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 Mathematics 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 mathematics 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: NIES = National Indian Education Study; 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 Mathematics Assessment.
All contrasts	2,367	0.90	0.64	1.00	13	105	1011	675	563
Student questionnaire	230	0.91	0.65	0.99	1	20	59	92	58
Major reporting variables	113	0.93	0.69	1.00	1	1	26	39	46
Interaction between reporting variables	583	0.92	0.64	0.99	10	22	142	193	216
Teacher questionnaire	322	0.90	0.76	0.98	0	16	130	84	92
School questionnaire	747	0.89	0.77	0.99	0	7	449	199	92
NIES questionnaire	328	0.87	0.68	0.99	1	37	192	58	40
SD/ELL questionnaire	44	0.92	0.78	0.99	0	2	13	10	19

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