Deceptive Areas

areas_circle.gifPeople are poor at accurately judging areas; they do much better comparing linear measures like the lengths of a bar or the heights of a point. Areas can be useful where precision’s not important—circles can be scattered over a map, for example, to allow readers to scan for trends. But too often designers indicate data with areas because shapes are cooler than lines and you can arrange them in pretty patterns.

Regardless of the shape chosen, because we have a hard time judging areas, it’s vitally important that sizes are calculated accurately: namely, proportional to the value they represent. Otherwise the designer is telling lies.

From the Sunday New York Times magazine for February 25, here’s another mess from Catalogtree. There are plenty of poor choices made here—note the particularly ugly way that circles have been doodled on top of the text, making the chart look like a printing error. Leave aside also the fact that half the wording consists of dull qualifiers that could have been easily turned into footnotes, and that the designer could think of no better way to arrange the text than just dumping it on the page in a block, as if they didn’t actually want anyone to read it. These pale into insignificance beside the circles being the wrong size.

areas_circle_lie.gifNote the largest value (892) and the fourth largest (436). One is just over twice the size of the other, and a circle twice the size of another should have a diameter √2 as big: about 1.4 times as wide. The larger circle in the graphic is actually about twice as wide, and it’s about four times as wide as the 204–225 circles. To see this amount of distortion this creates, compare the original proportions of the two largest circles, (right, top), with the corrected ones (right, below). I bet the designer just halved or doubled the circle diameters rather than actually calculated the areas required, which is pretty inexcusable.

To see the the way it should be done, check out the circles from an earlier New York Times article reporting frequency of the word “Iraq” in different presidential State of the Nation addresses. The first circle is twice the area of the second, not twice the width. Note the elegant overlapping too.


It’s understandable that some designers might mess up circular areas, as it takes a little algebra to work back from the desired area to calculate the right diameter to use; namely, 2√(area/π). But even simple squares can defeat a designer’s math abilities. Below is another example from a much earlier NYT magazine—the design firm 5W infographic, discussed in a previous posting, is no longer used by the Times.


How do we know if there might be a problem with an information graphic? One clue is weird instructions on how one should interpret it; a good data graphic doesn’t need instructions in how to read it. Note, for example, a key that points out that area only 25% of the original somehow equals 50% of the value. Again, this looks like a math-phobic designer at work. Illustrator’s Info palette works in widths and heights, not areas, so it’s easy for a designer to drag to draw a square where one pixel of linear distance, not area, equals 1% in value. Actually calculating the correct widths, from √area, was obviously too difficult.


The result is a graphic that makes large values too large and small ones too small. In this case, the designer chose to use only some of the data in the survey, mostly the pro-US results, so the graphic is not only inaccurate but biased.

It’s really not even necessary to use a data graphic at all when there are just a few data points, if you arrange them carefully. I tracked down the original report and summarized the questions in tabular form, arranging the columns in a different and more intuitive order. The margin of error was such that I wasn’t happy pulling out trends with anything more than some boldface type; in fact, that 41 probably shouldn’t be highlighted at all, since it’s not really different from the 37. And I had room to add a couple of extra questions. The whole thing could I’m sure be squeezed into the area the original graphic occupied, but I’m getting tired of fixing the work of highly-paid, supposedly-professional designers, so will spend the next couple of posts looking at something else and give Catalogtree a break.