# Gains and Not So Much, III

Brian Davison suggests that the increased number of retakes benefits the divisions with low pass rates, i.e., with lots of students who might be eligible for retakes.  But, since the State Department of Data Suppression does not tell us about retakes, we can’t know about that.

I’ll suggest there is a more subtle problem: If a division with a 90% overall pass rate increases that rate by 1%, it has decreased the failure rate by 10%.  In contrast, a division with a 50% pass rate that increases the pass rate by 1% leaves 49% of its students failing; it decreases the failure rate by 2% of the failure rate.  To achieve a result equivalent to the first division, this division must increase its overall pass rate by 5%.  But then, it is shooting at a larger target:  A division with a high pass rate has little room for improvement; a division with a low pass rate has plenty of room for (and needs to make lots of) improvement.

The estimable Carol Wolf suggests that I use a simpler analogy: If your pass rate is 50%, you get fifty shots per hundred kids at improving it; if the pass rate is 90%, you get only ten.

That is, a fairer measure of progress is the overall pass rate change divided by the percentage of students who failed to pass the previous year.

Here are those data for Lynchburg: