Junk Charts

Shower of bullets

Here's one of those infographics that makes the reader work hard (via Dustin J).  The graphic in its full glory is here; it's much too large to be reproduced, and I have clipped off the bottom half.

Much to the designer's credit, he extracted data of interest, rather than trying to cram everything onto the page.  In particular, he was most interested in the distribution of deaths among different age groups, the types of deaths (suicides, homicides) and the identities of the deceased (race, gender).

Just like the election fraud graphic, such rich data lend themselves to multiple levels of aggregation.  Here, the designer focuses on the most detailed level, making it easiest to see facts like "among the 18-25 age group, there were 6 black men murdered per day".

However, it takes much more attention to notice higher-level facts like "homicides per day are relatively flat across age groups while suicides heavily skew toward 40+".

In the junkart version, I decided to emphasize the more aggregated data, showing the number of deaths of each type across age groups. The detailed break-down of race and gender is shoved into parentheses, as they can be omitted by less serious readers.

The reader who discovers that the homicide/suicide pattern described above may surmise that homicide gunfire deaths are more "random" while suicides, being  premeditated, may affect older people disproportionately.  More research would be needed to confirm such and other suspicions.

Source: "An Accounting of Daily Gun Deaths", New York Times, April 21 2007.

 

Embedding logic

Bernard L. (from France) submitted this bubble chart for consideration.  It accompanied an NYT article claiming the absence of evidence of election fraud.  (Of course, as is well-known, absence of evidence is not the same as evidence of absence.  Here, I'm purely interested in data presentation.)

As a seasoned consultant, Bernard asked if a Marimekko chart would be superior.

This is one ambitious chart.  Ignoring the bubbles (which are more nuisance than anything), we are asked to interpret data at three different levels of aggregation in one go.

First, there were 95 cases classified into five indictment types.  Second, these cases resulted in either convictions or acquittals/dismissals.  Third, among the cases ending in convictions (the highlighted area), we were shown the occupations of those convicted.

By flattening three levels into one table, some key information is obscured.  For example, how many cases resulted in conviction?  The reader has to compute either 95-25 or 26+31+10+3.  What percent of civil rights violation convictions were committed by party/campaign workers?  It's not 2/3 = 67% (bottom row) but rather 2/2 = 100%.

The following junkart brings out the logic that is embedded in the complicated bubble-table.  While there is a lot on the page, the text labels plus the flow directions allow readers to absorb the data one level at a time.

I have not attempted the Marimekko as I am not a fan of such charts.  You're welcome to try.

Source: "In 5-Year Effort, Scant Evidence of Voter Fraud", New York Times, April 2007.

PS. I will be working through the backlog of reader submissions.  Thanks for your patience.  Keep them coming!

 

Remark (Apr 25 2007): Thanks to readers for keeping me honest (see comments below).  The conviction rates shown previously were indeed the inverse.  I have now fixed them.

Peripherals 2

In terms of interactive charting, Google Finance did much more than hide the legend.  In their main stock price chart, they used a number of neat features.

This chart effectively conveys a huge amount of information in a small space.  The bottom strip which shows relative prices for the past two years provides context to interpret the five-day movement shown in the main chart area.  I prefer to see a scale on the bottom strip as well. 

The sliding scrollbar can be dragged to show historical data.  Besides, the width of the window shown in the main area can be controlled.  For instance:

Without any effort, we are now looking at a 3-month chart for Q2 2006.  Notice the summary statistic on the top right corner also morphed.  The axis scale changed, and it never did start from zero to begin with.  (This shortcoming is alleviated by the profile chart in the bottom strip.)

Further, by placing the cursor in the chart area, we can highlight a particular day: a dot appeared on the price curve, the volume on that day was highlighted, and the text on the top right switched.  That text is what we typically place inside the chart area as a "data label".  The effect of moving it to the corner is similar to hiding the legend: it makes the graph more legible and provides space for longer descriptions.  As we move the cursor from left to right, the graph dynamically adapts.  Marvellous!

It may not be obvious the amount of data processing that has to take place to implement these sorts of features. I don't have space to address the data issue but maybe some of our readers can comment on it. 

Smoking-Screening

Behind the smokescreen lies the informative conclusion: among households with smokers, about 40% smoke in residence all the time while about half never smoke in residence.

This graphic, unfortunately chosen, contains many distractions from the main message, including:

• the liberal sprinkling of colors
• the inclusion of data for 1, 2, 3, 4, 5, 6 days, almost all of which were effectively zero
• the redundant vertical scale, as all the data already appeared on the chart itself
• the comparison of smokers to "total sample" (rather than non-smokers)

 

The last point merits special attention.  The total sample contains households with smokers as well as households without smokers. Any data from the total sample is a weighted average of these two types of households.  It is better to directly compare the two household types than to indirectly compare one type to the overall.

Further, households without smokers should be extremely likely to have no smoking in residence all week.  And if most households have no smokers (76% of this sample), then the statistics of the total sample will mimic those of no-smoker households. That is to say, the total sample statistics do not add much to the analysis.  Our junkart version below corrects for this as well as other things.

One of the key functions of a graph is data reduction, i.e. to aggregate data in such a way as to expose the information contained within.  Typically, a graph that uses aggregated data is clearer and stronger than one that plots every piece of data.  In this example, by combining 1-6 days into a single category ("smokes in residence part of the week"), we have a graph that is much more readable.

I want to thank Dr. Mike Rabinoff for inspiring me to look up these second-hand smoking statistics.  Mike recently published a book called "Ending the Tobacco Holocaust", which tells you more than you want to know about the tobacco industry.

Reference: "Second Hand Smoke Survey: Final Report", Madison Department of Public Health, Dec 2003.

Wading in waste

A poor graphic leaves readers wading in waste, in this case, the waste of time.  (Thanks to a tip from Dr. Bruce W.)

This very busy chart conveys a simple research finding, that the density of bacteria increases with the prevalence of impervious surfaces.  As Bruce pointed out, underlying this chart is but six observations taken at selected tidal creeks, each observation being a (paired) measurement of bacteria count and prevalence of impervious surfaces.

A factory worth of graphical elements was employed, including columns, pies, colors, data labels, legends and so on.  The result is utter confusion.  How is it that the tip of each column does not coincide with the center of each pie?  Do equal-sized pies imply equal surface areas?  What is the bacteria count at each location?

A scatter plot brings out the key correlation with minimal fuss.

Reference: "Wading in Waste", Scientific American, June 2006

Flight of fancy

The venerable Wired magazine has surely gone too far with this flight of fancy!  Consider:

• The zig-zagging lines streaming across the map
• The redundant white dots, each of equal size, contradicting the black dots, with size proportional to prevalence
• The inexplicable use of 00, 01, 02, ...
• The use of a taller column for human cases, when tallied, amounting  to about 1/20 the number for bird cases
• The inclusion of Australia (with zero cases) while excluding the Americas (also zero cases)
• Ordering the countries neither by bird nor human cases but by convenience of placement on the map

As with a previous example, the map adds nothing to the data except for providing a lesson in geography.  We prefer a parallel bar chart, shown on the right.  Here, the continents are given different colors.  In an unusual move, I chose different scales for each side as I am more interested in the distribution among countries, rather than the relative prevalence of bird/human cases.

Reference: "Flight H5N1: Delayed", Wired Magazine, October 2006.

Calming the rip tide

Xan Gregg at Forth Go helpfully scraped the auto market share data off the NYT chart discussed here before.  He even created an improved chart based on histograms.

I have created another view of the data, using boxplots.  Tukey's boxplot is one of the most spectacular graphical inventions, as I have said before (see here, for example).  Its power is evident again for this data set.

This chart is in fact two boxplots superimposed on the same surface.  I forgot to put on the legend: the green boxes represent U.S. market shares, and the blue boxes Europe shares.

The automakers are ordered by decreasing U.S. market shares (with apologies to European readers).

Lots of information can be immediately read off this chart:

• The European market is much more fragmented than the U.S. market.
• The Big 2 (GM, Ford) has had mixed fortunes over this period (as indicated by the large variance)
• The Big 2 are competitive in Europe although they are definitely not dominant there
• Several key players in Europe (Peugot, Renault, Fiat, BMW) have negligible shares in the U.S

Most importantly, there is little evidence that the U.S. market is "looking more like Europe".

One weakness of the above chart is the suppression of temporal information: there is no indication whether the recent shares are moving to the left or the right of the medians (center of each box). 

In the next chart, with the Europe data removed, I highlighted the data for the most recent 5 years in red.  I can make the general statement that there is a small movement towards less concentration and more parity in the U.S. market but one have to conclude that the U.S. market shares in 2000-2006 look more similar to the U.S. market shares in 1990-1999 than to Europe market shares.

P.S. I added legends to the charts.

Rip tide

As if a rip tide has torn through, this chart drowned the data in the depths of colors, scales and graffiti.

Scales - every chart has its own scale, rendering it impossible to read across charts.

Colors - every brand has its own color.  This feature is redundant since the data labels already serve the purpose of linking the two columns of charts.

Compression - it is impossible to judge the growth or decline of individual companies, especially since only the current market share is provided.

If anyone has access to the data, please send them over so we can remake this chart.  Or just send in your charts and I'll put them up here.

Reference: "Now Playing in Europe: The Future of Detriot", New York Times, Oct 28 2006.

Arming the competition

At the TCS blog, Tim Worstall attacked a chart comparing global levels of income inequity, originally published by the Economic Policy Institute.  His post is here.  Tim claimed that this chart proved precisely the opposite of what the EPI intended it to show, that is, that the chart showed that "the poor in America have exactly the same standard of living as the poor in Finland (and Sweden)", two countries which he derided as "redistributionist paradises".  From this, Tim concluded that the U.S. is doing enough for the poor.

Stephen C., who sent in this chart, was very confused by the length of the bars: left of the divider, the larger the income index, the shorter the bar; right of the divider, the larger the income index, the longer the bar.

For the EPI, this is a case of arming the competition.  Echoing Robert's comment from yesterday, this is one chart that opines but should have murmurred. 

The chart is a very convoluted way to study the idea of income inequality.  The first bar states that the 90th percentile income in Finland is 1.11 times the median U.S. income, after adjusting for PPP.  Notice the simultaneous change in percentile and country, which complicates our understanding of the difference.

The median income is perhaps the simplest (not most informative) measure of income equality.  In the EPI chart, the edges of each bar describe the 10th and 90th percentile income in a country.  We only know 80% of the population lie within each bar but nothing about how they are distributed.

In the revised chart, I plotted another popular measure of income equality, the ratio of 90th percentile to 10th percentile (since the data is readily available from the EPI chart).  It's clear that inequality is highest in the English-speaking Western world where the top earners get 4-6 times more than the bottom earners.

This income ratio is computed for each country, and can be used to compare across countries without resorting to another index. 

Reference: "America: More Like Sweden Than You Think", TCS Daily, Aug 26 2006.

Jamming

Readers may have noticed that I'm not a fan of the graphics aesthetics of the Economist.  (I love their subtle sarcasm, a way of saying something without saying it.  For example, the title of this chart is "where they are".  They let us read any meaning into the word "they".  As for their charts, I have taken issue on several occasions.)

This particular example uses one of their standard formats, stacked bars with an extra data series tagged on the right, its boxed annotation calling attention to itself.  It's a case of too much apparatus for a simple task.

The chart's purpose is to show that the US and France have the largest Muslim populations by numbers while France is by far the top country by percentage.

Our junkart version is very much cleaner.  Line segments indicating the low, mid and high estimates replaced the stacked bars (which falsely imply significance in adding the low and high estimates).  As usual, the minimum of gridlines and axes is used.  Instead of jamming two ideas onto one chart, if percentages are more important, then a separate chart should be produced, now ordered by decreasing percentages (see below).

The most crucial improvement is the fine print.  Perhaps extending their subtle sarcasm too far, the chart maker omitted context for interpreting the data: namely, that the low-mid-high range represents estimates by up to 5 different sources, each using potentially different methodologies for estimation.  This partially explains the huge variance in estimates for the US (or does it?).

Also missing is a comment on why these particular 6 countries were selected.  It may give a misleading picture of "where they are" in the context of world population.

Reference: "Where They Are", Economist, June 2006.