misunderstanding statistics

US News and World Report has several current stories that illustrate the problem with aggregate measures. These are attempts to pull something ‘newsworthy’ out of an average. Anytime you see news based on an average – a single number or comparison representing a large group – you should put on your skeptics hat and start looking at the underlying statistics. Statistics provides a number of means to qualify and understand averages because large groups can be quite different yet have some similar numbers like their averages.

The first example is Girls as Good as Boys at Math. This is related to the recent idea that Title IX ideas should be applied to science faculties as well as sports participants in schools. What the news stories don’t tell you is that, although the average of math capability by gender is essentially the same, the distributions are not. The distribution for boys is flatter and that means it is more spread out. You’ll find fewer boys in the middle, near the average, than girls and more at each end than girls. This means that when you start selected by either the very math gifted or the very math dumb you are going to find more boys there than girls. But the average is the same!

Are Americans Really Getting Poorer? has the problem of trying to track an average over time and choosing what to use as a reference point. This particular issue also has the problem of defining wealth and poverty, which isn’t as simple as it seems because that has to be a weighed collection of concepts and measures in itself.

Dude, Where’s My Recession? The Series gets into the ongoing observation about how economic measures and public perceptions are not well correlated to each other. The economic indicators are attempts to aggregate many measures of economic activity. The news and public perceptions, on the other hand, are determined by a selected sample whose selection criteria often place the sample towards one end of the distribution.

All of these issues – gender differences, wealth distribution, economic strength – are hot topics. None are simple. If decisions must be made it will probably be the case that a careful consideration of the distribution and not just the average should be accomodated.