Junk Charts

A shocking failure to communicate

So said a reader, Stephen B., of the following graphic (note: pdf) in the London Times concerning Andy Murray's recent tennis triumphs.

How can we disagree?  Shocking?  Yes.  Failure?  Definitely.  Failing to communicate?  No doubt.

Let's first start with the five tennis balls at the bottom.  It fails the self-sufficiency test.  It makes no difference whether the balls (bubbles) are the same size, or different sizes.  Readers will look at the data and ignore the bubbles.

Amazingly, the caption said that "Murray has one of the best returns of serve in the game."  And yet, the graphic showed the five players who were better than Murray, and nobody worse!  For those unfamiliar with tennis statistics, it does not provide any helpful statistics like averages, medians, etc. to help us understand the data.

But that is only the beginning.

Take a look at these two donuts.

(The color scheme from light to dark: first, second, third, fourth round of tournament)

So we're told: the 75% of first-serve points won in the fourth round was 25.6% of the sum of the percentages of first-serve points won from first to fourth rounds (75%+70%+71%+76%).  What does this mean?  Why should we care?

The challenge with these two statistics is that they are correlated and have to be interpreted together.  If a first-serve is won, then there would be no second serve, etc.  Here's one attempt at it, using statistics from the Soderling-Federer match.  It's clear that Federer was better on both serves.

Reference: "Murray's march to the last eight", London Times.

 

Spinning multi-color

New York Times has a great pointer to the Global Warming Art website.  The author Robert Rohde wants to popularize environmental science by visualization of the data.  There are many interesting charts and well worth repeated visits.

These pie charts cry out for some re-dressing:

The pie charts, the colors, the whole works.  Most troubling is that each pie has its own sorting scheme, and because the text labels were not reproduced in the smaller pies, the reader is sent scrambling around to find the right labels.

In addition, these pie charts, as with almost every other pie chart, fail the self-sufficiency test.  Without all the data printed next to each sector, the reader is simply unable to judge the size of each sector.

Further, the aggregate data (larger pie) may not be as relevant after realizing that the smaller pies show very different patterns.  The following junkart version tries to bring out this fact by treating both dimensions (type of greenhouse gas; source of emission) equitably.

While I picked on this particular chart, I must say I support Robert's effort and wish him luck in this very well-intentioned project.

Animal racetrack

We introduced the racetrack chart before.  Via Zero Hedge, we find a version of it, perhaps a race for animals.  In a race for humans, they run in concentric circles; animals are not so tame, they may stray off the track, or just refuse to continue.

The designers certainly tried very hard to make the numbers palatable.  Indeed, given how much of our taxpayer funds are being thrown to the fire these days, any informed citizen ought to know how the money was being spent.  Their hard work, unfortunately, was not rewarded as the various constructs failed to improve our understanding of the data.

The three annotations on the right tell us that the arc width at the left indicates the allocated funds while the arc width at the right indicates the actual amounts spent as of end of April.  In addition, the breakpoint on each arc in relationship to the fan of lines indicate the date at which the funds were allocated. 

In reality, things are a bit more complicated.  When all allocated funds have been spent, as apparently the case of Fed funds for AIG, the arc has no break point and thus the date of the allocation is missing.  Also, when the same use soaks up funds from multiple sources, the width on the right gets confusing: take for example FDIC funds for unlocking credits; it's unclear how the two arcs add up to 1.8 trillion.

Perhaps a flow chart might work well for this sort of data.

Reference: "Visual Representation of the Government Intervention Programs", Zero Hedge blog, April 8 2009.

Knowing what one is doing

Jess B. sent in some entertainment.

In case the font is too small:

There is a lot more here, including the author's note in the comments section.

Exemplary

From Bernard L., another exemplary effort by the Times.  This one really got me excited.  

The set of line graphs shows how demographics of students in American schools have evolved in the last two decades.  Here, I selected New York City schools, and the tool sensibly decided to compare those with New York State schools (gray line).

There is so much to learn from one simple chart:

• The blue and gray lines are almost parallel everywhere, which tells us that in terms of the change in demographic composition, New York City pretty much resembled New York State during this entire period.
• However, in terms of demographic composition, rather than the change in composition, New York City schools are very different from the rest of the state, in that the proportion of white is lower by a third while that of minorities are much higher, especially black and Hispanic students.
• State-wide (as well as city-wide), black and white students have been declining as a proportion while Hispanics and Asians have increased. 
• The extent of the change is immediately visible, Asians have jumped from 7% to 14% for example.  

  
From a graph design perspective, the execution is very clean.  Data labels are limited to the first and last values.  A small multiples concept is used with the ethnic groups placed side by side.  A great awareness of foreground and background as well.  And imagine how much data has been visualized here, and be impressed.  You can look at any county in the country.

Here's one where the county change does not exactly mirror the state change (Napa in California):

Reference: "Diversity in the classroom", New York Times, March 12 2009.

Scale restoration

The original graph threw us off our sense of scale.  It seemed to be saying all these oil companies are roughly the same size but one grew much faster than the others.  The red color and the setting off of the data above the title of the chart seemed to announce some important find.

The junkart version on the right reversed everything to our normal sense of scale.  It is a version of the bumps chart, one of my favorites.

So we find that Total is the smallest of these oil companies, about half the size of ExxonMobil -- you wouldn't know that from those abysmal bubbles!   Adding to the problem is that the growth data is used to sort the companies while the actual production data is hidden in the data labels.

Total is indeed growing faster but BP is not far behind.  The fall of ExxonMobil and Royal Dutch Shell is equally intriguing.


Reference: "Total, the French Oil Company, Places Its Bets Globally", New York Times, Feb 21, 2009.

The shackle of time 1

I ran across this hugely successful chart on Dean Foster's home page (and noted that he and his Wharton colleagues have a nice blog picking apart statistical errors committed in public.)

This is a histogram plotting the historical year-on-year returns of the S&P 500 index, binned into 10%-levels.  It succeeds on two levels: the innovation of printing the years inside little blocks provides extra information without distracting the overall picture; the key message of this plot, that the negative return of 2008 is a negative outlier in the history of returns, is extremely clear.

This, in my mind, is a superior presentation than the usual time-series line chart that we see in every economics publication.  For some purposes, it is better to unshackle ourselves from the linear time dimension, and this is a good example.

One question/comment: within each 10% level, the years are arranged in reverse chronological order fro top to bottom.  This facilitates searching for a particular year.  The obvious alternative is to order by the actual level of return, so that the result is akin to a stem-and-leaf plot.

While I like the graphical aspect of the chart, I feel like it has limited function.  This graph appears useful to anyone who has a one-year investment horizon.  If I want to predict what next year's S&P 500 return is, I might take a random sample from this distribution.  However, as a lazy investor, I never look at a one-year horizon so this creates two problems: if I am looking five years out, I can't take five samples from this distribution because there is serial correlation in this data for sure; even if I could take those five samples, it is difficult to compute the five-year return in my head.

So what I did was to take the data and replicate this histogram for 2-year, 3-year, 5-year, 10-year, etc. returns.  The results are as follows.  I decided to simplify further and use Tukey's boxplot instead of the histogram.  The data are real compounded total returns from S&P 500 from 1910-2008.

 The boxplot on the top right shows that there is about a 25% chance that an investment in the S&P 500 will return negative in real terms in any three-year period (below the green line).  At the other end, there is a 25% chance of getting earning more than 50% on the principal during those three years.

The next set of boxplots compared 5-year returns to 10-year returns and 10-year returns to 20-year returns.  If we have a 10-year horizon, there is still positive chance of reaching the end of the decade and finding the investment under water!  The median 10-year return is approximately doubling the principal (about 8% per annum compounded).  

In a twenty-year period, there is hardly any chance of not making money on the S&P.  There were two positive outliers of over 1000% (about 13% per annum compounded over 20 years).

Reference: Data from Global Financial Data

Seen at Starbucks

Merry Christmas!

If you happened to be in a Starbucks recently, you might have picked up some charts, which was what happened to one of our regular readers and commentators, ZBicyclist, who then tried his hand at chart critique here.  He is worried they may reach millions soon.  So look out!

This graph on the right -- which should rightfully be called a "tree ring graph" -- seems to me a fantastic concept although it is hard to think of data that would deserve this treatment.  Certainly not the retail sales series plotted here! 

This is an object lesson in why bubble charts often fail.

One issue is scale: note the awkward way in which the innermost ring is used to designate the oldest sales data of $375 billion presumably in 1996, and think about how you would decide where to place the 2007 ring.  (It's arbitrary.)

Another problem is labeling: when the growth is slow, the rings are close together, and labels have to be jittered (look at 2001 and 2002).  In this case, a relatively simple solution is to have the entire series of years run diagonally.

Yet another challenge is relative radii versus relative areas.  Inevitably, some readers will respond to the areas while others will respond to radii  ZBicyclist, for example, belongs to the first group while in this case, I find myself siding with the latter.  When the bubbles/rings overlap, it is difficult to assess areas.

Of course, a simple line chart would do the job with minimal fuss.  The following chart issued by the National Retail Federation actually plots the growth rates, rather than the annual sales.

(Please lose the grid-lines, or else add a vertical axis and lose the data labels.  A column or dot chart is also slightly preferred.)

Now go read ZBicyclist's point of view.  In the meantime, let us know if you think of ways to use the tree ring graph.

Food art

Adam, who is the designer behind the Wired graphics special on "The Future of Food", asked about the rest of the series.  We previously made some comments on a set of mini donut charts.

The first thought that came to mind after browsing through all the charts was: what a great job they have done to generate interest in food data, which has no right to be entertaining.  Specifically, this is a list of things I appreciated:

• An obvious effort was undertaken to extract the most thought provoking data out of a massive amount of statistics collected by various international agencies.  There weren't any chart that is overstuffed, which is a common problem.
• It would be somewhat inappropriate to use our standard tools to critique these charts.  Clearly, the purpose of the designer was to draw readers into statistics that they might otherwise not care for.   Moreover, the Wired culture has long traded off efficiency for aesthetics, and this showed in a graph such as this, which is basically a line chart with two lines, and a lot of mysterious meaningless ornaments:
• 
  
• A nice use of a dual line chart, though.  It works because both data series share the same scale and only one vertical axis is necessary, which is very subtly annotated here.
• The maintenance of the same motifs across several charts is well done.  (See the pages on corn, beef, catfish)
  

Further suggestions:

• It would be nice if Wired would be brave enough to adopt the self-sufficiency principle, i.e. graphs should not contain a copy of the entire data set being depicted.  Otherwise, a data table would suffice.  The graphical construct should be self-sufficient.  This rule is not often followed because of "loss aversion"; there is the fear that a graph without all the data is like an orphan separated from the parents.  Since, as I noted, these graphs are mostly made for awe, there is really no need to print all the underlying data.  For instance, these "column"-type charts can stand on their own without the data (adding a scale would help).
• Not sure if sorting the categories alphabetically in the column chart is preferred to sorting by size of the category.  The side effect of sorting alphabetically is that it spreads out the long and the short chunks, which simplifies labelling and thus reading.
• Not a fan of area charts (see below).  Although it is labelled properly, it is easy at first glance to focus on the orange line rather than the orange area.  That would be a grave mistake.  The orange line actually plots the total of the two types of fish rearing, not the aquaculture component.  The chart is somewhat misleading because it is difficult to assess the growth rate of aquaculture.  Much better to plot the size of both markets as two lines (either indiced or not).
  
•  

Reference: "The Future of Food", Wired, Oct 20 2008.

The matter of bad choice

Right on the heels of the disastrous bubble chart comes another, courtesy of the NYT Magazine.  Bubble charts are okay for the conceptual ("this is really big, and that is really tiny").  This chart wants readers to compare the sizes of the bubbles, which highlights the worst part of such graphs.

Poor scaling is the huge issue with bubble charts.  They are the prototype of what I call not "self-sufficient" charts.  Without printing all the data, the chart is unscaled, and thus useless (see below middle).  When all the data is printed (as in the original, below left), it is no better than a data table.

In the above right chart, we simulated the situation of a bar or column chart, i.e. we provide a scale.  For this chart, the convenient "tick marks" are at 10, 20, 34, 41.  Unfortunately, this scaled version also fails to amuse.

Note further that the data should have been presented in two sections: the party affiliation analysis and the gender analysis.  Also, it is customary to place "Independents" between "Republicans" and "Democrats" because they are middle-of-the-road.

A profile chart is an attractive way to show this data.  Here, we quickly learn a couple of things obscured in the bubble chart.

On the issue of abortion, Independents are much closer to Democrats than Republicans.  Also, there is barely any difference between the genders, the only difference being the strength of support among those who want to legalize.

Reference: "A matter of Choice", New York Times Magazine, Oct 19 2008.

PS. Based on RichmondTom's suggestion, here are the cumulative profile charts.

 

Bernard L. suggested a "tornado" chart: