Junk Charts

Digging it out

Another sunset photo compilation?  Not quite.

This chart acts and smells like the sunset chart, being generated by many unknowing collaborators, this time, visitors to the content aggregation site, Digg.  For those unfamiliar, web browsers can "digg" any web page they find interesting (by clicking on an image), which causes a link to be generated at Digg's web-site.  We can use the number of Diggs to judge the value or popularity of a web page.

In effect, Digg is a gigantic save folder for the masses.  What happens when we have huge amounts of data?  We have to work really hard to dig out the useful information.  This chart goes quite a long way to answer one specific question.

Digg users are plotted horizontally and the stories they Digged are plotted vertically.  The bright white vertical strip represents suspicious activity; some user digged a large number of stories within the time window of the chart, most likely a bot trying to usurp the mass rating system.

Flickr and Digg are two of the more prominent stories of the so-called "Web 2.0", or mass collaboration on the Web.    Between my last post and this post, I have kind of lost enthusiasm for this type of charts, at least from a statistical perspective.  There is no real collaboration: the photographer who contributed sunset No. 103 does not know the one who uploaded No. 31, for example.  Using this logic, every survey or census ever conducted qualifies as mass collaboration, just because there are many participants providing data. 

What's worse, a typical survey brings together results from a random sample.  These charts all have highly biased samples, and I haven't seen any discussion yet of this issue.  They cannot be interpreted without understanding who participated.

Reference: "How Digg Combats Cheater", Technology Review, Jan 24, 2007.

Emergent patterns

It's always a pleasure to read blow-by-blow accounts of how charts were constructed.  The piece on time-travel maps was instructive.  Similarly in the previous post, I quoted the following:

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.

At first sight, this appears as a case of removing outliers, which many statisticians recommend.  Except that the data omitted were not outliers.  Indeed, when both x- and y-variables are bounded (between 0% and 100% share of the House seats; between -100% and +100% change in share), there can be no extreme values.

In effect, when the author eliminated those eight points, he followed the "emergent pattern" theory, by which I mean the notion of removing data until a pattern "emerges".  (By the way, emergence is now a science, as expounded here.)  If enough data is removed, one can produce any pattern as one pleases.  One can find subsets of data to support a hypothesis of positive linear, flat linear or quadratic, as shown below.

Focusing now on the full data set on the upper left corner, one is hard pressed to conclude that a positive correlation exists between the two variables. In particular, most states experienced no changes in the share of House seats, and in these states, the income growth ranged from under 20% to over 40%, which is pretty much the extent of variability across the full data set.

The elusive catchup

Thanks to Michael S. for sending in this chart from the economists at IMF (via this blog).

At its heart, this is a scatter plot that displays the correlation between a country's development stage (indicated by its PPP GDP) and the importance of the industrial sector to its economy.

On top of that, the chart adds a third dimension of time by linking the dots together with lines.  The lines trace the evolution in each country or set of countries.  Some countries (mostly developed nations) have a clear trend; others exhibit choppy curves which imply fluctuating economic conditions.

We have created this type of chart when discussing the fabulous Gapminder site.

The shading in the chart is supposed to draw attention to an inflection point around $15,000 per capita GDP, wherefrom the industrial sector starts to decline in importance.

In my view, that conclusion is forced because Korea is the only curve displayed on the chart that bridged the $15,000 divide.  Thus, one can say there exists only one data point supporting this hypothesis.

However, one aspect of this chart jumps out at us, which is the chasm between developed and developing countries, right at the $15,000 divide.   On the right side, the rich gets richer in a relatively steady fashion.  On the left side, the poor remains poor.  These nascent economies suffer from a great deal of volatility.  What's worse, the slopes are much sharper on the left than on the right, meaning that the gains in GDP are much smaller on the left of the divide.  Even more troubling are the cases of Brazil and Mexico which seemed to have endured a decline in the industrial sector without much gain in GDP.

The only bright spot is Korea.  (And China is the outlier.)