The Science of Visual Data Communication: What Works

The Importance of Visualization Design and Literacy

Who Studies the Design and Comprehension of Visualizations?

The Structure of Our Review

The Power of Visualization

Visualizations allow powerful processing of an entire two-dimensional rectangle of information at once, in stark contrast to the limitation of reading handfuls of symbolic numbers per second. As a demonstration, Figure 1 (top left) contains four sets of 11 pairs of values. Take a moment to compare those columns, and notice that reading symbolically represented numbers takes time. As you seek patterns within each set, or make comparisons among the four sets, progressively processing more pairs of values becomes increasingly difficult. Worse, these tasks quickly exhaust memory capacity, such that new numbers or patterns tend to displace ones that were previously seen. These limitations on symbolic processing of numbers lead viewers to rely instead on summary statistics that compress data sets into a single group of numbers. For the four sets of numbers in Figure 1, those statistics on the bottom row—means, standard deviations, and correlation coefficients—are identical, which might lead you to believe that the numbers contributing to the statistics are similar (Anscombe, 1973). However, because statistics summarize larger sets of numbers by abstracting over them and making assumptions about the patterns that they might contain, many sets of numbers can generate the same statistics. For these four sets of numbers, relying on statistics turns out to be dangerous.

The differences between the four sets of numbers in Figure 1 are immediately visible when translated into images in the form of scatterplots (bottom left). These images allow you to leverage the two-dimensional processing power of your visual system, the largest single processing system of the brain (Van Essen et al., 1992). If you are familiar with statistics, then the first image at the bottom left likely matches what you assumed the numbers should look like given the statistics on the bottom rows: an orderly positive relationship. But the other sets are clearly different in important ways. The right side of Figure 1 depicts frames of an animation that provides a more sophisticated example (Matejka & Fitzmaurice, 2017), in which visual processing allows one to immediately see that, despite identical statistics (to the second decimal place) for each scatterplot, the nine plots contain saliently different patterns. When exploring a new data set, it is good practice to visualize every column of data with a histogram, and every potentially interesting pairing of columns with scatterplots, before turning to statistical summaries (Moore et al., 2017; Wongsuphasawat et al., 2015).

Visualizations rely on several visual channels to transform numbers into images that the visual system can efficiently process (Bertin, 1983; Mackinlay, 1986; see Munzner, 2014, for a more complete list). Knowing these channels allows a designer to consider which might be best suited for a given data set and context—particularly given that each is associated with differential levels of precision and potential illusions, as described in the following sections. The first column of Figure 2 depicts five of the more frequently used channels. Dot plots and scatterplots, such as those in Figure 1, represent values as position. Bar graphs represent values not only as positions (of the tips of the bars) but also as one-dimensional lengths (and, some argue, even two-dimensional areas; Yuan et al., 2019). If two bars do not rest on the same baseline, such as segments within the same bar in a stacked bar graph, the comparison relies only on length or area. Next, two circles code numbers exclusively as two-dimensional areas (typically circles), a technique often used to overlay values across maps. Angle typically emerges when points are connected to form a line graph, organically allowing an encoding of the difference between adjacent points (a bigger difference creates a steeper slope and, typically, a longer line). Outside of pie charts, angle is less frequently used to depict numbers directly—perhaps on local areas of a map to represent wind directions. Numerosity is omitted from the figure, but it often implicitly shows higher-level attributes of data. For example, you can immediately estimate the number of points in a scatterplot, segments in a stacked bar chart, or icons in an infographic. Intensity is an umbrella term (often also called lightness or value) for either luminance contrast or color saturation, as used in a heat map or fMRI activation map. Motion is also not included in the figure, but animating a scatterplot to show values changing over time can encode the rate and direction of change in the speed and direction of the dots’ motion.

How to Design a Perceptually Accurate Visualization

Beyond illusions and biases, certain combinations of colors in visualizations can be problematic for people who are color-blind or have other color-vision impairments. Color-vision impairments are estimated to affect 4% of the global population (Olson & Brewer, 1997), or roughly 300 million people. Further, older adults can have less sensitivity to color (Silva et al., 2011). Some color blindness results in viewers not being able to distinguish between various colors; protanopia, or red–green color blindness, is the most common, but various other versions of color blindness exist. Color-vision impairments are highly problematic for visualizations, as a portion of the audience may literally not see important patterns in data.

Numerous online color-blindness simulators allow users to upload an image to learn how someone with color blindness would see it (Asada, 2019). For example, the first row in Figure 5 shows a scatterplot encoded with two colors, green and purple. People with typical vision can see that the green dots have a steep positive correlation and the purple dots make a flat line. However, when the scatterplot is processed through a color-blindness simulator, the colors look the same, and all the dots appear to show a positive correlation. The simplest way to make visualizations accessible to viewers with color blindness is to avoid using hue as the only encoding channel or allow viewers to change the color palette (Silva et al., 2011). Designers can also double-encode a variable, using hue and another encoding channel (Plaisant, 2005), as in the second row of Figure 5. The most thorough and inclusive option is to use color palettes that are safe for people with color-blindness, such as those proposed by Harrower and Brewer (2003), as seen in the bottom row of Figure 5.

The ranking of precision for visual channels depicted in the first column of Figure 2 is based on a measure of precision in a particular task: the average error in verbal reports of the ratio between two depicted values (1:7 for each of the examples in the first column; Cleveland & McGill, 1984; Heer & Bostock, 2010).

Although this task is surely important when comparing two values, it is not the only task (or perhaps even the primary task) that viewers complete when examining visualizations (Bertini et al., 2020). One proposed taxonomy of graph-interpretation tasks separated them into three levels: elementary, intermediate, and “overall,” roughly corresponding to simple fact retrieval, comparison and identification of trends, and gist understanding (Bertin, 1981). Additional taxonomies have been developed in the context of cognitive models of graph comprehension. Other taxonomies are based on analyses of cognitive processes involved in different tasks (Tan & Benbasat, 1990), reliance on local versus global features (Carswell, 1992), or other criteria (MacDonald-Ross, 1977; Washburne, 1927; Wickens, 1989). Work in the data-visualization literature has begun to catalog such tasks and to test the types of displays that best support performance for each. One list of tasks is distilled from questions submitted by students who were asked to analyze a large data set (Amar et al., 2005). This list includes analytic tasks such as “retrieve value,” “sort,” “determine range,” “correlate,” and “characterize distribution.” Another list of tasks focuses on how people generate summary statistics for plotted data (Szafir et al., 2016).

The ranking derived from performance on two-value ratio judgments does not always extrapolate across these alternative tasks. For example, depicting data with a line graph, which relies on “precise” position coding, can lead to lower efficiency in seeing big-picture statistical properties such as means. Intriguingly, the opposite is true for intensity coding. Multiple studies have shown that for identifying particular values, position is far more precise than intensity, but for judging an average across many values, intensity is more precise (Albers et al., 2014; Correll et al., 2012). The reason for this dissociation is not well understood. It is possible that the lower precision of intensity better allows its values to blend together to construct aggregate values, or perhaps intensity is simply processed by a different mechanism that affords aggregate judgments (Szafir et al., 2016). Some visualization designs purposely use the low precision of the intensity channel to focus viewers on the big-picture trend of the data instead being distracted by precise details, as in the visualization from the cover of The Economist magazine (Fig. 3), which focused viewers on the big picture of climate while de-emphasizing more detailed (but less relevant) variability in monthly weather.

Other work has tested whether people can more quickly or accurately complete the types of tasks listed above (judge mean, correlate, etc.) given different graph formats (scatterplots, bar graphs, tables, etc.) and data-set sizes (small vs. large; Y. Kim & Heer, 2018) or different arrangements of data within a graph (Jardine et al., 2019; Ondov et al., 2019). Although such studies have found consistent interactions—better performance on Task X with Design Y in Arrangement Z for Data-Set Size S—the existing pattern of results is currently too complex to generalize to novel combinations. To create generalizable guidelines, the research community will likely require a more complex model of the underlying perceptual operations that produce these complex interactions (Jardine et al., 2019; Ondov et al., 2021).

Among these alternative tasks, the perception of correlation is particularly well studied (Harrison et al., 2014; Jardine et al., 2019; Rensink & Baldridge, 2010; F. Yang et al., 2019; Yuan et al., 2019), leading to initial suggestions of its underlying perceptual operations. For example, scatterplots allow for more accurate judgments of correlation than pairs of bar charts presenting the same data (Harrison et al., 2014).

Scatterplots present two metric variables in relation to each other. Imagine that the horizontal position represents the longitude of a collection of oil wells and the horizontal position represents their latitude. This example makes clear that scatterplots and data maps share DNA. Suppose the designer now wants to differentiate the set of points according to a nominal (categorical) variable, such as the company that owns the oil well. Because the two dimensions of position (vertical and horizontal) are already being used to represent the metric variables, designers would typically differentiate points from each group with either different colors or shapes.

Plotting the groups as categorically different colors is often the first choice because the visual system processes color differences more efficiently than shape differences across the two-dimensional visual plane, as measured by performance in visual-search and texture-segmentation tasks (Wolfe & Horowitz, 2017). These findings, based on simple displays used in laboratory studies, extrapolated to a data-visualization context in which viewers compared the average heights of multiple color-coded or shape-coded clouds of points in a scatterplot: Color coding produced far better performance (Correll et al., 2012).

When color differences distinguish data from two separate groups or classes, differentiating those classes is easier if the encoded colors are farther apart in a perceptual color space. For example, it is easier to differentiate red from blue than from orange-red. Researchers have constructed effective palettes from perceptually informed color spaces (e.g., CIELAB; Y. Liu & Heer, 2018) to suggest colors to use to differentiate N nominal classes; colors become progressively crowded together as N increases. One such set that is viewable (and customizable) online is ColorBrewer 2.0 (Brewer, 1994a, 1994b). Another tool, Colorgorical, balances perceptual differentiation with aesthetic considerations (Gramazio et al., 2016).

Picking a color for a nominal value should also be constrained by the semantic congruence of the value and the color. If the nominal values are lemons and cherries, it is easier for viewers to answer questions about a chart that labels those values with yellow and red, compared with a standard palette that does not consider semantic congruence (Lin et al., 2013; Schloss et al., 2018). An algorithm can automatically generate intuitive color choices for a given noun by analyzing the color profile of images pulled from Web searches for the noun and then optimizing color assignments in terms of perceptual spacing and semantic fit. Such algorithms can perform as well as human experts in quickly picking color palettes for nominal data (Lin et al., 2013; Setlur & Stone, 2015).

Sometimes a visualization designer needs to show a second set of nominal values in the same plot. Thinking back to our map, imagine that we have used a unique color to represent each oil company (A, B, C) but also wish to depict each company’s nationality (Canada, Brazil, Mexico). Typically, shape would be used to show that second nominal variable. Because it is less perceptually effective than color, it should be used for the less important variable, or the one with fewer values to differentiate. The shape sets used in commercial software (e.g., Microsoft Excel) gravitate toward intuitive shapes, such as circles, triangles, squares, and diamonds, that are not actually well separated in perceptual space.

Researchers have begun to explore perceptual shape space, and some have extrapolated from pairwise subjective similarity ratings of combinations of candidate shapes (Demiralp et al., 2014). Other work has relied on objective performance tasks on actual simulated scatterplots (Burlinson et al., 2017; Huang, 2020). This work is also new, but so far, human shape space (at least for the simple shapes used in visualizations, and at least for the types of tasks tested so far) appears to prioritize the difference between open (circle, square, triangle) and closed (×, +, *) shapes, such that differentiating points is easier when they differ in that property (Burlinson et al., 2017; Huang, 2020). An initial full three-dimensional perceptual shape space (Huang, 2020) adds the additional properties of intersection and spikiness; Figure 6 depicts a clear improvement in shape differentiability compared with the typical sets used even in professional data-visualization software.

Finally, some software automatically differentiates nominal variables with both color and shape, under the assumption that more differentiation is better. However, work has shown that color is already so dominant in its effectiveness that redundant encoding does not substantially improve visual processing efficiency (Gleicher et al., 2013) unless the viewer has color-vision impairments or the viewer’s task is exceptionally difficult (Nothelfer et al., 2017). Given anecdotal claims from some expert designers that redundant encoding can cause confusion in viewers, who typically expect color and shape to signal different nominal variables (Tufte, 1983), the lack of evidence for a perceptual advantage suggests that redundant encoding should be avoided in most cases, except when used to make visualizations accessible for viewers with color-vision impairments.

How to Design a Perceptually Efficient Visualization

One core advantage of visualizations is that they capitalize on our visual system’s ability to extract information efficiently. The encoding properties in the first column of Figure 2 are properties that we process in parallel across two-dimensional images (Treisman, 1998; Wolfe & Horowitz, 2017). Faster than an eyeblink, we can pull statistics from data encoded as positions, one-dimensional lengths, two-dimensional areas, angles, or intensities. In the natural world, we typically use these statistics to recognize the type of scene we are in (e.g., a beach scene containing light brown, blue, and horizontal angles from the sand, sky, and horizon; Oliva, 2005) and to help provide a summary of an otherwise complex world (Brady et al., 2009; M. A. Cohen et al., 2016). A substantial literature in visual cognition has examined the power and limits of this ability to explore what types of statistics can be extracted under what conditions (e.g., Baek & Chong, 2020; Haberman & Whitney, 2012).

Much of this work in visual cognition relies on simplified laboratory displays of colored squares and circles, which are conveniently similar to the structure of the artificial worlds of data visualizations (for a review of insights from this literature for data-visualization design, see Szafir et al., 2016). The third column of Figure 2 summarizes the types of statistics (minimums, means, maximums, and outliers) that can be pulled from any of the five visual properties in the first column. In the dot plot (encoding numbers as positions), a viewer can easily extract the minimum, mean, or maximum height. In the stacked bar chart below, the lighter segments present numbers through both their lengths and the positions of their tips because their bases are aligned. The darker segments are offset in arbitrary ways by the lighter segments underneath, so only their lengths visually represent values—yet the observer can still pick out minimum, mean, or maximum values quickly. The same is true for the bubble chart and the angles of the slope graph (a specialized line graph whose lines have only two points). Finally, for the heat map at the bottom that represents values as luminance contrasts, the lightest (minimum) and darkest (maximum) values are easy to pick out, and one can also quickly imagine the contrast of the mean value.

Within their first glance at a data visualization, viewers can immediately pull general statistics from the positions, lengths, areas, slopes, and intensities (Szafir et al., 2016). This provides viewers with a starting point in understanding the distribution of the data and whether there might be outliers. However, the second step is to extract relations from the data by making a sequence of comparisons, a critical mental operation when viewing visualizations (Franconeri, 2021; Gleicher et al., 2011; Tufte, 1983). Comparisons include local comparisons between elements (“this point is higher than that point”; “this line segment is shallower than that one”), groups of elements (“these two bars have a greater range than those two”; “these red circles are on average larger than the green ones”), or global trends (“this section of the heat map is more saturated than that section”).

Each of those verbal sentences describes a single visual comparison that must be extracted serially, as part of a sequence (Michal & Franconeri, 2017; Roth & Franconeri, 2012). These comparisons can each take hundreds of milliseconds to process (Franconeri et al., 2012; Logan & Compton, 1998; Wolfe, 1998), so that viewers tend to process only a handful per second (Franconeri et al., 2012). Extracting the necessary multitude of comparisons from a visualization is therefore not like instantly recognizing a particular face, place, or Pokémon but instead more like the serial and controlled reading of a paragraph (Carpenter & Shah, 1998; Shah et al., 2005; see Franconeri, 2013, for a discussion of the different types of attention demanded by these two scenarios). Each single comparison is limited in its complexity as well—by some estimates, encompassing interactions among approximately four variables at maximum (Halford et al., 2007).

This severe capacity limit has been confirmed for realistic comparison tasks in data visualizations. When viewers are asked to perform the types of tasks shown in the fourth column of Figure 2—for example, to locate pairs of graphed values in which the second value is bigger among pairs in which the second value is smaller—the time need to make each of those comparisons cumulates in painfully slow overall performance (Nothelfer & Franconeri, 2019). Likewise, the bar graph in Figure 7 (left) shows two test scores for each student, one before and one after an intervention. You can feel the sluggishness of those comparisons by answering the question: Who is the only student who got worse?

As a second example, when viewers are challenged to complete a tough comparison task with the blue dots of the scatterplot shown in Figure 7 (right), they can fail to process the positions of the green dots, such that 93% fail to notice the presence of a dinosaur shape among them (Boger et al., 2021).

A few hundreds of milliseconds of processing time for a single comparison is not noticed. However, across many comparisons, that time quickly adds up. Imagine a bar graph showing the performance of two groups, A and B, in both treatment and control conditions, for a total of four bars. Even in this small set, there are six possible pairwise comparisons, plus two main effects, plus multiple ways to look at interactions. In a graph with 12 bars, there are 66 pairwise comparisons alone!

When visualization designers create data-heavy displays that require fast processing, such as a business-metric-monitoring dashboard, many implicitly realize that comparisons are a sluggish visual operation. One common solution is to remove the need for the viewer to explicitly compare values by providing a second view of the data plotting the differences between values (Fig. 2, upper right; Few, 2009). Known as directly depicting deltas, these dashboards commonly show differences between current financial values, such as revenue, and baseline financial values, such as revenue from the same month in the previous year, or between financial and budget values.

A visualization that is designed to guide viewers to make the “right” visual comparisons can lead those viewers to make meaningful insights than they would gain on their own. One major cue for this guidance is to visually group the data values that should be compared with each other or should be compared as a group to other groups. The same classic grouping cues studied in the perception literature can control which values are selected and compared. Figure 8 depicts four of the primary cues roughly in order of strength: connecting lines, position proximity, and similarity in either color or shape (Brooks, 2015; Palmer, 1995). The two rightmost columns of Figure 2 also show examples of grouping-defined comparisons.

Many of these grouping cues may stem from metaphors about real-world scenarios (Tversky, 2001). Objects that are spatially nearby are likely to stem from the same source, such as tomatoes from the same plant or birds nesting in the same nest. When three objects fall close to a common line, their spatial arrangement naturally conveys conceptual ordering because of how processes produce spatial ordering: If an animal leaves a trail, the order of the prints naturally reflects the timing of how they were laid down. Lines imply connections because connected things in the world tend to belong to the same objects, such as grapes connected by vines. Closed contours such as circles or blobs define objects because objects in the world tend to have closed, discernible borders or boundaries.

In line graphs, the choice of which variable is grouped by connecting lines (e.g., Fig. 8) has a profound impact on the interpretation of data. For example, one study presented viewers with graphs that showed the effects of two independent variables on a third variable. The data were depicted in line graphs; one variable was plotted as separate lines and the other was plotted as connected lines. Viewers could answer more sophisticated questions about the quantitative relationships depicted by the connected lines but only relatively simple questions about relationships between the separate lines (Shah & Carpenter, 1995). In many cases, viewers were unable to recognize the same data plotted with a different choice of how points were connected by lines. Relationships between values that straddle different lines or different panes need to be integrated with multiple comparisons, which requires controlled processing, taxes working memory, and introduces a risk of error.

The graphs at the top of Figure 9 show how these grouping cues can control which comparisons are prioritized. In the example to the left, both proximity and color facilitate comparisons among categories (Social Security is highest) and overall between years (the yellow bars have a larger range than the green bars). However, you are less likely to compare a single category across the same year, which requires a jump of your eye to find the companion bar. The opposite is true of the example to the right (Shah & Freedman, 2011; Shah et al., 1999). The word clouds at the bottom of Figure 9 show an example of controlling comparisons with proximity grouping. In the word cloud on the left, the relatively weak color grouping makes it tougher to identify the common theme in each of five groups of words. On the right, identifying the common themes (restaurant, baseball, hands, etc.) is easier because the more powerful cue of proximity grouping has been added (Hearst et al., 2020).

A good visualization relies on the grouping techniques described in the previous section, including connectivity and proximity, to help guide a viewer to compare one set of values or another. However, even within that one set, there are still many possible comparisons to make.

When multiple groups compete for comparison, that competition tends to be won by groups that are different or brighter in color, largest in size, or presented at the top or left of a display. Such visual salience can be modeled by showing viewers pictures or visualizations, recording their eye movements, and then feeding the images and responses into computational models that predict human attention (Bylinskii et al., 2017). Many of these models exist for salience in natural scenes, ranging in complexity from simpler weighted linear combinations of relative differences in features (uniqueness in color, or orientation, at various locations and spatial scales) to more complex models that extract object contours or predict salience in movies (Borji et al., 2013). But many of these models fail to predict salience in the novel context of visualizations because the statistical profiles of those images differ substantially, containing large areas of blank space, text, axes, and titles (Haass et al., 2016). New models of salience for artificial information displays, trained on eye movements or on mouse-tracking data that are closely correlated with eye movements (N. W. Kim et al., 2017), can reach higher levels of predictive power (Bylinskii et al., 2017; Matzen et al., 2018).

Visualization designers will often deliberately control visual salience to bring the viewer’s eye straight to the critical comparison. One technique is to add salient color highlighting a single group of items (Fig. 10) to ensure that viewers process that comparison first (Ajani et al., 2021; Grant & Spivey, 2003; Hullman & Diakopoulos, 2011; Mayer & Moreno, 2003). Some practitioner guides also recommend using color-coded accompanying text, as in the graph at the top of Figure 10, to ensure that the viewer will match the pattern in the data to the relevant reference in the visualization designer’s argument (e.g., Knaflic, 2015). More generally, a good visualization should place verbal information near relevant visual information so that viewers do not need to glance back and forth in a time-consuming search to see what text matches what visual pattern (Moreno & Mayer, 1999). These methods of guiding viewers to the most relevant comparisons are particularly important for low-knowledge readers, who benefit from visualizations that present or highlight only the relevant comparisons (Canham & Hegarty, 2010). These techniques are less important for experts, who rely on prior experience to guide their attention.

Some research has studied the techniques of data journalists, who are tasked with clearly communicating data-based arguments to nonexperts. This work has cataloged techniques used by news outlets such as The New York Times Upshot, The Washington Post, The Economist, and FiveThirtyEight (Hullman & Diakopoulos, 2011; Hullman, Diakopoulos, & Adar, 2013; Segel & Heer, 2010) and has used computation to automatically generate visualizations that use particular strategies (Gao et al., 2014; Hullman, Drucker, et al., 2013; N. W. Kim et al., 2017). These outlets employ specially trained reporters who convey data-based political, economic, health, and science stories to the lay public. They will often show a single pattern in the data at a time, relying on the viewer to step or scroll (Amabili, 2019) through a sequence of patterns. In each step, a pattern of data is highlighted to ensure that the viewer’s limited processing capacity is directed to the values simultaneously described in a verbal annotation. The bottom row of Figure 10 illustrates how data journalists might redesign the example on the left, which requires viewers to navigate text that is placed far from the patterns that it describes and to use their imagination to fill in the patterns referred to by the text. The example on the right addresses both of these issues, leading to more effective communication of a key data pattern (Ajani et al., 2021). The two rightmost columns of Figure 2 summarize these techniques, showing that grouping, highlighting, and annotating can help viewers quickly make the right comparisons.

If helping viewers prioritize critical comparisons in a visualization is so important, then why do so few presenters do it? One likely reason is that presenter have a curse of knowledge—an inability to simulate the perspective of the naive viewer because they cannot ignore what they know and see (Birch & Bloom, 2007; Camerer et al., 1989). Figure 11 presents an empirical demonstration of this curse from a lab study (Xiong, Van Weelden, & Franconeri, 2020). Participants heard an intriguing story about a dip and rise of a political candidate’s popularity in the polls (the top line in the top left graph); the story made those patterns stick out to the participants. They were then told to forget the story and predict what patterns another person, naive to the story, would find interesting or salient in the graph. The graph at the upper right presents their collective predictions—and makes it clear that people think that others will see what they see, even when they know that others do not have the same expertise. The graphs in the bottom row show how, when the original story concerned a different candidate, the pattern of results changed accordingly. It is impossible to “turn off” your own expertise, which makes it difficult to see through the eyes of nonexperts.

If grouping, highlighting, and annotation can guide viewers toward a certain comparison or pattern, then for better or worse, a visualization designer has some control over what their viewers see in a data set. Figure 12 shows an example, adapted from The New York Times, in which the same unemployment data might be seen—or designed to be seen—in different ways. During Barack Obama’s presidency, a member of his party (the blue glasses) might see a drop in unemployment rates and highlight that downward-sloping pattern in the orientation channel. But a member of the rival party (the red glasses) might see a failure to meet a goal of 8% unemployment and emphasize the information in the area channel by highlighting the area under the curve (Bostock et al., 2012). These visual manipulations are similar in spirit to choosing which of those features to highlight in a verbal argument.

An analysis of distortions and biased annotations in news media visualizations showed that rhetorical biases are pervasive in data graphics and that labels and framing may be skewed toward progressive or conservative positions, depending on the news outlet (Mehta & Guzmán, 2018). A taxonomy of “visualization rhetoric” likens visualization design to an editorial process in which decisions about what data to include, how to encode them, how to use titles and labels, how to describe the data’s provenance, and what interactions to allow represent rhetorical choices aimed at guiding viewers toward preferred interpretations (Hullman & Diakopoulos, 2011). People’s perceptions of a visualization’s message, and their ability to recall it, are particularly influenced by the visualization’s title (Kong et al., 2018, 2019). For an engaging tour of the complexities of truth and deception in visualization with an emphasis on a journalism perspective, we point the curious reader to the books of Alberto Cairo (2016, 2019).

Viewers can also be influenced by expectations or social pressures, even for relatively low-level visual judgments. For example, when participants made judgments about correlations in scatterplots, their estimates were higher when the data were labeled as personality variables, which one would expect to be correlated, than when the data were unlabeled (Freedman & Smith, 1996). In another study, participants were asked to make judgments about visualizations (e.g., rating the linear association in a scatterplot) presented either alone or with a histogram plotting other people’s ratings. The other ratings were either true ratings or a distribution of the true ratings shifted by 1 SD. When participants were provided with the manipulated histograms, their judgments were biased in the direction of the social influence (Hullman et al., 2011).

Finally, the format of a visualization can also guide the types of conclusions that viewers draw from the underlying data. Imagine data showing that students who eat breakfast more often tend to have higher GPAs. A viewer might see this correlation and assume a causal relationship whereby a good breakfast causes better grades. Although plausible, this conclusion cannot be drawn from these data. When shown visualizations like these, viewers made unwarranted claims about similar correlational data, and they did so more often when the visualizations aggregated the data into fewer groups (e.g., a two-bar graph), compared with more groups (e.g., a scatterplot showing all of the individual data values; Xiong, Shapiro, et al., 2020), perhaps because seeing the data in fewer groups is implicitly associated with those data being gathered by an experimental manipulation.

Given that comparisons are already highly capacity limited, any extraneous demands on working memory due to the design of visualizations should be avoided. Interpreting the graphs in the middle and right sides of Figure 13 requires individuals to map the symbols and colors in the graphs to their referents in the legends below. This task is highly demanding of limited working memory resources. If information is lost in interpreting a graph, viewers might make interpretation errors or require extra time to reinspect the legend. Indeed, one study found that people answered questions about data both faster and more accurately when the data were directly labeled in graphs compared with when there was a legend (Lohse, 1993). Therefore, instead of legends, use direct labels whenever possible (e.g., Wong, 2010). Note that there may be exceptions to this recommendation, if legends provide a way to index data values that labels cannot. For example, a map of an amusement park might list locations under the map to allow the viewer to browse the locations alphabetically or clustered by type (rides, food, etc.), which is not possible for map locations that are already organized in space.

When visualizations are well designed, they can help viewers overcome working memory limits by offloading information storage and some types of processing to a page or screen (Kirsh, 2005; Tversky, Heiser, et al., 2002). Compared with the slow difficulty of reading and comparing symbolic numbers, a visualization can allow these steps to unfold far more quickly and efficiently. For example, older adults with normal cognitive decline were asked to compare multiple health-care plans. They were given plan information (e.g., about monthly premiums, deductibles, and gap coverage [supplementary insurance to cover medical costs incurred before reaching the deductible]) either in a table full of text and numbers or in a table with visual categorical encodings of the information (e.g., green circles for the best gap coverage and red circles for no coverage). The adults using the visually encoded table made better and, in some cases, faster decisions about which health-care plan to select because they found it easier to make comparisons (Price et al., 2016).

Given the limited working memory resources of visualization viewers, designers often recommend a minimalist aesthetic that strips away any design elements that are not critically needed (Few, 2004; Knaflic, 2015; Tufte, 1983). One popular mantra is to keep a maximal “data–ink ratio” (Tufte, 1983), though the definition of “ink” can be frustratingly vague (Correll & Gleicher, 2014a). Figure 15 depicts variants of a visualization based on this prescription. The visualization at the top is filled with “clutter”: grid lines, a background pattern, and varied colors across the bars. The middle image is a “decluttered” visualization that omits these elements. Although newer editions of Microsoft Excel have eliminated some forms of clutter shown in the top image, critics of the 2007 edition argued that the software encouraged users to create graphs containing dense grid lines, unnecessary labels, unneeded color variation, and even three-dimensional effects that transformed simple bars into cylinders or pyramids (Kirk, 2012; Kosslyn, 2010; Su, 2008; Ware, 2010, 2019).

Despite strong calls to declutter visualizations (e.g., Tufte, 1983), there is only mixed evidence that this practice improves aesthetic ratings and little evidence that the prescription affects objective performance. Several studies have measured aesthetic ratings for cluttered versus decluttered charts, and some have shown clear preferences for decluttered versions (Ajani et al., 2021) and others, surprisingly, showing the opposite (Hill et al., 2017; Inbar et al., 2007). Researchers who have found the opposite have typically argued either that viewers’ higher level of familiarity with cluttered charts make those charts more attractive or that decluttered charts that are too minimalistic become boring. Another possibility is that users may prefer particular depiction styles for particular purposes, mindful of their audience and goals (Levy et al., 1996). Objective performance measures, such as the speed with which viewers can compute means across values in a bar graph, also present mixed evidence. For example, that speed can be slightly faster when some forms of “clutter,” such as axis tick marks, are removed but slower when other elements are removed (Gillan & Richman, 1994). Given the large number of design elements that could count as clutter, combined with the large number of tasks that one could complete on a visualization, some have argued that a simple rule for whether to declutter is unlikely to arise and have discouraged further empirical testing given the small and mixed effects found so far (Ajani et al., 2021).

The bottom of Figure 15 shows the same bar graph embedded within a cartoonish monster. The addition of such pictorial elements that embellish data with anthropomorphic or metaphorical elements—intended to enhance engagement or memory—has been demonized as “chartjunk” (e.g., Tufte, 1983). Various studies have shown that adding these elements leads to no improvement in memory for the data (Helgeson & Moriarty, 1993; Kelly, 1989), mixed results depending on the details of the task and context (Gillan & Richman, 1994; Li & Moacdieh, 2014), or better memory for the data content or message (Bateman et al., 2010; Borkin et al., 2016; Haroz et al., 2015b). Like animation, these visual embellishments can increase ratings of engagement and aesthetic value (Li & Moacdieh, 2014). And despite mixed evidence as to whether their presence improves memory for the data, pictorial elements do improve memory for the fact that a visualization was previously seen, both in the short and the longer term (Borkin et al., 2013).

How to Design an Understandable Visualization

Visualizations can be powerful, but a poorly designed visualization can easily confuse or even mislead (Burns et al., 2020; Cairo, 2019; Szafir, 2018). Because the interpretation of visualized data is in the eye and mind of the human beholder, we must consider the psychology of the observer as the translator of images into an understanding of the original data and the patterns that they hold. Below, we outline a set of common translation errors that can confuse and mislead.

Understanding a visualization can depend on a graph schema: a knowledge structure that includes default expectations, rules, and associations that a viewer uses to extract conceptual information from a data visualization. Figure 16 serves as an example of why a graph schema is often needed to interpret a data visualization. It depicts the GDP (on a log scale) and population of the 10 most populous countries. Take a moment to interpret the data.

If you are having trouble extracting the data from this visualization, it is not your fault—you do not have the needed schema. First, if you have never seen this type of visualization, you cannot know which aspects of its variation are meaningful. The bubbles differ in their areas, hues, horizontal positions, vertical positions, proximity and enclosure relationships, and depth planes, which causes confusion. Why are Russia, Brazil, and the USA “hiding” behind the other countries? Why does India enclose Mexico? Why are there two main clusters? Is it meaningful that Bangladesh and Pakistan have the same horizontal position? Which of these many sources of variability should the viewer translate back to the original data?

You are experiencing the same confusion felt by a novice viewer encountering a given type of visualization for the first time. A young student might see rectangles with widths, heights, tops, bottoms, left sides, right sides, legend entries, and gridlines that vary in vertical position. Reading a bar graph requires a schema that allows the viewer to do what you do when viewing a bar graph: to focus instantly on the positions of the bar tops, because they signal the numbers depicted by the bars.

Here is a hint for Figure 16: Only the size and hues matter; the rest of the variation is irrelevant. Areas map to population, and hues to GDP. Now, how does the variability in those channels map back to numeric values? You will guess that larger sizes are linearly related to a larger population because you have implicitly memorized that association from previous experience with visualizations. However, how do the hues map to GDP? It looks like the variance scales between red and blue, but is red high because it is “hot” or low because it is “bad”? You may have already inferred that red maps to higher by stepping back to your knowledge of the data to realize that China has a high GDP, so red probably maps to high. However, if you did not have that knowledge, your existing schema would not have allowed you to recover that relationship confidently.

Humans develop similar schemas for many other domains. A face schema, for example, specifies what features are typically in a face (eyes, ears, mouth, nose . . .), how those features tend to vary (many eyes have brown irises, but some are blue, green, or gray), what their relations tend to be (noses are between, and below, the eyes; Palmer, 1975). Having well-developed schemas enables a viewer to more effectively perceive, understand, and remember—without a face schema, a face presents a set of tens of thousands of independent pixels that vary in unpredictable ways. When one views a graph, one may depend on graph schemas that encode knowledge about the graph type, and also schemas that encode knowledge about what the graph is about—for example, understanding a high-low graph of stock prices requires knowledge about that graph type and also about stocks and the stock market.

Schemas can bias judgments when a new instance deviates from the schema (Mandler & Ritchey, 1977; Rumelhart, 1980; Tversky, 2001). In one example of bias in the context of graphs, participants saw simple displays labeled as either “graphs” or “maps” and were asked to draw the displays from memory. When the displays were called “graphs,” participants distorted a central line as being closer to a 45° angle. When these same displays were called “maps,” the participants distorted the lines as being closer to horizontal or vertical, suggesting that their memory for the image was influenced by canonical representations of these two types of visualizations (Tversky & Schiano, 1989).

In much of the world, children learn about common graph types such as bar graphs, line graphs, and scatterplots in school—but an audience without such schooling may not appreciate the conventions for how Cartesian space is used and how axes are drawn and labeled. Even relatively common visualizations such as scatterplots are misunderstood by 37% of adults in the United States (Goo, 2015).

Given that the reader of this article is likely familiar with common visualizations, we remind the reader of the need to learn how a new visualization works, by introducing examples that are less likely to be familiar. Expert communities have developed idiosyncratic visualizations that serve important data-analysis or -communication purposes, but they require learning new graph schemas. This can lead to severe difficulties for new viewers. For a broader tour of a curated “zoo” of novel visualizations, see Heer et al. (2010). For those ready for a true safari of new visualization schemas, we recommend browsing the Xenographics website (Lambrechts, n.d.).

The left column of Figure 17 depicts four visualizations that are likely familiar to the reader, and the right column shows four equivalent visualizations that likely require a new schema. The first row shows two line graphs, plotted in the same space. An alternative way to plot those data is with a connected scatterplot shown at right (Haroz et al., 2015a; Peebles & Cheng, 2003). For each time point on the x-axis of the two-line graph, plot the point for Line 1 on the x-axis of the scatterplot and Line 2 on the y-axis. Now connect all points with a line, in a temporal order. Engineers and economists use this format because it facilitates views of relationships between two sets of data: The line segments’ slope and direction reflect their ratios and changes in polarity.

The second row depicts standard bar graphs on the left, showing the square footage, price, and time on the market for three houses. It becomes tougher to find relationships among similar houses in the bar graph as the number of metrics increase or the data set’s size grows because both the measures and the houses become more spatially separated. Parallel coordinates, as shown on the right, are a popular visualization format for analysts facing a much larger data set. The same data are now plotted as the height of lines that straddle parallel lines representing each measure. When combined with interactivity, this format allows users to extract individual values and perceive correlations between neighboring measures: flat lines reflect positive relationships, and slanted lines, negative relationships.

The third row shows a simple hierarchy of the content of a hard drive, in the style of an organizational diagram. In this representation, vertical position relies on a “levels of height” metaphor to indicate a folder’s place in the hierarchy, whereas horizontal position is typically irrelevant. The alternative depiction at right is called a tree map: tree because it shows a hierarchy, and map because of its two-dimensional spatial layout (Shneiderman, 1992). Reading a tree map requires the schema of knowing that folders are now differently sized rectangles (with area indicating the size of each file and color somewhat arbitrarily mapping to different branches of the hierarchy). Critically, the hierarchy itself is no longer shown through a vertical “levels” metaphor but is instead depicted through an “enclosure” metaphor, as in a physical file drawer. Higher-level folders are now akin to bento boxes enclosing other bento boxes.

The final row shows network data as a node-link diagram, which could depict a social network. A node-link diagram can intuitively show connections (e.g., between people) with lines, making it useful for lay audiences. However, for complex analysis of large data sets, specialists prefer variants of the depiction at the right, in which each “node” is both a row and a column in the matrix, and their intersecting square is filled only if those nodes are connected (Heer et al., 2010). Similar in spirit to the correlation matrix, it is symmetric across the diagonal if all connections are bidirectional. However, if the connections are directional, then the two halves carry specific information.

Some elements of schema are relatively universal for moderately experienced visualization users. For example, as illustrated in Figure 18, people have expectations for which “end” of some visual channels (e.g., bottom vs. top for position, light vs. dark for luminance) should map to smaller and larger numerical values. Larger values tend to be mapped to higher vertical positions, perhaps because of the natural metaphor of stacking more objects in higher piles, or larger people’s being taller. Likewise, many communities—particularly those whose languages are read from left to right—use a consistent mapping of larger values as being on the right side of horizontal space, as in the number lines found on the walls of elementary school classrooms (Tversky, 2000, 2001). Note that you implicitly knew that the phrase “first column” at the start of this paragraph indicated the column on the far left.

When these mappings are violated, viewers can become confused (Gattis & Holyoak, 1996). The brain electrophysiology research community shifted from a convention of plotting negative values (for microvolts) up on the y-axis to a more intuitive convention of plotting positive values up, forcing experienced researchers to relearn how to read familiar patterns that were now inverted (Handy, 2005). Visualizations from popular news media have been criticized for violating the convention of using higher position to indicate larger numbers, leading to confusion among viewers (Gattis & Holyoak, 1996). One such visualization depicted an increase in gun deaths in Florida after a permissive gun law was passed (Engel, 2014; see also Kosara, 2014). Each used a counterintuitively inverted y-axis, smaller values at the top and larger values at the bottom, so that the designer could evoke a metaphor of downward streams of blood. Critics reported being initially confused by the break in convention, seeing increases in deaths as decreases. One study found that when graphs used this unconventional mapping (Fig. 18), viewers incorrectly assumed that positive values plotted below the y-axis midpoint were negative values, failing to notice the critical change in the y-axis labels (Pandey et al., 2015).

For length and area, the mapping is straightforward: Larger is more. Because these channels cannot intrinsically represent negative numbers (sizes cannot be negative), other channels must pitch in to differentiate negative values: Lengths are placed with a position under an axis, and negative areas could be red in color. For angle, larger angles correspond to more, perhaps relying on the metaphor of climbing a hill: A steeper slope leads one higher, a flat slope does not change elevation, and a downward slope leads one lower. Of course, all of that assumes that you are “walking” from left to right, relying on a standard mapping of time and narrative as progressing from left to right (Boroditsky, 2011; Tversky et al., 1991).

For intensity, some previous work had shown that people tend to map larger values to darker colors, whereas other work had suggested the same for colors that appear more opaque. One study appears to have solved this long-standing uncertainty by showing that both factors affect the mapping depending on the background color. In Figure 18, in the map at the upper right with a white background, darker colors also appear more opaque, so darkness and opacity predict the same mapping: Either appears to show the larger number. However, in the map with a dark background, the darker areas can be seen as “see-through” so that the lighter areas seem comparatively opaque. Now, associations with darker as larger compete with associations of more opaque as larger. The clear mapping on the left is preferred, and the unclear mapping on the right must be rescued with adjustments to color combinations (Schloss et al., 2018).

One could imagine many alternative rules that could govern the mappings from numbers to visual properties. A computer vision system could be programmed to map larger numbers to higher positions, as humans do, or just as easily programmed to map them to lower positions, leftward positions, shorter lengths, or lighter values. Continua need not even be mapped consistently over continuous space: one could map the number 1 to position 1, 2 to 9, 3 to 5, and so on; as long as that translation is available to the computer vision system, it could easily recover the original values. The fixed architecture of the human visual system could not efficiently process those mappings.

We have so far focused only on metric visualization—the visualization of continuous magnitudes that can be positive or negative. There are other types of data (Stevens, 1946) that are frequently shown in visualizations (Bertin, 1983; Mackinlay, 1986; Munzner, 2014). One is nominal data, categorical values that can be counted or can be used to divide a set of metric numbers. Data sets often include both metric and nominal data. For example, a company might have a spreadsheet recording sales with columns of metric values (number of orders, sales in dollars, shipping time in hours) and columns of nominal values (customer name, product ID, country code). One might sum over all of the metric sales numbers or split those numbers by product ID to compute averages for each ID. Another type of data falls in between metric and nominal: ordinal values, which represent ranks that can be compared and ordered but do not reflect continuous metric differences. Examples include stars or dollar signs for restaurant ratings or price levels; designations of coach, business, and first class on an airplane; or rankings of colleges in a magazine. These values may have been generated with metric data (e.g., the cost of airplane tickets, numeric ratings of colleges), but they do not contain metric information per se.

Viewers expect particular types of data to be mapped to particular visual properties. Metric data are typically mapped to position, length, area, angle, or intensity. Nominal data can be mapped to position (e.g., a bar graph showing sales for each product ID might spread those IDs from left to right or from top to bottom) or to color or shape (e.g., to identify each point’s country code on a scatterplot pitting sales against shipping time). But if nominal data are plotted with lengths or areas, viewers can become confused. An example of this type of confusing mapping is depicted in Figure 18 (adapted from Mackinlay, 1986). The varied lengths of the bars make their values “feel” metric, such that the viewer wonders why Japan is “larger” than Italy.

Figure 18 also shows that the visual system responds to points or bars as separate objects, whereas a line connecting points “feel like” a single object that has been stretched or has moved over time and left a path (Tversky, 2001). This has led to a convention of using bars to depict values from different nominal categories and using lines to depict values from different places on a metric continuum. This mapping of nominal data to bars and metric data to lines is commonly described in textbooks and guides on graphing—however, there is more to the story. What matters more than the class of the data is the intended message to be conveyed by the visualization. Suppose one wants viewers to compare two values along a continuous dimension—for example, mood at 5 p.m. versus 9 a.m. Using bars to represent mood at those two time points would encourage interpretations such as “Mood is more positive at 5 p.m. than 9 a.m.”; this could be the right choice despite the fact that time is a metric variable. Using the wrong visualization for a given conceptual message can lead to odd conclusions: In the height examples at the bottom right Figure 18, the graphs violate both the data-type convention and the intended conceptual convention. Showing values as a function of weight using a bar graph tends to lead people to conclude that “150-pounders are taller than 125-pounders,” which is reasonable but perhaps not as helpful an insight as “Height increases with increasing weight.” Likewise, showing values as a function of nationality using a line graph could lead a substantial number of viewers to conclude that “One tends to become taller as one becomes more Dutch” (Zacks & Tversky, 1999).

Even if a viewer can extract values and data relationships from a visualization, they can fail to connect those to important real-world concepts in ways that are critical for reasoning. For example, consider the graph and corresponding text at the top of Figure 19, given to 673 high school students by Farrar (2012, as cited in Whitacre & Saul, 2016). Only 4% of the students noted that the text did not correspond to the graph’s information. In another study, high school students in honors chemistry and environmental science received similar materials on the topic of teen pregnancy, and only 25% noted a discrepancy between the text and graph (Whitacre & Saul, 2016). In a more complex task (Fig. 19, bottom), sixth through eighth graders were asked to create a position–time graph on the basis of a description of a runner’s training routine. Only 1% of the students did so correctly, and most drew “graphs” representing a map of the runner’s position.

Although students can easily extract individual values and relationships from the climate and running visualizations shown in Figure 19, they have difficulty linking the depicted patterns with the accompanying text because graphing is often taught with a focus on plotting data points and representing quantitative functions. Instead, solving the example problems in Figure 19 requires that they see the underlying link between the visual and verbal representations of the patterns. This problem arises when visualizations must be linked to text, tables, or mathematical equations. One intriguing proposal for helping students see past extracting values, to focus on making external links, is to omit numbers on axes entirely and provide only “qualitative” graphs that distill critical categorical relations. In one study, activities in which students constructed or critiqued qualitative graphs distinctly contributed to their understanding of cancer cell division and treatment impact (Matuk et al., 2019).

In the classroom, another effective method for helping students see these links is to give them abundant and explicit practice in translating between such representations. One study found that prealgebra students generated better solutions for word problems involving simple linear functions when they first generated graphical, tabular, and equation representations of those problems, compared with a control group who generated and solved equations for similar word problems (Brenner et al., 1997). The intervention group also gained a substantially better conceptual understanding of functions compared with the control group. Graphing calculators can also help students quickly see how changing features of equations affects visualized functions (Doerr & Zangor, 2000; Hollar & Norwood, 1999; Mesa, 2008); a meta-analysis of 42 studies of graphing-calculator use found benefits from middle-school mathematics through first-semester college calculus (Ellington, 2006). Another useful technique was to switch rapidly (within seconds) among multiple representations of similar concepts (tables, graphs, equations, and verbal rules), which helped students develop an understanding of functions (Kalchman & Koedinger, 2005).

Another way to facilitate these links is by starting with familiar contexts, such as earning money for each mile walked in a walkathon, allowing students to see abstractions of those functions from concrete meaningful situations (Kalchman & Koedinger, 2005). Likewise, instructors can provide students with scenarios in which they collect and summarize data and guide them toward inventing visualizations, so that the mappings between the statistical concepts and visualizations are clear (Lehrer & English, 2018; Lehrer & Romberg, 1996; Lehrer et al., 2000).

Visually Communicating Uncertainty and Risk

Quantifying uncertainty is critical for analysts and scientists who want to make informed decisions from data. Uncertainty is inherent in the generation of data and models, and it comes from multiple sources. Individual measurements contain noise. Measurements of a population of values typically rely on a sample of those values that is incomplete, or even biased. To estimate average human height, for example, we must rely on measuring a subset of all people. Averaging 100 people’s heights produces an estimate, but an uncertain one, because we did not definitively measure the height of every person in the world. If we assume that the 100 people are randomly sampled from the population, then our uncertainty can be calculated using statistical theory. However, if we were to sample 100 people who all happen to be NBA players, our sample would not be representative of the world, and standard statistical approaches for random samples would not adequately capture the true uncertainty.

Effective communication of uncertainty is necessary for scientific literacy among the public; without understanding uncertainty, people cannot accurately calibrate their internal sense of how reliable a pattern or claim is. Yet communicating uncertainty is challenging as a result of many well-documented biases related to decision making, many of which are characterized by misuse of statistical evidence in reasoning (e.g., Tversky & Kahneman, 1974). Unfortunately, the level of uncertainty in analysts’ calculations is often judged to be too complex or time-consuming to communicate to lay readers or busy decision makers (Fischhoff & Davis, 2014).

Communicating uncertainty is also important for maintaining public trust. In weather forecasts, when uncertainty is presented counterintuitively (or not presented at all), people tend to discount it. Unfortunately, when the forecast turns out to be “wrong,” this can lead to a lack of trust in scientific forecasting (Binder et al., 2016; Joslyn & LeClerc, 2012). Among scientists, underemphasis or misunderstandings of sampling error (a form of uncertainty) and the likelihood of replicating experimental results may contribute to continued use of underpowered studies and the “replication crisis” across many previously accepted findings (Ioannidis, 2005).

Some common cognitive biases are related to misunderstandings of uncertainty. One reason this may be so is that many core statistical concepts, such as variability, estimation, and sampling, are complex and can be defined clearly only with reference to statistical theory. A key challenge in communicating uncertainty is that lay audiences may not appreciate that estimates are subject to variability and may not be familiar with the statistical abstractions commonly used to express these concepts (Gal, 2002).

This lack of understanding of statistical constructs is present even among researchers. In a frequentist statistical paradigm, it is not possible to make statements about the probability that a specific interval contains the true population parameter value (e.g., the true average height of U.S. males) because probability can be defined only as frequency over a long run of trials. Instead, the frequentist 95% confidence interval refers to the probability that a confidence interval constructed in the same way as the plotted interval contains the population parameter. However, even users with statistical training, such as graduate students, are prone to mistakenly conclude that it is 95% probable that a 95% confidence interval contains the true parameter (Hoekstra et al., 2012). Likewise, the relationship between statistical significance and whether or not two error bars overlap is often misunderstood: When two frequentist 95%-confidence-interval error bars do not overlap, it is correct to assume that there is a significant difference between the two quantities at an alpha level of 0.05. However, when the two intervals do overlap, researchers incorrectly assume that there is no significant difference between the two quantities (Belia et al., 2005).

Errors such as these likely stem from challenges that students of statistics and others face concerning how to interpret the sampling distribution of the mean implied by a 95% confidence interval or standard-error interval (Chance et al., 2004; Hullman et al., 2017). The sampling distribution is the distribution of means expected if one were to repeatedly draw samples of a given size n for a population. Although the sampling distribution is a more natural choice when trying to answer questions about the probability that a difference is not zero (i.e., statistical significance) and is systematically related to the variance in the underlying measurements (and in estimates of the parameter value in the population), this distribution does not directly address the sorts of questions one might ask about the effect of applying a treatment in the world.

Uncertainty is challenging to communicate because the concept of uncertainty is difficult to understand in the first place. In graphs designed for a lay audience, depictions of uncertainty are often simply omitted, even when the graphs are intended to support inferences beyond the data sample that is shown (Hullman, 2019). When uncertainty is presented, it is most frequently shown through error bars. They typically represent either a standard-deviation range, a standard-error range, or a confidence interval (e.g., a frequentist 95% confidence interval or a Bayesian 95% credible interval). Which of these constructs is depicted has a large influence on a viewer’s impression of effect size—referring to a set of quantitative measures of the magnitude of a difference, such as the difference in means between two distributions, divided by their pooled standard deviation (Hofman et al., 2020). For example, when viewing results of an evaluation of a new drug relative to a control, one might wonder how much taking the new drug is likely to help a randomly drawn patient. When shown frequentist 95% confidence intervals representing uncertainty on bars representing the control and treatment outcomes (Hofman et al., 2020; see Fig. 20, left), lay viewers were inclined to pay more for a treatment and overestimate effect size relative to when they saw error bars showing a predictive interval representing uncertainty in the underlying measurements (Fig. 20, middle). Although not as effective as showing predictive intervals, rescaling the y-axis of a chart showing 95%-confidence-interval error bars to display the range required for the predictive interval slightly reduced overpayment and bias in effect-size estimations (Fig. 20, right).

Error bars can lead lay participants to use visual reasoning strategies that result in error-prone perceptions of effect size. For example, when lay participants were asked to evaluate the respective effect size between two distributions shown as bars representing means with error bars, their answers appeared to differ mostly on the basis of the difference between the means and were unaffected by the level of uncertainty around those means (Hullman et al., 2015). One investigation of the visual reasoning strategies employed by lay participants to make effect-size judgments and decisions from error bars and other common uncertainty visualizations found that many participants used approximations based on visual distances in the chart rather than reasoning more deliberately about the size and uncertainty of effects (Kale et al., 2021).

If lay viewers are unfamiliar with standard-deviation and confidence intervals, it is perhaps unsurprising that they tend to misunderstand the depictions of those parameters through error bars or confidence envelopes. Error bars are not seen as parameter estimates for a continuous distribution but are instead mistaken as depicting the discrete range of the data. When shown bars representing 95% confidence intervals of a forecasted nighttime low temperature, participants incorrectly believed that the upper and lower bounds represented forecasted high and low temperatures (Joslyn & LeClerc, 2012). This mistake occurred despite the presence of a highly visible key that depicted the correct interpretation. Figure 21 illustrates how not just error bars but bar graphs themselves can lead to similar misunderstandings of uncertainty: Viewers appear to implicitly believe that a bar contains the full distribution of data values that it summarizes because of its metaphorical status as a container. When reminded that the tip of a bar graph represents the mean of a distribution of values, viewers still rate points that fall slightly below the tip as more likely to belong to that distribution than points placed slightly above it (Correll & Gleicher, 2014b; Newman & Scholl, 2012).

Another notable example of this “discrete range” error occurs with hurricane-forecast visualizations. The most popular method for displaying hurricane paths, produced by the National Hurricane Center (see Fig. 21), uses a “cone of uncertainty” to represent 66% confidence intervals across thousands of storm-track simulations. Note that this means that many predicted storms would travel outside of this cone. Unfortunately, people incorrectly believe that the cone depicts a discrete range, such that areas in the cone are in danger and areas outside are relatively safe (e.g., Padilla et al., 2017, 2020). Even worse, many viewers do not recognize the cone as reflecting the storm’s potential paths, instead assuming that it depicts growth in the storm’s size over time.

Instead of depicting summary statistics (e.g., confidence intervals) that are rarely well understood by lay audiences, a better approach is to show the underlying probability distribution. Density plots (Fig. 22, top left) and violin plots (similar, but typically mirrored to show a single symmetric shape) show distributions by mapping the probability of a given value to width. These plots can help viewers intuitively understand the predicted variability of values, location (e.g., mean), and distribution shape (e.g., normal, skewed). They can also promote intuitive assessments of how likely or surprising different values are, in ways that are more closely aligned with normative statistical definitions (Correll & Gleicher, 2014b). Several studies have found that density plots lead to better-quality decisions than error bars showing predictive or confidence intervals (Fernandes et al., 2018; Hofman et al., 2020; Kale et al., 2021).

In other work, some researchers have argued that visual features such as fuzziness, color value, and unorderly line arrangement convey probability more naturally than more abstract mappings, such as mappings between uncertainty and size (MacEachren et al., 2012; see Fig. 23, left). However, representations that were judged to be more associated with uncertainty did not necessarily lead to faster or more accurate judgments. These findings illustrate a trade-off whereby some encoding types provide a subjective impression of uncertainty but may also reduce precision, making some tasks hard to complete. Experts might therefore prefer more precise representations because they have no trouble understanding how these visualizations convey uncertainty, whereas lay viewers likely benefit more from less precise visualizations that are more semantically resonant (or more naturally interpreted as uncertainty).

Yet another approach for showing statistical uncertainty intuitively is to rely on visual depictions that are inherently perceptually uncertain, preventing the viewer from resolving a value precisely. If the location of a point on a map could be blurred proportionally to the uncertainty in the position, then the recovered position would intuitively contain at least that level of uncertainty. Value-suppressing uncertainty palettes attempt this for color, taking advantage of a natural relationship among hue, saturation, and lightness: Hues are easier to tell apart when they are more saturated and darker (Correll et al., 2018; Fig. 23, right). Value is mapped to hue and certainty to saturation and lightness (darker for more certain). As a result, value judgments are more difficult for more uncertain values—the most uncertain values all appear as the same shade of gray. When this approach is applied to maps, users weigh uncertainty more heavily than they do when using conventional bivariate maps separating value and uncertainty.

The rapid advancement of technology has made it increasingly easy to collect and analyze massive amounts of health-related data (Ola & Sedig, 2016). In addition to traditional medical records, doctors and patients now have access to information from population surveys, genomic sequencing, ancestral records, wearable devices, and medical implants. Given the high volume, rapid development, and diversity of this information, it is understandable that making decisions with health data can be complicated. A large body of research is dedicated to examining if visualizations can help doctors and patients incorporate data into health and wellness planning (for reviews, see Ancker et al., 2006; Garcia-Retamero & Cokely, 2017; Garcia-Retamero et al., 2012; Lipkus, 2007; Lipkus & Hollands, 1999).

A consistent finding from research on the visual communication of health data is that visual aids can clarify numeric information for both patients and doctors. A systematic review of visual aids in health research found that effectively designed visual aids can improve risk assessments, resulting in reductions in health-decision biases, improvements in healthy behaviors, and increased trust in treatments (Garcia-Retamero & Cokely, 2017). It is noteworthy that the benefits of visual aids are strongest for individuals with low numeracy (Lipkus et al., 2001) and low risk literacy (i.e., ability to evaluate one’s risk; Ancker & Kaufman, 2007). Low numeracy tends to correlate with less advanced education, which disproportionately affects minoritized groups (Rodríguez et al., 2013)—however, one study with 463 college-educated participants found that 16% to 20% incorrectly answered relative simple questions about risk and probability (e.g., “Which represents the larger risk: 1%, 5%, or 10%?”; Lipkus et al., 2001).

For visual aids to effectively help people reason about health-care data, visualizations must be designed with care (Fagerlin et al., 2011). The following section provides a summary of what works in the communication of health-care data, drawing from the most consistent and reliable evidence-based findings to date.

Summary of Key Guidelines

Acknowledgements

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