In NAEP, substitute schools are selected to replace originally sampled nonresponding schools. The objective was to select substitute schools whose size and characteristics were most similar to those of the originally sampled schools. To accomplish this goal in implementing this substitution, the implicit stratification used in the school sampling steps was utilized, as schools that are close in this ordering have similar characteristics. (This is also important in systematic sampling.)
Substitute schools were defined to be the 'nearest neighbors' in the sort order to the originally sampled schools (see 2004 Long-Term Trend School Stratification for a discussion of the implicit stratification for school selection), excluding as potential substitutes any schools that were sampled for any of the 2004 samples (i.e., long-term trend sample for any age cohort, foreign language assessment sample, field test sample), and schools that crossed boundaries of the next-to-last sort hierarchy field (i.e., race/ethnicity stratum for public schools, school type for private schools). The preceding school in the sort order was selected as a substitute, if it was eligible. Otherwise, the succeeding school in the sort order was chosen as a substitute. If a given school was chosen as a substitute for two schools (by being a predecessor to one sampled school and a successor to another), it was randomly assigned to one or the other. If neither the preceding or succeeding school was eligible to be a substitute, the sampled school was assigned no substitute.
Substitute schools were selected from the same geographic area in which original refusals were located. To accomplish this objective, the sampling stratification order was modified to place PSU (primary sampling unit) stratum as a primary sort variable for all cases (public and private schools, certainty and noncertainty PSUs). Similarly, an effort was made to select substitute schools of roughly the same size as the original schools. Accordingly, the estimated number of age-eligible students was assigned as the last sort-order variable in all cases.