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 9 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 9 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	557	0.90	0.61	0.99	20	27	178	175	157
Student questionnaire	60	0.89	0.63	0.99	7	4	8	22	19
Major reporting variables	63	0.90	0.66	0.99	1	7	24	10	21
Interactions between reporting variables	391	0.90	0.61	0.99	12	13	134	129	103
SD/ELL questionnaire	43	0.91	0.76	0.98	0	3	12	14	14

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