A critique of Raju and Oshima's prophecy formulas for assessing the reliability of item response theory-based ability estimates

Raju and Oshima (2005) proposed two prophecy formulas based on item response theory in order to predict the reliability of ability estimates for a test after change in its length. The first prophecy formula is equivalent to the classical Spearman-Brown prophecy formula. The second prophecy formula is misleading because of an underlying false assumption. It can yield negative reliability estimates, especially if the reliability of ability estimates for the old test is low and the new test is shorter. This article identifies the fallacy of the second prophecy formula and demonstrates the scope of its bias in predicting test reliability.