Faddish Figures

In this post I thought I’d offer a sort of case study of an intriguing infographic that library graph designers may be able to learn from. And then discuss a couple of recent trends in data visualization and statistical charting that appear in a recent PEW Research Center report on eBooks and reading.

The infographic is from statistical forecaster Nate Silver’s website www.fivethirtyeight.com. Silver and his colleagues prove that it’s possible to design high-quality and engaging data visualizations without abandoning the core principles of good statistical graph design. This makes the graphic an example worth looking at. So let’s take a look!

natesilverpathchart_oct19_480Source: www.fivethirtyeight.com. Accessed Oct 19, 2016. Click to see larger image.

Even though the image is a variation on a stacked bar chart,1  it is amazingly informative! First, I should note that this graphic doesn’t present fixed data. It presents likelihoods or probabilities. Since Nate Silver and his team are forecasters, most of their tables and charts report data that involve uncertainty.2  That is, guesses accompanied by statements of the researchers’ confidence in the guesses. Like a meteorologist reporting, “I predict snow today and I have 60% confidence in this prediction.”

The uncertainty shown in the chart takes the form of calculations called expected margins of victory that Nate Silver and his team did for every U.S. state. These margins estimate the likelihood that each state will be won by either the Republican or Democratic candidate in the U.S. presidential election in November 2016.

Nate Silver et al. encoded this uncertainty using a simple graphical element, color density. Darker red and blue represent predictions with fairly high margins and thus fairly high certainty. Lighter red or blue are predicted outcomes having less certainty. Higher certainty Republican-leaning states (darkest red) appear towards the right of the image and higher certainty (darkest blue) Democratic-leaning states appear towards the left. The leanings of less certain red or blue states appear towards the center.

The best thing about this infographic is its ingenious design. A two-dimensional map in the form of a pathway dramatizing the candidates’ state-by-state journeys to next month’s election results. To those of us who are westerners and read left to right, the journey seems to show Hillary Clinton’s progress past the 270 electoral vote threshold (dotted vertical line). But wait! The graphic is just as readable right-to-left, showing Donald Trump advancing towards, but not reaching, the same threshold.

One way to view this graphic is as a sorted list in the form of a continuum, albeit a squiggly one! (Continua are typically flat and horizontal and this one would be too if it were stretched out.) The data are U.S. states and their associated electoral vote counts sorted high-to-low not by vote counts, but rather by the expected margins that Nate Silver and his crew calculated.

Another way to view the pathway graphic is as a variation on a stacked bar chart having two separate bars as shown here:

adapted548barchart_370Data source: www.fivethirtyeight.com. Accessed Oct 19, 2016. Click to see larger image.

Essentially, the pathway graphic layout is equivalent to taking bars from this bar graph and laying them sideways, joining them together with blue left and red right, and stretching them into twists and turns. (Notice that the stretched bars meet to the right of 270 threshold line.) Since the bar graph presents the same data as the pathway graphic, blue versus red portions of both graphs depict the same electoral vote counts. (Although the pathway graphic doesn’t show the counts, if you add up votes for each state by color, you’ll get the counts shown in the bar graph.)

You may have noticed that the bar chart doesn’t include segments for the U.S. states. The bars are too short for that. And the chart has only two-color graduations to indicate the strength (level of confidence) of the predictions. As seen in the legend, darker and lighter blue and red represent two categories: Likely and Maybe.

Thus, the bar chart isn’t as informative as the pathway chart, except for providing electoral vote counts. This is what’s so amazing about the infographic: How the snaky path squiggles around kinetically while encoding so much information: Which direction each state appears to be leaning, the strength of these leanings, relative sizes of the states’ electoral vote count, how these add up compared to the 270 threshold and between the two candidates. All packed into such a visually fun image!

Nate Silver’s infographic does have a few elements that go against best practices for designing statistical graphs. One is that the graph has no explicit (numbered) measurement scale (axis). A horizontal axis is implied, but the nearby labeling doesn’t tell us what the scale units are. Instead, that labeling explains the arrangement of the states horizontally. In case you haven’t figured it out, a hint is the graphic’s pale gray key at the bottom right. The chart’s horizontal scale units are electoral college vote counts, since each state’s segment is sized based on its allotted number of votes.

The infographic presents a couple of minor obstacles to readers like requiring state names to be read sideways. But that can be part of the fun! And few readers will care because the information is clear and available. This isn’t true, however, for the information communicated via the chart’s graduated coloring. Readers will recognize that the darkest shades mean highest likelihood one of the candidates will win a given state, and the palest the lowest likelihood. But estimating margin differences between two or more states is a different matter. To illustrate this better, here is an earlier version of the chart posted on Silver’s website the first week of October:

natesilverpathchart_oct5_520Source: www.fivethirtyeight.com. Accessed Oct 5, 2016. Click to see larger image.

Suppose I told you I learned from other data available on fivethirtyeight.com the same week this chart was posted that a few states were on the fence, meaning not clearly leaning for or against either candidate. The color density in the graphic just above should tell us which states these are. They must be the palest state segments visible, which appear just to the right of the 270 threshold line. Note there that the segment coloring transitions from pale blue to pale red (pale red to pale blue if you read right-to-left) between Ohio and Iowa. From this we’d guess that these two states must be undecided.

But what about two adjacent segments, Arizona and North Carolina? Are their margins low enough that they were undecided also? Well, yes and no. That week Arizona was on the fence, but North Carolina was leaning slightly in favor of Clinton. The shading alone doesn’t tell us this. Shaded bars like this chart uses can only give a rough impression of relative amounts associated with any give shade. Even if the graphic’s designers had posted a color-coded key indicating the numeric ranges each shade represents, it would barely be possible to determine exact numeric differences. Exactly how many margin points less than pale pink is pale, pale pink?

Fivethirtyeight.com had another graphic posted showing predicted blue versus red states for that same week, the map shown here:


Source: www.fivethirtyeight.com. Accessed Oct 19, 2016. Click to see larger image.

This image is so refreshing because it’s rare to encounter a statistical map that sizes U.S. states according to the statistics being reported. Usually, statistical maps render states (or countries in international maps) true to their geographical boundaries and sizes. The problem with this is that it makes geographically large entities (like Utah, Arizona, Nevada, and Montana in a U.S. map) prominent whether or not their statistical data should be. While geographically small countries or states (like Rhode Island, Delaware, and Connecticut in a  U.S. map), whose data can easily exceed the large countries’ or states’ data, end up in the shadows, so to speak.

Nate Silver and colleagues solve this problem by drawing fantasy shapes made up of honeycomb cells, each cell representing an electoral vote. The result is an almost comedic but completely faithful portrayal of the data seen in the map above. This satisfies a prime directive in good statistical graph design: Show data accurately.

American readers familiar with a regular U.S. map will find it easy and enjoyable to identify the fantastical shapes of the states. However, when viewing the map in its entirety, American reader or not, the total areas covered by Clinton- versus Trump-leaning states are difficult to judge. The Trump proportion appears to be almost 40%. (The real proportion, again, is 36%). Whether statistical maps are proportioned correctly or not, it can be challenging to visually sum up data categories based on swaths of color spread around the image.

But no matter. All three fivethirtyeight.com charts I’ve shown so far communicate quantitative information meaningfully and accurately. Most readers will be happy to approach these charts as challenges and overlook the minor inconveniences required to interpret them. The important thing is that the charts paint the general picture just fine: Trump has somewhere between 30% and 35% of the total electoral votes, while Clinton has 65% to 70%.

Speaking of stacked bar charts, here’s one published in the New York Times last week that is also about the 2016 U.S. presidential election:

nytimesbarchart_470Source: Wasserman, D. “What Are the New Battle Ground States?” www.nytimes.com.
Oct. 17, 2016. Click to see larger image.

A stacked bar chart such as this one is called a segmented bar chart. In segmented bar charts each bar depicts 100% of the membership of a larger group of interest, in this case the population of the state named at the left of each bar. Just like wedges in a pie chart, segments in a segmented bar chart indicate the size of each category relative to the whole group. In this chart the color-coded segments correspond with the labeled categories, Whites with No College, College Educated Whites, African-American, Hispanic, and Asian/Other.

Stacked bar charts, including segmented bar charts, have one unfortunate drawback: It’s very difficult to visually gauge the lengths of bar segments accurately (see footnote #1). Creators of the New York Times chart tried to address this problem by adding data values to the chart—62%, 32%, and 6% in the Iowa bar, for example. Since the chart provides each bar segment’s length as a percentage, there is no need for readers to struggle estimating these for themselves.

Unfortunately, the locations of the data values make the chart confusing. In a regular (vertical) bar chart data values are typically placed at the top of bars For horizontal bar charts these are placed at the far right. Data values can also be positioned inside the bar segment in the middle or at the bottom. (I show a chart below with both of these placements.)

This last option is the one designers of the New York Times graph chose. In a horizontal bar graph this puts data values at the far left end of each bar segment, wherever the segment is located along the axis. As you can see in the Iowa bar, the 32% just to the right of the dark gray segment looks like it belongs to that segment. Yet it belongs to the lighter gray segment. This placement also has the peculiar effect of putting the 32% value to the right of the 50% vertical reference line. The value for the dark gray segment (62%) appears in a boldface blue font at the far left, away from the right edge, which readers would normally use to judge a segment’s length. The designers tried to assist readers by color-coding the data values fonts (like the dark gray segments’ boldface blue font), but most readers will think the colors are just decoration.

Will readers be able to overlook these oddities and interpret this chart correctly?  Probably they will. But the question is, why would designers create extra confusion for readers?

These shortcomings bring another issue with stacked/segmented bar charts to light. Embedding data values can get messy. This is true for the New York Times chart where the only workable option was listing total Non-white/Hispanic data values outside the bars. And omitting values for the African-American, Hispanic, and Asian/Other categories. (Wouldn’t it have been nice to see percentages for African-American populations in Georgia, North Carolina, and Virginia? And for Hispanic populations in Florida, Arizona and Nevada?  And Asian/Other populations in Nevada, Arizona, and Virginia?)

Maybe the best compromise is locating data labels in the middle of segments as seen in this chart from a U.S. National Center for Education Statistics style guide:


Bar Chart with Data Labels Placed at the Inside Middle of Bar Segments. Excerpted from: U.S. National Center for Education Statistics, Statistical Standards, Appendix G. Guidance for Producing Figures in Excel That Meet NCES Standards. Accessed Oct. 25, 2016. Click to see larger image.

Returning to the New York Times bar chart above, there is another reason for showing this chart to you: To illustrate one of the new trends I mentioned at the opening of this post. This new trend happens also to involve data values. You will already have noted that the chart has no horizontal axis label and the vertical axis contains a list of 15 selected states (with one row representing the national averages, 42%, 31%, and 27%, inserted according to the chart’s sort order, which is percentage of non-college educated whites, high-to-low).

The horizontal axis measurement units turn out to be percentages, referring to the relative sizes of the categories already mentioned—African-American, Asian/Other, and so on. But you wouldn’t know what these units were based on the chart title alone. To figure out what the units are you have to look at the data values visible on the Iowa bar. And it is here we see the new graphing fashion I’m talking about:  Denoting percentages by displaying percent signs (%) only at the beginning of a data series, and omitting them for the rest of the series.

This seems to be a style standard at the Pew Research Center as seen in this chart:


Source: Perrin, A. 2016. Book Reading 2016. Pew Research Center.

This graph is missing its vertical axis, another apparent styling practice of the Pew Research Center. Like the New York Times graph, this one also skimps on cues to readers about what the measurement units are. The graph title is not the usual style (I’ll discuss this further on). And the more traditional title appears as a subtitle beginning with the percent sign (%) rather than the English words percent of. The tiny % symbol is the title’s only hint about measurement units. The only other clue is four percent signs vertically arranged above the 2011 horizontal axis label. The other 16 data values have no percent signs.

Still, it’s not uncommon for charts to omit percent signs, as the black-and-white U.S. National Center for Education Statistics (NCES) chart shown above does. However, in that chart the measurement units are clearly indicated in the title and on the vertical axis. Maybe this new omit-the-percent-sign fad is just one minimalist step away from charts styled like the NCES one.

I can only surmise that this new charting practice must be about minimizing visual clutter. (Why else bother?) This is fine as long as designers work consistently towards this aim without handicapping readers. In the case of the PEW chart, the lack of informative chart titles and labeled axes does handicap readers. They have to mentally append the signs to each data values visible. Not a big deal, except that readers have to stop and examine the chart closer to see whether different measurement units might legitimately appear together, as happens with dual-axis charts.

Examining graph layouts and contents is the reader’s job, of course. But the graphical designer’s job, at least according to Ranganathan’s 4th Law, is to help rather than hinder this process. Unfortunately, PEW’s chart designers must be unaware of this Law. Rather than saving the reader’s time by decreasing chart clutter, they added clutter. First, by occupying white space with thick and wordy data labels (Read a book in any format and so on). Readers should be able to ignore these when they need to examine trend line angles. But this is not so easy when readers try to estimate distances between the top and bottom two lines. Second, additional clutter comes in the form of trend lines extended from 2012 to 2014 when there were apparently no survey data for 2013. (I suggest an alternative to this below.) Since the 2013 segments have no line markers (circles), they are more prominent than than any of the other segments. Yet, the evidence they represent is less substantial.

A primary statistical graphing standard espoused by data visualization pioneers William S. Cleveland and Edward Tufte is:  Show the data. Tufte also added:  Be Honest about the Data. With these admonitions in mind, I re-drew the PEW line chart as seen here:

PEW_BookReading2016LineChart_Adapted_500.jpgPEW Line Chart Adapted to Make the Data More Prominent. Adapted from: Perrin, A. 2016. Book Reading 2016. Pew Research Center. Click to see larger image.

If the purpose for omitting percent signs is to make the data prominent, this could  be better accomplished with a design something like this chart. The added white space makes the trend lines more visible, as does using a smaller data values font even with percent signs intact! The curved arrow at the top helps readers find the fill-in-blank in the middle of the small-print subtitle. (I left the understated % in the subtitle as is.) On the horizontal axis the distance between 2012 and 2014 has been shortened. The purpose is to de-emphasize these segments rather than emphasize them as they were in the original chart.

The PEW chart contains the second cutting edge graphing innovation which I want to bring to your attention:  Using statistical chart titles to announce conclusions rather than to describe chart contents. As mentioned already, the PEW graph relegates the description of the graph’s contents to the subtitle, rendering this in the faintest text found in the chart other than the data source footnote. This makes no sense given that the subtitle is a fill-in-the-blank sentence that requires the reader’s attention.

I realize that statistical graphs are published in executive summaries, reports, pamphlets, and other advocacy media intended for general audiences, whose attention authors hope to captivate. That’s why I began this post with Nate Silver’s ingenious infographic. Silver and his colleagues designed engaging graphs without ignoring a host of statistical graphing best practices, as most infographics do. (Nate Silver and team,  however, didn’t insert conclusions into the graphics themselves.)

Using graph titles as a means for delivering reasonable interpretations of data can be very useful since it can help readers become aware of salient features of the data. But this assistance should not come at the price of limiting readers’ access to information about chart contents. Neither should graph designers imply that conclusions reached are necessarily valid and complete without providing corroborative evidence that these things are true.

Take the title of the PEW chart, for instance. Rather than popularity being the explanation for print book use, it could be that limited e-book availability contributes to this equally. What I am afraid of with this new titling fad is that it runs counter to the main purpose of statistical charts, which is facilitating the exploration of data and whatever variety of conclusions the data might support. The title of the PEW graph could have read, e-Book Reading Continues to Grow or Overall Book Reading Is Shrinking, as both conclusions are evident in the data. The question then becomes what the justification is for reporting one conclusion over others?

Here’s an example of graph title where the conclusion misses the mark:


Chart Title with Understated Conclusions. Source: Hanaeur, A. & D. Granados. Still Struggling: The State of Working Ohio 2016. Policy Matters Ohio.

Somehow these researchers ended up fixated on data peaks and missed the conclusions that are apparent in this chart. (Note in the chart footnote that the data have been adjusted for inflation.) First, movement—backward or forward—from a peak is always downward.  So the title phrase down from peaks is redundant. I’m guessing the researchers wanted to draw a distinction between college educated and other wage earners, but felt the decreased Bachelor’s or higher trend after 1999 dampened this message. In any case, the data communicate the distinctions needed. The three lower trend lines (a) are significantly less than the Bachelor’s or higher line and (b) decreased moderately or markedly by 2015. For these wage earner categories education didn’t pay off much at all. The one story worth editorializing about could be titled, Earnings for High School Dropouts Tanked!

So you can see the danger in this new and stylish graphing practice. It is a tool to be used carefully and thoughtfully.


1   Because stacked bar charts have segments that are connected instead of displayed separately, visually estimating segment lengths reliably is difficult. The stacked arrangement deprives the reader of a baseline to make the comparisons from. On regular (non-stacked) bar charts the horizontal axis serves as this baseline.
2   I’ve written before about uncertainty here. On the fivethirtyeight.com website Nate Silver references the term uncertainty nine times in his explanation of his methodology.

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