Junk Charts

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!

Trying too hard

In the course of business and governing, a lot of charts are generated.  An anonymous tipster pointed us to a set created by the "Communities and Local Government" division in the UK government.  Judging from the content, this division has responsibility for economic development in local neighborhoods.

Below are a pair of exhibits.  Truly they are trying too hard!  What we see is a hybrid scatter-bubble chart.  Between the jargon, the acronyms (LAD, LSOA), the boxed text, the multi-color circles, the colored axis labels and lack of title, the reader is plunged into a state of confusion.

The chart can be unraveled.  Each district was evaluated based on two measures of "gaps in worklessness".  The vertical axis compares each district to the national average; positive numbers indicate an above-average district relative to the nation.  The horizontal axis compares the most deprived 10% neighborhood within each district to the local average; positive numbers indicate worst neighborhoods improving. 

Thus, the policy goal would be to move all districts into the upper right quadrant.  The multi-color bubbles were designed to show us the state of the nation.  On the left chart, 41% of the districts (or population?) reside in the improving districts while 19% live in deteriorating areas.

The following strategies can help improve readability:

• use English on the axis
• relegate technical definitions to the legend
• add succinct title to tell the story
• use color on the data rather than on axis or data labels
• use color to draw attention to the upper right quadrant
• remove bubbles
• define acronyms

 

Ordering and grouping

The Times reported that January retail sales generally disappointed, and consumers showed a preference for discount retailers over department stores.

Taking the bar chart on the right, re-ordering by change in same-store sales, and grouping companies by type of retailer, we can present the data to match the text more closely.  The divergent performance between discount retailers and department stores is readily visible.

Reference: "Weak January dashed retailers' gift-card hopes", Feb 8 2008.

 

Light entertainment

Christopher P submitted this chart, which is great for our light entertainment series.

Apparently it came from the Netherlands and showed how privileged their citizens are compared to the rest of the world.  It would appear that they need to reverse the color scheme (and font size?) to highlight the privileged.  Comments welcome.

Source: AdsoftheWorld.com

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.

On the bubble

A couple of you noticed this table of bubbles in the Times, and asked what I think of it.  Dustin J suggested that this could be considered a decent application of bubble charts.  I agree, with some reservations.

The data set is the best thing about this chart.  The riches that lay beneath!  Many questions can be addressed, including:

• Which Presidential candidates are getting the most face time?
• Are candidates seen equally often across the stations?
• Are there differences between network and cable stations in terms of total face time?  In terms of individual face time?
• Are there Democratic/Republican leanings by station?  by type of station?

The intrepid can even build a regression out of it.

The bubble chart contains answers to all those questions but nothing jumps out. Okay, it's easy to see the station that gives each candidate the most face time.  Anything else requires moderate to a lot of effort.  Here's the junkart version.

The list of things done to the data is long:

• Candidates are grouped together by party
• Candidates within each party are arranged in order of decreasing maximum face time
• Stations are arranged by increasing total face time, this order happens to retain the network vs cable divide
• A heat map construct is used instead of bubbles: the legend is missing but there are four hues for each color: darkest = top 10%; medium = 10th - 50th percentile; light = bottom 50th percentile excepting zeroes; white = no face time.  In raw numbers, 90th percentile = 81 minutes, 50th percentile = 19 minutes.
• The only data shown are the totals by candidate and totals by station.
• On the right margin are little bar charts that show the distribution of network/cable for each candidate.
• On the bottom margin are little column charts showing the distribution of party affiliation by station.

A few observations follow:

• Cable stations gave much more face time to the candidates in general.  Fox, no surprise, gives Republicans 85% of its time while all the others were roughly equal.
• The more mainstream the candidate, the balanced was the time spent on networks versus cable.  John McCain (R), Hillary Clinton (D) and John Edwards (D) had the highest proportion of network time.
• More time is not necessarily good since McCain was the clear winner but his campaign is struggling

Source: "Tracking Face Time", New York Times, August 1, 2007.

Gauging the water level

This set of charts covered the back page of one of New York Times' sections this weekend.

Regular readers will share my enthusiasm for the top chart.  It makes a clear, cogent case to support the article's thesis concerning the rise of bottled water.  Various renditions of this type of chart have appeared here, for example.

Specifically, the smart use of color to cluster the line objects helps interpret the trends.  Blue sets out the two primary interests.  (It's a mystery to me why the gray lines were separated into darker and lighter hues.)

The twenty-year horizon used is another nice touch. I'd remove the gridlines although they aren't too distracting here.

Sadly, the second graphic does not meet the high standard of the first.  The biggest problem concerns the red rectangle, purportedly showing how much of the bottled water was imported.  The choice of differently-sized bottles as objects makes it impossible to gauge what proportion of the total was imported.  If the rectangle was placed over 1-litre bottles instead, it would look smaller.

Source: "A Battle Between the Bottle and the Faucet", New York Times, July 15, 2007.

More prevalent versus more likely

Aleks pointed to an interesting Business Week chart used to explain what people in different age groups are doing on-line.  This is a pretty chart that does an admirable job with a difficult data set.

The key to this chart, unfortunately missing, is that the percentages must be read as vertical columns to make sense.  So the top left square says 34% of "Young Teens" who answered the survey said they create web pages on-line.  In addition, the total of each column can be much more than 100% because multiple responses were allowed.

Realizing the above, we should interpret the bottom (grey) row as saying: "Older boomers" and "seniors" are more likely to be "Inactives" than younger people.  A tempting interpretation is: "Inactives" are more likely to be "seniors" and "older boomers".  But this is wrong because the chart hides the age distribution.  While 70% of "Seniors" are inactive, "Seniors" may represent a small proportion of the population, and thus they may not account for a large proportion of "Inactives".  This is the difference between prevalence and incidence rate.  (Another way to grasp this is to add the percentages across a row and try and fail to understand what the row sum could mean.)

The construct of the square grids is less damaging than it seems.  In effect, the data has been rescaled by dividing by 10.  The reader is then forced to apply "rounding".  If you are someone who sees $19.95 as $19, then you'd round down the partial rows.  If you see $19.95 as $20, you'd round up the partial rows.  So the designer has pushed you to think in terms of whole numbers between 0 and 10, in other words, in units of 10%, rather than units of 1% or, horror of horrors, 0.1% or at some other unrealistic precision.

Here's another example where the profile chart shines.  Because the percentages don't sum up to 100%, the other alternatives like stacked bar charts and "Merrimeckos"/mosaic charts don't work.  (Prior discussion of this issue here.)

This version gives a column view of the data, the lines linking percentages of each age group performing on-line activities.  The profiles nicely cluster into three groups: the younger people are more likely to say they are "joiners", "spectators" or "creators" but less likely to be "inactives".  We also see that the likelihood of being "Collectors" has little to do with age.

Source: "Inside Innovation -- In Data", Business Week, June 11 2007.

Less is more

Derek pointed me to the style.org site which also parses political speeches.  Their preferred graphic is not the tag cloud but a labeled bar chart.

From top to bottom, each bar represents a sentence; the length of each bar is the length of each sentence.  Further, the user can specify word pairs for comparison.  Here the red bars are sentences containing the word "freedom"; the blue bars, "security".

It's a good illustration of the "small multiples" principle in constructing comparative graphics.

However, the choice of dimensions is perplexing.  I'd be much more interested in the timing of mentions of those words, rather than which sentence they appeared in.  I also find the length of each sentence to be irrelevant.

Here's one concept that brings out the point better.  It uses less space and voluntarily gives up some of the data (the sentence structure).

The trouble with percentages

In the aftermath of the Democratic victory in the 2006 mid-term election, the NYT published a column floating the idea that "it was the economy, stupid".  For statistics buffs, this column provides much food for thought. 

Suffice it to say, if you were my student, you would not want to hand this in as an essay.  To the author's credit, he did backload the article with lots of disclaimers.

The key thesis of the piece is:

if your state wasn’t among the best economic performers in the last six years, judged by the growth of personal income, it appears that you were three times as likely to vote to throw the bums out.

(We'll just assume he didn't mean "you" but "your state".) To help us understand the author's logic, I created a scatter plot, relating the change in state average personal income (2000-2006) to the change in percent of Republican seats.

He first segmented the states into two groups: the red dots had the top 10 income growth rates; the blue dots were the remaining states.  Then for each group, he computed the average drop in % Republican.  For the reds, it was 2%; for the blues, it was 7%.  (These levels are indicated by the horizontal lines.  My data are slightly different from his.)  Case proven -- with disclaimers.

Some of you are already counting the dots.  If you only find 42, you'd have counted correctly.  The following explanation provided by the analyst is classic:

It’s easier to answer this question if you leave out the six states that didn’t elect any Republicans in 2000; after all, they didn’t have any to throw out. If you also remove New Hampshire and South Dakota, where the percentage of Republicans elected dropped to 0 from 100 — New Hampshire only has two seats in the House and South Dakota has one — a pattern starts to appear.

I will leave the emergent pattern thesis to a future post.  For this post, I am interested in the trouble with percentages.  He is right to point out that for those 100% Blue states, the change in %Republican is constrained to be positive, from 0% up to 100%.  For most other states, the change can be positive or negative.

Good observation but wrong remedy -- those six states with 0% Republicans in 2000 are not special; removing them from the analysis is wrong-headed.  What about those states with 100% Republicans in 2000?  There, the change in %Republican can only be 0% or negative.  In fact, the possible range for the change in seats for each state is different, and it depends on the Republican proportion in 2000!  For example, if in 2000 the Republicans held 30% of the seats, then in 2006, the change must be between -30% and +70%.

The situation is worse: the range of possible values also depends on the number of seats in each state.  The fewer total seats there are, the fewer possible values that can be taken.  As the author notes, with only 1 seat, you either lose it, gain it or retain it, so that the change will be either -100%, +100% or 0%.  No other values are possible!

Both the above troubles arise because we use percentages to describe something discrete (number of seats).  This is a difficult problem and I don't know of a general solution. However, in this example, because the change in seats is small across all states, regardless of the total number involved, I recommend that we avoid percentages and stick with positive, zero and negative changes.

The boxplot shows that there is little correlation between income growth and whether Republicans would win or lose House seats in 2006.  Here, the states are divided into three groups depending on whether the Republicans gained, lost or retained seats in the 2006 mid-term election.  The median income growth are similar in all three groups and the boxes overlap heavily.

Reference: "Maybe You Did Vote Your Pocketbook", New York Times, Nov 12 2006.

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