Junk Charts

The hard work of entertaining

Stefan pointed us to his work for the UN GEO (United Nations Global Environment Outlook) data portal.  This set of information posters highlights a vexing issue that crops up on Junk Charts from time to time, that is, the proper balance between information and entertainment value of data displays.  While this blog concerns itself primarily with the former, it does not mean that we are blind to the flashier side of the enterprise.

Let's take Stefan's recycling spiral chart as an example.  One must admit that visually this presentation is more appealing than either a data table or a set of bar charts.  The reader can obtain the primary piece of information, which is the ranking of different countries in terms of the proportion of collected waste that is recycled. 

And if the reader is curious enough, the chart also provides the data on the per-capita amount of waste collected in each of these countries.  (Like the table and bar chart, this display also has the problem that it is one-dimensional, thus the countries can be sorted by proportion of recycling but then the waste collected data will be out of order.)

For those readers who would like to understand the data better, they would want to know some of the following:

• Is there a relationship between amount of waste collected and amount of waste recycled?
• Are there differences in culture resulting in different recycling rates?
• Is the level of development of a country predictive of its recycling rate?
• Why are some countries recycling more of its waste, and others less?

To address these types of questions, one can start with the following scatter plot.

 

With the exception of South Korea, there is a general pattern of positive correlation: the more waste collected per capita, the larger proportion of such waste recycled.  Any dots that are not in the bottom left or top right quadrant are exceptions to the rule.  These countries are labeled in red or blue, the former indicating that the amount of collection is above average while the rate of recycling is below average. 

Because there is sampling error, dots that are close to the average dot (the center of this scatter plot) are probably just average.  Roughly speaking, dots in the gray circle are close enough to the center that I would not consider them exceptional cases.  That leaves Spain and Iceland in the red corner, and South Korea in the blue corner.  If both data series are considered together, these three countries should merit attention; if only the proportion of recycling is considered, then one would pay attention to Italy, Turkey and Slovak Republic on the lower end and South Korea on the high end.

Scatter plots are very versatile.  The following one explores the issue of development level.  Surprisingly, the level of recycling seems to have little to do with development; the countries are quite widely scattered.

 

Technical note: The data on both axes are expressed in "standardized" units.  So the zeroes represent the average per-capita waste collected, and the average proportion of waste recycled (only of those countries depicted in the original chart).  +1 indicates an amount that is one standard deviation above the average.  Think of "standardized units" as measuring how extreme is a particular country with respect to the average. 

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.

An art class?

Robert F. pointed us to these charts, via the Digital Design Blog.  A larger version is found here.  These look like scraps from an art class, exploring perspective and 3D.

These types of charts are quite prevalent in the web analytics area.  We have a long way to go in terms of producing good visualization of such data.

For even more light entertainment, click here.  (Warning: not for the easily offended, language purists, and mildly not safe for work).  (This is via Pete S).

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.

Popping the bubble, so to speak

Matt H., who authored the previous post, and Charles G. both pointed to a great example of how people like readers here can make a difference.   A bad chart got made over!

The Financial Times published a chart from a JP Morgan report, using ... you guessed it ... bubbles to illustrate the deep plunge in market capitalization of many banks.

Some readers at the blog were none too happy with the choice of bubble charts.   Among other things, the designer made the common mistake of plotting proportional diameters rather than proportional areas.  This is clear from looking at JP Morgan's bubble.

This chart exposes the weakness of bubble charts well.  Look at the top row of bubbles.  Most of them look so similar it is impossible to know, without spending much time studying the circles, which bank was hurt more.

Eventually, a bar chart was produced.  Felix Salmon linked to it.  I am not sure how the banks were ordered in this chart.  It isn't one of the two obvious dimensions, nor is it in alphabetical order.

In fact, neither the bubble nor the bar chart works well for this case.  What we need is the Case-Schiller style asset-bubble life cycle chart.  In order to interpret these changes in market caps, we need to know how big was the bubble, and then how steep was the consequent decline.  Take a look at our discussion of real estate bubble charts here.

Reference: "Bank capitalization chart of the day", Felix Salmon at Portfolio.com and "Bank picture du jour", FT Alphaville, Jan 21 2008.

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

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.

From bad to worse

Pie charts can range from bad to worse.  Brent L. pointed us to a few on the right end of that spectrum.

Brent wrote: "The background image makes it almost totally unreadable.  And what does the forest scene have to do with programming?  *sigh*"

That's not to mention the oval rather than circle, the dizzling array of colors, the Excel-style legend that inverts the order of importance ("Other" at the top), etc. etc.

Again, a column chart would have been much clearer.  Since the total number of famous programmers is arbitrary, a chart of counts would work at least as well as one that plots proportions.

More here.

Reference: "Famous programmers from Adleman to Zimmerman", grokcode.

Political theater

Jens, a long-time reader, tried to re-make the boring data tables used to report poll data.  Here is an example from USA Election Polls (left) and his enhanced version (right).

Like Jens, I find most of the tabular presentation of poll data underwhelming.  Too much data hiding all the useful information.  For example, the pollster and polling date data provide a context for super-serious poll watchers to interpret the data; however, they do not present themselves in a way that actually help readers.  Read further for versions that bring out this data much better.

Meanwhile, Jens' revision uses color and ordering to bring out the current state of affairs.  The addition of electoral votes allows us to understand the relative weight of each row, countering the weakness of the tabular format, that each row has the same height, implying erroneously that they have the same importance.

There are a number of good web-sites where this type of data is presented in attractive ways.

I have been a fan of Political Arithmetik, which made great use of the pollster and polling date data mentioned above.  Those data have been averaged to show the overall trend while the individual poll results are plotted as dots in the background.  The polling date data is embedded in the horizontal positions of the dots.  Even more impressively, the margins of error are presented.  Remarkably, this race has been a statistical tie for all these months, the 95% lower limit never quite making it above the zero level.

Another great site is fivethirtyeight.com.  Below, they essentially turned Jen's enhanced table into a map.  The legend on the right perhaps represents what they call "East Coast bias"?  All of Nathan's graphs are very attractively produced; I just wish he'd put more labels on them (such as the differentials corresponding to shades of red and blue.)

Bubbles of the same size

Frederic M. sent in this chart, together with his commentary.

He wrote:

Bubbles across rows have vastly different numbers but their circles are of identical size (or vice versa). It borders on the ridiculous that all bubbles of the US row have the same size... The question if teenage birth rates and teen sex are correlated cannot be eye-balled with this kind of display. The fact that you cannot compare across rows make this an instance of “chart junk”.

I add:

White spaces -- always dangerous.  Does lack of bubble imply no data or no abortions/sex?

Sorting -- this is what Howard Wainer called "Arizona first" with a twist (United States)

Loss aversion -- would U.S. readers be resentful if countries like Iceland are excluded?  A much reduced version comparing U.S. to say Canada, U.K, Japan and Germany may yield more information for the reader.

Sufficiency -- if all the data are printed as in a table, why do we need the bubbles?

Reference: "Let's Talk About Sex ", New York Times, Sep 6 2008.