Wacky Wheel of Wedges

preacher.gifNot particularly wanting to harsh on the same design company twice, but the New York Times Magazine included another screwed-up chart on Sunday, February 18th. In this one there are only nine actual data points, which could have been adequately shown with a plain bar chart, but that wouldn’t have looked cool enough, would it? So the designer decided to groove things up by repeating each very thin bar multiple times, and pulling the whole thing into a circle.

Well, it does look exciting and retro. One problem is there’s no room to label the bars directly, so we have to laboriously go back and forth to puzzle out which is which, distinguishing 9 from upside-down 6 (if your chart requires upside-down reading to interpret, you’re probably doing something wrong), making pairwise mental rotations of clumps of bars, and so forth. Quite a bit of work for nine data points; a simple table would be clearer.

But it gets worse. Again the designer helpfully annotated the bars with actual data. The first thing I noticed was that 92% looks rather more than four-and-a-bit times as high as 21%. So I traced over one member of each clump in Illustrator, and measured their lengths. (The easiest way to measure the lengths of angled lines in Illustrator is Window > Document Info > Objects. If I wasn’t intending to reconstruct the graph, I could have just used the Measure tool, of course.) preacher2.gifSure enough, the bars weren’t even remotely to scale. I rotated them all to vertical, turning on the invisible grid to help, then typed the actual data into Excel and produced a quick bar chart, and juxtaposed the two (the Excel bars are flipped to make comparison easier).

We can see straight away that the shorter bars are disproportionately small. This has a pretty serious effect on the political slant of the chart, as it minimizes the amount of time the clergy seem to spend holding forth on immigration and stem-cell research, and overemphasizes their sermonizing on hunger and poverty. (I’d be interested in knowing if clergy really only talked about nine things, and if this is a subset what was left out and why—but another time). What’s caused this distortion? It’s not from stretching the 92% bar too much; there’s progressive distortion of all the other bars. tinypreacher2.gifAfter playing around with scaling—see the inset—it seemed more like an arbitrary fixed chunk has been lopped off each bar… Then I realized that the bars originally ran all the way to the center of the circle. That’s where we’re supposed to be mentally measuring to! Go check the original chart—was this obvious to you? Or were you fooled by the virtual baseline, and the numbers, into thinking the bars stopped there? (Me, I have enough trouble comparing ink I can see without factoring in imaginary ink that I can’t.) The designer felt they had to fill the middle with white so they could arrange their numerical labels there, and the numbers were only required because the chart’s groovy circularity left no room for anything better. So the path to the resulting mess seems clear.

preacher3.gifBut there’s another problem. If there were just one bar for each value, we’d at least all agree we should be comparing their heights. But using multiple bars creates a sort of exploded pie chart, with a wedge for each datum. Pie charts, clunky as they are, are a type of chart most people recognize, and we’re used to comparing areas, even if we don’t do it very accurately. But look at the exaggeration caused by mistaking the wedges for pie slices. I traced over the largest and smallest wedges and compared their areas; the larger has what Tufte calls a Lie Factor of 6.9 (doesn’t that sound imposing?), meaning it’s nearly seven times as large as it should be.

(An aside for the geeky: there is in fact a way to measure the area of closed paths in Illustrator, though it seems so s00per-seekret that I’m reluctant to share it. Briefly, open the debug window (on a Mac, command-option-shift-F12), click on Objects and Object Tree to expand then, select your closed path and see it become bold in the object tree, click its bold underlined name, and lots of terrifying numbers will appear in the Objects section, including the area—in points, I think, but it scarcely matters.)

So a cascade of bad design choices has led to a needless distortion of the relevant data, for those readers who weren’t so rebuffed by this wacky graphic that they just skipped it. At least the designer left the numbers on there, or we’d never even have known. The whole thing could have been avoided with a simple bar graph—not as sexy, but comprehensible, no larger, and (most importantly) not a big lie.