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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 of the Group-Defining Contrasts Accounted for by the Principal Components Used in NAEP Student Group Distribution 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: 2005

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: 2005

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	0.96 - 1.00
1(Total Variance – Residual Variance)/Total Variance, where Total Variance consists of both sampling and measurement error variance. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment.
All contrasts	1,489	0.90	0.58	1.00	29	107	470	412	471
Student questionnaire	209	0.89	0.58	0.99	4	20	66	80	39
Major reporting variables	101	0.93	0.74	1.00	0	3	25	23	50
Interactions between reporting variables	629	0.91	0.59	0.99	17	41	163	161	247
Teacher questionnaire	361	0.89	0.64	0.99	6	27	160	73	95
School questionnaire	189	0.89	0.66	0.98	2	16	56	75	40

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