Junk Charts

Worthy of the Times

Andrew Gelman has put up a great post, discussing how he collaborated with the New York Times editors to transform his chart to a publishable form.  Some time ago, there was a discussion here about the publish-worthiness of my charts (actually, the lack thereof), and I explained that to take my charts to that level would require quite a bit of extra work.  Gelman speaks here from first-hand experience.

Here are the two versions side-by-side.  Readers on the Gelman blog are debating which version is "better" with Gelman himself voting for the revised NYT version:

Let's compile a list of the changes:

1. Removed 2000 data and relied on only 2004 data
2. Reduced number of groups of senators from 7 to 5 (with a special calling out of Senator Lieberman)
3. Re-ordered senators to facilitate classifying into Democrats, Independent, Republicans
4. Added annotation explaining the grouping of senators; in particular, qualified why the 49 Democrats and 32 Republicans were set aside
   
5. Removed scale labels on the top of the chart, retaining only the bottom labels
6. Vastly increased the area devoted to text labels, which now covered half of the chart
7. Added white vertical gridlines
8. Instead of coloring the cross marks, colored the background of the chart; introduced the yellow color for Lieberman (which Gelman originally colored blue)
9. Removed reference to the national average but explained clearly in the legend that the percentages are relative to the national average.
   

Of these, 2,3,4 are definite improvements. 1 is acceptable since 2000 and 2004 data are quite highly correlated (note, however, Iowa, Virginia and Ohio.) 7 looks brilliantly here although we typically don't recommend adding gridlines and such. 5 is also acceptable because of 7 -- with the gridlines, one doesn't need to have two sets of labels. 8 can be debated: I'd like to see a version with large colored squares instead of cross marks in lieu of the background; the current look is not bad. 9 can also be mulled over: would it be so bad as to insert in parentheses 73% after the words "national average" in the legend?  I suspect some feel that this may cause confusion because readers now need to understand relative versus absolute values. 6 is the most debatable because the data-ink ratio has been vastly reduced. 

There are several good features of the original chart that they left unaltered, which should also be duly noted:

• Allowed the positive side of the scale to extend to 10% even though the largest data only reached about 6%. While this creates empty space, it helps readers judge the magnitude of negative numbers relative to positive ones.
• Subdued horizontal gridlines
• Retained the title of the chart (I actually prefer that they use the title to summarize the finding as opposed to the current one which takes a neutral stance.)
• Retained the horizontal scale labels at 5% apart

One final comment on something omitted from both charts: I'd prefer that they plot all the dots for the 49 + 32 senators, on the top and bottom lines respectively, instead of just plotting the group averages.  It would be really interesting to see what the spread is around the 0% point.

Degrees of likeness 1

The NYT team just put up a fantastic visualization of the American Time Use Survey data, which purports to measure how the average American spends the time of a day.  (Apparently, thousands of people recalled what they did every minute of an average day.)  The amount of data collected is massive, and this graphic allows readers to explore the data in intuitive ways.

The chart shows for each minute of the day (horizontal axis) the proportion of people doing specific activities.  Not surprisingly, we spend more time sleeping than any other type of activity.  The axis and data labeling as well as gridlines are very restrained.

Normally, I am not a big fan of these proportional area charts because the only relevant dimension to look at is the vertical distance from one curve to the next but the focus on areas put equal weight on the horizontal and vertical distances.   The horizontal distance is meaningless, and thus the area is meaningless.

These designers found a solution to the problem, and good for them!  Because of the mouse-over effect, I could not save the actual appearance -- here, I show what it looks like.

By mousing over different parts of the graph (say, moving vertically), we can compare the actual proportions.  Terrific!

The key interest of this graphic is the following legend.

While the above graphic shows the use of time by all Americans in aggregate, this panel allows us to zoom in on specific groups of Americans.  How alike are Americans?

Reference: "How Different Groups Spend Their Day", New York Times, July 31 2009.

 

The trouble with two lines

It's never a good idea to put two scales on one chart, and this is another example of what not to do:

The ugliest part of this chart are the duelling gridlines. Because neither axis starts at zero, it is difficult to access whether the number of newspapers was declining at a faster pace than the circulation was. Also, line charts would be better able to trace the evolution over time. The interspersed blue and red columns interfere with each other. Note that the designer lessened our pain by plotting every other year, thus halving the number of columns.

The junkart version also puts two data series on the same chart but on the same scale. Instead of plotting the raw data, we plot indices, with 2008 as 100. This reveals a pattern that was not apparent in the original chart. There appeared to have been four periods of evolution: up till 1980, both the number of newspapers and total circulation were at a plateau; from 1980 to 1990, the circulation stayed stable while the number of papers dropped drastically, indicating perhaps consolidation; then from 1990 to 2003, both series declined at roughly equal rates; and finally, the bottom dropped off the circulation from 2003.

See our previous discussion of dual axes here, here, and here

Reference: "Channel Shift: Online Circulars: the first step by retailers toward web-to-store harmony? ", Internet Retailer (print), May 2009. Data from the Newspapers Association of America.

Bonus 1: Thinking about the column interspersing trick some more, I realize that it is, em, possible, em, that one series was plotted for odd years and the other series plotted for even years!

Bonus 2: Here is the requested scatter plot (still indiced):

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.

The shackle of time 2

In the last post, we removed the time dimension in order to clarify certain aspects of the S&P 500 returns.  We found that with an investment horizon of five years, there was historically about a 25% chance of losing money and a 25% chance of more than doubling.

Even though we looked at cumulative returns, it was still the case that the data was serially correlated; in other words, it could be that the eventual return was not independent of the starting year of the five-year period.  To gauge this, we must return to the time dimension that was previously removed.

The chart on the right plots the five-year returns for all five-year periods starting from 1910.  What it shows is that even with longer time frames, timing or luck still plays a key role. 

For example, any such investment in the S&P 500 between late 1950s and 1980 did not double in five years no matter which year the investment was made.  Then again, if the investment was made in the 40s and 50s, no one lost money in a five-year period, similarly in the 1980s.

So the fact that we saw a 25% chance of doubling (or losing money) over history says much less about what might happen in the next 5 years than the simple number suggests.

In response to a reader's comment - the data series was described as "real total return" so these are inflation-adjusted.

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.

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.

Knit-picking

In celebrating the recent trend by "elite" colleges to lowering the cost of education, the Times printed this chart, the top part of which is shown here.

The three colors represent different levels of aid.  Blue means "grants replace loans"; red means "free tuition"; yellow means "parents pay nothing".  The colleges are grouped by the minimum qualifying income for the blue category.

The whole effect is of a knit.  We shall call this the "knit chart".

I believe a simple data table will do the job nicely.  If any reader has other ideas, please show us your work!

A few points to note about the original:

• Ordering by the minimum income to qualify for "grants replace loans" is arbitrary, as is alphabetizing colleges within each group
• Qualifying "at any income level" should be shown on the left of "$40,000 or below" rather than to the right of $100,000.  The current order is such that qualifying level increases with income from left to right, except from $100,000 to "any income", where it falls off a cliff.
• Qualifying at any income level is better shown as a separate column on the right disconnected from the income scale.  The current configuration devalues the effort spent in making a proper income scale.
  
• Too many lines of equal length, and too few yellow and red lines to make the knit chart effective
  
• Should the graph cater to parents interested in seeing what aid they qualify for given their income level?  Or should the graph highlight the breadth of aid available at individual colleges?

Reference: "The (Yes) Low Cost of Higher Ed", New York Times, April 20 2008.

PS. The original point about the "any income level" was incorrect as pointed out by Chris below.  I have replaced that with a different issue.

PPS. Matias' version (see comments) is a superb demonstration of the power of data tables, well-applied.   It is clean and simple, and addresses both the questions pointed out in the last bullet point.  The only thing sacrificed was the visual representation of the relative size of the income requirements, which I agree is the least valuable part of the original.  As usual, many thanks to our readers for coming up with great ideas!

Hanging tough

Reader Nick B. sent in this example calling it "interesting".  The chart tells a compelling story once we figure out what it is.  Grasping the tree structure is key.

It illustrates the important idea that averaging sometimes masks  variations in the data.  For example, while the province of Guerrero scored 78% on literacy, the municipalities within Guerrero had scores ranging from 28% to 90%.

It also shows that the gender gap was larger in lesser Metlatonoc municipality than in more literate Cuautitian.

In addition, it tells us that while Mexico on average measured very well on literacy, subpopulations within Mexico spanned the world's best and worst (from about Mali's level to Italy's).

While I find this chart adequate, the pieces hanging off each other did not seem ideal, especially the two overlapping municipality pieces which were placed next to each other.  However, it is tough to come up with an alternative.  Here's one attempt; the changes are mild.

I prefer the horizontal orientation.

The branches are emphasized (as opposed to the "T" junction) because that's a key part of the story.

The national level, especially the span between Mali and Italy, is de-emphasized; I treat it as gridlines.

Instead of placing the overlapping pieces next to each other, I let the ranges literally overlap, which serves to stress this feature.