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Use of Replicate Weights for the State Assessment

Estimates of the variance of sample-based estimates were calculated as:

where

  • x hat sub r denotes an estimated total based on replicate r (with 62 replicates), and

  • X hat denotes the corresponding estimate based on the full sample.

The formula for the estimated total based on replicate r is as follows:

x hat sub r = summation over all possible i and j of open paren W superscript final sub r k double prime i j multiplied by X sub r k double prime i j closed paren

where

  • W superscript final sub r k double prime i j is the final replicate student weight, and

  • X sub r k double prime i j is the estimate associated with the final replicate student weight.

The standard error of an estimatex hat is estimated by taking the square root of the estimated variance, VarJK(x hat).

This estimate of variance is an application of the jackknife procedure.


Last updated 26 August 2008 (FW)

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National Center for Education Statistics - http://nces.ed.gov
U.S. Department of Education