Saturday, July 17, 2010
Believing your lying eyes
PZ Myers over at Pharyngula is more pleased than he should be with some “flashy illustrations” of the creationism menace. “Use these!” he admonishes. Um, maybe not.
While the graphs are flashy and, in their way, are informative (though I'm not crazy about the choice of pale red [is not explicitly mentioned] as intermediate between green [is mentioned directly] and dark red [isn't mentioned]—pick a better color palette, guys!), there are significant scaling problems. When one ostensibly represents ratio data with the linear dimensions of objects possessing area, the visual impact is seriously misleading. Perhaps this sounds fancy, but it's not.
Suppose you want to compare a data value of 16% with a data value of 32%. The latter is twice as much as the former. In a bar chart, one would be twice as tall as the other. Simple:
You can't get much more basic than that. However, what if you decide to represent your data with cute little gingerbread men? It's quite obvious that the one representing 32% must be twice as tall as the one representing 16%, right? Except look at what happens:
It's the classic problem of scaling. Doubling the linear dimensions of a two-dimensional figure results in a quadrupling of its area, immediately creating an exceedingly misleading visual impact. To maintain a correct visual impression in a situation where two-dimensional area rather than one-dimensional length catches the eye, the linear scaling factor should be the square root of 2 (approximately 1.4142) rather than 2 itself. The results are much better:
This is exactly the problem with the Campus Explorer's iconic graph of teachers' personal beliefs in evolution vs. creationism and intelligent design creationism. The purple figure representing 28% looks like it's quite a bit more than twice the 16% icon. The 16% icon similarly looks a lot bigger relative to the 9% icon than it should. The Discovery Institute will certainly be delighted with the colossus representing adherence to ID creationism.
With some elementary (and not particularly elegant) picture editing, I offer this statistically improved version, whose visual impact is not misleading:
Darrell Huff warned us about misleading data graphs in How to Lie with Statistics, originally published in 1954. We have yet to learn the lesson he tried to teach us.