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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 for student k from school s in jurisdiction j (STU_BWT_{jsk}) is the product of the seven weighting components and is expressed as:
where
SCH_BWT_{js} is the school base weight;
SCHSESWT_{js} is the school-level session assignment weight which reflects the conditional probability, given the school, that the particular assessment type was assigned to the school;
WINSCHWT_{js} is the within-school student weight which 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 the particular assessment type was assigned to the school, that the student was assigned to that assessment type;
SUBJFAC_{j} is the subject adjustment factor which reflects the conditional probability, given the student was assigned to a particular assessment 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;
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 for sample; and
The within-school sampling student weight (WINSCHWT_{js}) is the inverse of the student sampling rate in the school.
The subject adjustment factor (SUBJFAC_{j}) adjusts the student weight to account for the pattern used in distributing reading or mathematics booklets to the students. The subject factor varies by age and assessment type.
For cooperating substitutes of nonresponding sampled original schools, the substitution adjustment factor (SUBADJ_{js}) is equal to the ratio of the estimated age enrollment for the originally sampled school to the estimated age enrollment for the substitute school. The student sample from the substitute school then "represents" the set of age-eligible students from the originally sampled school.
The year-round factor (YRRND_AF_{js}) adjusts the student weight for students who do not attend school during the time of the assessment in year-round schools. This situation typically arises in overcrowded schools. 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}) does not attend school and thus cannot be assessed. The YRRND_AF_{js} factor for a school is calculated as (1-OFF_{js}/100). The weights including this factor allow the assessed sample to represent the full student body within the originally sampled schools.