Junk Charts

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. 

***

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.

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.

***

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.

***

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.

 

 

 

 

Crazy rich Asians inspire some rich graphics

On the occasion of the hit movie Crazy Rich Asians, the New York Times did a very nice report on Asian immigration in the U.S.

The first two graphics will be of great interest to those who have attended my free dataviz seminar (coming to Lyon, France in October, by the way. Register here.), as it deals with a related issue.

The first chart shows an income gap widening between 1970 and 2016.

This uses a two-lines design in a small-multiples setting. The distance between the two lines is labeled the "income gap". The clear story here is that the income gap is widening over time across the board, but especially rapidly among Asians, and then followed by whites.

The second graphic is a bumps chart (slopegraph) that compares the endpoints of 1970 and 2016, but using an "income ratio" metric, that is to say, the ratio of the 90th-percentile income to the 10th-percentile income.

Asians are still a key story on this chart, as income inequality has ballooned from 6.1 to 10.7. That is where the similarity ends.

Notice how whites now appears at the bottom of the list while blacks shows up as the second "worse" in terms of income inequality. Even though the underlying data are the same, what can be seen in the Bumps chart is hidden in the two-lines design!

In short, the reason is that the scale of the two-lines design is such that the small numbers are squashed. The bottom 10 percent did see an increase in income over time but because those increases pale in comparison to the large incomes, they do not show up.

What else do not show up in the two-lines design? Notice that in 1970, the income ratio for blacks was 9.1, way above other racial groups.

Kudos to the NYT team to realize that the two-lines design provides an incomplete, potentially misleading picture.

***

The third chart in the series is a marvellous scatter plot (with one small snafu, which I'd get t0).

What are all the things one can learn from this chart?

• There is, as expected, a strong correlation between having college degrees and earning higher salaries.
• The Asian immigrant population is diverse, from the perspectives of both education attainment and median household income.
• The largest source countries are China, India and the Philippines, followed by Korea and Vietnam.
• The Indian immigrants are on average professionals with college degrees and high salaries, and form an outlier group among the subgroups.

Through careful design decisions, those points are clearly conveyed.

Here's the snafu. The designer forgot to say which year is being depicted. I suspect it is 2016.

Dating the data is very important here because of the following excerpt from the article:

Asian immigrants make up a less monolithic group than they once did. In 1970, Asian immigrants came mostly from East Asia, but South Asian immigrants are fueling the growth that makes Asian-Americans the fastest-expanding group in the country.

This means that a key driver of the rapid increase in income inequality among Asian-Americans is the shift in composition of the ethnicities. More and more South Asian (most of whom are Indians) arrivals push up the education attainment and household income of the average Asian-American. Not only are Indians becoming more numerous, but they are also richer.

An alternative design is to show two bubbles per ethnicity (one for 1970, one for 2016). To reduce clutter, the smaller ethnicites can be aggregated into Other or South Asian Other. This chart may help explain the driver behind the jump in income inequality.

 

 

 

 

 

Two views of earthquake occurrence in the Bay Area

This article has a nice description of earthquake occurrence in the San Francisco Bay Area. A few quantities are of interest: when the next quake occurs, the size of the quake, the epicenter of the quake, etc. The data graphic included in the article fails the self-sufficiency test: the only way to read this chart is to read out the entire data set - in other words, the graphical details have no utility.

The article points out the clustering of earthquakes. In particular, there is a 68-year "quiet period" between 1911 and 1979, during which no quakes over 6.0 in size occurred. The author appears to have classified quakes into three groups: "Largest" which are those at 6.5 or over; "Smaller but damaging" which are those between 6.0 and 6.5; and those below 6.0 (not shown).

For a more standard and more effective visualization of this dataset, see this post on a related chart (about avian flu outbreaks). The post discusses a bubble chart versus a column chart. I prefer the column chart.

This chart focuses on the timing of rare events. The time between events is not as easy to see. 

What if we want to focus on the "quiet years" between earthquakes? Here is a visualization that addresses the question: when will the next one hit us?

 

 

Big Macs in Switzerland are amazing, according to my friend

Note for those in or near Zurich: I'm giving a Keynote Speech tomorrow morning at the Swiss Statistics Meeting (link). Here is the abstract:

The best and the worst of data visualization share something in common: these graphics provoke emotions. In this talk, I connect the emotional response of readers of data graphics to the design choices made by their creators. Using a plethora of examples, collected over a dozen years of writing online dataviz criticism, I discuss how some design choices generate negative emotions such as confusion and disbelief while other choices elicit positive feelings including pleasure and eureka. Important design choices include how much data to show; which data to highlight, hide or smudge; what research question to address; whether to introduce imagery, or playfulness; and so on. Examples extend from graphics in print, to online interactive graphics, to visual experiences in society.

***

The Big Mac index seems to never want to go away. Here is the latest graphic from the Economist, saying what it says:

The index never made much sense to me. I'm in Switzerland, and everything here is expensive. My friend, who is a U.S. transplant, seems to have adopted McDonald's as his main eating-out venue. Online reviews indicate that the quality of the burger served in Switzerland is much better than the same thing in the States. So, part of the price differential can be explained by quality. The index also confounds several other issues, such as local inflation and exchange rate

Now, on to the data visualization, which is primarily an exercise in rolling one's eyeballs. In order to understand the red and blue line segments, our eyes have to hop over the price bubbles to the top of the page. Then, in order to understand the vertical axis labels, unconventionally placed on the right side, our eyes have to zoom over to the left of the page, and search for the line below the header of the graph. Next, if we want to know about a particular country, our eyes must turn sideways and scan from bottom up.

Here is a different take on the same data:

I transformed the data as I don't find it compelling to learn that Russian Big Macs are 60% less than American Big Macs. Instead, on my chart, the reader learns that the price paid for a U.S. Big Mac will buy him/her almost 2 and a half Big Macs in Russia.

The arrows pointing left indicate that in most countries, the values of their currencies are declining relative to the dollar from 2017 to 2018 (at least by the Big Mac Index point of view). The only exception is Turkey, where in 2018, one can buy more Big Macs equivalent to the price paid for one U.S. Big Mac. compared to 2017.

The decimal differences are immaterial so I have grouped the countries by half Big Macs.

This example demonstrates yet again, to make good data visualization, one has to describe an interesting question, make appropriate transformations of the data, and then choose the right visual form. I describe this framework as the Trifecta - a guide to it is here.

(P.S. I noticed that Bitly just decided unilaterally to deactivate my customized Bitly link that was configured years and years ago, when it switched design (?). So I had to re-create the custom link. I have never grasped  why "unreliability" is a feature of the offering by most Tech companies.)

Two thousand five hundred ways to say the same thing

Wallethub published a credit card debt study, which includes the following map:

Let's describe what's going on here.

The map plots cities (N = 2,562) in the U.S. Each city is represented by a bubble. The color of the bubble ranges from purple to green, encoding the percentile ranking based on the amount of credit card debt that was paid down by consumers. Purple represents 1st percentile, the lowest amount of paydown while green represents 99th percentile, the highest amount of paydown.

The bubble size is encoding exactly the same data, apparently in a coarser gradation. The more purple the color, the smaller the bubble. The more green the color, the larger the bubble.

***

The design decisions are baffling.

Purple is more noticeable than the green, but signifies the less important cities, with the lesser paydowns.

With over 2,500 bubbles crowding onto the map, over-plotting is inevitable. The purple bubbles are printed last, dominating the attention but those are the least important cities (1st percentile). The green bubbles, despite being larger, lie underneath the smaller, purple bubbles.

What might be the message of this chart? Our best guess is: the map explores the regional variation in the paydown rate of credit card debt.

The analyst provides all the data beneath the map. 

From this table, we learn that the ranking is not based on total amount of debt paydown, but the amount of paydown per household in each city (last column). That makes sense.

Shouldn't it be ranked by the paydown rate instead of the per-household number? Divide the "Total Credit Card Paydown by City" by "Total Credit Card Debt Q1 2018" should yield the paydown rate. Surprise! This formula yields a column entirely consisting of 4.16%.

What does this mean? They applied the national paydown rate of 4.16% to every one of 2,562 cities in the country. If they had plotted the paydown rate, every city would attain the same color. To create "variability," they plotted the per-household debt paydown amount. Said differently, the color scale encodes not credit card paydown as asserted but amount of credit card debt per household by city.

Here is a scatter plot of the credit card amount against the paydown amount.

A perfect alignment!

This credit card debt paydown map is an example of a QDV chart, in which there isn't a clear question, there is almost no data, and the visual contains several flaws. (See our Trifecta checkup guide.) We are presented 2,562 ways of saying the same thing: 4.16%.

 

P.S. [6/22/2018] Added scatter plot, and cleaned up some language.

 

 

 

Lines, gridlines, reference lines, regression lines, the works

This post is part 2 of an appreciation of the chart project by Google Newslab, advised by Alberto Cairo, on the gender and racial diversity of the newsroom. Part 1 can be read here.

In the previous discussion, I left out the following scatter bubble plot.

This plot is available in two versions, one for gender and one for race. The key question being asked is whether the leadership in the newsroom is more or less diverse than the rest of the staff.

The story appears to be a happy one: in many newsrooms, the leadership roughly reflects the staff in terms of gender distribution (even though both parts of the whole compare disfavorably to the gender ratio in the neighborhoods, as we saw in the previous post.)

***

Unfortunately, there are a few execution problems with this scatter plot.

First, take a look at the vertical axis labels on the right side. The labels inform the leadership axis. The mid-point showing 50-50 (parity) is emphasized with the gray band. Around the mid-point, the labels seem out of place. Typically, when the chart contains gridlines, we expect the labels to sit right around each gridline, either on top or just below the line. Here the labels occupy the middle of the space between successive gridlines. On closer inspection, the labels are correctly affixed, and the gridlines  drawn where they are supposed to be. The designer chose to show irregularly spaced labels: from the midpoint, it's a 15% jump on either side, then a 10% jump.

I find this decision confounding. It also seems as if two people have worked on these labels, as there exists two patterns: the first is "X% Leaders are Women", and second is "Y% Female." (Actually, the top and bottom labels are also inconsistent, one using "women" and the other "female".)

The horizontal axis? They left out the labels. Without labels, it is not possible to interpret the chart. Inspecting several conveniently placed data points, I figured that the labels on the six vertical gridlines should be 25%, 35%, ..., 65%, 75%, in essence the same scale as the vertical axis.

Here is the same chart with improved axis labels:

Re-labeling serves up a new issue. The key reference line on this chart isn't the horizontal parity line: it is the 45-degree line, showing that the leadership has the same proprotion of females as the rest of the staff. In the following plot (right side), I added in the 45-degree line. Note that it is positioned awkwardly on top of the grid system. The culprit is the incompatible gridlines.

 

The solution, as shown below, is to shift the vertical gridlines by 5% so that the 45-degree line bisects every grid cell it touches.

***

Now that we dealt with the purely visual issues, let me get to a statistical issue that's been troubling me. It's about that yellow line. It's supposed to be a regression line that runs through the points.

Does it appear biased downwards to you? It just seems that there are too many dots above and not enough below. The distance of the furthest points above also appears to be larger than that of the distant points below.

How do we know the line is not correct? Notice that the green 45-degree line goes through the point labeled "AVERAGE." That is the "average" newsroom with the average proportion of female staff and the average proportion of leadership staff. Interestingly, the average falls right on the 45-degree line.

In general, the average does not need to hit the 45-degree line. The average, however, does need to hit the regression line! (For a mathematical explanation, see here.)

Note the corresponding chart for racial diversity has it right. The yellow line does pass through the average point here:

 ***

In practice, how do problems seep into dataviz projects? It's the fact that you don't get to the last chart via a clean, streamlined process but that you pass through a cycle of explore-retrench-synthesize, frequently bouncing ideas between several people, and it's challenging to keep consistency!

And let me repeat my original comment about this project - the key learning here is how they took a complex dataset with many variables, broke it down into multiple parts addressing specific problems, and applied the layering principle to make each part of the project digestible.

 

 

Well-structured, interactive graphic about newsrooms

Today, I take a detailed look at one of the pieces that came out of an amazing collaboration between Alberto Cairo, and Google's News Lab. The work on diversity in U.S. newsrooms is published here. Alberto's introduction to this piece is here.

The project addresses two questions: (a) gender diversity (representation of women) in U.S. newsrooms and (b) racial diversity (representation of white vs. non-white) in U.S. newsrooms.

One of the key strengths of the project is how the complex structure of the underlying data is displayed. The design incorporates the layering principle everywhere to clarify that structure.

At the top level, the gender and race data are presented separately through the two tabs on the top left corner. Additionally, newsrooms are classified into three tiers: brand-names (illustrated with logos), "top" newsrooms, and the rest.

The brand-name newsrooms are shown with logos while the reader has to click on individual bubbles to see the other newsrooms. (Presumably, the size of the bubble is the size of each newsroom.)

The horizontal scale is the proportion of males (or females), with equality positioned in the middle. The higher the proportion of male staff, the deeper is the blue. The higher the proportion of female staff, the deeper is the red. The colors are coordinated between the bubbles and the horizontal axis, which is a nice touch.

I am not feeling this color choice. The key reference level on this chart is the 50/50 split (parity), which is given the pale gray. So the attention is drawn to the edges of the chart, to those newsrooms that are the most gender-biased. I'd rather highlight the middle, celebrating those organizations with the best gender balance.

***

The red-blue color scheme unfortunately re-appeared in a subsequent chart, with a different encoding.

Now, blue means a move towards parity while red indicates a move away from parity between 2001 and 2017. Gray now denotes lack of change. The horizontal scale remains the same, which is why this can cause some confusion.

Despite the colors, I like the above chart. The arrows symbolize trends. The chart delivers an insight. On average, these newsrooms are roughly 60% male with negligible improvement over 16 years.

***

Back to layering. The following chart shows that "top" newsrooms include more than just the brand-name ones.

The dot plot is undervalued for showing simple trends like this. This is a good example of this use case.

While I typically recommend showing balanced axis for bipolar scale, this chart may be an exception. Moving to the right side is progress but the target sits in the middle; the goal isn't to get the dots to the far right so much of the right panel is wasted space.

 

A gem among the snowpack of Olympics data journalism

It's not often I come across a piece of data journalism that pleases me so much. Here it is, the "Happy 700" article by Washington Post is amazing.

 

When data journalism and dataviz are done right, the designers have made good decisions. Here are some of the key elements that make this article work:

(1) Unique

The topic is timely but timeliness heightens both the demand and supply of articles, which means only the unique and relevant pieces get the readers' attention.

(2) Fun

The tone is light-hearted. It's a fun read. A little bit informative - when they describe the towns that few have heard of. The notion is slightly silly but the reader won't care.

(3) Data

It's always a challenge to make data come alive, and these authors succeeded. Most of the data work involves finding, collecting and processing the data. There isn't any sophisticated analysis. But a powerful demonstration that complex analysis is not always necessary.

(4) Organization

The structure of the data is three criteria (elevation, population, and terrain) by cities. A typical way of showing such data might be an annotated table, or a Bumps-type chart, grouped columns, and so on. All these formats try to stuff the entire dataset onto one chart. The designers chose to highlight one variable at a time, cumulatively, on three separate maps. This presentation fits perfectly with the flow of the writing. 

(5) Details

The execution involves some smart choices. I am a big fan of legend/axis labels that are informative, for example, note that the legend doesn't say "Elevation in Meters":

The color scheme across all three maps shows a keen awareness of background/foreground concerns.