Schoolective statistics

Bill Gates is spending a lot of money to make schools better. And for some reason it’s not working. Gates says it’s bad teachers:

Gates, naturally, has looked at lots of data and a new area of interest for him is teacher effectiveness. He started with a data point: "Research shows that there is only half as much variation in student achievement between schools as there is among classrooms in the same school. If you want your child to get the best education possible, it is actually more important to get him assigned to a great teacher than to a great school."

So let’s say a typical elementary school has 20 students in each class and 4 classes in each grade level. What Gates is saying is that the variance in means between samples of 20 students within a school is greater than the variance in means between samples of 80 students among schools.

Uhh…the standard error in a sample of 20 is twice the standard error in a sample of 80. Seems like Gates’ point is pretty easily explained by statistics without blaming the teachers.

Maybe it is bad teachers, I’m not saying it isn’t. Heck, that statistical point of view is consistent with the idea that teachers do nothing at all. But I think Gates’ numbers are over-massaged to make a point, and somebody needs to call him on it.