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Substitutes were preselected for the private school samples by sorting the school frame file according to the actual order used in the sampling process (the implicit stratification). Each sampled school had each of its nearest neighbors on the school frame file selected as a potential substitute. The last sort ordering was by grade enrollment; the nearest neighbors had grade enrollment values very close to that of the sampled school.
Schools were disqualified as potential substitutes if they were already selected in the private school sample or assigned as a substitute for another private school (earlier in the sort ordering). Schools assigned as substitutes for twelfth-grade schools were disqualified as potential substitutes for fourth- and eighth-grade schools, and schools assigned as substitutes for eighth-grade schools were disqualified as potential substitutes for fourth-grade schools.
If both nearest neighbors were still eligible to be substitutes, the one with a closer grade enrollment was chosen. If both nearest neighbors were equally distant from the sampled school in their grade enrollment (an uncommon occurrence), one of the two was randomly selected.
In the process described above, only Catholic schools were chosen as substitutes for other Catholic schools, and non-Catholic schools for other non-Catholic schools.