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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 Mathematics Combined National and State Assessment, by Type of Contrast: 2019

​​NAEP Technical DocumentationProportion of Variance of the Group-Defining Contrasts Accounted for by the Principal Components Used in the Population-Structure Model, Grade 8 Mathematics Combined National and State Assessment, by Type of Contrast: 2019

Proportion of variance of the group-defining contrasts accounted for by the principal components used in the population-structure model, grade 8 mathematics combined national and state assessment, by type of contrast: 2019
Type of contrastNumber of contrastsMeanMinimumMaximumNumber of contrasts by proportion of variance explained
.00 - .70.70 - .80.80 - .90.90 - .95.95 - 1.00
(Total Variance – Residual Variance) / Total Variance, where Total Variance includes variance accounted and unaccounted for by the variables in the population-structure model.
SD/EL = Students with disabilities/English learners.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
All contrasts1584.90.621.0012100554579339
Student questionnaire428.91.68.99120108176123
Major reporting variables133.91.731.0005464042
Interactions between reporting variables268.89.62.9811159212030
Teacher questionnaire419.91.73.99018162135104
School questionnaire305.88.70.980331429931
SD/EL questionnaire31.88.74.9909499
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Last updated 05 October 2023 (SK)