NAEP Assessment Weighting Procedures → Weighting Procedures for the 2008 Assessment → Weighting Procedures for the 2008 LTT Assessment → Computation of Full-Sample Weights for the 2008 LTT Assessment → Computation of Base Weights for the 2008 LTT Assessment → Student Base Weights for the 2008 LTT Assessment

NAEP Technical DocumentationStudent Base Weights for the 2008 LTT 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 stratum j (STU_BWT_jsk) is the product of seven weighting components and can be expressed as follows:

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 the particular session type was assigned to the school, that the student was assigned to that session type;

• SUBJFAC_js is the subject spiral 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;

• 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 for assessment.

The within-school student weight (WINSCHWT_js) is the inverse of the student sampling rate in the school.

The subject spiral adjustment factor (SUBJFAC_js) adjusts the student weight to account for the spiral pattern used in distributing reading or mathematics booklets to the students. The subject factor is equal to the inverse of the proportion of mathematics (or reading) booklets in the overall spiral for a specific sample. 

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 adjustment 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. 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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