​NAEP Technical DocumentationStudent Base Weights

Every sampled student received a student base weight, whether or not the student participated in the assessment. The student base weight is the reciprocal of the probability that the student was sampled to participate in the assessment for a specified subject. The student base weight \(STU\_BWT_{jsk}\) for student \(k\) from school \(s\) in stratum \(j\) is the product of seven weighting components and can be expressed as

\begin{equation} STU\_BWT_{jsk} = SCH\_BWT_{js} \times SCHSESWT_{js} \times WINSCHWT_{js} \times \\ STUSESWT_{jsk} \times SUBJFAC_{jsk} \times SUBADJ_{js} \times YRRND\_AF_{js}, \end{equation}

where

• \(SCH\_BWT_{js}\) is the school base weight;

• \(SCHSESWT_{js}\) is the school-level session assignment weight that reflects the conditional probability, given the school, that the particular session type was assigned to the school;

• \(WINSCHWT_{js}\) is the within-school student weight that reflects the conditional probability, given the school, that the student was selected for the NAEP assessment;

• \(STUSESWT_{jsk}\) is the student-level session assignment weight that reflects the conditional probability, given that the particular session type was assigned to the school, that the student was assigned to the session type;

• \(SUBJFAC_{jsk}\) is Stu_factor the subject spiral adjustment factor that reflects the conditional probability, given that the student was assigned to a particular session type, that the student was assigned the specified subject;

• \(SUBADJ_{js}\) is the substitution adjustment factor to account for the difference in enrollment size between the substitute and original school; and

• \(YRRND\_AF_{js}\) is the year-round adjustment factor to account for students in year-round schools on scheduled break at the time of the NAEP assessment and thus not available to be included in the sample.

The within-school student weight \((WINSCHWT_{js})\) is the inverse of the student sampling rate in the school. For long-term trend (LTT), due to the oversampling of certain race/ethnicity student groups, some schools have two student sampling rates.

The subject spiral adjustment factor \((SUBJFAC_{jsk})\) adjusts the student weight to account for the spiral pattern used in distributing civics, mathematics, reading, or U.S. history booklets to the students. The subject factor varies by grade (or age, for LTT) and subject; it is equal to the inverse of the booklet proportions (civics, ​mathematics, reading, or U.S. history) in the overall spiral for a specific sample.

For cooperating substitutes of nonresponding original sampled schools, the substitution adjustment factor \((SUBADJ_{js})\) is equal to the ratio of the estimated grade (or age-specific) enrollment for the original sampled school to the estimated grade (or age-specific) enrollment for the substitute school. The student sample from the substitute school then "represents" the set of grade-eligible (or age-eligible) students from the original sampled school.

The year-round adjustment factor \((YRRND\_AF_{js})\) adjusts the student weight for students in year-round schools who do not attend school during the time of the assessment. This situation typically arises in overcrowded schools. School administrators in year-round schools randomly assign students to portions of the year in which they attend school and portions of the year in which they do not attend. At the time of assessment, a certain percentage of students (designated as \(OFF_{js}\)) do not attend school and thus cannot be assessed. The \(YRRND\_AF_{js}\) for a school is calculated as \(1/(1 - OFF_{js}/100)\).

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