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. 

 

 

 

Visualizing the 80/20 rule, with the bar-density plot

Through Twitter, Danny H. submitted the following chart that shows a tiny 0.3 percent of Youtube creators generate almost 40 percent of all viewing on the platform. He asks for ideas about how to present lop-sided data that follow the "80/20" rule.

In the classic 80/20 rule, 20 percent of the units account for 80 percent of the data. The percentages vary, so long as the first number is small relative to the second. In the Youtube example, 0.3 percent is compared to 40 percent. The underlying reason for such lop-sidedness is the differential importance of the units. The top units are much more important than the bottom units, as measured by their contribution to the data.

I sense a bit of "loss aversion" on this chart (explained here). The designer color-coded the views data into blue, brown and gray but didn't have it in him/her to throw out the sub-categories, which slows down cognition and adds hardly to our understanding.

I like the chart title that explains what it is about.

Turning to the D corner of the Trifecta Checkup for a moment, I suspect that this chart only counts videos that have at least one play. (Zero-play videos do not show up in a play log.) For a site like Youtube, a large proportion of uploaded videos have no views and thus, many creators also have no views.

***

My initial reaction on Twitter is to use a mirrored bar chart, like this:

I ended up spending quite a bit of time exploring other concepts. In particular, I like to find an integrated way to present this information. Most charts, such as the mirrored bar chart, a Bumps chart (slopegraph), and Lorenz chart, keep the two series of percentages separate.

Also, the biggest bar (the gray bar showing 97% of all creators) highlights the least important Youtubers while the top creators ("super-creators") are cramped inside a slither of a bar, which is invisible in the original chart.

What I came up with is a bar-density plot, where I use density to encode the importance of creators, and bar lengths to encode the distribution of views.

Each bar is divided into pieces, with the number of pieces proportional to the number of creators in each segment. This has the happy result that the super-creators are represented by large (red) pieces while the least important creators by little (gray) pieces.

The embedded tessellation shows the structure of the data: the bottom third of the views are generated by a huge number of creators, producing a few views each - resulting in a high density. The top 38% of the views correspond to a small number of super-creators - appropriately shown by a bar of low density.

For those interested in technicalities, I embed a Voronoi diagram inside each bar, with randomly placed points. (There will be a companion post later this week with some more details, and R code.)

Here is what the bar-density plot looks like when the distribution is essentially uniform:

The density inside each bar is roughly the same, indicating that the creators are roughly equally important.

 

P.S.

1) The next post on the bar-density plot, with some experimental R code, will be available here.

2) Check out my first Linkedin "article" on this topic.

 

 

 

 

 

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.

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.

 

 

Transforming the data to fit the message

A short time ago, there were reports that some theme-park goers were not happy about the latest price hike by Disney. One of these report, from the Washington Post (link), showed a chart that was intended to convey how much Disney park prices have outpaced inflation. Here is the chart:

I had a lot of trouble processing this chart. The two lines are labeled "original price" and "in 2014 dollars". The lines show a gap back in the 1970s, which completely closes up by 2014. This gives the reader an impression that the problem has melted away - which is the opposite of the designer intended.

The economic concept being marshalled here is the time value of money, or inflation. The idea is that $3.50 in 1971 is equivalent to a much higher ticket price in "2014 dollars" because by virtue of inflation, putting that $3.50 in the bank in 1971 and holding till 2014 would make that sum "nominally" higher. In fact, according to the chart, the $3.50 would have become $20.46, an approx. 7-fold increase.

The gap thus represents the inflation factor. The gap melting away is a result of passing of time. The closer one is to the present, the less the effect of cumulative inflation. The story being visualized is that Disney prices are increasing quickly whether or not one takes inflation into account. Further, if inflation were to be considered, the rate of increase is lower (red line).

What about the alternative story - Disney's price increases are often much higher than inflation? We can take the nominal price increase, and divide it into two parts, one due to inflation (of the prior-period price), and the other in excess of inflation, which we will interpret as a Disney premium.

The following chart then illustrates this point of view:

Most increases are small, and stay close to the inflation rate. But once in a while, and especially in 2010s, the price increases have outpaced inflation by a lot.

Note: since 2013, Disney has introduced price tiers, starting with two and currently at four levels. In the above chart, I took the average of the available prices, making the assumption that all four levels are equally popular. The last number looks like a price decrease because there is a new tier called "Low". The data came from AllEars.net.

Visual Exploration of Unemployment Data

The charts on unemployment data I put up last week are best viewed as a collection. 

I have put them up on the (still in beta) JMP Public website. You can find the project here. 

I believe that if you make an account, you can grab the underlying dataset.

 

The ebb and flow of an effective dataviz showing the rise and fall of GE

A WSJ chart caught my eye the other day – I spotted someone looking at it in a coffee shop, and immediately got a hold of a copy. The chart plots the ebb and flow of GE’s revenues from the 1980s to the present.

What grabbed my attention? The less-used chart form, and the appealing but not too gaudy color scheme.

The chart presents a highly digestible view of the structure of GE’s revenues. We learn about GE’s major divisions, as well as how certain segments split from or merged with others over time. Major acquisitions and divestitures are also depicted; if these events are the main focus, the designer should find ways to make these moments stand out more.

An interesting design decision concerns the sequence of the divisions. One possible order is by increasing or decreasing importance, typically indicated by proportional revenues. This is complicated by the changing nature of the business over the decades. So financial services went from nothing to the largest division by far to almost disappearing.

The sequencing need not be data-driven; it can be design-constrained. The merging and splitting of business units are conveyed via linking arrows. Longer arrows are unsightly, and meshes of arrows are confusing.

On this chart, the long arrow pointing from the orange to the gray around 2004 feels out of place. What if the financial services block is moved to the right of the consumer block? That will significantly shorten the long arrow. It won’t create other entanglements as the media block is completely disjoint and there are no other arrows tying financial services to another division.

 

***

To improve readability, the bars are spaced out horizontally. The addition of whitespace distorts the proportionality. So, in 2001, the annotation states that financial services (orange) accounted for “about half of the revenues,” which is directly contradicted by the visual perception – readers find the orange bar to be clearly shorter than the total length of the other bars. This is a serious deficiency of the chart form but this chart conveys the "ebb and flow" very well.

NYT hits the trifecta with this market correction chart

Yesterday, in the front page of the Business section, the New York Times published a pair of charts that perfectly captures the story of the ongoing turbulence in the stock market.

Here is the first chart:

Most market observers are very concerned about the S&P entering "correction" territory, which the industry arbitrarily defines as a drop of 10% or more from a peak. This corresponds to the shortest line on the above chart.

The chart promotes a longer-term reflection on the recent turbulence, using two reference points: the index has returned to the level even with that at the start of 2018, and about 16 percent higher since the beginning of 2017.

This is all done tastefully in a clear, understandable graphic.

Then, in a bit of a rhetorical flourish, the bottom of the page makes another point:

When viewed back to a 10-year period, this chart shows that the S&P has exploded by 300% since 2009.

A connection is made between the two charts via the color of the lines, plus the simple, effective annotation "Chart above".

The second chart adds even more context, through vertical bands indicating previous corrections (drops of at least 10%). These moments are connected to the first graphic via the beige color. The extra material conveys the message that the market has survived multiple corrections during this long bull period.

Together, the pair of charts addresses a pressing current issue, and presents a direct, insightful answer in a simple, effective visual design, so it hits the Trifecta!

***

There are a couple of interesting challenges related to connecting plots within a multiple-plot framework.

While the beige color connects the concept of "market correction" in the top and bottom charts, it can also be a source of confusion. The orientation and the visual interpretation of those bands differ. The first chart uses one horizontal band while the chart below shows multiple vertical bands. In the first chart, the horizontal band refers to a definition of correction while in the second chart, the vertical bands indicate experienced corrections.

Is there a solution in which the bands have the same orientation and same meaning?

***

These graphs solve a visual problem concerning the visualization of growth over time. Growth rates are anchored to some starting time. A ten-percent reduction means nothing unless you are told ten-percent of what.

Using different starting times as reference points, one gets different values of growth rates. With highly variable series of data like stock prices, picking starting times even a day apart can lead to vastly different growth rates.

The designer here picked several obvious reference times, and superimposes multiple lines on the same plotting canvass. Instead of having four lines on one chart, we have three lines on one, and four lines on the other. This limits the number of messages per chart, which speeds up cognition.

The first chart depicts this visual challenge well. Look at the start of 2018. This second line appears as if you can just reset the start point to 0, and drag the remaining portion of the line down. The part of the top line (to the right of Jan 2018) looks just like the second line that starts at Jan 2018.

However, a closer look reveals that the shape may be the same but the magnitude isn't. There is a subtle re-scaling in addition to the re-set to zero.

The same thing happens at the starting moment of the third line. You can't just drag the portion of the first or second line down - there is also a needed re-scaling.

The merry-go-round of investment bankers

Here is the start of my blog post about the chart I teased the other day:

 

Today's post deals with the following chart, which appeared recently at Business Insider (hat tip: my sister).

It's immediately obvious that this chart requires a heroic effort to decipher. The question shown in the chart title "How many senior investment bankers left their firms?" is the easiest to answer, as the designer places the number of exits in the central circle of each plot relating to a top-tier investment bank (aka "featured bank"). Note that the visual design plays no role in delivering the message, as readers just scan the data from those circles.

Anyone persistent enough to explore the rest of the chart will eventually discover these features...

***

The entire post including an alternative view of the dataset is a guest blog at the JMP Blog here. This is a situation in which plotting everything will make an unreadable chart, and the designer has to think hard about what s/he is really trying to accomplish.

Report from Data Visualization Meetup

On Monday, Principal Analytics Prep sponsored the Data Visualization Meetup, organized by the indefatigable Naomi Robbins. The keynote speaker is NYU professor Kristen Sosulski, who just published a book titled “Data Visualization Made Simple” (link).

At the Meetup, we announced a Part-Time Immersive Program. This allows the completion of the Certified Data Specialist program in three levels on a more relaxed, evening schedule. Level 1 will run two nights a week for 12 weeks, starting Spring 2019. For more details, contact us here.

***

Kristen, a professor in the Stern School, has an interesting take on the data visualization function – placing it within the larger enterprise. In the first part of her talk, she presents a number of real-world case examples of how data analysts used data visualization to create impact within an organization.

The end goal in each of these projects is a “business insight” that is delivered to decision-makers with the primary goal of persuasion – something I also emphasize in my own seminars. It’s not that data visualization isn’t used for analysis, exploration, and story-telling (see postscript), and so on but at the tail end of the process, the need to persuade becomes paramount.

***

For example, the graphic on the cover of her book is from a project undertaken by Jet.com, the online retailer purchased by Walmart. The managers are interested in the patterns of purchasing of the customers, and generally views products as “consumables” or “durables,” the latter have lower purchasing frequencies. The nodes in the network graph are colored accordingly. Through the links between these nodes, the analyst concluded that certain products (an example given was batteries) are considered durables but have purchasing patterns that appear more like consumables.

Kristen’s message is how the data turned into a business insight (the “story”) which impressed the managers enough so that they took action by adjusting orders and inventories.

Kristen described other examples such as the use of salary data to place employees into bands, or the use of predictive models to predict which partners in a venture-capital firm will bring in more investment. Many of these examples make me believe that a course of causal reasoning should be required for all data analysts.

***

The second half of Kristen’s talk addresses how to raise the profile of data visualization within an enterprise. This is a clearly needed discussion. More and more industry jobs are created that are specific to data visualization so these new teams must establish themselves within the corporate culture. Kristen recommends a five-step process, starting with establishing a data practice and ending with measuring one’s impact.

In answering my question about evangelizing new visualization formats to replace inferior existing chart designs, she emphasizes the need to involve stakeholders early in the process. Don't surprise them with something novel during a meeting.

We were pleased that people braved the adverse weather to attend Kristen’s talk, and good pizza was served at the end of the evening.

 

P.S.

The word “story-telling” seems to have gone from hero to villain lately. Some commenters are thinking the word “story” implies made-up fiction, and thus oppose its use. A related complaint concerns the “subjectivity” of stories. Once you realize that most of our data sources are observational in nature, you will soon discover that causal reasoning entails the selection of the most plausible story among many. Statisticians and others have come up with causal models, which are sets of equations used to describe relationships between data, but all of these rely on causal assumptions. In essence, they are structured ways to select the most plausible story. It’s dangerous to see these models as “objective.”