SOME FORMULAS FOR USE WITH BAYESIAN ABILITY ESTIMATES

Relationships between Bayesian ability estimates and the parameters of a normal population distribution are derived in the context of classi cal test theory. Analogues are provided for use as approximations in w ork with item response theory. The following questions were addressed: What is the relationship between the distribution of the latent abili ty variable in a population, and the distribution of ability estimates ? Because calculating Bayesian estimates typically requires knowing th e population distribution, how should one proceed if it is not known? What if Bayesian ability estimates have been calculated in accordance with a common population distribution, but it is later desired to esti mate the distributions of specified subpopulations?