Critical thinkingArticle: CohenItem response theory (IRT) The procedures of item response theory provide a way to model the probability that a person with X ability will be able to perform at a level of Y.Because so often the psychological or educational construct being measured is physically unobservable (latent), and because the construct being measured may be a trait, a synonym for IRT is latent-trait theory.IRT is not a term used to refer to a single theory or method.It refer to a family of theories and methods, and quite a large family at that, with many other names used to distinguish specific approaches.Difficulty: the attribute of not being easily accomplished, solved, or comprehended.Discrimination: the degree to which an item differentiates among people with higher levels or lower levels of the trait, ability, or whatever it is being measures.A number of different IRT models exists to handle data resulting from the administration of tests with various characteristics and in various formats.Dichotomous test items: test items or questions that can be answered with only one or two alternative responses.Polytomous test items: test items or questions with three or more alternative responses, where only one is scored correct or scored as being consistent with a targeted trait or other construct.Other IRT models exits to handle other types of data.In general, latent-trait models differ in some important ways from CTT.In CTT, no assumptions are made about the frequency distribution of test scores.Such assumptions are inherent in latent-trait models.Rasch model: an IRT model with very specific assumptions about...