Summary Statistics for Scale Scores of Groups
The objective of the National Assessment of Educational Progress (NAEP) is to estimate population and subpopulation characteristics. For these groups, not only an indication of proficiency is estimated, but also the confidence in those estimates. The confidence is quantified as a standard error, containing two sources of variability: sampling and measurement. Sampling variability is a result of the fact that not the whole population is observed, but only a sample from that population. Therefore, a different sample might have yielded slightly different results and this uncertainty is represented in the standard error. Measurement variability is a result of the fact that the statistic of interest (e.g., an indication of proficiency) is not observed directly but informed from a set of observed responses to cognitive tasks. Therefore, a different sample of tasks might have yielded slightly different results and this uncertainty is also represented in the standard error. The sampling part of the standard error is computed by a re-sampling method (jackknife repeated replications). The measurement part is derived from Item Response Theory models, which are used to provide a link between the observations and the latent proficiency variable θ. This variable is represented through plausible values. Last updated 22 July 2008 (RF) |
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