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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 Combined National and State Main Assessment, by Subscale and Grade: 2005

NAEP Technical DocumentationProportion of scale score variance accounted for by the population-structure models, mathematics combined national and state main assessment, by subscale and grade: 2005

Grade	Number of initial conditioning contrasts2	Number of principal components2	Proportion1 of scale score variance
			Number, properties, and operations	Measurement	Geometry	Data analysis and probability	Algebra
4	3,196	538	0.44	0.46	0.43	0.45	0.44
8	3,527	598	0.56	0.57	0.52	0.58	0.57
12	2,469	371	0.70	0.713	0.713	0.69	0.74
1 (Total Variance – Residual Variance)/Total Variance, where Total Variance consists of both sampling and measurement error variance. 2Excluding the constant term. 3 In 2005, the grade 12 Measurement and Geometry subscales were combined for scaling. NOTE: There were no state assessments for grade 12 in 2005. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment.

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