The Program statute set two conditions for any lotteries conducted under the OSP. First, scholarships would be awarded by lottery when the Program is "oversubscribed"-that is, the number of eligible applicants exceeds the number of available slots in participating private schools. However, because the extent of oversubscription varied significantly by grade, in practice the determination of whether to hold a lottery was considered within grade bands: those applying for grades K–5, those applying for grades 6–8, and those applying for grades 9–12. Second, the statute specified that certain groups be given priority in any such lotteries, which led to the following classifications for the lottery:
These conditions led to somewhat different scholarship award opportunities in years 1 and 2 of Program implementation (figure 3-1). In cohort 1, for example, there were more slots in participating schools than there were applicants for grades K–5; therefore, all eligible K–5 applicants automatically received scholarships, and no lotteries were conducted at that level. By contrast, in cohort 2 there were 1,178 K–5 applicants vying for scholarships to fill 643 slots, requiring a lottery to determine which students received an award. In both years, there was a high degree of oversubscription at the high school level and moderate oversubscription at the middle school level. In contrast to the first year, in year 2 there was sufficient demand from public school applicants that lotteries were conducted only for them; applicants who were already attending a private school (the lowest priority group) were not entered into a lottery.
The design of the lotteries for cohort 2 applicants was similar to that for the first year, with the exception of how the priority treatment of SINI applicants was implemented. For cohort 1, the 79 eligible applicants from previously designated SINI schools were all automatically awarded scholarships, consistent with their status as the highest priority client group. For cohort 2, the 655 eligible applicants from previously designated SINI schools were all subject to lotteries, with scholarship award probabilities approximately one-third higher than non-SINI applicants within their respective grade bands (table 3-3).14 Randomly assigning cohort 2 SINI students, but with a higher probability of award than non-SINI students, accomplished the dual objectives of including a significant number of SINI students in the experimental evaluation of Program impact while also treating them as the highest priority for access to the Program.
In general, the probability of receiving a scholarship through a lottery was based on the ratio of slots to applicants in each grade band. Given the likelihood that some students would choose not to use the scholarships that were awarded to them, based on the first-year experience, award probabilities were then adjusted to "over-award" scholarships by approximately 20 percent. As a result of the spring 2005 lotteries, 1,088 scholarships were awarded to cohort 2 eligible applicants-429 to applicants from SINI public schools and 659 to the larger group of applicants from non-SINI public schools (table 3-3).
In total, then, after 18 months of Program implementation, the OSP has awarded scholarships to 2,454 students (table 3-4). The total awards to the three priority subgroups are:
14 The cohort 2 SINI award probability advantage actually was 32.7 percent in K–5, 35.6 percent in 6–8, and 33.5 percent in 9–12. In the end, it did not equal exactly 33.3 percent in any of the grade bands because a handful of students deemed eligible on appeal were randomly assigned through small lotteries that are inherently less precise than are large lotteries.