidence that the automatically activated numerical
representation supports the classification of visual stimuli
as targets and distractors. This indicates that the perception
of arrays of Arabic digits simultaneously activates multiple
magnitude representations associated with different digits
in a display. Interestingly, it has recently been demon-
strated that the impact of numerical information on visual
Psychological Research (2017) 81:664–677 665
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search performance can even be observed if the semantic
and visual similarity between target and distractor items is
varied simultaneously (Godwin, Hout, & Menneer, 2014).
Even though these studies show that multiple numerical
magnitude representations become automatically activated
when searching for a target digit among distractor digits, it
remains unclear at this point whether the numerical rep-
resentations interfere with the processing of size-related
visual stimulus features during visual search.
The current study further investigates the impact of
numerical information on visual search performance and
asks whether the availability of numerical magnitude infor-
mation does selectively affect the processing of physical size
during a feature search. To be precise, we presented a set of
digits and asked participants to find the item that was phys-
ically larger (or smaller) than the other items. The congruity
between physical size and the task-irrelevant numerical size
of the target item was systematically varied. Since the
intention to search for an item of a particular physical size
should lead to more attentional capture of all objects carrying
this feature (e.g. Proulx & Egeth, 2008; Kiss & Eimer, 2011),
it seems plausible to assume that if physical size interacts
with numerical size, a size congruity effect during visual
search should be observed.
Experiment 1
The goal of this experiment was to explore the interaction
between the processing of numerical size and physical size
in a visual search task. In a new paradigm, we presented a
set of 8 or 18 different digits, with the target digit deviating
from the distractor digits in physical size. A size congruity
effect during visual search was expected; that is, the time it
takes to detect a physically large target among physically
smaller distractors should be faster when the task-irrelevant
numerical size of the target is large, and vice versa for
physically small targets.
Method
Participants
Nineteen students of Radboud University Nijmegen (15
females) between 18 and 26 years of age (mean =20.89,
SD =2.21) participated in the study in return of credit
points or 5 Euro. All of them reported to have normal or
corrected-to-normal vision.
Set-up and material
Participants were seated in front of a table with a built-in
horizontally oriented touch-sensitive computer screen and a
custom-made response button (distance between response
button and screen centre: 21 cm). The viewing distance was
approximately 60 cm. Releasing the response button recorded
the detection of a target. The experiment was controlled using
the software Expyriment (Krause & Lindemann, 2014).
All stimuli in the visual search task consisted of the
Arabic digits ‘2’, ‘3’, ‘8’ and ‘9’ printed in grey colour
(photometric luminance: 62.01 cd/m
2
) on a black back-
ground (photometric luminance: 0.75 cd/m
2
) using a sans
serif font type (see Fig. 1for an illustration). Search sets
comprised either 8 (small set size) or 18 (large set size)
items arranged randomly, but equally spaced, in a circle
with a visual angle of 19.85. The distractor digits sub-
tended a vertical visual angle of 0.57and a horizontal
visual angle of 0.38. The target deviated from the dis-
tractors in physical size (larger: vertical visual angle of
0.86, horizontal visual angle of 0.57; smaller: vertical
visual angle of 0.28, horizontal visual angle of 0.19).
Half of the items in each set were instances of one
numerically small digit (‘2’ or ‘3’). The other items com-
prised instances of one numerically large digit (‘8’ or ‘9’).
Two different sets of digits were used (‘2’–‘8’ and ‘3’–’9’).
Procedure
The experiment comprised two different blocks in which
the target item was either defined as being (1) physically
smaller or (2) physically larger, compared to the distrac-
tors. Participants received a verbal as well as written
Fig. 1 Illustration of an incongruent trial in a search set with 18 items
(large search set size). Stimuli in the experiments were presented in
grey colour on a black background
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description of the experiment and were informed before
each block about the next target type.
Each trial started with the presentation of a central fix-
ation cross. After the participants depressed the response
button, a blank screen was presented for a random duration
between 1000 and 2000 ms, followed by the display of the
circular search set. Participants were instructed to search
for the target item. As soon as the target was detected,
participants had to release the response button and point to
the target location. A button release in the first 200 ms was
considered to be an anticipatory response, and a button
release later than 1500 ms was considered to be a too slow
response (based on average search times from previous
pilot data). To ensure that the target was found before
response initiation, all items in the search set were masked
at the moment of response button release.
Design
The order of experimental blocks (physically small target,
physically large target) was counterbalanced across par-
ticipants. Each block comprised 160 trials consisting of all
possible combinations of the two different digit set types
(‘2’–’8’, ‘3’–’9’), the two set sizes (small: 8 items, large:
18 items) and the two relative numerical sizes of the target
(small, large). The order of trials was randomised. The total
duration of the experiment was approximately 20 min.
Results
One participant stopped the experiment prematurely and
was excluded from further statistical analysis. The
remaining participants made few errors and identified the
target incorrectly or responded anticipatorily (i.e. search
times shorter than 200 ms) in less than 1 % of the trials. In
2.90 % of all trials, the target was detected too slowly (i.e.
search times greater than 1500 ms). Incorrect, anticipatory
and slow trials were removed from further response time
analyses.
Average search times, defined as the median duration
between search set onset and response button release, were
calculated for each participant and condition and were
submitted to a 2 9292 analysis of variance (ANOVA)
with the within-subject factors Physical Size of Target
(small, large), Numerical Size of Target (small, large) and
Search Set Size (8 items, 18 items). Figure 2depicts the
mean search times as a function of all three factors. The
ANOVA revealed a main effect of Search Set Size, F(1,
17) =197.09, MSE =2045.85, p\0.001, g
p
2
=0.92 (7
distractors =640 ms; 17 distractors =745 ms), reflecting
the classical phenomenon that targets are detected faster
among fewer distractors (e.g. Sagi & Julesz, 1987). There
was furthermore a significant main effect of Numerical
Size of Target, F(1, 17) =50.17, MSE =831.58,
p\0.001, g
p
2
=0.75. Search times were shorter when the
target item was numerically large (675 ms) compared to
when it was numerically small (709 ms). The interaction
between Physical Size of Target and Search Set Size was
significant as well, F(1, 17) =12.50, MSE =2094.76,
p\0.01, g
p
2
=0.42; that is, the effect of Physical Size of
Target was stronger for search sets with 8 items, F(1,
17) =2.36, MSE =8392.58, p=0.14, g
p
2
=0.12, com-
pared to search sets with 18 items, F(1, 17) =0.61,
MSE =12,739.26, p=0.45, g
p
2
=0.03.
Physically Small
Target
Physically Large
Target
550
600
650
700
750
800
850
8 items 18 items 8 items 18 items
Search Set Size
Mean Search Time (ms)
Numerical Size of Target
Small (’2’ or ’3’)
Large (’8’ or ’9’)
Fig. 2 Mean search times for
each task in Experiment 1.
When searching for the
physically larger target item,
search times were shorter when
the target items was numerically
large as well, compared to when
it was numerically small. Error
bars represent 95 % confidence
intervals for within-subject
designs (Morey, 2008)
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Importantly, in line with our hypothesis, there was a
significant interaction between Physical Size of Target and
Numerical Size of Target, F(1, 17) =24.11, MSE =
2467.95, p\0.001, g
p
2
=0.59. For physically large targets,
search times were significantly shorter, when the target was
numerically large (658 ms), compared to when the target
was numerically small (733 ms), t(17) =6.32, p\0.001,
d=1.49, reflecting a size congruity effect. Interestingly,
the reversed pattern for physically small targets (faster
search times if the target is numerically small as well) was
not statistically reliable (numerically small: 686 ms
numerically large: 693 ms), t(17) =1.00, p=0.33,
d=0.24. No further effects were observed.
It is worth noticing that the data showed no trace of the
well-known association between numerical size and spatial
positions (e.g. Dehaene et al., 1993); that is, an additional
analysis showed no difference between search times for
targets with a horizontal position congruent to its numerical
value (i.e. a numerically small target on the left side or a
numerically large target on the right side; 683 ms) com-
pared to incongruent ones (i.e. a numerically large target on
the left side or a numerically small target on the right side;
677 ms), t(17) =1.31, p=0.21. Looking at lateral posi-
tions only (i.e. distance to centre of the display larger than
50 % of the radius of the circular search array) yielded
comparable results, t(17) =0.67, p=0.51).
Discussion
Consistent with our hypothesis, a congruity effect between
the physical and numerical size of the target was found. The
time it took to detect a physically large target was shorter
when the numerical size of the target was large as well,
compared to when it was small. The visual search size
congruity effect was only present when participants were
searching for a physically large item among physically small
distractors. When the target digit was the physically smallest
item in the search set, no interaction between numerical and
physical magnitudes was observed. Given the design of the
experiment, at least two factors could have led to this dis-
sociation between the effects of the two physical size con-
ditions: (a) the absolute size of the physically small targets
could have been too small and their semantic value could not
be processed, and (b) the stimuli used for the large digits (‘8’
and ‘9’) might be easier to detect in general. To control for
these aspects, a second experiment was conducted.
Experiment 2
To ensure that the absence of a reversed effect when
searching for a physically small target found in the first
experiment was not an artefact of the design, the goal of the
present experiment was to examine the effects of numerical
magnitude on the visual search performance as found in
Experiment 1 with two modifications: (a) the overall
stimulus size was increased by 100 % to ensure legibility,
(b) a control condition was included in which the target
item was indicated by a change in colour, while the
physical size was the same as that of the distractor items.
Moreover, to exclude that the dissociation of effects
observed in Experiment 1 was a result of too low statistical
power, the sample size was increased.
Method
Participants
Thirty students of Radboud University Nijmegen (26
females) between 17 and 27 years of age (mean =19.83,
SD =2.44) participated in the study in return of credit
points or 5 Euro. All of them reported to have normal or
corrected-to-normal vision.
Set-up and material
The stimuli and material used in this experiment were
identical to the ones used in Experiment 1 with minor
modifications. The distractor digits subtended a vertical
visual angle of 1.15and a horizontal visual angle of 0.76.
The target deviated from the distractors in either physically
size (larger: vertical visual angle of 1.72, horizontal visual
angle of 1.15; smaller: vertical visual angle of 0.57,
horizontal visual angle of 0.38). In addition to being
physically larger or smaller than the distractors, the target
item could also be depicted in a light brown colour (pho-
tometric luminance: 54.82 cd/m
2
), but in the same size as
the distractors. Furthermore, pairing each small digit with
each large digit resulted in four different sets of digits (i.e.
‘2’–’8’, ‘2’–’9’, ‘3’–’9’, ‘3’–’8’).
Procedure and design
Each block comprised 160 trials consisting of all possible
combinations of the four different digit set types (‘2’–’8’,
‘2’–’9’, ‘3’–’9’, ‘3’–’8’), the two set sizes (small: 8 items,
large: 18 items) and the two relative numerical sizes of the
target (small, large). The order of trials was randomised.
The total duration of the experiment was approximately
30 min.
Results
Trials with incorrect (\1 %), anticipatory (\1 %) and slow
responses (2.51 %) were removed from the response time
analyses.
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Average search times, defined as the median duration
between search set onset and response button release, were
calculated for each participant and condition and were
submitted to a 3 9292 ANOVA with the within-subject
factors Physical Size of Target (small, large, same),
Numerical Size of Target (small, large) and Search Set Size
(8 items, 18 items). Figure 3depicts the mean search times
as a function of all three factors. The ANOVA revealed a
main effect of Search Set Size, F(1, 29) =263.07,
MSE =3661.57, p\0.001, g
p
2
=0.90 (7 distrac-
tors =606 ms; 17 distractors =709 ms), reflecting that
targets are detected faster among fewer distractors. There
was also a significant main effect of Physical Size of
Target, F(2, 58) =9.02, MSE =18,551.91, p\0.001,
g
p
2
=0.24. Search times were faster for physically small
targets (621 ms) compared to both physically large targets
(655 ms), t(29) =-2.66, p\0.05, d=0.49, and
coloured targets of the same size (696 ms), t(29) =-3.90,
p\0.01, d=0.71. Furthermore, the effect of Numerical
Size of Target reached significance, F(1, 29) =57.96,
MSE =1807.05, p\0.001, g
p
2
=0.67, with numerically
large targets (640 ms) being detected faster than numeri-
cally small targets (674 ms). There was also a significant
interaction between Numerical Size of Target and Search
Set Size, F(1, 29) =13.00, MSE =1396.15, p\0.01,
g
p
2
=0.31; that is, the effect of Numerical Size of Target
was stronger for search sets with 18 items, F(1,
29) =47.03, MSE =2234.08, p\0.001, g
p
2
=0.62,
compared to search sets with 8 items, F(1, 29) =18.41,
MSE =969.12, p\0.001, g
p
2
=0.39.
Crucially, consistent with our earlier results, there was a
significant interaction between Physical Size of Target and
Numerical Size of Target, F(2, 58) =40.06,
MSE =2158.07, p\0.001, g
p
2
=0.58. For physically
large targets, search times were significantly shorter, when
the target was numerically large (608 ms), compared to
when the target was numerically small (703 ms),
t(29) =10.75, p\0.001, d=1.96, reflecting a size con-
gruity effect. Once again, the reversed pattern for physi-
cally small targets (faster search times if the target is
numerically small as well) was not statistically reliable
(numerically small: 619 ms numerically large: 623 ms),
|t(29)| \1. There was no effect of numerical size for tar-
gets with unchanged physical size (numerically small:
701 ms; numerically large: 690 ms), t(29) =1.40,
p=0.17, indicating that the size congruity effect is not
due to generally faster search times for numerically large
targets. Furthermore, there was a significant three-way
interaction between Physical Size of Target, Numerical
Size of Target and Search Set Size, F(2,58) =8.02,
MSE =1197.66, p\0.01, g
p
2
=0.22, reflecting that the
interaction between physical and numerical size of the
target was larger in search sets with 18 items, F(2,
58) =33.54, MSE =2288.97, p\0.001, g
p
2
=0.54,
compared to search sets with 8 items, F(2, 58) =18.08,
MSE =1066.76, p\0.001, g
p
2
=0.38. Finally, no con-
gruency effect between the numerical size of the target and
its horizontal position was observed in the overall search
times (mean congruent =635 ms; mean incongru-
ent =632 ms), t(29) =0.53, p=0.60 (lateral positions
only: t(29) =0.44, p=0.66). No further effects were
observed.
To obtain a clearer picture of the non-significant size
congruity effect for the physically small target, congruent
Physically Small
Target
Physically Large
Target
Coloured Target
(Same Size)
550
600
650
700
750
800
850
8 items 18 items 8 items 18 items 8 items 18 items
Search Set Size
Mean Search Time (ms)
Numerical Size of Target
Small (’2’ or ’3’)
Large (’8’ or ’9’)
Fig. 3 Mean search times for
each task in Experiment 2. With
a doubled stimulus size, the
addition of a control condition,
and a larger sample size, the
findings of Experiment 1 were
replicated. Error bars represent
95 % confidence intervals for
within-subject designs (Morey,
2008)
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and incongruent trials of each participant were divided into
six equally sized bins, with the first bin containing the
shortest and the last bin containing the slowest search
times. Then, a 6 92 repeated-measures ANOVA with the
within-subject factors Time Bin (1, 2, 3, 4, 5, 6) and
Congruency (congruent, incongruent) was performed.
Besides a main effect of Time Bin, F(1.233,
35.745) =306.17, MSE =21,524.67, p\0.001,
g
p
2
=0.91, the ANOVA revealed a significant interaction
effect between Time Bin and Congruency, F(2.068,
59.986) =3.71, MSE =2191.74, p\0.05, g
p
2
=0.11,
showing a difference in congruency effects across the time
bins. A post hoc paired-samples ttest (one-tailed) on
congruency in the last time bin indicated a size congruity
effect, t(29) =1.91, p\0.05, d=0.35; that is, for long
search times, finding the physically small target was sig-
nificantly faster when the target was numerically small as
well. Notably, when applying the same analysis to the
control condition in which a differently coloured target of
the same physical size had to be searched for, no significant
interaction between Time Bin and Congruency was
observed, F(2.33, 67.55) =10.8, MSE =2108.5,
p=0.35.
Discussion
Experiment 2 replicated the results from the previous
experiment using larger stimuli and an additional control
condition. A congruity effect between the physical and
numerical size of the target was again observed when
searching for a physically large target. In the control con-
dition where the target was differently coloured, but of
equal physical size as the distractors, the target’s numerical
value had no influence on search times. This is of particular
importance, as it controls for general effects induced by
perceptual differences between the stimuli, which were
implicated by the significant main effect of numerical size.
As in the first experiment, no congruency effect was
observed when searching for a physically small target.
Notably, the physical size of all stimuli has been doubled in
the current experiment, compared to the previous one.
Moreover, the statistical power of Experiment 2 has been
increased substantially.
Obtaining the same pattern of results under these con-
ditions suggests that it was not the absolute size of the
target item in Experiment 1 that led to the observed
asymmetry of the size congruity effect during visual search
between the two physical size conditions. Interestingly,
when searching for a physically small target, a congruity
effect was present in the slowest search times, indicating a
delayed interaction between numerical and physical size in
this condition. Taken together, the results seem to imply a
more general impaired semantic processing of physically
small target items in the presence of relatively larger dis-
tractors (see also ‘General discussion’). Future research
with a focus on this issue is needed to detail the specifics of
this phenomenon.
More crucial for the current study, however, there might
still be an alternative explanation for the size congruity
effect observed in both experiments when searching for the
physically large target. While the colour condition in
Experiment 2 successfully controlled for a general facili-
tated processing of numerically large targets, it needs fur-
thermore to be excluded that the observed effect is a result
of local perceptual properties of the stimuli ‘8’ and ‘9’ (cf.
Wong & Szu
¨cs, 2013), whose relevance in a feature search
might scale with the physical size the stimuli are presented
in. Such a difference in local perceptual properties com-
pared to the other stimuli could theoretically explain a
facilitation of detecting the numerically large stimuli when
searching for the physically large target, while not finding
the same facilitation for those stimuli in the other two
conditions. To control for this potential confound, a third
experiment was conducted.
Experiment 3
To further control for the possible confound that the size
congruity effect observed in Experiments 1 and 2 is merely
a result of differences in local perceptual stimulus prop-
erties which get enhanced when the stimulus is enlarged,
rather than being due to an interaction between the physical
and numerical size of the target, an additional experiment
aimed to replicate the finding of a size congruity effect in
visual search using two different sets of LCD-style digits
(as known from digital alarm clocks and watches).
Importantly, the visual characteristics of LCD-style digits
made it possible to construct stimulus sets in such a way
that, while the semantic distance of the numerical values
was systematically varied, they ensured minimal deviations
of visual features between the physical symbols, by
applying shape transformations (i.e. 180-degree rotation of
a ‘6’ results in a ‘9’ and vertically mirroring a ‘2’ results in
a ‘5’; see also Sobel, Puri, & Hogan, 2015). If the size
congruity effect in visual search is indeed the result of an
interaction between the physical and numerical size of the
target, two predictions can be made: first, the size congruity
effect in visual search should be replicated for LCD-style
numbers and second, since semantic distance between
numbers is known to affect a numerical size comparison
between them, by varying the amount of representational
overlap between the numbers (Moyer & Landauer, 1967;
Dehaene, Dupoux, & Mehler, 1990), a congruity effect
between numerical and physical size should be modulated
by the semantic distance of the two different numerical
670 Psychological Research (2017) 81:664–677
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sizes in the search array; that is, a larger size congruity
effect should be observed for the stimulus set with the
larger semantic distance between the two numerical sizes,
due to the smaller amount of representational overlap.
Importantly, participants only had to search for large tar-
gets and this change of the procedure implies that the
congruity effect is not to be found in an interaction between
Physical Size and Numerical Size, as in the preceding
experiments, but instead is manifested in a main effect of
Numerical Size.
Method
Participants
Twenty students of Radboud University Nijmegen (18
female) between 17 and 25 years of age (mean =20.45,
SD =2.14) participated in the study. All of them had
normal or corrected-to-normal vision. Participants received
credit points or 5 Euro for their participation.
Set-up and material
The experimental set-up and material were identical to
Experiment 2; merely the stimuli were modified. First,
stimulus sets consisted of grey LCD digits (visual angle:
horizontal =0.57or 0.86, vertical =1.15or 1.72;
photometric luminance: 62.01 cd/m
2
). Second, the number
stimuli were matched for maximal physical similarity, such
that one set of numbers consisted of either a vertically
mirrored or a by 180rotated version of the symbols from
the other set (see Sobel et al., 2015, for a previous appli-
cation of this approach). The semantically distant set
consisted of digits ‘2’ and ‘9’ and the semantically close set
consisted of digits ‘5’ and ‘6’. See Fig. 4for an illustration
of the physical similarity matching.
Procedure and design
The procedure was the same as in Experiment 2, with the
exception that displays with a physically small target were
not realised and the only task was to search for the
physically large item in each display. The experimental
design consisted of one block, comprising 256 trials con-
sisting of all possible combinations of the two different
stimulus sets (semantically distant: ‘2’–’9’, semantically
close: ‘5’–’6’), the two set sizes (small: 8 items, large: 18
items) and the two relative numerical sizes of the target
(small, large). The order of trials was randomised. The
total duration of the experiment was approximately
20 min.
Results
Participants made erroneous responses (identifying an
incorrect item to be the target) or responded faster than
200 ms in less than 1 % of all trials. Too slow detection of
the target (i.e. search times larger 1500 ms) occurred in
6.35 %. These trials were removed from further response
time analyses.
A29292 ANOVA on the median search times with
the within-subject factors Semantic Distance (distant,
close), Numerical Size of Target (small, large) and Search
Set Size (8, 18 items) was conducted. Figure 5depicts the
mean search times as a function of all three factors. As in the
first two experiments, the analysis revealed an effect of the
factor Search Set Size, F(1, 19) =83.88, MSE =3174.98,
p\0.001, g
p
2
=0.82, with faster search times for small
search sets with 8 items than for large search sets with 18
items (663 ms vs. 745 ms), as well as an effect of the factor
Numerical Size of Target, F(1, 19) =51.43,
MSE =2980.49, p\0.001, g
p
2
=0.73, reflecting that
numerically large targets were detected faster than numeri-
cally small targets (673 ms vs. 735 ms). Furthermore, there
was a significant main effect of Semantic Distance, F(1,
19) =4.55, MSE =1583.78, p\0.05, g
p
2
=0.19, reflect-
ing that participants were faster to detect the target when the
digits in the stimulus set were semantically close (697 ms),
compared to when they were semantically distant (712 ms).
Importantly, the effect of Numerical Size of Target was
modulated by Semantic Distance, F(1, 19) =7.43,
MSE =1928.19, p\0.05, g
p
2
=0.28, as predicted by the
notion that search time differences are driven by an inter-
action with semantic information. While numerically large
targets were detected significantly faster than numerically
small targets, this visual search size congruity effect was
larger when the semantic distance between the target and
the distractors was distant (671 ms vs. 752 ms),
t(19) =8.49, p\0.001, d=1.90, compared to a when
the semantic distance was close (676 ms vs. 719 ms),
Fig. 4 Illustration of matching the stimuli in each set in Experiment
3 for local perceptual features. The semantically close set contained
LCD digits ‘5’ and ‘6’, while the semantically distant set contained
LCD digits ‘2’ and ‘9’. Importantly, ‘2’ is identical to a vertically
mirrored ‘5’ and ‘9’ is identical to a by 180rotated ‘6’
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t(19) =3.46, p\0.01, d=0.77. No further effects were
observed.
Finally, no congruency effect between the numerical
size of the target and its horizontal position was observed
in the overall search times (mean congruent =680 ms;
mean incongruent =689 ms), t(19) =1.06, p=0.30
(lateral positions only: t(19) =0.77, p=0.45).
Discussion
Experiment 3 replicated the size congruity effect in visual
search for LCD-style numbers: participants were faster to
detect the physically larger target when this target was one
of the numerically large digits. Importantly, this visual
search size congruity effect was modulated by the semantic
distance between the numerical sizes of the presented
items. In other words, the effect was stronger when the
numerical sizes of the target and the distractors were
semantically more distant (cf. Pansky & Algom, 1999 for a
similar modulation in the classical size congruity para-
digm). This modulation reassures us that the observed
congruity effect is actually dependent on the processing of
the numerical size information, rather than a mere facili-
tation of the physically enlarged target stimulus due to
increased saliency.
General discussion
The present study provides the first empirical evidence for
an interaction between physical and numerical size during
visual search; that is, targets with congruent physical and
numerical size were detected faster compared to targets
with an incongruent configuration. Perceptual differences
of the stimuli that might account for the observed differ-
ences in search performance (cf. Wong & Szu
¨cs, 2013)
were controlled by a condition in which the target item was
defined by the colour and not by the size, showing no
difference between the numerical stimuli (Experiments 2),
and by demonstrating a modulation of semantic distance on
the size congruity effect, using different search sets with
LCD-like stimuli that were perceptually matched by mir-
roring and rotation (Experiment 3).
The observation of a size congruity effect during visual
search provides a substantial advancement over previous
number processing research by demonstrating that an
interaction between numerical and physical size can also
occur outside the experimental specifics of classical size
congruity paradigms. To be more precise, classical size
congruity paradigms are centred around an explicit com-
parison task; that is, participants have a binary choice of
which of two presented digits is numerically larger (e.g.
Besner & Coltheart, 1979; Henik & Tzelgov, 1982; Pansky
& Algom, 1999) or whether a single presented digit is
numerically larger than a pre-defined standard (e.g. Sch-
warz & Heinze, 1998; Schwarz & Ischebeck, 2003). Par-
ticipants then indicate their decision by pressing one of two
response buttons, each representing one of the two choice
alternatives. Several authors have argued that the specifics
of this experimental set-up might explain the observed
apparent interaction between numerical and physical size
(e.g. Risko, Maloney, & Fugelsang, 2013; Santens &
Verguts, 2011). For instance, Risko et al. (2013) argued
that in an explicit binary comparison task reaction times
Semantically Close Set
(’5’s & ’6’s)
Semantically Distant Set
(’2’s & ’9’s)
550
600
650
700
750
800
850
8 items 18 items 8 items 18 items
Search Set Size
Mean Search Time (ms)
Numerical Size of Target
Small (’2’ or ’5’)
Large (’6’ or ’9’)
Fig. 5 Mean search times in
Experiment 3. The size
congruity effect in visual search
was larger for the semantically
distant set, compared to the
semantically close set. Error
bars represent 95 % confidence
intervals for within-subject
designs (Morey, 2008)
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are subject to attentional capture effects which lead to a
temporal congruity effect (Schwarz & Stein, 1998), rather
than to a size congruity effect. Furthermore, Santens and
Verguts (2011) pointed out that in a typical size congruity
paradigm, congruity can be defined only relative to the
comparison task at hand: if the right of two presented
stimuli is physically larger and also numerically larger,
both the task-relevant physical and the task-irrelevant
numerical magnitude will activate a ‘right larger’ code,
leading to a faster response than in a situation where only
one magnitude is activating a ‘right larger’ code, while the
other is activating a ‘left larger’ code. Given these task-
specific explanations of the nature of the classical size
congruity effect, a demonstration of a similar interaction
between numerical and physical size in an experimental
paradigm that does not entail an explicit comparison
between two stimuli would indicate that size congruity is
not limited to occur within the experimental constraints of
a binary comparison task. The current study is an instance
of such a demonstration, since the response latencies
revealed a size congruity effect in a visual search task in
which a target item had to be found in a display with many
stimuli. Since the congruity effect in the current study was
measured with the same responses—the release of the start
button once the target had been detected—for both large
and small targets, any explanation relying on response
competition (cf. Santens & Verguts, 2011) cannot account
for the present congruity effect.
Moreover, with the current visual search paradigm we
exclude the presence of a temporal congruity effect (Sch-
warz & Stein, 1998) resulting from attentional capture (cf.
Risko et al., 2013), since temporal congruity applies merely
to situations in which two stimuli (one numerically small
and one numerically large digit) are processed sequentially.
Even if one supposes that items were processed strictly
sequentially and that the target digit in the present para-
digm was always processed first, the account of temporal
congruity requires the additional assumption that partici-
pants stopped their visual search after they have processed
the first distractor. First, this assumption of an early ter-
mination is in conflict with the set size effects found in all
experiments. Second, even if the processing would some-
times be restricted to the target and one distractor, this
distractor was in 43 to 47 % of the cases of the same
numerical size as the target and could not induce any
cognitive interference. We therefore consider this expla-
nation for the observed size congruity effect as very
unlikely.
The present findings are, however, in line with different
recent general proposals which assume that attention and
the coding of magnitude information are two mutually
dependent processes (e.g. Risko et al., 2013; Fischer et al.,
2003). While Fisher et al. (2003) argued that numerical size
has an influence on spatial attention, Risko et al. (2013)
further discuss a possible influence of attention on mag-
nitude judgements. More specifically, they speculated that
if different types of magnitude share a common code
(Walsh, 2003), then ‘bias[ing] attention to one type of
magnitude […] could produce a bias to attend to a similar
dimension of other types of magnitude’ and ‘looking for
larger objects might bias one to attend to large numbers’
(Risko et al., 2013, p. 1146). The present study now pro-
vides the first direct evidence for exactly this notion:
directing attention to the physically larger item during a
visual search seems to produce an unintentional bias to
attend to the numerically large items as well. Importantly,
this was not the case if the visual search was guided by
stimulus features that are not size-related (e.g. colour),
emphasising that the current finding represents an interac-
tion between two sources of magnitude information.
Moreover, magnitude interaction was enlarged when tar-
gets and distractors were numerically more distant, even if
perceptual features were kept constant. Based on earlier
findings which demonstrated that semantic distance
between numbers affects a numerical size comparison
between them (Moyer & Landauer, 1967; Dehaene et al.,
1990), an enlarged congruity effect between numerical and
physical size for the numerically more distant target and
distractor items in the search array indicates that numerical
size is being processed and affects the visual search.
Together, these findings are reassuring us that the search
time differences observed in the two experiments are not
the consequence of an advantage of numerically larger
target digits in visual search, but are indeed a result of an
interaction between number meaning and physical size,
that is, a size congruity effect in visual search. The current
findings are therefore in line with the notion that numerical
information is processed by a generalised magnitude sys-
tem (Walsh, 2003) which originally emerged to serve
perception and action.
While the inclusion of different search set sizes was
initially motivated by gaining more insights over partici-
pants engagement in the experimental task (since larger
search sets should lead to longer search times
1
; Sagi &
Julesz, 1987), the observed interaction of the size congruity
effect with the search set size in Experiment 2 is not in
conflict with the notion of a generalised magnitude system.
Since larger set sizes result in longer search times, the
modulation of the size congruity effect is most parsimo-
niously explained by differences in processing times:
longer processing times should lead to a deeper processing
of the task-irrelevant numerical information and should
1
Especially given the large radius of the circular search array used in
the current study, since this effect is often even more pronounced in
the periphery (Meinecke & Donk, 2002).
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therefore cause a stronger size congruity effect (see Sch-
warz & Ischebeck, 2003). Alternatively, one could argue
that this finding is in line with studies showing that the
amount of items in a display automatically activates
numerical representations (Naparstek & Henik, 2010).
Search set size could therefore be conceived as a third
source of magnitude information in the visual search task,
and it could be speculated that this third magnitude affects
the processing of the two other magnitudes (physical size
and numerical size). Any interaction between set size and
numerical and physical magnitude information might
hence be interpreted as an additional instance of within
magnitude interference (cf. Walsh, 2003). However, the
impact of search set size on the congruity effect as well as
on physical size and numerical size did not manifest itself
as a consistent pattern across the three experiments and we
belief that future experimentation will be needed in order
to better understand the underlying mechanisms.
The finding of a size congruity effect during visual
search shows an impact of numerical size congruity on
early visual attentional processes. As known from several
studies on visual perception, top-down guidance of atten-
tion towards a certain stimulus feature (e.g. physical size)
enhances the visual saliency of objects containing this
feature (e.g. Wolfe, 1994; Proulx & Egeth, 2008; Kiss &
Eimer, 2011). Recent evidence for the notion that numer-
ical information guides visual search comes from Schwarz
and Eiselt (2012), who demonstrated that the performance
to find a target number among distractor digits is system-
atically influenced by the numerical distance between the
target and the distractors. The current data extend this
finding by showing that a visual search for a target that is
solely defined by its physical size is also affected by task-
irrelevant information about numerical size; that is, when
attending to one particular type of physical target size (i.e.
a physically large or a small target), the numerical size of
the same target seems to guide attention as well, with faster
search times if the numerical size matches the current
target’s physical size. The role of non-visual stimulus
features like semantic information in guiding spatial
attention is still controversially discussed (Wolfe &
Horowitz, 2004; Moores, Laiti, & Chelazzi, 2003; Belke,
Humphreys, Watson, Meyer, & Telling, 2008). The present
findings of size congruity in visual search might therefore
additionally contribute to this ongoing debate in visual
attention research by showing that semantic knowledge
about number symbols under some conditions affects the
performance in a visual feature search.
Importantly, in contrast to the vast majority of research
on attentional effects of number processing (e.g. Fischer
et al., 2003; Ranzini et al., 2009; Bonato et al., 2009), the
present study examined the modulations of visual attention
caused by non-spatial number features. It therefore
provides empirical evidence for a number–perception
interaction driven by a congruity between physical and
numerical size of an item during visual search, irrespective
of its spatial location. The additional analyses of spatial
effects revealed that search performance in the present
paradigm was not affected by spatial–numerical associa-
tions (see Hubbard et al., 2005 for a review), that is the
congruency between the horizontal position of a target item
and its numerical value. While earlier research showed that
numerical size can bias attention to spatial positions (Fisher
et al., 2003), the current finding suggests that participants
do not use these spatial–numerical associations (e.g.
Dehaene, 1992) to guide a visual search and that digits of
different physical and numerical size are found equally
well at all spatial positions.
To our surprise, a congruity effect between the physical
and numerical size of the target was only observed when
searching for a physically large target. An explanation for
the lack of a size congruity effect in the small target con-
dition is speculative at this point. One might assume that
this finding reflects an impaired automatic processing of
the target’s semantic meaning if the target digit is dis-
played in a small physical size. This weaker semantic
activation of the number meaning could be due to the
higher perceptual demands to process the detailed visual
pattern of small symbols compared to large symbols.
Alternatively, the impaired semantic processing of physi-
cally small targets might be driven by the fact that the
feature search was performed significantly faster in this
condition, compared to the colour and large target condi-
tion. Searching for the small target was thus perceptually
easier and possibly more bottom-up driven by global visual
stimulus features (e.g. total covered area or changes in
luminance). In both cases, an impaired semantic processing
would result in a delayed interaction between physical and
numerical size. This notion receives empirical support by
our data, since a size congruity effect could be found when
looking only at the trials with the longest search times in
Experiment 2. The replication of the same pattern of results
with the doubled stimulus size (Experiment 2) further
suggests that the impaired semantic processing of smaller
stimuli is not the result of a too small absolute physical
size. Instead, it seems that it was the relative size difference
to the surrounding distractors which resulted in an impaired
semantic processing of the relatively smaller target, pos-
sibly due to stimulus-driven attention to the many larger
stimuli in the set (Proulx, 2010). This more general phe-
nomenon might explain that the semantic information of
targets was not processed to an extent that affected beha-
viour, if all distractor items were of larger size. Further-
more, in the design of the current experiments, the distance
between the centre of each target and the centre of the
distractors was fixed, leading to smaller distractor–target
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distances when the target was physically large, and larger
distractor–target distances when the target was physically
small. The resulting disproportionately in crowding could
have also persistently undermined the congruity effect with
the small targets (cf. Whitney & Levi, 2011). Taken
together, it seems plausible to assume that semantic effects
of number meaning predominately emerge in the present
paradigm if the target is a larger symbol among smaller
distractors. Future research with a specific focus on the
effects of relative size differences between target and dis-
tractors on semantic processing in visual search is needed
to better understand the details of the underlying cognitive
mechanisms.
Eventually, the presented experiments give some new
insights about the origin of behaviourally observed inter-
actions between numerical and physical size (see, e.g.
Schwarz & Heinze, 1998; Cohen Kadosh & Walsh, 2009;
Santens & Verguts, 2011 for this debate). In general, two
opposing accounts have been formulated: The first account
holds that numerical and physical size interact at an early
processing stage at which both stimulus features are coded
into a common analogue magnitude representation (e.g.
Schwarz & Heinze, 1998). Reaction time differences
between congruent and incongruent configurations are
thought to reflect a difference in the cognitive demand to
create a common representation in the case that numerical
and physical size are of different magnitude, compared to
when they convey the same relative size (i.e. both small or
both large). Empirical evidence for an interaction at an
early representational stage comes from electrophysiolog-
ical data, suggesting that the facilitations and interference
in a size congruity task arise quickly with onsets well
before 300 ms (Schwarz & Heinze, 1998; Szu
¨cs & Solte
´sz,
2008).
The second account of the size congruity effect holds,
however, that interference effects do not emerge at the
level of magnitude representation. For instance, Cohen
Kadosh and Walsh (2009) argue for a dual-code model of
magnitude representation in which first, fast automatic
representations are thought to be non-abstract and depen-
dent on the notation or modality, while only later, slower
intentional abstract representations might follow, depend-
ing on task and context. This notion of dual magnitude
codes would not predict an interaction between physical
and numerical size in early perception, because the auto-
matic and unintentional processing of physical and
numerical size is assumed to be initially based on inde-
pendent representations. However, in contradiction to this
prediction, the current study suggests the presence of an
early interference effect as the presence of task-irrelevant
numerical size automatically and unintentionally affected
the detection of a target defined by its physical size. Fur-
thermore, Santens and Verguts (2011) assume that, similar
to Cohen Kadosh and Walsh (2009), different sources of
magnitude information from different domains are repre-
sented entirely separately and interact only at later
response-related stages of processing. The authors pointed
out that the classical size congruity paradigm relies on a
one-to-one mapping between the two choice alternatives
(i.e. ‘left larger’, ‘right larger’) and the two motor
responses (‘left’, ‘right’) and proposed a dual-route model,
assuming a parallel processing of task-relevant and task-
irrelevant stimulus dimensions of the digits that after a
certain time results in a co-activation of both visual and
numerical size information. In congruent trials, both size-
related stimulus features activate the same response code,
while in incongruent trials, the two stimulus dimensions
map onto different response codes, resulting in a conflict at
the level of response selection. This conflict is accompa-
nied by longer response times. Recent evidence for such an
explanation of the size congruity effect, which rejects the
assumption of shared representations of numerical and
physical size, comes from ERP and fMRI studies that
suggest the presence of interference during response
selection (e.g. Cohen Kadosh, Cohen Kadosh, Henik, &
Linden, 2008;Sz
}
ucs & Solte
´sz 2007).
In contrast to a classical size congruity paradigm, the
visual search task used in the present study comprised
several simultaneously presented digits and a single motor
response (releasing the start button) to mark detection.
While the finding of a size congruity effect in the longest
search times only when searching for a physically small
target (see ‘Experiment 2’) could in principle be interpreted
as an indication for a relatively late effect, in our view, it is
unlikely that the numerical and physical dimensions of
each of the up to 18 digits in our experiments pre-activated
up to 18 different motor responses, and hence more plau-
sible that the observed cognitive conflict is not originating
from response-related stages of processing. Notably, all
experiments included an additional pointing response to the
(masked) target position, and it can be argued that partic-
ipants prepared the pointing response not as a second step,
but as part of the initial response of releasing the start
button. An interpretation of the results in terms of a conflict
of pre-activated responses, however, assumes the rather
unlikely parallel pre-activation of 8 (small search set) or
even 18 (large search set) different responses. Furthermore,
opposed to a classical size congruity paradigm, the task-
irrelevant information of numerical size would not pre-
activate one single response of these 8 or 18, but multiple
ones (since half of the digits in the search display were of
large numerical size and the other half was numerically
small). The task-relevant information of physical size, on
the other hand, would pre-activate exactly one response
(since there was only one physically larger digit). This
would lead to contradicting pre-activations in both
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congruent and incongruent situations. Given these sub-
stantial differences between the current visual search task
and the classical size congruity paradigm, it is difficult to
assume that the classical size congruity paradigm consti-
tutes a visual search with only two items (a target and a
distractor). Nevertheless, even if one interprets a classical
size congruity paradigm this way, the current demonstra-
tion of a size congruity effect in a visual search with 8 and
18 items is a substantial extension of former findings, as it
has been suggested that the processes underlying detection
performance in small display sizes (e.g. 2 items close to
each other as in the classical size congruity paradigm)
differ from those underlying detection performance in
larger displays (e.g. 18 items in a larger circular array as in
the current study; see Meinecke & Donk, 2002).
Taken all together, the results of the present study seem to
rather support an interaction between numerical and physi-
cal size on an early than on a late level. Eventually, more
research will be needed to answer this question with suffi-
cient certainty. For instance, an important open question the
current study cannot answer is whether the interaction
between numerical and physical size affects the initial
allocation of attention or the stage of accepting or rejecting
an item as the target in a serial process (see also Moores
et al., 2003; Belke et al., 2008). The new visual search
paradigm presented here, combined with eye-tracking
techniques should stimulate future research in this direction.
Conclusion
The current study is the first to observe an interaction
between numbers and physical size (i.e. size congruity)
during a visual feature search with multiple distractors.
This novel finding demonstrates that interactions between
numerical and physical size can occur beyond the experi-
mental specifics of classically used binary comparison
tasks, and provides important new evidence for the notion
that numbers share cognitive codes with sensorimotor
magnitudes (Walsh, 2003;2015).
Compliance with ethical standards
Conflict of interest The authors declare that they have no conflict
of interest.
Ethical approval All procedures performed in studies involving
human participants were in accordance with the ethical standards of
the institutional and/or national research committee and with the 1964
Helsinki declaration and its later amendments or comparable ethical
standards.
Informed consent Informed consent was obtained from all indi-
vidual participants included in the study.
Open Access This article is distributed under the terms of the
Creative Commons Attribution 4.0 International License (http://crea
tivecommons.org/licenses/by/4.0/), which permits unrestricted use,
distribution, and reproduction in any medium, provided you give
appropriate credit to the original author(s) and the source, provide a
link to the Creative Commons license, and indicate if changes were
made.
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