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Some Formulas for Use With Bayesian Ability Estimates IRT

Mislevy, Robert J.
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Ability Distribution, Bayesian Statistics, Item Response Theory (IRT), Population Distribution, Test Theory


(18pp.) Relationships between Bayesian ability estimates and the parameters of a normal population distribution are derived in the context of classical test theory. Analogues are provided for use as approximations in work with item response theory. The following questions are addressed: (1) What is the relationship between the distribution of the latent ability variable in a population and the distribution of ability estimates? (2) Because calculating Bayesian estimates typically requires knowing the population distribution, how should one proceed if it is not known? (3) What if Bayesian ability estimates have been calculated in accordance with a common population distribution, but it is later desired to estimate the distributions of specified subpopulations?

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