A method for medical screening is adapted to differential item functioning (DIF). Its essential elements are explicit declarations of the level of DIF that is acceptable and of the loss function that quantifies the consequences of the two kinds of inappropriate classification of an item. Instead of a single level and a single function, sets of…

Many well-known equations in classical test theory are mathematical identities in populations of individuals but not in random samples from those populations. First, test scores are subject to the same sampling error that is familiar in statistical estimation and hypothesis testing. Second, the assumptions made in derivation of formulas in test…