NAEP Analysis and Scaling → Estimation of Population and Student Group Distributions → Examining the Population-Structure Models Used in NAEP → Proportion of Scale Score Variance Accounted for by the Population-Structure Models → Proportion of Scale Score Variance Accounted for by the Population-Structure Models, Mathematics National Assessment, By Scale and Grade: 2011

NAEP Technical DocumentationProportion of scale score variance accounted for by the population-structure model,  mathematics national assessment, by scale and grade: 2011

Grade	Number of initial  group-defining contrasts2	Number of principal components2	Proportion1 of scale score variance by the population-structure model
			Number sense, properties, and operations	Measurement	Geometry	Data analysis, statistics, and probability	Algebra
1 (Total Variance – Residual Variance)/Total Variance, where Total Variance consists of both sampling and measurement error variance. 2 Excluding the constant term. NOTE: In 2011, grade 12 was not assessed. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2011 Mathematics National Assessment.
4	3031	782	0.55	0.57	0.51	0.56	0.56
8	3548	928	0.63	0.62	0.59	0.65	0.66

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