573316
research-article2015
JCCXXX10.1177/0022022115573316Journal of Cross-Cultural PsychologyGanayim and Ibrahim
Article
Number Processing in Arabic
and Hebrew Bilinguals:
Evidence Supporting the
Compatibility Effect
Journal of Cross-Cultural Psychology
1­–14
© The Author(s) 2015
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DOI: 10.1177/0022022115573316
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Deia Ganayim1 and Raphiq Ibrahim2
Abstract
In the current study, a direct assessment of the effect of presentation language and format on
the compatibility effect of two-digit numbers was made by contrasting performance of Arabic/
Hebrew bilinguals in a digital (Hindi digits/Arabic digits) and verbal numerical comparison task
(Arabic an inverted language: units-decades and Hebrew a non-inverted language: decadesunits). Our data revealed in digital presentation format a regular compatibility effect in Hindi
digits and Arabic digits characterized by lower reaction-time (RT) means for compatible number
pairs than incompatible ones with no difference in the RT means of participants in the two
languages, Arabic language–Hindi digits as a mother tongue and Hebrew language–Arabic digits
as a second language. However, in verbal presentation format, different patterns of compatibility
effect were found in Arabic and Hebrew verbal numbers. In Arabic number words, a regular
compatibility effect was found, while in Hebrew number words, no compatibility effect was
found. This reflects the influence and modulation of the lexical-syntactic structure of the
language in two-digit numbers comparison. Evidently, these differences in the compatibility
effect advocate and strengthen the claim that two-digit numbers comparison is influenced by
the numbers presentation format. Different modes of presentation of two-digit numbers (digital
vs. verbal) can lead to different number comparison styles. The parallel model accounts for
the numerical comparison in digital presentation, while for the verbal numbers presentation, a
revised sequential-syntactic model is preferable.
Keywords
Arabic, Hebrew, number processing, compatibility effect, digital format, verbal format, Hindi,
sequential model, parallel model
The interplay between language and thought is pivotal to the study of human cognition
(Butterworth, Reeve, Reynolds, & Lloyd, 2008; Frank, Everett, Fedorenko, & Gibson, 2008;
Gordon, 2004). Numerical cognition is one of the interesting complex cognitive operations that
involve both verbal and non-verbal skills (Li & Gleitman, 2002). Language-specific processes
1The
Arab Center for Mind, Brain & Behavior, Sakhnin, Israel
of Haifa, Israel
2University
Corresponding Author:
Deia Ganayim, The Arab Center for Mind, Brain & Behavior, P.O. Box 6079, Sakhnin 30810, Israel.
Email: [email protected]
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Journal of Cross-Cultural Psychology 
have already been observed in different domains of numerical cognition such as, for instance,
calculation processes (Brysbaert, Fias, & Noel, 1998), place-value understanding (Miura,
Okamoto, Kim, Steere, & Fayol, 1993), or number comparison (Nuerk, Weger, & Willmes,
2005). However, supplementary data are needed to further understand which conditions influence the type of numerical processing involved with two-digit numbers (Castronovo & Crollen,
2011) as few studies used the Arabic language to study a number processing theory. As the debate
concerning the nature and organization of number mental representations in the cognitive neuropsychology field involves those who claim an abstract semantic system (Caramazza, Hillis,
Rapp, & Romani, 1990) and those who claim specific representations of format or Modality
(Shallice, 1987), the differential linguistic effects in two-digit numbers comparison would be
very informative.
To our knowledge, there is no study that has used Hindi digits, Arabic digits, and Arabic and
Hebrew number words to study this semantic number debate. The goal of this study was to test
Arabic/Hebrew bilinguals to investigate whether the magnitude comparison involves semantic
access or whether they are primarily compared through a non-semantic route, as in number
words. In the current study, we tried also to bring new data by further investigating under which
circumstances different processing styles of two-digit numbers can be found. More particularly,
we further studied how differences at language lexical-syntactic number systems (Arabic vs.
Hebrew) of bilinguals can induce differences in a task as basic as the two-digit numerical
comparison.
In the remaining sections of the “Introduction,” I will describe the compatibility effect. Next,
I will introduce the different models of two-digit number processing. Finally, I will explain how
these models can be tested in the bilingual contexts studied in the current experiment.
Compatibility Effect
The study of numerical magnitude processing and representation has demonstrated the existence
of compatibility effect characterized by faster reaction time (RT) and decreased error rates for
unit-decade compatible number pairs (i.e., separate comparisons of tens and units resulted in
congruent decision biases, for example, 42_57: 4 < 5 and 2 < 7) than unit-decade incompatible
number pairs (i.e., separate comparisons of tens and units yielded incongruent decision biases,
for example, 47_62: 6 > 4 but 2 < 7).
The compatibility effect has been replicated in previous studies (Korvorst & Damian, 2008;
Verguts & De Moor, 2005; Zhang & Wang, 2005), expanded to different numerical tasks: carryover effects (e.g., Deschuyteneer, De Rammelaere, & Fias, 2005; Kong et al., 2005), borrowing
effects in subtraction (e.g., Kong et al., 2005), and effects of decade crossing in a number bisection task (Hoeckner et al., 2008; Nuerk, Geppert, van Herten, & Willmes, 2002; Wood et al.,
2008). Although the compatibility effect has been observed in different languages such as German
(Nuerk, Weger, & Willmes, 2001, 2004), Dutch (Verguts & De Moor, 2005), and English
(Moeller, Fischer, Nuerk, & Willmes, 2009), it was not explored in the Arabic language.
This offers the unique opportunity to use compatibility effect in Arabic language for the first
time as a marker of semantic access in number processing. However, to explain the compatibility
effect of two-digit numbers, numerous models are used, and each model assumes different representations of numbers where the characteristics and nature of these representations depend on the
numerical format.
Models of Two-Digit Number Processing
There are two main assumptions regarding the comparison of two-digit numbers: The first
accounts for a holistic processing based on an analog magnitude represented by distance
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Ganayim and Ibrahim
measures on a holistic mental number line—similar to single-digit numbers (Dehaene, Piazza,
Pinel, & Cohen, 2003). Dehaene (1996) tested the difference between Arabic numerals and verbal numbers in a numerical comparison task by using Event Related Potentials (ERP) and behavioral measures. He proposed that the distance effect results from an abstract semantic magnitude
representation independent of the numbers notational format (Arabic or verbal). The distance
effect is characterized by an inverse relationship between RTs and numerical distance. As the
numerical distance between two numbers increases, the RT for deciding which of the two numbers is larger increases. For instance, the RT to decide which number is larger for the numbers 7
to 9 (numerical distance—2) is longer than the RT for the numbers 3 to 9 (numerical distance—6).
The second assumption argues for decomposed tens and units, representations of two-digit number processing leads to a distance effect independent of display layout and notation format
(Moeller et al., 2009; Nuerk et al., 2001; Nuerk, Kaufmann, Zoppoth, & Willmes, 2004; Nuerk,
Weger, & Willmes, 2002; Nuerk & Willmes, 2005; Ratinckx, Nuerk, van Dijck, & Willmes,
2006; Wood, Nuerk, & Willmes, 2006).
Over the past few years, a few models of decomposed processing have been proposed, but the
nature of this processing (sequential, parallel) is still questionable (Zhang & Wang, 2005).
Poltrock and Schwartz (1984) proposed a sequential decomposition model postulating that comparing two numbers with respect to their magnitude involves comparing the corresponding digits
according to their position within the two numbers (i.e., tens and units). Accordingly, a serial
comparison process comparing the leftmost digit pair is executed until a difference between the
digits is found.
Another group of researchers proposed a parallel decomposition model (Korvorst & Damian,
2008; Liu, Wang, Corbly, Zhang, & Joseph, 2006; Nuerk et al., 2001, 2002, 2004, 2005; Nuerk,
Kaufmann, et al., 2004; Ratinckx et al., 2006; Verguts & De Moor, 2005; Wood et al., 2006;
Zhang & Wang, 2005; Zhou, Chen, Chen, & Dong, 2008). According to this model, decomposed
but parallel processing of tens and units is involved in number comparison (Knops, 2006; Nuerk
& Willmes, 2005). For incompatible trials, an interference of decomposed comparison of tens
and units leading to incongruent response biases causes slower RT. On the contrary, for compatible trials, the decomposed comparison of tens and units leading to congruent decision biases
yields facilitation and faster RT (Knops, 2006; Nuerk & Willmes, 2005).
Thus, although previous research has suggested that decomposed processing exists, it is still
controversial as to what extent and under which conditions it is modulated or even replaced by
holistic processing (Nuerk & Willmes, 2005; Verguts & De Moor, 2005; Zhang & Wang, 2005;
Zhou et al., 2008).
Following this line of research, it is interesting to investigate the differential influences of
language syntactic processes and lexical numerical forms (digital, verbal) on two-digit number
processing. These processes seem to differ in the way they interact with the semantic system of
monolinguals but even more so for bilinguals who may have similar or even different lexicalsyntactic representations in their L1 and L2 (e.g., Arabic/Hebrew).
Bilingualism as an Ideal Context to Study Numerical Cognition
Bilingual people have different lexical/form representations, according to their native (L1) and
second language (L2), to express the same (or highly similar) meaning. An interesting aspect of
numbers is that bilinguals have more than one lexical form (orthographic) representation of the
same magnitude-related meanings, which can be represented by digits (e.g., in Arabic, Hindi
digits: ٠١٢٣٤٥٦٧٨٩; in Hebrew, Arabic digits: 0123456789) as well as number words (e.g., in
Arabic, ٢١=‫واﺣﺪ وﻋﺸﺮون‬ = one-and-twenty; in Hebrew, 21 = ‫עשרים ואחד‬ = twenty-and-one).
Here, a key question is whether the numerical processing of two-digit numbers and number
words in L1 and L2 requires mandatory semantic access or not.
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Journal of Cross-Cultural Psychology 
Early research suggests selective processing of the two languages in bilinguals. This has been
interpreted to suggest that bilinguals can access each language independently without interference from the other language and that only one lexicon can be used at any given time. A variety
of research suggests that number processing changes in accordance with the number lexical format in which the number is presented, either as an input or as a stimulus, as numerical-digital or
a verbal format (Brysbaert et al., 1998; Fias, 2001). Since different two-digit number lexical
modes of presentation can lead to different number comparison styles (Ganor-Stern, Pinhas, &
Tzelgov, 2009; Zhang & Wang, 2005; Zhou et al., 2008), differences in encoding involve differences in the processing of two-digit numbers (Nuerk et al., 2005; Nuerk & Willmes, 2005).
Brysbaert et al. (1998) showed that in addition tasks, the effects change in accordance with the
presentation format across languages, especially in the verbal format.
However, more recent evidence seriously challenges this account. In a recent study, Duyck,
Lagrou, Gevers, and Fias (2008) investigated the importance of the semantic route for the processing of a third representation of magnitude, namely, Roman digits. Using an interference paradigm, they showed that the processing of Roman target digits is influenced by Arabic digit
distractors, both in a naming task and a parity judgment task. Roman digits were processed faster
if the target and distractor were of the same magnitude. If the distractor and target numeral were
of a different magnitude, processing speed slowed down as the numerical distance between target
and distractor increased. This strongly suggests that semantic access is mandatory when naming
Roman digits.
One of the several factors that seem to influence whether a bilingual’s actual performance is
more or less specific with respect to language (Grosjean, 1997) is the bilingual’s relative language fluency. In fact, it is likely that one’s fluency in a language will influence the magnitude of
competition from lexical items in that language both within and between languages (Marian &
Spivey, 2003). Van Hell and Dijkstra (2002) showed that even when multilinguals function in a
native language context and are unaware of the experiment’s multilingual nature, native language
performance can be influenced by a weaker knowledge of second language, provided that fluency in the weaker language is relatively high. These results support the theoretical position that
the multilingual’s processing system is profoundly nonselective with respect to language.
Dewaele (2007) argues that bilingual and multilingual people prefer to use their native language
for mental calculations due to faster encoding and/or response times in the dominant language
(see also, McClain & Shih Huang, 1982). However, the fact that there are multilingual people
who use non-native language for calculation (Dewaele, 2007) demonstrates that the dominance
of a native language decreases with the length of residence in a foreign language speaking country. From this, it logically follows that cross-linguistic effects may arise in both directions, manifesting themselves not only in a non-dominant but also in a dominant target language. Thus, the
effect of bilingualism on number processing is under scrutiny.
The inversion property—reading units first and decades second on two-digit numbers—is one
of the number word features present in many languages, for instance, in Arabic, Danish, Dutch,
German, Malagasy, and Maltese, as well as partly in Czech and Norwegian (Comrie, 2005,
2006). This inversion of units and decades of all two-digit numbers from 21 to 99 affects the
performance in calculative tasks too (Helmreich et al., 2011). Two-digit numbers are complex
symbols and are probably difficult to process as syntactic decomposition (e.g., in inverted language: units-decades order, in non-inverted language: decades-units order) is needed. This syntactic decomposition is of critical importance especially for bilinguals of an inverted language
(e.g., in Arabic, ٢١=‫=واﺣﺪوﻋﺸﺮون‬ one-and-twenty) and a non-inverted language (e.g., in Hebrew,
21 = ‫=עשרים ואחד‬ twenty-and-one).
Previous research has indicated differences in the way bilinguals of Basque and Romance
languages (Italian, Catalan) solved a set of additions. These differences reflect the syntactic
structure of the number words in the specific language (Colomé, Laka, & Sebastián-Gallés,
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Ganayim and Ibrahim
2010). By using the dichotic listening and synchronous or asynchronous presentation of the target numerals’ decade- and unit-digits, Castronovo and Crollen (2011) manipulated the attention
weight of decades and units in two-digit numerals and consequently produced different patterns
of performance. Their results showed that differences in the encoding stage of two-digit numerals
involve (a) different comparison processes (tens-first and units-first conditions: parallel comparison; synchronous condition: parallel and holistic comparison), and (b) differences in the weight
of the tens- and units-effects. Therefore, attentional mechanisms at the encoding stage, which
determine how much attention is paid to the two-digit numerals’ components, might account for
the different types of processing of two-digit numbers.
In a recent study, Macizo, Herrera, Román, and Martín (2011a) investigated the influence of
bilingual L2 proficiency on processing numerical information in a comparison task in which
participants had to decide which number is the largest. Regardless of their L2 proficiency, all
German/English bilinguals showed a regular compatibility effect with Arabic digits as was
observed in previous studies with both monolingual (Macizo & Herrera, 2010; Nuerk et al.,
2005) and bilingual speakers (Macizo, Herrera, Paolieri, & Román, 2010, Macizo, Herrera,
Román, & Martín, 2011b). These results suggest that the processing of Arabic digits is not modulated by L2 proficiency. Thus, regardless of L2 proficiency, bilinguals compare two-digit numbers according to a decomposed model by decades and units (Nuerk & Willmes, 2005). However,
the processing of verbal numbers was influenced by the bilinguals’ proficiency. Less proficient
bilinguals presented the same compatibility effect as monolinguals in each of their languages, a
regular compatibility effect in German (L1) and a reverse compatibility effect in English (L2).
These findings suggest that participants with less proficiency in L2 are vulnerable to influences
of the linguistic structure in which numbers are presented (i.e., the word that is presented first in
two-digit verbal numbers). Thus, in German, the unit word is presented first and participants
focused more on it relative to the word denoting the decade when they performed the task in L1.
But, in English, the decade word is presented first and bilinguals focused more on it relative to
the word denoting the unit when they performed the task in L2. The variability of the compatibility effect in less proficient bilinguals depending on the verbal format indicates that their processing was lexically driven and it was sensitive to the linguistic-syntactic structure of number words.
This pattern replicates previous findings with Italian/German bilinguals (Macizo et al., 2010) and
German/English bilinguals (Macizo et al., 2011a).
The lexical-syntactic structure of the language number system as reflected in the inversion
(units-decades) or non-inversion (decades-units) is more evident in the verbal number format. In
the verbal format, the sequence of the number words follows the language syntactic structure and
reading direction, while in the digital format, such sequence is absent.
Current Research
In this study, we used the uniqueness of the numerical system of the Arabic language, in which
numbers in general and two-digit numbers in particular are different from the numerical system
of Hebrew in the lexical (in Arabic, Hindi digits: ٠١٢٣٤٥٦٧٨٩; in Hebrew, Arabic digits:
0123456789) and the syntactic structure (inversion). The inversion of digits in the Arabic language is a basic and inherent quality of two-digit numbers, unlike the artificial synchronization
of the decade and unit digits used in earlier studies (Castronovo & Crollen, 2011; Dehaene,
Dupoux, & Mehler, 1990; Knops, Nuerk, & Willmes, 2003). In addition, this order of decades
and units appears in the same direction of reading and writing in Arabic but reversed in Hebrew
(in Arabic from right to left: ٢١=‫=واﺣﺪ وﻋﺸﺮون‬ one-and-twenty; in Hebrew from left to right:
21 = ‫= עשרים ואחד‬ twenty-and-one).
As it has been postulated that differences in the encoding of two-digit numbers involve differences in processing (Nuerk et al., 2005) and as relatively little is known about numerical
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Journal of Cross-Cultural Psychology 
comparison in Arabic and Hebrew, the study of the compatibility effect as a semantic marker to
investigate semantic access in two-digit number systems of Arabic/Hebrew bilinguals is novel.
From the bilingual perspective, these stimuli offer an interesting opportunity to see whether
strong lexico-semantic connections exist for number representations in Arabic (Hindi digits),
Hebrew (Arabic digits), and L1 and L2 number words of two-digit numbers that differ
syntactically.
To investigate the effects of numerical lexical-syntactic structure and semantic access of
two-digit numbers in Arabic, an inverted language, and Hebrew, a non-inverted language, this
study’s experiment examined in four blocks the influence of the lexical-syntactic representation of Arabic language numbers (Hindi digits, for example, ٢١), Hebrew language numbers
(Arabic digits, for example, 21), verbal Arabic language numbers (L1-Arabic number words,
for example, ‫)واﺣﺪ وﻋﺸﺮون‬, ), and verbal Hebrew language numbers (L2-Hebrew number words,
for example, ‫)עשרים ואחד‬ ) on the task of number comparison in general and compatibility effect
in particular as a semantic marker. In this examination, we used a paradigm of numerical comparison, in which two numbers were visually presented. The participants were asked to point
out the bigger number by pressing one of two keys. We manipulated the unit-decade compatibility in presenting the number pairs. For this purpose, we selected fluent and proficient bilingual participants whose mother tongue is Arabic and tested them in Arabic and Hebrew
linguistic abilities. Bilinguals may compare two-digit numbers in each of their languages independently, the same way monolingual speakers of these languages do. Alternatively there may
be a modulation of L1-Arabic on number comparison in L2-Hebrew as previous research
argues for cross-language influences of L1 on L2 (Dijkstra, 2005), or a modulation of
L2-Hebrew on number comparison in L1-Arabic. Accordingly, the compatibility effect may
differ depending on the language and the format of numbers presentation. While no or even
reversed compatibility effect is expected in Hebrew because of the larger role of decades (sufficient for compatible and incompatible number pairs comparison), a regular compatibility
effect is expected in Arabic because of the larger role of units (sufficient for compatible number pairs comparison but not for incompatible number pars comparison). Thus, the compatibility effect will disappear in Hebrew because of its non-inversion (decade-units), whereas a
regular compatibility effect may be observed in Arabic because of its inversion feature (unitsdecades). This pattern will be more evident in the number words than the digits because the
relation between number words and syntactic structure is a bit more transparent than the mapping from Arabic digits to syntactic, given the fact that number words may partly be composed
of an analogical structure. Alternatively, number comparison in Arabic may be modulated by
Hebrew, or the reverse may be true.
In the current study, we also distinguished between the different models of two-digit number
processing introduced above. It is outlined latter how these basic models can be distinguished
using the compatibility effect in Hindi, Arabic, and verbal numbers of Arabic and Hebrew twodigit numerical comparisons. Participants’ mean response time and compatibility effect patterns
were measured to allow for a clear differentiation between the processing of tens and units as the
contribution of tens and units in inverted (Arabic) and non-inverted (Hebrew) languages can be
taken into account.
Specific predictions of mean response time and compatibility effect can be derived from these
models to differentiate between decomposed sequential, decomposed but parallel, or holistic
processing of two-digit numbers. According to the sequential decomposed model, comparing
two-digit numbers (Poltrock & Schwartz, 1984) always starts with the leftmost (decade) digit. As
for compatible and incompatible number pairs, the decades comparison is sufficient. This may
lead to the disappearance or even reversion of the compatibility effect (see Table 1).
According to the parallel decomposed model (Nuerk & Willmes, 2005; Verguts & De Moor,
2005), for incompatible number pairs, the units comparison will interfere with the decades
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Ganayim and Ibrahim
Table 1. Numerical Comparison of Two-Digit Number Pairs According to the Sequential Model and
the Resulting Compatibility Effect.
Decades-units
Sequential
Decades comparison
Compatible
Incompatible
Compatibility effect
+
+
No compatibility effect
Units comparison
Decision
0
0
+
+
Note. + = Digits comparison leads to the bigger two-digit number.
0 = irrelevant digits comparison.
Table 2. Numerical Comparison of Two-Digit Number Pairs According to the Parallel Model and the
Resulting Compatibility Effect.
Decades-units
Parallel
Decision
Compatible
Incompatible
Compatibility effect
+
+
Regular compatibility effect
Units comparison
+
-
Decades comparison
++
+-
Note. + = Digits comparison leads to the bigger two-digit number.
- = Digits comparison leads to the smaller two-digit number.
++ = Decade digits comparison and Unit digits comparison lead to the same bigger two-digit number.
+- = Decade digits comparison leads to the bigger two-digit number while the Unit digits comparisons lead to the
smaller two-digit number.
comparison. This will lead to larger mean response time for incompatible number pairs in Arabic
and Hebrew, especially in the verbal format. (Table 2)
According to the holistic model, when two-digit numbers are compared as two analogue entities (Dehaene et al., 1990), no systematic difference of tens and units should be observed. As in
this holistic view, no difference between Arabic and Hebrew is expected in the mean response
time for each compatible and incompatible number pairs.
In short, (a) decomposed and sequential processing will be indicated by no difference between
compatible and incompatible trials because of the sufficient decade digits comparison in Hebrew
especially in the verbal format, while in Arabic, a compatibility effect is expected because of the
insufficient unit digits comparison; (b) decomposed but parallel processing of tens and units
should be reflected by compatibility in both languages and both formats; (c) holistic processing
of two-digit numbers should be characterized by no compatibility effect in both languages and
equally distributed contribution of tens and units.
Method
Participants
A total of 18 bilingual students studying at Ben-Gurion University (average age: 23.9, SD = 1.93,
nine males and nine females) volunteered to participate in the study. All the participants had
Arabic as their mother tongue and Hebrew as their second language. They learned Hebrew formally and intensively since the third grade, attaining high enough proficiency to study in Hebrew
at the university. According to self-report, all the participants have normal or corrected eyesight
and did not have any reading or mathematical deficiencies.
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Journal of Cross-Cultural Psychology 
Stimuli
A white stimulus was presented on a computer screen on a black background. The stimulus consisted of two between-decade two-digit numbers, which appeared in the center of the screen. The
distance between the center and the numbers’ center was 10 cm, and the participants sat 55 cm
away from the screen. There were two number formats (digital, verbal), each presented in two
different blocks according to the presentation language (Arabic, Hebrew): Arabic language digital format (Hindi digits, ٠١٢٣٤٥٦٧٨٩), for instance (٥٤ ٥١); Hebrew language digital format
(Arabic digits, 01234567890), for instance (51 54); Arabic language verbal format (numbers in
words, Arabic Language, ‫أرﺑﻊ وﺧﻤﺴﻮن‬-‫;)واﺣﺪ وﺧﻤﺴﻮن‬ ); and Hebrew language verbal format (numbers in words, Hebrew Language, ‫ארבעים וחמש‬-‫)חמשים ואחד‬.
). The digital format was positioned at a vertical sight angle of 0.7° and a horizontal sight angle
of 0.6° to 0.9°. A balancing was conducted of the number of steps in which an Arabic number (in
Arabic and in Hebrew) appeared at the right and left side of the screen.
In the verbal format, the word length in number of letters and number of syllables were
matched in Arabic and Hebrew. Stimuli were presented in white letters (48-point Courier New
font) on a black background. One character subtended a vertical visual angle of 1.91° and a horizontal visual angle of 1.67°.
The presented numbers in Arabic and Hebrew were in a range of 11 to 99, excluding for numbers
with zero as unit digit (In Hebrew, 20, 30, 40, 50, 60, 70, 80, 90; In Arabic, .٢,.٣,.٤,.٥,.٦,.٧,.٨,.٩) to
neutralize the zero effect since these numbers consist of only one word in the verbal format (twenty,
. . . ).
thirty, ‫ שלושים‬,‫ ﺛﻼﺛﻮن‐עשרים‬,‫ﻋﺸﺮون‬ . . . ) The number pairs could be different in the numerical distances between them, when the
numerical distances could be 12, 13, 14, 15, 16. The numerical distances 1, 9, 10, 11 were not
chosen because, in these distances, compatible and incompatible number pairs cannot be found.
The numbers were organized in four blocks: an Arabic numbers pair (Hindi digits), a Hebrew
numbers pair (Arabic digits), an Arabic verbal numbers pair (numbers in Arabic words), and a
Hebrew verbal numbers pair (numbers in Hebrew words). Each block included 80 trials presented at random. For each of the five numerical distances, 16 number pairs were presented (8
compatible and 8 incompatible). Each number appeared in the left and in the right side. Before
each experimental block, there was a training block containing 16 trials. The order of the blocks
was counterbalanced across the participants.
Procedure
The participant’s task was to decide, in each presentation, which number is the bigger one out of
the two given numbers. Each participant was presented four blocks: a block with Arabic number
pairs (Hindi digits), a block with Hebrew number pairs (Arabic digits), a block with Arabic verbal number pairs (numbers in Arabic words), and a block with Hebrew verbal number pairs
(numbers in Hebrew words). The order of the two blocks was counterbalanced across participants. In each block, the number pairs were presented randomly.
The participants were asked to compare the two numbers, which were presented on the computer screen, and react as fast and as accurately as possible, by clicking the key P (located on the
right of the keyboard) when the right number is bigger and clicking the key Q (located on the left
of the keyboard) when the left number is bigger.
Every trial started with an asterisk presented for 300 ms as a fixation point in the center of the
screen. Then, 500 ms after the disappearance of the fixation point, a pair of two-digit numbers
was presented. The pair stayed on the screen until the participant pressed a key (but not longer
than 5,000 ms). A new stimulus appeared after 1,500 ms following the participant’s reaction. The
whole experiment lasted for 30 min.
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Ganayim and Ibrahim
Table 3. Reaction-Time Means in Milliseconds of Participants in Digital Presentation Format (Hindi
Digits, Arabic Digits), as a Function of the Unit-Decade Compatibility and the Resulting Compatibility
Effect.
Compatible
Incompatible
Compatibility effect
Hindi digits
Arabic digits
709
756
Regular compatibility effect
713
748
Regular compatibility effect
Design
The independent variables were the number presentation format (digital, verbal), the language
presentation (Arabic Language, Hebrew language), and the unit-decade compatibility of the
number pairs (compatible, incompatible). Our experiment was a three-factor design of 2 × 2 × 2.
In the analysis, all variables (number presentation format, language presentation, unit-decade
compatibility) were manipulated within-participants.
Results
A calculation of the reaction-time means of each participant in the correct trial was made according to the number presentation format (digital, verbal), the language presentation (Arabic
Language, Hebrew language), and the unit-decade compatibility of the number pairs (compatible, incompatible). Furthermore, a calculation was made of the error percentage of each participant in all the above-mentioned conditions. The error percentage was low (in Arabic
language–Hindi digits block 1.1%, in the Hebrew language–Arabic digits block 1%, in the Arabic
language verbal numbers 1.3%, in the Hebrew language verbal numbers 1.4%); therefore, an
analysis of the error percentage was not conducted. A three-way repeated measures ANOVA was
conducted of the reaction-time means when the variables of the number presentation format
(digital, verbal), the language presentation (Arabic language, Hebrew language), and the unitdecade compatibility of the number pairs (compatible, incompatible) were manipulated withinparticipants variables.
The three-way interaction of the within factors was found significant, F(1, 17) = 12.32,
MSE = 16,361.25, p < .05, η2 = 0.82. In the digital presentation format, a simple main effect for
the unit-decade compatibility appeared when presenting the numbers in the Arabic language
(Hindi digits) and Hebrew language (Arabic digits), F(1, 17) = 69, MSE = 29,718, p < .0001,
η2 = 0.9. A regular compatibility effect was found by which participants tended to react faster in
compatible number pairs than in incompatible numbers. No significant effect was found either
for the language presentation, F(1, 17) = 0.026, MSE = 16,171, p = .874, η2 = 0.002, or for the
simple two-way interaction between the language presentation and the unit-decade compatibility,
F(1, 17) = 2.4, MSE = 13,758, p = .47, η2 = 0.03 (see Table 3).
In the verbal presentation format, a simple main effect was found for the presentation language of the verbal number pairs, F(1, 17) = 16.11, MSE = 17,297.9, p < .05, η2 = 0.35. Participants
tended to react faster to verbal number pairs in the Arabic language (M = 1,568) than in the
Hebrew language (M = 1,685; see Table 4).
In addition, the simple two-way interaction of the language in which the two-digit verbal
numbers were presented and the unit-decade compatibility of the numbers was found significant,
F(1, 17) = 22.24, MSE = 18,964.5, p < .05, η2 = 0.65. In presenting the numbers in the Arabic
language, a regular compatibility effect was found, while in the Hebrew language, no compatibility effect was found (see Table 4).
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Journal of Cross-Cultural Psychology 
Table 4. Reaction-Time Means in Milliseconds of Participants in Verbal Presentation Format (Number
Words in Arabic, Number Words in Hebrew), as a Function of the Unit-Decade Compatibility and the
Resulting Compatibility Effect.
Compatible
Incompatible
Compatibility effect
Number words in Arabic
Number words in Hebrew
1,517
1,542
Regular compatibility effect
1,615
1,619
No compatibility effect
Discussion
In the current study, a direct assessment of the effect of language lexical-syntactic structure and
magnitude of semantic access on numerical processing was made by contrasting the performance
of Arabic/Hebrew bilinguals in a digital and verbal numerical comparison task. Our data revealed
in digital presentation format a regular compatibility effect in Arabic-L1 (Hindi digits) and
Hebrew-L2 (Arabic digits) characterized by lower reaction-time means for the compatible number pairs than for the incompatible number pairs. This is in line with previous studies (Macizo &
Herrera, 2011, Macizo et al., 2010, Nuerk & Willmes, 2005). As predicted by the parallel decomposed model (Table 2), when presenting the numbers in the Arabic language presentation format
(Hindi digits) and the Hebrew language presentation format (Arabic digits), a regular compatibility effect was found by which participants tended to react faster (a facilitating effect) in the compatible number pairs than in the incompatible number pairs (an interfering effect). The parallel
comparison of decade digits and unit digits causing this pattern of similar response time in each
numerical distance can be explained neither by the classical sequential model nor by the holistic
model.
Evidently, this similar pattern and mean response time of the regular compatibility effect
across the languages that bilinguals are proficient in advocate and strengthen the parallel units
and decades’ digits processing claim. Our results support the theoretical position that the bilingual’s numerical comparison in a digital format is semantically achieved regardless of the lexical-syntactic structure (Hindi digits vs. Arabic digits) of L1 and L2. This indicates that both
lexical digits of two-digit numbers in L1 and L2 essentially constitute orthographic codes that are
arbitrary symbolic representations of the same underlying meaning.
However, in verbal presentation format, different patterns of compatibility effects were found
in Arabic and Hebrew verbal numbers: A regular compatibility effect was found in Arabic-L1
(Arabic number words), but no compatibility effect was found in Hebrew-L2 (Hebrew number
words). These different patterns of compatibility effects across languages in each numerical distance reflect the influence and modulation of the lexical-syntactic structure of the language on
numerical magnitude comparison.
The syntactic structure of the language number system as reflected in the inversion (unitsdecades) or non-inversion (decades-units) determines the numerical processing of two-digit
numbers. This influence is more evident in the verbal number format since the relation between
number words and syntactic structure is a bit more transparent than the mapping from Arabic
digits to syntactic, given the fact that number words may partly be composed of an analogical
structure (numbers in words, Arabic Language: 51-one and fifty‐‫واﺣﺪ وﺧﻤﺴﻮن‬ ; Hebrew Language:
51-fifty one -‫)חמשים ואחד‬. ). The absence of the compatibility effect in Hebrew verbal numbers can
be explained by the sequential decomposed model (Table 1) with some revision. Comparing 2
two-digit numbers (Poltrock & Schwartz, 1984) starts with the leftmost (decade) digit as Hebrew
is a non-inverted language and the decades are read first. It should be exclusively sufficient to
compare the decade digits without the involvement of the unit digits leading to the absence of the
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Ganayim and Ibrahim
compatibility effect. In this case, the compatible trails do not differ from the incompatible ones.
However, in Arabic, an inverted language, the unit digits are read first, but it is not exclusively
sufficient to compare the unit digits without the involvement of the decade digits leading to
decomposed sequential comparison (unit digits then decade digits), causing the compatibility
effect in Arabic.
To sum up, the present study suggests that bilingual speakers of Arabic (inverted language)
and Hebrew (non-inverted language) have learned to compare two-digit numbers focusing on
units and decades in parallel when numbers are presented in digital notation. In addition, these
results support the possibility that with increasing familiarity with written number words, the
syntactic structure and the left-to-right (in Hebrew) or right-to-left (in Arabic) configuration in
which numbers are presented depending on the language, bilinguals of Arabic and Hebrew
learned to focus on the unit in Arabic but learned to focus on the decade in Hebrew. Our results
suggest that people seem to use the semantic sequential processing mode in accordance with the
syntactic numerical structure of each language, especially in verbal presentation of numbers.
The present findings raise new evidence that the magnitude processing as reflected in the
compatibility effect is mediated by numerical presentation format. Evidently, these findings
advocate and strengthen the claim that two-digit numbers comparison is influenced by the numbers presentation format. Different modes of presentation of two-digit numbers (digital vs. verbal) can lead to different number comparison styles. It is important to note that bilingual
participants in both languages demonstrated faster RT for the digital numerical format (M = 731)
compared with the verbal format (M = 1,573). The difference in the response time means in the
numerical distances between the digital and verbal can be explained by visual features. Arabic
and Hebrew verbal numbers consist of five to six letters for every word number, so that another
eye movement is required to focus on the other verbal digit to make a magnitude comparison
possible. This eye movement to get quantitative information is not required for a digital format
that consists of two digits for every two-digit number.
In addition, it is important to note that the regular compatibility effect observed in the Arabic
verbal numbers was not observed in Hebrew verbal numbers in contrast to the digital format.
Although the bilinguals participating in our study learned Hebrew formally and intensively since
the third grade, gaining enough proficiency to enable them to study in Hebrew at the university,
there was a regular compatibility effect in L1 (Arabic) relative to no compatibility effect in L2
(Hebrew). This advantage is in line with previous research where Frenck-Mestre and Vaid (1993)
found that bilinguals solve arithmetic problems with greater speed and accuracy when the problems are presented in their L1. This difference can be explained not only by faster numeral
decoding processes but also by fluent, semantic processing and better familiarity of Arabic-L1
verbal numerals relative to Hebrew-L2 verbal numerals (Dewaele, 2007; McClain & Shih Huang,
1982). As the bilingual Arabic/Hebrew participants of the study are highly proficient and familiar
with Hebrew verbal numbers, which are used even on a daily basis, we argue that this difference
is partially explained also by the different processing styles of each language. This processing
style is determined by the syntactic structure of two-digit numbers (Colome et al., 2010).
A final recommendation for future studies that examine cross-linguistic influences on numerical cognition among bilinguals is to develop a more detailed understanding of the compatibility
effect in formats, modes, assignments, languages, and with different participants. This may contribute to a wider array of information beyond the study of not only the languages’ quantitative
representation but also numeracy skills and numerical processes, especially of the Arabic
language.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or
publication of this article.
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Journal of Cross-Cultural Psychology 
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
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