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 Mathematics 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 4 mathematics 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
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 Mathematics Assessment.
All contrasts	1802	0.90	0.63	1.00	12	82	721	590	397
Student questionnaire	48	0.90	0.70	0.99	1	8	9	14	16
Major reporting variables	198	0.92	0.66	1.00	2	5	50	65	76
Interactions between reporting variables	278	0.89	0.63	0.98	7	15	93	127	36
Teacher questionnaire	522	0.91	0.74	0.99	0	15	190	156	161
School questionnaire	422	0.90	0.76	0.99	0	7	203	155	57
NIES questionnaire	291	0.87	0.64	0.99	2	31	160	65	33
SD/ELL questionnaire	43	0.92	0.79	1.00	0	1	16	8	18

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