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). For operational reasons, the original selection order was embedded within the sampled primary sampling unit (PSU). Each sampled school had each of its nearest neighbors within the same sampling stratum on the school frame file identified as a potential substitute. When grade enrollment was used as the last sort ordering variable, the nearest neighbors had grade enrollment values very close to that of the sampled school. This was done to facilitate the selection of about the same number of students within the substitute as would have been selected from the original sampled school.
Schools were disqualified as potential substitutes if they were already selected in any of the original private school samples or assigned as a substitute for another private school (earlier in the sort ordering), or if they were already selected in the original 2011 Trends in International Mathematics and Science Study (TIMSS) sample. TIMSS substitutes were eligible to be used as substitutes for the writing computer-based assessment (WCBA). Schools assigned as substitutes for twelfth-grade schools were disqualified as potential substitutes for eighth-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. If the grade enrollment of the nearest neighbor school was less than half of the expected student sample size of the original sampled school, then it was considered ineligible as a substitute for that school.
Of the approximately 330 originally sampled private schools for the WCBA, about 100 had a substitute activated because the original school, although eligible, did not participate. Ultimately, about 40 substitute private schools participated in the WCBA.