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

Substitutes were preselected for the public 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 had each of its nearest neighbors within the same sampling stratum on the school frame file identified as a potential substitute. Because race/ethnicity percentage was used as the last sort ordering variable, the nearest neighbors had race/ethnicity percentage values very close to that of the sampled school. This helped ensure that expected yields of students in the oversampled race/ethnicity groups were maintained when originally sampled schools were replaced by their substitutes. 

Schools were disqualified as potential substitutes if they were already selected in any of the original public school samples or assigned as a substitute for another public school (earlier in the sort ordering).

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

Of the approximately 410 originally sampled public schools for age 9, about 30 schools had a substitute activated because the original eligible school did not participate, and a handful of those activated substitutes participated. For age 13 the corresponding numbers were approximately 460 originally sampled schools, with approximately 30 substitutes activated. ​Similar to age 9, only a handlful of activated substitutes participated for age 13.

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