Before school selection began for the state assessment, the school sampling frame underwent a hierarchical sort of schools based on selected demographic variables. This stratification process ensured that the state assessment would represent a variety of school and student groups. This stratified sampling also improved the precision of the NAEP estimates by allowing separate estimates of population parameters for each stratum and removing the variation between strata.
As is the case for all NAEP state assessments, the 2000 stratification variables provided the NAEP sampling statisticians with information about each school, its students, and its environment. The 2000 state assessment used such stratification variables as
achievement data, and
median household income.
The school sampling frame underwent two levels of stratification. Primary stratification breaks down the school sampling frame by selected demographic detail. Implicit stratification provides a measure of control over additional school variables after the primary stratification occurs.
Primary stratification variables for public schools, listed in hierarchical order, are as follows:
small or large school district class,
school size class,
urbanization classification, and
Implicit stratification variables for public schools include achievement data and median household income. If available for a participating jurisdiction and grade, achievement data becomes the implicit stratification variable. If no viable achievement data are found, the median household income of the school location's ZIP code serves as the implicit stratification variable.
Prior to the selection of the school samples, the public schools are sorted by the four primary stratification variables in an order such that changes occur on only one variable at a time. Serpentine sorting accomplishes this feat by alternating between ascending and descending sort order on each variable successively through the sort hierarchy. For example, if schools are to be sorted by urbanicity (urban, suburban, rural) and size (enrollment):
Urban schools are sorted in ascending order of enrollment.
Suburban schools are sorted in descending order of enrollment.
Rural schools are sorted in ascending order of enrollment.
This sorting pattern places the large urban schools next to large suburban schools and the small suburban schools next to small rural schools. A traditional sort places the large urban schools next to small suburban schools and the large suburban schools next to small rural schools, which is less desirable for variance estimation purposes.
The implicit stratification of public schools by either achievement data or median household income maintains the established serpentine order. This final sorting stage results in implicit stratification of either variable.