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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, Age 17 Mathematics Long-Term Trend Assessment: 2004

NAEP Technical DocumentationProportion of variance of the group-defining contrasts accounted for by the principal components used in the population-structure model, age 17 mathematics long-term trend assessment: 2004

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 and school questionnaires were not included in the long-term trend assessments in 2004. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004 Mathematics Long-Term Trend Assessment.
All contrasts	784	0.90	0.61	0.98	9	43	277	319	136
Student questionnaire	57	0.88	0.61	0.97	3	8	15	22	9
Major reporting variables	39	0.91	0.67	0.97	2	0	10	15	12
Interactions between reporting variables	688	0.90	0.62	0.98	4	35	252	282	115

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