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:

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:

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

This 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.

 

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.

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:

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:

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:

(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.

 

More visuals of the economic crisis

As we move into the next phase of the dataviz bonanza arising from the coronavirus pandemic, we will see a shift from simple descriptive graphics of infections and deaths to bivariate explanatory graphics claiming (usually spurious) correlations.

The FT is leading the way with this effort, and I hope all those who follow will make a note of several wise decisions they made.

• They source their data. Most of the data about business activities come from private entities, many of which are data vendors who make money selling the data. In this article, FT got restaurant data from OpenTable, retail foot traffic data from Springboard, box office data from Box Office Mojo, flight data from Flightradar24, road traffic data from TomTom, and energy use data from European Network of Transmission System Operators for Electricity.
• They generally let the data and charts speak without "story time". The text primarily describes the trends of the various data series.
• They selected sectors that are obviously impacted by the shutdowns so any link between the observed trends and the crisis is plausible.

The FT charts are examples of clarity. Here is the one about road traffic patterns in major cities:

The cities are organized into regions: Europe, US, China, other Asia.

The key comparison is the last seven days versus the historical averages. The stories practically jump out of the page. Traffic in Paris collapsed on Tuesday. Wuhan is still locked down despite the falloff in infections. Drivers of Tokyo are probably wondering why teams are not going to the Olympics this year. Londoners? My guess is they're determined to not let another Brexit deadline slip.

***

I'd hope we go even further than FT when publishing this type of visual analytics involving "Big Data." These business data obtained from private sources typically have OCCAM properties: they are observational, seemingly complete, uncontrolled, adapted and merged. All these properties make the data very challenging to interpret.

The coronavirus case and death counts are simple by comparison. People are now aware of all the problems from differential rates of testing to which groups are selectively tested (i.e. triage) to how an infection or death is defined. The problems involving Big Data are much more complex.

I have three additional proposals:

Disclosure of Biases and Limitations

The private data have many more potential pitfalls. Take OpenTable data for example. The data measure restaurant bookings, not revenues. It measures gross bookings, not net bookings (i.e. removing no-shows). Only a proportion of restaurants use OpenTable (which cost owners money). OpenTable does not strike me as a quasi-monopoly so there are competitors with significant market share. The restaurants that use OpenTable do not form a random subsample of all restaurants. One of the most popular restaurants in the U.S. are pizza joints, with little of no seating, which do not feature in the bookings data. OpenTable also has differential popularity by country, region, or probably cuisine. 

I believe data journalists ought to provide such context in a footnote. Readers should have the information to judge whether they believe the data are sufficiently representative. Private data vendors who want data journalists to feature their datasets should be required to supply a footnote that describes the biases and limitations of their data.

Data journalists should think seriously about how they headline this type of chart. The standard practice is what FT adopted. The headline said "Restaurant bookings have collapsed" with a small footnote saying "Source: OpenTable". Should the headline have said "OpenTable bookings have collapsed" instead?

Disclosure of Definitions and Proxies

In the road traffic chart shown above, the metric is called "TomTom traffic congestion index". In order to earn this free advertising (euphemistically called "earned media" by industry), TomTom should be obliged to explain how this index is constructed. What does index = 100 mean?

[For example, it is curious that the Madrid index values are much lower across the board than those in Paris and Roma.]

For the electric usage chart, FT discloses the name of the data provider as a group of "43 electricity transmission system operators in 36 countries across Europe." Now, that is important context but can be better. The group may consist of 43 operators but how many of them are in the dataset? What proportion of the total electric usage do they account for in each country? If they have low penetration in a particular country, do they just report the low statistics or adjust the numbres?

If the journalist decides to use a proxy, for example, OpenTable restaurant bookings to reflect restaurant revenues, that should be explained, perhaps even justified.

Data as a Public Good

If private businesses choose to supply data to media outlets as a public service, they should allow the underlying data to be published.

Speaking from experience, I've seen a lot of bad data. It's one thing to hold your nose when the data are analyzed to make online advertising more profitable, or to find signals to profit from the stock market. It's another thing for the data analysis to drive public policy, in this case, policies that will have life-or-death implications.

Graphing the economic crisis of Covid-19

My friend Ray Vella at The Conference Board has a few charts up on their coronavirus website. TCB is a trusted advisor and consultant to large businesses and thus is a good place to learn how the business community is thinking about this crisis.

I particularly like the following chart:

This puts the turmoil in the stock market in perspective. We are roughly tracking the decline of the Great Recession of the late 2000s. It's interesting that 9/11 caused very mild gyrations in the S&P index compared to any of the other events. 

The chart uses an index with value 100 at Day 0. Day 0 is defined by the trigger event for each crisis. About three weeks into the current crisis, the S&P has lost over 30% of its value.

The device of a gray background for the bottom half of the chart is surprisingly effective.

***

Here is a chart showing the impact of the Covid-19 crisis on different sectors.

So the full-service restaurant industry is a huge employer. Restaurants employ 7-8 times more people than airlines. Airlines employ about the same numbers of people as "beverage bars" (which I suppose is the same as "bars" which apparently is different from "drinking places"). Bars employ 7 times more people than "Cafeterias, etc.".

The chart describes where the jobs are, and which sectors they believe will be most impacted. It's not clear yet how deeply these will be impacted. Being in NYC, the complete shutdown is going to impact 100% of these jobs in certain sectors like bars, restaurants and coffee shops.

Proportions and rates: we are no dupes

Reader Lucia G. sent me this chart, from Ars Technica's FAQ about the coronavirus:

She notices something wrong with the axis.

The designer took the advice not to make a dual axis, but didn't realize that the two metrics are not measured on the same scale even though both are expressed as percentages.

The blue bars, labeled "cases", is a distribution of cases by age group. The sum of the blue bars should be 100 percent.

The orange bars show fatality rates by age group. Each orange bar's rate is based on the number of cases in that age group. The sum of the orange bars will not add to 100 percent.

In general, the rates will have much lower values than the proportions. At least that should be the case for viruses that are not extremely fatal.

This is what the 80 and over section looks like.

It is true that fatality rate (orange) is particularly high for the elderly while this age group accounts for less than 5 percent of total cases (blue). However, the cases that are fatal, which inhabit the orange bar, must be a subset of the total cases for 80 and over, which are shown in the blue bar. Conceptually, the orange bar should be contained inside the blue bar. So, it's counter-intuitive that the blue bar is so much shorter than the orange bar.

The following chart fixes this issue. It reveals the structure of the data, Total cases are separated by age group, then within each age group, a proportion of the cases are fatal.

This chart also shows that most patients recover in every age group. (This is only approximately true as some of the cases may not have been discharged yet.)

***

This confusion of rates and proportions reminds me of something about exit polls I just wrote about the other day on the sister blog.

When the media make statements about trends in voter turnout rate in the primary elections, e.g. when they assert that youth turnout has not increased, their evidence is from exit polls, which can measure only the distribution of voters by age group. Exit polls do not and cannot measure the turnout rate, which is the proportion of registered (or eligible) voters in the specific age group who voted.

Like the coronavirus data, the scales of these two metrics are different even though they are both percentages: the turnout rate is typically a number between 30 and 70 percent, and summing the rates across all age groups will exceed 100 percent many times over. Summing the proportions of voters across all age groups should be 100 percent, and no more.

Changes in the proportion of voters aged 18-29 and changes in the turnout rate of people aged 18-29 are not the same thing. The former is affected by the turnout of all age groups while the latter is a clean metric affected only by 18 to 29-years-old.

Basically, ignore pundits who use exit polls to comment on turnout trends. No matter how many times they repeat their nonsense, proportions and rates are not to be confused. Which means, ignore comments on turnout trends because the only data they've got come from exit polls which don't measure rates.

 

P.S. Here is some further explanation of my chart, as a response to a question from Enrico B. on Twitter.

The chart can be thought of as two distributions, one for cases (gray) and one for deaths (red). Like this:

The side-by-side version removes the direct visualization of the fatality rate within each age group. To understand fatality rate requires someone to do math in their head. Readers can qualitatively assess that for the 80 and over, they accounted for 3 percent of cases but also about 21 percent of deaths. People aged 70 to 79 however accounted for 9 percent of cases but 30 percent of deaths, etc.

What I did was to scale the distribution of deaths so that they can be compared to the cases. It's like fitting the red distribution inside the gray distribution. Within each age group, the proportion of red against the length of the bar is the fatality rate.

For every 100 cases regardless of age, 3 cases are for people aged 80 and over within which 0.5 are fatal (red).

So, the axis labels are correct. The values are proportions of total cases, although as the designer of the chart, I hope people are paying attention more to the proportion of red, as opposed to the units.

What might strike people as odd is that the biggest red bar does not appear against 80 and above. We might believe it's deadlier the older you are. That's because on an absolute scale, more people aged 70-79 died than those 80 and above. The absolute deaths is the product of the proportion of cases and the fatality rate. That's really a different story from the usual plot of fatality rates by age group. In those charts, we "control" for the prevalence of cases. If every age group were infected in the same frequency, then COVID-19 does kill more 80 and over.

 

 

 

Comparing chance of death of coronavirus and flu

The COVID-19 charts are proving one thing. When the topic of a dataviz is timely and impactful, readers will study the graphics and ask questions. I've been sent some of these charts lately, and will be featuring them here.

A former student saw this chart from Business Insider (link) and didn't like it.

My initial reaction was generally positive. It's clear the chart addresses a comparison between death rates of the flu and COVID19, an important current question. The side-by-side panel is effective at allowing such a comparison. The column charts look decent, and there aren't excessive gridlines.

Sure, one sees a few simple design fixes, like removing the vertical axis altogether (since the entire dataset has already been printed). I'd also un-slant the age labels.

***

I'd like to discuss some subtler improvements.

A primary challenge is dealing with the different definitions of age groups across the two datasets. While the side-by-side column charts prompt readers to go left-right, right-left in comparing death rates, it's not easy to identify which column to compare to which. This is not fixable in the datasets because the organizations that compile them define their own age groups.

Also, I prefer to superimpose the death rates on the same chart, using something like a dot plot rather than a column chart. This makes the comparison even easier.

Here is a revised visualization:

The contents of this chart raise several challenges to public health officials. Clearly, hospital resources should be preferentially offered to older patients. But young people could be spreading the virus among the community.

Caution is advised as the data for COVID19 suffers from many types of inaccuracies, as outlined here.

It's impossible to understand Super Tuesday, this chart says

Twitter people are talking about this chart, from NPR (link):

This was published on Wednesday after Super Tuesday, the day on which multiple states held their primary elections. On the Democratic side, something like a third of the delegates were up for grabs (although as the data below this chart shows, a big chunk of the delegates, mostly from California and Texas, have yet to be assigned to a candidate as they were still counting votes.)

Here, I hovered over the Biden line, trying to decipher the secret code in these lines:

I have to say I failed. Biden won 6 delegates on Feb 3, 9 on Feb 22, 39 on Feb 29, and 512 on Mar 3. I have no idea how those numbers led to this line!

***

Here is what happened so far in the Democratic primary:

The key tradeoff the designer has to make here is the relative importance of the timeline and the total count. In this chart, it's easiest to compare the total count across candidates as of the Wednesday morning, then to see how each candidate accumulates the delegates over the first five contest days. It takes a little more effort to see who's ahead after each contest day. And it is almost impossible to see the spacing of the contest days over the calendar.

I don't use stacked bar charts often but this chart form makes clear the cumulative counts over time so it's appropriate here.

Also, the as-yet-unassigned delegates is a big part of the story and needs to be visualized.

 

P.S. See comment below. There was a bug in the code and they fixed the line chart.

So, some of the undecided delegates have been awarded and comparing the two charts, it appears that the gap went down from 105 to 76. Still over 150 delegates not assigned.