NAEP Analysis and Scaling → Estimation of Population and Student Group Distributions → Examining the Population-Structure Models Used in NAEP → Proportion of Variance Accounted For by Principal Components Used in NAEP Population-Structure Models → Proportion of Variance of the Group-Defining Contrasts Accounted for by the Principal Components Used in the Population-Structure Model, Grade 8 Science Combined National and State Main Assessment: 2009

NAEP Technical DocumentationProportion of variance of the group-defining contrasts accounted for by the principal components used in the population-structure model, grade 8 science combined national and state main assessment: 2009

Type of contrast	Number of contrasts	Mean	Minimum	Maximum	Number of contrasts by proportion1 of variance explained
					0.00 - 0.70	0.71 - 0.80	0.81 - 0.90	0.91 - 0.95	0.95 - 1.00
1(Total Variance – Residual Variance)/Total Variance, where Total Variance consists of both sampling and measurement error variance. NOTE: SD/ELL = Students with disabilities/English language learners. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Science Assessment.
All contrasts	2,171	0.90	0.59	1.00	14	89	928	623	517
Student questionnaire	218	0.90	0.59	0.99	2	24	64	77	51
Major reporting variables	113	0.93	0.64	1.00	1	0	35	33	44
Interaction between reporting variables	578	0.91	0.62	0.99	11	26	140	203	198
Teacher questionnaire	469	0.90	0.71	0.98	0	21	189	145	114
School questionnaire	749	0.89	0.76	0.99	0	12	491	157	89
SD/ELL questionnaire	44	0.91	0.74	0.99	0	6	9	8	21

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