​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​NAEP Technical ​DocumentationComputation of Full-Sample Student Weights

The full-sample or final student weight is the sampling weight used to derive NAEP student estimates of population and subpopulation characteristics for a specified grade (4, 8, or 12) and assessment subject (mathematics, reading, or science). The full-sample student weight reflects the number of students in the population that the sampled student represe​nts for purposes of estimation. The summation of the final student weights over a particular student group provides an estimate of the total number of students in ​that group within the population.

The full-sample weight, which is used to produce survey estimates, is distinct from a replicate weight that is used to estimate variances of survey estimates. The full-sample weight is assigned to participating students and reflects the student base weight after the application of the various weighting adjustments. The full-sample weight \(FSTUWGT_{jsk}\) for student \(k\) from school \(s\) in stratum \(j\) ​can be expressed as

\[\begin{array}{rcl} FSTUWGT_{jsk} & = & STU\_BWT_{jsk} \times SCH\_NRAF_{js} \times STU\_NRAF_{jsk} \times \\ & & SCH\_TRIM_{js} \times STU\_TRIM_{jsk} \times STU\_RAKE_{jsk},\\ \end{array}\]​

where​

• \(STU\_BWT_{jsk}\) is the student base weight;​
  
• \(SCH\_NRAF_{js}\) is the school-level nonresponse adjustment factor;
  
• \(STU\_NRAF_{jsk}\) is the student-level nonresponse adjustment factor;​
  
• \(SCH\_TRIM_{js}\) is the school-level weight trimming adjustment factor;
  
• \(STU\_TRIM_{jsk}\) is the student-level weight trimming adjustment factor; and
  
• \(STU\_RAKE_{jsk}\) ​is the student-level raking adjustment factor.
  

School sampling strata for a given assessment vary by school type (public or private), assessment subject (mathematics, reading,​ or science), and grade (4, 8, or 12)​. See the links below for descriptions of the school strata for the various assessments.

• State public school samples for mathematics and reading at grades 4 and 8
• National private school samples for mathematics and reading at grades 4 and 8
• National public school sample for science at grade 8
  
• National private school sample for science at grade 8
• National public school samples for mathematics and reading​ at grade 12
  
• National private school samples for mathematics and reading at grade 12​​
  

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