Visualizing change over time: case study via Arstechnica

ArsTechnica published the following chart in its article titled "Grim new analyses spotlight just how hard the U.S. is failing in  pandemic" (link).

There are some very good things about this chart, so let me start there.

In a Trifecta Checkup, I'd give the Q corner high marks. The question is clear: how has the U.S. performed relative to other countries? In particular, the chart gives a nuanced answer to this question. The designer realizes that there are phases in the pandemic, so the same question is asked three times: how has the U.S. performed relative to other countries since June, since May, and since the start of the pandemic?

In the D corner, this chart also deserves a high score. It selects a reasonable measure of mortality, which is deaths per population. It simplifies cognition by creating three grades of mortality rates per 100,000. Grade A is below 5 deaths, Grade B, between 5 and 25, and Grade C is above 25. 

A small deduction for not including the source of the data (the article states it's from a JAMA article). If any reader notices problems with the underlying data or calculations, please leave a comment.

***

So far so good. And yet, you might feel like I'm over-praising a chart that feels distinctly average. Not terrible, not great.

The reason for our ambivalence is the V corner. This is what I call a Type V chart. The visual design isn't doing justice to the underlying question and data analysis.

The grouped bar chart isn't effective here because the orange bars dominate our vision. It's easy to see how each country performed over the course of the pandemic but it's hard to learn how countries compare to each other in different periods.

How are the countries ordered? It would seem like the orange bars may be the sorting variable but this interpretation fails in the third group of countries.

The designer apparently made the decision to place the U.S. at the bottom (i.e. the worst of the league table). As I will show later, this is justified but the argument cannot be justified by the orange bars alone. The U.S. is worse in both the blue and purple bars but not the orange.

This points out that there is interest in the change in rates (or ranks) over time. And in the following makeover, I used the Bumps chart as the basis, as its chief use is in showing how ranking changes over time.

 

Better clarity can often be gained by subtraction:

Avoid concentric circles

A twitter follower sent me this chart by way of Munich:

The logo of the Munich Security Conference (MSC) is quite cute. It looks like an ear. Perhaps that inspired this, em, staggered donut chart.

I like to straighten curves out so the donut chart becomes a bar chart:

The blue and gray bars mimic the lengths of the arcs in the donut chart. The yellow bars show the relative size of the underlying data. You can see that three of the four arcs under-represent the size of the data.

Why is that so? It's due to the staggering. Inner circles have smaller circumferences than outer circles. The designer keeps the angles the same so the arc lengths have been artificially reduced.

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The donut chart is just a pie chart with a hole punched in the middle. For both pie charts and donut charts, the data are encoded in the angles at the center of the circle. Under normal circumstances, pie charts can also be read by comparing sector areas, and donut charts using arc lengths, as those are proportional to the angles.

The area and arc interpretation fails when the designer alters the radii of the sections. Look at the following pair of pie charts, produced by filling the hole in the above donuts:

The staggered pie chart distorts the data if the reader compares areas but not so if the reader compares angles at the center. The pie chart can be read both ways so long as the designer does not alter the radii.

 

Bloomberg made me digest these graphics slowly

Ask the experts to name the success metric of good data visualization, and you will receive a dozen answers. The field doesn't have an all-encompassing metric. A useful reference is Andrew Gelman and Antony Urwin (2012) in which they discussed the tradeoff between beautiful and informative, which derives from the familiar tension between art and science.

For a while now, I've been intrigued by metrics that measure "effort". Some years ago, I described the concept of a "return on effort" in this post. Such a metric can be constructed like the dominating financial metric of return on investment. The investment here is an investment of time, of attention. I strongly believe that if the consumer judges a data visualization to be compelling, engaging or  ell constructed, s/he will expend energy to devour it.

Imagine grub you discard after the first bite, compared to the delicious food experienced slowly, savoring every last bit.

I'm writing this post while enjoying the September issue of Bloomberg Businessweek, which focuses on the upcoming U.S. Presidential election. There are various graphics infused into the pages of the magazine. Many of these graphics operate at a level of complexity above what typically show up in magazines, and yet I spent energy learning to understand them. This response, I believe, is what visual designers should aim for.

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Today, I discuss one example of these graphics, shown on the right. You might be shocked by the throwback style of these graphics. They look like they arrived from decades ago!

Grayscale, simple forms, typewriter font, all caps. Have I gone crazy?

The article argues that a town like Ambridge in Beaver County, Pennslyvania may be pivotal in the November election. The set of graphics provides relevant data to understand this argument.

It's evidence that data visualization does not need whiz-bang modern wizardry to excel.

Let me focus on the boxy charts from the top of the column. These:

These charts solve a headache with voting margin data in the U.S.  We have two dominant political parties so in any given election, the vote share data split into three buckets: Democratic, Republican, and a catch-all category that includes third parties, write-ins, and none of the above. The third category rarely exceeds 5 percent.  A generic pie chart representation looks like this:

Stacked bars have this look:

In using my Trifecta framework (link), the top point is articulating the question. The primary issue here is the voting margin between the winner and the second-runner-up, which is the loser in what is typically a two-horse race. There exist two sub-questions: the vote-share difference between the top two finishers, and the share of vote effectively removed from the pot by the remaining candidates.

Now, take another look at the unusual chart form used by Bloomberg:

The catch-all vote share sits at the bottom while the two major parties split up the top section. This design demonstrates a keen understanding of the context. Consider the typical outcome, in which the top two finishers are from the two major parties. When answering the first sub-question, we can choose the raw vote shares, or the normalized vote shares. Normalizing shifts the base from all candidates to the top two candidates.

The Bloomberg chart addresses both scales. The normalized vote shares can be read directly by focusing only on the top section. In an even two-horse race, the top section is split by half - this holds true regardless of the size of the bottom section.

This is a simple chart that packs a punch.

 

Making better pie charts if you must

I saw this chart on an NYU marketing twitter account:

The graphical design is not easy on our eyes. It's just hard to read for various reasons.

The headline sounds like a subject line from an email.

The subheaders are long, and differ only by a single word.

Even if one prefers pie charts, they can be improved by following a few guidelines.

First, start the first sector at the 12-oclock direction. Like this:

The survey uses a 5-point scale from "Very Good" to "Very Bad". Instead of using five different colors, it's better to use two extreme colors and shading. Like this:

I also try hard to keep all text horizontal.

For those who prefers not to use pie charts, a side-by-side bar chart works well.

In my article for DataJournalism.com, I outlined "unspoken rules" for making various charts, including pie charts.

 

 

 

Election visuals: three views of FiveThirtyEight's probabilistic forecasts

As anyone who is familiar with Nate Silver's forecasting of U.S. presidential elections knows, he runs a simulation that explores the space of possible scenarios. The polls that provide a baseline forecast make certain assumptions, such as who's a likely voter. Nate's model unshackles these assumptions from the polling data, exploring how the outcomes vary as these assumptions shift.

In the most recent simulation, his computer explores 40,000 scenarios, each of which predicts a split of the electoral vote, from which the winner of the election can be determined. The model's outcome is usually summarized by a winning probability, which is just the proportion of scenarios under which one candidate wins.

This type of forecasting was responsible for the infamous meltdown in 2016 when most of these models - Nate's being an exception - issued extremely confident predictions that Hillary Clinton wins with 95% or higher probability. Essentially, the probability distribution collapses to a point. This is analogous to an extremely narrow confidence band, indicating almost zero uncertainty about the event. It was as if almost all of the 40,000 scenarios predicted Clinton to be the winner.

The 538 data team has come up with various ways of visualizing the outputs of the model (link). The entire post is worth reading. Here, I'll highlight the most scientific, and direct visual representation, which is the third display.

We start by looking at the bottom of the two charts, showing the predicted electoral votes won  by Democratic challenger Joe Biden, in each of the 40,000 scenarios. Our attention is directed to the thick line that gives the relative chance of Biden's electoral-vote tally. This line is a smoothed summary of the columns in the background, which show the number of times the simulation produces each electoral-vote count.

The highlighted, right side of the chart recounts scenarios in which Biden becomes President, that is to say, he wins more than 270 electoral votes (out of 538, doh). The faded, left side represents scenarios in which Biden is defeated and Trump wins a second term.

The reason I focused on the bottom chart is that the top chart is merely a mirror image of this one. Just reflect the bottom chart around the vertical axis of 270 electoral votes, change the color scheme to red, and swap annotations related to Trump and Biden, and you get the other chart. This is because the narrative has excluded third-party and write-in candidates, leaving us with a zero-sum situation.

Alternatively, one can jam both charts into one, while supplying extra labels, like this:

I prefer the denser single chart because my mind wanders away searching for extra meaning when chart elements are mirrored.

One advantage of the mirrored presentation is that the probability profiles of the potential Trump or Biden wins can be directly compared. We learn that Trump's winning margins are smaller, rarely above 150, and never above 250.

This comparison is made easier by flipping left side of the chart onto the right side:

Those are three different visualizations using the same chart form. I'd have to run a poll to figure out which is the best. What's your opinion?

Putting vaccine trials in boxes

Bloomberg Businessweek has a special edition about vaccines, and I found this chart on the print edition:

The chart's got a lot of white space. Its structure is a series of simple "treemaps," one for each type of vaccine. Though simple, such a chart burns a few brain cells.

Here, I've extracted the largest block, which corresponds to vaccines that work with the virus's RNA/DNA. I applied a self-sufficiency test, removing the data from the boxes. 

What proportion of these projects have moved from pre-clinical to Phase 1?  To answer this question, we have to understand the relative areas of boxes, since that's how the data are encoded. How many yellow boxes can fit into the gray box?

It's not intuitive. We'd need a ruler to do this task properly.

Then, we learn that the gray box is exactly 8 times the size of the yellow box (72 projects are pre-clinical while 9 are in Phase I). We can cram eight yellows into the gray box. Imagine doing that, and it's pretty clear the visual elements fail to convey the meaning of the data.

Self-sufficiency is the idea that a data graphic should not rely on printed data to convey its meaning; the visual elements of a data graphic should bear much of the burden. Otherwise, use a data table. To test for self-sufficiency, cover up the printed data and see if the chart still works.

***

A key decision for the designer is the relative importance of (a) the number of projects reaching Phase III, versus (b) the number of projects utilizing specific vaccine strategies.

This next chart emphasizes the clinical phases:

 

Contrast this with the version shown in the online edition of Bloomberg (link), which emphasizes the vaccine strategies.

If any reader can figure out the logic of the ordering of the vaccine strategies, please leave a comment below.

A testing mess: one chart, four numbers, four colors, three titles, wrong units, wrong lengths, wrong data

Twitterstan wanted to vote the following infographic off the island:

(The publisher's website is here but I can't find a direct link to this graphic.)

The mishap is particularly galling given the controversy swirling around this year's A-Level results in the U.K. For U.S. readers, you can think of A-Levels as SAT Subject Tests, which in the U.K. are required of all university applicants, and represent the most important, if not the sole, determinant of admissions decisions. Please see the upcoming post on my book blog for coverage of the brouhaha surrounding the statistical adjustments (to be posted sometime this week, it's here.).

The first issue you may notice about the chart is that the bar lengths have no relationship with the numbers printed on them. Here is a scatter plot correlating the bar lengths and the data.

As you can see, nothing.

Then, you may wonder what the numbers mean. The annotation at the bottom right says "Average number of A level qualifications per student". Wow, the British (in this case, English) education system is a genius factory - with the average student mastering close to three thousand subjects in secondary (high) school!

TES is the cool name for what used to be the Times Educational Supplement. I traced the data back to Ofqual, which is the British regulator for these examinations. This is the Ofqual version of the above chart:

The data match. You may see that the header of the data table reads "Number of students in England getting 3 x A*". This is a completely different metric than number of qualifications - in fact, this metric measures geniuses. "A*" is the U.K. equivalent of "A+". When I studied under the British system, there was no such grade. I guess grade inflation is happening all over the world. What used to be A is now A+, and what used to be B is now A. Scoring three A*s is tops - I wonder if this should say 3 or more because I recall that you can take as many subjects as you desire but most students max out at three (may have been four).

The number of students attaining the highest achievement has increased in the last two years compared to the two years before. We can't interpret these data unless we know if the number of students also grew at similar rates.

The units are students while the units we expect from the TES graphic should be subjects. The cutoff for the data defines top students while the TES graphic should connote minimum qualification, i.e. a passing grade.

***
Now, the next section of the Ofqual infographic resolves the mystery. Here is the chart:

This dataset has the right units and measurement. There is almost no meaningful shift in the last four years. The average number of qualifications per student is only different at the second decimal place. Replacing the original data with this set removes the confusion.

While I was re-making this chart, I also cleaned out the headers and sub-headers. This is an example of software hegemony: the designer wouldn't have repeated the same information three times on a chart with four numbers if s/he wasn't prompted by software defaults.

***

The corrected chart violates one of the conventions I described in my tutorial for DataJournalism.com: color difference should reflect data difference.

In the following side-by-side comparison, you see that the use of multiple colors on the left chart signals different data - note especially the top and bottom bars which carry the same number, but our expectation is frustrated.

***

[P.S. 8/25/2020. Dan V. pointed out another problem with these bar charts: the bars were truncated so that the bar lengths are not proportional to the data. The corrected chart is shown on the right below:

8/26/2020: added link to the related post on my book blog.]

Ask how you can give

A reader and colleague Georgette A was frustrated with the following graphic that appeared in the otherwise commendable article in National Geographic (link). The NatGeo article provides a history lesson on past pandemics that killed millions.

What does the design want to convey to readers?

Our attention is drawn to the larger objects, the red triangle on the left or the green triangle on the right. Regarding the red triangle, we learn that the base is the duration of the pandemic while the height of the black bar represents the total deaths.

An immediate curiosity is why a green triangle is lodged in the middle of the red triangle. Answering this question requires figuring out the horizontal layout. Where we expect axis labels we find an unexpected series of numbers (0, 16, 48, 5, 2, 4, ...). These are durations that measure the widths of the triangular bases.

To solve this puzzle, imagine the chart with the triangles removed, leaving just the black columns. Now replace the durations with index numbers, 1 to 13, corresponding to the time order of the ending years of these epidemics. In other words, there is a time axis hidden behind the chart. [As Ken reminded me on Twitter, I forgot to mention that details of each pandemic are revealed by hovering over each triangle.]

This explains why the green triangle (Antonine Plague) is sitting inside the large red triangle (Plague of Justinian). The latter's duration is 3 times that of the former, and the Antonine Plague ended before the Plague of Justinian. In fact, the Antonine occurred during 165-180 while the Justinian happened during 541-588. The overlap is an invention of the design. To receive what the design gives, we have to think of time as a sequence, not of dates.

***

Now, compare the first and second red triangles. Their black columns both encode 50 million deaths. The Justinian Plague however was spread out over 48 years while the Black Death lasted just 5 years. This suggests that the Black Death was more fearsome than the Justinian Plague. And yet, the graphic presents the opposite imagery.

This is a pretty tough dataset to visualize. Here is a side-by-side bar chart that lets readers first compare deaths, and then compare durations.

In the meantime, I highly recommend the NatGeo article.

Everything in Texas is big, but not this BIG

Long-time reader John forwarded the following chart via Twitter.

The chart shows the recent explosive growth in deaths due to Covid-19 in Texas. John flagged this graphic as yet another example in which the data are encoded to the lengths of the squares, not their areas.

Fixing this chart just requires fixing the length of one side of the square. I also flipped it to make a conventional column chart.

The final product:

An important qualification lurks in the footnote; it is directly applied to the label of July.

How much visual distortion is created when data are encoded to the lengths and not the areas? The following chart shows what readers see, assuming they correctly perceive the areas of those squares. The value for March is held the same as above while the other months show the death counts implied by the relative areas of the squares.

Owing to squaring, the smaller counts are artificially compressed while the big numbers are massively exaggerated.

Working with multiple dimensions, an example from Germany

An anonymous reader submitted this mirrored bar chart about violent acts by extremists in the 16 German states.

At first glance, this looks like a standard design. On a second look, you might notice what the reader discovered- the chart used two different scales, one for each side. The left side (red) depicting left-wing extremism is artificially compressed relative to the right side (blue). Not sure if this reflects the political bias of the publication - but in any case, this distortion means the only way to consume this chart is to read the numbers.

Even after fixing the scales, this design is challenging for the reader. It's unnatural to compare two years by looking first below then above. It's not simple to compare across states, and even harder to compare left- and right-wing extremism (due to mirroring).

The chart feels busy because the entire dataset is printed on it. I appreciate not including a redundant horizontal axis. (I wonder if the designer first removed the axis, then edited the scale on one side, not realizing the distortion.) Another nice touch, hidden in the legend, is the country totals.

I present two alternatives.

The first is a small-multiples "bumps chart".

Each plot presents the entire picture within a state. You can see the general level of violence, the level of left- and right-wing extremism, and their year-on-year change. States can be compared holistically.

Several German state names are rather long, so I explored a horizontal orientation. In this case, a connected dot plot may be more appropriate.

The sign of a good multi-dimensional visual display is whether readers can easily learn complex relationships. Depending on the question of interest, the reader can mentally elevate parts of this chart. One can compare the set of blue arrows to the set of red arrows, or focus on just blue arrows pointing right, or red arrows pointing left, or all arrows for Berlin, etc.

 

[P.S. Anonymous reader said the original chart came from the Augsburger newspaper. This link in German contains more information.]