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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 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, Grade 8 Reading Combined National and State Assessment: 2013
NAEP Technical DocumentationProportion of variance of the group-defining contrasts accounted for by the principal components used in the population-structure model, grade 8 reading combined national and state assessment: 2013
Type of contrast Number of contrasts Mean Minimum Maximum Number of contrasts by proportion1 of variance explained
.00 - .70 .70 - .80 .80 - .90 .90 - .95 .95 - 1.00

1 (Total Variance – Residual Variance)/Total Variance, where Total Variance consists of sampling, measurement, and other sources of error.
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), 2013 Reading Assessment.
All contrasts 1512 .90 .64 1.00 11 79 553 556 313
Student questionnaire 181 .89 .64 .99 3 25 41 61 51
Major reporting variables 120 .93 .71 1.00 0 3 28 40 49
Interactions between reporting variables 377 .90 .64 .98 8 21 102 193 53
Teacher questionnaire 275 .91 .70 .99 0 11 81 90 93
School questionnaire 525 .89 .74 .98 0 17 293 163 52
SD/ELL questionnaire 34 .92 .77 1.00 0 2 8 9 15
Last updated 21 May 2017 (DC)