NAEP Technical DocumentationRaking of Weights

Raking Dimensions for Full Sample Student Weights

The 2000 state assessment used two different sets of administration rules indicated by accommodations for disabled and limited English proficiency (SD/LEP) students. To enable the analysis of the subject specific assessments by omitting either SD/LEP students using accommodations or SD/LEP students not using accommodations, the SD/LEP student weights were raked separately for the two subsets as defined by sample type. Agreement was forced with totals estimated using both of the subsets combined for each of the sample types. The purpose of this was to enhance the reliability (i.e., reduce the sampling error) of estimates produced by using information about student characteristics from the whole sample to enhance the estimates. Non-SD/LEP students were assigned dummy raking factors of one.

Raking (also known as iterative proportional fitting) is done in place of poststratification. Unlike poststratification, raking is performed iteratively to two or more different distributions of a population total (e.g., gender and age). It is typically used in situations in which the interior cells of a cross-tabulation are either unknown, or some sample sizes in the cells are too small for efficient estimation.

In raking, the marginal population totals, N_i. and N_.j are known (i.e., age and gender population counts); however, the interior cells of the crosstabulation N_ij (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:

and

View tables that show the distribution of the raking factor STURAKFC among the 2000 state assessment's participating jurisdictions by grade (fourth and eighth), assessment subject (mathematics and science), and reporting population (non-accommodated and accommodated). Reporting populations differ by whether accommodations were offered to students with disabilities or limited English proficient (SD/LEP) students. The non-accommodated reporting population, also known as the R2 reporting population, includes all non-SD/LEP students plus SD/LEP students from non-accommodated sessions. The accommodated reporting population, also known as the R3 reporting population, includes all non SD/LEP students plus SD/LEP students from accommodated sessions.

The distribution of the factors was computed on the set of assessed and excluded students.

Distribution of the Student-Level Raking Factor (STURAKFC)

Grade 4 Mathematics (Accommodations Not Permitted [R2])
Grade 4 Mathematics (Accommodations Permitted [R3])

Grade 8 Mathematics (Accommodations Not Permitted [R2])
Grade 8 Mathematics (Accommodations Permitted [R3])

Grade 4 Science (Accommodations Not Permitted [R2])
Grade 4 Science (Accommodations Permitted [R3])

Grade 8 Science (Accommodations Not Permitted [R2])
Grade 8 Science (Accommodations Permitted [R3])

Last updated 13 August 2008 (KL)

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