For the 2005 NAEP, the calculation of school-level replicate base weights varied by whether a school was selected with certainty or not since replicates were formed using first-stage sample units. In certainty schools, where replicates were formed at the student-level, the school base weight for each of the 62 replicates (r = 1, ..., 62) was set equal to the full-sample school base weight. That is,
SCH_BWT(r) = SCH_BWT
For noncertainty schools, where replicate strata were formed at the school-level by grouping schools into pairs or triplets, school base weights were calculated for each of the 62 replicates based on this grouping. For schools in replicate strata comprising pairs of schools, the school-level replicate base weights SCH_BWTjs(r), r = 1, ..., 62, were calculated as follows:
SCH_BWTjs is the school base weight for school s in primary stratum j,
Rjr is the set of schools within the r-th replicate stratum for primary stratum j, and
Ujs is the variance unit (1 or 2) for school s in primary stratum j.
For schools in replicate strata comprising three schools, two sets of school-level replicate base weights were computed (see replicate variance estimation for details): one for the first replicate r1 and another for the second replicate r2. The two sets of school-level replicate base weights SCH_BWTjs(r1), r1 = 1,..., 62, and SCH_BWTjs(r2), r2 = 1,..., 62, were calculated as described below.
To illustrate, consider a primary stratum with 111 noncertainty schools in which the first 54 final replicate strata contain two schools each (doublets), and replicate stratum 55 contains 3 schools (triplet). Replicate stratum 55 is paired with replicate stratum 23 (i.e., r2 = 23).
In the first replicate stratum, for the first school:
In the first replicate stratum, for the second school:
In the 55th replicate stratum, for the first school:
In the 55th replicate stratum, for the second school:
In the 55th replicate stratum, for the third school:
In primary strata with fewer than 62 replicate strata, the replicate weights for the “unused” replicate strata (the remaining ones up to 62) for these schools were set equal to the school base weight (so that those replicates contribute zero to any replicate sum of squares).