Last month, Vox published an article that was quite critical of the ALS Ice Bucket challenge, pointing out that donations for curing prevalent diseases don’t always match the actual deaths caused by those diseases. The author included the following graphic to make her point:
The point of this post is not to debate personal or utilitarian motivations for charitable giving or to contest the main point of the author’s article.. Instead, I just want to take a focused, hard look at the above picture, which I argue is utterly misleading but has been circulated widely in social media and by reputable news organizations.
In this post, I’ll accept without argument the validity of the given numbers. For example, on the right hand side, there are about a quarter as many deaths in the United States due to Chronic Obstructive Pulmonary Disease (142,942) than Heart Disease (596,577). However, the light blue circle on the right looks microscopic compared to the purple circle. It should appear to be about one-fourth the size, but it doesn’t.
In any statistics class, we teach that in a properly drawn historgram, areas should represent relative frequencies. However, in the above picture, the numbers appear to be represented by the radii of the circles, not the areas. So the light blue circle has a radius about one-fourth of the big purple circle, and so the ratio of the areas is about one-sixteenth, not one-fourth.
Second, the area of the biggest circle on the left is not the same as the area of the biggest circle on the right, even the though the units of the two sets of circles (dollars and deaths) are not comparable. A much fairer comparison would draw the biggest circles to be the same size.
So, in my opinion, here’s a much fairer rendering of the same numbers. Notice that the difference in the areas of the purple circles (for heart disease) and the pink circles (for breast cancer) is not nearly as dramatic as in the picture below.
Mean Green Math 