Student Base Weights for the 2005 Assessment

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_BWTjsk) is the product of seven weighting components and can be expressed as follows:

where

• SCH_BWTjs is the school base weight;
• SCHSESWTjs is the school-level session assignment weight that reflects the conditional probability, given the school, that the particular assessment type was assigned to the school;
• 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 assessment type was assigned to the school, that the student was assigned to that assessment type;
• SUBJFACj is the subject spiral adjustment factor that reflects the conditional probability, given the student was assigned to a particular assessment 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 within-school student weight (WINSCHWTjs) is actually the inverse of the student sampling rate in the school.

The subject spiral adjustment factor (SUBJFACj) adjusts the student weight to account for the spiral pattern used in distributing mathematics, reading, or science booklets to the students. The subject factor varies by subject, school type (public/private), and jurisdiction (Puerto Rico/all others), and it is equal to the inverse of the proportion of math (or reading or science) booklets 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. 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) for the school. The weights including this factor allow the assessed sample to represent the full student body within the originally sampled schools.

Last updated 17 April 2009 (JL)