School Trimming Adjustment for the 2000 National Main Assessment

School trimming is a weighting adjustment procedure that involves reducing the weights of schools that are extremely large. Extremely large weights can inflate the variance of survey estimates. Weight reduction methods are typically used to reduce the impact of large weights. The motivation behind weight reduction methods is to reduce the mean square error of survey estimates. Although trimming large weights reduce variances, it also introduces bias. However, it is assumed that the reduction in the variances outweighs the increase in the bias, thereby reducing the mean square error of survey estimates.

There are several analytic approaches for detecting extremely large weights. For school trimming, a school's weight is considered extremely large if it contributes too much to variances. The school trimming process involves estimating the variance of the estimated number of eligible students within a given domain. Any school that contributed more than a specified proportion—referred to here as Γ—to the variance had their weight "trimmed" so that the school contributes exactly Γ to the variance. School trimming was done separately by grade, subject, and school type (public/private). School weights were trimmed within religious affiliation for private schools and within NAEP regions for public schools. The variance cutoff Γ for each domain was 10/M, where M is the number of schools within the domain. The value Γ is believed to provide negligible bias while substantially reducing variance.

A value Γ, calculated for each school in a given domain, is defined

where

If there exists at least one school in the domain where Γ > 10/M, the weight of the school with the largest Γ among schools with X_i > is trimmed by the following factor:

New values forand V are recomputed, and Γ for each school is recalculated. Checks are made again for any schools with Γ > 10/M. If one or more exists, the above process is repeated. The process continues until all Γ are less than or equal to 10/M. If a school's weight is not trimmed, SCH_TRIM is assigned the value 1.

Last updated 03 March 2008 (PE)

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