A modification to angoff and bookmarking cut scores to account for the imperfect reliability of test scores

It is shown that the Angoff and bookmarking cut scores are examples of true score equating that in the real world must be applied to observed scores. In the context of defining minimal competency, the percentage "failed'' by such methods is a function of the length of the measuring instrument. It is argued that this length is largely arbitrary, being heavily influenced by practical educational constraints. Hence, there is an ambiguity or nonuniqueness about the percentage failed. An argument is advanced that the failure rate should reflect the percentage of true scores below the cut score. A modification to the cut score is derived that achieves this outcome and simultaneously removes the nonuniqueness in the percentage failed.