Base weights are assigned to schools separately by grade and subject. The base weight assigned to a school is calculated as the reciprocal of the overall probability of selection of that school. The school base weight depends on the assessment subject because some schools are so small that students are tested in only one subject. For "new" schools added during the selection of new public schools, the school base weight reflects the combined probability of selection of the district, and school within district.
Thus the base weight for school i is calculated as
if the school was in the original sample, or
if the school was a new school, where (for both originally sampled schools and new schools)
In each participating jurisdiction in the 2000 state assessment, all schools included in the sample with certainty were assigned school base weights of one. Schools sampled with certainty were sometimes selected more than once in the systematic sampling process. For example, a school that was selected twice was allocated twice the usual number of students for the assessments, or two sessions; a school that was selected three times was allocated three times the usual number of students for the assessments, or three sessions. All schools with less than 25 students were assigned one subject. For these schools, the base weight included a factor of two, since only half the schools were assigned the subject.
A school that replaced a refusing school (i.e., a substitute school) was assigned the weight of the refusing school. Thus the substitute school was treated as if it were the original school that it replaced, for purposes of obtaining school base weights.
Note that this treatment is reasonable since substitutes were chosen to be similar to the schools they replaced (see School Substitution and Retrofitting).