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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 12 Mathematics National 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 12 mathematics national 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. NOTE: Teacher questionnaire was not included at grade 12 in 2005. 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	1007	0.90	0.67	1.00	9	53	399	289	257
Student questionnaire	266	0.89	0.69	0.99	1	22	128	79	36
Major reporting variables	58	0.92	0.80	1.00	0	0	22	7	29
Interactions between reporting variables	511	0.92	0.67	0.98	8	22	140	151	190
School questionnaire	172	0.87	0.75	0.95	0	9	109	52	2

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