Junk Charts

Visual analogies

Many a startling faux pas in graphics start with the desire to utilize visual analogies: the recent shopping mall chart is a good example.  There is something inviting about making a chart about shopping malls look like a shopping mall, or a chart about breakfast foods look like a donut, and so on.

The New York Times (or maybe OECD) makes a chart about economic cycles look like, you guess it, cycles.  Don't really have too much to say about this one - except these two points:

• Much of the validity of the chart depends on the theory behind it.  Do the two variables being tracked (amount produced relative to trend; change in production in last 6 months) capture everything?
• The focus on generating cycles visually left out one of the most important dimension - that of time scale.   For this chart to work, we would like to know not just where we are in the cycle but how much time we'd spend at each point in the cycle.  The interactive charts (graphs 4, 5, 6, 7) show us that the cycles are traversed not at constant speed.  A proper rendering of this data needs to play up the time scale.

If you have ideas of how to improve this, feel free to comment.

Reference: "Turning a corner?", New York Times, July 2 2009.  

Colorful maps

Bernard L. loved the recent NYT take on immigration in America.

The very pretty maps are found here.

An amazing amount of data is being visualized here.  Mousing on the map will pick up the specific data for each county.  There is a bar up top for discovering the evolution over time.  It would be great if there is an animation button so the map can be played out without clicking.  An animated gif will also do (similar to the disease map we featured some time ago).

The colors on the first map represent the origin of the top ethnic group in each county.  Within each group, the tint of the color further displays the percentage of the population that group accounts for.  The subgroups appear to be 0-2%, 2-5%, over 5%.  The last subgroup is very wide.

Not so keen on the second map with all those bubbles.  They show the number of people from each country by county.  The bubble size is proportional to population.  Every version of this map looks the same because the population is concentrated in the cities and the interior is sparsely populated, no matter what ethnic group.

Regardless, this is another laudable effort by the crew at the Times.

Reference: "Immigration Explorer", New York Times, March 10 2009.

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.

Eternal optimist

Chris P pointed us to the "Financial Comeback" calculator, surely a well-meaning joke from the folks at the Times.  Here is how one gets to make a 40% loss back in just six years!


Surely, someone has to tell them about simulation.  They have to assume a probability distribution on the annual returns, and show us some sample paths.  Using the average annualized historical return in essence wipes out all variability and no wonder it's smooth sailing upwards.  Eternal optimist.  

Here is Chris' comment:

The bad news is that the range of values it offers does not include the return on the market from last year (-31% to -36%).  I guess they are optimistic.

The interactive features of this chart, however, impressed me.  The smooth adjustment to the chart as one slides the control, including the automatic choice of appropriate axis labels, is very nice indeed.

Okay, they want to trademark the name of the calculator so perhaps this is serious.

Reference: "Calculate your financial comeback", Jan 6 2009.

How to read a graph

Via Gelman, here is a nifty book-buying map from Amazon, displaying the split between "red books" and "blue books" bought by Amazon users in each state in the months leading up to the 2004 and 2008 presidential elections.



Gelman noted the similarity between the Amazon map and the red-blue split of rich voters.

This post is about how to read a graph.  Here are some things that come to mind looking at the map:

• Sampling bias: how does Amazon's customer base compare with the U.S. population, or rich voters?  It would be prudent to check this before making generalizations.  Gelman's point may be that Amazon customers behave like rich voters.

• Sampling period: is the period long enough to capture the average inclination of the book buyers?  As is well known, book sales follow a long-tail distribution (Chris Anderson wrote an entire book based on this observation.)  Best-sellers have a disproportionate influence on average values.  If the time period is too short, the data may only represent the best-sellers.  Consider the following two maps in successive periods in 2004:

Much of the red in the first map was due to John O'Neill's "Unfit for Command", published in August 2004, and much of the blue in the second map was due to John Dean's "Worse Than Watergate", published in April 2004.  If one of these two-month periods was used to draw conclusions, we would make big mistakes!

• Classification: The long-tailed nature of book sales has wide-reaching implications on interpreting the data.  The most essential feature is that single books (bestsellers) have a disproportionate impact on average sales.  Since the key metric here is proportion of red (or blue) books, it follows that whether a best-seller is classified as red or blue makes a huge difference. 
  

Thus, one of the first things to look at is Amazon's helpful explanation of how they classified books as "red" or "blue".  We learn that they also have "purple" books which are those they could not decide if it's red or blue.  Each red or blue book is given equal weight but it appears that purple books are not tallied.  Glancing at the list of purple books, I see some hugely important books, e.g. Ron Paul's "The Revolution: A Manifesto" (Amazon rank #56  among all books), Tom Friedman's "Hot, Flat and Crowded" (#15).

If the purple books include best-sellers, then the decision to call it purple rather than red or blue causes an influential book to be excluded from the calculation.  We often forget that the decision to exclude is not a neutral decision; it is an active decision that says the excluded data contains no useful information.
 
This is not to say that excluding those books is the wrong decision.  We must make these decisions with considerable care, and realize that excluding best-sellers when book sales have a long-tailed distribution must not be taken lightly.

• Causality: Lets say we are sufficiently satisfied that we can make a statement about book buying habits and voting behavior.  Then we need to think about the direction of causality.  Is the map saying that red book buyers are likely to vote red?  Or that red voters are likely to buy red books?  No prolonged staring at this data set will resolve this issue as other data would be needed to address it.

The more data is used to create a graph, the harder our task is to interpret it.  But the pay-off for spending the time is all the sweeter.  Happy graph-reading!

One final note: there is no doubt that this interactive map feature is a brilliant marketing move by Amazon.  This is a great and fun way for readers to find interesting books.

Reference: "Amazon, U.S.A.", Gelman blog, Oct 5 2008.

Olympic tallies

Andrew N., a reader from Australia, wasn't too impressed with the way National Nine News presents the Olympic medal table on its home page.  To the extent that we want to venture beyond the typical tabular presentation, this bar chart is in fact quite appropriate.  Let me explain.

Lets take a tour around the world.  It's the battle of the data tables. 

 

The Boston Globe's is the cleanest of the bunch.  I especially like the way they set up the USA count at the top; the use of country codes is inferior to spelling out country names, as done in all of the other examples.  The New York Times is the only one to utilize colors to set aside gold, silver and bronze, which lets readers easily assess the two dominant metrics, total golds and total medals.  A small touch but very nice.

The biggest design issue here is the existence of the two different metrics.  In any tabular presentation, the countries can be ranked by only one metric so the designer must make a choice.  The American papers present ranking by total medals; the French paper by total golds; the two Canadian ones shown here are split.  The American papers also choose to carry the ranking implicitly while the others explicitly provide a numerical rank.  Le Monde and Globe and Mail provide ranks that are consistent with ordering of countries, both by total golds.  The Star, by contrast, wants it both ways: the order reflects total medals while the "POS" column shows total golds.  This extra column does help the readers who prefer ranking by golds but the primacy of the other ranking has not been overcome.

So what about National Nine News?  I have not been a fan of stacked bar charts but surprisingly, this is a great application.  Stacked bars have the disadvantage that the stacked segments don't share the same base and thus it is difficult to compare their lengths.  Here, though, our two metrics are total medals and total golds so readers should be drawn to compare the total lengths, and the lengths of the first segments.  Those wanting to compare silvers and bronzes must make a stronger effort but they will be in the minority.

What can be improved are the distracting data labels, especially the gold circles.  Instead, one should provide a scale, or use symbols such as one circle per medal.  (See this old post.)  Here is a version with a scale:

One cannot end this post without mentioning the attempt by NYT editors to insert levity into these proceedings with first a cartogram and then a bubble chart.

A graphical playground

RichmondTom pointed us to this New York Times article, which made what I consider a sloppy argument for the inflation rate being over-stated rather than understated.  This article was accompanied by a colorful and playful chart to describe which components make up the index, and which price changes were most drastic.

 

Like most "infographics", this chart has an interactive feature which you need to click here to sample: mousing over the strangely-shaped areas leads to annotations describing the weight of the relevant component, and the change experienced in that component during the past year.  Like Sherlock Holmes holding a magnifying glass, the reader can use the Zoom In, Zoom Out buttons to drill down.

Here is an expanded view on the color scale, with my comments.

We have no issues with the blue or the red & orange regions but what with using light blue and light green for increases between 0 and 4 percent (when all other increases use red)?  Readers not looking at the color palette will be caught off guard, misinterpreting the data.  This is a big problem since those two appear to be the most frequently occurring colors on the chart.

The designer of this chart surely is aiming for entertainment, creating a playground for the data sleuth.  It succeeds if readers take up the invitation to explore the data.  Unfortunately, it is not the most accessible for more sophisticated numerates interested in understanding the data.

It is impossible to ascertain the relative size of pieces that are close in size but often in arbitrary shapes.  We can roughly read out which components are most important to the index: turns out to be "owner's equivalent rent" by a mile.  Owner's equivalent rent, as discussed by Leonhardt, is the most problematic and inaccurate component, and also, I might add, most susceptible to manipulation since it is an estimate, not a measure.  The next biggest pieces -- food and gasoline (excepting rent) -- are taken out because of "volatility".

The most interesting information in this data set is missing: how much does each component contribute to the overall inflation rate?  This requires multiplying the weight of each component with the change of each component.

It would also be helpful to label which components are taken out of the Bernanke calculation that claims only a 4% inflation when my cable company seems to have raised prices every six months, and groceries and meals and so on are rising at 10-20%.  (Of course, Leonhardt thinks this is all loss aversion.)

Reference: "Seeing Inflation Only in the Prices That Go Up", New York Times, May 7 2008.

Joining the fun

We hope this is indication that the British paper Guardian (with one of the best websites out there) is joining the fun.  It appears that they have quietly debuted an interactive graphics feature.  The first edition addressed the oil price crisis.

This time-series chart has much to be commended:

The use of inflation-adjusted figures seems obvious but we don't see much of these in the press.  Highlighting the peaks and providing annotation (when moused over) is an excellent touch.  The gridlines and axis labels (especially the year axis) are thankfully restrained.  We don't see the need for the unadjusted series (blue line), however.  The fact that the gap grew larger the more time we went back told us little, as it invited readers to read into it more than what it truly was, the time value of money.

Later on, they used an oil barrel object to illustrate the components of retail oil price.  The height of the cylinder is indeed proportional to the data plotted.  If only they colored the end of the cylinder gray instead of green!  As it stands, the green portion has about the same area as the red.

Reference: "Interactive: oil price", Guardian, July 14 2008.

Bound to extremes

The New York Times continued to push the envelope by printing super-complicated data graphics (while the Economist regrettably seemed to have picked the USA Today route... more on that in a future post).  The following graphic was used to illustrate the relationship between CEO compensation and their company's stock performance.

The two dotplot lookalikes depicted the percent change in CEO pay and the change in companies stock price, in both cases, from 2006 to 2007.  The size of the dots indicates the relative value of the CEO's pay.  The gray dots depict "similarly sized" companies for comparability.

In this post, I will focus on the comparison between change in pay and change in stock price for a given CEO.  In particular, the calibration of the axis/scale is problematic.  The scale is automatically determined by an algorithm; as one switches from one CEO to another,  the graphs take on different ranges, use different axis labels, and the zero-percent points shift.

This means that the two charts have different scales.  In this example, each tick mark advances 6% in the top chart but 12% in the bottom chart.

Since the zero points do not line up, the distance between the zero and the orange dot loses meaning:  the 2.5x longer distance in the top chart actually represented the same percentage change as in the bottom chart (31% versus 28%).

In order to respect the grid-lines (white lines), the tick marks fall onto stray percentages (24%, 36%, 48%, etc.).  That's unfortunate.

What's the culprit?  This chart is "bound to extremes".  In other words, the range of the depicted data is used to determine the plot area.  The bottom chart had zero on the left edge because all the stocks depicted rose between 2006 and 2007.  It is often better to use domain knowledge to determine the plot area.  Extreme values should be omitted if they don't add to the message.  Oftentimes, by leaving extreme values in the picture, we squash the rest of the data.

This is also why programs like Excel do a poor job picking a scale.

As an aside, the use of bubbles is almost always troubling. Bubbles do not have a scale so the only information we get is relative size.  However, we can't estimate areas properly so we get the relative size wrong.  Sometimes, even the chart designer may get stumped.  In the chart of Steve Jobs, you would think his bubble (total compensation $1) would be dwarfed by all the other bubbles, as in the WSJ chart we showed the other day.  Not so.

Thanks to Todd B. for submitting this chart.

Reference: "Executive Pay: the bottom line for the those at the top", New York Times, April 5 2008.

Graphs as catalogs

Junk Charts typically concerns itself with statistical graphics a la Tufte and Cleveland, treating charts as a means to summarize, elucidate and highlight aspects of data.  We haven't been too kind on so-called infographics, often finding these cluttered and confusing.  Recently, I have a small change of heart.

I now see infographics as innovative in one way, and a complement to traditional graphics.  This is the idea of graphs as catalogs.  What many of these graphs try to do is to present a structured way for users to explore massive amounts of data.  They don't serve the traditional purpose of summarization and that's why they are innovations.

The following chart from NYT tracing Serena Williams' tennis ranking prompted this post.

As a traditional statistical graphic, this chart leaves much to be desired.  The general outline of her career could be described in one sentence without the need for any graphic.  The colorful vertical lines serve little purpose, nor the short line segments on the other side of the axis.

However, as a catalog of data on Serena's career, this graphic is fascinating.  Mousing on the vertical lines changes the information on the top right corner, including the tournament being played and the media event she participated in, as well as photos and her rankings.  Similarly, the left and right arrows on the top left allow readers to browse through the list of events chronologically. (You need to click on the link to use the interactive features.)  Without this chart, it would have been very difficult to learn about Serena's record at a particular tournament or point in time.  It acts like a data table but presents the information in a much more accessible way.

Thus, relying on interactivity, this compact graphic enables any of us to browse to a user-defined depth a reservoir of data.  Bravo!

Reference: "Serena William's Professional Career", New York Times, June 2008.