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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 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, Grade 8 Arts National Main Assessment: 2008

NAEP Technical DocumentationProportion of variance of the group-defining contrasts accounted for by the principal components used in the population-structure model, grade 8 arts (music) national main 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 Arts Assessment.
All contrasts 886 0.90 0.69 0.99 1 55 361 283 186
Student questionnaire 159 0.87 0.70 0.99 0 23 75 45 16
Major reporting variables 53 0.92 0.77 0.99 0 2 20 10 21
Interactions between reporting variables 431 0.91 0.69 0.98 1 28 126 145 131
School questionnaire 207 0.90 0.81 0.98 0 0 114 78 15
SD/ELL questionnaire 36 0.87 0.79 0.98 0 2 26 5 3

Proportion of variance of the group-defining contrasts accounted for by the principal components used in the population-structure model, grade 8 arts (visual arts) national main 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 Arts Assessment.
All contrasts 869 0.90 0.69 0.99 1 50 353 288 177
Student questionnaire 153 0.88 0.70 0.99 0 22 60 51 20
Major reporting variables 50 0.92 0.75 0.99 0 3 21 5 21
Interactions between reporting variables 426 0.91 0.69 0.98 1 22 137 145 121
School questionnaire 204 0.90 0.83 0.98 0 0 111 80 13
SD/ELL questionnaire 36 0.87 0.74 0.98 0 3 24 7 2
Last updated 14 December 2011 (GF)
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