States participating in the National Assessment of Educational Progress State Assessment program (state NAEP) are required to sample at least 2,500 students selected from at least 100 schools per subject assessed. In this ideal situation, 25 students are assessed for a subject in each school selected for that subject. If more than one subject is being assessed for the given state and grade, say k subjects (with k usually 2), then as many as 25k students may be assessed at a single school for the target grade if the grade enrollment is sufficiently large.

Two problems have arisen in implementing the required design: (1) some states have too few schools—sometimes fewer than 100 within a target grade—and (2) some states have small schools, thereby requiring many more than 100 schools to obtain a sample of 2,500 students per subject. Specific policies have been developed to exempt states from the stringent sample design requirement above for each case.

This paper explores the application of finite population correction factors to the between-school component of variance and examines how this might effect sample size requirements in the types of states that currently require exemptions from the minimum sample requirements for the state NAEP.