This study addresses statistical techniques the might ameliorate some of the sampling problems currently facing states with small populations participating in State NAEP. The author explores how the application of finite population correction factors to the between-school component of variance could be used to modify sample sizes required of states that currently qualify for the exemptions from State NAEP's minimum sample requirements. He also examines how to preserve the infinite population assumptions for hypothesis testing related to comparisons between domain means. Results lend support to alternate sample size specifications both in states with few schools and in states with many small schools. The author notes that permitting states to use design options other than the current State NAEP requirement could reduce costs related to test administration, scoring, and data processing.
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