The same instruments are administered to the state assessment sample and the national main assessment sample. The national main and state-by-state assessments are linked so that state and national results can be reported on a common scale. The linking is achieved by using part of the sample representing a common population from each assessment. For the national main samples, this consists of fourth-grade or eighth-grade public-school students from participating states, including the District of Columbia, who were assessed in the mathematics and science R2 reporting sample and R3 reporting sample.
Each sample of students receives appropriate weights from the weighting procedure used for the national main assessment. In an effort to increase the precision of the linking process, an additional weighting adjustment was developed and applied to each subsample by grade, subject, and reporting sample solely for use in linking. For each subsample, the distributions of the national main sample reporting weights for three categorical variables are adjusted to agree closely with those obtained from the weighted aggregate sample from the state assessments from the participating states. The three variables are as follows: