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 Model, Mathematics National Assessment, by Scale and Grade: 2009

NAEP Technical DocumentationProportion of scale score variance accounted for by the population-structure model, mathematics national assessment, by scale and grade: 2009

Grade	Number of initial  group-defining contrasts2	Number of principal components2	Proportion1 of scale score variance by the population-structure model
			Number 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: At grade 12, the Measurement and Geometry subscales were combined for scaling. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Mathematics National Assessment.
4	4,455	1,055	0.58	0.58	0.49	0.59	0.56
8	4,334	938	0.63	0.63	0.59	0.66	0.67
12	3,450	563	0.73	0.74		0.71	0.77

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