A Good Table Can Beat a Bad Graph: It Matters Who Plays Mozart

Visual Revelations

On a Sunday more than 25 years ago, I was in bed with both an awful cold and that day’s New York Times and Washington Post. I hoped the joy of having the time to read through both would mitigate the misery I felt.

I found enough data-based graphical displays to provide most of the examples of my The American Statistician oft-cited article “How to Display Data Badly.” In those days, it was easy to find awful displays, even in the best of newspapers.

Happily, things changed profoundly over the intervening decades, at least for the Times. (I no longer read the Post regularly and so cannot comment authoritatively about its graphics.) The graphs in the Times are remarkably good, especially considering the complexity of the data they often contain and the time pressures under which their designers often operate. In an essay in 2007, I compared the Times graphics favorably to those in the scientific literature. But, there is still an occasional slip.

The slip I now bring to your attention was an enormous plot that filled most of the back page of the News of the Week in Review section of the Sunday Times. In this graphic, the goals of communication and decoration collided—and decoration came out well ahead.

The display (a monochrome version is shown in Figure 1) is trying to show how badly retail sales fared for the first quarter of 2008 through the first quarter of 2009. To do this, the editors chose a representative sample of stores that might be found at a typical suburban mall (actually not—I have yet to find a mall with both Nordstrom’s and Walmart, but that is not among the flaws I care about).

Figure 1. A <em>New York Times</em> graphic in which the goals of communication and decoration collided.

Figure 1. A New York Times graphic in which the goals of communication and decoration collided.

In the top panel is this “gedanken” mall with stores sized (presumably) according to their sales in the first quarter of 2008. In the panel beneath, the same stores are rescaled to show their sales in the first quarter of 2009. We are supposed to be able to see by the relative differences in size how the recession has affected each store. To aid our judgment, the stores in the lower panel are colored to reflect the change in sales.

Does this display work? Alas, a resounding “No!” The sizes appear to be monotonically related to sales, but that’s all. If they were directly related, the area of Walmart would have to be almost 1,000 times greater than Build-a-Bear Workshop, rather than 20 by my measure. And changes are small relative to sizes, so trying to judge change visually is almost impossible. In fact, it is so difficult that the people who constructed the graph got confused and colored the stores that gained backward.

How can this display be improved? As I recently learned, I can get 50 or more spectacular alternative displays from talented readers by offering a year’s subscription to CHANCE (see graphic contest of Vol. 22, No. 2). But for now, the goals of this essay will be satisfied with a humble table.

In Table 1 are the data that generated Figure 1. The rows of this table are ordered by the percentage gain in sales over the year. Spaces are inserted between rows when there are substantial gaps in the percentage gains.

Table 1. Comparing First Quarter Sales of 27 Retailers in 2008 and 2009 Sales Figures (in Millions of Dollars)

Table 1. Comparing First Quarter Sales of 27 Retailers in 2008 and 2009 Sales Figures (in Millions of Dollars)

Note: The gaps were calculated by first transforming the percentages to logits and weighting the gaps by their location using approximately Gaussian weights. A substantial weighted gap was judged to be one that was larger than the median one.

We can easily see that only five of the 27 retailers showed a gain in sales, and they were not high-end stores. The chains with the biggest sales drop were higher-end or focused on a special market.

The table also reveals some mysteries. Restaurants McDonald’s, Denny’s, and Jack in the Box had losses of 10% to 17%. What makes Burger King different?

Of course, different orderings are informative for different questions; we could order by total sales or, if we wanted a simple graph, we could plot log (2008 sales) vs. log (2009 sales) and see other aspects. But, my goal here is to show how much of the original purpose of the display the designer could have achieved with a simple well-thought-out table.

Which brings me to Mozart. Sometimes I hear the question, “What’s better, a table or a graph?” I ask, “Is the music of Radiohead played by the Boston Philharmonic better than Mozart played by Spike Jones on the washboard?”

The implementation is often more important than the format. Until the options are implemented, the question has no answer.

Some readers will undoubtedly take the opportunity provided by the data in Table 1 to send me displays that are vastly superior to my table. But a table prepared with a little thought can beat a badly conceived graph—even if that graph took up a whole page of the Sunday New York Times.

howard wainer
Visual Revelations covers many topics, but generally focuses on two principal themes: graphical display and history. Howard Wainer, column editor, encourages using this column as an outlet for popular statistical discourse. If you have questions or comments about the column, please contact Wainer at hwainer@nbme.org.

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Further Reading

Wainer, H. 1983. Gapping. In Encyclopedia of statistical sciences 3:301-304. New York: John Wiley & Sons.

Wainer, H. 1984. How to display data badly. The American Statistician 38:137-47.

Wainer, H. 2007. Improving data displays: Ours and the media’s. (PDF) CHANCE 20(3):8-16.

Wainer, H., and M. Larsen. 2009. Pictures at an exhibition. CHANCE 22(2):46-54.

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