Welcome to Lesson 7! During the course so far, we have discussed many ways in which cartographers symbolize data on maps. We used visual variables to create category and order for basemap and label design. We have also examined the usefulness of choropleth, flowlines and isarithmic symbolization methods to represent data. In most cases, our maps have focused on one data variable (e.g., % of people with health insurance), or layered different kinds of data (e.g., race routes layered over terrain). This week, we introduce multivariate mapping—maps that visualize more than one data attribute at once. We also continue with our exploration of Tableau and the interactivity that this application provides.

Following our discussion of multivariate maps in this lesson, we will introduce a special type of data—uncertainty. When mapping predicted flood zones, for example, we might want the reader to understand not only the predicted flood values across the map, but their associated uncertainty—how certain those values are to reflect reality across different locations. As uncertainty plays a pivotal role in decision-making (e.g., cones of uncertainty in predicting the path of a tornado or hurricane), we close out our discussion of uncertainty visualization with a short summary of its influence on decision-making with maps. In Lab 7, we explore both multivariate data and uncertainty visualization techniques while creating maps based on data from the US Census.

Learning Outcomes

By the end of this lesson, you should be able to:

• anticipate the influence of uncertainty visualization on decision-making with map-based displays based on knowledge of related research.
• interpret advanced multivariate maps that use visuals such as Chernoff faces and glyphs.
• use appropriate combinations of visual variables to design multivariate maps.
• describe cluster analysis and its function in multivariate thematic mapping.
• understand geographic uncertainty and the role of its visualization in map design.
• evaluate the benefits and downsides of multivariate mapping compared to designing multiple maps (i.e., compare vs. combine) for a specific mapping purpose.

Lesson Roadmap

Questions?

If you have questions, please feel free to post them to the Lesson 7 Discussion forum. While you are there, feel free to post your own responses if you, too, are able to help a classmate.

So far in this course, we have discussed many different ways of symbolizing data using visual variables. Our focus has been primarily on univariate maps—maps that show only one thematic data variable.

There are many cases where mapping a single variable is needed. More complex data and purposes often require mapping a number of different variables at once. This is called multivariate mapping. The term multivariate map is typically defined as a map that displays two or more variables at once (Field 2018). Note however, that bivariate mapping (mapping only two variables is distinct). When creating multivariate maps, you will think about the best way to symbolize each variable, as well as how they can be combined to suit your map's audience, medium, and purpose. 

Figure 7.1.1: A map of Section 8 housing and rent prices in Portland, Oregon.

Credit: Oregon Metro Council

Figure 7.1.1 shows a multivariate map. The map visualizes two variables at each location: rent prices and the number of Section 8 vouchers. These variables are individually symbolized appropriately. First, rental prices are visually encoded with a sequential color scheme—a good symbolization choice for normalized data such as rates. Second, the number of Section 8 vouchers at each location is visualized by adjusting symbol size—an appropriate visual variable for mapping count data. Together, these symbols work to visualize this housing data from Portland.

Note that the legend in Figure 7.1.1 is more complicated than many of the legends that we’ve seen so far. The format shown—one variable along the x-axis, and one along the y-axis, is common in bivariate maps, or maps that display two variables. Doing so not only explains how to data is visually encoded, but helps the map reader understand how the data are related to each other. The more visually complicated a map becomes, the more challenging it will be to design a useful legend. However, your legend is central to the reader accurately interpretating your map, so don’t treat legend design as an afterthought. The map in Figure 7.1.2 below uses short text blurbs to assist the reader in this interpretation.

Figure 7.1.2: A multivariate map about the AIDS epidemic in Africa.

Credit: US Census Bureau

As we continue through this lesson, keep an eye on the legend designs. Some maps, such as bivariate choropleth maps, have a more standardized legend designs. Others, such as what appears in Figure 7.1.2, are somewhat less conventional; they are designed and customized by the cartographer to suit the map’s data and purpose. Legend design is an important component of cartographic design in general, but is particularly important for multivariate maps.

As choropleth maps are the most popular type of univariate thematic map, it is not surprising that they are also commonly used in multivariate mapping. Bivariate choropleth maps visualize two variables. Note that while cartographers have historically described maps of two data variables as bivariate, these maps can also be described as multivariate (more than one variable). In the context of this lesson and course, we will generally use the more comprehensive description multivariate maps.

The map in Figure 7.2.1 is an example of a bivariate (or multivariate) choropleth map from a research article on COVID-19 and population movement. Examine the legend. Note that a hue progression (purple to yellow – vertically on the legend) has been applied to visually encode population vulnerability. Color lightness (horizontally on the legend) to visually encode population movement, or “stay-at-home behavior.” The legend text explains the logic behind the ordering of the color chips in the 3x3 diamond legend in the lower right of the map.

Figure 7.2.1: County-level bivariate map comparing overall 2018 CDC Social Vulnerability Index (SVI) to median stay-at-home behavior (April 7–20, 2020), United States.

Credit: Annals of Epidemiology Volume 64, December 2021, Pages 76-82. Licence: CC BY 4.0

Using color hue to encode population vulnerability is a sequential quantitative variable—a design choice we have discouraged in previous lessons. In general, color lightness is a much better choice for encoding quantitative data. In this map, however, color lightness is already being used to map the other variable—population movement (stay-at-home behavior). Creating multivariate maps sometimes requires bending the rules of cartographic conventions a bit so as to best represent all of your data.

Another commonly-used thematic map type for multivariate mapping is the proportional symbol map. As you can infer from the description, this symbolization method sizes symbols (often circles) according to individual data values. Making these types of maps can be easier than making bivariate choropleth maps. As the main visual variable used in proportional symbol mapping is size, another variable can be added quite easily (e.g., color hue, filling the interior of the symbols with unique colors representing a qualitative variable). The challenge to the map reader lies in the interpretation: as the visual variables of size and color hue are quite different, this can make it challenging for the multiple variables on the map to be directly compared by readers.

Figure 7.3.1: A bivariate proportional symbol map using size and color hue.

Credit: US Census Bureau

Figure 7.3.1 above is a bivariate proportional symbol map that visualizes two variables: population by county (a quantitative variable, with the visual variable size) and coastline vs. interior (a qualitative variable, with the visual variable color hue).

Another method of multivariate map design is to stack multiple layers so they can be viewed simultaneously. Often, this is done by displaying proportional or graduated symbols on top of a choropleth or isoline map. An example is shown in Figure 7.3.2.

Figure 7.3.2: Using layering to create a multivariate thematic map.

Credit: National Science Foundation

In the map above, visual emphasis is placed on the proportional symbols: they use size to symbolize a primary variable of interest—the estimated count of people in each city who arrived there after visiting a country on the CDC’s Zika travel advisory list. Another variable, Ae. aegypti (a mosquito capable of transporting the Zika virus) abundance, is visualized with color hue. A third variable—the approximate observed maximum extent of this mosquito, is visualized using a color fill for additional context. Note the careful descriptive legend design.

The outline of the maximum extent of the mosquito's range does not have a solid line. The light color fill contrasts against the remaining white fill to create a natural boundary interface. Not only is this design approach visually appealing, the lack of a solid outline to the mosquito's extent also implies a level of uncertainty in the exactness of that extent. We will discuss this idea later in this lesson.

Making a map such as this one is a challenge but is an example of how related variables can be mapped together to create an engaging and useful map.

Thus far, we have discussed several methods for visually encoding maps with multiple variables via the addition of map symbols. There is another option: encoding data by altering the map’s shape or size itself. Area cartograms are maps in which the areal relationships of enumeration units are distorted based on a data attribute (e.g., the relative sizes of states on a map might grow or shrink proportional to their respective populations) (Slocum et al. 2009). So the larger the attribute value, the larger the feature on the map, and vice-versa.

Figure 7.4.1 shows a choropleth map of Social Capital Index ratings (Lee 2018) at the top, and two cartograms beneath it. Each of these maps encode every state's Social Capital Index ranking using a multi-hue sequential color scheme. The bottom two cartograms also distort the area of each state by sizing them based on their population—but they use different techniques for doing so.

Figure 7.4.1: A choropleth map, and two related cartograms.

Credit: Mike Lee US Senator for Utah

In Figure 7.4.1, the map on the bottom left is a density-equalizing, or contiguous cartogram. Though areas are distorted, connections between the areal units (here, states) are maintained (e.g., the border between Alabama and Georgia is maintained). The map on the right, conversely, is a noncontiguous cartogram. States are still sized according to their population, but this method used does not require the maintenance of connections at areal boundaries. The relaxation of this requirement allows areas to be re-sized without their shapes being particularly distorted. The inclusion of state political boundaries on this map also allows the reader to make an interesting comparison: which states are sparsely populated relative to their original areal size, and which are less so?

An alternative technique to constructing cartograms, called “Value-by-Alpha” mapping, was recently defined by Roth, Woodruff, and Johnson (2010). Rather than re-sizing areas based on their population, value-by-alpha maps use transparency to fade less-populated areas into the background, giving areas of higher population greater visual prominence. Thus, they serve a similar purpose to cartograms, but do not distort the map’s geography. This is not to say that they should always be used instead of cartograms—but they are perhaps an appropriate alternative when the shock value of a cartogram is undesirable, and maintenance of both area borders and shapes is desired (Roth, Woodruff, and Johnson 2010), which is not possible with traditional cartogram maps. Pay particular attention to the fact that in order to effectively show the subtle differences in the transparencies, a dark background is selected. 

Figure 7.4.2: A Value-by-Alpha Map of results of the United States 2008 Presidential Election.

Credit: Axis Maps / CC BY-NC-SA 4.0

The examples we have explored so far have visualized two or three variables at once. Occasionally, you may want to visualize even more. One possible solution is to design data graphics that can then be incorporated into your map. A classic example of this is the use of pie charts as proportional symbols: an example is shown in Figure 7.5.1.

Figure 7.5.1: A map using pie charts by Charles Minard.

Credit: Charles Joseph Minard - Scanned from the book by Gilles Palsky, "Des chiffres et des cartes: la cartographie quantitative au XIXè siècle". Paris: Comité des travaux historiques et scientifiques, 1996. ISBN 2-7355-0336-4. Public Domain.

Interpreting the information in Figure 7.5.1 is rather straight-forward. The circle diameters represent the weight of butchered meat in kilograms supplied by departments to Paris. The individual colors assigned to the "pies" include black = ox or cow, red = veal, and green = sheep.

A more recent (and more complicated) example is shown in Figure 7.5.2.

Figure 7.5.2: A Multivariate Map using Pie Charts

Credit: Humanitarian Information Unit - US Department of State.

Though the introduction of data graphics does permit the addition of many variables onto the map, this does not mean it is always the best solution. As shown in Figure 7.5.2, including a large amount of data in a map using multiple symbolization methods can make it challenging to interpret. Additionally, multivariate graphics in general—and pie charts in particular—have well-documented disadvantages in terms of reader comprehension (Tufte 2001). Adding graphics that are already challenging for people to understand to maps tends to exacerbate such issues. Furthermore, the size of the graphics may lead them to obscure data in underlying layers. This is not to say that they should never be used, however—just with caution. And fortunately, there are ways in which such maps can be made easier to interpret.

Glyphs

One way that multivariate maps can be made more comprehensible is through the addition of user interaction. Figure 7.5.3, for example, is challenging to interpret as a static image, particularly as the glyphs (i.e., a pictograph) used are quite small and some of the color choices are not easily distinguishable. However, this is an interactive map. Clicking on a state creates an informative pop-up, shown in Figure 7.5.4.

Figure 7.5.3 An example of a map created with multivariate glyphs.

Credit: Blooming States, US Census Bureau.

While you will explore interactivity in this assignment, we will discuss the merits and challenges of map interactivity further in Lesson 8.

Figure 7.5.4: The pop-up created on-click in Figure 7.5.3.

Credit: US Census Bureau.

Chernoff Faces

Despite the difficulty of creating maps with multivariate glyphs, cartographers have long attempted to tackle this challenge through interesting experimentation. One particularly whimsical example of this is Chernoff faces. Chernoff faces are glyphs created by mapping variables onto facial attributes. When mapping the variable average household income, for example, a bigger smile might indicate a higher income level.

Figure 7.5.5 An example of Chernoff faces.

Credit: Avenue, Wikimedia Commons, public domain

The Chernoff face technique was first proposed by Herman Chernoff in 1973. Chernoff's intention was to capitalize on the ability of humans to intuitively interpret differences in facial characteristics. One the one hand, humans can subconsciously note important differences in expressions that are almost unmeasurable. In addition, humans can ignore large differences that are common between faces (Chernoff 1973). Chernoff also noted that his method was desirable as it permitted the designer to map many variables (as many as 18!) onto just one graphic.

Chernoff’s original application of his technique used fossil and geological data, but Chernoff mapping is more commonly used to depict social thematic data such as well-being, or other topics related to human emotion. Chernoff mapping has been a contentious method since its introduction— some Chernoff maps such as this one: Life in Los Angeles by Eugene Turner, 1977 [14], have been heavily criticized for their use of stereotypical facial attributes and a cartoonish over-simplification of complex issues.

In response to these critiques, some cartographers have developed techniques for utilizing the advantages of Chernoff faces without some of the contentiousness. Heather Rosenfeld and her colleagues, for example, proposed using “Zombieface” glyphs rather than human faces—maintaining the emotive content and still capitalizing on people's ability to intuitively interpret facial features, but removing the human context and thus lowering the likelihood of reinforcing harmful stereotypes (Figure 7.5.6).

Figure 7.5.6: Unknowns in our hazardous landscape, a map by Heather Rosenfeld and colleagues which uses the Chernoff Zombies mapping technique.

Credit: Heather Rosenfeld; co-authors: Sarah Moore, Eric Nost, Robert Roth, Kristen Vincent. View her conference talk to learn more about Chernoff maps and the Chernoff Zombie mapping technique here! Chernoff Zombies, Nacis 2017.

Take a closer look at the legend of this map—which demonstrates how the hazardous waste data was mapped to Zombie facial attributes—in the image below. As you can see, the map focuses on visualizing the presence of unknowns and uncertainty in the mapped dataset (we'll discuss further techniques for visualizing uncertainty later in this lesson).

Figure 7.5.7: The legend from this Chernoff Zombies map, Unknowns in our hazardous landscape.

Credit: Heather Rosenfeld; co-authors: Sarah Moore, Eric Nost, Robert Roth, Kristen Vincent. You can learn more about this project as a whole at their website: HazMatMapping.

Chernoff Zombies are among several creative solutions recently proposed: a fun example is shown in the following quasi-Chernoff map: Mapping Happiness. It maps happiness, or well-being, across the United States using emoticons. Though these icons do not encode as many variables as Chernoff faces, they share the benefit of visualizing data at-a-glance using facial expressions.

Of course, the novelty of this "zombie-chernoff" symbolization method is interesting. As shown in the legend, there are many subtle differences in symbols that may be difficult for readers to distinguish. Thus, despite the inventiveness of such symbolization experimentations, the cartographer should always question how easily it is for the map reader to encode the information and make sense of what they see.

As demonstrated by previous examples, multivariate maps are often challenging—both for cartographers to create and for readers to interpret. However, if you need to map multiple variables simultaneously, but want to avoid a complex multivariate map (for example, when creating a map for a presentation slide) there is another option: simply creating multiple, adjacent maps. This is called small multiple mapping.

Figure 7.6.1: An example of the small multiples mapping technique. 

Credit: US Census Bureau

Small multiple maps are particularly useful for depicting data over time, as they can be arranged in a linear sequence, the way that time is typically depicted. With the increasing popularity of web maps, small multiple maps can be more easily replaced with a animated maps, where each map appears as an individual frame. Despite the advantages of animated maps (e.g., creating visual interest, efficient use of layout space), there are still benefits to traditional small multiple mapping. One primary advantage is the ability to simultaneously compare the various maps. 

We can imagine combing the set of maps in Figure 7.6.1 with some sort of transparent layering, or perhaps turning it into an animated map. However, a single map with multiple transparent layers would be visually complex, and viewers of an animation would have to wait for the animation to loop—or scrub through the frames—in order to compare two specific maps. Here, simple works well. If your presentation is still too complex, you may consider reducing the amount of information being presented. Figure 7.6.2 is an example of small multiple mapping that only uses two multiples.

Figure 7.6.2: A successful side-by-side map comparison of voting districts in North Carolina.

Credit: Furfur, CC BY-SA 4.0, from Wikimedia Commons.

So far, we have discussed two ways of mapping multiple variables—combining visual variables to encode multiple variables into one map, and visually comparing sets of maps of different data. There is a third, considerably different method that is often used for mapping multivariate data sets: cluster analysis. Cluster analysis is a form of data reduction and refers to mathematical methods used to combine multiple quantitative variables into one map (Slocum et al. 2009).

There are multiple methods for clustering (e.g., hierarchical and non-hierarchical). One of the more simple to understand is the K-Means algorithm. With K-means, the goal is to identify groups (k) of similar observations based on several attributes. The groups are assigned in a way that minimizes intra-group differences, while maximizing inter-group differences. Consider, for example, that you are interested in visualizing education, income, and access to green space in the US by county. You could map these three variables individually creating a small multiple, or you could use cluster analysis to identify groups of counties that are similar along all three dimensions on a single map using a qualitative color scheme (or a chorochromatic map).

Figure 7.7.1: An example output of cluster analysis with k-Means.

Credit: Chire, Wikimedia Commons, (CC BY-SA).

Cluster analysis is a complicated topic, and we will not go into the mathematical details in this course. What is important to understand is that it provides a mathematical alternative to the other more design-based multivariate mapping techniques we have explored so far. You are encouraged to explore the recommended readings if you are interested in learning more about cluster analysis and about implementing it in GIS.

Of the many variables you may wish to include in your maps, there is one that has received particular focus from cartographers due to its unique characteristics—uncertainty. Uncertainty is a complex concept that has been defined differently by various authors. For example, Longley et al. (2005) define uncertainty as "the difference between a real geographic phenomenon and the user’s understanding of the geographic phenomenon." We use this definition as it encompasses the many variations of uncertainty that in emerge during multiple stages of map-making—during data collection, data classification, visualization, map-reader interpretation, and more (Kinkeldey and Senaratne, 2018).

It can be assumed that all geographic data contain some level of uncertainty. A map of average income by county, for example, might classify a county as having an average household income of $58,234. Despite this, it is possible, even likely, that the actual value is different—this is due to survey response errors, non-response to survey (e.g., Census) requests by some residents, or changes in the data over time (e.g., some survey respondents have moved in or out of the county since the data was collected). A map of precipitation levels, similarly, will also contain uncertainty, due to factors including the lack of ubiquitous measurement instruments, their imprecision or inaccuracy, and possibly human error or related factors. Soil mapping is another example of uncertainty. On soil maps, definitive boundaries are shown through outlines of soil types. Yet, we know that soil does not have definitive edges as soil types gradually change over space often mixing together at their boundaries.

Traditionally, researchers have grouped geodata uncertainty into three categories – the what (attribute/ thematic uncertainty), the where (positional or locational uncertainty), and the when (temporal uncertainty) (MacEachren et al. 2005). The success of visual variables for depicting uncertainty depends on the type of uncertainty to be mapped. For example, containing a point within a colored circle showing your location on a map, such as Google’s “blue dot,” might be most effective for depicting positional uncertainty (Google Maps; McKenzie et al. 2016). Use of another variable such as transparency might be more effective for depicting attribute uncertainty, such as uncertainty of unemployment rates in a county-level map.

Like other multivariate data, uncertainty can be combined with the other visualized data in a map, or compared by visualizing it in a separate map view. Figure 7.8.1 shows two maps that use different techniques to visualize the uncertainty in the data. Figure 7.8.1 (top) uses a combining technique, in which a visual overlay (diagonal lines on top of a univariate choropleth symbolization) is used to show attributional uncertainty. Figure 7.8.1 (bottom) uses a reliability diagram—an inset map that the reader can reference to understand which locations on the map contain the most certain data values. In general, the combining method is a more popular technique, though a compare technique might be more appropriate if the primary map is sufficiently complex, and thus adding overlay would make the map difficult to comprehend. 

Figure 7.8.1: Combining (top) vs. comparing (bottom) uncertainty visualization techniques.

Credit: Cary Anderson© Penn State is licensed under CC BY-NC-SA 4.0.
Data Source: The World Happiness Report (Helliwell et al. 2018), Natural Earth.

Among combined uncertainty visualization techniques, methods for visualizing uncertainty are typically classified as either intrinsic or extrinsic. Intrinsic uncertainty visualization techniques cannot be visually separated from the visualization of one or more other variables, while extrinsic visualization techniques are easier to interpret separately. An example of the difference between these two techniques is shown in Figure 7.8.2.

Figure 7.8.2: Extrinsic (top) vs. intrinsic (bottom) uncertainty visualization techniques.

Credit: Cary Anderson© Penn State is licensed under CC BY-NC-SA 4.0.
Data Source: The World Happiness Report (Helliwell et al. 2018), Natural Earth.

In Figure 7.8.2, both extrinsic (top) and intrinsic (bottom) uncertainty visualization techniques are shown. The extrinsic visualization uses a hatched fill overlay to denote uncertain values—thus, the visualization of uncertainty is visually separable from the visualization of the data underneath. Figure 7.8.2 (bottom) by contrast, uses an intrinsic visual variable—transparency—to visualize data uncertainty. The two variables are combined together to create the legend as well. Examine the top and bottom maps in Figure 7.8.2. Ask yourself how easily it is to visually separate the variables in each map. Can you think of a different approach to map the two variables that would be easier for the map reader to visually separate and at the same time combine the two variables?

Any visual variable can be adapted to demonstrate uncertainty. However, some are more intuitively associated with uncertainty than others. MacEachren (1995) proposed the idea of clarity as a visual variable for static maps, an overarching concept that can be further divided into three visual variables: transparency, crispness, and resolution (MacEachren 1995). Transparency is a familiar visual variable, as it has been adapted for purposes other than displaying uncertainty, such as in the value-by-alpha maps described earlier in this lesson. 

Crispness is a particularly intuitive way of visualizing uncertainty. Features are depicted on a continuum from crisp to blurry, with less certain values appearing appropriately blurry or out-of-focus (Figure 7.8.3).

Figure 7.8.3: Crisp (left) vs. blurry (right) areal unit boundaries – higher crispness indicates greater certainty.

Credit: Cary Anderson© Penn State is licensed under CC BY-NC-SA 4.0.

Resolution creates a similar effect—features with less certain boundaries or attributes are depicted in courser resolution, suggesting a lack of certainty in the map.

Figure 7.8.4: High vs. low resolution - higher resolution indicates greater certainty.

Credit: Cary Anderson© Penn State is licensed under CC BY-NC-SA 4.0.
Data Source: NASA.

These visual variables have long been associated with uncertainty due to use or presence in other visual media—e.g., a photograph “coming into focus”—and so provide a design option with substantial precedent. Just as higher data values are visually encoded with larger symbols, less certain boundaries, for example, may be visually encoded with fuzzy boundaries. Look at maps of the Middle East published by the CIA or US State Department. In many instances, these maps will use dashed or other non-solid lines styles to indicate disputed country boundaries.

Though uncertainty is often discussed in terms of imprecise instruments, imperfect collection methods, etc., an important additional context where uncertainty plays a role is in the mapping of future scenarios. Climate models, for example, use past and present data to predict future conditions, but these predictions are inherently uncertain. Figure 7.8.5 below contains maps of temperature and precipitation change predictions. The first map (top left) maps the average result of 37 predictive models intended to estimate temperature change by 2050 (Kennedy 2014). The middle map shows the warmest 20% of models—the 20% coldest models are summarized at the right. The bottom three maps show a similar comparison of maps created from precipitation models. In all three maps, the "boundaries" of each projected temperature area are visually set by the interface of the two dis-similar color fills. No solid line is present.

Figure 7.8.5: Prediction maps of Temperature and Precipitation change in the American West.

Credit: NOAA Climate.gov

Unlike previous examples, these maps do not use intuitive visual depictions of uncertainty. However, the map-maker's inclusion of all three maps for each data variable shows the range of possibilities that might lie ahead: the future is always an uncertain entity. It is implied that these maps depict not all possible scenarios but a range of likely ones; they intend not to precisely predict the future but to help users understand what future conditions they might expect to come about.

In the last section, we discussed how to conceptualize uncertainty, and ways in which it can be visualized. One important question remains: why should we do so? Creating well-designed maps is already challenging, and adding a depiction of uncertainty makes this process even more so.

Uncertainty is typically depicted in maps for two primary reasons: (1) its inclusion may be regarded as an ethical necessity—many maps are created with significantly uncertain data, and a cartographer might feel that withholding this information from the map reader would be misleading, and (2) consideration of uncertainty plays an important role in decision-making, and thus its visualization might be necessary in some contexts—for example, maps of predictive hurricane paths tend to include a “cone of uncertainty” (Figure 7.9.1)—and such maps often play an important role in decisions made by residents of storm-affected areas.

Figure 7.9.1: A Map of Hurricane Michael which includes the cone of uncertainty, showing a probable path of the storm based on NOAA’s model predictions.

Credit: Official Site of the Town of Fort Mill, SC

So how does the visualization of uncertainty affect decision-making with maps? Kinkeldey et al. (2015) conducted a review of studies that attempted to answer this question. Most of the studies they analyzed suggested that the visualization of uncertainty does have an effect on task performance with maps and similar spatial displays (Kinkeldey et al. 2015). Simpson et al. (2006), for example, studied the use of uncertainty visualization in surgical tasks with graphic displays, and noted that the inclusion of uncertainty visualization improved performance accuracy. The positive influence of uncertainty visualization on task-completion accuracy with maps is a somewhat common finding. Though findings are less consistent with regards to task completion times (i.e., speed), uncertainty visualization seems at least not to significantly increase task-completion times (Kinkeldey et al. 2015).

Despite this, there is still not a consensus concerning whether uncertainty visualization is always helpful for decision-makers—some studies note that participants perceive uncertain data as risky, which can induce irrational decision-making via loss-aversion (Hope and Hunter 2007). Whether uncertainty visualization is useful—and whether it is useful enough to warrant the design efforts it requires—is context dependent and still thoroughly up for debate.

Critique #4 will be your third critique involving a peer review of a map created by someone in this class. In this activity, you will be assigned a colleague's map from this class to critique from Lab 6: Proportional Symbolization.

Your peer review assignment includes writing up a 300+ word critique of one of your colleague’s Lesson 6 Lab.

In your written critique please describe:

• three (3) things about the map design that you think works well and why.
• three (3) suggestions you have for improvement of the map design and why these improvements would be helpful.

According to the two prompts above, a map critique is not just about finding problems, but about reflecting on a map in an overall context. Your critique should focus on the map design that works well as much as it does on suggestions for design improvements. In your discussion, you should connect your ideas back to what we learned in the previous lessons.

Remember, your critique should be as much about reflecting upon design ideas well-done as it is about suggesting improvements to the design. In your discussion, connect your ideas to concepts from previous lessons where relevant.

You may find these two resources helpful as you write your critiques:

• Daniel Huffman’s 2020 blog post on how to “Critique with Empathy"
• Ordnance Survey’s (Wesson, Glynn and Naylor, 2013) list of effective cartographic design principles

Grading Criteria

Registered students can view a rubric for this assignment in Canvas.

Peer Review Canvas Help

• How do I know if I have a peer review assignment to complete?
• How do I submit a peer review to an assignment?

Multivariate Symbolization

In Lab 6, we explored representing discrete and abrupt data using proportional symbols. Specifically, you worked with proportional and graduated symbols. You also explored mapping qualitative data using the chorochromatic symbolization. In Lab 7, you will continue to apply design and symbolization ideas. In most cases, your maps have focused on one representing a single data variable (e.g., % of people with health insurance), or layered different kinds of data (e.g., race routes layered over terrain). Univariate data is one of the more common data that is mapped. However, symbolization methods exist that allow more than one variable to be mapped. This Lab, we introduce multivariate mapping—maps that visualize more than one data attribute at once. 

Following our general discussion of multivariate maps, we introduce a special type of data—uncertainty. When mapping predicted flood zones, for example, we might want the reader to understand not only the predicted flood values across the map, but their associated uncertainty—how certain those values are to reflect reality across different locations. As uncertainty plays a pivotal role in decision-making, we close out our discussion of uncertainty visualization with a short summary of its influence on decision-making with maps. In Lab 7, we explore both multivariate data and uncertainty visualization techniques while creating maps using the reported margin of error reported in census data.

As with Lab 6, Lab 7 will continue using Tableau to create the maps. However, the emphasis on using Tableau for Lab 7 will extend beyond multivariate symbolization to creating an interactive dashboard where maps and graphics will be linked together, allowing relations in the data to be seen.

Lab Objectives

• Create a single dashboard in Tableau that includes the following main elements:
  • a multivariate map using proportional symbols (separate legends for each variable)
  • a chart showing the variable of interest
  • a chart showing the margin of error values
• Create a single multivariate map using census data (either the same data from Lab 6 or new data).
• Visualize the census data and uncertainty data on a single map using an appropriate combination of visual variables and colors to create a multivariate map.
• Create two charts (e.g., scatterplots) that illustrate the census data values and the uncertainty (e.g., margin of error)
• Integrate the multivariate map and two charts together on a single dashboard through linking so that relations highlighted on one object (e.g., the map) are also highlighted on another (e.g., both charts), creating a dynamic environment.
• Implement an effective unified design practice (color choices, balancing negative space, etc.)

Overall Lab Requirements

For Lab 7, you will create a single dashboard of a unified design in Tableau. The specific requirements for each dashboard element are listed below. 

Lab Requirements

Multivariate Map: Variable of Interest and Uncertainty Data

• Choose a variable of interest to map from the provided American Community Survey (ACS) data to create a single multivariate map.
• You can use the same data from Lab 6 (or choose a different dataset), but the data must also include a measure of uncertainty (for census data, this uncertainty can be considered the margin of error values included as a separate column with the census data).
• The chosen data will be mapped using a bivariate symbolization (e.g., symbols and color values).
• Use appropriate visual variables to encode your data using a bivariate symbolization.

Chart One: Census Data (choose your own variable) 

• Select an appropriate chart representation method (e.g., scatterplot, barchart, etc.) to represent the pattern between the census data value and each county.
• This chart must be linked to the bivariate map and another chart so that data relations highlighted on one element are also highlighted on another, creating a linked environment.
• The chart title must correspond to the data appearing on the chart.
• Consideration must also be given to the chart's design (e.g., unique color choice for the symbols, axes titles, data order along both axes, etc.).

Chart Two: Census Data (use the variable's margin of error) 

• Select an appropriate chart representation method (e.g., scatterplot, barchart, etc.) to represent the pattern between the census data and the margin of error by county (note, you can use the same chart type as with Chart One or choose a different one).
• This chart must be linked to the bivariate map and another chart so that data relations highlighted on one element are also highlighted on another, creating a linked environment.
• The chart title must correspond to the data appearing on the chart.
• Consideration must also be given to the chart's design (e.g., unique color choice for the symbols, axes titles, data order along both axes, etc.).

Tableau Dashboard

• Appropriately arrange and size each object in the available dashboard space (e.g., consider the distribution of negative space).
• Ensure that each object is linked to the other objects on the dashboard.
• All objects must be clearly visible and readable (e.g., be mindful of text size).
• Create an overall descriptive title and individual object titles.
• Use a consistent design appearance and feel throughout the story.

Lab Instructions

The data for this lab will be self-selected from the US Census Bureau’s data explorer website. The Lesson 6 Lab Visual Guide provided details on how to access this site, search for data, and format the data for download.

Grading Criteria

Registered students can view a rubric for this assignment in Canvas.

Ready to Begin?

Detailed instructions on creating these objects are available in the Lesson 7 Lab Visual Guide.

You've reached the end of Lesson 7! In this lab, we designed an interactive map-based story using the visual analytics platform Tableau. Though this lab focused heavily on concepts from Lessons 6 and 7, we also drew from concepts throughout this lesson including multivariate symbolization and mapping uncertainty. However, you also appreciated and relied upon ideas from earlier lessons such as designing layouts, symbolizing data, choosing colors, and thinking critically about map audience and purpose. You should consider publishing your Tableau cartographic creations on your website for you to share with others as demonstration of your skills in map design and data visualization. You're now ready and able to create, analyze, critique, and share high-quality interactive maps! In Lab 8, we will continue exploring web-based mapping with a new application.

Reminder - Complete all of the Lesson 7 tasks!

You have reached the end of Lesson 7! Double-check the to-do list on the Lesson 7 Overview page to make sure you have completed all of the activities listed there before you begin Lesson 8.