Junk Charts

Too much of a good thing

Several of us discussed this data visualization over twitter last week. The dataviz by Aero Data Lab is called “A Bird’s Eye View of Pharmaceutical Research and Development”. There is a separate discussion on STAT News.

Here is the top section of the chart:

We faced a number of hurdles in understanding this chart as there is so much going on. The size of the shapes is perhaps the first thing readers notice, followed by where the shapes are located along the horizontal (time) axis. After that, readers may see the color of the shapes, and finally, the different shapes (circles, triangles,...).

It would help to have a legend explaining the sizes, shapes and colors. These were explained within the text. The size encodes the number of test subjects in the clinical trials. The color encodes pharmaceutical companies, of which the graphic focuses on 10 major ones. Circles represent completed trials, crosses inside circles represent terminated trials, triangles represent trials that are still active and recruiting, and squares for other statuses.

The vertical axis presents another challenge. It shows the disease conditions being investigated. As a lay-person, I cannot comprehend the logic of the order. With over 800 conditions, it became impossible to find a particular condition. The search function on my browser skipped over the entire graphic. I believe the order is based on some established taxonomy.

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In creating the alternative shown below, I stayed close to the original intent of the dataviz, retaining all the dimensions of the dataset. Instead of the fancy dot plot, I used an enhanced data table. The encoding methods reflect what I’d like my readers to notice first. The color shading reflects the size of each clinical trial. The pharmaceutical companies are represented by their first initials. The status of the trial is shown by a dot, a cross or a square.

Here is a sketch of this concept showing just the top 10 rows.

Certain conditions attracted much more investment. Certain pharmas are placing bets on cures for certain conditions. For example, Novartis is heavily into research on Meningnitis, meningococcal while GSK has spent quite a bit on researching "bacterial infections."

It's hot even in Alaska

A twitter user pointed to the following chart, which shows that Alaska has experienced extreme heat this summer, with the July statewide average temperature shattering the previous record;

This column chart is clear in its primary message: the red column shows that the average temperature this year is quite a bit higher than the next highest temperature, recorded in July 2004. The error bar is useful for statistically-literate people - the uncertainty is (presumably) due to measurement errors. (If a similar error bar is drawn for the July 2004 column, these bars probably overlap a bit.)

The chart violates one of the rules of making column charts - the vertical axis is truncated at 53F, thus the heights or areas of the columns shouldn't be compared. This violation was recently nominated by two dataviz bloggers when asked about "bad charts" (see here).

Now look at the horizontal axis. These are the years of the top 20 temperature records, ordered from highest to lowest. The months are almost always July except for the year 2004 when all three summer months entered the top 20. I find it hard to make sense of these dates when they are jumping around.

In the following version, I plotted the 20 temperatures on a chronological axis. Color is used to divide the 20 data points into four groups. The chart is meant to be read top to bottom. 

 

Clarifying comparisons in censored cohort data: UK housing affordability

If you're pondering over the following chart for five minutes or more, don't be ashamed. I took longer than that.

The chart accompanied a Financial Times article about inter-generational fairness in the U.K. To cut to the chase, a recently released study found that younger generations are spending substantially higher proportions of their incomes to pay for housing costs. The FT article is here (behind paywall). FT actually slightly modified the original chart, which I pulled from the Home Affront report by the Intergenerational Commission.

One stumbling block is to figure out what is plotted on the horizontal axis. The label "Age" has gone missing. Even though I am familiar with cohort analysis (here, generational analysis), it took effort to understand why the lines are not uniformly growing in lengths. Typically, the older generation is observed for a longer period of time, and thus should have a longer line.

In particular, the orange line, representing people born before 1895 only shows up for a five-year range, from ages 70 to 75. This was confusing because surely these people have lived through ages 20 to 70. I'm assuming the "left censoring" (missing data on the left side) is because of non-existence of old records.

The dataset is also right-censored (missing data on the right side). This occurs with the younger generations (the top three lines) because those cohorts have not yet reached certain ages. The interpretation is further complicated by the range of birth years in each cohort but let me not go there.

TL;DR ... each line represents a generation of Britons, defined by their birth years. The generations are compared by how much of their incomes did they spend on housing costs. The twist is that we control for age, meaning that we compare these generations at the same age (i.e. at each life stage).

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Here is my version of the same chart:

Here are some of the key edits:

• Vertical blocks are introduced to break up the analysis by life stage. These guide readers to compare the lines vertically i.e. across generations
• The generations are explicitly described as cohorts by birth years
• The labels for the generations are placed next to the lines
• Gridlines are pushed to the back
• The age axis is explicitly labeled
• Age labels are thinned
• A hierarchy on colors
• The line segments with incomplete records are dimmed

The harmful effect of colors can be seen below. This chart is the same as the one above, except for retaining the colors of the original chart:

 

 

Clearing a forest of labels

This chart by the Financial Times has a strong message, and I like a lot about it:

The countries are by and large aligned along a diagonal, with the poorer countries growing strongly between 2007-2019 while the richer countries suffered negative growth.

A small issue with the chart is the thick forest of text - redundant text. The sub-title, the axis titles, the quadrant labels, and the left-right-half labels all repeat the same things. In the following chart, I simplify the text:

Typically, I don't put axis titles as a sub-header (or, header of the graphic) but as this may be part of the FT style, I respected it.

Measles babies

Mona Chalabi has made this remarkable graphic to illustrate the effect of the anti-vaccine movement on measles cases in the U.S.: (link)

As a form of agitprop, the graphic seizes upon the fear engendered by the defacing red rash of the disease. And it's very effective in articulating its social message.

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I wasn't able to find the data except for a specific year or two. So, this post is more inspired by the graphic than a direct response to it.

I think the left-side legend should say "1 case of measles in someone who was not vaccinated" (as opposed to 1 case of measles in aggregate).

The chart encodes the data in the density of the red dots. What does the density of the red dots signify? There are two possibilities: case counts or case rates.

2013 is a year in which I could find data. In 2013, the U.S. saw 187 cases of measles, only 4 of them in someone who was vaccinated. In other words, there are 49 times as many measles cases among the unvaccinated as the vaccinated.

But note that about 90 percent of the population (using 13-17 year olds as a proxy) are vaccinated. The chance of getting measles in the unvaccinated is 0.8 per million, compared to 0.002 per million in the vaccinated - 422 times higher.

The following chart shows the relative appearance of the dot densities. The bottom row which compares the relative chance of getting measles is the more appropriate metric, and it looks much worse.

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Mona's instagram has many other provocative graphics.

 

Say it thrice: a nice example of layering and story-telling

I enjoyed the New York Times's data viz showing how actively the Democratic candidates were criss-crossing the nation in the month of March (link).

It is a great example of layering the presentation, starting with an eye-catching map at the most aggregate level. The designers looped through the same dataset three times.

This compact display packs quite a lot. We can easily identify which were the most popular states; and which candidate visited which states the most.

I noticed how they handled the legend. There is no explicit legend. The candidate names are spread around the map. The size legend is also missing, replaced by a short sentence explaining that size encodes the number of cities visited within the state. For a chart like this, having a precise size legend isn't that useful.

The next section presents the same data in a small-multiples layout. The heads are replaced by dots.

This allows more precise comparison of one candidate to another, and one location to another.

This display has one shortcoming. If you compare the left two maps above, those for Amy Klobuchar and Beto O'Rourke, it looks like they have visited roughly similar number of cities when in fact Beto went to 42 compared to 25. Reducing the size of the dots might work.

Then, in the third visualization of the same data, the time dimension is emphasized. Lines are used to animate the daily movements of the candidates, one by one.

Click here to see the animation.

When repetition is done right, it doesn't feel like repetition.

 

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.

 

 

 

 

 

Visually exploring the relationship between college applicants and enrollment

In a previous post, we learned that top U.S. colleges have become even more selective over the last 15 years, driven by a doubling of the number of applicants while class sizes have nudged up by just 10 to 20 percent. 

The top 25 most selective colleges are included in the first group. Between 2002 and 2017, their average rate of admission dropped from about 20% to about 10%, almost entirely explained by applicants per student doubling from 10 to almost 20. A similar upward movement in selectivity is found in the first four groups of colleges, which on average accept at least half of their applicants.

Most high school graduates however are not enrolling in colleges in the first four groups. Actually, the majority of college enrollment belongs to the bottom two groups of colleges. These groups also attracted twice as many applicants in 2017 relative to 2002 but the selectivity did not change. They accepted 75% to 80% of applicants in 2002, as they did in 2017.

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In this post, we look at a different view of the same data. The following charts focus on the growth rates, indexed to 2002. 

To my surprise, the number of college-age Americans  grew by about 10% initially but by 2017 has dropped back to the level of 2002. Meanwhile, the number of applications to the colleges continues to climb across all eight groups of colleges.

The jump in applications made selectivity surge at the most selective colleges but at the less selective colleges, where the vast majority of students enroll, admission rate stayed put because they gave out many more offers as applications mounted. As the Pew headline asserted, "the rich gets richer."

Enrollment has not kept up. Class sizes expanded about 10 to 30 percent in those 15 years, lagging way behind applications and admissions.

How do we explain the incremental applications?

• Applicants increasing the number of schools they apply to
• The untapped market: applicants who in the past would not have applied to college
• Non-U.S. applicants: this is part of the untapped market, but much larger

Light entertainment: the crack pie that escaped and then resurfaced on TV

A famous restaurant bowed to pressure recently to rename its famous item, previously known as the "crack pie" (link).

The crack pie that escaped the Milk Bar showed up here:

Thanks to twitter friend DorsaAmir for alerting us to this chart.

An exercise in decluttering

My friend Xan found the following chart by Pew hard to understand. Why is the chart so taxing to look at? 

It's packing too much.

I first notice the shaded areas. Shading usually signifies "look here". On this chart, the shading is highlighting the least important part of the data. Since the top line shows applicants and the bottom line admitted students, the shaded gap displays the rejections.

The numbers printed on the chart are growth rates but they confusingly do not sync with the slopes of the lines because the vertical axis plots absolute numbers, not rates. 

The vertical axis presents the total number of applicants, and the total number of admitted students, in each "bucket" of colleges, grouped by their admission rate in 2017. On the right, I drew in two lines, both growth rates of 100%, from 500K to 1 million, and from 1 to 2 million. The slopes are not the same even though the rates of growth are.

Therefore, the growth rates printed on the chart must be read as extraneous data unrelated to other parts of the chart. Attempts to connect those rates to the slopes of the corresponding lines are frustrated.

Another lurking factor is the unequal sizes of the buckets of colleges. There are fewer than 10 colleges in the most selective bucket, and over 300 colleges in the largest bucket. We are unable to interpret properly the total number of applicants (or admissions). The quantity of applications in a bucket depends not just on the popularity of the colleges but also the number of colleges in each bucket.

The solution isn't to resize the buckets but to select a more appropriate metric: the number of applicants per enrolled student. The most selective colleges are attracting about 20 applicants per enrolled student while the least selective colleges (those that accept almost everyone) are getting 4 applicants per enrolled student, in 2017.

As the following chart shows, the number of applicants has doubled across the board in 15 years. This raises an intriguing question: why would a college that accepts pretty much all applicants need more applicants than enrolled students?

Depending on whether you are a school administrator or a student, a virtuous (or vicious) cycle has been realized. For the top four most selective groups of colleges, they have been able to progressively attract more applicants. Since class size did not expand appreciably, more applicants result in ever-lower admit rate. Lower admit rate reduces the chance of getting admitted, which causes prospective students to apply to even more colleges, which further suppresses admit rate.