Junk Charts

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!
  

The case of the shrinking mall

I had a similar reaction when reading this chart but I will let our reader take center stage.

Top portion

Bottom portion

The back of today's New York Times' Week in Review section devotes half of its space to a lame infographic that wastes space and has a major error (which has been corrected lazily in the version now online at http://www.nytimes.com/interactive/2008/10/14/opinion/20090531_OPCHART.html ) The chart shows the recent decline (or in some cases, rise) of retail sales at 27 common mall chains. My main objection is that the top half of the chart is useless. Yes, it provides a baseline from which shrinkage in area (visual metaphor of income = floor space) in the bottom half can represent the relative declines in sales, but this is redundantly handled better by color. The only part of the chart that I got any information from was the bottom half, and it took me a while before I figured out why the top half was even there. Meanwhile, the error in the printed version is that the +5-10% stores were colored light green while the +0-5% store (Burger King) was colored dark green. It should have been vice-versa. The online version simply swapped the colors in the legend, rather than on the map itself, which works logically but begs the question: why do you have dark red at one end of the spectrum and light green at the other, with dark green in the middle? Thank you for listening-- just blowing off a little steam here. It's a lot of wasted space and I'll bet the New York Times paid a lot for it.

Reference: "Op-Chart: The Fall of the Mall", New York Times. (Ed: I am not sure why the date is given as October 2008.)

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.

The trouble with maps

Todd B. pointed us here.  These are maps that supposedly show the distribution of respondents for each answer choice in a survey exploring accents in different parts of the country.  The full set of maps for every question can be found here.  

Amusingly, the researchers also provided a map of "all respondents".  (I won't ask how the proportions of respondents were reduced to binary output to produce the above maps.)

Here is Todd to lead off the discussion:

Just because you put data on a map doesn't make it effective. Check out these mapped responses that either tell us that there is no difference in dialects or fails to illustrate differences effectively.

Reference: "Dialect Survey", University of Wisconsin-Madison.

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.

Political theater

Jens, a long-time reader, tried to re-make the boring data tables used to report poll data.  Here is an example from USA Election Polls (left) and his enhanced version (right).

Like Jens, I find most of the tabular presentation of poll data underwhelming.  Too much data hiding all the useful information.  For example, the pollster and polling date data provide a context for super-serious poll watchers to interpret the data; however, they do not present themselves in a way that actually help readers.  Read further for versions that bring out this data much better.

Meanwhile, Jens' revision uses color and ordering to bring out the current state of affairs.  The addition of electoral votes allows us to understand the relative weight of each row, countering the weakness of the tabular format, that each row has the same height, implying erroneously that they have the same importance.

There are a number of good web-sites where this type of data is presented in attractive ways.

I have been a fan of Political Arithmetik, which made great use of the pollster and polling date data mentioned above.  Those data have been averaged to show the overall trend while the individual poll results are plotted as dots in the background.  The polling date data is embedded in the horizontal positions of the dots.  Even more impressively, the margins of error are presented.  Remarkably, this race has been a statistical tie for all these months, the 95% lower limit never quite making it above the zero level.

Another great site is fivethirtyeight.com.  Below, they essentially turned Jen's enhanced table into a map.  The legend on the right perhaps represents what they call "East Coast bias"?  All of Nathan's graphs are very attractively produced; I just wish he'd put more labels on them (such as the differentials corresponding to shades of red and blue.)

Loss aversion

Loss aversion manifests itself in chart-making, as it does in economics.  In chart-marking, loss aversion can be defined as the tendency to avoid losing data at any cost.  Given a rich data set, designers often make the mistake of cramming as much data into the chart as possible.  This is taking Tufte's concept of maximizing data-ink ratio to the extreme, and it often leads to awkward, muddled charts.

Gelman provided a great example of this recently.  See here. 


Every piece of data is given equal footing, which results in nothing standing out.  The reader gasps for air.


Here is a recent example from the New York Times, in which the designer showed admirable restraint.

  The best evidence is the set of small multiples shown at the bottom.  These give the amount of phosphorus flowing into the lake annually since 1973, as measured from four locations.

The point is that the pollution has been most serious on the northern shores, especially in recent years.  Thus, the Florida plan focusing on the southern region is likely to make limited impact.

The choice of vertical lines is smart, as the typical time-series connected-line chart would jump up and down crazily.  A simple vertical axis marks the amounts, avoiding the temptation to print all the data.  The designer realizes it is the trend, rather than individual values, that is the issue.

Taken together, the three components tell a good story.  This is a well-executed effort.  The Times once again proves itself the leader in developing sophisticated graphics.



Reference: "Florida Deal for Everglades May Help Big Sugar", New York Times, Sep 13 2008.

Lining things up

Guess where I went for vacation (clue in the chart).

This long, narrow country is divided into 15 regions.  In the chart below, an uneven parade of 13 bubbles was used to present some sort of economic projections.  The capital of the country was singled out as the top of the table.

The unevenness has a side effect, that the guiding lines are forced to have differing lengths and bewildering turns.  Further, because bubbles have no intrinsic scale, the designer must put all the data onto the map as well, thus failing our self-sufficiency test..

The following bar chart version respects the wide, thin space and yet delivers the data more clearly.  The top version displays all the data while the bottom one uses a simple axis.  The bottom chart is my preference since most readers are probably interested in approximate and relative comparisons, rather than exact projections.  (The map would be better off without colors.)

Reference: "Inversiones entre 2008 y 2012 llegaran a US$ 57 mil millones impulsadas por mineria y energia", El Mercurio, Aug 25 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.

Making maps

I love articles that expose the behind-the-scenes of creating complex graphs.  This Wall Street Journal blog post tells us some dirty secrets behind these cartograms that depict the "influence" of different media outlets throughout the world.

(Via Andrew Sullivan; he's dissing NYT again)

Additional links of interest:

Original posting at Paris-based L’Observatoire des Médias blog

Boing Boing

Gawker

Online Journalism Blog (warning: this link is taken over by a rogue script from an advertiser or some other entity that distributes scripts so it wasn't loading when I tried)