A replication method known as the jackknife is used to estimate the variance of statistics derived from the full sample. This type of replication involves repeatedly selecting portions of the sample (replicates) and calculating the desired statistic (replicate estimates). The variability among the calculated replicate estimates is then used to obtain the variance of the full-sample estimate.
In each jurisdiction that included schools in the 2000 state assessment, 62 jackknife replicates were formed. Each link to the right gives more detail about a part of this process. The links are described briefly below:
"Jackknife Procedure" describes the motivation for using the jackknife procedure and provides the formula used to estimate variance with this replication method.
"Formation of Replicate Groups for Variance
Estimation" provides an overview of how schools and students were assigned to the 62 replicates.
"Replicate Group Assignments for Non SD/LEP Students" describes in detail how non SD/LEP students were assigned to the 62 replicates.
"Replicate Group Assignments for SD/LEP Students" describes in detail how SD/LEP students were assigned to the 62 replicate groups. The reason that SD/LEP students have different replicate assignments than non SD/LEP students is also explained.
"School-Level Replicate Weights" describes how the replicate weights for each school were computed.
"Student-Level Replicate Weights" describes how the replicate weights for each student were computed. "Student Replicate Weight Trimming" describes how the nonresponse-adjusted student replicate weights were trimmed.
"Student Replicate Weight Raking" describes how the trimmed student replicate weights were raked.
"Use of Replicate Weights" describes how the final student replicate weights were used to estimate the variance of sample-based estimates in NAEP.