Two Prophecy Formulas for Assessing the Reliability of Item Response Theory-Based Ability Estimates

Two new prophecy formulas for estimating item response theory (IRT)-based reliability of a shortened or lengthened test are proposed. Some of the relationships between the two formulas, one of which is identical to the well-known Spearman-Brown prophecy formula, are examined and illustrated. The major assumptions underlying these formulas are outlined and discussed. Both prophecy formulas appear to provide comparable estimates of reliability in the IRT context as well as in the classical test theory context.