Junk Charts

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. 

 

 

 

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.

 

 

 

 

This chart advises webpages to add more words

A reader sent me the following chart. In addition to the graphical glitch, I was asked about the study's methodology.

I was able to trace the study back to this page. The study uses a line chart instead of the bar chart with axis not starting at zero. The line shows that web pages ranked higher by Google on the first page tend to have more words, i.e. longer content may help with Google ranking.

On the bar chart, Position 1 is more than 6 times as big as Position 10, if one compares the bar areas. But it's really only 20% larger in the data.

In this case, even the line chart is misleading. If we extend the Google Position to 20, the line would quickly dip below the horizontal axis if the same trend applies.

The line chart includes too much grid, one of Tufte's favorite complaints. The Google position is an integer and yet the chart's gridlines imply that 0.5 rank is possible.

Any chart of this data should supply information about the variance around these average word counts. Would like to see a side-by-side box plot, for example.

Another piece of context is the word counts for results on the second or third pages of Google results. Where are the short pages?

***

Turning to methodology, we learn that the research team analyzed 1 million pages of Google search results, and they also "removed outliers from our data (pages that contained fewer than 51 words and more than 9999 words)."

When you read a line like this, you have to ask some questions:

How do they define "outlier"? Why do they choose 51 and 9,999 as the cut-offs?

What proportion of the data was removed at either end of the distribution?

If these proportions are small, then the outliers are not going to affect that average word count by much, and thus there is no point to their removal. If they are large, we'd like to see what impact removing them might have.

In any case, the median is a better number to use here, or just show us the distribution, not just the average number.

It could well be true that Google's algorithm favors longer content, but we need to see more of the data to judge.

 

 

GDPR: justice for data visualization

Reader LG found the following chart, tweeted by @EU_Justice.

This chart is a part of a larger infographic, which is found here.

The following points out a few issues with this effort:

The time axis is quite embarrassing. The first six months or so are squeezed into less than half the axis while the distance between Nov and Dec is not the same as that between Dec and Jan. So the slope of each line segment is what the designer wants it to be!

The straight edges of the area chart imply that there were only three data points, with straight lines drawn between each measurement. Sadly, the month labels are not aligned to the data on the line.

Lastly, the dots between May and November intended to facilitate reading this chart backfire. There are 6 dots dividing the May-Nov segment when there should only be five.

***

The chart looks like this when not distorted:

 

Labels, scales, controls, aggregation all in play

JB @barclaysdevries sent me the following BBC production over Twitter.

He was not amused.

This chart pushes a number of my hot buttons.

First, I like to assume that readers don't need to be taught that 2007 and 2018 are examples of "Year".

Second, starting an area chart away from zero is equally as bad as starting a bar chart not at zero! The area is distorted and does not reflect the relative values of the data.

Third, I suspect the 2007 high point is a local peak, which they chose in order to forward a sky-is-falling narrative related to China's growth.

So I went to a search engine and looked up China's growth rate, and it helpfully automatically generated the following chart:

Just wow! This chart does a number of things right.

First, it confirms my hunch above. 2007 is a clear local peak and it is concerning that the designer chose that as a starting point.

Second, this chart understands that the zero-growth line has special meaning.

Third, there are more year labels.

Fourth, and very importantly, the chart offers two "controls". We can look at China's growth relative to India's and relative to the U.S.'s. Those two other lines bring context.

JB's biggest complaint is that the downward-sloping line confuses the issue, which is that slowing growth is still growth. The following chart conveys a completely different message but the underlying raw data are the same:

 

Message-first visualization

Sneaky Pete via Twitter sent me the following chart, asking for guidance:

This is a pretty standard dataset, frequently used in industry. It shows a breakdown of a company's profit by business unit, here classified by "state". The profit projection for the next year is measured on both absolute dollar terms and year-on-year growth.

Since those two metrics have completely different scales, in both magnitude and unit, it is common to use dual axes. In the case of the Economist, they don't use dual axes; they usually just print the second data series in its own column.

***

I first recommended looking at the scatter plot to see if there are any bivariate patterns. In this case, not much insights are provided via the scatter.

From there, I looked at the data again, and ended up with the following pair of bumps charts (slopegraphs):

A key principle I used is message-first. That is to say, the designer should figure out what message s/he wants to convey via the visualization, and then design the visualization to convey that message.

A second key observation is that the business units are divided into two groups, the two large states (A and F) and the small states (B to E). This is a Pareto principle that very often applies to real-world businesses, i.e. a small number of entities contribute most of the revenues (or profits). It is very likely that these businesses are structured to serve the large and small states differently, and so the separation onto two charts mirrors the internal structure.

Then, within each chart, there is a message. For the large states, it looks like state F is projected to overtake state A next year. That is a big deal because we're talking about the largest unit in the entire company.

For the small states, the standout is state B, decidedly more rosy than the other three small states with similar projected growth rates.

Note also I chose to highlight the actual dollar profits, letting the growth rates be implied in the slopes. Usually, executives are much more concerned about hitting a dollar value than a growth rate target. But that, of course, depends on your management's preference.

 

Finding simple ways to explain complicated data and concepts, using some Pew data

A reader submitted the following chart from Pew Research for discussion.

The reader complained that this chart was difficult to comprehend. What are some of the reasons?

The use of color is superfluous. Each line is a "cohort" of people being tracked over time. Each cohort is given its own color or hue. But the color or hue does not signify much.

The dotted lines. This design element requires a footnote to explain. The reader learns that some of the numbers on the chart are projections because those numbers pertain to time well into the future. The chart was published in 2014, using historical data so any numbers dated 2014 or after (and even some data before 2014) will be projections. The data are in fact encoded in the dots, not the slopes. Look at the cohort that has one solid line segment and one dotted line segment - it's unclear which of those three data points are projections, and which are experienced.

The focus on within-cohort trends. The line segments indicate the desire of the designer to emphasize trends within each cohort. However, it's not clear what the underlying message is. It may be that more and more people are not getting married (i.e. fewer people are getting married). That trend affects each of the three age groups - and it's easier to paint that message by focusing on between-cohort trends.

***
Here is a chart that emphasizes the between-cohort trends.

A key decision is to not mix oil and water. The within-cohort analysis is presented in its own chart, next to the between-cohort analysis. It turns out that some of the gap between cohorts can be explained by people deferring marriage to later in life. The steep line on the right indicates that a bigger proportion of people now gets married between 35 and 44 than in previous cohorts.

I experimented a bit with the axes here. Several pie charts are used in lieu of axis labels. I also plotted a dual axis with the proportion of unmarried on the one side, and the corresponding proportion of married on the other side.

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.)

Headless people invade London, chart claims

Some 10 days ago, Mike B. on Twitter forwarded me this chart from Time Out:

Mike added: "Wow, decapitations in London have really gone up!"

A closer look at the chart reveals more problems.

The axis labels are in the wrong places. It appears that the second dot represents 1940 and the second-last dot represents 2020. There are 12 dots between those two labels, corresponding to three evenly-spaced labels. This works out to be  6.154 years between each dot, and 20.0 years between labels. The labels actually do not fall on top of the dots but between them! We have to conclude that the axis labels were independently applied onto the chart.

I found another chart of London's population growth from here.

Superimposing the two charts:

The lowest point seemed to be around 1990-ish in the second chart but in the Time Out chart, the reader most likely assumes it occurred around 2000.

***

What else? The Time Out chart has no vertical axis, and therefore, the chart fails to deliver any data to the reader: how many people actually live in London? This style - chart with no vertical axis - has been made popular by Google (Google Trends, etc.). 

Further, one should differentiate between historical data and projections. It seems like everything on the right side that exists above the previous peak in 1940 is projected.

***

Just for giggles, I made this:

 

 

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.