Theoretical evaluation of partial credit scoring of the multiple-choice test item

Abstract In multiple-choice tests, guessing is a source of test error which can be suppressed if its expected score made negative by either penalizing wrong answers or rewarding expressions partial knowledge. Starting from the most general formulation necessary and sufficient scoring conditions for to lead an loss beyond test-taker’s knowledge, we formulate class optimal functions, including proposal Zapechelnyuk (Econ. Lett. 132 , 24–27 (2015)) as special case. We then consider arbitrary taken rational test-taker whose knowledge item defined fraction answer options ruled out. For this model, study statistical properties obtained both standard marking (where not penalized), where expensive penalties incorrect different schemes that reward