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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 Scale Score Variance Accounted for by the Population-Structure Model

Proportion of Scale Score Variance Accounted for by the Population-Structure Model

For each assessment scale, the proportions of scale score variance accounted for by the population-structure models are given for each grade level. The numbers of principal components and group-defining variable contrasts used in the population-structure model are also provided.

The proportions in the tables indicate how strongly the scale score distributions are related to the groups to which students belong, as represented by the principal components. If the proportion of scale score variance accounted for by the population-structure model is one, all of the variability in the scores can be related to group membership as defined by the full set of variables in the population-structure model. The proportion of scale score variance accounted for by the population-structure model is

The quantity total variance minus residual variance divided by total variance

where the total variance includes sampling error, measurement error, and other sources of error.

Values of the proportion of scale score variance accounted for by the population-structure models range from approximately 0.50 to 0.98 in the national sample, depending on the subject area scale and sample for which it is calculated. The appropriateness and value of NAEP's population-structure model does not depend on having a high proportion of explained variance. The values are provided as documentation for each sample.

Links to proportion of scale score variance accounted for by the population-structure model, main assessments: 2000–2008
Subject area Year National main assessment Grade 4 state assessment Grade 8 state assessment
Arts 2008 R3
Civics 2006 R3
Economics 2006 R3
Geography 2001 R2/R3
Mathematics 2007 R3 R3 R3
2005 R3 R3 R3
2003 R3 R3 R3
2000 R2/R3 R2/R3 R2/R3
Reading 2007 R3 R3 R3
2005 R3 R3 R3
2003 R3 R3 R3
2002 R3 R3 R3
2000 R2/R3
Science 2005 R3 R3 R3
2000 R2/R3 R2/R3 R2/R3
U.S. history 2006 R3
2001 R2/R3
Writing 2007 R3
2002 R3 R3 R3
† Not applicable; subject was not assessed at this grade in this year.
NOTE: "R2" links to data for the R2 reporting population; "R3" links to data for the R3 reporting population.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), Various Years, 2000-2008 Assessments.

Links to proportion of scale score variance accounted for by the population-structure model, long-term trend assessments: 2004 and 2008
Subject area Year Assessment National main assessment
Mathematics 2008 Long-term trend R3
Reading Long-term trend R3
Mathematics 2004 Long-term trend R3
Reading Long-term trend R3
NOTE: "R3" links to data for the R3 reporting population.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004 and 2008 Long-Term Trend Assessments.

Last updated 14 December 2011 (GF)
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National Center for Education Statistics - http://nces.ed.gov
U.S. Department of Education