The focus of this paper is on the empirical relationship between item difficulty and item discrimination. Two studies--an empirical investigation and a simulation study--were conducted to examine the association between item difficulty and item discrimination under classical test theory and item response theory (IRT), and the effects of the…

Takers of educational tests often receive proficiency levels instead of or in addition to scaled scores. For example, proficiency levels are reported for the Advanced Placement (AP®) and U.S. Medical Licensing examinations. Technical difficulties and other unforeseen events occasionally lead to missing item scores and hence to incomplete data on…

Administrative problems such as computer malfunction and power outage occasionally lead to missing item scores and hence to incomplete data on mastery tests such as the AP and U.S. Medical Licensing examinations. Investigators are often interested in estimating the probabilities of passing of the examinees with incomplete data on mastery tests.…