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 Assessments: 2011

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 assessments: 2011

Type of contrast	Number of contrasts	Mean	Minimum	Maximum	Number of contrasts by proportion1 of variance explained
					0.00 - 0.70	0.70 - 0.80	0.80 - 0.90	0.90 - 0.95	0.95 - 1.00
† Not applicable. 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), 2011 Science Assessment.
All contrasts	1,877	0.90	0.64	1.00	8	78	795	649	347
Student questionnaire	63	0.90	0.74	0.98	0	11	15	18	19
Major reporting variables	274	0.91	0.73	1.00	0	17	81	101	75
Interactions between reporting variables	341	0.90	0.64	0.98	8	21	108	157	47
Teacher questionnaire	461	0.91	0.75	0.98	0	16	165	171	109
School questionnaire	700	0.89	0.76	0.99	0	10	418	193	79
NIES questionnaire	†	†	†	†	†	†	†	†	†
SD/ELL questionnaire	38	0.92	0.77	0.99	0	3	8	9	18

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