Nemanja Memarovic
email: nemanja.memarovic@usi.ch

Ava Fatah Gen Schieck

Efstathia Kostopoulou

Moritz Behrens

Martin Traunmueller
email: martin.traunmueller.11@ucl.ac.uk

Moment Machine: opportunities and challenges of posting situated snapshots onto networked public displays

Keywords: networked public displays, urban screens, situated snapshots, community interaction, public space, urban computing, urban informatics

Large public displays are becoming a ubiquitous resource in the urban environment. Interconnected over the Internet these hitherto isolated "ad displays" could become a novel and powerful communication mediumnetworked public displays. One example for such a novel type of communication is their use as community tools. Scattered across the urban landscape and equipped with additional sensors, such as cameras, they provide the opportunity for local community members to take images of themselves and leave their "mark" in the setting, e.g., on their way to school, work, or meeting with friends. In order to understand the potential of posting situated snapshots on networked public displays in the context of place-based communities we designed and developed the Moment Machinea networked public display application that allows one-click photo capture. In this paper we report on identified opportunities and challenges emerging from 6 user trials in the wild at 2 locations.

Introduction

The urban landscape is getting "painted" with large public screens: from streets across small cafes to building facades we can find digital displays showing street maps, restaurant menus, or latest brand advertisement [START_REF] Kostakos | Public Displays Invade Urban Spaces[END_REF]. Although most of public displays represent singular installations that run locally stored power points or images, it is not hard to imagine that they will soon be connected and networked over the Internet [START_REF] Davies | Open Display Networks: A Communications Medium for the 21st Century[END_REF][START_REF] North | Tension Space Analysis[END_REF][START_REF] Ojala | UBIhotspot 1.0[END_REF]. Networked and empowered with additional sensors such as cameras networked public displays will constitute a novel and powerful communication medium for the 21 st century [START_REF] Davies | Open Display Networks: A Communications Medium for the 21st Century[END_REF].

Dispersed across the urban landscape and embedded in the setting, they offer an opportunity to connect local community members, e.g., by having them support picture taking and sharing across the display network. For example, a school kid on his/hers way to school could be capturing images with his friends on a network of public screens, a group of teenagers could take photos while they are out-and-about on a Friday night, while adults with jobs could be taking photos to and from their way to work.

By taking images and leaving them in the settings (1) community members will express themselves and will leave their "mark". In return the photos taken by people in display locality could [START_REF] Clinch | Reflections on the long-term use of an experimental digital signage system[END_REF] stimulate community awareness by providing information on "who is around". They could also [START_REF] Davies | Open Display Networks: A Communications Medium for the 21st Century[END_REF] enrich their locality and provide insights into other locations through photos captured in different environments, thus stimulating one of the human needs in public spaces: the need for discovery of new features and places [START_REF] Memarovic | Using Public Displays to Stimulate Passive Engagement, Active Engagement, and Discovery in Public Spaces[END_REF].

As part of an ongoing "Screens in the Wild" research project [START_REF]Screens in the Wild[END_REF] and in order to better understand the implications of posting situated snapshots onto networked public displays in the context of place-based communities we designed and developed Moment Machinea networked public display application that allows one-click ondisplay photo capture. The Moment Machine is described in detail in section 3, right after the related work section (section 2). Our study design is summarized in section 4 where we describe six user trials "in the wild" at 2 locations where we conducted 55 interviews with passers-by. We present findings from our study in section 5, organized around (1) possible motivations for posting situated snapshots onto networked public displays, (2) discussion on where the images could be displayed once they are taken, and (3) challenges in promoting and sustaining their use. Finally we provide concluding remarks in section 6.

Related Work

Research on networked public displays has seen its pioneering work in the early 80s where one of the prominent examples from that period is the 'Hole in Space' [5], a project that connected two urban spaces in New York and Los Angeles through a video link. Connected Urban Spaces [START_REF] Fatah Gen | Connected urban spaces[END_REF] and Telectroscope [START_REF]Telectroscope[END_REF] are examples of similar and more recent projects.

In more recent years work in the area has shifted from creating simple video links between two places into creating more interactive multimedia applications [START_REF] Clinch | Reflections on the long-term use of an experimental digital signage system[END_REF][START_REF] Memarovic | Designing "interacting places" for a student community using a communicative ecology approach[END_REF] and how they can enrich urban spaces and promote community interaction and place awareness [START_REF] Memarovic | The interacting places framework[END_REF]. For example, Alt et al. [START_REF] Alt | Digifieds: insights into deploying digital public notice areas in the wild[END_REF] investigated how networked public displays can support exchange within urban communities by creating a digital version of traditional/analog notice boards.

The work of Ojala et al [START_REF] Ojala | UBIhotspot 1.0[END_REF], Hosio et al. [START_REF] Hosio | From School Food to Skate Parks in a Few Clicks[END_REF], North et al. [START_REF] North | Tension Space Analysis[END_REF], Peltonen et al. [START_REF] Peltonen | Extending Large-Scale Event Participation with User-Created Mobile Media on a Public Display[END_REF], and Taylor and Cheverst [START_REF] Taylor | Supporting Community Awareness with Interactive Displays[END_REF] falls closest to the work described in this paper as they have investigated how images can be used on networked public displays. Ojala et al.'s UBI-Postcard allows passers-by to take photos using a camera attached to a display.

Once the photos are taken users can send the photo to an email address. Hosio et al.'s Ubinion similarly used public displays as input devices: young adults/teenagers could use them to create posters with speech bubbles that would represent their concerns about the city of Oulu. Posters created on displays (i.e., a network of displays) would be posted on dedicated Facebook and Twitter accounts. While UBI-Postcards and Ubinion used displays as input devices, Taylor and Cheverst's Wray Photo Display showed images uploaded from a dedicated website (images were uploaded by Wray villagers). Similarly, Peltonen et al.'s CityWall display showed user-contributed images from Flickr tagged with a specific tag. In the same manner North et al.'s ScreenGram shows images from Instagram with a predefined hashtag on a display network.

While all the above work used public displays for either taking the images [START_REF] Hosio | From School Food to Skate Parks in a Few Clicks[END_REF][START_REF] Ojala | UBIhotspot 1.0[END_REF] or showing them on networked displays [START_REF] North | Tension Space Analysis[END_REF][START_REF] Taylor | Supporting Community Awareness with Interactive Displays[END_REF] the study described here is the first one that used networked public displays for both. Also, our work complements the current body of research on networked public displays by (1) describing possible motivation for taking and posting situated snapshots onto public display networks, (2) discussing where could the images be displayed once they are taken, as well as [START_REF] Davies | Open Display Networks: A Communications Medium for the 21st Century[END_REF] summarizing challenges in promoting and sustaining their use.

The Moment Machine

The Moment Machine is a networked public display application that allows passersby to simply capture their everyday moments by taking an image through a display and spreading it across the network. The Moment Machine's user interface is shown in Fig. 1-a. Its simple user interface was inspired by previous research that showed that passers-by do not spend a lot of time looking at public displays [START_REF] Huang | Overcoming assumptions and uncovering practices[END_REF] and that live video feed represent a good mean for getting their attention [START_REF] Müller | Looking glass[END_REF]. For this reason we show a live video feed (1 in Fig. 1-a) and allow passers-by to take an image by simply pressing a button (3 in Fig. 1-a). Users can also change the "look" of their snapshot by selecting a filter before they take a photo (2 in Fig. 1-a), somewhat similar to the popular social media application Instagram [9]. In order to give the passers-by enough time to prepare themselves, image capture is delayed by five seconds, which is indicated through a countdown timer appearing instead of the "hands" button (2 in Fig. 1-a).

Once the moment is captured users have thirty seconds to decide if they want to leave the moment on a display (shown in Fig. 1-b). After that the moment appears on the screen and across the display network (4 in Fig. 1-a). Passers-by also have the possibility to browse through moments captured at all locations (4 in Fig. 1-a).

Study Design

In order to uncover the potential of posting situated snapshots onto networked public displays we conducted six user trials "in the wild" at 2 locations in London, i.e., Walthamstow and Leytonstone. Both locations had a display in a public urban setting provided by the "Screens in the Wild" project [START_REF]Screens in the Wild[END_REF] and were connected thus making a small display network ideal for technology probing [START_REF] Hutchinson | Technology probes: inspiring design for and with families[END_REF]. User trials were conducted between 12AM and 5PM on working days. They lasted between 2.5 and 4.5 hours and partially overlapped. In total we conducted of 7.5 hours of trials at Leytonstone and 10.5 hours of trials at Walthamstow. Because the goal of the study was to "probe" and understand the implications of taking situated snapshots on local community members we decided to invite users to interact with the Moment Machine. During the trials we conducted 55 interviews (27 individual and 18 group interviews) with 71 people who interacted with the Moment Machine. At each location there were between 1 and 3 researchers who invited passers-by to interact with it. Passers-by were asked to take a photo and browse through existing ones on the display. After taking the snapshot researchers conducted semi-structured interviews and asked the participants about their general impression of the Moment Machine, e.g., would they come back to take more photos and browse through the ones shown on a display, and where they would like to see the images appear. After conducting the interview researchers wrote down the notes with some verbatim.

Findings

After collecting all the data we conducted an affinity diagram analysis and categorized the data, focusing on (1) possible motivations for taking images through networked public displays and leaving them in urban settings. We were also interested in (2) uncovering other digital places where the images could appear, e.g., Facebook or personal email as well as (3) understanding the challenges in promoting and sustaining the use of the Moment Machine application. Each interview received an identifier comprising from the first letter of the location (L -Leytonstone, W -Walthamstow) and a sequential number of the interview, e.g., L01 would be the first interviewed person/group from Leytonstone while W04 would be the fourth interviewed person/group from Walthamstow. Considering the qualitative nature of our study our results are not intended as statistical evidence for expected behavior. Instead our results serve as an input to the design process by identifying potential tendencies of passers-by.

We first describe possible motivation for taking situated images and effects of posting them in urban settings, then we discuss where could the images taken through networked public displays appear, and in the end we present some of the challenges in sustaining their use.

Motivations and Effects

One of the possible reasons why passers-by would take images and leave them on public displays would be to "capture everyday life" (L04). For example, L06 stated that he would simply take pictures while going to or coming back from his work. Similar comment was received from L12 who said that he would take images on his way to and from school. Although we ran six user trials "in the wild" on arbitrary days this type of behavior was somewhat confirmed as we did get 3 returning users (L12, W18, W19) who brought additional participants to the display.

Taking images of oneself alone or in company of friends and family is another reason (W12, W13). This is also reflected with types of images people would like to see on public displays, i.e., images of people they know and have seen in their locality. As W12 points out "It is interesting if there is a photo of someone I know." As mentioned previously, the Moment Machine was tested in settings where displays were already running scheduled content. As interviewees from L01 point out "[we] will now pay more attention to the screen… [because we] expect to see images of people from Leytonstone [where they are residents] and our friends from Walthamstow." Similar comments were received from W31 who was commenting on people in the images "I know him… he lives there… he has a store…" Seeing images of people from the locality can bring up community awareness, i.e., who is around the neighborhood. This was explicitly stated by L05 and L13. However this type of communication can go even further and target individuals. For example, when capturing the moment W29 made a heart symbol with his hands. When asked why he did it he said that it is a sign between him and his girlfriend who was at work.

Another reason for taking the images would be getting "5 minutes of fame". This is best captured by tongue-in-cheek shouting from two young girls "We are going to be famous!" Similarly, while a girl from L19 was taking a picture a man passing-by stated "Look, you're famous!" when he saw her picture on a display. Also, L16 stated that she likes that people can see her, while W17 was fascinated that people can see him at Leytonstone. Another benefit from capturing the moments outside would be to actually spend time in the physical environment. As L13 points out "Kids these days spend too much time in front of the computer, this might get them to play outside." Mashing of images/moments from the 2 locations can lead to universal connections, or "universality" as stated by L15. She liked the universality of the machine and that everyone can get connected and mashed through the Moment Machine.

In general people were interested in seeing images from the "other" location, thus reflecting the need for discovery of new features and places [START_REF] Memarovic | Using Public Displays to Stimulate Passive Engagement, Active Engagement, and Discovery in Public Spaces[END_REF]. For example, the two people from L01 showed their interest in the Moment Machine application because they were from Leytonstone and had friends in Walthamstow. However, W11 from Walthamstow said that "[I] know the place [Leytonstone]. I don't know the people who live there." Because he did not know people from Leytonstone he was indifferent to seeing images from it. This shows that displays could connect to locations where users have friends/family/acquaintances, e.g., by harvesting a Facebook profile form users in the display vicinity.

While some people wanted to get more information from the other location, e.g., a live video feed (L09), others (W29) were concerned with this stating "I don't want just to spy on others through a website which connects me to cameras" and favored the asynchronous connection through images which allowed them to browse on their own.

Where Should the Images Appear

While most of the participants were comfortable to take the photo and leave it on displays, some wanted to know where will the image appear before taking the photo asking "Is it gonna stay here?" (L17, W14)

When we asked the participants where else would they like to see the images we received two types of answers: (1) either seeing them on a Facebook page, email, or dedicated website (18/26 participants) or (2) leaving the images to stay on the display (8/26 participants). Some of the participants did not see the point of leaving the image on the network unless they could "take" the moment with them. This is best captured by L14 who asked for her image to be removed since she could not take it with her. Interesting insight is also offered by L17 who wanted to get a printout of her photothis was preferred method over email. In essence this finding points out that networked public screens maybe need to be better connected with users "communicative ecology" [START_REF] Memarovic | Designing "interacting places" for a student community using a communicative ecology approach[END_REF], i.e., with current information and communication technologies such as Facebook and email.

On the other hand we also had participants who were satisfied with having the images appearing across the network, i.e., they did not want them to appear anywhere else: "absolutely not" stated L15 when asked if the images should appear somewhere else. She liked that the images are staying at the "machine" as they are "just capturing moments of everyday life."

Challenges in Promoting and Sustaining Use

One of the most prominent challenges in having people interested in interacting with the Moment Machine was scalability, i.e., the number of displays deployed in the urban space that run it (L07, W13, W34, W36). For example W13 points out that there are only two locations now that have this type of application while W36 stated that networked screens have to have a bigger scope and purpose. Some of the challenges are posed by the urban environment that changes during the day. The research team noticed that when it was too bright it was hard to notice the video feed and participants had difficulties in understanding what is wrong and where they should position themselves to take the photo. Additional problems with positioning can be caused by camera placement. For example, some of the participants at Walthamstow had problems in positioning themselves to take a desired snapshot, e.g., a portrait. The camera used for photo taking was attached to the right side of the screen so if participants wanted to take a portrait they would have to look at the camera. However, some participants found this difficult and looked at the live video feed instead. Similar problems can be caused by the positioning of the screen itself. In order to make the user interface reachable to kids we intentionally made the buttons a bit lower. At Leytonstone the display is positioned a bit higher and both kids and adults did not report any problems interacting with it. However, W31 at Walthamstow commented that it is not comfortable to bend down in order to browse the photos.

Although the purpose of the application was clear to most of the participants, some had difficulties and questions regarding its purpose (L09, W26, W31, W34). A possible solution for this challenge would be to have a more obvious message on ta display, e.g., "Capture your daily moment" or "Strike a pose for the world!" Finally some of the participants mentioned that the Moment Machine could benefit from adding new features (L09, W31, W33, W34). Some of the suggested features are relatively easy to add, e.g., adding the number of overall images that were taken (W31) while others are more sophisticated, e.g., adding image manipulation and ability to play with the background image (L09, W34). Adding new features could lead to users staying interested in the application, as suggested by Memarovic et al. [START_REF] Memarovic | Using Public Displays to Stimulate Passive Engagement, Active Engagement, and Discovery in Public Spaces[END_REF].

Conclusions

In this study we used technology probe based approach to understand how posting situated snapshots on networked public displays could be beneficial for place-based communities. For this purpose we designed and developed the Moment Machine application and conducted 6 user trials "in the wild" at 2 locations in London. Our findings from observing 71 people interacting with the Moment Machine and conducting 55 interviews are promising and show that networked public displays can be used by local community members to capture images "on the go." In this paper we reported on (1) potential motivation for and effects of posting situated snapshots onto networked public displays, [START_REF] Clinch | Reflections on the long-term use of an experimental digital signage system[END_REF] where the images could be displayed once they are taken, and (3) challenges in promoting and sustaining their use.

Fig. 1 .

 1 Fig. 1. The Moment Machine: a) user interface and b-c) passers-by interacting with it.

Acknowledgments

The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 244011, the EPSRC-funded project "Exploring the potential of networked urban screens for communities and culture" under the grant agreement no. EP/I031839/1, with the support of UCL VEIV center. We would also like to thank professor Marc Langheinrich for his useful comments on the early version of the paper and "Screens in the Wild" members for invaluable contribution.


Luz Rello
email: luzrello@acm.org

Susana Bautista
email: subautis@fdi.ucm.es

Ricardo Baeza-Yates

Pablo Gervás
email: pgervas@sip.ucm.es

Raquel Hervás
email: raquelhb@fdi.ucm.es

Horacio Saggion
email: horacio.saggion@upf.edu

One Half or 50%? An Eye-Tracking Study of Number Representation Readability

Keywords: textual accessibility, dyslexia, user testing, eye-tracking, readability, comprehension, number representation

Are numbers expressed as digits easier to read and understand than written with letters? What about fractions and percentages? Exact or rounded values? We present an eye-tracking study that attempts to answer these questions for Spanish, using fixation and reading time to measure readability as well as comprehension questions to score understandability. We find that digits are faster to read but do not help comprehension. Fractions help understandability while percentages help readability. No significant results were found concerning the influence of rounding. Our experiments were performed by 72 persons, half of them with dyslexia. To the best of our knowledge, this is the first study that addresses the cognitive load of number representation in any language, even more for people with dyslexia.

Introduction

Worldwide, around 15-20% of the population has a language-based disability; where 70-80% of it is likely dyslexic [START_REF]Definition of dyslexia[END_REF]. Some of the these disabilities make more difficult the comprehension of texts written for a generic public. For this reason, United Nations [START_REF] Nations | Standard Rules on the Equalization of Opportunities for Persons with Disabilities[END_REF] recommend that all public information services and documents should be accessible to the widest possible readership. Given this, there are different initiatives that propose guidelines to help rewriting a text to make it more comprehensive. Some of them are Plain Language1 and the European Guidelines for the Production of Easy-to-Read Information [START_REF] Freyhoff | European guidelines for the production of easy-to-read information for people with learning disability[END_REF].

In addition, a large percentage of information expressed in daily news or reports contain numerical expressions (economical statistics, demographic data, etc.), but many people have problems understanding complex expressions, including non-native speakers, and people with limited education or some kind of social or cognitive disability, such as dyslexia. Numerical information can have different representations such as: using digits or words, rounded numbers or decimals, fractions instead of percentages, etc. According to cognitive studies, numbers in a text are processed in a different way than words [START_REF] Dehaene | Varieties of numerical abilities[END_REF], and the presence of numbers in the text impacts the reading process [START_REF] Mccloskey | Cognitive mechanisms in number processing and calculation: Evidence from dyscalculia[END_REF].

Dyslexia is a neurological reading disability characterized by difficulties with accurate and/or fluent word recognition and by poor spelling and decoding abilities [START_REF] Vellutino | Specific reading disability (dyslexia): What have we learned in the past four decades[END_REF]. Depending on the language, the estimation of the prevalence of dyslexia varies from 10-17.5% for the population in the U.S.A. [START_REF]Learning Disabilities: A Report to the U.S. Congress[END_REF] to 8.6-11% for the Spanish speaking population [START_REF] Carrillo | Evaluación de la dislexia en la escuela primaria: Prevalencia en español (Evaluation of dyslexia in primary school: The prevalence in Spanish)[END_REF][START_REF] Jiménez | Prevalencia de las dificultades específicas de aprendizaje: La dislexia en español (the prevalence of specific learning difficulties: Dyslexia in Spanish)[END_REF][START_REF] Rello | The presence of English and Spanish dyslexia in the Web[END_REF]. People with dyslexia find problems to recognize and recollect not only letters but also numbers [START_REF] Cohen | Number words and number non-words: A case of deep dyslexia extending to Arabic numerals[END_REF][START_REF] Newell | The use of lexical and spelling aids with dyslexics[END_REF]. Although dyscalculia 2 and dyslexia are two different disabilities, they are comorbid [START_REF] Landerl | Dyslexia and dyscalculia: two learning disorders with different cognitive profiles[END_REF] 3 and people with dyslexia are more likely to have Math learning difficulties [START_REF] Landerl | Developmental dyscalculia and basic numerical capacities: A study of 8-9-year-old students[END_REF]. For this reason we are particularly interested in studying how the complexity of numerical expressions affects the comprehension of a text.

In this context, the main goal of this paper is to study how number representation impacts text readability and understandability for native Spanish speakers with or without dyslexia. Readability refers to the legibility of a text, that is, the ease with which text can be read, while understandability refers to comprehensibility, the ease with which text can be understood. With this goal in mind, we conducted three experiments with 72 persons (36 with dyslexia) using eye-tracking and comprehension questionnaires. From our results we can quantify the impact of numerical expressions in the reading process for people with or without dyslexia, and it is possible to apply this information to the adaptation of numerical information so texts are more accessible to the widest number of readers.

To the best of our knowledge, this is the first time that numerical representations are measured in terms of readability and comprehension using our methodology. Therefore, this paper presents three main contributions:

• The first analysis of how numerical information impacts text readability and understandability for people with or without dyslexia using a methodology that includes eye-tracking and comprehension questionnaires.

• Numerical information represented as digits improve readability for people with dyslexia. • Numerical information represented as percentages improve readability for people with dyslexia.

The rest of the paper is organized as follows. Section 2 covers the related work. In Section 3 we present the details of the experimental methodology. Section 4 presents our results and Section 5 discusses them. Conclusions and future work are drawn in Section 6. Finally, in the Appendix, the data used are presented.

Related Work

Experimental psychology and cognitive neuropsychology have dealt with the study of number processing and calculation over the last two decades. Many researchers have studied the cognitive processes that are responsible for number processing and calculation, with the goal of contributing to the improvement of teaching and learning processes. For example, [START_REF] Herrera | ¿Cómo leemos los números? (How we read numbers?)[END_REF][START_REF] Salguero | El procesamiento de los números y sus implicaciones educativas (Number processing and its educational implications)[END_REF] present findings about how the frequency of use of a word or number is an influential variable in the reading process. In addition, it seems that numerical expressions most frequently used require less time for recognition. Researchers in psychophysics [START_REF] Rayner | Eye movements in reading and information processing: 20 years of research[END_REF] have also studied various aspects of reading: impact of text context on readability and eye movements during reading, among others. When numerical expressions are expressed in digits there is a faster access to its semantic representation than when expressed in words [START_REF] Damian | Asymmetries in the processing of Arabic digits and number words[END_REF][START_REF] Fias | Two routes for the processing of verbal numbers: Evidence from the snarc effect[END_REF][START_REF] Fias | The importance of magnitude information in numerical processing: Evidence from the snarc effect[END_REF][START_REF] Ito | Semantic processing of Arabic, Kanji and Kana numbers: Evidence from interference in physical and numerical size judgments[END_REF].

From experimental psychology there is evidence regarding the importance of the frequency of use of numerical expressions. For example, Brysbaert [START_REF] Brysbaert | Arabic number reading: On the nature of the numerical scale and the origin of phonological recoding[END_REF] investigated number processing by looking at reading time using eye-tracking and showing that subjects have longer eye fixations with more frequently used numbers.

Overall, it is a generally accepted hypothesis that the probability of making a fixation on a particular linguistic unit is determined by the perceptual or informational relevance of the unit, and the degree of difficulty of processing required for its identification. Due to the quantitative nature of this measure, it is not easy to unravel what are the specific reasons justifying the preference for fixations on certain kinds of linguistic units. Thus, the visual processing of words has been shown to be affected significantly by factors such as length, frequency, type of vocabulary, predictability, or word ambiguity [START_REF] Rayner | Lexical complexity and fixation times in reading: Effects of word frequency, verb complexity, and lexical ambiguity[END_REF].

There is an extensive body of knowledge that takes into consideration eye movements of readers with dyslexia using eye-tracking. While some found differences among people with or without dyslexia [START_REF] Eden | Differences in eye movements and reading problems in dyslexic and normal children[END_REF], others did not [START_REF] Stanley | Eye-movements and sequential tracking in dyslexic and control children[END_REF]. Hyönä et al. [START_REF] Hyönä | Eye fixation patterns among dyslexic and normal readers: Effects of word length and word frequency[END_REF] studies the effect of word length and word frequency in relation with eye fixation patterns. Their results show that low frequency and long words present longer gaze durations and more re-inspections although in [START_REF] Rello | Frequent words improve readability and short words improve understandability for people with dyslexia[END_REF] only more frequent words presented significantly shorter fixation durations. However, we found no previous work that investigates numerical representations in readers with dyslexia using eyetracking, nor for people in general. In fact, it is the first user evaluation of numerical representations.

Currently there is plenty of automatic text simplification research based on cognitive aspects. The main objectives are to identify simplification operations that can be applied to adapt a text using some kind of automatic means. Most of the text simplification approaches disregard the treatment of numerical expressions [START_REF] Bott | Can Spanish be simpler? LexSiS: Lexical simplification for Spanish[END_REF][START_REF] Carroll | Practical simplification of English newspaper text to assist aphasic readers[END_REF] except from [START_REF] Bautista | A system for the simplification of numerical expressions at different levels of understandability[END_REF] that is a numerical expressions simplification system designed on the basis of corpus analyses [START_REF] Bautista | Análisis de la Simplificación de Expresiones Numéricas en Español mediante un Estudio Empírico (Analysis of the Simplification of Numerical Expressions in Spanish through an Empirical Study)[END_REF][START_REF] Drndarevic | Automatic text simplification in Spanish: A comparative evaluation of complementing components[END_REF]. However, to the extent of our knowledge there are no user evaluations regarding the impact of simplifying numerical expressions as the one we present in this paper.

Methodology

We designed three different experiments to study the effect of different representations of numerical expressions with respect to readability and understandability. In the experiments, 72 participants (36 with dyslexia) had to read several texts in Spanish with different representations of numerical expressions. We tested the following hypotheses:

• H1.1: Readability will increase if digits are used instead of words for representing numerical expressions. • H1.2: Understandability will increase if digits are used instead of words for representing numerical expressions. • H2.1: Readability will increase if rounded numerical expressions are used instead of unrounded expressions (with decimals). • H2.2: Understandability will increase if rounded numerical expressions are used instead of unrounded expressions (with decimals). • H3.1: Readability will increase if numerical expressions are expressed in percentages instead of fractions. • H3.2: Understandability will increase if numerical expressions are expressed in percentages instead of fractions.

Design

In the first experiment, Digits vs. Words, the independent variable [±digits] had two levels: [+digit] denotes the condition where numbers in the text were written in digits, i.e. 22, and [-digit] denotes the condition where numbers were written using words, i.e. veintidos ('twenty two').

In the second experiment, Rounding vs. Decimals, the independent variable [±round] had again two levels: [+round] denotes the condition where numbers were rounded, without decimals i.e. 19 and[-round] denotes the condition where numbers in the text were written with decimals i.e. 19.45. In the third experiment, Percentages vs. Fractions, the independent variable [±percentage] also had two levels: [+percentage] denotes the condition where numbers in the text were written using percentages, i.e. 25% and [-percentage] denotes the condition where numbers in the text were written using fractions i.e. 1/4.

The experiment followed a within-subjects design, so every participant contributed to each of the conditions in the experiments. The order of conditions was counterbalanced to cancel out sequence effects. To measure understandability and readability, we measured fixation duration and the correct answers from the questionnaires, respectively. Sometimes both terms, readability and understandability, have been used interchangeably. However, previous research with people with dyslexia has shown that both concepts need to be taken into consideration separately. For instance, in [START_REF] Rello | Lexical quality as a proxy for web text understandability[END_REF] comprehension has been found to be independent of readability for people with dyslexia, while text readability can be used as an indicator of comprehension for people without dyslexia. Therefore, in this study we distinguish between readability and understandability.

Fixation Duration. When reading a text, the eye does not move contiguously over the text, but alternates saccades and visual fixations, i.e. jumps in short steps and rests on parts of the text. Fixation duration denotes how long the eye rests still on a single place of the text. Fixation duration has been shown to be a valid indicator of readability. According to [START_REF] Just | A theory of reading: From eye fixations to comprehension[END_REF][START_REF] Rayner | Lexical complexity and fixation times in reading: Effects of word frequency, verb complexity, and lexical ambiguity[END_REF][START_REF] Sereno | Measuring word recognition in reading: eye movements and event-related potentials[END_REF], shorter fixations are associated with better readability while longer fixations can indicate that processing loads are greater. Hence, we use fixation duration across the whole text as measure to quantify readability.

Correct Answers.

To measure text comprehension we used questionnaires, one per text. We used multiple-choice questions with three possible choices, one correct and two incorrect. From these answers, we computed the percentage of correct answers, where the correct choice scored 100% and the others 0%.

Participants

Seventy-two Spanish native speakers undertook the experiments, 36 without dyslexia (group N) and 36 with dyslexia (group D). Their ages ranged from 16 to 50, with a mean age of 26.94 for group N and 23.38 for group D. All the participants were asked to bring their dyslexia diagnosis to the experiment. Except from 3 participants with dyslexia and 2 without who had no higher education, the rest were attending school or high school (17 participants with dyslexia and 13 participants without dyslexia) or were studying or had already finished university degrees (16 participants with dyslexia and 21 participants without dyslexia).

Materials

To study the effects of numerical expressions we need to study target numerical expressions in context, i.e. as part of a text. To isolate the effects of these variables, the texts need to be comparable in complexity. In this section, we describe how we designed the texts and the target numerical expressions that were used in this study.

Base Texts. As basis for our manipulations, we created six texts with an average length of 62.33 words. To meet the comparability requirements among the texts belonging to the same experiment, we took into account the parameters that different complexity measures take into consideration [START_REF] Drndarevic | Towards automatic lexical simplification in Spanish: an empirical study[END_REF]. Next, we present the characteristics shared by the texts in each experiment: The presentation of the text has an effect on reading speed so we used the same layout for all the texts. We chose a recommended font type for reading in a screen, sans serif arial, a large size (20 points) and 62 characters/column and unjustified text and recommended color and brightness contrast using a black font with crème background [START_REF] Al-Wabil | Web navigation for individuals with dyslexia: an exploratory study[END_REF][START_REF] Rello | Layout guidelines for web text and a web service to improve accessibility for dyslexics[END_REF]. 4Target Numerical Expressions. For the numerical expressions we used the following criteria:

(a) We chose pairs of numerical expressions denoting the same number because the frequency of the number expressed has an impact on its processing time [START_REF] Herrera | ¿Cómo leemos los números? (How we read numbers?)[END_REF][START_REF] Salguero | El procesamiento de los números y sus implicaciones educativas (Number processing and its educational implications)[END_REF]. Therefore the same numerical expressions with different representation were chosen for the three experiments. (b) We did not include ambiguous numerical expressions because they require more processing than unambiguous ones [START_REF] Rayner | Lexical complexity and fixation times in reading: Effects of word frequency, verb complexity, and lexical ambiguity[END_REF]. For instance, depending on the context cien ('hundred') could also mean "very fast" in Spanish i.e. Estoy trabajando a cien ('I am working very fast') and Las manzanas están a cien ('The apples cost one hundred'). (c) We did not used orthographically similar numerical expressions, (i.e. mirror numbers '6' and '9') in the same text since such representations can be a major difficulty for people with dyslexia [START_REF] Ellis | Reading, writing and dyslexia[END_REF]. (d) In the experiment Digits vs. Words, we selected different numerical expressions, i.e., with decimals, rounded, two or three digits and percentages (see the Appendix for the data used).

(e) In the experiment Rounding vs. Decimals, we rounded the original numbers, always using modifiers when there was a loss of precision, i.e. un poco ('a little'), casi ('almost'). (f) In the experiment Percentages vs. Fractions, we selected frequently occurring percentages and their corresponding fractions Comprehension Questionnaires. Each questionnaire is composed by two items, one inferential question i.e. to be answered correctly the question requires a deep understanding of the content of the text) and one question about details of the text which were expressed using a numerical expression. For each text there were two comprehension questions. The first was about the overall content of the text and the second was about the numerical part of the text. The later question always was phrased with the same number representation that was used in the text. Two examples, an inferential question (i) and a question devoted to details (ii) are given in Figure 1. Preference Questionnaires. Each participant performed a questionnaire with 20 questions that were rated using a 5 level Likert scale. For 10 of the statements the participant was asked about how easy was to read the text, that is, readability, while for the other 10 statements the participant was asked about how easy was to comprehend the text, that is, understandability. Each of the statements contained a numerical expression, using one of the following representations: rounded, unrounded, percentage and fractions, where 8 were written in words and 12 in digits. In the Appendix we present the set of numerical expressions used.

Equipment

The eye tracker used was the Tobii T50 [START_REF]Product description Tobii 50 Series[END_REF] that has a 17-inch TFT monitor with a resolution of 1024x768 pixels. The eye tracker was calibrated for each participant and the light focus was always in the same position. The distance between the participant and the eye tracker was constant (approximately 60 cm. or 24 in.) and controlled by using a fixed chair.

3.5

Procedure

The sessions were conducted at Universitat Pompeu Fabra and they lasted from 20 to 30 minutes, depending on the participant. In each session, the participant was alone with the interviewer in the quiet room prepared for the study, performing the following three steps. First, we began with a questionnaire designed to collect demographic information. Second, we conducted the experiments that were recorded using eye-tracking. Out of the 72 participants, 40 participated in the experiment Digits vs. Words (20 D, 20 N) and 32 carried out the Rounding vs. Decimals experiment (16 D, 16 N). Finally, The experiment Percentages vs. Fractions was carried out by 32 participants (16 D, 16 N) who had already participated in either the first or the second experiment, were not tired of reading, and were willing to read more. The participant was asked to read the texts in silence and to complete the comprehension tests. Third, we carried out a user preferences survey.

Results

In this section we present the analysis of the results of the eye-tracking and comprehension tests. The measures used for the comparison of the text passages were the means of the fixation duration, the total duration of reading, and the correct answers.

In order to test our hypotheses, differences between groups and conditions were tested by means of (Bonferroni-corrected) Student's t-tests. Shorter fixations are preferred to longer ones because faster reading is related to more readable texts [START_REF] Williams | Experiments with discourse-level choices and readability[END_REF]. We compare readability with understandability through the inferential items of the comprehension questionnaires.

First, we study the differences between both groups. Then, we analyze the impact of the different numerical expressions in readability and understandability.

Digits vs. Words

We did not find statistical significance in readability (p < 0.444) for group N (see Table 1). However, we found statistical significance for readability in group D taking into account the mean of fixation time (p < 0.054). This result supports our H1.1 hypothesis.

No statistical significance was found for both groups. Hence we reject hypothesis H1.2 (p < 0.241 for group N and p < 0.269 for group D).

Rounding vs. Decimals

We reject hypothesis H2.1, since we did not find statistical significance in readability in group N (p < 0.867) nor in group D (p < 0.685) when reading texts with rounded numerical expressions taking into account the mean of fixation time (see Table 2).

We also refute H2.2 because we did not found statistical significance for understandability in both groups (p < 0.310 in group N and p < 0.695 in group D).

Percentages vs. Fractions

We did not find statistical significance in readability for group N (p < 0.462) taking into account the mean of fixation time (see Table 3). However, our results confirm H3.1 because we found statistical significance for readability in group D (p < 0.046) when reading texts with numerical expressions in percentages. This group reads faster texts with expressions in percentages than texts with numerical information in fractions.

On the other hand, we reject H3.2 because we did not found statistical significance results for understandability in both groups (p < 0.170 for group N and p < 0.474 for group D, see again Table 3.

Survey

We found a high Pearson correlation of 0.95 between the answers of both groups. Therefore, groups N and D generally agreed in their answers with respect to readability and understandability. In Figure 2 we show the histograms of the survey results. Then, we calculated the standard deviation for all the statements. For the readability answers the standard deviation was significantly higher in group D (μ = 1.20 seconds, s = 0.41) than in group N (μ = 0.87 seconds, s = 0.46), with p = 0.007. This means that participants with dyslexia had a higher variability in their ratings. For the understandability answers, we found no significant difference between groups in their standard deviation (p = 0.157) for group D (μ = 1.04 seconds, s = 0.44) and for group N (μ = 0.89 seconds, s = 0.37). Digits vs. Words. Participants significantly found numbers written in digits more readable than in letters (p < 0.001) as well as more understandable (p < 0.001). We also found significance within groups for readability (p < 0.001 in group D and p < 0.001 in group N) and understandability (p < 0.001 in group D and p = 0.014 in group N).

Rounding vs. Decimals. We did not find statistical significance for readability between rounded and unrounded numbers (p = 0.272) nor for understandability (p = 0.446). No significant differences were found within groups for readability (t(53.937) = 0.479, p = 0.634 in group D and p = 0.111 in group N) and understandability (p = 0.163 in group D and p = 0.888 in group N).

Percentages vs. Fractions. Participants significantly found percentages more readable than fractions (p < 0.001) as well as more understandable (p < 0.001). We also found significance within groups for readability (p < 0.001 in group D and p < 0.001 in group N) and understandability (p < 0.001 in group D and p < 0.001 in group N).

Discussion

With respect to differences between the use of digits and the use of numerical expressions in words, results indicate a statistically significant improvement in performance for readability in people with dyslexia when digits are employed. In contrast, in group N, we found no significant differences. This agrees with the fact that numerical expressions described using words require a longer number of words and/or characters in comparison with the corresponding versions using digits. Overall length is an already known parameter that creates difficulties for people with dyslexia, so the reduction in length involved in phrasing a number in digits should make it easier to read for them. Results for understandability in experiment digits vs. words are not statistically significant for both groups.

With respect to differences between the use of rounded and unrounded numbers, none of the differences found are statistically significant. Rounding numbers even with modifiers such as "around" or "almost" did not have the expected effect in our experiments.

With respect to differences between the use of percentages and fractions, there is a statistically significant increase in readability for group D when percentages are used instead of fractions. In contrast, no differences were found for group N. Again, results for understandability are not statistically significant in either case. There is an apparent contradiction in that for group D percentages seem to be easier to read but more difficult to understand. A possible explanation might be related to the nature of these expressions. From a conceptual point of view, both percentages and fractions convey the relative proportion between two quantities: the value of the percentage and 100 in the case of percentages, and the value of the numerator and the value of the denominator in fractions. However, the reference value in the case of percentages is implicit (or conveyed by the % sign). This implies that for fractions, two quantities have to be read, whereas only one needs to be read for percentages. This may account for the comparative ease for group D of reading percentages (only one quantity to read) vs. fractions (two different quantities to read). Participants that took this experiment did it because they were not tired and still willing to read more. In most cases participants with dyslexia were adults, and as such they have reading skills that are similar to adults without dyslexia. Note that fixation duration for these participants is shorter when reading percentages. More over, the percentages used in the texts were the most commonly used (see Appendix) and the more frequent the word, the shorter the eye fixation [START_REF] Hyönä | Eye fixation patterns among dyslexic and normal readers: Effects of word length and word frequency[END_REF].

The standard deviations of the survey reveal that people with dyslexia made a greater difference between readability and understandability than people without dyslexia. For people without dyslexia, easier reading was correlated to text comprehension while participants with dyslexia dissociated these two elements, perhaps due do the nature of dyslexia, which affects reading but not comprehension of the language.

The higher variability of scores indicates that for people with dyslexia the representation of numbers has a much bigger impact on readability. However, the correlation of the answers of people with or without dyslexia is high. Hence, both groups generally agree in their rates with respect to readability and understandability.

The significant difference in the number representations of the survey for Digits vs. Words and Percentages vs. Fractions, are consistent with the quantitative data from the eye tracker where we found significant variations. Hence, the performance and the preferences of our participants with respect to these number representations are consistent.

6

Conclusions and Future Work

The presence of numerical information in a text impacts its readability. We have analyzed some of the different representations of numerical expressions in text to study their influence in the reading process of people with or without dyslexia. For each experiment our hypotheses have been tested and depending on the kind of numerical information for each group we have obtained different results.

The main contribution of this research is that numbers represented as digits instead of words as well as percentages instead of fractions improve readability of people with dyslexia.

These results may prove to be of value in providing empirical basis for the development or refinement of guidelines for the simplification of text. These guidelines exist in very general form [START_REF] Freyhoff | European guidelines for the production of easy-to-read information for people with learning disability[END_REF] and they are currently employed as reference in a number of efforts to improve accessibility of text for groups of users with special needs. An empirical grounding that correlates particular expressions with particular user groups would be a very positive contribution.

This work can motivate work on text simplification for textual accessibility regarding numerical expressions [START_REF] Bautista | How to Make Numerical Information Accessible: Experimental Identification of Simplification Strategies[END_REF][START_REF] Bautista | A system for the simplification of numerical expressions at different levels of understandability[END_REF][START_REF] Power | Generating numerical approximations[END_REF]. Also, these findings can have an impact on current interactive systems for people with dyslexia that modify the text presentation but not its content such as Claro ScreenRuler Suite [START_REF] Clarosoftware | [END_REF], SeeWord [START_REF] Gregor | Seeword: a personal word processing environment for dyslexic computer users[END_REF] or IDEAL e-Book reader [START_REF] Kanvinde | IDEAL: a dyslexic-friendly e-book reader (poster)[END_REF]. We plan to integrate these findings in DysWebxia 2.0 [START_REF] Rello | Dyswebxia 2.0!: Accessible text for people with dyslexia (demo)[END_REF], a tool that modifies text content and layout for people with dyslexia.

Another field in which these results can be expected to have an impact is that of the assessment of readability. In general terms, computational models for predicting readability of texts are used, like FOG [START_REF] Gunning | The technique of clear writing[END_REF], Flesch, Flesch-Kincaid [START_REF] Flesch | A new readability yardstick[END_REF], and SMOG [START_REF] Mclaughlin | Smog grading: A new readability formula[END_REF]. Current efforts along this line are considering a number of factors like average num-ber of characters per word and average syllables per word to predict a readability score, but include no specific account for numerical expressions. Based on the results presented here, an effort might be made to expand the set of features used in the assessment of readability to include numerical expressions.

Future work includes the evaluation of numerical representation of other target groups and other measures of readability. We also need to evaluate other representations for specific numerical expressions, for example to represent time.

  (a) They have the same number of target words: Seven [±digits] numerical expressions pairs for each of the texts in Digits vs. Words, seven [±round] expressions pairs for each of the texts in Rounding vs. Decimals, and four [±percentages] target numerical expressions in Percentages vs. Fractions. (b) They share the same genre and are about similar topics: fast food ingredients. (c) They contain the same number of sentences: three sentences in Percentages vs. Fractions and four sentences in the other two experiments. (d) The base texts of each experiment have the same number of words per text (39 words in Percentages vs. Fractions and 63 words for the other two experiments). (e) All the texts have a similar word length average ranging from 4.88 to 5.24 letters. (f) They do not contain named entities, foreign words, or numerical acronyms.

Figure 1 .

 1 Figure 1. Two examples of questions in the comprehension tests.

Fig. 2 .

 2 Fig. 2. Survey results for readability and understandability.

Table 1 .

 1 Experimental results for Digits vs. Words.

Table 2 .

 2 Experimental results for Rounding vs. Decimals.

Table 3 .

 3 Experimental results for Percentages vs. Fractions.

  67.857142857 57.14285714 16.07142857 19.64285714 64.28571429 67.857143 71.42857143 46.42857143 64.2857142857143 66.07142857 10.7142857142857 23.2142857142857 .571428571 3.703703704 3.57142857142857 1.851851852 23.2142857142857 22.2222222222222 10.714285714 11.11111111 19.64285714 18.51851852 7.142857143 11.111111 14.28571429 7.407407407 17.8571428571429 14.81481481 26.7857142857143 22.2222222222222 32.142857143 20.37037037 21.42857143 29.62962963 25 22.222222 28.57142857 51.85185185 33.9285714285714 31.48148148 32.1428571428571 33.3333333333333 55.357142857 59.25925926 19.64285714 35.18518519 67.85714286 55.555556 53.57142857 37.03703704 44.

	very well
	Understandibility	+Digit_Dys	+Digit	-Digit_ Dys -Digit	+Round_ Dys +Round		-Round_ Dys -Round	+Percentage_ Dys +Percentage -Percentage_ Dys -Percentage
	very bad		0 1.851851852 8.928571429 1.851851852		0 3.7037037	0	0	0 1.851851852 10.7142857142857 7.40740740740741
	bad normal well very well	1.7857142857 7.407407407 30.35714286 14.81481481		0 7.4074074 36428571428571	50 7.14285714285714 14.8148148148148
	1
	2
	3
	4
	5
			-Percentage -Percentage +Percentage +Percentage -Percentage +Percentage	28	28
			4	2	0		0	3	0 10.71428571	0
			6	7	0		2	6.5	1 23.21428571 3.57142857142857
			7	8	1		9	7.5	5 26.78571429 17.8571428571429
			9	9	8		11	9	9.5 32.14285714 33.9285714285714
			2	2	19		6	2	12.5 7.142857143 44.6428571428571	100	100 99.9999999999999
			-Percentage -Percentage +Percentage +Percentage -Percentage +Percentage	27	27
			2	2	0		1	2	0.5 7.407407407 1.85185185185185
			8	4	0		1	6	0.5 22.22222222 1.85185185185185
			6	6	2		6	6	4 22.22222222 14.8148148148148
			8	10	5		12	9	8.5 33.33333333 31.4814814814815
			3	5	20		7	4	13.5 14.81481481	50	100	100
	%						Readability
	75
	56
	38
	19
	0
		+Digit	+Digit	-Digit	-Digit +Round +Round -Round -Round +Percent. +Percent. -Percent. -Percent.
		D group N group D group N group D group N group D group N group D group N group D group N group
		I could read the text...	very bad	bad		normal	well	very well
	%						Understandability
	75
	56
	38
	19
	0
		+Digit	+Digit	-Digit	-Digit +Round +Round -Round -Round +Percent. +Percent. -Percent. -Percent.
		D group N group D group N group D group N group D group N group D group N group D group N group
		I could understand the text...	very bad	bad		normal	well	very well

http://www.plainlanguage.gov/

A specific learning disability involving innate difficulty in learning or comprehending arithmetic. It is akin to dyslexia and includes difficulty in understanding numbers, learning how to manipulate numbers, learning mathematical facts, and a number of other related symptoms[START_REF] Butterworth | Foundational numerical capacities and the origins of dyscalculia[END_REF]

].[START_REF] Bautista | How to Make Numerical Information Accessible: Experimental Identification of Simplification Strategies[END_REF] Comorbidity indicates a medical condition (in this case dyscalculia) existing simultaneously but independently with another condition (dyslexia).

The CYMK are crème (FAFAC8) and black (000000). Color difference: 700, Brightness difference: 244[START_REF] Rello | Layout guidelines for web text and a web service to improve accessibility for dyslexics[END_REF].

Acknowledgments

We thank Mari-Carmen Marcos for her assistance with the eye-tracker hardware, Martin Pielot for his help with statistics, and Jerónimo Bautista Velázquez for his help in distributing our experiments announcement among experts. The research of the first author was funded by the Spanish Ministry of Education and Science (Grant TIN2009-14560-C03-01) and the Catalonian FI scholarship program while the research of the second, fourth and fifth authors was funded by the Spanish Ministry of Education and Science (Grant TIN2009-14659-C03-01 Project), Universidad Complutense de Madrid and Banco Santander Central Hispano (GR58/08 Research Group Grant).

Appendix: Synonyms Pairs

Experiment 1: Digits vs. Words and Experiment 2: Rounding vs. Decimals (the set of target numerical expression used for each experiment are written in brackets, that is, [Digits / Words -Decimals / Rounding]).

Composición de una hamburguesa: El pan supone entre el [30% / treinta por ciento -18,53% / casi el 20%] y el [50% / cincuenta por ciento -29,57% / casi el 30%] del peso de una hamburguesa. La hamburguesa tiene un valor energético que oscila entre las [250 / doscientas cincuenta -297 / casi 300] y [300 / trescientas -398 / casi 400] kilocalorías. Un adulto con actividad moderada necesita en torno a [2.500 / dos mil quinientas -2.489 / unas 2.500] kilocalorías diarias, por lo que una hamburguesa a la semana no desequilibra ninguna dieta ni siquiera incorporándole un sobre de [11 / once -11,8 / casi 12] gramos de ketchup, que contiene [70 / setenta -70,8 / un poco más de 70] kilocalorías.

Composition of a burger:

The bread is between [30% / thirty percent -18.53% / almost 20%] and [50% / fifty percent -29.57% / almost 30%] of the weight of a hamburger. The burger has an energy value of between [250 / two hundred fifty -297 / almost 300] and [300 / three hundred -398 / almost 400] kilocalories. A moderately active adult needs about [2,500 / two thousand five hundred -2,489 / around 2.500] kilocalories a day, so a burger a week not even unbalanced diet incorporating any one of [11 / eleven -11 Numerical expressions used in the survey: 18.3%, menos de 1/5 ('less than 1/5'), menos del 20% ('less than 20%'), menos de un quinto ('less than a fifth'), menos de veinte por ciento ('less than twenty per cent'), más de 1/4 ('more than 1/4'), más del 25% ('more than 25%'), más de un cuarto ('more than a quarter'), más del veinte y cinco por ciento ('more than twentyfive per cent'), 27%, casi el 50% ('almost 50%'), menos de la mitad ('less than a half'), casi el cincuenta por ciento ('almost fifty per cent'), 48.6%, menos de 1/2 ('less than 1/2'), más de tres cuartos ('more than three quarters'), más del setenta y cinco por ciento ('more than seventy-five per cent'), 76.3%, más de 3/4 ('more than 3/4') and más del 75% ('more than 75%').