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


The direction of time’s arrow

Once again, the target of our arrow of criticism is the estimable New York Times, and their estimable Charles M Blow, whose op-ed contributions are always interesting but almost equally often decorated with sadly defective graphics. In this example, we have a graph that is wrong in at least five ways. Can you spot them? Here is the graph.

The subject of the graph is the change in approval rating of President Obama following the killing of Osama bin Laden, for various selected groups. It is certainly possible to extract the information for any given group from the chart, especially because the artist kindly prints all the numbers, but in this regard it is little better than a table. And a graph should be more than a table, it should use your native perception of form to make a point.

The first error is the use of space. As is often the case with Mr Blow, the graph occupies a remarkable amount of vertical space, considering the modest data it contains. For this reason, you may have to expand the graph just to be able read its contents. As we will show, these data can be plotted in much less space, with an increase in clarity.

The second thing that is wrong with the chart is the selection of colors. Since before and after are depicted with color, we would like a strong contrast between the two. Instead we get a weak difference in brightness and saturation of two greens. Quick, tell me whether any subgroup showed a decrease in approval! I suspect you had to scrutinize each pair of bars, carefully ensuring that the darker one was shorter.

The third thing that is wrong is that the bar depicting “after” is about twice as wide as the “before” bar. Thus the area of the “after” bar is much larger, even if there were no change in approval. This is potentially confusing, ad certainly biased against the before figure.

The fourth thing that is wrong is that the bars are overlapping. This makes it harder to see the length of the “before” bar.

The fifth thing that is wrong is that the graph fails to exploit our native sense of how to depict an increase over time. By convention, in graphs time is always shown as proceeding from left to right. And positive quantities are always shown as increasing from bottom to top. The horizontal arrangement of the chart, and the overlapping of the before and after bars, fails to observe either of these conventions.

Another way to be absolutely sure that the viewer understands the direction of time is to actually show it as an arrow. This is especially appropriate when only two points in time are involved.

Correcting all of these errors, we produce the following chart.

While this chart should require no explanation, I will make a few comments on design. First, unlike the New York Times, I do not have an army of graphologists to tweak my product to perfection. This is a first draft, created in a couple of minutes, and could doubtless be improved. But it clearly shows that every group showed an increase, and the relative size of each increase. In each bar, time goes left to right, and approval increases from bottom to top, just as we expect. The arrows reinforce each trend with a strong graphic element, while the single green bar shows the absolute values of approval, and ties each arrow to its group name. We omit the actual numbers, but provide a 50% line for guidance.

My chart makes all the essential points, and does so in a way that is immediate and transparent. Mr. Blows chart has a certain graphical panache to it, and that is not a bad thing. But panache should never replace clarity.


 New York Times
The Bin Laden Bounce
Published: May 6, 2011

Razing the bar

Like most folks, I am convinced that my prejudices are grounded in logic and common sense. But in my case, they really are. Really.

For example, I have an outsized contempt for the bar graph. In my view, it almost always makes relationships difficult to discern, and masks what information is present with massive amounts of obscuring ink. I will have more contemptuous things to say about the bar graph in the future, but for now, lets consider an example.

Here is a chart that appeared recently in the New York Times (Rethinking Early Retirement in Europe, Oct 29, 2010). The context is an otherwise worthy article by Floyd Norris on early retirement in various countries. The chart shows, for men and women separately, the proportion in each age group who are working or seeking employment.

Now most of you will struggle to make out anything here, because everything is too small. And that’s because the artist was dealing with a lot of data. Well, actually, no. The amount of data here is rather modest. It is only the amount of space used that is extravagant.

And what point do you get when you first “grok” the picture? At best, with a moment’s study, you might appreciate that people work less as they get older. But that is hardly the point of the story. Rather that point is that the French retire early. Does that jump out at you from the figure? I didn’t think so.

Now lets see if we can do better. Here is my quick version. I have plotted the data as a line graph, and the data for each country form a line, coded by color. This immediately shows the rate of decline for each country, and quickly shows how France stands out from the rest.

Of course, if the point of the story is only that the french retire early, then why not show that instead? In my next graph I have shown the french male labor force participation, as a fraction of average participation across the other five countries. Here the point is even more obvious. It jumps out at you. That is what should happen with a good graph.

In my first graph I showed shown men and women separately, as in Mr. Norris’s graphic, but here again, what is the point being made? If it is the relative participation in he workforce of men and women, and how that changes over time, then show that! In my next figure I show the ratio of men and women, for each country, over time. This makes it easy to see, for example, that in all countries men outnumber women in the workplace, and that the imbalance increases with age. It also makes it easy to see the relatively high participation of US women, over all age groups.

So, what are the lessons? First, avoid the bar graph. Second, use lines to connect related quantities and show trends. Third,allow the reader to easily make comparisons, where that is intended. Fourth, use a graph that makes your point. Don’t force the reader to do their own analysis. Otherwise, you might as well provide (horrors!) a table of numbers.


Rethinking Early Retirement in Europe, New York Times, Oct 29, 2010.

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