The weighting process involves the development of survey student weights for each participating school in each of the states, territories, and defense-related schools of the United States. Following the collection of assessment and background data from and about assessed and excluded students, the processes of deriving sampling weights and associated sets of replicate weights are carried out. The sampling weights are needed to make valid inferences from the student samples to the respective populations from which they are drawn. Replicate weights are used in the estimation of sampling variance, through the procedure known as jackknife repeated replication.
In 2000, weights were developed for students sampled at grades 4 and 8 for the state assessments in mathematics and science. Each student was assigned a weight to be used for making inferences about each state’s students. This weight is known as the full-sample or overall sample weight. The full-sample weight contains several components. These components are described briefly below. Additional details may be obtained by using the links to the right.
Calculation of the base weight, established as the inverse of the overall probability of selecting the sampled student, incorporated the calculation of school base weights and the calculation of student base weights. The method for computing the base weights for new schools is different than the method used for non-new schools because the method for sampling the new schools was somewhat different. For all schools, the base weight reflects the probability of selection.
The base weight is then adjusted for two sources of nonparticipation—school-level nonresponse and student-level nonresponse. These weighting adjustments seek to reduce the potential for bias due to nonparticipation by increasing the weights of students from schools similar to those schools not participating, and by increasing the weights of participating students similar to those students (from within participating schools) who did not attend the assessment session (or makeup session) as scheduled. The characteristics of nonresponding schools and students must also be examined.
Furthermore, the full-sample weights reflect the variation in weights at each stage in the weighting process.
Two different sets of administration rules indicated by the sample type field were used in the 2000 state assessment program for each subject. To analyze these subsets separately, the student weights for each subset were raked in order to force agreement with the totals estimated using both subsets combined. This raking of weights is described in detail. The process of trimming extremely large raked student weights is also described.
In addition to the full-sample weights, a calculation of replicate weights was done for each student. These replicate weights are used in calculating the sampling errors of estimates obtained from the data, using the jackknife repeated replication method. The methods of deriving these weights were aimed at reflecting the features of the sample design appropriately in each jurisdiction, so that when the jackknife variance estimation procedure is implemented, approximately unbiased estimates of sampling variance are obtained.