The purpose of stratification is to increase the efficiency of the school samples by reducing (or eliminating) variability in the sample size for important school reporting groups within each jurisdiction. NAEP school sampling utilizes two types of stratification: explicit and implicit.
Explicit stratification assigns each school to a mutually exclusive and exhaustive stratum, and assigns an optimal sample size to each stratum. (Here, "optimal" is defined as being proportional to the share of estimated student enrollment in the grade for that student group.) This stratification allows each stratum to have a sample size exactly equal to the optimal sample size according to its enrollment.
Under implicit stratification, schools are ordered within an explicit stratum and sampled systematically using this ordering. This stratification reduces the variability of the sample size around the optimal sample size for important reporting groups within the explicit stratum, but not to zero as in explicit stratification. Implicit stratification leaves some variability in the sample size, but avoids distortion of the measures of size so that they can add up to integer totals to "fit" the explicit strata. In the 2003 state assessment sampling process, all stratification within a jurisdiction is implicit. The jurisdictions themselves represent the explicit strata.