​​​​NAEP Technical DocumentationSubstitute Private Schools for the 2022 Long-Term Trend Assessment

Substitutes were preselected for the private school samples by sorting the school frame file for each of ages 9 and 13 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) and state. Each sampled school with known affiliation had each of its nearest neighbors within the same sampling stratum on the school frame file identified as a potential substitute. Sampled schools with unknown affiliation were not assigned substitutes. Since age-specific enrollment was used as the last sort ordering variable, the nearest neighbors had age-specific 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, assigned as a substitute for another private school (earlier in the sort ordering), or were not the same affiliation as the originally sampled school.

If both nearest neighbors were still eligible to be substitutes, the one with a closer age-specific enrollment was chosen. If both nearest neighbors were equally distant from the sampled school in their age-specific enrollment (an uncommon occurrence), one of the two was randomly selected.

Of the approximately 160 originally sampled private schools for age 9, about 80 schools had a substitute activated because the original eligible school did not participate, and a handful of those activated substitutes participated. For age 13, of the approximately 180 originally sampled private  schools, about 80 also had a substitute activated because the original eligible school did not participate. Similar to age 9, only a handful of activated substitutes for age 13 participated.

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