I've been contemplating the prevelance of vague or misleading statistics in the media and in advertising lately. My first example is food products that sport a label claiming, for instance, that the contents are "99% fat free." I think what they mean is that 1% of the product's weight is fat, but it sure is an odd way to say it. Usually, if we heard a general claim that "99% of Iraq is now free of insurgents," we wouldn't interpret him as saying that 1% of the country is solidly covered in shoulder-to-shoulder resistance fighters. No, we'd imagine that in only 1% of Iraq's area are insurgents still regularly a problem. But that reading would make no sense applied to, say, yogurt -- is all the fat just causing trouble in a tiny section of the container?
While the above is stated in a weird way, at least I believe I know what it really says. Not so with a common type of assertion made by weather forecasters, e.g., "There is a 10% chance of rain in Boston today." Are they saying it is likely to be raining 10% of the time all across the city? Or that 10% of the area is likely to see at least some rain? That there is a 10% chance that any rain at all will fall anywhere in Boston? A 10% chance that rain will fall everywhere in the city? That 10% of the time a few drops will be falling on at least one neighborhood?
The last case I present I ran across in the sports pages of the NY Daily News. The reporter mentioned that while Vince Carter of the Nets had scored 29 points in the game he was reporting on, he had scored "only 7 points" in the 4th quarter. I stopped reading to wonder if the writer had tried dividing 29 by 7. Vince was only .25 points below his average for the game in the closing period -- you could hardly expect him to be any nearer.
While I find these sorts of things amusing in themselves, I also think they are signs of a more serious phenomenon: all of us are to ready to accept statements made by these "authoratative" sources as sensible and clear even though, upon examination, they turn out to be quite funky.
NEW EXAMPLE: On ESPN today, the anouncer was backing the assertion by the coach of the Tennessee women's team, that her quartile of the NCAA tournament was too hard, by pointing out that "Five of the team's in the bracket were in the top 25!" Of course, given that all of the top-25 teams are likely to make the 64-team tournament, and there are four brackets, the average number of top-25 teams in a bracket is always 6.25 -- so he was actually presenting evidence that Tennessee's bracket was too easy!