Numerical and Visual Representations of Uncertainty Lead to Different Patterns of Decision Making

Although visualizations are a useful tool for helping people to understand information, they can also have unintended effects on human cognition. This is especially true for uncertain information, which is difficult for people to understand. Prior work has found that different methods of visualizing uncertain information can produce different patterns of decision making from users. However, uncertainty can also be represented via text or numerical information, and few studies have systematically compared these types of representations to visualizations of uncertainty. We present two experiments that compared visual representations of risk (icon arrays) to numerical representations (natural frequencies) in a wildfire evacuation task. Like prior studies, we found that different types of visual cues led to different patterns of decision making. In addition, our comparison of visual and numerical representations of risk found that people were more likely to evacuate when they saw visualizations than when they saw numerical representations. These experiments reinforce the idea that design choices are not neutral: seemingly minor differences in how information is represented can have important impacts on human risk perception and decision making.


D
ecision making in the face of uncertainty is very difficult.People can struggle to understand complex information under the best of circumstances, but when that information is uncertain, even the most carefully thought-out decision can result in an undesirable or unanticipated outcome.Visualizations can be useful tools for people who must make decisions or predictions based on uncertain information, and there is a large body of research concerned with developing methods for visualizing uncertainty. 1,2However, it is often difficult to determine what method of representing uncertainty will best support human comprehension and decision making. 3e field of visualization cognition studies how people derive meaning from and reason about data visualizations. 4A common finding in this literature is that different visual representations of the same information can lead to performance differences for a wide variety of tasks. 5This is particularly problematic for visualizations that convey information about uncertainty.People find it difficult to reason about uncertainty, 3,6 and visualizing that information can introduce additional biases into their reasoning. 1,4,7here is not yet a systematic understanding of when and how visualizations of uncertainty lead to different perceptions of risk or different patterns of decisions. 3hile several studies have assessed the impact of different types of uncertainty visualizations on decision making, relatively few have systematically compared visualizations to other representations of uncertainty, such as numerical or verbal representations.In one of the few studies to do so, Bisantz et al. 8 manipulated how probabilistic information about stock performance was represented to participants, changing both the specificity of the information (the width of the probability band shown) and the representation of the information (verbal, numerical, or visual).They found that people made more cautious decisions when shown visual representations of probability, spreading their risk across more small stock purchases.However, as the specificity of the information increased, the participants in the visualization condition began to act more similarly to the participants in the numerical condition, making fewer, larger stock purchases.
In another study that directly compared visual and numerical representations of uncertainty, Cheong et al. 9 gave participants a wildfire evacuation task in which they saw maps or numerical probabilities indicating the likelihood that their house would be in the burn zone of a wildfire.They found that the participants were more likely to evacuate when shown the numerical information, making the correct decision more often.However, when the participants had to make decisions under time pressure, their performance was significantly worse for the numerical information than for the visualizations.
Different patterns of performance in response to text and visual representations of uncertainty were also noted by Joslyn and LeClerc 10 in the context of weather forecasts.They found that participants frequently misinterpreted a simple representation of the uncertainty in a temperature forecast, interpreting the uncertainty in the forecast as if it were a deterministic forecast showing the high and low temperatures for the day.They refer to this as a deterministic construal error, where people interpret information about uncertainty as if it were deterministic rather than uncertain, which allows people to simplify their decision making.They note that visualizing uncertainty may make it seem more concrete and therefore more certain than the equivalent verbal or numerical representation.In other words, visualizations of uncertainty may be more prone to deterministic construal errors than other representations of the same information, producing unintended consequences for viewers' perception of risk and their consequent decisions.
In the prior studies that have compared visual and numerical representations of uncertainty, participants generally had to estimate a value based on a visual or numerical range, whether that value was the likelihood of a stock being profitable 8 or the likelihood of a house being in the burn zone of a wildfire. 9It is not clear whether that process of estimation is less precise for visual representations, leading to more cautious patterns of decision making, 8 or whether the fact that information about uncertainty has been visualized makes the risk seem more concrete and deterministic to viewers. 10 In this article, we present two experiments that attempted to tease apart the effects of visualizing uncertain information and estimating a point value of probability based on a visual representation.In these experiments, we showed participants visual representations of probability (icon arrays) and numerical representations of probability (natural frequencies) in the context of a wildfire evacuation task.Icon arrays, sometimes referred to as "pictographs," are matrices of representative images that are color coded to represent proportion or probability.They are particularly popular in medical decision-making contexts, because they have been shown to improve comprehension of probability, particularly for individuals with less developed numerical skills. 1,6,11,12Specifically, icon arrays have been demonstrated to benefit both gist and precise understanding of risk. 13,14con arrays and natural frequencies provide a specific point value, eliminating the need for estimation.This allowed us to compare identical values, represented visually and numerically, to determine whether the representation itself impacted decision making.Icon arrays also allow for manipulations of the specificity of the information presented to participants.Bisantz et al. 8 found that people had more similar patterns of decision making for numerical and visual representations of probability when the information provided was more specific, but that participants generally made more cautious, risk-averse decisions when shown visualizations of probability.We manipulated the specificity of the icon arrays by presenting probabilities with a denominator of 10 or 100.We also manipulated the iconicity and the ordering of the icons in the icon arrays.Prior research suggests that these factors can influence viewers' decisions.Iconicity refers to the extent to which a representation resembles the referent. 15Icon arrays with low iconicity typically use abstract shapes such as squares while those with higher iconicity use shapes that represent the items in question, such as silhouettes of people.High iconicity can make viewers feel that the information is more personally relevant. 12Randomizing the order of the icons in an array has been shown to convey a greater sense of randomness, reinforcing the probabilistic nature of the outcome. 11We hypothesized that these manipulations might change how the participants perceive the risk information conveyed by the icon arrays, leading to different patterns of evacuation decisions.
Across two experiments, we found that participants were more likely to make the decision to evacuate when shown icon arrays than when shown natural frequencies.Manipulating the visual features of the icon arrays, such as the iconicity and the ordering of the icons, could exacerbate this effect.These findings show that even when people are provided with specific point values, visual representations of those values can lead to more cautious decisions than numerical representations of the same information.

EXPERIMENTAL STRUCTURE
The experiments described below were conducted online, using Amazon Mechanical Turk.The participants received a base payment for their participation plus bonus payments based on the decisions they made during the tasks.Although these online experiments do not replicate the real-world consequences of making decisions under risky or uncertain circumstances, the participants were motivated to make the best decisions possible in order to maximize their bonus payments.
Based on the costs and benefits associated with different decisions and the outcomes of those decisions, there was an objective pattern of "optimal" responses that would produce the highest expected value for the bonus payments.Our goal in these experiments was to compare participants' responses to different representations of the same underlying information.We wanted to see whether changing the representation changed their assessment of the risk, and therefore their evacuation decisions.
While these experiments do not carry a real-world risk, tightly controlled experiments like these are a necessary first step for understanding how visualizations of uncertainty can influence human decision making.By comparing different representations of uncertainty within the same decision-making context, we can identify fundamental patterns in human reasoning that are likely to translate to real-world decision making as well.

NUMERICAL AND VISUAL REPRESENTATIONS OF NATURAL FREQUENCIES
Across two experiments, we compared the participants' responses to the same risk information when it was presented numerically (e.g., "a 60 in 100 chance") or visually, in the form of an icon array.As discussed above, we chose to compare icon arrays to natural frequencies because they can convey precisely the same risk information, allowing us to test the impact of visualization on decision making in a situation where participants do not need to estimate a point value.
Instead of seeing a range of probabilities, they were given point values in both the visual and numerical conditions.
The experiments used a wildfire evacuation task based on the work by Cheong et al. 9 The participants were shown a picture of a cabin in the woods and were asked to imagine that they lived there.On each trial in the experiment, the participants were given information about the risk that their cabin would be in the burn zone of a wild fire.Based on that information, they decided whether to stay or to evacuate.After clicking a button to indicate what they had decided, they were shown the outcome-whether or not the cabin had burned down.The experimental trials were independent of one another, so the outcome of one trial had no bearing on the outcome of future trials.Each time the participants responded correctly (choosing to evacuate in a scenario where the house burned down or choosing to stay when it did not), they received a five cent bonus.However, there were also costs associated with the different decisions.Each time a participant chose to evacuate, they had to pay two cents from their bonus.This payment represented the costs associated with evacuation.On the other hand, if a participant chose to stay in their cabin and it ended up burning down, they lost 10 cents from their bonus.This reflected the greater cost of the risk associated with failure to evacuate in a dangerous situation.
The expected value of each decision can be calculated by subtracting the expected cost of an incorrect decision (the cost multiplied by the probability of incurring the cost) from the expected profit of a correct decision (the profit multiplied by the probability of gaining the profit).Based on the cost/benefit structure of this experiment, the optimal pattern of decisions would be to stay in the cabin if the probability of being in the burn zone was 30% or lower, and to evacuate if the probability was 40% or higher.This would maximize the expected value and therefore maximize the participants' bonus.Throughout the experiment, the participants saw a reminder of the cost structure on the screen.However, they were not told the optimal strategy based on the expected value of the decisions.
The experiments manipulated how the information about risk was presented to the participants.Our primary comparison of interest was between visual and numerical representations of probability.However, we also manipulated the specificity of the information and factors that might impact the perceived risk.To manipulate the specificity of the information, we showed participants natural frequencies and icon arrays with a denominator of 10 (less specific) or 100 (more specific).We also manipulated the iconicity by presenting icon arrays with blue and orange squares (low iconicity) or with blue house icons and burning orange house icons (high iconicity).Finally, we manipulated the order of the icons by grouping icons in the same category or by randomizing their order.
If visualizing probabilistic information leads to more cautious decision making than numerical representations of the same information, we would expect the participants to have higher evacuation rates when shown icon arrays than when shown natural frequencies.Furthermore, we expect that different visual cues will lead to different patterns of decisions, as has been shown in prior studies of uncertainty visualizations. 1,4,5,7Higher iconicity has been shown to make information seem more personally relevant to viewers, 12 which could make them less likely to accept risks.Similarly, randomization of icons can make the probabilistic nature of the outcome more salient, 11 which could also increase the perceived risk.Based on these past findings, we predicted that more people would chose to evacuate when shown the higher iconicity and randomized icon arrays.

Participants
The experiments in this study were reviewed and approved by the Human Studies Board at Sandia National Laboratories.The participants were recruited from Amazon Mechanical Turk and were required to have the "masters" qualification, to be located in the United States, and to have an approval rate greater than 95 percent for prior tasks.The participants completed a pretest containing individual difference measures, described in more detail below.Upon completion of the pretest, they were given a qualification that allowed them to participate in the wildfire evacuation experiments.Fifty participants completed Experiment 1 and 48 different participants completed Experiment 2.

Measures of Individual Differences
Prior to completing the wildfire evacuation task, the participants completed a pretest containing five measures of individual differences.The pretest assessed the participants' numerical abilities, graph literacy, and risk-taking propensity.Each of these measures relates to cognitive characteristics that could influence the decisions that participants made during the wildfire evacuation task.
The participants' numeracy was assessed using the Subjective Numeracy Scale 16 and the Objective Numeracy Scale. 17These two questionnaires scored the participants according to their self-reported comfort with different kinds of mathematical operations and their ability to perform a set of mental calculations.
Graph literacy was assessed using the Short Graph Literacy Scale, which scores participants based on ability to correctly interpret a pie chart, bar graphs, an icon array, and a line graph. 18inally, participants were asked to complete the Dohmen measure, a one-item survey question assessing their general risk-taking propensity.They were asked, "How do you see yourself?Are you generally a person who is fully prepared to take risks or do you try to avoid taking risks?" and responded using a 7-point Likert-scale ranging from 1 (not at all willing) to 7 (very willing).Although this measure is very simple, past research has found that it is a good predictor of reallife risk-taking behavior. 19

Wildfire Evacuation Task
In Experiment 1, participants saw a total of 94 unique trials, all of which were independent of one another (i.e., the probability of the house being in the burn zone on one trial had no relationship to the probability on the next trial).Four of the trials were "catch" trials, where participants were told that there was a 0% or 100% chance of their house being in the burn zone.For the remaining 90 trials, there were 10 trials at each of nine levels of probability: 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, or 90% chance of being in the burn zone.For each probability level, participants saw the information presented in ten different ways, twice as a natural frequency, and eight times as an icon array.The natural frequency stimuli represented the probability as a number out of 10 or out of 100.The icon arrays could have 10 or 100 icons, the icons could be squares or houses, and the icons could be ordered or randomized.The different combinations of these variables created a total of eight possible icon array representations.Examples of the stimuli are shown in Figure 1.
The outcomes of the trials corresponded to the probability levels.For example, for the ten trials where the probability of the cabin being in the burn zone was 50%, five resulted in the cabin being safe and five resulted in the cabin burning down.The outcomes were balanced across conditions so that no one stimulus type had more negative outcomes than the others.

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The trials were presented in a different random order for each participant.We might expect that the outcome of one trial might impact participants' decisions for the next trial.For example, if a person chose to stay and the house burned down, they might make a more cautious decision on the next trial.However, with 94 trials per participant, presented in a different random order each time, we would expect any ordering effects to balance out so that they would not have differential impacts on any particular type of stimulus.
The participants were instructed that all trials were independent and that the outcome of one trial had no bearing on the outcome of other trials.They were instructed to use the probability information to make whatever decision they thought was best for each trial.
Experiment 2 used the same task as Experiment 1.The key difference was that the "out of 100" items were modified so that the probabilities were 1%-2% above or below the 10% increments used in Experiment 1, as shown in Figure 2. Instead of a 40% chance of being in the burn zone, there was a 38%, 39%, 41%, or 42% chance.This did not substantially change the risk to the house, but might change the participants' perception of the risk.The stimuli were divided into four counterbalanced lists so that each percentage was represented by a different icon array condition across lists.This ensured that there were no systematic biases where the lowest or highest percentages were more likely to be in one visualization condition than another.

RESULTS
Very few participants made consistent evacuation decisions across all stimulus types.There were only two participants in each experiment who made consistent decisions regardless of how the risk information was shown.In Experiment 1, one participant used  the optimal strategy of evacuating whenever the probability of the house being in the burn zone was 40% or higher and staying in the house otherwise.Another participant in Experiment 1 and both of the consistent participants in Experiment 2 chose to evacuate whenever the probability was 50% or higher.The other 94 participants had different "tipping points" for evacuation when the probability information was presented in different ways.

Individual Differences
The first step in our analysis was to test whether there were any correlations between the participants' evacuation decisions and the individual difference measures collected during the pretest.We found significant correlations between the participants' overall evacuation rates and their scores on the graph literacy scale (r (98) ¼0.34, p <0.001) and the risk propensity question (r (98) ¼ À0.28, p ¼0.01).Participants with higher graph literacy scores tended to evacuate more often, as did participants who reported that they were less willing to take risks.Due to these significant relationships, graph literacy and risk propensity were included as covariates in the subsequent analyses.

The Impact of Representation Type on Evacuation Decisions
The analyses used mixed effects logistical models to predict participants' evacuation decisions (stay or evacuate) from fixed effects of representation type with the risk level (the probability of the house burning down), graph literacy, and risk propensity scores as covariates, and with random intercepts for participants.The first analysis compared the natural frequency stimuli to the icon arrays.It found a significant main effect of representation type on the evacuation decisions, with participants being more likely to evacuate when they saw icon arrays than when they saw natural frequencies.Figure 3 shows how often the participants chose to evacuate at each risk level for the visual and numerical representations.At the extremes, when the house is very likely or very unlikely to be in the burn zone, the participants made very similar decisions regardless of the representation type.However, when there was an intermediate level of risk, the evacuation rates were higher when participants saw visualizations of probability.
A second analysis focused on the different icon array conditions.That analysis revealed a significant main effect of icon order, with participants more likely to evacuate when the icons were randomized.There was also a significant interaction between icon order and icon number.Bonferroni pairwise comparisons showed that the ordering of the icons had a significant impact on participants' evacuation rates when they were shown 100 icon arrays, but not when they were shown 10 icon arrays.These results are shown in Figure 4. Finally, there was a significant interaction between icon order and icon type.As shown in  Figure 5, the participants were more likely to evacuate when they saw randomized square icons than when they saw ordered square icons.However, when they saw the higher iconicity house icons, the ordering of the icons had no effect on their evacuation rates.
An analysis of the participants' response times showed that there were no significant differences between conditions.The average response time was around two seconds for all trial types, with slightly longer times for the natural frequencies than for the icon arrays.
The results of Experiment 1 show that different representations of uncertainty have an impact on human decision making even when people are provided with a point estimate of probability.The participants were more likely to evacuate when the probability of the house being in the burn zone was represented visually.In addition, the design of the icon arrays had an impact on decision making.Participants were less likely to evacuate when they saw an array of 100 ordered icons than when they saw an array of 10 icons.This is consistent with the findings of Bisantz et al. 8 in the sense that visualizations with higher specificity (the 100 icon arrays) produced decisions that were more similar to the numerical representations of probability.In this case, the evacuation rates were lower for both the numerical representations and the more specific visualizations relative to the less specific visualizations.This pattern is also consistent with prior research on icon arrays in the medical decision-making literature, where participants have been found to focus on the denominator of icon arrays, interpreting a larger number of items in the "safe" category as an indication of a lower level of risk. 20andomizing the order of the icons significantly increased the evacuation rates in the 100 icon conditions, but not in the 10 icon conditions, and for the square icons but not the house icons.The participants' response times indicated that they did not take the time to count the number of icons in the risky group when they were shown a randomized icon array.Instead, they quickly estimated the risk level.The increase in evacuation rates for the 100 icon arrays indicates that the participants estimated the risk to be higher when the icons were randomized.For the iconicity manipulation, the evacuation rates were higher for houses than for squares in the ordered icon conditions, so the randomization did not lead to an additional increase in the participants' perception of the risk.

The Impact of Small Changes in Probability
In Experiment 2, we changed the 100 icon arrays so that they showed more precise probabilities that were either just above or just below the 10% increments used in Experiment 1.These more precise probabilities added or subtracted 1%-2%, which was a very small change in terms of the risk to the house.However, in the ordered icon arrays, where the 100 icons were arranged in rows of 10, adding 1%-2% began to fill in a new row.If visualizations make uncertain risks seem more concrete, deterministic, or salient to viewers, we would expect this small increase in risk to lead to an outsized increase in the participants' evacuation rates.
Experiment 2 used the same mixed effects logistical modeling approach as Experiment 1.The analysis of the different types of icon arrays found that there was a significant main effect of icon order, with participants evacuating more often when shown randomized icons, just as in Experiment 1.There was also a significant main effect of the "just above" and "just below" manipulation.The participants were significantly more likely to evacuate when shown risk probabilities that were slightly above the 10% increments, as shown in Figure 6.As predicted, small differences in the probability of the house being in the burn zone could have a big impact on participants' decisions.For example, when the risk was 38%-39% and the participants saw ordered icon arrays, they chose to evacuate 25% of the time, on average.When the risk was 41%-42%, they chose to evacuate 42% of the time.This effect was even larger for the randomized icon arrays.The participants were more likely to evacuate overall when the icons were randomized, and the addition of 3-4 additional icons in the risky category had a large impact on the participants' decisions.When participants saw a risk probability of 41%-42% in a randomized icon array, their average evacuation rate was 60%.
A second analysis was done to compare the "just above" and "just below" arrays to the 100 icon arrays in Experiment 1 that had only 10% increments.This analysis found that there was not a significant difference in evacuation rates between the "just below" stimuli and the 10% increment stimuli.However, participants were significantly more likely to evacuate in the "just above" condition than in either of the other two conditions.In other words, changing the probability from 40% to 39% did not have a significant impact on evacuation rates, but changing the probability to 41% led to a significant increase.
The participants' average response times for the ordered and randomized icon arrays are shown in Figure 7.The participants had significantly longer response times when they were shown randomized arrays.However, their average response times were around two seconds, which is not enough time to count the icons and determine the precise probability of the house being in the burn zone.Instead, it seems that the participants were estimating the risk level when the icons were randomized.Given their high evacuation rates in that condition, they may have been overestimating the risk.

DISCUSSION
The results of these experiments show that numerical and visual representations of probability can lead to different decisions.In both experiments, we found that participants were more likely to evacuate when they saw icon arrays than when they saw natural frequencies.The design of the icon arrays also had an impact on decision making.The number and ordering of the icons in the arrays also influenced the participants' evacuation rates.
Prior research on icon arrays has shown that changing the number of icons in an array changes participants' perception of risk.When participants were presented with icon arrays of human figures with some of them highlighted to convey risk of disease, participants reported that arrays with one highlighted figure out of ten seemed to convey more risk than arrays with ten highlighted out of 100 or arrays with 100 highlighted out of 1000. 20lthough the ratios were identical in all cases, participants appeared to fixate on the denominator size, noting that larger arrays contained more disease-free icons than the smaller arrays.This led participants to interpret the larger arrays as conveying less risk.We observed a similar effect in Experiment 1.When participants were shown ordered 100 icon arrays, they were significantly less likely to evacuate than when they saw 10 icon arrays.
Randomizing the order of the icons eliminated this effect.Across both experiments, we observed the

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highest rates of evacuation when the icons were randomized, and the differences between the ordered and randomized conditions were often quite large.Prior studies have shown that randomizing icon arrays can make the probabilistic nature of the outcome more salient. 11It may make people more aware that this risk could impact them.The response times in our studies indicate that the participants were not stopping to count the icons in the randomized arrays.They spent slightly more time on the randomized arrays than on the ordered arrays, but not enough to do more than estimate the risk.It appears that they consistently overestimated that risk, since their evacuation rates were much higher than when they saw the equivalent ordered icon arrays.
In Experiment 2, we explored the effects of slight variations in probability.We added or subtracted 1%-2% of risk from the 10% increments that were used in Experiment 1.Although the changes to the risk level were quite small, moving onto a new row in the icon arrays led to a significant increase in evacuation rates.Randomizing the order of the icons further increased this effect, even though it eliminated the visual cue of filling in a new row.These results indicate that people are likely to overestimate risk in randomized icon arrays.In addition, they can be quite sensitive to small changes in probability when it is represented visually.
Several prior studies have compared the effects of different methods of visualizing uncertainty on viewers' task performance or decision making. 1,2,3,4,5,7,9Those experiments, like the ones in this article, have consistently found that different visual encodings can lead to different patterns of decision making.However, very few studies have systematically compared visualizations to other representations of uncertainty, such as numerical and visual representations.These types of comparisons are also important, because uncertainty visualizations can elicit cognitive biases such as the deterministic construal error. 10In some cases, verbal or numerical representations may be preferable.
The few prior studies that have compared visualizations to other representations of uncertainty have also found different patterns of decision making in response to different types of representations. 8,9People appear to make more cautious decisions when given visualizations of probability than when given equivalent numerical information.It is possible that visualizing uncertainty fundamentally changes how people perceive the information.Visualizations may make uncertain information seem more deterministic, 10 which could in turn make risky outcomes seem more likely or more salient.However, most of the prior studies that have compared visual and numerical representations of uncertainty used ranges of probability rather than point values.Participants' reasoning about those ranges may have been less precise when the information was presented visually. 8It is not clear which of these possibilities led participants to make more cautious decisions when shown visualizations.
In our experiments, we sought to tease apart these possibilities by using visual and numerical representations of probability that gave participants a single point value rather than a range.We found that the visualizations still elicited a more cautious pattern of decision making, even when participants were provided with identical point values across the visual and numerical conditions.
Although the participants were provided with point values on every trial, the response time data indicate that the participants estimated the probability in the randomized icon arrays rather than counting the icons.Randomization consistently led to higher evacuation rates.This pattern suggests that people may overestimate risk when performing mental estimation based on a visualization of probability.Our results suggest that both the visual representation itself and mental estimation processes related to interpreting a visualization of probability can produce more cautious patterns of decision making.

CONCLUSION
These experiments highlight the fact that choices about the design of uncertainty visualizations are not neutral: Choosing one encoding over another can have substantial impacts on viewers' perception of risk and on their subsequent decisions.Visualizations may be perceived as more deterministic than numerical information, producing more cautious decisions.Small differences in probability can also lead to dramatically different estimates of risk when the information is presented visually.
This work has real-world implications for conveying information about risk.Different representations of the same information can push people toward different decisions.This can be a beneficial or a harmful effect, depending on the circumstances.Additional research using tightly controlled, systematic manipulations of stimuli are needed to deepen our understanding of when, why, and how different representations of uncertain information lead to different patterns of decision making.Additional research in this area will help to develop robust theories that can explain and predict interactions between different representations of uncertainty and human perception of risk.

FIGURE 1 .
FIGURE 1. Examples of a 60% probability shown in all ten of the experimental conditions used in Experiment 1.

FIGURE 2 .
FIGURE 2. Examples of the stimuli used in Experiment 2. The top row shows a 41% probability represented as a natural frequency and an ordered icon array.The bottom row shows a 39% probability represented in an array of randomized square icons and a 42% probability represented in an array of randomized house icons.

FIGURE 3 .
FIGURE 3. The average proportion of participants choosing to evacuate for the numerical and visual stimuli used in Experiment 1 for each level of risk, where the risk is the probability that the house will be in the burn zone of the wildfire.

FIGURE 4 .
FIGURE 4. The average proportion of participants choosing to evacuate for the ordered and randomized icon arrays with 10 or 100 icons.

FIGURE 5 .
FIGURE 5.The average proportion of participants choosing to evacuate for the ordered and randomized icon arrays with low iconicity (square) or high iconicity (house) icons.

FIGURE 6 .
FIGURE 6.The average proportion of participants choosing to evacuate for ordered and randomized icon arrays at each risk level.

FIGURE 7 .
FIGURE 7. The average response times for ordered and randomized icon arrays at each risk level.