According to this test, it appears small schools are better than large schools. Five out of the top 10 schools have 100 or fewer students. But how can this be? We constructed the simulation so that...

According to this test, it appears small schools are better than large schools. Five out of the top 10 schools have 100 or fewer students. But how can this be? We constructed the simulation so that quality and size are independent. Repeat the exercise for the worst 10 schools.

The same is true for the worst schools! They are small as well. Plot the average score versus school size to see what’s going on. Highlight the top 10 schools based on the true quality. Use the log scale transform for the size.