While reading a bit about KIPP schools, a compensatory education program for minority students, I found a report that has some interesting, adjacent paragraphs:
[The KIPP Performance gains do] not appear to be attributable to a selective admissions process. KIPP serves minority and high-need students, many of whom performed poorly before they entered the schools. Some unobservable biases may be present in student motivation and support, but except for a tendency to attract more girls than boys, there is as yet no strong observable evidence of a systematic selection bias.
Where it has been monitored, student attrition is high and seemingly selective. Those who leave KIPP tend to have been performing less well than those who stay, and at least one study suggests that those who leave were lowerperforming when they entered. Such attrition, if it were taken into consideration, would reduce the size of gains in reports that simply compare KIPP eighth graders with those in their host districts. However, the evidence does not go so far as to suggest that attrition fully accounts for the observed KIPP advantage.
So, there is no bias on which students enter the program, but there is a bias on which students leave. Which of course means that there is a bias in the students that were evaluated to assess the gains in performance. It hardly matters if the poorer performing students didn’t get in, or if they dropped out; it is only important they the were not part of the assessment.