On the Importance of Double-Checking Graphs

The Daily Progress has twice used extremely misleading charts in the past few weeks, and this seems like a good opportunity to highlight the importance of being a critical reader of charts and graphs. In both instance they employed bubble charts, a type of chart that is often avoided because people have an awfully hard time understanding them. At right is the chart that the paper employed on Sunday in Ranchana Dixit and Brandon Shulleeta’s “Can we afford our future?,” which tracked expensive capital improvement projects being planned in Charlottesville and Albemarle. As you can see, a minuscule amount is being spent on water and sewer improvements in comparison to Places29—in fact, more is being spent on Places29 than the other three combined. But the dollar values don’t add up. What’s going on?

The problem here is that people are really bad at comparing area. We do well with comparing colors, lengths, shapes, etc., but our brains are not well-equipped to figure out bubble charts. Doubly problematic is that this math behind the visuals in this chart is flat-out wrong. The area represented by the bottom bubble is $45.5M so, proportionally, the top bubble should represent $1,300M, not $312M. It’s 320% too big. Likewise, the middle two bubbles are significantly too large. The effect is to significantly exaggerate the disparity of the area’s spending priorities. Though having that big “$312 million” graphic above the fold on the front page of the paper is eye-catching, it’s misleading.

Here’s a side-by-side of the chart as it was presented in the Progress and how it should have looked:

As you can see, the effect isn’t nearly as striking. But it does have the benefit of being correct.

Stats-geek blog Junk Charts has a whole category to keep track of misleading bubble charts, because they’re so commonly misused. Understand, though, they’re not being misused maliciously by newspapers; they’re just easy to get wrong. In this case, the paper used an area-based chart with math that applies only to diameter leading to a geometric exaggeration of the data. The solution for the Progress is to use a simpler chart. (I’ve mocked it up as a bar chart, which is a much better format for this data.) This is certainly a minor sin, but it’s the sort of thing that (quite wrongly) leads readers to cry “bias!” when “mistake!” is a more appropriate response. And if you read this story in the paper yesterday, and didn’t think something was funny about that graph, the solution for you is to be a critical reader of charts and graphs. Look at the numbers, do a quick comparison and see if you’ve been given a false impression by the visuals.

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