All Schools, Except Schools in American Samoa, Guam, Virgin Islands and the Department of Defense Domestic Dependent Elementary and Secondary Schools DDESS Grade 8. Noncertainty schools were sorted by sample type within jurisdiction. Then within sample type, schools were sorted by new-school status and the order in which they were selected from the sampling frame. The schools were then grouped in pairs. Where there was an odd number of schools, the last replicate group contained three schools instead of two. If a jurisdiction had more than 62 pairs, the pair numbering would have gone up to 62, and then decreased backward from 62 for the last few pairs.
Each of the certainty public schools was assigned to one or more distinct replicate groups. If a school was selected three or more times in the sampling process, then it was assigned to two replicate groups. Here, schools were sorted by the estimated grade enrollment prior to group assignments. Again, depending on the jurisdiction, a maximum of 62 replicate groups was formed. The group numbering resumed from the last group number used for the noncertainty schools if the total number of replicate groups was less than 62. Otherwise, the numbering started from 62 down to the number needed for the last certainty school. In jurisdictions where the number of replicates created by certainty schools exceeded 62, the numbering of the groups started at 62 and went downward to 1, and then went back to 62 downward to the number needed for the last certainty school. For instance, in the District of Columbia grade 4 mathematics, which had 117 schools, all certainties, group numbers started at 62 and continued down to 1 and then back to 62 and down to 7. One of the 117 certainty schools in the District of Columbia was selected three or more times and therefore was assigned to two replicate groups. A replicate was formed by randomly deleting one half of the students in a certainty school from the sample. For certainty schools that were assigned to two replicate groups, the students were split equally between four "halves," two halves in each of the two replicate groups. This process was repeated for each certainty school.
The purpose of this scheme was to assign as many replicates to a jurisdiction's schools as permitted by the design, to a maximum of 62. When more than 62 replicates were assigned, the procedure ensured that no subset of the replicate groups (pairs of noncertainty schools, individual certainty schools, or groups of these) was substantially larger than the other replicate groups. The aim was to maximize the degrees of freedom available for estimating variances.
A single replicate estimate was formed by dropping half of the members assigned to a particular replicate group and adjusting the weights of the other members. This process was repeated successively across replicate groups, giving up to 62 replicate estimates.
American Samoa, Guam, Virgin Islands, DDESS Grade 8. Schools were assigned to a number of replicate groups proportional to their estimated grade enrollment so that a total of 62 replicate groups were assigned.