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 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: 2012

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: 2012

Type of contrast	Number of contrasts	Mean	Minimum	Maximum	Number of contrasts by proportion1 of variance explained
					0.00 - 0.70	0.70 - 0.80	0.80 - 0.90	0.90 - 0.95	0.95 - 1.00
1 (Total Variance – Residual Variance)/Total Variance, where Total Variance consists of both sampling and measurement error variance. NOTE: SD/ELL = Students with disabilities/English language learners. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2012 Mathematics Long-Term Trend Assessment.
All contrast	509	0.90	0.68	0.99	4	47	145	205	108
Student questionnaire	81	0.91	0.75	0.99	0	10	17	25	29
Major reporting variables	77	0.90	0.76	0.99	0	5	32	15	25
Interactions between reporting variables	316	0.90	0.68	0.98	4	30	83	157	42
SD/ELL questionnaire	35	0.91	0.78	0.98	0	2	13	8	12

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