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 4 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 4 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	2,507	0.90	0.61	1.00	10	98	1075	737	587
Student questionnaire	201	0.91	0.61	0.99	2	7	48	101	43
Major reporting variables	112	0.93	0.69	1.00	2	2	26	39	43
Interaction between reporting variables	465	0.91	0.62	0.99	6	24	114	162	159
Teacher questionnaire	977	0.90	0.71	0.99	0	56	440	232	249
School questionnaire	704	0.89	0.76	0.99	0	8	431	194	71
SD/ELL questionnaire	48	0.92	0.79	0.99	0	1	16	9	22

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