Weighting

Base Weights

In large-scale educational survey, observations are often selected following a multistage framework, within which weights are provided for each stage. A typical three-stage survey, for example, may include the selection of geographic areas, schools in those selected areas, and then students within the selected schools. Two-stage surveys are also common in education, including the selection of schools, followed by the selection of students. The units being selected at each stage (e.g., the county, the school, or the student) are based on some predefined probability of selection.

Consider a two-stage sample as an example. It is rare that schools are selected using a simple random design; instead, the school has a given selection of probability and thus has a sampling weight that may differ from other schools. Researchers frequently use a sampling procedure called probability proportional to size sampling. In particular, the selection probabilities for schools vary depending on, and are proportional to, the schools’ size. In other words, large schools have relatively larger selection probabilities, πj, as compared to smaller schools, and vice versa. Therefore, larger schools tend to have smaller sampling weights (taking the inverse 1/πj = wj) than smaller schools. The school sampling weight for a given selected school is the number of schools it represents in the sampling frame. Once schools are selected, in the second stage, students are selected perhaps using categories of a given characteristic (e.g., age and race). These categories are referred to as strata. Because the student selection probability, πi|j, is the selection probability of the student within the selected school, it reflects the conditional selection probability. Thus, the second-stage within-school conditional sampling weight is 1/πi|j = wi|j.

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