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Common Population Linking Procedure for the 2000 National Main Assessment

The linking of each weight distribution is achieved using a common population linking procedure and a method known as iterative proportional fitting. In raking, the marginal population totals, Ni. and Nj. are known (i.e., age and gender population counts); however, the interior cells of the cross-tabulation Nij (the age by gender cells) are estimated from the sample by N hat sub i j, where these are the sum of weights in the cells. The raking algorithm proceeds by proportionally scaling the N hat sub i j, such that the following relations are satisfied:

Summation over j of N hat sub i j = N sub i


Summation over i of N hat sub i j = N sub j

At the end of the fitting, adjustment factors are derived and multiplied to the national main sample weights for each student group to force their distribution to agree with the aggregated state samples, for each of these three variables in turn. This process is then repeated, until the final set of adjusted weights, compared with the state sample weights on all three distributions, shows close agreement. The table below shows the distribution of the adjustment factors for each of the grades and subjects assessed.

Distributions of raking adjustments for national linking weights, by reporting population, national main assessment: 2000
Statistic R2 reporting population R3 reporting population
Grade 4 Grade 8 Grade 4 Grade 8
Mathematics Science Mathematics Science Mathematics Science Mathematics Science
Minimum 0.70 0.66 0.77 0.77 0.76 0.68 0.80 0.79
10th percentile 0.79 0.86 0.84 0.82 0.82 0.81 0.84 0.84
25th percentile 0.86 0.88 0.86 0.86 0.87 0.87 0.87 0.86
Median 0.91 0.93 1.00 1.01 0.93 0.95 0.99 0.99
75th percentile 1.08 1.10 1.11 1.09 1.10 1.13 1.15 1.12
90th percentile 1.21 1.24 1.14 1.19 1.18 1.27 1.19 1.21
Maximum 1.30 1.48 1.38 1.44 1.30 1.50 1.45 1.41
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2000.

Last updated 17 June 2008 (MH)

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