On Drivers’ Reasoning About Traffic Signs: The Case of Qualitative Location

Abstract

General Audience Summary
A controversial aspect that arises from the use of different traffic signaling devices is that drivers often have to understand messages they are seeing for the very first time. This article analyzes the results of a series of empirical studies carried out with the aim of internationalizing variable message signs (VMS) by substituting keywords (e.g., prepositions) for abstract graphic signs (e.g., an arrow). Faced with novel elements in a traffic message about which drivers must conclude something in real time, they have no choice but to reason. This article explores the most appropriate arrangement (vertical, horizontal) and the frame of reference adopted by drivers (intrinsic, relative) as determinants of the comprehension of novel and complex VMS (e.g., congestion before arriving to Milan). Our study focuses on the design variants tested to inform drivers about two cases for location (event-before-city and event-after-city), following two basic layouts: H (horizontal, left–right) and V (vertical, bottom–up). Four comprehension tests carried out between 2006 and 2013 with 10,099 drivers in four countries (Italy, Netherlands, Spain, Sweden) were analyzed in a 2 (case: Before vs. After) × 2 (disposition: H, V) × 4 (Country) between-subject design. The comprehension of the V variants (78.1%) exceeded the comprehension of the H variants (54.1%) in all the countries in the “before” case. However, in no country did the V or H variants come close to functional understanding in the “after” case. The results provided evidence of the preferred model and relative frame of reference as determinants of message understanding. Although it is not realistic to expect national or international drivers to memorize all possible traffic messages, it is feasible to understand how their prior knowledge and preferences modulate their conclusions to design more functional traffic messages.

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On drivers’ reasoning about traffic signs: the case of qualitative
location
Ana Hernando1, Antonio Lucas-Alba1*, Maria Teresa Blanch2, Andrés Sebastián Lombas1, Alberto
Arbaiza3, Hans Remeijn4, Gunilla Thyni5, Gilberto Tognoni6
1Departament of Psychology and Sociology, Universidad de Zaragoza, C/Ciudad Escolar s/n, 44003,
Teruel, Spain (lucalba@unizar.es)
2Faculty of Psychology. Universidad Católica de Valencia, Valencia, Spain
3Dirección General de Tráfico, Madrid, Spain.
4Rijkswaterstaat, Delft, The Netherlands
5Trafikverket, Stockholm, Sweden
6SINA S.p.A., Verona, Italy
Abstract
This article explores the most appropriate arrangement (vertical, horizontal) and the frame of reference
adopted by drivers (intrinsic, relative) as determinants of the comprehension of new traffic messages
(e.g., congestion before arriving to Milan). Two specific cases for location (event-before-city, event -after-
city) were tested following two layouts: H (horizontal, left-right) and V (vertical, bottom-up). Four
comprehension tests carried out between 2006 and 2013 with 10,099 drivers in four countries (Italy,
Netherlands, Spain, Sweden) were analyzed in a 2 (case: Before vs. After) x 2 (disposition: H, V) x 4
(Country) between-subject design. The comprehension of the V variants (78.1%) exceeded the
comprehension of the H variants (54.1%) in all the countries in the “before” case. In no country did the V
or H variants come close to functional understanding in the "after" case. The results provided evidence of
the preferred model and relative frame of reference as determinants of message understanding.
Keywords: frame of reference, preferred mental models, reasoning, traffic sign co mprehension
General Audience Summary
A controversial aspect that arises from the use of different traffic signaling devices is that dri vers often
have to understand messages they are seeing for the very first time. This paper analyzes the results of a
series of empirical studies carried out with the aim of internationalizing variable message signs (VMS) by
substituting key words (e.g., prepositions) for abstract graphic signs (e.g., an arrow). Faced with novel

elements in a traffic message about which drivers must conclude something in real time, they have no
choice but to reason. This article explores the most appropriate arrangement (vertical, horizontal) and the
frame of reference adopted b y drivers (intrinsic, relative) as determinants of the comprehension of novel
and complex VMS (e.g., congestion before arriving to Milan). Our study focuses on the design variants
tested to inform drivers about two cases for location (event-before-city and event-after-city), following
two basic layouts: H (horizontal, left-right) and V (vertical, bottom-up). Four comprehension tests carried
out between 2006 and 2013 with 10,099 drivers in four countries (Italy, Netherlands, Spain, Sweden)
were analyzed in a 2 (case: Before vs. After) x 2 (disposition: H, V) x 4 (Country) between-subject
design. The comprehension of the V variants (78.1%) exceeded the comprehension of the H variants
(54.1%) in all the countries in the “before” case. However, in no country did the V or H variants come
close to functional understanding in the "after" case. The results provided evidence of the preferred model
and relative frame of reference as determinants of message understanding. Although it is not realistic to
expect national or international drivers to memorize all possible traffic messages, it is feasible to
understand how their prior knowledge and preferences modulate their conclusions to design more
functional traffic messages.
On drivers’ reasoning about traffic signs: the case of qualitative location
Simple painted road signs are rightly assumed to be part of the driver's long-term memory (Ben-Bassat,
2019; Crundall & Underwood, 2001). But as road signs become complex, our understanding of the
cognitive processes involved also becomes complex. So me researchers then adopt a pragmatic
perspective, exploring the particular demographics of drivers who understand certain messages (Ben-
Bassat & Shinar, 2015; Ng & Chan, 2008) and obey them (Ben-Elia & Shiftan, 2010), or proposing the
adoption of text messages (Roca, Insa & Tejero, 2018; Shinar & Vogelzang, 2013). Focusing on the
ergonomic principles of traffic signs (Ben-Bassat, 2019; Ben-Bassat & Shinar, 2006; Jamson & Mrozek,
2017) recent studies point to a relevant fact: faced with a complex or novel situation (e.g., road signs
placed in an ambiguous traffic context), long-term memory may not be sufficient, so drivers need to
reason before concluding on their meaning (Castro, Moreno-Ríos, Tomay & Vargas, 2008; Vargas,
Moreno-Ríos, Castro & Underwood, 2011).
This paper addresses the evaluation of co mplex electronic traffic signs, providing more empirical data to
identify suitable formulas for international signage. More specifically, this article analyzes the results of

comprehension tests carried out with Variable Message Signs (VMS) designed to inform European
drivers about variable events (congestion, roadworks, wind, or snow) located qualitatively, that is, by
reference to a city placed before or after such events. One of the basic difficulties of this goal arose with
the VMS template that many European countries adopted in the 1980s and 1990s, originally designed to
combine a pictogram with words and phrases from a certain language (Italian, French, Swedish, etc.)
(COST30 BIS, 1985; Ellenberg & Fabre, 1995). In the specific case under study, the goal was to replace a
preposition (before, after) with a language-independent element that could be displayed in a VMS. Due to
its simplicity, the possibility of adapting it to a 5x7 pixel matrix (see Fig. 1) and its versatility, the arrow
was the most obvious choice. Arrows are ‘meaningful graphic forms’ that encourage people to interpret
causal and functional aspects in a diagram (Tversky, 2005; Tversky, Zacks, Lee & Heiser, 2000),
capturing a large variety of semantics with their simple shape.
Clearly, the contextual versatility of arrows was both a strength and a weakness. Drivers infer on the fly
the possible meanings of the arrows from their immediate visual context, taking into account the
surrounding elements and their reciprocal congruence (Di Stasi, Megías, Cándido, Mandonado & Catena,
2012), forming an “arrow diagram” (Kurata & Egenhoffer, 2005). For example, by looking at the fourth
sign in the upper right corner (Fig. 1), some drivers may infer that congestion occurs after the city, while
other drivers may think that it occurs when heading into the city (i.e. before). So this paper answers this
basic question: how should the three main elements of the VMS (pictogram, arrow, city name) be
combined in the available VMS template for drivers to understand their meaning?
1.1. Drivers’ reasoning the way forward
The answer to this question must integrate two determinants of drivers' understanding: novelty and the
contextual interpretation of the arrow. As these VMS did not take advantage of the well-learned structure
and layout of painted signs, drivers participating in these studies had to infer their meaning. To discuss
how drivers reason about VMS we are adopting the preferred mental models theory (PMMT, Ragni,
Fangmeier, Webber & Knauff, 2007; Ragni & Knauff, 2013) a theoretical variant of the mental models
theory (MMT, Johnson-Laird, 1983; 2006). The PMMT assumptions better fit the objective of this study,
a case of spatial relational reasoning with a set of ambiguous premises about which drivers must reach
one fundamental conclusion (the VMS meaning). Unlike the MMT, the PMMT states that, in most cases,
people “construct just a single, simple and typical model” (Ragni & Knauff, 2013, p. 564), the preferred

model, and ignores the rest, unless we explicitly ask them to consider alternatives (requirement that we do
not raise). Figure 1 shows the four basic configurations analyzed. We will start by assuming the
construction of a simple one-dimensional model from a basic spatial array (e.g., a ro w of n cells)
representing the road line. We have to locate an object (LO) by reference to a referent object (RO) and we
would usually locate the RO first. However, since the starting point is the construction of an incremental
model, we will assume that individuals tend to prefer to change this role in the first premise, placing the
LO first (Oberauer & Wilhelm, 2000; Ragni & Knauff, 2013). This yields one preferred model for each
premise (Fig. 1). If participants have a preferred initial representation based on the event (LO is placed
first), the following predictions can be tested empirically: (1) If the interpretation of the arrow is that it
represents the event with respect to the city, then both messages (before/after) should obtain similar
comprehension rates regardless of the layout displayed (horizontal, left-right, or vertical, bottom-up). (2)
However, previous studies (Ulrich & Maienborn, 2010; Ulrich et al., 2011) suggest that representing the
scene would be easier if the event is “before” the city. RO (cit y) is added after LO (event) and people who
read and write from left to right represent elements in this way (Ragni et al., 2007). Conversely, the
"after" condition will be more difficult as it requires participants to reverse the sequence to place the
tokens (city, then event). (3) Similarly, some studies predict a temporal order of the sequence from behind
(past) to front (future) (e.g., Fuhrman & Boroditsky, 2010; Rinaldi, Vecchi, Fantino, Merabet & Cattaneo,
2018). If participants prefer to represent the sequence of events according to the bottom-up timeline, the
same preference as in (2) follows for "before", which maintains the time sequence of the event-then-city,
but not for "after" which requires reversing the order of placement of the elements.
Figure 1. Plausible preferred mental models for “event before/after city”
1.2. The drivers’ point of view

A complementary determinant of drivers’ reasoning that we explore in this analysis is the potential
synergy between the drivers’ frame of reference and the VMS frame of reference (Johnson-Laird, 2006;
Levinson, 2003). On the one hand, most road signs make sense from a relative frame of reference; the
driver is the observer to whom road signs should make sense in the road environment: “[From here where
you are] 50 km to arrive at [city]”; “To the Airport take the next exit to [the/your] right”, and the like. On
the other hand, arrows are asymmetric devices (tail-body-head) that both impact and are nuanced by near
elements in diagrams, maps, or panels, configuring an intrinsic frame of reference on the fly (e.g., VMS
on Fig. 1). Intrinsic frames of reference involve "an object-centered coordinate system, where the
coordinates are determined by the 'inherent features' or facets of the object to be used as the ground or
relatum." (Levinson, 2003, p. 41). Figure 2 exemplifies this by showing the variations of the dangerous
cur ve pictogra m over 63 years (Krampen, 1983).
Figure 2. Dangerous curve traffic signs 1905-1968 (redone in digital format by the authors).
Drivers are likely to have a preferred spatial array in traffic (e.g. bottom-up vertical arrangement) in
which LO and RO are placed when building a preferred mental model. Our last prediction is (4) that this
preference will favor the modeling and understanding of the messages in the vertical layout that adopt a
relative frame of reference compared to other designs.
2. Goals of the present work
The aim of this work is to determine how drivers’ reasoning strategies and most preeminent frame of
reference i mpinge upon comprehension of novel VMS messages. Recently, Hernando et al. (2022)
confirmed predictions 4-6 by comparing the vertical, bottom-up and the horizontal, left-righ t axis, so now
we focus on the vertical axis, including the top-down order. Another important goal is to determine which
alternatives are more robust, by testing and verifying how functional the explicit versus generic arrows
are in the VMS templates under study. Besides Between 2006 and 2013, a series of comprehension tests
were carried out within the framework of EasyWay, the European Union program for the implementation
of Intelligent Transport Systems (https://www.its-platform.eu/). Most European national road agencies

displayed word-dependent messages in VMS, and the aim of these studies was to explore ways to
imp ro ve common understanding among (European) drivers. This article analyzes the results of
comprehension tests performed with messages designed to report on variable events (congestion,
roadworks, wind, or snow) located before or after a city. Studies were carried out in 2006, 2010, 2011,
and 2013, with Dutch (NL), Italian (IT), Spanish (ES), and Swedish (SE) samples.
3. Method
3.1. Participants
A total of 10,099 drivers responded to comprehension tests dealing with the variants shown in Fig. 3. The
sample included 2938 Dutch, 1988 Italian, 2510 Spanish, and 2663 Swedish drivers, distributed among
the different test editions and sign variants (Table 2). The resulting grid included 60 cells (4 countries x
15 signs), with an average number of 168.32 participants per cell (SD = 74.81, MIN =43, MAX = 370).
Averaged percentages of main demographics and variables concerning driving experience per country
across the four studies (2006-2013) are shown in Table 1. Howe ve r, the fi ve-level age classification
shown in Table 1 has only been adopted since 2010; in 2006, a three-level age classification was used: 18
to 30 years (ES: 45.39; IT: 21.71; NL: 34.39; SE: 28.09; Average: 32.40), 31 to 50 years (ES: 46.64; IT:
63.46; NL: 52.59; SE: 54.14; Average: 54.21), and more than 50 years (ES: 7.97; IT: 14.82; NL: 13.01;
SE: 17.77; Average: 13.39). The N.A. (Not Applicable) response was intended for drivers who did not
currently dri ve very much, regardless of how long they have had a driving license. In general, the drivers
in our sample were predominantly male, middle-aged (26-45 years), with university studies, long driving
experience (> 15 years), and annual mileage (> 20,000 km/year), the y drove frequ ently on motorways,
and were familiar with VMS.
Variable
Level
ES
IT
NL
SE
TOTAL
Gender
Male
76.58
75.41
80.48
72.94
76.35
Female
23.42
24.59
19.52
27.06
23.65
Age
18-25
22.05
7.88
10.95
14.17
13.76
26-35
36.24
21.79
23.29
24.08
26.35
36-45
25.99
34.75
23.29
24.30
27.08
46-55
11.74
22.32
16.38
19.36
17.45

>55
3.98
13.27
26.11
18.10
15.36
Education
Elementary
9.86
0.46
1.51
5.54
4.34
Vocational
22.39
34.53
55.71
12.83
31.36
Secondary
20.34
27.66
16.89
29.72
23.65
University
47.41
37.36
25.90
51.92
40.65
Dr i ving
experience
N.A.
5.68
1.79
1.70
3.44
3.15
< 5 years
18.39
6.10
8.12
11.32
10.98
5-15 years
35.44
21.96
29.76
26.56
28.43
> 15 years
40.50
70.16
60.43
58.68
57.44
Annual
Mileage
N.A.
6.10
2.10
1.55
4.98
3.68
< 10,000 km
18.64
17.01
14.31
26.16
19.03
10-20,000 km
35.70
37.14
31.70
35.22
34.94
> 20,000km
39.57
43.76
52.45
33.65
42.36
Motorways
N.A.
2.10
1.30
1.03
2.04
1.62
Never
2.65
1.59
0.30
2.38
1.73
Occasionally
16.07
22.92
10.14
12.12
15.31
Often
79.18
74.21
88.54
83.46
81.35
Familiar
With VMS?
Yes
93.12
94.84
89.80
81.24
89.75
No
6.89
5.16
10.21
18.77
10.25
Table 1. Main demographics and driving experience across countries
3.2. Procedure
The modus operandi of the four studies was very similar, through electronic tests posted on public
websites (usually official traffic administrations, but also drivers' associations or highway companies).
Participats who accessed these websites in their national languages could see a banner inviting them to
collaborate in a set of studies to improve understanding of road signs in Europe. The design and structure
of the test followed ISO-9186 (2001; 2007) recommendations for computer tests. Typically, subjects had
access to the test simply by clicking on the invitation banner and reading a brief explanation of the
context of the test and its purpose (i.e., to check European drivers’ understanding of road signs shown in
VMS). Participants were then invited to fill in demographics, such as age, gender or driving experience
(Table 1), and then read an explanation of the task context: “On each page of this test, there is a variable

message sign (VMS). Look at each VMS and write in the box below it what you think that variable
message sign means. Write ‘I don't know’ if you cannot assign a meaning to the VMS. An example is
given on the next page”. Participants then read “This is an example. Context: on a motorway or dual
carriageway” and then saw a sign showing a standard traffic situation (e.g., “caution, road works”) for
about 8 s. Below, this sentence was shown “What do you think this variable message sign means?” and
then a self-informed response followed: “I am driving towards a dangerous road section due to road
works” (the pictogram in the example was not displayed later in the test). Clicking on the “continue” box
led to the first stimulus of the set. Drivers were required to pay attention to the sign first, then type in their
response. Participants were invited to respond to a set of 8 consecutive signs (each study included 6 sets,
totaling 48 signs, most of them not considered here) and took an average of 567.7 s (SD = 1003.6), about
10 minutes, to perform the whole task.
The document ISO-9186 (2001; 2007) establishes that the answers of the participants must be assigned
independently by the judges who compare them with one of seven basic categori es: 1) the correct
understanding of the sign is true (the judge estimates that the probability of a correct understanding is
greater than 80%), 2) the correct understanding of the sign is very likely (between 66 and 80%), 3) the
correct understanding of the sign is likely (between 50 and 60%), 4) the understanding is the opposite of
what is expected, 5) any other answer, 6) the answer "I don't know", 7) no answer. In our studies, this
basic structure was assu med, although with some modifications. On the one hand, only the safe
understanding of the sign (that is, the phrase that describes the meaning of the message or a very similar
one) was considered correct (coded as category 1). On the other hand, along with categories 4-7, different
categories of misunderstanding were also considered, reflecting alternative possibilities in the context of
locating variable events (Fig. 5). The objective of this adaptation in the correction procedure was to learn
from the different types of incorrect answers to improve the design in successive studies. All the countries
involved assumed the same correction criteria and the same response categories.
Instruments adopted to present the signs differed between the first three studies (2006; 2010; 2011) and
the 2013 study. The first three studies presented the messages to participant drivers in a static fashion. In
the 2013 study, a web-based driving simulator was used to display the messages. Participants were not
asked (and could not) drive. Using the simulator only meant that the message presentation was dynamic.
The basic scenario placed the driver in a car moving towards a VMS gantry in the right lane of a two-lane
motorway (drivers could not select the speed nor change lane or direction). A reading window of about 8

s was set as the driver approached the VMS at 90 km/h. Therefore, the time available for participants to
read the message was set to be the same for the two types of presentation (static, simulator). The driver
passed under the gantry (simulator), or the message was removed fro m the screen (static), and then the
same basic question "What do you think this variable message sign means?" appeared on screen. Then a
writing box appeared allowing participants to type in their answers (without time restriction).
3.3. Materials
The V MS template adopted in all studies (a 32x32-pixel matrix plus three rows with 12 to 16 5x7-pixel
matrices) is shown in Fig. 3 (bottom-right). In line with the objective of internationalizing the messages, a
basic rule followed in the studies was that all the elements displayed in the VMS must be known (e.g., the
congestion pictogram), understandable (e.g., an arrow) or easily inferred (a city name). Other words (e.g.,
prepositions, conjunctions, and the like) were not allowed. Some tests performed in parallel in 10
European countries (ES, IT, NL and SE included) determined that these danger warning pictograms used
in these studies obtained average comprehension rates above 89.8% with or without the red triangle
(Luc as -Alba et al., 2011). Showing the same silhouette without the red triangle prompted significantly
fewer mentions of the word “danger” or “caution”, and allowed extra space for the pictogram. This makes
sense when the event is far away (i.e., not so dangerous), the most prevalent case for qualitative location
(e.g., German dWiSta panels show a congestion silhouette without triangle, Hartz & S chmidt, 2005).
Therefore, after 2010, most tests displayed messages without the red triangle. On the other hand, given
that some VMS had 8x11 pixel matrices, being able to show lowercase, this possibility was later included
in our stimuli. The city names were the same for all participants in the 2006 test, using place names
belonging to a non-participating third country (Germany and Austria). However, local examples were
introduced to rule out potential problems with unknown place names (although later results would
confirm that this was not the case, see table 2), therefore in the 2010, 2011 and 2013 studies all countries
used the same message templates but with city names in their territories. Last but not least, exploring the
qualitative location of variable events also had practical implications. Most road operators in different
countries avoid reporting changing events such as congestion, wind, or fog by using a quantitative
location (e.g., "congestion in 15 km"), especially if there is only one VMS available before the critical
road section (Arbaiza & Lucas-Alba, 2012).

The first attempts to identify an international location set for VMS (2006, 2010) explored the basic top-
down, left to right horizontal (H) layout (the standard parsing for official langua ges in Europe; see Bergen
& Chan, 2005; Spalek & Hammad, 2005). The four “before” variants tested are sho wn in Fig. 3 (first
row): horizontal-dangerous congestion, horizontal-congestion, horizontal-wind, and horizontal-snow.
Only “after” variant tested (Fig. 3).
A complementary approach was explored in the 2011 and 2013 tests: the vertical (V), bottom-up layout.
The four “before” V variants tested are shown in Fig. 3: vertical-congestion, vertical-roadworks, vertical-
wind, and vertical-snow. The six “after” V variants tested are shown also in Fig. 3: vertical-congestion12
(12=in the first and second rows), vertical-congestion23 (23=in the second and third rows), vertical-
roadworks23, vertical-wind23, vertical-congestion(e) (city name enclosed), and vertical-congestion-sa
(special arrow).
Figure 3. Horizontal and Vertical layout design variants for before and after explored in 2006-2013.
4. Results
4.1. Descriptive statistics
Table 2 presents the weighed average comprehension rate (1 = 100% comprehension) of the eight
“before” and the seven “after” messages per country, with the corresponding Horizontal and Vertical
2006
2010
2010
2010
2011
2011
2013
2013
2006
2011
2011
2011
2011
2013
2013

layout variants. Pictogram variation, however, was not part of our analysis and was only meant to explore
responses to qualitative location under differing events. In bold total comprehension rates per country
under Horizontal and Vertical layout formats.
Case
layout (H: horizontal, V: vertical)
ES
IT
NL
SE
BEFO RE
H, dangerous congestion
.568
.665
.785
.506
(n=5076)
H, wind
.277
.419
.797
.306
H, congestion
.202
.233
.811
.425
H, snow
.213
.395
.777
.351
Total H, before (n=2253)
.422
.535
.792
.415
V, snow
.879
.880
.853
.733
V, road work
.641
.901
.921
.888
V, wind
.812
.842
.845
.712
V, congestion
.597
.766
.726
.764
Total V, before (n=2823)
.700
.833
.817
.775
AFTER
H, dangerous congestion
.069
.284
.450
.156
(n=5023)
Total H, after (n=476)
.069
.284
.450
.156
V, congestion-sa
.555
.366
.403
.508
V, road work23
.387
.374
.298
.374
V, wind23
.257
.262
.216
.347
V, congestion(e)
.024
.140
.067
.042
V, congestion23
.033
.100
.019
.080
V, congestion12
.035
.081
.000
.071
Total V, after (n=4547)
.216
.213
.151
.222
Table 2. Weighed average comprehension rates of “before” and “after” Horizontal and Vertical layout
variants per country.
4.2. Inferential statistics
A bet ween-subject ANOVA was carried on for a 2 (Case, before/after) x 2 (Disposition,
horizontal/vertical) x 4 (Country, ES / IT / NL / SE) design. Overall, the “before” messages (M = .661)
yielded better comprehension rates than the “after” messages (M = .220), F(1, 10083) = 1296.06, p = .0001,

ηp2 = .114 (Table 2). Also the V variants obtained better comprehension rates (M = .491) than the H
variants (M = .390), F(1, 10083) = 67.49, p = .0001, ηp2 = .007. Both factors yielded a significant interaction,
F(1, 10083) = 129.91, p = .0001, ηp2 = .013. Comprehension rates for the V (M = .201) and H variants (M =
.240) were similar (F(1, 10083) = 3.36, p = .067, ηp2 = .000) when the event was located after the city;
however, when the event was located before the city, the comprehension of the V dispositions (M = .781)
was significantly better than that of the H dispositions (M = .541; F(1, 10083) = 391.17, p = .001, ηp2 = .037).
Comprehension also differed in terms of the country of origin, F(3, 10083) = 59.14, p = .0001, ηp2 = .017.
Bonferroni post hoc comparisons showed a linear order: ES (M = .352), then SE (M = .392), IT (M =
.466), and NL (M = .553; all differences were significant at p < .05). Country presented an interaction
with Case, F(3, 1083) = 3.48, p = .015, ηp2 = .001: comprehension for “before” was significantly higher than
comprehension for “after” in every country (ES, M (before) = .561, M (after) = .143; F(1, 10083) = 409.27, p
= .0001, ηp2 = .039; IT, M (before) = .684, M (after) = .248; F(1, 10083) = 210.86, p = .0001, ηp2 = .020; NL,
M (before) = .805, M (after) = .300; F(1, 10083) = 433.25, p = .0001, ηp2 = .041; SE, M (before) = .595, M
(after) = .189; F(1, 10083) = 338.81, p = .0001, ηp2 = .033). Although IT and NL fared a bit bet ter than the
rest (Table 2), the average worse (ES: M = .143) and better (NL: M = .300) comprehension rates for
“after” differed little yet significantly (F(1, 10083) = 12.12, p = .0001, ηp2 = .004). Comprehension rates for
“before” were significantly better, but countries differed significantly from each other (except for SE and
ES, p = .209): the lowest rate (ES: M = .561) was comparatively lower than the highest one (NL: M =
.805: F(1, 10083) = 94.23, p = .0001, ηp2 = .027). In all cases, Bonferroni adjustment was applied for multiple
comparisons. Country also presented an interaction with Disposition, F(3, 10083) = 50.08, p = .0001, ηp2 =
.015. All countries achieved better averaged comprehension results for V than for H (ES, M (V) = .458, M
(H) = .245; F(1, 10083) = 105.683, p = .0001, ηp2 = .010; IT, M (V) = .523, M (H) = .409; F(1, 10083) = 14.371,
p = .0001, ηp2 = .001; SE, M (V) = .499, M (H) = .285; F(1, 10083) = 93.312, p = .0001, ηp2 = .009), except
for NL (V: M = .484; H: M = .621; F(1, 10083) = 31.95, p = .0001, ηp2 = .003; Table 2). Finally, the Case,
Disposition and Country factors yielded a significant interaction, F(3, 10083) = 5.12, p = .002, ηp2 = .002.
Participants from all countries reached high compreh ension rates with the V set in the “before” case (ES,
M (V) = .700, M (H) = .422; F(1, 10083) = 141.58, p = .0001, ηp2 = .014; IT, M (V) = .833, M (H) = .535, F(1,
10083) = 107.18, p = .0001, ηp2 = .011; SE, M (V) = .775, M (H) = .415, F(1, 10083) = 254.66, p = .0001, ηp2 =
.025); except for Dutch drivers who obtained sufficient comprehension rates in the “before” case in both
V (M = .817) and H (M = .792; F(1, 10083) = 1.34, p = .248, ηp2 = .000) cases (Fig. 4).

Figure 4. Event-before-city (left) and event-after-city (right): comprehension rates per country for V and
H dispositions.
4.3. Qualitative analysis: most frequent errors in answers to the "before" case.
The representations that emerged from drivers' correct and incorrect responses in the “before” case are
depicted in Fig. 5. We will examine the incorrect answers qualitatively, assu ming a rule of thumb, that is,
considering that the answers that accumulate at least 5% of answers are sufficiently representative. We
will focus first on the less fortunate horizontal (H) variants (weighed averages). The vertical (V) variants
constrained the inferential mechanism quantitatively (fewer incorrect answers), and qualitatively: the
most frequent wrong answer was E (Fig. 5), hardly present with H variants. Tables 3 and 4 show the
descriptive results, incorrect answers and their representation in Fig. 5.
Sign (event-before-city)
Incorrect answers
M (%)
S.D.
Fig. 5.
horizontal dang. cong.
Congestion at the exit to Salzburg
10.9
6.3
A
Departure/recommended direction to Salzburg
9.2
5.6
B
horizontal congestion
Congestion at the exit to [city]
21.5
16.7
A
Route recommend by the following exit to avoid congestion
12.3
10.9
C
Recommended exit/direction to [city]
10.1
2.6
B
Congestion in [city]
7.5
3.5
D
horizontal wind
Wind in [city]
31.5
11.3
D
Wind at the exit of [city]
11.1
6.7
A
Danger (no location mentioned)
9.0
11.5
E
horizontal snow
Snow in [city]
35.7
12.6
D
Snow at the exit to [city]
8.8
7.5
A
Danger
18.0
12.6
E
vertical congestion
Specific recommendation to [city]
6.0
5.2
B
Congestion (no location mentioned)
5.9
4.3
E

vertical roadwork
Roadwork (no location mentioned)
4.7
4.5
E
vertical wind
Wind (no location mentioned)
8.7
6.1
E
vertical snow
Snow (no location mentioned)
8.1
6.8
E
Table 3. Descriptive results for incorrect answers to the ‘before’ cases.
4.4. Qualitative analysis: most frequent errors in answers to the “after” case.
The representations of drivers' correct and incorrect an s wers in the “after” case are depicted in Fig. 5.
Again, only sufficiently representati ve incorrect responses (≥ 5%) are examined. We will focus first on
the horizontal (H) variant (weighed averages), which presented a rich panoply of wrong answers. Bottom-
up vertical (V) variants were also unsuccessful, although to a varying degree (see table 4).
Sign (event-after-city)
Incorrect answers
M (%)
S.D.
Fig. 5
horizontal dang. cong-
Congestion (no location mentioned)
24.4
11.2
E
Congestion at the entrance to Siegsdorf
13.7
13.4
D
Alternative exit to Siegsdorf available
12.1
11.1
B
Congestion before Siegsdorf
9.6
6.8
G
Alternati ve exit to Siegsdorf congested
8.1
5.6
A
vertical congestion12
Congestion before [city]
59.7
15.1
G
Go straight to get to [city]
9.7
3.5
F
Congestion (no location mentioned)
6.3
1.8
E
Congestion at the exit from the [city]
4.7
3.2
A
vertical congestion 23
Congestion before [city]
55.5
18.5
G
Go straight to get to [city]
8.4
7.3
F
Congestion (no location mentioned)
7.7
3.3
E
Congestion at the exit form the [city]
5.5
3.8
A
vertical wind23
Wind before [city]
52.6
12.8
G
Wind (no location mentioned)
12.3
4.3
E
Wind near of [city]
4.7
2.2
G
vertical roadworks 23
Works before [city]
42.9
10.8
G
Works near [city]
6.6
2.7
D
Road works (no location mentioned)
5.8
3.9
E
vertical congestion-e
Congestion going to [city]
56.3
10.6
G
Congestion at the exit from [city]
14.7
4.8
A
Congestion (no location mentioned)
7.8
4.4
E
Rerouting recommendation formula
6.0
2.7
B
vertical congestion-sa
Congestion going to [city]
35.5
10.4
G
Congestion at the exit from [city]
9.6
1.9
A
Table 4. Descriptive results for incorrect answers to the ‘after cases.

Figure 5. Correct vs. incorrect model representations after participants’ ans wers.
5. Discussion
Clearly, not the first, but the second and third predictions were confirmed. Results for “before” (above
50%) were better than for “after” (around 20%). However, while H vs V did not differ with “after”, V
yielded better results with “before” (confirming the fourth prediction), while H yielded better results with
before than V with after. Also, the "before" and "after" errors differed in nature: errors with before were
less frequent and mostly in vo l ve d incomplete information (e.g., indicating there was a congestion, but not
where). Errors with after were more frequent and problematic because people understood the opposite of
the intended meaning (e.g., Fig. 5 G). The obvious recommendation is to avoid using "after" information
with the event-city-arrow triad: most drivers will understand otherwise (except about 20% who will be
correct).
According to the PMMT, representing the scene would be easier if the event is before the city, because
the after condition requires participants to reverse the LO-RO sequence to place the tokens. The second
prediction aligns with this statement (see Jahn, Knauf & Johnson-Laird, 2007, Ulrich & Maienborn, 2010;
Ulrich et al., 2011). However, participants interpreted more correctly the V (predictions 3 and 4) than the
H set (prediction 2). The third prediction aligns with findings on embodied cognition that expect a
temporal order of the sequence from behind (past) to front (future) (Fuhrman & Boroditsky, 2010; Rinaldi
et al., 2018), favoring the adoption of a PMM based on a bottom-up timeline. The location of objects in
the front-back dimension is fast, because it maintains a bodily and functional asymmetry that is not so
marked in the left-right dimension (De Vega, 2002; Franklin & Tversky, 1990). Generic metaphors in
langua ge also present the future in front of the Ego (Núñez & Sweetser, 2006). Finally, the results with V

"before" fit with Posner's (1980) function of orientation and anterior attention networks (Posner &
Dehaene, 1994).
A better compreh ension of V “before”, compared to H “before”, also fits with the fourth prediction: VMS
consistent with the drivers' relative frame of reference (Levinson, 2003; Johnson-Laird, 2006; Fig. 2)
facilitated model representation. Most drivers did not adopt the intrinsic diagrams perspective: an arrow
pointing right was seen as a compulsory, advised, or recommended exit or diversion route (Fig. 5 A-C),
and placing an upward-pointing arrow above a city name was interpreted as the next location on route
(Fig. 5 D, G). The arrow pointing up departs from an empty space that drivers may identify with their
own position: if we fold that plane forward 90°, it will coincide with the projection of the driving plane
(road), where down is near (driver, base of the arrow) and up is far (location, tip of the arrow). This
rotation is common in traffic signs. However, drivers would need to make a 90° turn counterclockwise
and then a 90° turn forward to model "before" from a relative frame of reference. But interpreting the
arrow as "exit" (Fig. 5, A-C) would fit directly into the relative frame of reference, and a frontal rotation
of 90° would yield a plausible iconic model for the sign. Concluding that the arrow represented an exit
could reflect a modulation of former knowledge (Johnson-Laird & Byrne, 2002), and would require less
cognitive effort.
Regardi ng prior knowledge, most drivers would not expect information about open-ended events that
occur somewhere after a section of the road (the arrow is pointing to "nothing" in the after condition-
something a little odd). Classical experiments on indeterminate location (Bransford, Barclay, & Franks,
1972; Ehrlich & Johnson-Laird, 1982; Mani & Johnson-Laird, 1982) would predict drivers' reluctance to
delve into this possibility as well (indeterminate locations block the elaboration of iconic mental models).
Considering the deictic character of the arrow (Eco, 1996) drivers likely converted "after" into "towards
there", a very successful wrong answer, hovering around 50% (Fig. 5-G).
All in all, the V-messages “before” successfully restricted the models of possibilities, favoring the
preferred model, and achieved acceptable comprehension ratings from drivers from four different
countries. Predictions 3 and 4 present a number of interesting theoretical synergies that could be the
subject of future research. One last note to address the good performance of the Dutch drivers in H
"before". Although the VMSs studied were not part of the Dutch catalog of signs, Dutch drivers were
used to reading relatively complex messages with small arrows interspersed in the text and with small

pictograms (Fig. 6), a not so common practice in the rest of the participating countries (Blanch, Lucas-
Alba & Messina, 2011). This may have contributed to more flexible representational mechanisms both for
the V and H variants under the “before” case. Clearly, this speculation would require further study.
Fig. 6. Dynamic Route Information Panels (DRIP) in The Netherlands (after Blanch et al., 2011).
5.1. Limitations, extensions and future work
Future studies should make an additional effort controlling variability. The changes in VMS and display
formats tried to improve studies with large international samples. Message presentation (static in 2006-
2011 vs. web-based simulator in 2013) provided the same reading window (8 s), and the simulator did not
allow drivers to manipulate lane change or speed. Although studies focused on location formulations and
pictograms enjoyed similarly high comprehension rates (Lucas-Alba et al., 2011), variants were unevenly
distributed across studies. None of these factors abo ve showed a statistically significant effect on
comprehension, but all these methodological issues should be considered as a limitation to be overcome
in further studies. Finally, not all samples were the same and not all signs had the same number of
responses. However, all countries provided data from large samples that included participants of different
characteristics (sex, age, driving experience, education). Future studies could benefit from greater
methodological and procedural control, as do laboratory studies with smaller samples.
Author Contributions
Acknowledg ments
We thank the reviewers for their comments, which really helped improve this article. We thank
Professor Cándida Castro (University of Granada) and Dr. Tamar Ben-Bassat (Tamar Grap hic Design) for
helping us improving the paper with their comments. We thank Federico Fernández (then DGT traffic
deputy director) and Professor Luis Montoro (University of Valencia) for supporting the research on
VMS harmonization. Support came from Dirección General de Tráfico, Spain (grant SPIP 2014-01345).
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