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NAEP Weighting Procedures → Weighting Procedures and Variance Estimation for the 2000 National Main Assessment → Variance Estimation for the 2000 National Main Assessment → Sampling Variability in the 2000 National Main Assessment → Jackknife Procedure → Weights for Certainty Strata

NAEP Technical DocumentationWeights for Certainty Strata

The procedure for obtaining the weights for certainty strata to estimate the sampling variance from the certainty PSUs is similar to the procedure for obtaining the weights for noncertainty strata but more complex. The first stage of sampling is at the school level and the derivation of replicate weights must reflect the sampling of schools within certainty PSUs. Since each of the three grade classes in the national main assessment involves different samples of schools, the procedure for forming replicate base weights is individualized for each of these sample components. Among these three samples are the 22 certainty PSUs and the fact that 26 replicate weights are formed in each case.

A sample of schools is drawn systematically within the 22 certainty PSUs for each grade. Successive schools were grouped in order of sample selection (see School Sorting and Sample Selection) within type of school (public, nonpublic) and additional school sampling strata for nonpublic schools. Generally schools were grouped into pairs. If there was an odd number of public schools or nonpublic schools in a given sampling stratum, the last three schools were grouped into a triple. Each school grouping was systematically assigned to one of 26 replicate groups. Within each school grouping, schools were alternately numbered 1 or 2 (or 3 if the grouping was a triple) starting randomly. If there had been a school group that contained three schools, the weights of the students in these schools were perturbed for two sets of replicates, say i1 and i2, as follows:

	{	if the student is in school number 1 of a PSU in set i if the student in school number 2 or 3 of a PSU in set i if the student does not belong to a PSU in set i
	{	if the student is in school number 1 or 2 of a PSU in set i if the student in school number 3 of a PSU in set i if the student does not belong to a PSU in set i

Without 'triplets', the method of forming replicate base weights in variance groups (i.e., PAIR) is the same as for the noncertainty strata.

The nonresponse, trimming, and poststratification adjustments are applied to each set of replicate base weights to derive the final replicate weights in each case, exactly as in the noncertainty PSUs. These procedures are applied to the full set of weights from all parts of the given sample. For example, poststratification factors are derived from the full set of data for each replicate, not separately for certainty and noncertainty PSUs.

A separate estimate of the contribution to variance is made and added to the jackknife estimate of variance, due to measurement error associated with individual proficiencies. The variance component could have reflected the jackknife variance estimates by applying the item response theory (IRT) computations to each jackknife replicate separately. This was not done because of the heavier IRT computational load. Less work is involved by making separate estimates of this component and adding it to the jackknife variance estimates. Additionally a separate measure of this component of variance is available, which would not be so if it were reflected in the jackknife variance estimate.

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