## Computation of Student Base Weights

The student base weights wij for school i, student j were computed as

where

• wi is the final school weight for school i.

• YRNi is a special adjustment for year-round schools (see Student Sample) that equals the total number of eligible students in the school divided by the total number of students who were available to be assessed at the time of assessment. Note that YRNi equals 1 for non year-round schools.

• INTij is the reciprocal of the probability of selection of a student within a school. The quantity is subscripted as ij, where "j" is student j, which is necessary as different students had differing probabilities of selection based on their SD/LEP and minority status.

• SHGi is the reciprocal of the probability that a student within the school was in a session assigned as geography/U.S. history rather than a session assigned as a field test session. (In the latter case, no weight is assigned to the student at all.) For example, in some cases, the probability of being assigned to a geography/U.S. history session was 75 percent (with the probability of being assigned to the field test then 25 percent). SHGi in this case is 1/0.75, or 1.33. Assignment of Sample Types of Schools presents the sample design for the assignment of sessions, and Weighted Percentages of Students Excluded from the Assessment shows the breakdown of participating schools by session assignment.

This table shows the numbers of these schools in each grade's cooperating school sample, with their reported percentages of off-track students and the adjustment factor (which is the reciprocal of the complement of this percentage). Off-track students are those in year-round schools who are not in school at the time of the assessment (in year-round schools a certain percentage of students are "off" at any given time and on vacation).

Year-round schools in the set of cooperating schools, national main assessment: 2001
Cooperating year-round schools with off-track students YRNi
factor