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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 Models

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

For each assessment scale, the proportions of scale score variance accounted for by the population-structure model 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 model 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 do 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, by year and subject area: Various years, 2000–2012
Subject area Year National main assessment Grade 4 state assessment Grade 8 state assessment Grade 12 state assessment
Arts 2008 R3
Civics 2010 R3
2006 R3
Economics 2012 R3
2006 R3
Geography 2010 R3
2001 R2/R3
Mathematics 2011 R3 R3 R3
2009 R3 R3 R3 R3
2007 R3 R3 R3
2005 R3 R3 R3
2003 R3 R3 R3
2000 R2/R3 R2/R3 R2/R3
Reading 2011 R3 R3 R3
2009 R3 R3 R3 R3
2007 R3 R3 R3
2005 R3 R3 R3
2003 R3 R3 R3
2002 R3 R3 R3
2000 R2/R3
Reading vocabulary 2011 R3
2009 R3
Science 2011 R3 R3
2009 R3 R3 R3
2005 R3 R3 R3
2000 R2/R3 R2/R3 R2/R3
U.S. history 2010 R3
2006 R3
2001 R2/R3
Writing 2011 R3
2007 R3
2002 R3 R3 R3
† Not applicable; subject was not assessed at this grade in this year.
NOTE: R2 is the non-accommodated reporting sample; R3 is the accommodated reporting sample. It samples students who are classified students with disabilities (SD) or English language learners (ELL), plus SD/ELL students from sessions in which accommodated were allowed. The R3 sample is more inclusive and excludes a smaller proportion of sampled students. The R3 sample type was the only sample type used in NAEP after 2001.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), Various years, 2000-2012 Assessments.

Links to proportion of scale score variance accounted for by the population-structure model, long-term trend assessments, by year and subject area: 2004, 2008, and 2012
Subject area Year Assessment National main assessment
Mathematics 2012 Long-term trend R3
Reading Long-term trend R3
Mathematics 2008 Long-term trend R3
Reading Long-term trend R3
Mathematics 2004 Long-term trend R3
Reading Long-term trend R3
NOTE: R2 is the non-accommodated reporting sample; R3 is the accommodated reporting sample. It samples students who are classified students with disabilities (SD) or English language learners (ELL), plus SD/ELL students from sessions in which accommodated were allowed. The R3 sample is more inclusive and excludes a smaller proportion of sampled students. The R3 sample type was the only sample type used in NAEP after 2001.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004, 2008, and 2012 Long-Term Trend Assessment.

Last updated 24 February 2016 (GF)