Estimates obtained from a sample and not a population also have a predictable amount of sampling variability. Estimates of sampling variability provide information about how much the value of a given statistic is likely to change if the statistic is based on an equivalent sample of individuals drawn in exactly the same manner as the achieved sample.
For NAEP, another important source of variability is imprecision in the measurement of individual proficiencies. For the 2000 assessment, proficiencies in all subject areas are summarized through item response theory (IRT) models, but not in the way that these models are used in standard applications where each person responds to enough items to allow for precise estimation of that person's proficiency. In NAEP, each individual responds to relatively few items so that individual proficiency values cannot be well determined; instead, NAEP provides plausible values, which are not NAEP scores. Consequently, the variance of any statistic based on plausible values has a component due to measurement error.