Junk Charts

Disentangle

In an article called "Off the Charts", Floyd Norris wanted to let readers know that unemployment does not hit citizens equally -- it affects some age groups and men/women to differing degrees. 

As befits the article's title, he included several charts, from which I extracted the one shown on the right.  At first glance, this seems like a normal chart.

But when one pays attention, one notices that the chart is rather complicated.  This chart is like a piece of modern music, in which the composer allows two voices to jar and talk past one another.

Think of it as a data table vying for attention with a bar chart.  The data table is a cross-tabulation of the change in employment by age and gender.  In this view, the men sit on the left, and the women on the right.

Lurking around is a bar chart, for which the point of zero change sits in the middle.  Positive growth extends to the right, while negative growth points to the left.  The gender labels at the top are irrelevant  for this bar chart: the narrow black bars indicate women, the fat colored ones, men.  The data labels are also irrelevant: see, for example, the 45-54 age group, the label for females, at -2.3, should really be placed on the left side of the middle divide!

Here is how these two charts look, disentangled: (I have converted the bar chart to a dot chart.)

 

  

Reference: "Off the Charts: Job losses mount, enduring and deep", New York Times, Nov 14 2009.

Pie Cubed

Omegatron also did away with a set of cascading pie charts on Wikipedia, a particularly ineffective use of this chart type.  Whenever there are more than two or three categories, the necessary use of many colors can really make one's head spin.

Here, the cascade is being used like a log scale, to artificially elevate the small pieces, which unfortunately are also the least significant pieces of the energy pie.  There is no reason for nuclear, bio-mass, hydro and "others" to add to 100% except that the author decides to group them together.  The 41% nuclear or the 41% solar heating in the second and third charts, respectively, have no meaning in the larger context.

In deference to the original author, Omegatron's new version preserves the arbitrary three-level cascade.  He converts to stacked bar charts, which brings out the differences better.


He also sensibly exposes the original proportions rather than the arbitrary relative proportions.  For example, nuclear energy accounts for 6% of the total, not 41% of the arbitrary "others" bucket which in turn contains 14% of the total.

I'd prefer an even cleaner presentation with unstacked bar charts.  This can be done in either one chart with all eleven categories, or in two charts, as shown below.  The two-chart version assumes that the reader have two key questions: alternative energy sources as a proportion of the total, and the mix of different sources within the alternative category.

With the ordinary bar chart, many fewer colors are needed, and there is no need to print out each data point, nor a need to use guides to point to labels and data.  The trouble of the latter is its tendency to draw attention to the least important aspects of the data.

With this further example, I continue to find the Wikipedia rule to discourage text annotations on graphs bewildering.   Such a rule apparently does not apply to data labels, as can be seen here.  Of course, a graph without any labeling of categories is robbed of meaning but if labels can be saved, so should annotations!

Reading comprehension

Note: I am in the middle of a holiday and so posting will be limited.

Andrew posted a pretty chart that caught my attention.  This is the sort of sophisticated chart that rewards careful reading. 

Below is a guide to reading the chart:

• It is a small multiples chart with the components arranged in two dimensions (income levels, and a race-religion hybrid category).  The top row is a summary of voters of all race-religion grouped by income.  Note that there is no corresponding summary column for voters of all incomes grouped by race-religion.
• Source of data: 2000 poll but applied to 2008 demographic patterns.  In other words, there is an underlying assumption that opinions have stayed stable within the demographic groups.
  
• The chart is in fact three dimensional because each map gives us the geographical (state by state) breakdown.
• It is useful to figure out the smallest unit of data: in this case, this is the percentage support of federal school vouchers by voters of a given race-religion-income-and-state category.
• The color scheme is such that red represents highest support and blue lowest support, with pink and purple in the middle
• It's almost always better to start from the aggregate (that is, the average) and then study variations along different dimensions, and this is how the chart is arranged from top to bottom
  
• On the top row, the higher income groups tended to favor vouchers more than lower income groups, with a break point around $75k; even here, the regional differences are significant, with northeast and southwest hotter for vouchers at all income levels
• As we move from row to row, we realize that the aggregate data hides many disparities.  For example, white Catholics (second row) are more likely to support vouchers regardless of income level while white non-evangelical Protestants (fourth row) are much less likely than average to support vouchers at all income levels.
• Notice that the statistician (Andrew) has carefully defined the race-religion categories to balance between collapsing subgroups that are distinct and showing too many subgroups so as to cloud the patterns.  That is why there are many more race-religion subgroups that are not shown.  The ones shown are of special interest.  Consider the white protestants, evangelical vs. non-evangelical (third and fourth rows).  If one were to fix the race, geography and income dimensions, and even fix half of the religion dimension, we still find the two subgroups to be on different ends of the spectrum relating to the voucher issue.  This is why the evangelical or not dimension has been included.
  
• The white space is interesting.  Here, the issue faced by the statistician is sparse data when one gets down to multi-dimensional subgroups.  Andrew chose to ignore all the data, which is the wise thing to do.  With so few samples, it is particularly easy to draw bad conclusions.   
• Because of the white space, we get additional information on the spatial distribution of the demographic subgroups.  The black population (at least the voters) are predominantly found in the southeast while Hispanics are in the southwest.  The subgroup of income higher than $150k is essentially all white.  Admittedly, this is a very crude read because we only have two levels (below 2% of state population and above).  Of the colored states, we cannot differentiate between densely populated and not.

  

Such rich graphics deserve careful reading.  Enjoy!
  

A Harvard mess 1

There are some innocent-looking charts that throw up more and more problems, the more you look at it.  This example comes from a magazine sent to Harvard alumni.  We have all heard that their endowment fund suffered some horrific losses in the last few months and so the magazine editor thought it useful to describe the potential impact on the different departments.

It's a safe bet our readers would not think to present two related data series as a combination of one bar chart and one column chart. 

As the chart stands, the intended message is completely lost.  It takes a bit of fishing to learn that the Radcliffe Institute has a tiny stake in the endowment fund but supports over 80% of its operating funds from the endowment.

Now looking a little deeper, we find that the scales of the two charts are not standardized so the length of a bar and the length of a column cannot be directly compared.  Nor can the grid-lines as each section accounts for 10% in the bar chart but 20% in the column chart (to make it worse, the larger section represents the smaller percentage!)

Looking further still, we find that "Other" accounts for some 15% of the endowment but apparently consists of entities that do not have operating funds and thus goes missing in the column chart.  In our versions below, we will ignore the "Other" category completely; this is equivalent to assuming that we have allocated to the individual schools a proportional share of "Other"'s share.

Not to mention arranging the schools by alphabetical order.

Much of this mess became apparent when we put the two charts into a uniform setting, like this:

 

A scatter plot provides good information, especially if there is clustering  although we can debate whether it is fit for general publication.

More in our next post.

Reference: "The Endowment: Each school's stake", Harvard Magazine, Jan-Feb 2009.

PS.  The initial post switched the axis labels on the two bar charts. Thanks to Jon for pointing this out.

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.

Opinion graph

Sharon P. pointed us to this graph, which can make one speechless.

Reference: "Bulls, Bears, Donkeys, Elephants", New York Times, Oct 14 2008.

Sloppy statistics

As hinted in the previous post, there are rare situations in which pie charts are acceptable; typically, these charts must show proportions that add up to 100%.  If column charts (or line charts) are used instead, readers who aren't careful may assume incorrectly that the columns add up to the whole.

Pie charts show distributions.  How should one state the key message of the following pie chart?

I. Type A is the majority.

II. The most frequent type is Type A.

III. Type A is a minority.

IV. Every other type but A form the majority.

I would pick statement II, followed by statement I.  Statement I is the only false statement out of the four if one uses a strict definition of "majority" (more than half).  If one goes by the spirit rather than the word of the law, statement I does pick up the key message albeit imprecisely.  Statement III is a true statement but particularly misleading in the context of this pie chart.  For every type is a minority type if we define "minority" as less than half.  Statement IV is a tortuous way to define a "majority" where there is none.

Neither III nor IV points to a key feature of the data.  It seems ridiculous to even include them.  Lets reveal the underlying data.

Last week, a story coursed through the mainstream media, relating to the above projections published by the Census Bureau.   (Projections were created for 2050 but mention was made of the fact that the largest racial group would account for less than half the population by 2042.)  Here were some of the headlines:

"2042 to see a white minority" (New York Post, 8/14/2008) -- III

"Minorities fixed to become new majority" (Daily Vidette, Illinois State University, 8/20/2008) -- IV

"US set for dramatic change as white America becomes minority by 2042" (Guardian, 8/15/2008) -- III

"...minorities collectively will make up the majority of people in America by 2042..." (Detroit Free Press, 8/21/2008) -- IV

Like I said, statement III is strictly speaking true but by 2042 every race is projected to be a minority.  Statement IV is just odd: of course, if one started adding up enough "minority" types, one will eventually attain majority.

Not all is lost, however.  The following headlines painted a more vivid image:

"Whites to lose majority status in US by 2042" (Wall Street Journal, 8/14/2008)

"White Americans no longer a majority by 2042" (Associated Press, 8/13/2008)

Elsewhere, a Boston Globe column makes an important observation: that Hispanic whites should probably be grouped with whites rather than Hispanics.  Technically, he argued that Hispanic is not a race.  From his point of view, the pie chart looks like this:

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.

Reconstruction

The following charts showed up in Internet Retailer, and ripe for some reconstruction.


There are few situations in which a grouped bar or column chart is the best choice.  In such charts, readers frequently have to examine the tips of the bars and yet the bodies of the bars obstruct comparisons.  Placing data labels instead of an axis is a nice touch; lining the labels up would be even better.   The junkart version below uses a dot plot which allows for comparisons within each payment type, and comparisons between payment types, to reveal themselves.



The second chart is also unnecessarily complex.  The use of double axes announces trouble, so too does the superposition of lines and columns.   The data to ink ratio of the chart is low because the data in the columns adds up to the numbers in the line.   Crucially, it is always important to clearly point out projected values (versus actual values).  Here is a junkart version.

The first revision focuses on dollar volume, showing that despite faster growth, alternative payments are merely catching up to traditional payment growth.   The higher growth rate is applied to a much smaller base!

The second revision focuses on growth rates.  Notice that all values here are projections.


Reference: "New way ahead for online payment methods", Internet Retailer, Nov 2007.

Structuring a chart

This chart from the NYT was intended to show how the EPA has moved the bar on vehicle mileage ratings: 2008 estimates were lower than 2007 estimates across the board, regardless of manufacturer, model and city/highway.

The chart was built from one basic component, repeated for each model.  I like the discreet gridlines (the white ticks) which enable readers to count off the mileage ratings.

The data is rich: ratings were given along three dimensions (model, year of estimate and city/highway).  Readers can benefit from a stronger guidance in where to look for the most pertinent information.  As the chart stands, it is merely a container for the data.  It fails our self-sufficiency test: all the data were printed on the chart, and the bars add little.

In the junkart version, I use knowledge of the data to structure the chart. First, noting that sedans, hybrids and trucks/SUVs/minvans have different levels of mileage ratings, I clustered the models into three groups.  Secondly, the city and highway ratings were separated into two columns as I consider the between-model comparisons more important than city-highway comparisons.  The chart is a dot plot, with a vertical tick for 2007 estimates and a dot for 2008 estimates.  It's easy to see that all dots sit to the left of vertical ticks.

More subtly, we can also see that the hybrids appeared to have been penalized more.  Or perhaps, the higher the rating, the larger the downward adjustment...

Source: "Mileage Ratings Are Still Estimates, Though Closer to Reality", New York Times, Sept 16 2007.