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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 Main Assessment: 2007

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 main assessment: 2007

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), 2007 Mathematics Assessment.
All contrasts	1490	0.90	0.60	1.00	22	118	476	451	423
Student questionnaire	92	0.89	0.63	0.99	1	14	23	26	28
Major reporting variables	118	0.93	0.64	1.00	1	5	23	31	58
Interactions between reporting variables	437	0.91	0.60	0.99	10	28	113	148	138
Teacher questionnaire	350	0.91	0.71	0.99	0	17	93	118	122
School questionnaire	230	0.89	0.71	0.99	0	10	107	84	29
NIES questionnaire	217	0.85	0.63	0.99	10	42	104	34	27
SD/ELL questionnaire	46	0.92	0.76	0.99	0	2	13	10	21

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