February 13, 2011, 6:03 pm
The Mystery Donut
By Henry Woodbury
The donut below shows that 53% agree and 47% disagree.
It is lucky that we have the numbers because visually we have an enigma. Red dominates the shape in which red is the smaller number. How do we interpret this? Let me count the ways.
- We could compare the area of the donut (the blue ring) to the area of the hole (the red circle).
- We could compare the area of the donut and the hole to the area of the hole.
- We could compare the diameters of both cases above.
- We could compare the radii.
In every case, we still have to answer the question: What is the whole?
As it turns out, the visually-most-counterintuitive answer is the answer.
The red circle has a radius of 35 pixels. The blue donut is 5 pixels wide, extending the radius to 40 pixels.
Each radius is a bar on an implicit chart (now we see the whole):
The donut is meaningless. All we really have are two linear values:
Hell, let’s make it a circle again. I’ll turn the donut into a pie:
Comments
I would argue the donuts aren’t meaningless, but actually wrong and grossly misleading. The radii may represent the true values, but by making them circles and coloring them, you are now comparing *areas*. That really exaggerates the difference, going from a difference of 6 percentage points to 21 [(0.53^2 - 0.47^2)/0.53^2 = 0.79].
Even then, our brains are bad at judging the difference between areas when displayed that way, making things even worse. I would’ve guessed the ratio of the two areas was much higher.
So I agree with you, but think the situation is even worse than you say! :)
Posted by Phil Plait on February 14, 2011 at 2:31 pm
Phil, your comment clarifies something that was bugging me. It’s always easy to call out the problem of linear values displayed as areas. But here the areas are pure invention. Their mathematical derivation from proportional radii is a conceit. The designer could just as well have used two line segments to drawn squares or triangles (which would have been just as pointless).
Another thing that bugs me on a second look is the misuse of transparency. One reads the shape of Pakistan as a background element showing through the circles. But if the circles are transparent, the red primary is impossible. The blue circle should reside either above or below the red. Red should be purple. Which would help clarify that the blue value is a circle, not a donut.
Posted by Henry Woodbury on February 15, 2011 at 9:23 am