Friends don’t let friends use bar charts

A recent article in the New York Times drew attention to the lack of economic mobility in the United States, as compared to Canada and much of Western Europe. The article was illustrated with a graphic, which we reproduce below. It illustrates, for the US and Denmark, the percent of men raised in each fifth (quintile) of the economic range who end up in each fifth.

This graphic is not terrible: with enough scrutiny you can probably figure out the point being made. But because we enjoy picking on the Times, we will explore its various failings just for fun.

First, if I have told you once, I have told you a thousand times: no bar charts! They are almost always inferior to a comparable point and line chart. They waste ink, obscure trends, and – most relevant here – make it hard to compare two quantities. Note the extremes to which the Times artist has gone: the the Denmark data are a fat light gray bar, while the US data are a superimposed thin dark shaft. This trick to display two quantities in one location violates several canons of graphology. The first is that it is not “equitable:” the two nations are not plotted with symbols of equal visual weight. The second is that it makes it hard to see trends. And the third is that, worst of all, it actually makes it hard to compare, at a glance, the data from the two countries.

Here is a roughly similar graph that uses boring old points and lines. Color is used to distinguish the two countries.

We immediately see two things. First, only the first panel shows interesting differences between the two countries. This is the graph for men raised in the bottom fifth, and it clearly illustrates the point of the article: most men raised poor stay poor, and this trend is much more severe in the US than in Denmark.

The authors might have done us a favor by pointing out that in a true “opportunity society,” in which everyone regardless of economic origins has an equal chance at success, all of the graphs should be flat at 20%. The middle three graphs approximate this ideal, but both the leftmost and the rightmost graphs are very non-flat. This shows that the poorest and the richest are the least mobile; only the middle classes approximate the ideal of equal opportunity. This is true in both countries, but more severe in the US for those raised in the poorest quintile.

It is interesting to look for a way to depict the mobility within a single country, that does not require five separate graphs. One solution is to plot the percentages as a surface or an array.

Here is an example. Here we represented the starting and ending quintiles by rows and columns. Each cell shows the percentage of men that started in a given quintile (row), and ended up in a given quintile (column).  We scale the colors so that a percentage larger than the ideal 20% is red, less than 20% is green, and the equal opportunity ideal of 20% is a neutral color.

In the US, it is evident that the two “hot spots” are the lower left and upper right corners. These are the too many folks born poor who stay poor, or who are born rich and stay rich, respectively. The Danes suffer only from too many born rich who stay rich; those Danes born poor appear to experience nearly perfect mobility.

What are the lessons?

  1. Avoid bar charts, especially when trying to depict the covariation of two quantities.
  2. Don’t use five graphs when one (or two) will do.
  3. Something is rotten in Denmark, but two things are rotten in the US.


New York Times

“Harder for Americans to Rise From Lower Rungs”


Published: January 4, 2012


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