In the NAEP 2007 assessment, replicates were formed separately for each sample [indicated by the level of the sample (national or state), school type (public or private), and grade (4, 8, or 12)]. The first step in forming replicates is to assign each first-stage sampling unit in a primary stratum to a replicate stratum. In 2007, first-stage units were generally schools, and their primary sampling strata were generally the highest level sampling stratum variable, described as follows:
However, for schools selected with certainty, the first-stage units were students within the school and the primary stratum was the school itself.
The general procedure for assigning first-stage units to replicate strata is to sort the first-stage units in the order of sample selection. For replicate strata involving noncertainty schools, the sampled schools were sorted by the order of sample selection to reflect the implicit stratification and systematic sampling features of the sample design. For students in certainty schools, sampled students were sorted by session number and position on the administration schedule.
The first-stage units were then paired off into preliminary replicate strata. Within each primary stratum with an even number of first-stage units, all of the preliminary replicate strata consisted of pairs of first-stage units. However, within primary strata with an odd number of first-stage units, all replicate strata consisted of pairs of first-stage units, except the very last one; it consisted of three first-stage units.
If there were more than 62 preliminary replicate strata within a primary stratum, the preliminary replicate strata were grouped to form 62 replicate strata. This grouping effectively maximized the distance in the sort order between grouped preliminary replicate strata. The first 62 preliminary replicate strata, for example, were assigned to 62 different final replicate strata in order (1 through 62), with the next 62 preliminary replicate strata assigned to final replicate strata 1 through 62, so that, for example, preliminary replicate stratum 1, preliminary replicate stratum 63, preliminary replicate stratum 125 (if there were that many), etc., were all assigned to the first final replicate stratum.
If, on the other hand, there were fewer than 62 preliminary replicate strata within a primary stratum, then the number of final replicate strata was set equal to the number of preliminary replicate strata.
For example, consider a primary stratum with 111 sampled schools, all of which were noncertainty schools. These 111 noncertainty schools were sorted in their order on the frame. The first two schools were in the first preliminary replicate stratum; the next two schools were in the second preliminary replicate stratum, and so on, resulting in 54 preliminary replicate strata with two schools each (doublets). The last three schools were in the 55th preliminary replicate stratum (triplet). Since there are no more than 62 preliminary replicate strata, these were also the final replicate strata.
Within each preliminary replicate stratum containing a pair of first-stage units, one first-stage unit was randomly assigned as the first variance unit and the other as the second variance unit. Within each preliminary replicate stratum containing three first-stage units, the three first-stage units were randomly assigned variance units 1 through 3.