Junk Charts

SCMP's fantastic infographic on Hong Kong protests

In the past month, there have been several large-scale protests in Hong Kong. The largest one featured up to two million residents taking to the streets on June 16 to oppose an extradition act that was working its way through the legislature. If the count was accurate, about 25 percent of the city’s population joined in the protest. Another large demonstration occurred on July 1, the anniversary of Hong Kong’s return to Chinese rule.

South China Morning Post, which can be considered the New York Times of Hong Kong, is well known for its award-winning infographics, and they rose to the occasion with this effort.

This is one of the rare infographics that you’d not regret spending time reading. After reading it, you have learned a few new things about protesting in Hong Kong.

In particular, you’ll learn that the recent demonstrations are part of a larger pattern in which Hong Kong residents express their dissatisfaction with the city’s governing class, frequently accused of acting as puppets of the Chinese state. Under the “one country, two systems” arrangement, the city’s officials occupy an unenviable position of mediating the various contradictions of the two systems.

This bar chart shows the growth in the protest movement. The recent massive protests didn't come out of nowhere. 

This line chart offers a possible explanation for burgeoning protests. Residents’ perceived their freedoms eroding in the last decade.

If you have seen videos of the protests, you’ll have noticed the peculiar protest costumes. Umbrellas are used to block pepper sprays, for example. The following lovely graphic shows how the costumes have evolved:

The scale of these protests captures the imagination. The last part in the infographic places the number of protestors in context, by expressing it in terms of football pitches (as soccer fields are known outside the U.S.) This is a sort of universal measure due to the popularity of football almost everywhere. (Nevertheless, according to Wikipedia, the fields do not have one fixed dimension even though fields used for international matches are standardized to 105 m by 68 m.)

This chart could be presented as a bar chart. It’s just that the data have been re-scaled – from counting individuals to counting football pitches-ful of individuals. 

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Here is the entire infographics.

Three estimates, two differences trip up an otherwise good design

Reader Fernando P. was baffled by this chart from the Perception Gap report by More in Common. (link to report)

Overall, this chart is quite good. Its flaws are subtle. There is so much going on, perhaps even the designer found it hard to keep level.

The title is "Democrat's Perception Gap" which actually means the gap between Democrats' perception of Republicans and Republican's self-reported views. We are talking about two estimates of Republican views. Conversely, in Figure 2 (not shown), the "Republican's Perception Gap" describes two estimates of Democrat views.

The gap is visually shown as the gray bar between the red dot and the blue dot. This is labeled perception gap, and its values are printed on the right column, also labeled perception gap.

Perhaps as an after-thought, the designer added the yellow stripes, which is a third estimate of Republican views, this time by Independents. This little addition wreaks havoc. There are now three estimates - and two gaps. There is a new gap, between Independents' perception of Republican views, and Republican's self-reported views. This I-gap is hidden in plain sight. The words "perception gap" obstinately sticks to the D-gap.

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Here is a slightly modified version of the same chart.

 

The design focuses attention on the two gaps (bars). It also identifies the Republican self-perception as the anchor point from which the gaps are computed.

I have chosen to describe the Republican dot as "self-perception" rather than "actual view," which connotes a form of "truth." Rather than considering the gap as an error of estimation, I like to think of the gap as the difference between two groups of people asked to estimate a common quantity.

Also, one should note that on the last two issues, there is virtual agreement.

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Aside from the visual, I have doubts about the value of such a study. Only the most divisive issues are being addressed here. Adding a few bipartisan issues would provide controls that can be useful to tease out what is the baseline perception gap.

I wonder whether there is a self-selection in survey response, such that people with extreme views (from each party) will be under-represented. Further, do we believe that all survey respondents will provide truthful answers to sensitive questions that deal with racism, sexism, etc.? For example, if I am a moderate holding racist views, would I really admit to racism in a survey?

 

 

Putting the house in order, two Brexit polls

Reader Steve M. noticed an oversight in the Guardian in the following bar chart (link):

The reporter was discussing an important story that speaks to the need for careful polling design. He was comparing two polls, one by Ipsos Mori, and one by YouGov, that estimates the vote support for each party in the future U.K. general election. The bottom line is that the YouGov poll predicts about double the support for the Brexit Party than the Ipsos-Mori poll.

The stacked bar chart should only be used for data that can be added up. Here, we should be comparing the numbers side by side:

I've always found this standard display inadequate. The story here is the gap in the two bar lengths for the Brexit Party. A secondary story is that the support for the Brexit Party might come from voters breaking from Labour. In other words, we really want the reader to see:

Switching to a dot plot helps bring attention to the gaps:

Now, putting the house in order:

Why do these two polls show such different results? As the reporter explained, the answer is in how the question was asked. The Ipsos-Mori is unprompted, meaning the Brexit Party was not announced to the respondent as one of the choices while the YouGov is prompted.

This last version imposes a direction on the gaps to bring out the secondary message - that the support for Brexit might be coming from voters breaking from Labour.

 

 

Tightening the bond between the message and the visual: hello stats-cats

The editors of ASA's Amstat News certainly got my attention, in a recent article on school counselling. A research team asked two questions. The first was HOW ARE YOU FELINE?

Stats and cats. The pun got my attention and presumably also made others stop and wonder. The second question was HOW DO YOU REMEMBER FEELING while you were taking a college statistics course? Well, it's hard to imagine the average response to that question would be positive.

What also drew me to the article was this pair of charts:

Surely, ASA can do better. (I'm happy to volunteer my time!)

Rotate the chart, clean up the colors, remove the decimals, put the chart titles up top, etc.

***

The above remedies fall into the V corner of my Trifecta checkup.

The key to fixing this chart is to tighten the bond between the message and the visual. This means working that green link between the Q and V corners.

This much became clear after reading the article. The following paragraphs are central to the research (bolding is mine):

Responses indicated the majority of school counselors recalled experiences of studying statistics in college that they described with words associated with more unpleasant affect (i.e., alarm, anger, distress, fear, misery, gloom, depression, sadness, and tiredness; n = 93; 66%). By contrast, a majority of counselors reported same-day (i.e., current) emotions that appeared to be associated with more pleasant affect (i.e., pleasure, happiness, excitement, astonishment, sleepiness, satisfaction, and calm; n = 123; 88%).

Both recalled emotive experiences and current emotional states appeared approximately balanced on dimensions of arousal: recalled experiences associated with lower arousal (i.e., pleasure, misery, gloom, depression, sadness, tiredness, sleepiness, satisfaction, and calm, n = 65, 46%); recalled experiences associated with higher arousal (i.e., happiness, excitement, astonishment, alarm, anger, distress, fear, n = 70, 50%); current emotions associated with lower arousal (n = 60, 43%); current experiences associated with higher arousal (i.e., n = 79, 56%).

These paragraphs convey two crucial pieces of information: the structure of the analysis, and its insights.

The two survey questions measure two states of experiences, described as current versus recalled. Then the individual affects (of which there were 16 plus an option of "other") are scored on two dimensions, pleasure and arousal. Each affect maps to high or low pleasure, and separately to high or low arousal.

The research insight is that current experience was noticably higher than recalled experience on the pleasure dimension but both experiences were similar on the arousal dimension.

Any visualization of this research must bring out this insight.

***

Here is an attempt to illustrate those paragraphs:

The primary conclusion can be read from the four simple pie charts in the middle of the page. The color scheme shines light on which affects are coded as high or low for each dimension. For example, "distressed" is scored as showing low pleasure and high arousal.

A successful data visualization for this situation has to bring out the conclusion drawn at the aggregated level, while explaining the connection between individual affects and their aggregates.

Re-thinking a standard business chart of stock purchases and sales

Here is a typical business chart.

A possible story here: institutional investors are generally buying AMD stock, except in Q3 2018.

Let's give this chart a three-step treatment.

STEP 1: The Basics

Remove the data labels, which stand sideways awkwardly, and are redundant given the axis labels. If the audience includes people who want to take the underlying data, then supply a separate data table. It's easier to copy and paste from, and doing so removes clutter from the visual.

The value axis is probably created by an algorithm - hard to imagine someone deliberately placing axis labels  $262 million apart.

The gridlines are optional.

STEP 2: Intermediate

Simplify and re-organize the time axis labels; show the quarter and year structure. The years need not repeat.

Align the vocabulary on the chart. The legend mentions "inflows and outflows" while the chart title uses the words "buying and selling". Inflows is buying; outflows is selling.

STEP 3: Advanced

This type of data presents an interesting design challenge. Arguably the most important metric is the net purchases (or the net flow), i.e. inflows minus outflows. And yet, the chart form leaves this element in the gaps, visually.

The outflows are numerically opposite to inflows. The sign of the flow is encoded in the color scheme. An outflow still points upwards. This isn't a criticism, but rather a limitation of the chart form. If the red bars are made to point downwards to indicate negative flow, then the "net flow" is almost impossible to visually compute!

Putting the columns side by side allows the reader to visually compute the gap, but it is hard to visually compare gaps from quarter to quarter because each gap is hanging off a different baseline.

The following graphic solves this issue by focusing the chart on the net flows. The buying and selling are still plotted but are deliberately pushed to the side:

The structure of the data is such that the gray and pink sections are "symmetric" around the brown columns. A purist may consider removing one of these columns. In other words:

Here, the gray columns represent gross purchases while the brown columns display net purchases. The reader is then asked to infer the gross selling, which is the difference between the two column heights.

We are almost back to the original chart, except that the net buying is brought to the foreground while the gross selling is pushed to the background.

 

Elegant way to present a pair of charts

The Bloomberg team has come up with a few goodies lately. I was captivated by the following graphic about the ebb and flow of U.S. presidential candidates across recent campaigns. Link to the full presentation here.

The highlight is at the bottom of the page. This is an excerpt of the chart:

From top to bottom are the sequential presidential races. The far right vertical axis is the finish line. Going right to left is the time before the finish line. In 2008, for example, there are candidates who entered the race much earlier than typical.

This chart presents an aggregate view of the data. We get a sense of when most of the candidates enter the race, when most of them are knocked out, and also a glimpse of outliers. The general pattern across multiple elections is also clear. The design is a stacked area chart with the baseline in the middle, rather than the bottom, of the chart.

Sure, the chart can disappoint those readers who want details and precise numbers. It's not immediately apparent how many candidates were in the race at the height of 2008, nor who the candidates were.

The designer added a nice touch. By clicking on any of the stacks, it transforms into a bar chart, showing the extent of each candidate's participation in the race.

I wish this was a way to collapse the bar chart back to the stack. You can reload the page to start afresh.

***

This elegant design touch makes the user experience playful. It's also an elegant way to present what is essentially a panel of plots. Imagine the more traditional presentation of placing the stack and the bar chart side by side.

This design does not escape the trade-off between entertainment value and data integrity. Looking at the 2004 campaign, one should expect to see the blue stack halve in size around day 100 when Kerry became the last man standing. That moment is not marked in the stack. The stack can be interpreted as a smoothed version of the count of active candidates.

I suppose some may complain the stack misrepresents the data somewhat. I find it an attractive way of presenting the big-picture message to an audience that mostly spend less than a minute looking at the graphic.

Seeking simplicity in complex data: Bloomberg's dataviz on UK gender pay gap

Bloomberg featured a thought-provoking dataviz that illustrates the pay gap by gender in the U.K. The dataset underlying this effort is complex, and the designers did a good job simplifying the data for ease of comprehension.

U.K. companies are required to submit data on salaries and bonuses by gender, and by pay quartiles. The dataset is incomplete, since some companies are slow to report, and the analyst decided not to merge companies that changed names.

Companies are classified into industry groups. Readers who read Chapter 3 of Numbers Rule Your World (link) should ask whether these group differences are meaningful by themselves, without controlling for seniority, job titles, etc. The chapter features one method used by the educational testing industry to take a more nuanced analysis of group differences.

***

The Bloomberg visualization has two sections. In the top section, each company is represented by the percent difference between average female pay and average male pay. Then the companies within a given industry is shown in a histogram. The histograms provide a view of the disparity between companies within a given industry. The black line represents the relative proportion of companies in a given industry that have no gender pay gap but it’s the weight of the histogram on either side of the black line that carries the graphic’s message.

This is the histogram for arts, entertainment and recreation.

The spread within this industry is very wide, especially on the left side of the black line. A large proportion of these companies pay women less on average than men, and how much less is highly variable. There is one extreme positive value: Chelsea FC Foundation that pays the average female about 40% more than the average male.

This is the histogram for the public sector.

It is a much tighter distribution, meaning that the pay gaps vary less from organization to organization (this statement ignores the possibility that there are outliers not visible on this graphic). Again, the vast majority of entities in this sector pay women less than men on average.

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The second part of the visualization look at the quartile data. The employees of each company are divided into four equal-sized groups, based on their wages. Think of these groups as the Top 25% Earners, the Second 25%, etc. Within each group, the analyst looks at the proportion of women. If gender is independent of pay, then we should expect the proportions of women to be about the same for all four quartiles. (This analysis considers gender to be the only explainer for pay gaps. This is a problem I've called xyopia, that frames a complex multivariate issue as a bivariate problem involving one outcome and one explanatory variable. Chapter 3 of Numbers Rule Your World (link) discusses how statisticians approach this issue.)

On the right is the chart for the public sector. This is a pie chart used as a container. Every pie has four equal-sized slices representing the four quartiles of pay.

The female proportion is encoded in both the size and color of the pie slices. The size encoding is more precise while the color encoding has only 4 levels so it provides a “binned” summary view of the same data.

For the public sector, the lighter-colored slice shows the top 25% earners, and its light color means the proportion of women in the top 25% earners group is between 30 and 50 percent. As we move clockwise around the pie, the slices represent the 2nd, 3rd and bottom 25% earners, and women form 50 to 70 percent of each of those three quartiles.

To read this chart properly, the reader must first do one calculation. Women represent about 60% of the top 25% earners in the public sector. Is that good or bad? This depends on the overall representation of women in the public sector. If the sector employs 75 percent women overall, then the 60 percent does not look good but if it employs 40 percent women, then the same value of 60% tells us that the female employees are disproportionately found in the top 25% earners.

That means the reader must compare each value in the pie chart against the overall proportion of women, which is learned from the average of the four quartiles.

***

In the chart below, I make this relative comparison explicit. The overall proportion of women in each industry is shown using an open dot. Then the graphic displays two bars, one for the Top 25% earners, and one for the Bottom 25% earners. The bars show the gap between those quartiles and the overall female proportion. For the top earners, the size of the red bars shows the degree of under-representation of women while for the bottom earners, the size of the gray bars shows the degree of over-representation of women.

The net sum of the bar lengths is a plausible measure of gender inequality.

The industries are sorted from the ones employing fewer women (at the top) to the ones employing the most women (at the bottom). An alternative is to sort by total bar lengths. In the original Bloomberg chart - the small multiples of pie charts, the industries are sorted by the proportion of women in the bottom 25% pay quartile, from smallest to largest.

In making this dataviz, I elected to ignore the middle 50%. This is not a problem since any quartile above the average must be compensated by a different quartile below the average.

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The challenge of complex datasets is discovering simple ways to convey the underlying message. This usually requires quite a bit of upfront analytics, data transformation, and lots of sketching.

 

 

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:

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:

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:

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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:

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:

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.

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

 

Form and function: when academia takes on weed

I have a longer article on the sister blog about the research design of a study claiming 420 "cannabis" Day caused more road accident fatalities (link). The blog also has a discussion of the graphics used to present the analysis, which I'm excerpting here for dataviz fans.

The original chart looks like this:

The question being asked is whether April 20 is a special day when viewed against the backdrop of every day of the year. The answer is pretty clear. From this chart, the reader can see:

• that April 20 is part of the background "noise". It's not standing out from the pack;
• that there are other days like July 4, Labor Day, Christmas, etc. that stand out more than April 20

It doesn't even matter what the vertical axis is measuring. The visual elements did their job. 

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If you look closely, you can even assess the "magnitude" of the evidence, not just the "direction." While April 20 isn't special, it nonetheless is somewhat noteworthy. The vertical line associated with April 20 sits on the positive side of the range of possibilities, and appears to sit above most other days.

The chart form shown above is better at conveying the direction of the evidence than its strength. If the strength of the evidence is required, we use a different chart form.

I produced the following histogram, using the same data:

The histogram is produced by first locating the midpoints# of the vertical lines into buckets, and then counting the number of days that fall into each bucket.  (# Strictly speaking, I use the point estimates.)

The midpoints# are estimates of the fatal crash ratio, which is defined as the excess crash fatalities reported on the "analysis day" relative to the "reference days," which are situated one week before and one week after the analysis day. So April 20 is compared to April 13 and 27. Therefore, a ratio of 1 indicates no excess fatalities on the analysis day. And the further the ratio is above 1, the more special is the analysis day. 

If we were to pick a random day from the histogram above, we will likely land somewhere in the middle, which is to say, a day of the year in which no excess car crashes fatalities could be confirmed in the data.

As shown above, the ratio for April 20 (about 1.12)  is located on the right tail, and at roughly the 94th percentile, meaning that there were 6 percent of analysis days in which the ratios would have been more extreme. 

This is in line with our reading above, that April 20 is noteworthy but not extraordinary.

 

P.S. [4/27/2019] Replaced the first chart with a newer version from Harper's site. The newer version contains the point estimates inside the vertical lines, which are used to generate the histogram.

 

 

 

 

 

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. 

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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.