This Wimbledon beauty will be ageless

Ft_wimbledonage


This Financial Times chart paints the picture of the emerging trend in Wimbledon men’s tennis: the average age of players has been rising, and hits 30 years old for the first time ever in 2019.

The chart works brilliantly. Let's look at the design decisions that contributed to its success.

The chart contains a good amount of data and the presentation is carefully layered, with the layers nicely tied to some visual cues.

Readers are drawn immediately to the average line, which conveys the key statistical finding. The blue dot  reinforces the key message, aided by the dotted line drawn at 30 years old. The single data label that shows a number also highlights the message.

Next, readers may notice the large font that is applied to selected players. This device draws attention to the human stories behind the dry data. Knowledgable fans may recall fondly when Borg, Becker and Chang burst onto the scene as teenagers.

 

Then, readers may pick up on the ticker-tape data that display the spread of ages of Wimbledon players in any given year. There is some shading involved, not clearly explained, but we surmise that it illustrates the range of ages of most of the contestants. In a sense, the range of probable ages and the average age tell the same story. The current trend of rising ages began around 2005.

 

Finally, a key data processing decision is disclosed in chart header and sub-header. The chart only plots the players who reached the fourth round (16). Like most decisions involved in data analysis, this choice has both desirable and undesirable effects. I like it because it thins out the data. The chart would have appeared more cluttered otherwise, in a negative way.

The removal of players eliminated in the early rounds limits the conclusion that one can draw from the chart. We are tempted to generalize the finding, saying that the average men’s player has increased in age – that was what I said in the first paragraph. Thinking about that for a second, I am not so sure the general statement is valid.

The overall field might have gone younger or not grown older, even as the older players assert their presence in the tournament. (This article provides side evidence that the conjecture might be true: the author looked at the average age of players in the top 100 ATP ranking versus top 1000, and learned that the average age of the top 1000 has barely shifted while the top 100 players have definitely grown older.)

So kudos to these reporters for writing a careful headline that stays true to the analysis.

I also found this video at FT that discussed the chart.

***

This chart about Wimbledon players hits the Trifecta. It has an interesting – to some, surprising – message (Q). It demonstrates thoughtful processing and analysis of the data (D). And the visual design fits well with its intended message (V). (For a comprehensive guide to the Trifecta Checkup, see here.)


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:

Counselors_Figure1small

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.

Trifectacheckup_junkcharts_imageThe 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:

Redo_junkcharts_amstat_feline

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.

Cetera_amd_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.

Redo_amdinstitution_1

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.

Redo_amdinstitution_2

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:

Redo_amd_1

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:

Redo_amd_2

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.

 


Pay levels in the U.S.

The Wall Street Journal published a graphic showing the median pay levels at "most" public companies in the U.S. here.

Wsj_mediancompanypay

People who attended my dataviz seminar might recognize the similarity with the graphic showing internet download speeds by different broadband technologies. It's a clean, clear way of showing multiple comparisons on the same chart.

You can see the distribution of pay levels of companies within each industry grouping, and the vertical lines showing the sector medians allow comparison across sectors. The median pay levels are quite similar with the energy sector leaning higher, and consumer sector leaning lower.

The consumer sector is extremely heavy on the low side of the pay range. Companies like Universal, Abercrombie, Skechers, Mattel, Gap, etc. all pay at least half their employees less than $6,000. The data is sourced to MyLogIQ. I have no knowledge of how reliable or valid the data are. It's curious to me that Dunkin Brands showed a median of $110K while Starbucks showed $13K.

Wsj_medianpay_dunkinstarbucks

***

I like the interactive features.

The window control lets the user zoom in to different parts of the pay range. This is necessary because of the extremely high salaries. The control doubles as a presentation of the overall distribution of median salaries.

The text box can be used to add data labels to specific companies.

***

See previous discussion of WSJ Graphics.

 


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:

Atlantic_sfrealestatepie

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:

Redo_atlanticsfrealestate_sufficiency

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:

Junkcharts_redo_atlanticsfrealestatebar

***

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:

Redo_atlanticsfrealestate_labeling_1

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:

Redo_atlanticsfrealestate_labeling_3

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.

Redo_atlanticsfrealestate_labeling_2

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

 


The French takes back cinema but can you see it?

I like independent cinema, and here are three French films that come to mind as I write this post: Delicatessen, The Class (Entre les murs), and 8 Women (8 femmes). 

The French people are taking back cinema. Even though they purchased more tickets to U.S. movies than French movies, the gap has been narrowing in the last two decades. How do I know? It's the subject of this infographic

DataCinema

How do I know? That's not easy to say, given how complicated this infographic is. Here is a zoomed-in view of the top of the chart:

Datacinema_top

 

You've got the slice of orange, which doubles as the imagery of a film roll. The chart uses five legend items to explain the two layers of data. The solid donut chart presents the mix of ticket sales by country of origin, comparing U.S. movies, French movies, and "others". Then, there are two thin arcs showing the mix of movies by country of origin. 

The donut chart has an usual feature. Typically, the data are coded in the angles at the donut's center. Here, the data are coded twice: once at the center, and again in the width of the ring. This is a self-defeating feature because it draws even more attention to the area of the donut slices except that the areas are highly distorted. If the ratios of the areas are accurate when all three pieces have the same width, then varying those widths causes the ratios to shift from the correct ones!

The best thing about this chart is found in the little blue star, which adds context to the statistics. The 61% number is unusually high, which demands an explanation. The designer tells us it's due to the popularity of The Lion King.

***

The one donut is for the year 1994. The infographic actually shows an entire time series from 1994 to 2014.

The design is most unusual. The years 1994, 1999, 2004, 2009, 2014 receive special attention. The in-between years are split into two pairs, shrunk, and placed alternately to the right and left of the highlighted years. So your eyes are asked to zig-zag down the page in order to understand the trend. 

To see the change of U.S. movie ticket sales over time, you have to estimate the sizes of the red-orange donut slices from one pie chart to another. 

Here is an alternative visual design that brings out the two messages in this data: that French movie-goers are increasingly preferring French movies, and that U.S. movies no longer account for the majority of ticket sales.

Redo_junkcharts_frenchmovies

A long-term linear trend exists for both U.S. and French ticket sales. The "outlier" values are highlighted and explained by the blockbuster that drove them.

 

P.S.

1. You can register for the free seminar in Lyon here. To register for live streaming, go here.
2. Thanks Carla Paquet at JMP for help translating from French.


Graphical advice for conference presenters

I've attended a number of talks in the last couple of days at the Joint Statistical Meetings. I'd like to offer some advice to presenters using graphics in their presentations.

Here is an example of the style of graphics that are being presented. (Note: I deliberately picked an example from a Google image search - this graphic was not used in a presentation but is representative of those I've seen.)

Example_presentation_graphic

Here are some tips to make your graphic much more impactful:

  • Use much larger font sizes. Typically, the same graphic published in a journal is used in the presentation. Other than the people sitting in the front row, no one can see any of the text, which means no one can understand anything. Most of us realize that for the bullet points on the slides, you have to pick a large font, say 20 points. The same goes for any labels or annotation on your graphics!
  • Use much thicker lines, larger dots, etc. Similar to the above, if you'd like people in the second to the last rows to be able to see your chart, you must enlarge everything. (For R users, cex comes in handy.)
  • Put a lot of text on the graphic itself. The graphic shown above has words but it lacks any context. In many of these presentations, the audience are statisticians, many of whom work in different industries or disciplines so we don't know what OpN, LIN, LIC mean. You may have explained this five slides prior but it's hard to expect the audience to remember. Why not just spell that out. Kendall's tau may be known to some in the audience but we still don't know - just based on what's on this chart - what correlation is being assessed. Any other text that helps explain what's on the chart should be added.
  • Add an informative title. These presentations are only 20 minutes long, and you'll spend maybe one minute explaining the graphic to someone who hasn't read the paper. You should spell out what is the message of your graphic - then we can look at the evidence to see how you drew that conclusion. In this example, it seems like there is a story around Flowering.
  • Avoid complex graphics. In a few occasions, the presenters show a grid of charts. These work well in a journal paper when we have time to figure out the layout. It's hard to grasp the message plus figure out how to read the chart all in a matter of a minute or so! Just like we recommend usually one message per slide, you should stick to one message per graphic used in an oral presentation.

The larger lesson is that the chart that is perfect for publication in a journal is less than perfect for an oral presentation.

 

PS. Please see here for an example of how one can remake the above chart for use in a conference presentation.


Two good charts can use better titles

NPR has this chart, which I like:

Npr_votersgunpolicy

It's a small multiples of bumps charts. Nice, clear labels. No unnecessary things like axis labels. Intuitive organization by Major Factor, Minor Factor, and Not a Factor.

Above all, the data convey a strong, surprising, message - despite many high-profile gun violence incidents this year, some Democratic voters are actually much less likely to see guns as a "major factor" in deciding their vote!

Of course, the overall importance of gun policy is down but the story of the chart is really about the collapse on the Democratic side, in a matter of two months.

The one missing thing about this chart is a nice, informative title: In two months, gun policy went from a major to a minor issue for some Democratic voters.

***

 I am impressed by this Financial Times effort:

Ft_millennialunemploy

The key here is the analysis. Most lazy analyses compare millennials to other generations but at current ages but this analyst looked at each generation at the same age range of 18 to 33 (i.e. controlling for age).

Again, the data convey a strong message - millennials have significantly higher un(der)employment than previous generations at their age range. Similar to the NPR chart above, the overall story is not nearly as interesting as the specific story - it is the pink area ("not in labour force") that is driving this trend.

Specifically, millennial unemployment rate is high because the proportion of people classified as "not in labour force" has doubled in 2014, compared to all previous generations depicted here. I really like this chart because it lays waste to a prevailing theory spread around by reputable economists - that somehow after the Great Recession, demographics trends are causing the explosion in people classified as "not in labor force". These people are nobodies when it comes to computing the unemployment rate. They literally do not count! There is simply no reason why someone just graduated from college should not be in the labour force by choice. (Dean Baker has a discussion of the theory that people not wanting to work is a long term trend.)

The legend would be better placed to the right of the columns, rather than the top.

Again, this chart benefits from a stronger headline: BLS Finds Millennials are twice as likely as previous generations to have dropped out of the labour force.

 

 

 

 


Fantastic visual, but the Google data need some pre-processing

Another entry in the Google Newslab data visualization project that caught my eye is the "How to Fix It" project, illustrating search queries across the world that asks "how." The project web page is here.

The centerpiece of the project is an interactive graphic showing queries related to how to fix home appliances. Here is what it looks like in France (It's always instructive to think about how they would count "France" queries. Is it queries from google.fr? queries written in French? queries from an IP address in France? A combination of the above?)

Howtofixit_france_appliances

I particularly appreciate the lack of labels. When we see the pictures, we don't need to be told this is a window and that is a door. The search data concern the relative sizes of the appliances. The red dotted lines show the relative popularity of searches for the respective appliances in aggregate.

By comparison, the Russian picture looks very different:

Howtofixit_russia_appliances

Are the Russians more sensible? Their searches are far and away about the washing machine, which is the most complicated piece of equipment on the graphic.

At the bottom of the page, the project looks at other queries, such as those related to cooking. I find it fascinating to learn what people need help making:

Howtofixit_world_cooking

I have to confess that I searched for "how to make soft boiled eggs". That led me to a lot of different webpages, mostly created for people who search for how to make a soft boiled egg. All of them contain lots of advertising, and the answer boils down to cook it for 6 minutes.

***

The Russia versus France comparison brings out a perplexing problem with the "Data" in this visualization. For competitive reasons, Google does not provide data on search volume. The so-called Search Index is what is being depicted. The Search Index uses the top-ranked item as the reference point (100). In the Russian diagram, the washing machine has Search Index of 100 and everything else pales in comparison.

In the France example, the window is the search item with the greatest number of searches, so it has Search Index of 100; the door has Index 96, which means it has 96% of the search volume of the window; the washing machine with Index 49 has about half the searches of the window.

The numbers cannot be interpreted as proportions. The Index of 49 does not mean that washing machines account for 49% of all France queries about fixing home appliances. That is really the meaning of popularity we want to have but we don't have. We can obtain true popularity measures by "normalizing" the Search Index: just sum up the Index Values of all the appliances and divide the Search Index by the sum of the Indices. After normalizing, the numbers can be interpreted as proportions and they add up to 100% for each country. When not normalized, the indices do not add to 100%.

Take the case in which we have five appliances, and let's say all five appliances are equally popular, comprising 20% of searches each. The five Search Indices will all be 100 because the top-ranked item is given the value of 100. Those indices add to 500!

By contrast, in the case of Russia (or a more extreme case), the top-ranked query is almost 100% of all the searches, so the sum of the indices will be only slightly larger than 100.

If you realize this, then you'd understand that it is risky to compare Search Indices across countries. The interpretation is clouded by how much of the total queries accounted for by the top query.

In our Trifecta Checkup, this is a chart that does well in the Question and Visual corners, but there is a problem with the Data.

 

 


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.

Goog_newsrooms_gender_2

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:

Jc_newsroomgender_1

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.

  Jc_newsroomgender_1

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.

Jc_newsroomgender_3

***

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:

Goog_newsrooms_race_2

 ***

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.