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, Grade 4 Science National Assessment, by Scale and Grade: 2009

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

Grade	Number of initial conditioning contrasts2	Number of principal components2	Proportion1 of scale score variance by the population-structure model
			Physical science	Earth & space science	Life science
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), 2009 Science National Assessment.
4	3,894	988	0.62	0.62	0.56
8	3,747	842	0.61	0.58	0.57
12	3,376	526	0.71	0.66	0.67

Proportion of scale score variance accounted for by the population-structure model, science national assessment, by scale and grade: 2009

Grade	Number of initial conditioning contrasts2	Number of principal components2	Proportion1 of scale score variance by the population-structure model
			Scale3
1 (Total Variance – Residual Variance)/Total Variance, where Total Variance consists of both sampling and measurement error variance. 2 Excluding the constant term. 3 Single overall scale. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Science National Assessment.
4	3,894	988	0.60
8	3,747	842	0.58
12	3,376	526	0.67

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