Accommodations play a key role in enabling individuals with disabilities to participate in the National Assessment of Educational Progress (NAEP) and other large-scale assessments. However, it can be difficult to know how accommodations affect the validity of results, thus making it difficult to determine which accommodations should be allowed.…

It is a common practice in item response theory (IRT) to treat estimates of item parameters, say "B" circumflex, as if they were the known, true quantities, "B." However, ignoring the uncertainty associated with item parameters can lead to biases and over-confidence in subsequent inferences such as ability estimation,…

Relationships between Bayesian ability estimates and the parameters of a normal population distribution are derived in the context of classical test theory. Analogies are provided for use as approximations in work with item response theory (IRT). The following issues are addressed: (1) the relationship between the distribution of the latent…

Relationships between Bayesian ability estimates and the parameters of a normal population distribution are derived in the context of classical test theory. Formulas are presented for practical work with Bayesian ability estimates, and a numerical illustration is provided. (SLD)

The basic equations of item response theory provide a foundation for inferring examinees' abilities and items' operating characteristics from observed responses. In practice, though, examinees will usually not have provided a response to every available item--for reasons that may or may not have been intended by the test administrator, and that…

It is only a slight exaggeration to describe the test theory that dominates educational measurement today as the application of twentieth-century statistics to nineteenth-century psychology. Sophisticated estimation procedures, new techniques for missing-data problems, and theoretical advances into latent-variable modeling have appeared--all…