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NAEP Sample Design → Sample Design for the 2001 Assessment → National Main Assessment Sample Design in 2001 → Sampling of Schools in the 2001 National Main Assessment → School Substitution for Adjusting School Nonresponse for the 2001 National Main Assessment → Substitute Frame Standard Deviations for the 2001 National Main Assessment

NAEP Technical DocumentationSubstitute Frame Standard Deviations for the 2001 National Main Assessment

In the process of school substitution to adjust for nonresponse, distance measures were computed for each sampled school and its potential matches. These distance measures for pairs of schools were computed by dividing the sum of squares of the differences of three values for the pair of schools divided by the corresponding variances, which can be seen as 'average' squared differences over all pairs of schools for each school. A pair of schools will register a large difference if any of these squared differences exceed considerably the corresponding variance. The distance measure was computed based on percent of Black students, percent of Hispanic students, and the square root of the grade enrollment. Note that values for the first pass were slightly different from the values for the second pass because of changes in the three variances: the second pass variance computations excluded the schools already selected as substitutes in the first pass.

Substitute frame standard deviations, national main assessment: 2001

Measure	Fourth-grade standard deviation	Eighth-grade standard deviation	Twelfth-grade standard deviation
Percent of Black students	28.7	27.9	25.5
Percent of Hispanic students	23.6	21.6	19.9
Mean percent Black-Hispanic	26.3	24.9	22.9
Square root grade enrollment	3.0	5.8	7.4
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2001.

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