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HomeTDWNAEP Analysis and ScalingEstimation of Population and Student Group DistributionsExamining the Population-Structure Models Used in NAEPProportion of Scale Score Variance Accounted for by the Population-Structure ModelProportion of Scale Score Variance Accounted for by the Population-Structure Models, Mathematics Combined National and State Main Assessment, By Scale and Grade: 2007

NAEP Technical DocumentationProportion of scale score variance accounted for by the population-structure model, mathematics combined national and state main assessment, by scale and grade: 2007

Grade	Number of initial  group-defining contrasts2	Number of principal components2	Proportion1 of scale score variance accounted for by the population-structure model
			Number properties and operations	Measurement	Geometry	Data analysis 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. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2007 Mathematics Assessment.
4	3130	585	0.54	0.56	0.48	0.55	0.53
8	3512	649	0.60	0.59	0.55	0.62	0.61

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