## Calculation of Student Base Weights

In the selection of eligible students for the assessment, the within-school probability of selection for each subject depends on the number of grade-eligible students in the school and the number of students selected for the assessment (usually 30).

The within-school weights for sampled schools are adjusted to account for the fact that some schools operate 12 months per year and have only a proportion of their total enrollment attending school at any one time. For substitute schools, the within-school weights are further adjusted to compensate for differences in the grade enrollments of the substitute and the originally sampled (replaced) schools.

For the 2000 state assessment, the within-school weight also incorporated a factor to account for

• cases in which small schools were assigned at random to do one subject (mathematics or science) and

• the random assignment of students to subjects.

Thus, in general, the within-school student weight for the jth student in school i was equal to:

where

• Ni equals the number of grade-eligible students enrolled in the school, as reported at the time of student sampling, and

• ni equals the number of students selected for the given subject in schooli.

Note that the within-school student weight is constant for all students in the same subject within a school.

The factors and in the formula for the within-school student weight generally apply to only a few schools in each jurisdiction. The factor adjusts the count of grade-eligible students in a substitute school to be consistent with the corresponding count of the originally sampled (replaced) school. Specifically, for substitute schools,

with

• equals the grade enrollment of the originally sampled (replaced) school and

• equals the grade enrollment of the substitute school.

For nonsubstitute schools,

The factor , which was applied to schools determined to be year-round schools, is defined as:

where is the proportion of students enrolled in the school who were not scheduled to attend school at the time of assessment. For schools that are not year-round schools (the great majority), .

The overall student base weight for a student j selected for the assessment for a given subject (mathematics or science) in school i was computed as follows:

where

• Witsch equals the trimmed school base weight for school i and

• Wijwithin equals the within-school student weight for the jthstudent in school i.

The following tables show the distribution of the substitute school weighting factor (SUBADJ) among the 2000 state assessment's participating jurisdictions by grade (fourth and eighth), assessment subject (mathematics and science), and reporting population. Reporting populations differ by whether accommodations were offered to students with disabilities or limited English proficiency (SD/LEP) students. The non-accommodated reporting population, also known as the R2 reporting population, includes all non SD/LEP students plus SD/LEP students from non-accommodated sessions. The accommodated reporting population, also known as the R3 reporting population, includes all non SD/LEP students plus SD/LEP students from accommodated sessions.

### Distribution of the Substitute School Weighting Factor (SUBADJ)

The following tables show the distribution of the year-round school weighting factor (YRRNDADJ) among the 2000 state assessment's participating jurisdictions by grade (fourth and eighth), assessment subject (mathematics and science), and reporting population (non-accommodated and accommodated).

### Distribution of the Year-Round School Weighting Factor (YRRNDADJ)

Last updated 07 March 2008 (TK)