Circles of hell

This began as a commentary on perception of one, two, and three dimensional graphics, but that will have to wait for another time. Instead we will spend our special time together excoriating just one little graph. Here it is, from a recent issue of the New York Times.


As (almost) always, we begin with a simple question: when you first glance at the graph, what fact or idea pops out? For me, the answer is: “how long until lunch?” In other words: nada. There are a bunch of big red balls, and a whole bunch of squirrelly little lines pointing every which way, and numbers all over the place. Something is going on, but it hardly seems worth the effort to figure it out.

Upon further tedious scrutiny, we deduce that the graphic is telling us something about rates of cellphone and landline usage. OK. How fast are they changing? Which is changing faster? Did rates cross? What year? Is the rate of change of either  accelerating? Decelerating?

I venture that you were able to answer none of these questions without careful study of the graph, perhaps even with a ruler. And if you had used a ruler, you would have been wrong, but we will get to that in a minute.

Below we will enumerate the five separate things that are wrong with this graph. First, a simple conventional graph of the same data.


Simple. Easy to understand. The trends jump right out at you. No rulers required.

But as John F. Kennedy really meant to say: “How much more fun to curse the darkness, than to light a candle.” Let us turn our attention to what is wrong with the original graph.

1. The use of disks or circles to depict quantity is problematic.

As will be discussed at greater length in a subsequent post, folks are not so good at judging area. If you represent quantities by areas of disks, that may not lead to correct judgements about the relative magnitudes of quantities.

2. The area of the disks does is not proportional to the quantity depicted.

Even if people could judge the area of circles, they would get the wrong answer. Amazingly, the artist appears to have just used “artistic judgement” to decide on the size of the disks. The actual areas are plotted by the dashed lines in the next figure. Not even close.


3. The diameter of the disks is not proportional to the quantity depicted.

Perhaps the artist intended the diameter to represent the quantity? We show this by dashed lines in the next figure. Closer, but not quite. But even had it been correct, why would the artist imagine that readers would sense diameter, rather than area? This ambiguity illustrates one reason why the use of 2D or 3D markers to indicate quantity is problematic.


4. The graph distorts the time dimension.

Notice that the disks in the original graph are all spaced evenly along the time (vertical) dimension? But the years involved are not equally spaced, as can be seen in our substitute graph. The gaps range from 5 years to 1 year. Failure to correctly depict the time dimension makes it impossible to correctly judge rates of change.

5. Maximum and Minimum cannot be depicted.

The quantities depicted here are percentages, so there is a clear and inviolate minimum and maximum of 0% and 100%. But how do you indicate either of those with a disk? 0% is impossible, and 100% is ambiguous. Thus the use of disks to represent quantity makes it impossible to indicate the bounds of the data. In contrast, a simple point-and-line graph like ours easily shows these bounds, and their proximity to the data.

To conclude, big colored disks make for a fun and bold graphic, but are pretty useless when it comes to actually conveying information. Real graphing artistry consists of beautiful graphic design that also conveys a clear and accurate message.



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