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 stratum j(STU_BWTjsk) is the product of seven weighting components and can be expressed as follows:
SCH_BWTjs is the school base weight;
WINSCHWTjs is the within-school student weight that reflects the conditional probability, given the school, that the student was selected for the NAEP assessment;
STUSESWTjsk is the student-level session assignment weight that reflects the conditional probability, given the particular session type was assigned to the school, that the student was assigned to that session type;
SUBJFACjsk is the subject adjustment factor that reflects the conditional probability, given the student was assigned to a particular session type, that the student was assigned the specified subject;
SUBADJjs is the substitution adjustment factor to account for the difference in enrollment size between the substitute and original school; and
YRRND_AFjs 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.
The school-level session weights (SCHSESWTjs) for all schools in the 2007 assessment were equal to 1.
The within-school student weight (WINSCHWTjs) is the inverse of the student sampling rate in the school.
All schools, except in Puerto Rico, were assigned one session type. In Puerto Rico, 70 schools were assigned two session types. The variable STUSESWTjsk is 2 for Puerto Rico schools assigned an operational and pilot test session type and 1 for all other schools.
The subject adjustment factor (SUBJFACjsk) adjusts the student weight to account for the spiral pattern used in distributing mathematics, reading, or writing booklets to the students. The subject factor varies by grade, subject, school type (public/private), jurisdiction (Puerto Rico/states participating in the writing assessment/states declining to participate in the writing assessment), and it is equal to the inverse of the booklet proportions (mathematics, reading, or writing) in the overall spiral for a specific sample.
For cooperating substitutes of nonresponding sampled original schools, the substitution adjustment factor (SUBADJjs) is equal to the ratio of the estimated grade enrollment for the originally sampled school to the estimated grade enrollment for the substitute school. The student sample from the substitute school then "represents" the set of grade-eligible students from the originally sampled school.
The year-round adjustment factor (YRRND_AFjs) 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. 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 OFFjs) do not attend school and thus cannot be assessed. The YRRND_AFjs for a school is calculated as 1/(1-OFFjs/100).