A comparison of joint national main and state assessments usually finds an overlap of sampled schools. Schools selected for both assessments spend a fair amount of time preparing and administering two sets of educational tests. Concern about school sample overlap arises each assessment cycle. NAEP has a policy of avoiding national and state sample overlap where possible. This policy avoids excess burden on individual schools without distorting the resulting school samples with either bias or substantial variance.
To control overlap between state and national main samples, a procedure is used that conditions on the national NAEP primary sampling unit (PSU) sample. National school selection probabilities (for the national main NAEP assessment) that are conditional on the selection of national main sample PSUs are used in determining state assessment school selection probabilities. Participating jurisdictions not containing national main PSUs do not have their state assessment school selection probabilities adjusted.
The overlap control procedure reduces the variance of the state samples, although it leads to a greater degree of sample overlap than using unconditional national selection probabilities. However, this degree of sample overlap is less than would be achieved without any overlap control at all. The procedure additionally recognizes the impact of within-PSU sampling in noncertainty PSUs in some jurisdictions. Schools necessary for the state sample are not subject to overlap control; such schools are self-representing in the state sample. Excluding such schools on a random basis adds undue variance to the state estimates.
The state assessment's conditional selection probabilities generated by the overlap control procedure tend to be smaller than the unconditional state selection probabilities for schools selected for the national main sample. Unconditional probabilities obtained by integrating over the national sampling process equal the required state assessment probabilities without any overlap control implementation. Such probabilities mean that a school's unconditional probability of state assessment selection stays the same regardless of overlap control implementation.
More information about the sample overlap procedures appears in the Technical Report of the NAEP 1994 Trial State Assessment Program in Reading (Mazzeo, Allen, and Kline 1995).