Improving the Service Quality of Public Transit with Exclusive Bus Lanes: A Perspective from Passenger Satisfaction

Exclusive bus lanes have been widely regarded as an effective way to promote bus priority and improve the service quality, while they have not attracted more passengers to travel by bus in China. Also, more attention is usually paid to the infrastructure and facilities of exclusive bus lanes, but not much attention is paid to the passenger satisfaction of public transit with them.)erefore, this paper studies how to improve the service quality of public transit with exclusive bus lanes from a perspective of passenger satisfaction. A Structural Equation Model (SEM) was developed to investigate the mechanism of relationships between passenger satisfaction and the factors influencing the service quality of public transit with exclusive bus lanes. A total of 2087 respondents from Shanghai, China, participated in this study. Also, a comparison model of different groups using public transit including captive riders, choice riders, and captive by choice riders was established. Results show that passengers were dissatisfied with the current service of public transit with bus lanes, while they would prefer to take buses in the near future. In addition, travel environment, facilities, and convenience, rather than operational efficiency, had significant effects on passenger satisfaction. )rough the comparisonmodel, it was found that choice and captive by choice users might prefer public transit with bus lanes and captive users might be unable to bear the financial burden of private motorized travel. “Crowdedness in the buses on bus lanes during peak hours” especially for choice riders and “driving stability” especially for captive riders were the improvement direction for attracting more passengers to travel by bus. )e results and the proposed policies of this study can benefit for the planning and operations of exclusive bus lanes in Shanghai and other similar cities around the world.

Introduction
Public transit has been considered as an effective way to reduce urban traffic congestion and pollution emissions. e Chinese government has long been committed to giving priority to the development of public transit. Among many initiatives, the construction of exclusive bus lanes is a sustainable strategy. Exclusive bus lanes in China are a part of the road which are intended to be used only by buses, and regular vehicles cannot drive on bus lanes during peak hours. Exclusive bus lanes can improve the bus speed [1], reveal significant safety benefits by reducing the quote of crashes [2], and lessen the impact of urban congestion on public transport, so as to promote bus priority and improve the service quality of public transit. Furthermore, exclusive bus lanes can help buses pass congested traffic quickly so that people commuting by car are expected to shift to commute by bus. Although a number of exclusive bus lanes have been constructed in China, they have not significantly benefitted the ridership of public transit and have not attracted much more passengers to travel by bus as expected [1]. It indicates that we do not know why the advantages of exclusive bus lanes cannot attract more people to travel by bus and what bus passengers really care about in terms of the service quality of public transit with exclusive bus lanes.
Meanwhile, during the construction of exclusive bus lanes, planners and transit operators usually pay more attention to the traditional indicators related with infrastructure construction and operation effect and not much attention to the passenger experience for bus lanes [3][4][5]. For instance, Shanghai authorities set the goal of the length of bus lanes in the related policy documents [6] without considering the service quality and passenger satisfaction of bus lanes. However, public transit users' satisfaction is strongly connected with their future behaviour and then affects the public transit market. When transit department aims to increase bus ridership through bus lanes, improvements in passenger satisfaction towards public transit with bus lanes are considered important for increasing the attractiveness of public transit [7].
Since passengers' demands for service quality of public transit with exclusive bus lanes are not clear and the passengers' feelings are not considered in the planning and construction of bus lanes, exclusive bus lanes do not play their role in attracting more people to travel by bus. Also, different types of passengers have their own evaluation standards for satisfaction and demands for the public transit system, and the user heterogeneity needs to be considered. erefore, it is necessary to find the points where passengers are really concerned to improve the service quality of public transit with exclusive bus lanes and formulate corresponding measures and strategies especially applied to bus lanes, so as to make bus lanes play their role more effectively.
is paper studies how to improve the service quality of public transit with exclusive bus lanes from a perspective of passenger satisfaction. A passenger satisfaction survey was conducted along sixteen main exclusive bus lanes in Shanghai, China, to obtain the data. A Structural Equation Model (SEM) approach was developed to investigate the mechanism of relationships between passenger satisfaction and the factors influencing the service quality of public transit with exclusive bus lanes. Satisfaction of captive riders (users who had no car and depended on public transit), choice riders (car owners who travelled by bus), and captive by choice riders (users who chose to travel by bus but could own a car) were compared. Based on the relationships between variables, policies related to exclusive bus lanes and public transit were proposed to the government and operators.
e main focus of this study is to explore the influential factors of passenger satisfaction of public transit with exclusive bus lanes and to help improve service quality of public transit with exclusive bus lanes not only to maintain the market share but also to attract more passengers to travel by bus. e study provides three contributions. First, we try to find the factors possibly to influence the passenger satisfaction of public transit with exclusive bus lanes and use the SEM approach to investigate the mechanism of relationship between different influential factors of passenger satisfaction. Second, we consider the user heterogeneity and study the difference of passenger groups for making different strategies.
ird, we provide constructive suggestions for improving the bus service quality on bus lanes. e rest of the paper consists of the following parts: Section 2 reviews the previous literatures. In Section 3, variables and hypotheses, the Structural Equation Model methodology, and calculating method of index score for measuring variable relationships are introduced. Section 4 introduces the designed survey and the collected data. In Section 5, the Structural Equation Model is built and the results are analysed. e discussion is given in Section 6. Section 7 presents the conclusions and future work.

Literature Review
For a long time, researchers have focused on public transit and exclusive bus lanes. e previous studies have made many efforts for improving bus service quality considering passenger experience and feelings and better planning and construction, design, and signal control of exclusive bus lanes. Also, the user segmentation is an important research topic for policy-making in the public transit market.

Research on Exclusive Bus Lanes.
Research on exclusive bus lanes focused on planning and construction from a macro perspective and traffic design and signal control from a micro perspective.
From the macro perspective, researchers mostly analysed the conditions and effectiveness of bus lanes through indicators related to public transit and clarified the implementation strategies of bus lanes. A series of methods were used to discuss the bus lane capacity [8], the construction conditions [9], the effectiveness evaluation [10,11], and the related environment and safety issues [2,12]. ese studies contributed to answering the following questions: Under what conditions is there a need to set up a bus lane? How can we evaluate the operation effect of bus lanes? How can we calculate the capacity of bus lanes? Can bus lanes improve the traffic environment and safety?
From the micro perspective, the design of bus lanes received great attentions due to the significant impacts of bus lanes on traffic flows and signal control. e related studies and methods included the bus lane design guides [13,14], the mathematical model formulation [15,16], and the simulation and optimization tools [17]. ese studies provided a lot of modelling methods to optimize the signal control strategy of bus lanes and then used one bus lane or several bus lanes in a small region for empirical analysis.
ese studies were very helpful to increase the bus speed on bus lanes and reduce passengers' travel time.

Research on Service Quality of Public
Transit. Bus service quality considering passenger experience and feelings is also an important research topic. e variables to assess the bus service quality were related to infrastructure and operations, for example, bus operation mileage, bus speed, and waiting time at stations, as well as passenger-oriented measures such as the coverage, comfort, cleanliness, and safety [18][19][20]. de Oña et al. [21] illustrated that the observed variables, including frequency, punctuality, speed, proximity, fare, and information, had the greatest influence on the overall bus transit service quality of Granada, Spain. Shiftan et al. [22] explored the intrinsic mechanism that influenced public transit loyalty in Israel. ey assumed that transportation mode choice involved emotional dependence gradually turning to alternative options and inserted a new latent variable to reflect passengers' hedonic value and uncovered how emotional dependence affected public transit loyalty. e variables related to the service quality of public transit in these studies had differences, but they generally described the aspects of operation, safety, environment, fare, comfort, and so on [23]. ere are standardized ways to assess service quality of public transit [24], but there are no common ways to assess passengers' satisfaction of public transit. e factors used to account for the objective are nearly different from each other, since the relationships between service quality and passenger satisfaction are complex. erefore, most of the variables are applicable to assess the service quality on bus lanes, but the variables in more aspects should be needed to describe passenger satisfaction with bus lanes. ese proposed variables were used to study service quality of public transit through a variety of comprehensive methods. ey included using the impact score to evaluate the service quality of public transit [25] and adopting the "SERVQUAL" method to evaluate the service quality in public transport, which was originally applied in retail banking, credit card services, repair and maintenance of electrical appliances, long-distance telephone services, and title brokerage [26]. In addition, the Structural Equation Model (SEM), which has been widely used in various fields [27,28], was used to account for the relationship between service quality and passenger satisfaction. Allen et al. [29] presented a full Structural Equation Multiple Indicators and Multiple Causes (SEM-MIMIC) model, which corrected for heterogeneity in the perceptions of users regarding satisfaction with the various service attributes, with the overall service, and with loyalty. Some researchers studied the bus service quality through a geographical analysis; for example, Sun et al. [30] used geographical information system tools, global positioning system data, and smart card data to evaluate bus lines; Zhang et al. [31] proposed a mixed data envelopment analysis-stochastic frontier analysis (DEA-SFA) model to evaluate the efficiency of an urban bus operation at different periods. Based on the previous studies, de Oña and de Oña [32] summarized the evolution of research related to the different methodological approaches for service quality evaluation in the public transport sector over the years and provided a discussion of future directions.
In summary, there was less research on passenger satisfaction of public transit with bus lanes. at is to say, the relationship between bus lanes and passenger satisfaction of public transit was less studied. A great number of researches focused on the customer satisfaction of public transport systems, but they did not focus on the variables related to bus lanes.

Research on User
Segmentation. Users in the public transit market were not homogenous, which means they consisted of different groups in the light of various characteristics. In this context, four basic classes of variables were typically used to identify the user segmentation [33], including socioeconomic and sociodemographic variables, spatial variables, behaviour-based variables, and attitudinal variables.
e most common sociodemographic categorizations for the first segmentation approach were based on age, gender, household, work status, and income [34]. e approach based on spatial variables focused on the home and work locations of residents and differentiates between urban, suburban, and rural areas [35]. Behaviour-based variables were used to define the behavioural patterns, such as the trip frequency and trip purpose. Attitudinal variables were used to explain and understand individual mobility behaviour to segment the population into meaningful groups [34].
Among all the user segmentation methods, the method based on socioeconomic and sociodemographic variables was the most feasible in policy-making. In this way, the concepts of captive riders and choice riders emerged, which were defined to segment the public transit market [36][37][38][39]. Captive riders were commonly defined as individuals who did not have a travel choice but public transit, and choice riders were those who chose to use public transit even though another mode, usually a car, was optional [36][37][38]. Recently, van Lierop and El-Geneidy [39] identified an additional group that they defined as "captive by choice." e captive by choice riders were individuals who were captive riders but were not limited to transit financially.
In a word, the core of improving the service quality of public transit with bus lanes depended on how passengers perceived the bus service quality and the mechanism of related factors interacting with their satisfaction. us, this paper adopted the Structural Equation Model (SEM) to study the passenger satisfaction of public transit with bus lanes. In order to consider the user heterogeneity, the concepts of captive, choice, and captive by choice riders were used to segment the public transit market in an empirical research in Shanghai, China. Distinguished from the previous studies, we study the feeling and experience of passengers using bus lanes and consider the factors related to bus lanes in the process of studying passenger satisfaction of public transit to help improve the service quality of public transit with bus lanes and the market share.

Variables and Hypotheses.
e selection of variables is the core of modelling the passenger satisfaction of public transit with bus lanes. e variables used to evaluate the service quality of public transport are also applicable in the evaluation of public transit with bus lanes, and variables related to bus lanes should be considered simultaneously. Referring to existing literature [22,23], "comfort of environment and facilities," "reliability of operation and efficiency," and "convenience of bus trip" are chosen to present the service quality of public transit on bus lanes. "Emotional value of bus lanes" is also a chosen variable, because it is used to explore whether bus passengers feel positive emotion towards bus lanes and show emotional dependence gradually turning to alternative options [22]. "Satisfaction with bus lanes" and "willingness to travel by public transport" are final results before alternative options, which show the passengers' current and future attitudes towards public transit with bus lanes. Each variable is described in detail and how to measure the variables is explained as follows.

Comfort of Environment and Facilities.
Comfort of environment and facilities refers to a clean and tidy situation related to the bus system with bus lanes, which can bring about superior comfort experience to the entire bus travel process [40]. e variable measures the level of trip comfort for the passenger in several aspects, so the questions should explore the perceived physical comfort of bus seats, air conditioning, and crowdedness in the bus. erefore, three items are used to measure "comfort of environment and facilities," namely, "crowdedness in the bus on bus lanes during peak hours," "clean and tidy condition in the bus," and "overall conditions of facilities at stations on bus lanes" [18,19].

Reliability of Operation and Efficiency.
Reliability of operation and efficiency and the related subvariables are key indicators in public transit services and are general in the application of the method. e service quality inside the vehicle considers the driver's behaviours and the driving stability [41], and the one outside the vehicle considers the vehicle speed, waiting time at stations [42]. ese variables are often used to evaluate the service quality of public transit, and this study pays more attention to passengers' feelings about these variables on bus lanes. Moreover, safety is an important issue passenger faces when riding a bus [2] so frequency of breakdown is taken into account. erefore, four items are used to measure "reliability of operation and efficiency," namely, "number of safety incidents," "speed of vehicles on bus lanes," "waiting time at bus stations along bus lanes," and " driving stability."

Convenience of Bus Trip.
Convenience of bus trip is explored in two aspects: the access into the public transit system and the part within the public transit system. As regards the access into the public transit system, walking distance from origins to stations and from stations to destinations is adopted to reflect whether it is convenient for passengers. As for the part within the public transit system, the convenience of transfers is adopted to reflect whether the bus route and station settings match the passengers' travel need [23]. erefore, in this study, two items are used to measure "convenience of bus trip," namely, "walking distance from origins to stations and from stations to destinations" and "convenience of transfers."

Emotional Value of Bus Lanes.
Emotional value is the part of the value that passengers feel positive emotion through the provision of services, and the chosen items should describe the emotional dependence, attention, and sense of belonging of passengers [22]. Considering the public transit with bus lanes, the attitudes and inclinations of passengers to the active and passive emotions and identification of bus lanes are chosen. ese variables explore the image of bus lanes in the minds of passengers. ree items from the aspects of active and passive emotions and identification of bus lanes are adopted to measure "emotional value of bus lanes," namely, "whether bus lanes can increase the number of public transport trips," "whether taking a bus is subject to other factors," and "taking bus lanes as a consideration for bus travel" [43].

Satisfaction of Public Transit with Bus Lanes.
e satisfaction index has been widely used in various fields. Satisfaction of public transit with bus lanes means the degree that a customer believes his/her requirements to public transit with bus lanes have been met. Besides the satisfaction degree variable, we drew lessons from Shiftan et al. [22] and took account of two other variables. ey are the current effect of bus lanes for public transit and the promotion of bus lanes.
erefore, three items are used to measure "satisfaction of public transit with bus lanes," namely, "overall satisfaction towards bus lanes," "whether bus lanes have improved the bus travel experience," and "how far the gap was from the ideal level of bus service."

Willingness to Travel by Public Transit.
"Satisfaction of public transit with bus lanes" is the current attitude towards bus lanes, and "willingness to travel by public transport" is used to observe the attitude and tendency of bus passengers towards bus lanes in the future. Since the purpose of bus lanes is to absorb more people who are used to travel by car to use public transport while ensuring the current number of bus trips, it is suitable to discuss the willingness of passengers to travel by public transport. Two items are adopted to measure "willingness to travel by public transit," namely, "whether bus services will be preferred when the quality of bus lanes remains at the current level" and "whether bus will be preferred when you can choose another travel mode" [22,23].
As for the relationship between variables, "comfort of environment and facilities," "reliability of operation and efficiency," and "convenience of bus trip" are three variables that affected the "emotional value of bus lanes" [22], because these variables that represented the service quality can form emotional dependence from the perspective of facilities, operations, and convenience. en, the "emotional value of bus lanes" exerted an impact on "satisfaction with bus lanes," which in turn affected passengers' willingness to travel by public transit [23], which means emotional value gradually turns to alternative options. e hypotheses are listed as follows: H1: passengers' satisfaction with comfort of environment and facilities of public transit with bus lanes has a positive effect on their emotional value of bus lanes. H2: passengers' satisfaction with reliability of operation and efficiency of public transit with bus lanes has a positive effect on their emotional value of bus lanes. H3: passengers' satisfaction with convenience of bus trip along bus lanes has a positive effect on their emotional value of bus lanes. H4: passengers' emotional value of bus lanes has a positive effect on their satisfaction of public transit with bus lanes.
H5: passengers' satisfaction of public transit with bus lanes has a positive effect on their willingness to travel by public transit.

Structural Equation Model (SEM).
As a general technique for statistical analysis, the concepts of SEM originated from the path analysis originally proposed by Wright [44], and then factors analysis was integrated into it and the concepts of SEM were put forward [45,46]. SEM consists of the measurement model based on factor analysis and the structural model based on path analysis. rough these two models, relationship between variables can be identified, estimated, and verified. ere are two categories of variables in SEM: latent variables and observed variables. Observed variables are those that can be directly measured. Latent variables corresponding to multiple observed variables are those that cannot be directly measured.
e most direct description method of SEM is the path diagram derived from path analysis and the basic framework of SEM is shown in Figure 1. Latent variables represented by circles consist of endogenous and exogenous ones. Endogenous latent variables η represent those affected by the variables inside the model, and exogenous latent variables ξ represent those influenced by the variables outside the model. Observed variables represented by rectangles consist of endogenous ones (y) and exogenous ones (x). e dotted line represents the measurement model, and the solid line represents the structural model. ζ is the error vector. β represents the effect of endogenous latent variables on other endogenous latent variables, and c represents the effect of exogenous latent variables on endogenous latent variables. λ x and λ y are the intermediate carriers. δ is the measurement error associated with the exogenous observed variable x, and ε is the measurement error associated with the endogenous observed variable y.
Generally, SEM is composed of three regression equations expressed in the three following equations: where equation (1)

Evaluation of Model's Goodness of Fit.
e goodness of fit of SEM is evaluated in two steps. First, data reliability and validity are analysed to ensure the reliability and effectiveness of the model. Second, the goodness of fit of the model is analysed to examine the model fit.
In the first step, data reliability is used to evaluate the data consistency or stability, and it is generally measured by Cronbach's alpha. In general, the data internal consistency is considered to be high, if Cronbach's alpha is greater than 0.7. If Cronbach's alpha is less than 0.4, it is considered to be less credible [22]. Data validity is generally measured by the Kaiser-Meyer-Olkin (KMO) test and the Bartlett's spherical test. Among them, value of KMO statistic is from 0 to 1. e closer to 1 the value is, the stronger the correlation between variables is. In general, the KMO value should be greater than 0.7 to show a strong correlation between the observed variables [22]. Once the data reliability and validity are confirmed, the SEM is established and we move to the second step.
In the second step, the model parameters are estimated with appropriate parameter estimation methods first. en, several indices, goodness of fit index (GFI), adjusted goodness of fit index (AGFI), root mean square error of approximation (RMSEA), and ratio of chi-square to degree of freedom (CMIN/DF), are used to examine the model fit [23]. e recommended cut-off values for GFI and AGFI are more than 0.900. It can be considered good when RMSEA is less than 0.080 and less than 0.050 is better. When CMIN/DF is less than ten, it is regarded as a good value. If it is less than five, it is better. After ensuring that the goodness of fit of the model meets the standard, the model can be analysed.

Index Score for Measuring Variable Relationships.
Most scholars analysed relevant conclusions based on the results of SEM, but the conclusions could be applied in general aspects. For the planners and policy-makers, they need more detailed approaches to improve the service quality of public transit with bus lanes and determine the improvement direction of bus services related to bus lanes. Consequently, an index score calculation method is Journal of Advanced Transportation proposed to study the relationship between variables. e American Customer Satisfaction Index (ACSI) calculation method [47] is used to calculate the index scores of variables. e equation for calculating the index score is as follows: where w i is the weight of the observed variable; z i denotes the observed variables including endogenous ones (y) and exogenous ones (x); z i is the average score of the observed variable; max z i is the highest score of the observed variable; min z i is the lowest score of the observed variable.

Survey and Sample
4.1. Survey. In this study, seventeen indicators as observed variables measured six latent variables. ese seventeen indicators formed the main parts of designed questionnaire ( Table 1). Most of the questions were set in a five-level Likert scale. We did not use the seven-level Likert scale or ten-level Likert scale because too many options made it difficult for investigators to express their true feelings. e interviewees need to answer these questions to show their attitude from "dissatisfy/disagree" to "satisfy/agree." ere were two reasons why some questions cannot be measured by the fivelevel Likert scale. One was the fact that the questions introduced a single alternative, a completely opposite alternative, and an uncertain option, and there was no intermediate option between them on the basis of reality. e other was that the questions required the respondents to answer a level of the specific number, and it was not clearly distinguished after being divided into five levels. In addition to these seventeen survey questions, basic socioeconomic relevant questions were designed in the last part of the questionnaire. e data were collected through a survey in Shanghai, China, in 2017. e investigation time was morning and evening rush hour from April 12 to April 14, 2017 (from Tuesday to ursday), namely, 7:00 to 10:00 and 16:00 to 19: 00. During this period, bus lanes, which gave priority to buses by the replacement of original ordinary lanes in road space, were accessible for buses only and not accessible for regular vehicles like cars, trucks, and taxis. At other times, regular vehicles can drive on these special lanes. e survey issued 2087 questionnaires in the aggregate. e survey was conducted on sixteen bus lanes in the central urban area of Shanghai, taking into account the morning and evening peak hours, as shown in Figure 2. e bus lanes were selected based on different level of bus passenger flows [1]. Investigators surveyed the respondents at the bus stops along the bus lanes. If the respondents need to get on the buses when the bus came, the investigators followed the respondents to get on the bus at the same time to ensure the integrity of the whole questionnaire. To avoid the sample bias caused by only investigating the passengers that used those bus stops, when the investigators got on the bus with the former respondent and finished the survey, they continued to investigate the passengers in the bus. Table 2 shows the distribution of sample size of each bus lane, and the maximum one-way volume of section passenger flow in peak hour [1] was considered to select the bus lanes for the analysis. At the very beginning of the survey, the investigators first introduced the background of Shanghai bus lanes to the respondents and asked them if they knew that the bus lines they were taking or they would take passed through the bus lanes. 60.6% of passengers did not know that the bus they were taking or would take would pass through the bus lanes. en, the investigators told respondents that buses were on a bus lane to ensure we can get feedback from respondents on the experience on the bus lanes, rather than the whole travel experience. Eventually, 1860 valid questionnaires were collected with completed replies.

Data Description.
According to the results of survey, the descriptive statistics are shown in Table 3. In the group of all users, 55.6% of the interviewees were female. e age of valid interviewees mostly fell in the range between 16 and 60. 35.9% of the interviewees were 25 to 34 years old, and the interviewees who were 35 to 44 years old accounted for 31.2%. As for the occupation, company employees (39.6%) and freelancers (17.6%) accounted for most of the samples. Almost 40% of the interviewees earned 5000-10,000 RMB (equal to 726-1453 US dollars) per month, and 23.9% of the interviewees earned 10,000-20,833 RMB (equal to 1453-3026 US dollars) per month. About 60% of the interviewees travelled for 4 days or more in the past week. e respondents travelled the most for commuting. Since the survey was conducted during the operation hours of bus lanes, the results were considered effective to reflect the passenger satisfaction.
In order to consider the user heterogeneity and study the difference of passenger groups, this study segmented the survey sample based on the variables of car ownership and income. 1860 respondents were divided into choice, captive, and captive by choice groups [39,48]

Data Reliability and Validity.
e reliability and validity of observed variables were examined first to ensure the reliability and effectiveness of the model. e results of data reliability and validity are shown in Table 5. To test the data reliability, the Cronbach's alpha value of whole data was 0.753, which was greater than 0.7. erefore, the whole sample data were reliable. We also examined the data reliability of captive group, choice group, and captive by choice group, and the Cronbach's alpha value of each group was also greater than 0.7. erefore, data of all groups were also reliable according to the Cronbach's alpha and the reliability degree was close.
As regards the data validity, the statistics of Kaiser-Meyer-Olkin (KMO) test and the results of Bartlett's spherical test were measured. Consequently, the KMO value was 0.809 (greater than 0.7) and the significance level of Bartlett's spherical test was less than 0.001, which means the latent variables could be measured by the observed variables well. After testing different group data, it was come to the same conclusion.

Results of the General Model.
e initial model of passenger satisfaction with bus lanes was established through the SEM approach shown in Figure 3. e coefficients of the model were estimated by using the whole data. e numbers attached to the solid lines represent the relationship between latent variables, and the ones attached to the dotted lines represent the relationship between latent variables and observed variables.
As shown in Figure 3, most of the indices were not in the criteria range; thus the goodness of fit of the initial model was unacceptable. e initial model needed to be adjusted. First of all, because of the strong correlation between the latent variable "comfort of environment and facilities (ENVI)" and "convenience of bus trip (CONV)" (0.934), the two variables may belong to one higher-order common latent variable. erefore, combining the observed variables, a new latent variable was obtained. Since the new latent variable explained "comfort of environment and facilities (ENVI)" and "convenience of bus trip (CONV)," the new latent variable was defined as "service level of the travel environment (SERV)." Moreover, the latent variable "reliability of operation and efficiency (OPER)" had little effect on the "emotional value of bus lanes (EMOT)" (0.124) and other latent variables, but, in order to preserve the integrity of the model, the latent variable and its associated observed variables were retained, and it was considered to influence "willingness to travel by public transport (WILL)" directly. Finally, there may be a covariation relationship between the new latent variable (SERV) and "reliability of operation and efficiency (OPER)." To make the model more perfect, a doubleheaded arrow was set to represent the covariance relationship. In addition, the covariation relationships between the measurement errors of observed variables were adjusted based on the modification indices provided in the output results.
e results of the adjusted model and estimation results are shown in Figure 4. e numbers in Figure 4 have the same meaning as those in Figure 3. All the relationships were significant, which means P value was less than 0.001. Although some indices still had room for improvement, the goodness of fit of the model was  x 3 x 4 x 5 x 6 x 7 x 8

Relationship between Variables.
e relationship between variables consisted of two parts, including the relationship between latent variables and the one between latent variables and observed variables. e relationship between variables in SEM was measured by the effects between latent variables. As shown in Table 6, the effects consisted of direct and indirect effect. e direct effect occurred between two adjacent latent variables, which could be represented by the normalized path coefficient. e indirect effect was regarded as the influence of one latent variable on another latent variable through the influence of multiple latent variables. e total effect between the latent variables was equal to the sum of direct and indirect effects.
As shown in Table 6, with one unit increase of "reliability of operation and efficiency (OPER)," passenger's willingness to travel by public transport would be promoted by 0.134 units. erefore, the effect of "reliability of operation and efficiency (OPER)" on the "willingness to travel by public transport (WILL)" was significantly less. Emotional value of bus lane has a significantly direct effect on the satisfaction with bus lane. "Emotional value of bus lanes (EMOT)" was increased by 1 unit, which increased "satisfaction of public transit with bus lanes (SATI)" by 0.831 units. e result indicated that the passengers were more satisfied with bus lanes when they had a more positive emotional value to them. "Satisfaction of public transit with bus lanes (SATI)" had a direct impact on willingness of using public transport, and the degree of direct effect was more than that of "reliability of operation and efficiency (OPER)." "Satisfaction of public transit with bus lanes (SATI)" was increased by 1 unit, which increased "willingness to travel by public transport (WILL)" by 0.483 units.
In summary, based on the total effect of willingness to travel by public transport, it could be considered that the service level of the travel environment had a significant impact on satisfaction with bus lane and bus trip willingness through a series of latent variables.
Relationship between latent and observed variables in SEM was measured by the index score calculation method. e index score could reveal the interviewees' attitudes towards the issue and help develop strategies related to bus lanes to expand the public transit market. e index scores of latent and observed variables calculated by equation (4) are shown in Table 7.
As reported in Table 7, the service quality of bus lanes still had much potential for improvement and targeted strategies should be taken in some aspects. Specifically, "crowdedness in the bus on bus lanes during peak hours (x 1 )" and "driving stability (x 7 )" scored under 50 points. It also reflected that many passengers were sceptical that bus lane could attract people who travelled by car to take the bus. e first and most important thing was that the passenger satisfaction for bus lanes scored more than 50 points (52.13 points), and the willingness to travel by bus was 57.57 points, which was greater than the current satisfaction score for bus lanes. Since willingness reflected the intention to use the bus service in the near future, it implied that passengers had a positive attitude towards the future public transit with bus lane, despite their little dissatisfaction. It also implied that passengers might prefer public transit or simply could not bear the financial burden of private motorization.

Captive, Choice, and Captive by Choice Models.
To explore whether the reason why passengers continued travelling by public transit in the near future in Shanghai was relevant with financial issues or not, the survey sample was segmented from the perspective of income and car ownership. Acknowledging that there were different groups that used transit was possible as the factors affecting satisfaction may not be consistent among all user types. As a result, it was necessary to establish comparison models to consider the user heterogeneity.
According to the analysis in Section 4, the transit users were recognized as choice, captive, and captive by choice.
e structural and measurement model was established based on the model in Figure 4. First, the goodness of fit of the comparison models was evaluated, as shown in Table 8. Almost all the estimation indexes fit the models.
Based on a comparison for different groups in Table 9, the findings for the comparison models were relatively similar to those of the general model, but there were a few differences in comparison models. e results of structural models revealed that captive users' emotional value of bus lane was influenced less by the service of the travel environment (0.399) compared to choice and captive by choice users (0.606 and 0.618). In contrast, captive users' satisfactions were influenced more by emotional value of bus lane compared to the other groups. Also, while for all groups satisfaction with operation and efficiency had greatly little effect on their willingness to travel by bus, this was much less for captive users. is might be because captive users did not have the opportunity to use an alternative mode and only travelled by bus regardless of this factor. In the measurement models, captive by choice users' preferences were closest to general groups' in the service of the travel environment. e results of captive users were lower than those of captive by choice users, while the results of choice users were higher. It is shown that the choice users had higher requirements for bus lanes. In addition, the traffic accident passengers encountered least influenced the operation and efficiency for captive users (0.324), which shows they did not care about this point. is result was different from the previous studies [39,48], and it may be said that bus lanes reduced the passenger's attention to the accidents. As for the influence of subjecting to other factors on emotional value, it was the least for choice users (0.319), possibly because they have the most choices of all groups. Meanwhile, there was no significant difference between the results of measurement models related to "satisfaction of public transit with bus lanes" and "willingness to travel by public transport" for all groups.

Discussion
e results of the general and comparison models could provide several targeted approaches to increase the service quality of public transit with bus lanes. In this section, these strategies are discussed to increase passenger satisfaction among different types of public transit users. Increasing the service quality and satisfaction of public transit with bus lanes was expected to increase the bus ridership among different groups.
As shown in Figure 5, the index score of each variable in each model was calculated. e first thing to pay attention to was the fact that choice users scored almost the same in "satisfaction of public transit with bus lanes" (54.06) and "willingness to travel by public transit" (56.56). It implied that choice users along bus lanes had a positive attitude towards the public transit with bus lanes at present and were confident in future transit services. Different from choice   us, it was difficult to increase user satisfaction by simply building bus lanes without improving the service quality of public transit.
e results also showed that what bus passengers most wanted to improve were "crowdedness in the bus on bus lanes during peak hours (x 1 )" and "driving stability (x 7 )." is result could be achieved from all groups. e results were consistent with previous studies on the whole bus system in other cities in China [23,43]. en, we compared our results with the research in [49] on Shanghai public transport system, including public transit without exclusive bus lanes. It is found that (1) service quality had a significant effect on satisfaction and (2) people were dissatisfied with the crowdedness in the bus. However, compared with other variables in the service quality, the dissatisfaction with the crowdedness in the bus in the whole bus system was less than that for the public transit with bus lanes. It indicated that people had high requirements for exclusive bus lanes to reduce the crowdedness in the bus.
To maintain or even improve the public transit market share, it was extremely necessary to focus on the demands of different groups of transit users. Several targeted approaches could be proposed to the transport departments and transit operators for reference. For "crowdedness in the bus on bus lanes during peak hours (x 1 )," the service could be improved by optimizing the frequency of the routes passing through the bus lanes during peak hours and the setting plan of bus stations and routes along bus lanes. For "driving stability (x 7 )," the service could be improved by strengthening driving training not only to improve the drivers' driving skills but also to make drivers change the driving habits  along bus lanes. It indicated that it was important to distinguish between the driving behaviours of bus lanes and nonbus lanes. is could create smoother driving conditions through bus lanes. ese results demonstrated that it is effective to improve the passenger satisfaction of different groups through adopting the policy suggestions which focused on the specific aspects of bus lanes. In addition, improvement strategies targeted at choice and captive by choice users were important. It could not only benefit these groups and retain these users but also improve the experience of travelling by bus for users who had no opportunity to switch the travel mode. In other words, the policies targeted at specific groups could motivate other ridership as well.

Conclusions and Future Work
is paper investigated how to improve the service quality of public transit with exclusive bus lanes in Shanghai, China, from a perspective of passenger satisfaction. Based on SEM and calculation of index score, the factors related to satisfaction of public transit with bus lanes and willingness to travel by public transit were identified. Meanwhile, the effect of heterogeneity among users on the performance of the model was investigated. e findings based on model results were as follows.
On one hand, passengers who took buses along exclusive bus lanes in Shanghai were dissatisfied with the current bus service, but they would still continue to choose buses for travel in the future. Among the whole passengers, choice users along bus lanes had a positive attitude towards the public transit with bus lanes at present and were confident in future transit services. Choice and captive by choice users might prefer public transit with bus lanes and captive users might be unable to bear the financial burden of private motorized travel and choose public transit.
On the other hand, travel environment, facilities, and convenience were found to be the key influential factors for travel willingness of passengers in Shanghai. ese results were confirmed by a number of studies [22,23]. However, operational efficiency, for example, bus speed and waiting time at the station, was not significant to passengers' perceptions towards bus service quality. is was quite different from a previous study [22]. e proposed model in this paper could benefit the understanding of passenger satisfaction of public transit with exclusive bus lanes. Since "crowdedness in the bus on bus lanes during peak hours" especially for choice users and "driving stability" especially for captive users were two key influential factors, transport departments and transit operators could consider these improvement strategies, for example, optimizing the frequency of the routes passing through the bus lanes during peak hours and strengthening driving training.
However, there were certain limitations in the current analysis and future works can be intended. e relevant investigations can be made before and after the exclusive bus lanes are constructed, respectively, not only to evaluate the effect of bus lanes more accurately but also to minimize the influence of other factors on the research. In addition, passengers were identified just by socioeconomic attributes and their behavioural characteristics were not considered. ere might be risks to adopt the inappropriate policy suggestions of bus service. erefore, groups with different socioeconomic attributes, behavioural characteristics, and attitudinal preference should be taken into consideration synthetically. For instance, temporal and spatial travel characteristics of passengers can be further studied. erefore, the specific improvement directions of bus lanes can be confirmed, and specific bus lanes can be targeted where strategies should be applied to.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.


The effects of communicating uncertainty around statistics on public trust: an international study

A growing body of research indicates that transparent communication of statistical uncertainty around facts and figures does not undermine credibility. However, the extent to which these findings apply in the context of the COVID-19 pandemic--rife with uncertainties--is unclear. In a large international survey experiment, (Study 1; N = 10,519) we report that communicating uncertainty around COVID-19 statistics in the form of a numeric range (vs. no uncertainty) may lead to slightly lower trust in the number presented but has no impact on trust in the source of the information. We also report the minimal impact of numeric uncertainty on trust is consistent across estimates of current or future COVID-19 statistics (Study 2) and figures relating to environmental or economic research, rather than the pandemic (Study 3). Conversely, we find imprecise statements about the mere existence of uncertainty without quantification can undermine both trust in the numbers and their source--though effects vary across countries and contexts. Communicators can be transparent about statistical uncertainty without concerns about undermining perceptions of their trustworthiness, but ideally should aim to use numerical ranges rather than verbal statements.

example Thiebach et al. (2015) report that the presence or absence of hedge words such as 'may' and 'possibly' has no bearing on the perceived credibility of statements. Han et al., (2018) reports that presence of vague statements describing uncertainty around influenza severity and vaccine efficacy ('…we are not sure exactly how effective it will be…') in a news release undermines trust in the primary source. Conversely, Nakayachi et al. (2018) find that coupling earthquake risk estimates with a statement explaining assessments come with 'high uncertainty' increased readers' trust in seismologists, though this effect was only detected when low (20% vs 70% or 100%) quake probabilities were communicated. This research, however, has been conducted only within a limited range of samples from WEIRD countries (Henrich et al., 2010), and on topics that may not have had immediate emotional salience to the audience (despite efforts to explore some topical and divisive issues such as climate change and immigration). In the current research we build and expand on the findings of van der , examining how inclusion of uncertainty information, expressed as a numeric range or verbal statement, impacts readers' trust in a COVID-19 related statistics and their source. We also investigate how these effects vary across different national contexts.
At the time of data collection for the current research (Studies 1 and 2) it is not an exaggeration to say that the world was preoccupied with COVID-19; citizens of many countries were under wide-ranging restrictions (Hale et al., 2021), news of the virus and its impact dominated mainstream and social media (Pearman et al., 2021;Tsao et al., 2021), and the perceived risk from the virus was high across many countries Schneider et al., 2021).
At the same time, the SARS-CoV2 pandemic brought uncertainties of all kinds to a broad range of people: uncertainty about the potential future course of the pandemic and rate of transmission; uncertainty about the current number of cases, or deaths, or mortality rate; uncertainty about the underlying disease course and risk factors associated with a poor outcome (Koffman et al., 2020). Inherent in communication of facts about the disease and the pandemic, then, is the need to communicate this uncertainty in a way that allows people to understand it and make appropriate judgements about how much to trust it and weight the information in their decision-making given its level of certainty.
Calls have been made for transparent, trustworthy communication of uncertainties around COVID-19 (Rutter et al., 2020;Veit et al., 2020). Yet many official communications on the topic do not explicitly acknowledge such uncertainties, possibly due to concerns over trust and credibility. Notably, one experiment examining the impact of uncertainty on public trust in science suggests these concerns are not unfounded. Kreps and Kriner (2020) report that participants presented with an estimate of future COVID-19 deaths expressed less general trust in scientists when that estimate was provided as a (relatively large) range rather than a single number. The authors conclude that expressing uncertainty as a range: "may be more intellectually honest, but it nonetheless comes at a cost of eroding public confidence." (p. 5) This worrying conclusion presents a challenge to calls for transparent communication as well as conflicting with much of the prior research on this matter. Indeed, a recent systematic review of uncertainty communication experiments found no studies in which communication of technical (i.e. statistical) uncertainty had a negative effect on credibility of either the claim or its source (Gustafson & Rice, 2020).
In the current studies, we seek to add to the limited empirical literature on how uncertainty around COVID-19 information is received. We examine how the presence and format of uncertainty in communications impacts perceptions of uncertainty, and message and source credibility. We first carried out an experimental study in 12 countries across Europe, North and Central America, and Asia (Study 1), conducted between mid-March and mid-April 2020, in which participants were randomised to one of three conditions: a control condition of receiving COVID-19 statistics with no uncertainty (a point estimate), a condition where the information included a numerical range around the estimate, and a condition in which the uncertainty was not quantified but communicated as an imprecise verbal statement.
The uncertainty in this study related to the COVID-19 infection hospitalisation ratethat is, the proportion of people infected with COVID-19 who require hospitalisation for treatment of symptoms. As such, the uncertainty can be considered epistemic, arising from a lack of data or knowledge. In this sense we use epistemic uncertainty to refer to uncertainty regarding past or current phenomena; unknowns which in theory could be known (van der Bles et al., 2019). Some often-reported COVID-19 statistics are imbued with another type of uncertainty -aleatory uncertainty-meaning that they simply cannot be known for certain due to the inherent indeterminacy or randomness of the world -such as predicted future numbers of cases or deaths (van der Bles et al., 2019). A number of uncertainty communication studies have examined how people perceive and interpret verbal and numeric expressions of uncertainty relating to future risks and events (e.g., Joslyn & LeClerc, 2016;Nakayachi et al., 2018). However we are not aware of any research which has systematically examined how the impact of uncertainty format (e.g. numeric or verbal) on trust varies depending on whether the information provided relates to the present (epistemic) or future (aleatory). In Study 2, we therefore explore potential differences in the impact of these two types of uncertainty by including a further experimental factor to the Study 1 design: varying whether COVID-19 death statistics presented refer to current estimates or future forecasts.
Finally, to further examine the generalisability of our findings to other domains, which participants may perceive as more psychologically distant, we also present results from a third experiment (Study 3). This study investigates how numeric or verbal uncertainty, presented as either epistemic or aleatory, is perceived when it relates to environmental or economic issues, rather than COVID-19.

Study 1 Methods
Participants were recruited across 12 countries. Participants in Australia were recruited through Dynata (dynata.com), participants in France were recruited by BVA (bvagroup.com) and US and UK samples were recruited via Prolific (prolific.ac  is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint  1 We acknowledge that the inclusion of the qualifier "about" in the sentence presented introduces some level of uncertainty to all participants. However we note this is consistent across conditions and previous research (van der Bles et al., 2020) has reported sentences with such qualifiers are not perceived as more uncertain or less trusted than statements without these words. To what extent do you think that the people responsible for producing this number are trustworthy?" (1 = 'Not at all' to 7 = 'Very'). Participants also answered questions about how positive or negative they felt about the information and how easy they found it to read.
Details and results for these secondary outcomes are reported in Appendix 1. Figure 1 shows the pooled means from all participants on perceived uncertainty, trust in numbers and trust in the source of the numbers across the three experimental format conditions.

Results
A one-way ANOVA analysing the pooled data from all country samples 2 revealed a significant effect of experimental condition on perceived uncertainty, F(2, 10472) = 56.54, p < .001, η 2 = 0.011. Post hoc analyses (Tukey's HSD), revealed that participants who read a message with a numeric expression of uncertainty, perceived, on average, more uncertainty than those who read the control message (Mcontrol = 3.82, SD = 1.38; Mnumeric = 3.98, SD = 1.35; p < .001, Cohen's d = .11). Participants who read the message containing a verbal expression of uncertainty perceived more uncertainty than those who read the numeric uncertainty message (Mverbal = 4.17, SD = 1.38; p < .001, d = .14), or the control message (p < .001, d = .25).
2 Given that the sample collected in France was much larger than all other samples and would have had more influence on the combined results, we repeated these analyses with the French sample excluded. The pattern of significant results remained the same. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; Figure 1: Mean levels of perceived uncertainty (A), trust in number (B) and trust in source (C) across experimental conditions. Whiskers indicate 95% confidence interval; horizontal brackets indicate significant difference between conditions: **p < .01, ***p < .001.
There was also a significant effect of message condition on reported trust in the numbers presented, F(2, 10454) = 30.50, p < .001, η 2 = 0.006. As detailed in Figure 1B Additional results focusing on secondary outcomes (difficulty of understanding and emotional response) are reported in the supplementary information (Appendix 1). Briefly, we find that participants rated the control format easiest to understand, followed by the verbal then numeric formats. In terms of emotion, participants in the verbal uncertainty condition reported feeling slightly more positive about the information compared to participants in the control condition. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; https://doi.org/10. 1101/2021 To investigate the results at the country-level, we ran individual one-way ANOVAs examining the effect of experimental condition on each of the three outcome variables, for each country. We summarise the results in Figure 2, with full details presented in Appendix 2.
The results of ANOVAs indicated that uncertainty format had a significant effect on perceived uncertainty in samples collected in France, Germany, Italy, South Korea, Spain, the UK and the US. The results of pairwise comparisons between conditions, for each country are presented in Figure 2. Due to the large number of comparisons, we applied a Benjamini-Hochberg correction across all tests to correct for multiple testing. Results revealed a pattern of effects consistent with those reported for the combined sample. Where significant differences in perceived uncertainty were detected between groups, we find that uncertainty is highest in the verbal uncertainty condition, followed by the numeric uncertainty condition and then the control condition. This pattern appears most clearly in our US and UK samples.
Experimental condition also had a significant effect on trust in the numbers in samples collected in China, France, Germany, South Korea, the US, and the UK. Considering pairwise comparisons between conditions, we find the inverse pattern to perceptions of uncertainty where significant differences were detected; reported trust was lowest in the verbal uncertainty condition, followed by the numeric uncertainty condition, then the control condition. There was one exception: in the South Korea sample, participants in the verbal condition reported, on average, a significantly higher level of trust in the numbers compared to those in the numeric condition. However, for most countries examined we report no significant differences between any conditions. Across all individual country samples, we did not find a significant effect of the uncertainty format condition on trust in the source of the information.
Considering the heterogeneity between countries, we conducted a series of exploratory analyses seeking to explain the variation in effect sizes (reported in Appendix 3).
These analyses drew on both external country-level data (risk tolerance data drawn from international studies) and additional items included in the surveys (numeracy and social trust). Given the small number data points (12 countries) no firm conclusions can be drawn.
However, we found a significant correlation between the mean level of numeracy (Cokely et al., 2012) in a given sample and the effect size of verbal uncertainty on trust in the numbers . CC-BY-NC 4.0 International license It is made available under a perpetuity.
is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; https://doi.org/10. 1101/2021 presented. Country samples with higher numeracy reported lower trust in numbers presented with verbal uncertainty (relative to control).
. CC-BY-NC 4.0 International license It is made available under a perpetuity.
is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; https://doi.org/10.1101/2021.09.27.21264202 doi: medRxiv preprint Figure 2: Effect of experimental condition on key outcome variables, across countries. Bars indicate mean and 95% confidence interval.

Interim Discussion
This large and international dataset, in an emotionally salient context for participants, broadly confirms the findings of our previous work in other contexts : when presented with uncertainty information, people perceived greater uncertainty in the reported hospitalization rate, but there was only a small decrease in trust in the numbers and this effect was larger for the verbal uncertainty condition than the numeric. Considering trust in the source of the numbers, we find that participants were less trusting of the source when verbal uncertainty was communicated. However, this small effect (d = .09) was only detectable in the pooled sample combining all countries.
Comparing between countries, we find that the US and UK were most sensitive to uncertainty information in terms of its impact on perceptions of uncertainty. In five of the twelve countries surveyed (Australia, China, Japan, Mexico, and Sweden) we find that neither verbal nor numeric expressions of uncertainty had a significant impact on how uncertain participants rated the information. Similarly, at the individual country level, we find that trust in the numbers presented is not consistently affected by uncertainty information; in four countries (China, France, US, UK) we find that statements with verbal uncertainty are considered significantly less credible than those without, and in South Korea numeric uncertainty is rated as less credible. One consistent finding across countries is that uncertainty information did not significantly impact trust in the source of the information in any one country (though we do report a small significant effect in the pooled sample). The current results suggest that effects of verbal uncertainty information on perceptions of trustworthiness and credibility may not be universal; cultural context may play an important role in how people respond to such information. Researchers and communicators should be aware that uncertainty communication advice and findings from one context may not translate to another. The reasons for such differences remain unclear. The current study did not aim to provide a cross-cultural examination of how uncertainty information is perceived (though we present an exploratory attempt in Appendix 3); further research is required to fully understand the inter-country variation observed. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; https://doi.org/10. 1101/2021 We find less inter-country variation when considering numeric uncertainty. Here, the results align with a key finding from van der Bles et al. (2020): communication of numeric uncertainty has little impact on trust in the numbers and no effect on trust in the source (though a small significant effect was detected in the pooled sample). Including statistical uncertainty such as confidence intervals in communications does not undermine credibility.
A final consideration for Study 1 is that the uncertainty presented in this study was purely epistemic: it did not involve the uncertainty of an unknown future event. To compare the public's reaction to aleatoric uncertainty (uncertainty about the future) to their reaction to this epistemic uncertainty, we carried out a further study.

Study 2
This study aimed to investigate how the effect of uncertainty information on trust differs as function of uncertainty type (epistemic or aleatory). We conducted a survey experiment similar to Study 1 with the addition of a further experimental factor, varying if the numbers communicated related to the present or future. As in Study 1, participants completed an online survey experiment on the Qualtrics platform. Participants were randomised to one of six conditions, in a 3 (uncertainty format) x 2 (uncertainty type) factorial experiment.

Methods
The stimuli in this experiment were drawn from statistics reported by modelling from Imperial College London (n.d.) . To ensure that the participants were not misled by using factually inaccurate statistics on such an important topic, real modelling figures had to be used. This does introduce a confound to the experimental design as there was necessarily a difference in point estimates and intervals presented to participants in the different uncertainty format conditions. We return to this point in discussing the results.
Those in the epistemic uncertainty condition were given the core information "Looking at the average number of deaths per day over a period of time helps to understand . CC-BY-NC 4.0 International license It is made available under a perpetuity.
is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; https://doi.org/10. 1101/2021 whether the COVID19 epidemic is stabilising in the United Kingdom. This past week, the average number of deaths in the UK was about 555 per day." Control participants received only this information. Those in the numeric uncertainty format condition were given the extra information "(range between 439 and 698)." Whilst those in the verbal uncertainty format condition were instead given the extra information "There is some uncertainty about this number, it could be somewhat higher or lower." Those in the aleatory uncertainty condition were given the information "Looking at the average number of deaths per day over a period of time helps to understand whether the COVID19 epidemic is stabilising in the United Kingdom. This upcoming week, the average number of deaths in the UK is expected to be about 591 per day." Control participants received only this information. Those in the numerical uncertainty format condition were given the extra information "(range between 371 and 1081)." Whilst those in the verbal uncertainty format condition were instead given the extra information "There is some uncertainty about this number, it could be somewhat higher or lower." Participants were then asked the same questions as in Study 1 to ascertain their perception of the uncertainty in the number, their trust in the number (three items; α = .94) and their trust in the people responsible for producing the number. Participants also answered questions about how positive or negative the information made them feel, how easy it was to understand and how competent they thought the source of the information was. Details and results for these secondary outcomes are reported in the supplementary material (Appendix 4).

Results
Considering first perceived uncertainty, a two-way ANOVA examining the effect of uncertainty format (control, numeric, and verbal) and uncertainty type (epistemic and aleatory), revealed a significant interaction, F(2, 2299) = 4.01, p = 0.02, ηp 2 = 0.003, indicating that the effect of condition differed across uncertainty types. This was followed up with one-way ANOVAs examining the effect of condition in each uncertainty type group. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; https://doi.org/10. 1101/2021 Post hoc tests revealed that, among participants presented with epistemic uncertainty, verbal uncertainty (Mverbal = 4.54, SD = 1.53) was perceived as more uncertain than numeric uncertainty (Mnumeric = 3.70, SD = 1.36; p < .001, d = .58) or no uncertainty (Mcontrol = 3.72, SD = 1.39; p < .001, d = .55). There was no significant difference between uncertainty ratings in the control and numeric conditions. A similar pattern was seen among those presented with aleatory uncertainty, though the effects were smaller: verbal uncertainty (Mverbal = 4.44, SD = 1.42) was perceived to be significantly more uncertain than numeric (Mnumeric = 3.94, SD = 1.35; p < .001, d = .36) or no uncertainty (Mcontrol = 3.99, SD = 1.39; p < .001, d = .23). There was no significant difference between uncertainty ratings in the control and numeric conditions. Pairwise differences are displayed graphically in Figure 3A (note that for clarity the p < .001 pairwise comparisons are collapsed across the epistemic and aleatory conditions).
We also examined pairwise differences between epistemic and aleatory uncertainty types within each of the three condition groups (means reported above). Among participants in the control format condition (who read no additional uncertainty information), aleatory uncertainty was perceived to be more uncertain than epistemic uncertainty (p = .008, d = .19).
Among participants presented with the numeric condition, aleatory uncertainty was also perceived to be more uncertain than epistemic uncertainty (p = .014, d = .17). In the verbal uncertainty condition, there was no significant difference in perceived uncertainty between aleatory and epistemic uncertainty types. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; https://doi.org/10.1101/2021.09.27.21264202 doi: medRxiv preprint Figure 3: The effect of uncertainty format and type on: (A) perceived uncertainty, (B) trust in numbers, and (C) trust in source (means and 95% CI). Horizontal bars indicate a significant pairwise difference between format conditions (for both epistemic and aleatory uncertainty types), greyed stars indicate significant pairwise difference between epistemic and aleatory uncertainty types within condition, *p < .05, **p < .01, ***p < .001.
Considering trust in the numbers, a two-way ANOVA found no significant main effect of uncertainty type (i.e. no significant difference between epistemic and aleatory uncertainty across conditions; F(1, 2302) = 0.62, p = 0.43). We did find a significant main effect of uncertainty format, F(2, 2302) = 22.69, p < .001, ηp 2 = .019. There was no significant interaction effect. There was no significant difference between control and numeric conditions ( Figure 3B).

Post-hoc tests revealed that participants who read a verbal uncertainty communication
Lastly, considering trust in the source of the information, a two-way ANOVA showed no significant effects of uncertainty type (F(1, 2299) = 0.08, p = 0.77) or of uncertainty format (F(2, 2299) = 0.70, p = 0.50): participants' trust in the people responsible for producing the number was not affected by the inclusion of uncertainty in any form ( Figure   3C). Additional analyses focusing on secondary outcomes (difficulty of understanding, emotional response, and perceived competence of source) found no significant effects of either experimental factor (see supplementary information, Appendix 4). is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; https://doi.org/10.1101/2021.09.27.21264202 doi: medRxiv preprint

Interim Discussion
Participants in Study 2 perceived communications including verbal uncertainty as more uncertain than communications without, and were less trusting of the numbers provided, but did not consider the communicators of such information less trustworthy. We also find that the presence or absence of numeric uncertainty has no significant impact on the trust in the number or the source. These effects were consistent across messages communicating either current (epistemic) or future (aleatory) uncertainty about COVID-19 deaths. The results are consistent with our UK findings in Study 1.
Future predictions were perceived as more uncertain than current estimates for control and numeric uncertainty communications, but this framing had no impact on participants' trust in the numbers or source. We do acknowledge that the aleatory and epistemic stimuli differed in terms of the numbers communicated as we did not want to mislead participants with inaccurate information in the midst of the pandemic (we address this confound in Study 3). As the numeric uncertainty range was substantially larger for the figures in the aleatory condition, we would expect the effect of such a confound to exacerbate, rather than diminish any effects on trust. Thus, we take the current results as evidence that numeric uncertainty, relating to either current or future estimates, does not negatively impact trust in the numbers or the source.
This supports previous work that has demonstrated no negative effect of communicating aleatory uncertainty on trust (Joslyn & LeClerc, 2012;Kuhn, 2000).
Although work in this area is not consistent, with some studies finding both positive and negative effects on trust (Johnson & Slovic, 1995), and others showing that the nature of trust effects break down according to participant characteristics such as education level (Schapira et al., 2001).
Considering the between-country differences reported in Study 1 we must also caveat these findings with the limitation that data was only collected from UK residents. We cannot generalise these effects to other cultural contexts where attitudes to uncertainty may differ.

Study 3
Study 2 examined the impact of both uncertainty type (aleatory, epistemic) and format (numeric, verbal) on trust in COVID-19 information and its source. These two factors have . CC-BY-NC 4.0 International license It is made available under a perpetuity.
is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; not been examined simultaneously in prior research, to our knowledge. However, as detailed in the introduction, COVID-19 may present an unusual context because of its extreme emotional salience. Do these results extend to other issues, which participants may perceive as more psychologically distant? In this study we present results from an earlier ) study investigating the effects of uncertainty type and format in relation to statistics in three other domains, namely climate science, tiger conservation, and unemployment.
The stimuli in this study also avoid the confound in Study 2 arising from the use of differing numbers and ranges for aleatory and epistemic uncertainty. Participants completed an online survey experiment on the Qualtrics platform.

Methods
Following informed consent, participants were randomly assigned to one of 18 conditions in a 2(uncertainty type)x3(format)x3(topic) between-subject design. Participants were first asked several questions about their current beliefs relating to the topics examined (not reported here). Participants then read a short paragraph about one of the following issues: the rise of the global surface temperature, the decline of the tiger population in India, or rise of the unemployment rate in the UK. All these statements were framed in a negative direction to control for valence effects (i.e., the statistics in presented each condition could broadly be considered 'bad news'). For instance, although the UK unemployment rate was declining at the time of the research, we stated that it is rising. The uncertainty about these estimates was either absent (control), included as a numerical range (presented as minimum-maximum range), or as a verbal statement that a (unquantified) level uncertainty exists around the estimate. This information was either presented as the present state for 2019 (epistemic condition) or as a prediction for 2025 for the unemployment and tiger numbers or 2050 for the climate numbers (aleatory condition).
For example, participants assigned to the tigers topic and aleatory numeric uncertainty conditions read the following information: "An official report has come out with new . CC-BY-NC 4.0 International license It is made available under a perpetuity.
is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ;https://doi.org/10.1101https://doi.org/10. /2021 information about the number of tigers in India. It shows that the number of tigers could fall to a historic low of 2,226 (minimum 1,945 to maximum 2,491) by 2025." Participants assigned to the unemployment topic and epistemic verbal uncertainty conditions read: "An official report has come out with new information about the unemployment rate in the United Kingdom. It shows that the UK's unemployment rate has risen to 3.8% in the first quarter of 2019. The report states that there is some uncertainty around this estimate, it could be somewhat higher or lower." The texts for all 18 experimental conditions are reported in Appendix 5.
After reading the information, participants were then asked the same questions as in Studies 1 and 2 to ascertain their perception of the uncertainty in the number, their trust in the number (three items; α = .91) and their trust in the people responsible for producing the number. Upon completion of the survey, participants were debriefed with information about the real statistics and sources of these numbers.

Results
For simplicity of reporting, and because numbers and time frames varied across topics, we report results for each of the three topics separately, examining the effect of uncertainty type and format with 2x3 two-way ANOVAs as in Study 2. For consistency, we report the results of Tukey's post hoc tests based on one-way ANOVAs examining the effect of format for epistemic and aleatory types separately (shown in Figures 4-6; cell means and SDs reported in Appendix 5). We note instances where these differ from the two-way ANOVA results (i.e. the pattern of significant pairwise comparisons between formats differs across uncertainty types despite no significant interaction between format and type in twoway ANOVAs). For completeness, we also report pairwise comparisons between uncertainty types and topics, at each level of the other experimental factors, in Appendix 6.

Perceived uncertainty
We consider first the effect of our experimental manipulations on perception of uncertainty. For participants in the climate topic condition, two-way ANOVA results revealed a significant interaction between uncertainty type and format, F(2, 747) = 4.41, p = .01, ηG² = 0.012. Separate one-way ANOVAs in the epistemic (F(2, 369) = 37.70, p < .001, ηG² = 0.170) and aleatory (F(2, 378) = 9.55, p < .001, ηG² = 0.048) uncertainty conditions both revealed a significant effect of format, though this effect was larger in the epistemic condition.
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is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; https://doi.org/10. 1101/2021 For participants who viewed information about tiger numbers, we report a significant main effect of format, F(2, 751) = 36.44, p < .001, ηG² = 0.088, but not uncertainty type, F(1, 751) = 3.30, p = .07, and no significant interaction.
Across all topics and uncertainty types, post-hoc tests comparing formats revealed a consistent pattern: verbal uncertainty was perceived as more uncertain than the control format (all p < .001, ds .48-.99) and numeric format (all p < .001, ds .46-.92), with no significant differences between numeric and control condition. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; Figure 4: The effect of uncertainty format on perceived uncertainty, plotted across uncertainty type (rows) and topics (columns; means and 95% CI). Horizontal bars indicate a significant pairwise difference between format conditions. ***p < .001.

Trust in numbers
Turning to trust in the numbers, we report for participants in the climate condition a significant interaction between uncertainty type and format, F(2, 747) = 5.60, p < .01, ηG² = 0.015. Follow up one-way ANOVAs indicated a significant effect of format for both epistemic, F(2, 369) = 26.43, p < .001, ηG² = 0.125, and aleatory uncertainty, F(2, 378) = 3.80, p = .02, ηG² = 0.020, with a larger effect for epistemic uncertainty. Pairwise comparisons revealed that, for epistemic uncertainty, verbal uncertainty was considered less trustworthy than control (p < .001, d = .78) or numeric formats (p < .001, d = .77). For is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; https://doi.org/10.1101/2021.09.27.21264202 doi: medRxiv preprint aleatory uncertainty, verbal uncertainty was considered less trustworthy than numeric uncertainty (p = .03, d = .33; with no other significant differences).
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is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; Figure 5: The effect of uncertainty format on trust in numbers, plotted across uncertainty type (rows) and topics (columns; means and 95% CI). Horizontal bars indicate a significant pairwise difference between format conditions. *p < .05, **p < .01***p < .001.

Trust in source
Lastly, we examine participant's trust in the source of the information presented in the experiment. Considering participants in the climate topic condition, a 2(type)x3(format) ANOVA revealed no significant main effects but a marginally significant interaction, F(2, 747) = 2.68, p = .07, ηG² = 0.007. Follow-up one-way ANOVAs indicated a significant effect of format in the epistemic uncertainty condition, F(2, 369) = 5.04, p < .01, ηG² = 0.027, but not aleatory condition, F(2, 378) = 0.00, p = 1.00. Post hoc tests investigating pairwise differences between formats for epistemic uncertainty revealed that the source of communications including the verbal uncertainty format was less trusted than the source of control (p = .03, d = .31), or numeric format communications (p = .009, d =.37).
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is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ;https://doi.org/10.1101https://doi.org/10. /2021 For participants in the tigers topic condition we report only a significant main effect of format, F(2, 751) = 4.84, p < .01, ηG² = 0.013, however separate sets of post hoc tests revealed a significant difference only in the epistemic uncertainty type condition: the source of verbal uncertainty was less trusted than the source of the control communication without uncertainty (p = .04, d = .30).
Considering participants who read information about unemployment numbers, we report a main effect of format only, F(2, 738) = 12.78, p < .001, ηG² = 0.033. However, separate post hoc tests for epistemic and aleatory uncertainty types indicated differing patterns of significant pairwise differences. In the epistemic uncertainty condition, the source of verbal uncertainty was less trusted than source of numeric uncertainty (p = .03, d = .32). In the aleatory uncertainty condition, the source of verbal uncertainty was less trusted than source of numeric uncertainty (p <.001, d = .58), and the source of control information without uncertainty (p = .001, d = .44).
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is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; Figure 6: The effect of uncertainty format on trust in source, plotted across uncertainty type (rows) and topics (columns; means and 95% CI). Horizontal bars indicate a significant pairwise difference between format conditions. *p < .05, **p < .01***p < .001.
Results for additional secondary outcomes-reported difficulty and emotional response-are reported in Appendix 7.

Interim discussion
In Study 3 we examined the impact of uncertainty format (a specific, numeric quantification of uncertainty or a vague and unquantified verbal expression of uncertainty) and how this is affected by whether the uncertainty is regarding the current state of affairs (epistemic) or looking to the future (aleatory). We find across all topics, and for both epistemic and aleatory uncertainty, that messages with no uncertainty information and messages with numeric uncertainty (a confidence interval) are perceived as essentially . CC-BY-NC 4.0 International license It is made available under a perpetuity.
is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ;https://doi.org/10.1101https://doi.org/10. /2021 equally uncertain. Expressions of verbal uncertainty, however, are consistently perceived as more uncertain.
Similarly, when considering trust in the numbers presented, we find a consistent pattern across topics and uncertainty types: statistics with no uncertainty or numeric uncertainty do not significantly differ in terms of how much participants trust the numbers, while messages with verbal uncertainty are considered less trustworthy. The one exception to this is future-focused climate predictions, where we report no significant difference between messages without uncertainty and messages with verbal uncertainty, in terms of trust.
Lastly, we find a slightly more heterogenous set of results when examining trust in the (unnamed) source of the numbers. We again report no significant differences between messages with no uncertainty or numeric uncertainty. However, the effect of verbal uncertainty (vs control) differs depending on both the topic and type of uncertainty. When the uncertainty is relating to current climate or tiger statistics, we find that verbal uncertainty leads to lower levels of trust in the source, but there is no effect when uncertainty relates to current employment rate estimates. We find the opposite pattern when considering aleatory uncertainty: verbal uncertainty has no impact on trust in the source of numbers when relating to climate or tiger statistics but does lead to lower trust when numbers relate to unemployment statistics. This suggests that the impact of verbal uncertainty on trust in the information source is context-specific, and caution should be exercised in generalizing effects from one domain to another.

Discussion
Across three different studies, covering multiple countries, topics, and temporal framings, we find a clear pattern in which communications expressing statistical uncertainty as a range around a point estimate are not perceived less trustworthy nor are the communicators considered less trustworthy. Only when drawing on the statistical power of a combined sample of more than 10,000 participants (Study 1) do we find a small negative effect of such uncertainty on trust in the numbers presented, and still no significant effect on trust in the source. In this regard, our results are consistent with the prior work of van der Bles (2020) and others (see Gustafson & Rice, 2020), and extend these findings to the new, and arguably more personally salient, context of the COVID-19 pandemic. As a further extension on van der Bles (2020), we also find minimal impact of numeric uncertainty on trust when claims relate to future predictions rather than current estimates. First and foremost, . CC-BY-NC 4.0 International license It is made available under a perpetuity.
is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; https://doi.org/10.1101/2021.09.27.21264202 doi: medRxiv preprint then, we echo previous recommendations that communicators should feel confident that they can use numerical ranges around their point estimates when communicating COVID-19 statistics or projections without risking a significant undermining of audience trust (Blastland et al., 2020;van der Bles et al., 2019).
Figures communicated with imprecise, verbal expressions of the existence of uncertainty regarding a statistic (e.g., 'could be higher or lower') may be considered less trustworthy and undermine the credibility of communicators. On this front, our results paint a more complicated picture. Regarding trust in numbers, the negative impact of this type of uncertainty when applied to COVID-19 statistics varies across countries (Study 1). In the UK we find that such expressions consistently lower trust across types of uncertainty (epistemic or aleatory; study 2) and topics (study 2 and 3). The extent to which this translates into decreased trust in the source of the information appears to vary by domain as well as type of uncertainty. Verbal uncertainty had little impact on trust in the source of COVID statistics (Studies 1 & 2) and for other topics effects vary by both type and topic (Study 3). The sources of unquantified verbal uncertainty may be considered trustworthy for some forecast statistics (COVID-19 deaths, climate warming, tiger numbers) but not others (unemployment). A possible explanation for these differences may be that some contexts are viewed as inherently more uncertain, and blunt admissions of uncertainty are considered more acceptable. But taken as whole, these findings suggest that communicators should be cautious in mentioning of the existence of uncertainty regarding a statistic without some description of the bounds of that uncertainty.
In no case did we find that expressions of uncertainty increase trust in numbers or their source. This is noteworthy as some previous research has found provision of uncertainty to increase credibility in some cases, for example in earthquake and climate projections (Joslyn & Demnitz, 2019;Joslyn & LeClerc, 2016;Nakayachi et al., 2018). However other studies have found no effect of uncertainty on credibility in other domains (e.g. GM food, Gustafson & Rice, 2019;health, Lipkus et al., 2001). These mixed findings are not surprising given the range of issues, forms of uncertainty and operationalizations of trust and credibility used in previous research (Gustafson & Rice, 2020). The current study contributes to ongoing work in identifying the broader factors that determine when communication of uncertainty does or does not garner greater trust. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ;https://doi.org/10.1101https://doi.org/10. /2021 While a single message with uncertainty may not increase trust, it might buffer against future damage to credibility if figures are revised. Batteux et al. (2021) report that the inclusion of a range (vs point estimate) in COVID-19 vaccine efficacy communications had no immediate impact on trust. However, when participants were later presented with conflicting evidence (updating the previous estimate), those who had first received a point estimate with no uncertainty reported lower trust in the communicator, compared to those receiving a range. This suggests that communicating uncertainty up front can mitigate later skepticism when scientific evidence is updated. Such findings are particularly relevant to situations such as the COVID-19 pandemic, where evidence and recommendations are constantly updated (Kreps & Kriner, 2020;Martin et al., 2020).
The consistency of our findings regarding numeric uncertainty and trust-across countries, issues, and temporal framings-gives us some confidence in our conclusions.
However, we must acknowledge some limitations. Firstly, the uncertainty ranges communicated in our messages were all drawn from existing reports. While this provides some ecological validity, it did mean we were not able to control for the magnitude of the range presented across some conditions. Previous research suggests people may be less trusting of uncertainty presented as a very large numeric range (Kreps & Kriner, 2020;. More research is needed to identify the effect of range magnitude and how this varies across contexts.
Secondly, Studies 2 and 3 were only conducted in UK samples. As shown in Study 1, there is between-country variation in how people respond to uncertainty. Therefore, we cannot confidently generalize our UK findings to other national contexts. Future research should seek to replicate these findings with other countries as well as investigating possible explanations for the variation seen in Study 1.
Lastly, the types of uncertainty we examined in the current research were narrowly defined. Thus, our findings may not map onto to other forms or formats of uncertainty. For example, statistical uncertainty could be expressed visually-rather than as numerals-and the existence of unquantified uncertainty could be phrased in a multitude of different ways.
Uncertainty can also be further attributed to different sources, with potentially differing impacts. For example, claims could be accompanied by statements about uncertainty due to a lack of data, poor quality research, disagreement among experts, or the nature of the scientific . CC-BY-NC 4.0 International license It is made available under a perpetuity.
is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; https://doi.org/10.1101/2021.09.27.21264202 doi: medRxiv preprint method itself. The inclusion of such explanations may moderate the effects of uncertainty on credibility and deserves further attention.
In conclusion, we find that acknowledging uncertainty in the form a range has minimal impact on the perceived trustworthiness of figures or their assumed source. This applies to COVID-19 statistics and claims in other domains, regardless of whether the figures relate to current estimates or future projections. Statements merely acknowledging the existence of uncertainty may be treated with more skepticism, though this appears to be context dependent.
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is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 29, 2021. ; https://doi.org/10.1101/2021.09.27.21264202 doi: medRxiv preprint

Data availability
Data and R analysis scripts are available on the Open Science Foundation website: https://osf.io/y982k/?view_only=07f2c4fd8000488f90f564f5a209bb9c