Value-Added by Schools
One way to look at the quality of schools is to look at the test scores of the students. This is unsatisfactory because some schools have students who are smarter.
A second way is to compare the national-percentile levels of the students in 1st grade at that school with those at the 6th grade. This is a value-added measure. In this case, a school with students in the 99th percentile at 1st grade has nowhere to go but down– but it might go down, so the measure is still valuable for those schools. Also, we could measure either number of percentiles gained or lost, or fraction of the possible percentile gain or loss (that is, going from 90 to 95 the school either gains (a) 5%, or (b) 50%).
A third way is to compare a school only with schools with the same 1st grade percentile.
All three ways have their independent value.