Working hard at clarity

As I am preparing another blog post about the pandemic, I came across the following data graphic, recently produced by the CDC for a vaccine advisory board meeting:

This is not an example of effective visual communications.

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For one thing, readers are directed to scour the footnotes to figure out what's going on. If we ignore those for the moment, we see clusters of bubbles that have remained pretty stable from December 2020 to August 2021. The data concern some measure of Americans' intent to take the COVID-19 vaccine. That much we know.

There may have been a bit of an upward trend between January and May, although if you were shown the clusters for December, February and April, you'd think the trend's been pretty flat. 

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But those colors? What could they represent? You'd surely have to fish this one out of the footnotes. Specifically, this obtuse sentence: "Surveys with multiple time points are shown with the same color bubble for each time point." I had to read it several times. I think it simply means "Color represents the pollster." 

Then it adds: "Surveys with only one time point are shown in gray." which simply means "All pollsters who have only one entry in the dataset are grouped together and shown in gray."

Another problem with this chart is over-plotting. Look at the July cluster. It's impossible to tell how many polls were conducted in July because the circles pile on top of one another. 

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The appearance of the flat trend is a result of two unfortunate decisions made by the designer. If I retained the chart form, I'd have produced something that looks like this:

The first design choice is to expand the vertical axis to range from 0% to 100%. This effectively squeezes all the bubbles into a small range.

The second design choice is to enlarge the bubbles causing copious amount of overlapping. 

In particular, this decision blows up the Pew poll (big pink bubble) that contained 10 times the sample size of most of the other polls. The Pew outcome actually came in at 70% but the top of the pink bubble extends to over 80%. Because of this, the outlier poll of December 2020 - which surprisingly printed the highest number of all polls in the entire time window - no longer looks special. 

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Now, let's see what else we can do to enhance this chart. 

I don't like how bubble size is used to encode the sample size. It creates a weird sensation for anyone who's familiar with sampling errors, and confidence regions. The Pew poll with 10 times the sample size is the most reliable poll of them all. Reliability means the error bars around the Pew poll outcome is the smallest of them all. I tend to think of the area around a point estimate as showing the sampling error so the Pew poll would be a dot, showing the high precision of that estimate. 

But that won't work because larger bubbles catch more of the reader's attention. So, in the following version, all dots have the same size. I encode reliability in the opacity of the color. The darker dots are polls that are more reliable, that have larger sample sizes.

Two of the pollsters have more frequent polling than others. In this next version, I highlighted those two, which reveals the trend better.

 

 

 

Metaphors, maps, and communicating data

There are some data visualization that are obviously bad. But what makes them bad?

Here is an example of such an effort:

This visualization of carbon emissions is not successful. There is precious little that a reader can learn from this chart without expensing a lot of effort. It's relatively easy to identify the largest emitters of carbon but since the data are not expressed per-capita, the chart mainly informs us which countries have the largest populations. 

The color of the bubbles informs readers which countries belong to which parts of the world. However, it distorts the location of countries within regions, and regions relative to regions, as the primary constraint is fitting the bubbles inside the shape of a foot.

The visualization gives a very rough estimate of the relative sizes of total emissions. The circles not being perfect circles don't help. 

It's relatively easy to list the top emitters in each region but it's hard to list the top 10 emitters in the world (try!) 

The small emitters stole all of the attention as they account for most of the labels - and they engender a huge web of guiding lines - an unsightly nuisance.

The diagram clings dearly to the "carbon footprint" metaphor. Does this metaphor help readers consume the emissions data? Conversely, does it slow them down?

A more conventional design uses a cartogram, a type of map in which the positioning of countries are roughly preserved while the geographical areas are coded to the data. Here's how it looks:

I can't seem to source this effort. If any reader can find the original source, please comment below.

This cartogram is a rearrangement of the footprint illustration. The map construct eliminates the need to include a color legend which just tells people which country is in which continent. The details of smaller countries are pushed to the bottom. 

In the footprint visualization, I'd even consider getting rid of the legend completely. This means trusting that readers know South Africa is part of Africa, and China is part of Asia.

Imagine: what if this chart comes without a color legend? Do we really need it?

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I'd like to try a word cloud visual for this dataset. Something that looks like this (obviously with the right data encoding):

(This map is by Michael Tompsett who sells it here.)

 

Circular areas offer misleading cues of their underlying data

John M. pointed me on Twitter to this chart about the progress of U.S.'s vaccination campaign:

This looks like a White House production, retweeted by WHO. John is unhappy about this nested bubble format, which I'll come back to later.

Let's zoom in on what matters:

An even bigger problem with this chart is the Q corner in our Trifecta Checkup. What is the question they are trying to address? It would appear to be the proportion of population that has "already received [one or more doses of] vaccine". And the big words tell us the answer is 8 percent.

But is that really the question? Check out the dark blue circle. It is labeled "population that has already received vaccine" and thus we infer this bubble represents 8 percent. Now look at the outer bubble. Its annotation is "new population that received vaccine since January 27, 2021". The only interpretation that makes sense is that 8 percent  is not the most current number. If that is the case, why would the headline highlight an older statistic, and not the most up-to-date one?

Perhaps the real question is how fast is the progress in vaccination. Perhaps it took weeks to get to the dark circle and then days to get beyond. In order to improve this data visualization, we must first decide what the question really is.

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Now let's get to those nested bubbles. The bubble chart is a format that is not "sufficient," by which I mean the visual by itself does not convey the data without the help of aids such as labels. Try to answer the following questions:

In my view, if your answer to the last question is anything more than 5 seconds, the dataviz has failed. A successful data visualization should not make readers solve puzzles.

The first two questions depict the confusing nature of concentric circle diagrams. The first data point is coded to the inner circle. Where is the second data point? Is it encoded to the outer circle, or just the outer ring?

In either case, human brains are not trained to compare circular areas. For question 1, the outer circle is 70% larger than the smaller circle. For question 2, the ring is 70% of the area of the dark blue circle. If you're thinking those numbers seem unreasonable, I can tell you that was my first reaction too! So I made the following to convince myself that the calculation was correct:

Circular areas offer misleading visual cues, and should be used sparingly.

[P.S. 2/10/2021. In the next post, I sketch out an alternative dataviz for this dataset.]

Atypical time order and bubble labeling

This chart appeared in a Charles Schwab magazine in Summer, 2019.

This bubble chart does not print any data labels. The bubbles take our attention but the designer realizes that the actual values of the volatility are not intuitive numbers. The same is true of any standard deviation numbers. If you're told SD of a data series is 3, it doesn't tell you much by itself.

I first transformed this chart into the equivalent column chart:

Two problems surface on the axes.

For the time axis, the years are jumbled. Readers experience vertigo, as we try to figure out how to read the chart. Our expectation that time moves left to right is thwarted. This ordering also requires every single year label to be present.

For the vertical axis, I could have left out the numbers completely. They are not really meaningful. These represent the areas of the bubbles but only relative to how I measured them.

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In the next version, I sorted time in the conventional manner. Following Tufte's classic advice, only the tops of the columns are plotted.

What you see is that this ordering is much easier to comprehend. Figuring out that 2018 is an average year in terms of volatility is not any harder than in the original. In fact, we can reproduce the order of the previous chart just by letting our eyes sweep top to bottom.

To make it even easier to read the vertical axis, I converted the numbers into an index, with the average volatility as 100 %  (assigned to 0% on the chart) .

Now, you can see that 2018 is roughly at the average while 2008 is 400% above the average level. (How should we interpret this statement? That's a question I pose to my statistics students. It's not intuitive how one should interpret the statement that the standard deviation is 5 times higher.)

 

 

This chart shows why the PR agency for the UK government deserves a Covid-19 bonus

The Economist illustrated some interesting consumer research with this chart (link):

The survey by Dalia Research asked people about the satisfaction with their country's response to the coronavirus crisis. The results are reduced to the "Top 2 Boxes", the proportion of people who rated their government response as "very well" or "somewhat well".

This dimension is laid out along the horizontal axis. The chart is a combo dot and bubble chart, arranged in rows by region of the world. Now what does the bubble size indicate?

It took me a while to find the legend as I was expecting it either in the header or the footer of the graphic. A larger bubble depicts a higher cumulative number of deaths up to June 15, 2020.

The key issue is the correlation between a country's death count and the people's evaluation of the government response.

Bivariate correlation is typically shown on a scatter plot. The following chart sets out the scatter plots in a small multiples format with each panel displaying a region of the world.

The death tolls in the Asian countries are low relative to the other regions, and yet the people's ratings vary widely. In particular, the Japanese people are pretty hard on their government.

In Europe, the people of Greece, Netherlands and Germany think highly of their government responses, which have suppressed deaths. The French, Spaniards and Italians are understandably unhappy. The British appears to be the most forgiving of their government, despite suffering a higher death toll than France, Spain or Italy. This speaks well of their PR operation.

Cumulative deaths should be adjusted by population size for a proper comparison across nations. When the same graphic is produced using deaths per million (shown on the right below), the general story is preserved while the pattern is clarified:

The right chart shows deaths per million while the left chart shows total deaths.

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In the original Economist chart, what catches our attention first is the bubble size. Eventually, we notice the horizontal positioning of these bubbles. But the star of this chart ought to be the new survey data. I swapped those variables and obtained the following graphic:

Instead of using bubble size, I switched to using color to illustrate the deaths-per-million metric. If ratings of the pandemic response correlate tightly with deaths per million, then we expect the color of these dots to evolve from blue on the left side to red on the right side.

The peculiar loss of correlation in the U.K. stands out. Their PR firm deserves a bonus!

Bubble charts, ratios and proportionality

A recent article in the Wall Street Journal about a challenger to the dominant weedkiller, Roundup, contains a nice selection of graphics. (Dicamba is the up-and-comer.)

The change in usage of three brands of weedkillers is rendered as a small-multiples of choropleth maps. This graphic displays geographical and time changes simultaneously.

The staircase chart shows weeds have become resistant to Roundup over time. This is considered a weakness in the Roundup business.

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In this post, my focus is on the chart at the bottom, which shows complaints about Dicamba by state in 2019. This is a bubble chart, with the bubbles sorted along the horizontal axis by the acreage of farmland by state.

Below left is a more standard version of such a chart, in which the bubbles are allowed to overlap. (I only included the bubbles that were labeled in the original chart).

The WSJ’s twist is to use the vertical spacing to avoid overlapping bubbles. The vertical axis serves a design perogative and does not encode data.  

I’m going to stick with the more traditional overlapping bubbles here – I’m getting to a different matter.

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The question being addressed by this chart is: which states have the most serious Dicamba problem, as revealed by the frequency of complaints? The designer recognizes that the amount of farmland matters. One should expect the more acres, the more complaints.

Let's consider computing directly the number of complaints per million acres.

The resulting chart (shown below right) – while retaining the design – gives a wholly different feeling. Arkansas now owns the largest bubble even though it has the least acreage among the included states. The huge Illinois bubble is still large but is no longer a loner.

Now return to the original design for a moment (the chart on the left). In theory, this should work in the following manner: if complaints grow purely as a function of acreage, then the bubbles should grow proportionally from left to right. The trouble is that proportional areas are not as easily detected as proportional lengths.

The pair of charts below depict made-up data in which all states have 30 complaints for each million acres of farmland. It’s not intuitive that the bubbles on the left chart are growing proportionally.

Now if you look at the right chart, which shows the relative metric of complaints per million acres, it’s impossible not to notice that all bubbles are the same size.

Water stress served two ways

Via Alberto Cairo (whose new book How Charts Lie can be pre-ordered!), I found the Water Stress data visualization by the Washington Post. (link)

The main interest here is how they visualized the different levels of water stress across the U.S. Water stress is some metric defined by the Water Resources Institute that, to my mind, measures the demand versus supply of water. The higher the water stress, the higher the risk of experiencing droughts.

There are two ways in which the water stress data are shown: the first is a map, and the second is a bubble plot.

This project provides a great setting to compare and contrast these chart forms.

How Data are Coded

In a map, the data are usually coded as colors. Sometimes, additional details can be coded as shades, or moire patterns within the colors. But the map form locks down a number of useful dimensions - including x and y location, size and shape. The outline map reserves all these dimensions, rendering them unavailable to encode data.

By contrast, the bubble plot admits a good number of dimensions. The key ones are the x- and y- location. Then, you can also encode data in the size of the dots, the shape, and the color of the dots.

In our map example, the colors encode the water stress level, and a moire pattern encodes "arid areas". For the scatter plot, x = daily water use, y = water stress level, grouped by magnitude, color = water stress level, size = population. (Shape is constant.)

Spatial Correlation

The map is far superior in displaying spatial correlation. It's visually obvious that the southwestern states experience higher stress levels.

This spatial knowledge is relinquished when using a bubble plot. The designer relies on the knowledge of the U.S. map in the head of the readers. It is possible to code this into one of the available dimensions, e.g. one could make x = U.S. regions, but another variable is sacrificed.

Non-contiguous Spatial Patterns

When spatial patterns are contiguous, the map functions well. Sometimes, spatial patterns are disjoint. In that case, the bubble plot, which de-emphasizes the physcial locations, can be superior. In our example, the vertical axis divides the states into five groups based on their water stress levels. Try figuring out which states are "medium to high" water stress from the map, and you'll see the difference.

Finer Geographies

The map handles finer geographical units like counties and precincts better. It's completely natural.

In the bubble plot, shifting to finer units causes the number of dots to explode. This clutters up the chart. Besides, while most (we hope) Americans know the 50 states, most of us can't recite counties or precincts. Thus, the designer can't rely on knowledge in our heads. It would be impossible to learn spatial patterns from such a chart.

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The key, as always, is to nail down your message, then select the right chart form.

 

 

How to describe really small chances

Reader Aleksander B. sent me to the following chart in the Daily Mail, with the note that "the usage of area/bubble chart in combination with bar alignment is not very useful." (link)

One can't argue with that statement. This chart fails the self-sufficiency test: anyone reading the chart is reading the data printed on the right column, and does not gain anything from the visual elements (thus, the visual representation is not self-sufficient). As a quick check, the size of the risk for "motorcycle" should be about 30 times larger than that of "car"; the size of the risk for "car" should be 100 times larger than that of "airplane". The risk of riding motorcycles then is roughly 3,000 times that of flying in an airplane. 

The chart does not appear to be sized properly as a bubble chart:

You'll notice that the visible proportion of the "car" bubble is much larger than that of the "motorcycle" bubble, which is one part of the problem.

Nor is it sized as a bar chart:

As a bar chart, both the widths and the heights of the bars vary; and the last row presents a further challenge as the bubble for the airplane does not touch the baseline.

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Besides the Visual, the Data issues are also quite hard. This is how Aleksander describes it: "as a reader I don't want to calculate all my travel distances and then do more math to compare different ways of traveling."

The reader wants to make smarter decisions about travel based on the data provided here. Aleksandr proposes one such problem:

In terms of probability it is also easier to understand: "I am sitting in my car in strong traffic. At the end in 1 hour I will make only 10 miles so what's the probability that I will die? Is it higher or lower than 1 hour in Amtrak train?"

The underlying choice is between driving and taking Amtrak for a particular trip. This comparison is relevant because those two modes of transport are substitutes for this trip. 

One Data issue with the chart is that riding a motorcycle and flying in a plane are rarely substitutes. 

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A way out is to do the math on behalf of your reader. The metric of deaths per 1 billion passenger-miles is not intuitive for a casual reader. A more relevant question is what's the chance of dying from the time I spend per year of driving (or riding a plane). Because the chance will be very tiny, it is easier to express the risk as the number of years of travel before I expect to see one death.

Let's assume someone drives 300 days per year, and 100 miles per day so that each year, this driver contributes 30,000 passenger-miles to the U.S. total (which is 3.2 trillion). We convert 7.3 deaths per 1 billion passenger-miles to 1 death per 137 million passenger-miles. Since this driver does 30K per year, it will take (137 million / 30K) = about 4,500 years to see one death on average. This calculation assumes that the driver drives alone. It's straightforward to adjust the estimate if the average occupancy is higher than 1. 

Now, let's consider someone who flies once a month (one outbound trip plus one return trip). We assume that each plane takes on average 100 passengers (including our protagonist), and each trip covers on average 1,000 miles. Then each of these flights contributes 100,000 passenger-miles. In a year, the 24 trips contribute 2.4 million passenger-miles. The risk of flying is listed at 0.07 deaths per 1 billion, which we convert to 1 death per 14 billion passenger-miles. On this flight schedule, it will take (14 billion / 2.4 million) = almost 6,000 years to see one death on average.

For the average person on those travel schedules, there is nothing to worry about. 

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Comparing driving and flying is only valid for those trips in which you have a choice. So a proper comparison requires breaking down the average risks into components (e.g. focusing on shorter trips). 

The above calculation also suggests that the risk is not evenly spread out throughout the population, despite the use of an overall average. A trucker who is on the road every work day is clearly subject to higher risk than an occasional driver who makes a few trips on rental cars each year.

There is a further important point to note about flight risk, due to MIT professor Arnold Barnett. He has long criticized the use of deaths per billion passenger-miles as a risk metric for flights. (In Chapter 5 of Numbers Rule Your World (link), I explain some of Arnie's research on flight risk.) The problem is that almost all fatal crashes involving planes happen soon after take-off or not long before landing. 

 

Is the visual serving the question?

The following chart concerns California's bullet train project.

Now, look at the bubble chart at the bottom. Here it is - with all the data except the first number removed:

It is impossible to know how fast the four other train systems run after I removed the numbers. The only way a reader can comprehend this chart is to read the data inside the bubbles. This chart fails the "self-sufficiency test". The self-sufficiency test asks how much work the visual elements on the chart are doing to communicate the data; in this case, the bubbles do nothing at all.

Another problem: this chart buries its lede. The message is in the caption: how California's bullet train rates against other fast train systems. California's train speed of 220 mph is only mentioned in the text but not found in the visual.

Here is a chart that draws attention to the key message:

In a Trifecta checkup, we improved this chart by bringing the visual in sync with the central question of the chart.

Check out the Lifespan of News project

Alberto Cairo introduces another one of his collaborations with Google, visualizing Google search data. We previously looked at other projects here.

The latest project, designed by Schema, Axios, and Google News Initiative, tracks the trending of popular news stories over time and space, and it's a great example of making sense of a huge pile of data.

The design team produced a sequence of graphics to illustrate the data. The top news stories are grouped by category, such as Politics & Elections, Violence & War, and Environment & Science, each given a distinct color maintained throughout the project.

The first chart is an area chart that looks at individual stories, and tracks the volume over time.

To read this chart, you have to notice that the vertical axis measuring volume is a log scale, meaning that each tick mark up represents a 10-fold increase. Log scale is frequently used to draw far-away data closer to the middle, making it possible to see both ends of a wide distribution on the same chart. The log transformation introduces distortion deliberately. The smaller data look disproportionately large because of it.

The time scrolls automatically so that you feel a rise and fall of various news stories. It's a great way to experience the news cycle in the past year. The overlapping areas show competing news stories that shared the limelight at that point in time.

Just bear in mind that you have to mentally reverse the distortion introduced by the log scale.

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In the second part of the project, they tackle regional patterns. Now you see a map with proportional symbols. The top story in each locality is highlighted with the color of the topic. As time flows by, the sizes of the bubbles expand and contract.

Sometimes, the entire nation was consumed by the same story, e.g. certain obituaries. At other times, people in different regions focused on different topics.

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In the last part of the project, they describe general shapes of the popularity curves. Most stories have one peak although certain stories like U.S. government shutdown will have multiple peaks. There is also variation in terms of how fast a story rises to the peak and how quickly it fades away.

The most interesting aspect of the project can be learned from the footnote. The data are not direct hits to the Google News stories but searches on Google. For each story, one (or more) unique search terms are matched, and only those stories are counted. A "control" is established, which is an excellent idea. The control gives meaning to those counts. The control used here is the number of searches for the generic term "Google News." Presumably this is a relatively stable number that is a proxy for general search activity. Thus, the "volume" metric is really a relative measure against this control.