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 , where these are the sum of weights in the cells. The raking algorithm proceeds by proportionally scaling the , such that the following relations are satisfied:
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.
|Statistic||R2 reporting population||R3 reporting population|
|Grade 4||Grade 8||Grade 4||Grade 8|
|SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2000.|