Ravitch's math

In a recent post, Diane Ravitch decries the fact that Chicago charters expel a higher percentage of kids than do the other public schools:

The data reveal that during the last school year, 307 students were kicked out of charter schools, which have a total enrollment of about 50,000. In district-run schools, there were 182 kids expelled out of a student body of more than 353,000. That means charters expelled 61 of every 10,000 students while the district-run schools expelled just 5 of every 10,000 students.

She credits this pattern of expulsions with helping the charter schools have higher test scores:

It makes perfect sense. If a school can kick out the kids with low scores, the school will have higher scores and the public school that gets the low-scoring kids will have lower scores. How simple!

If you give all the Chicago kids a test on which public school students score an average of 70 and charter school kids score an average of 75, but then take 307 charter kids who score 50 (quite a bit lower than the overall average) and move them to the traditional public schools instead, what will happen to the overall test scores? Public schools will now have an average of 69.98 instead of 70, and charter schools will how have an average of 75.154 instead of 75.

This is a somewhat artificial example, of course, but the point remains that even if every single kid expelled from charter schools had substantially lower test scores than everyone else, charter expulsions probably don't explain very much about the overall test score patterns.