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.

Germanextremists_bars

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".

Redo_junkcharts_germanextremists_sidebysidelines

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.

Redo_junkcharts_germanextremists_dots

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.]


What is the price for objectivity

I knew I had to remake this chart.

TMC_hospitalizations

The simple message of this chart is hidden behind layers of visual complexity. What the analyst wants readers to focus on (as discerned from the text on the right) is the red line, the seven-day moving average of new hospital admissions due to Covid-19 in Texas.

My eyes kept wandering away from the line. It's the sideway data labels on the columns. It's the columns that take up vastly more space than the red line. It's the sideway date labels on the horizontal axis. It's the redundant axis labels for hospitalizations when the entire data set has already been printed. It's the two hanging diamonds, for which the clues are filed away in the legend above.

Here's a version that brings out the message: after Phase 2 re-opening, the number of hospital admissions has been rising steadily.

Redo_junkcharts_texas_covidhospitaladmissions_1

Dots are used in place of columns, which push these details to the background. The line as well as periods of re-opening are directly labeled, removing the need for a legend.

Here's another visualization:

Redo_junkcharts_texas_covidhospitaladmissions_2

This chart plots the weekly average new hospital admissions, instead of the seven-day moving average. In the previous chart, the raggedness of moving average isn't transmitting any useful information to the average reader. I believe this weekly average metric is easier to grasp for many readers while retaining the general story.

***

On the original chart by TMC, the author said "the daily hospitalization trend shows an objective view of how COVID-19 impacts hospital systems." Objectivity is an impossible standard for any kind of data analysis or visualization. As seen above, the two metrics for measuring the trend in hospitalizations have pros and cons. Even if one insists on using a moving average, there are choices of averaging methods and window sizes.

Scientists are trained to believe in objectivity. It frequently disappoints when we discover that the rest of the world harbors no such notion. If you observe debates between politicians or businesspeople or social scientists, you rarely hear anyone claim one analysis is more objective - or less subjective - than another. The economist who predicts Dow to reach a new record, the business manager who argues for placing discounted products in the front not the back of the store, the sportscaster who maintains Messi is a better player than Ronaldo: do you ever hear these people describe their methods as objective?

Pursuing objectivity leads to the glorification of data dumps. The scientist proclaims disinterest in holding an opinion about the data. This is self-deception though. We clearly have opinions because when someone else  "misinterprets" the data, we express dismay. What is the point of pretending to hold no opinions when most of the world trades in opinions? By being "objective," we never shape the conversation, and forever play defense.


This exercise plan for your lock-down work-out is inspired by Venn

A twitter follower did not appreciate this chart from Nature showing the collection of flu-like symptoms that people reported they have to an UK tracking app. 

Nature tracking app venn diagram

It's a super-complicated Venn diagram. I have written about this type of chart before (see here); it appears to be somewhat popular in the medicine/biology field.

A Venn diagram is not a data visualization because it doesn't plot the data.

Notice that the different compartments of the Venn diagram do not have data encoded in the areas. 

The chart also fails the self-sufficiency test because if you remove the data from it, you end up with a data container - like a world map showing country boundaries and no data.

If you're new here: if a graphic requires the entire dataset to be printed on it for comprehension, then the visual elements of the graphic are not doing any work. The graphic cannot stand on its own.

When the Venn diagram gets complicated, teeming with many compartments, there will be quite a few empty compartments. If I have to make this chart, I'd be nervous about leaving out a number or two by accident. An empty cell can be truly empty or an oversight.

Another trap is that the total doesn't add up. The numbers on this graphic add to 1,764 whereas the study population in the preprint was 1,702. Interestingly, this diagram doesn't show up in the research paper. Given how they winnowed down the study population from all the app downloads, I'm sure there is an innocent explanation as to why those two numbers don't match.

***

The chart also strains the reader. Take the number 18, right in the middle. What combination of symptoms did these 18 people experience? You have to figure out the layers sitting beneath the number. You see dark blue, light blue, orange. If you blink, you might miss the gray at the bottom. Then you have to flip your eyes up to the legend to map these colors to diarrhoea, shortness of breath, anosmia, and fatigue. Oops, I missed the yellow, which is the cough. To be sure, you look at the remaining categories to see where they stand - I've named all of them except fever. The number 18 lies outside fever so this compartment represents everything except fever. 

What's even sadder is there is not much gain from having done it once. Try to interpret the number 50 now. Maybe I'm just slow but it doesn't get better the second or third time around. This graphic not only requires work but painstaking work!

Perhaps a more likely question is how many people who had a loss of smell also had fever. Now it's pretty easy to locate the part of the dark gray oval that overlaps with the orange oval. But now, I have to add all those numbers, 69+17+23+50+17+46 = 222. That's not enough. Next, I must find the total of all the numbers inside the orange oval, which is 222 plus what is inside the orange and outside the dark gray. That turns out to be 829. So among those who had lost smell, the proportion who also had fever is 222/(222+829) = 21 percent. 

How many people had three or more symptoms? I'll let you figure this one out!

 

 

 

 

 

 

 


When the visual runs away from the data

The pressure of the coronavirus news cycle has gotten the better of some graphics designers. Via Twitter, Mark B sent me the following chart:

Junkcharts_abccovidbiggestworries_sufficiency

I applied the self-sufficiency test to this pie chart. That's why you can't see the data which were also printed on the chart.

The idea of self-sufficiency is to test how much work the visual elements of the graphic are doing to convey its message. Look at the above chart, and guess the three values are.

Roughly speaking, all three answers are equally popular, with perhaps a little less than a third of respondents indicating "Getting It" as their biggest COVID-19 worry.

If measured, the slices represent 38%, 35% and 27%.

Now, here is the same chart with the data:

Abc_covidbiggestworries

Each number is way off! In addition, the three numbers sum to 178%.

Trifectacheckup_junkcharts_imageThis is an example of the Visual being at odds with the Data, using a Trifecta Checkup analysis. (Read about the Trifecta here.)

What the Visual is saying is not the same as what the data are saying. So the green arrow between D and V is broken.

***

This is a rather common mistake. This survey question apparently allows each respondent to select more than one answers. Whenever more than one responses are accepted, one cannot use a pie chart.

Here is a stacked bar chart that does right by the data.

Redo_junkcharts_abcbiggestcovidworries

 


The epidemic of simple comparisons

Another day, another Twitter user sent a sloppy chart featured on TV news. This CNN graphic comes from Hugo K. by way of Kevin T.

And it's another opportunity to apply the self-sufficiency test.

Junkcharts_cnncovidcases_sufficiency_1

Like before, I removed the data printed on the graphic. In reading this chart, we like to know the number of U.S. reported cases of coronavirus relative to China, and Italy relative to the U.S.

So, our eyes trace these invisible lines:

Junkcharts_cnncovidcases_sufficiency_2

U.S. cases are roughly two-thirds of China while Italian cases are 90% of U.S.

That's what the visual elements, the columns, are telling us. But it's fake news. Here is the chart with the data:

Cnn_covidcases

The counts of reported cases in all three countries were neck and neck around this time.

What this quick exercise shows is that anyone who correctly reads this chart is reading the data off the chart, and ignoring the contradictionary message sent by the relative column heights. Thus, the visual elements are not self-sufficient in conveying the message.

***

In a Trifecta Checkup, I'd be most concerned about the D corner. The naive comparison of these case counts is an epidemic of its own. It sometimes leads to poor decisions that can exacerbate the public-health problems. See this post on my sister blog.

The difference in case counts between different countries (or regions or cities or locales) is not a direct measure of the difference in coronavirus spread in these places! This is because there are many often-unobserved factors that will explain most if not all of the differences.

After a lot of work by epidemiologists, medical researchers, statisticians and the likes, we now realize that different places conduct different numbers of tests. No test, no positive. The U.S. has been slow to get testing ramped up.

Less understood is the effect of testing selection. Consider the U.S. where it is still hard to get tested. Only those who meet a list of criteria are eligible. Imagine an alternative reality in which the U.S. conducted the same number of tests but instead of selecting most likely infected people to be tested, we test a random sample of people. The incidence of the virus in a random sample is much lower than in the severely infected, therefore, in this new reality, the number of positives would be lower despite equal numbers of tests.

That's for equal number of tests. If test kits are readily available, then a targeted (triage) testing strategy will under-count cases since mild cases or asymptomatic infections escape attention. (See my Wired column for problems with triage.)

To complicate things even more, in most countries, the number of tests and the testing selection have changed over time so a cumulative count statistic obscures those differences.

Beside testing, there are a host of other factors that affect reported case counts. These are less talked about now but eventually will be.

Different places have different population densities. A lot of cases in a big city and an equal number of cases in a small town do not signify equal severity.  Clearly, the situation in the latter is more serious.

Because the virus affects age groups differently, a direct comparison of the case counts without adjusting for age is also misleading. The number of deaths of 80-year-olds in a college town is low not because the chance of dying from COVID-19 is lower there than in a retirement community; it's low because 80-year-olds are a small proportion of the population.

Next, the cumulative counts ignore which stage of the "epi curve" these countries are at. The following chart can replace most of the charts you're inundated with by the media:

Epicurve_coronavirus

(I found the chart here.)

An epi curve traces the time line of a disease outbreak. Every location is expected to move through stages, with cases reaching a peak and eventually the number of newly recovered will exceed the number of newly infected.

Notice that China, Italy and the US occupy different stages of this curve.  It's proper to compare U.S. to China and Italy when they were at a similar early phase of their respective epi curve.

In addition, any cross-location comparison should account for how reliable the data sources are, and the different definitions of a "case" in different locations.

***

Finally, let's consider the Question posed by the graphic designer. It is the morbid question: which country is hit the worst by coronavirus?

This is a Type DV chart. It's got a reasonable question, but the data require a lot more work to adjust for the list of biases. The visual design is hampered by the common mistake of not starting columns at zero.

 


Food coma and self-sufficiency in dataviz

The Hustle wrote a strong analysis of the business of buffets. If you've read my analysis of Groupon's business model in Numbersense (link), you'll find some similarities. A key is to not think of every customer as an average customer; there are segments of customers who behave differently, and creating a proper mix of different types of customers is the management's challenge. I will make further comments on the statistics in a future post on the sister blog.

At Junk Charts, we'll focus on visualizing and communciating data. The article in The Hustle comes with the following dataviz:

Hustle_buffetcost

This dataviz fails my self-sufficiency test. Recall: self-sufficiency is a basic requirement of visualizing data - that the graphical elements should be sufficient to convey the gist of the data. Otherwise, there is no point in augmenting the data with graphical elements.

The self-sufficiency test is to remove the dataset from the dataviz, and ask whether the graphic can stand on its own. So here:

Redo_hustlebuffetcost_selfsufficiency

The entire set of ingredient costs appears on the original graphic. When these numbers are removed, the reader gets the wrong message - that the cost is equally split between these five ingredients.

This chart reminds me of the pizza chart that everyone thought was a pie chart except its designer! I wrote about it here. Food coma is a thing.

The original chart may be regarded as an illustration rather than data visualization. If so, it's just a few steps from becoming a dataviz. Like this:

Redo_hustlebuffetcost

P.S. A preview of what I'll be talking about at the sister blog. The above diagram illustrates the average case - for the average buffet diner. Underneath these costs is an assumption about the relative amounts of each food that is eaten. But eaten by whom?

Also, if you have Numbersense (link), the chapter on measuring the inflation rate is relevant here. Any inflation metric must assume a basket of goods, but then the goods within the basket have to be weighted by the amount of expenditure. It's much harder to get the ratio of expenditures correct compared to getting price data.

 

 


Watching a valiant effort to rescue the pie chart

Today we return to the basics. In a twitter exchange with Dean E., I found the following pie chart in an Atlantic article about who's buying San Francisco real estate:

Atlantic_sfrealestatepie

The pie chart is great at one thing, showing how workers in the software industry accounted for half of the real estate purchases. (Dean and I both want to see more details of the analysis as we have many questions about the underlying data. In this post, I ignore these questions.)

After that, if we want to learn anything else from the pie chart, we have to read the data labels. This calls for one of my key recommendations: make your charts sufficient. The principle of self-sufficiency is that the visual elements of the data graphic should by themselves say something about the data. The test of self-sufficiency is executed by removing the data printed on the chart so that one can assess how much work the visual elements are performing. If the visual elements require data labels to work, then the data graphic is effectively a lookup table.

This is the same pie chart, minus the data:

Redo_atlanticsfrealestate_sufficiency

Almost all pie charts with a large number of slices are packed with data labels. Think of the labeling as a corrective action to fix the shortcoming of the form.

Here is a bar chart showing the same data:

Junkcharts_redo_atlanticsfrealestatebar

***

Let's look at all the efforts made to overcome the lack of self-sufficiency.

Here is a zoom-in on the left side of the chart:

Redo_atlanticsfrealestate_labeling_1

Data labels are necessary to help readers perceive the sizes of the slices. But as the slices are getting smaller, the labels are getting too dense, so the guiding lines are being stretched.

Eventually, the designer gave up on labeling every slice. You can see that some slices are missing labels:

Redo_atlanticsfrealestate_labeling_3

The designer also had to give up on sequencing the slices by the data. For example, hardware with a value of 2.4% should be placed between Education and Law. It is shifted to the top left side to make the labeling easier.

Redo_atlanticsfrealestate_labeling_2

Fitting all the data labels to the slices becomes the singular task at hand.

 


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)

Dailymail-image-a-35_1431545452562

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:

Dailymail_travelrisk_bubble

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:

Dailymail_travelrisk_bar

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.

***

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. 

***

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. 

***

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.

California_bullettrain

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

Highspeedtrains_sufficiency

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:

Redo_highspeedtrains

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


McKinsey thinks the data world needs more dataviz talent

Note about last week: While not blogging, I delivered four lectures on three topics over five days: one on the use of data analytics in marketing for a marketing class at Temple; two on the interplay of analytics and data visualization, at Yeshiva and a JMP Webinar; and one on how to live during the Data Revolution at NYU.

This week, I'm back at blogging.

McKinsey publishes a report confirming what most of us already know or experience - the explosion of data jobs that just isn't stopping.

On page 5, it says something that is of interest to readers of this blog: "As data grows more complex, distilling it and bringing it to life through visualization is becoming critical to help make the results of data analyses digestible for decision makers. We estimate that demand for visualization grew roughly 50 percent annually from 2010 to 2015." (my bolding)

The report contains a number of unfortunate graphics. Here's one:

Mckinseyreport_pageiii

I applied my self-sufficiency test by removing the bottom row of data from the chart. Here is what happened to the second circle, representing the fraction of value realized by the U.S. health care industry.

Mckinseyreport_pageiii_inset

What does the visual say? This is one of the questions in the Trifecta Checkup. We see three categories of things that should add up to 100 percent. With a little more effort, we find the two colored categories are each 10% while the white area is 80%. 

But that's not what the data say, because there is only one thing being measured: how much of the potential has already been realized. The two colors is an attempt to visualize the uncertainty of the estimated proportion, which in this case is described as 10 to 20 percent underneath the chart.

If we have to describe what the two colored sections represent: the dark green section is the lower bound of the estimate while the medium green section is the range of uncertainty. The edge between the two sections is the actual estimated proportion (assuming the uncertainty bound is symmetric around the estimate)!

A first attempt to fix this might be to use line segments instead of colored arcs. 

Redo_mckinseyreport_inset_jc_1

The middle diagram emphasizes the mid-point estimate while the right diagram, the range of estimates. Observe how differently these two diagrams appear from the original one shown on the left.

This design only works if the reader perceives the chart as a "racetrack" chart. You have to see the invisible vertical line at the top, which is the starting line, and measure how far around the track has the symbol gone. I have previously discussed why I don't like racetracks (for example, here and here).

***

Here is a sketch of another design:

Redo_mckinseyreport_jc_2

The center figure will have to be moved and changed to a different shape. This design conveys the sense of a goal (at 100%) and how far one is along the path. The uncertainty is represented by wave-like elements that make the exact location of the pointer arrow appear as wavering.