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 the 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, Age 13 Mathematics Long-Term Trend Assessment: 2008

NAEP Technical DocumentationProportion of variance of the group-defining contrasts accounted for by the principal components used in the population-structure model, age 13 mathematics long-term trend assessment: 2008

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), 2008 Mathematics Long-Term Trend Assessment.
All contrasts	678	0.90	0.64	0.99	14	56	193	226	189
Student questionnaire	79	0.90	0.64	0.99	2	12	13	26	26
Major reporting variables	65	0.89	0.69	0.99	1	10	25	9	20
Interactions between reporting variables	494	0.90	0.64	0.99	11	32	138	178	135
SD/ELL questionnaire	40	0.90	0.75	0.97	0	2	17	13	8

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