ITEM RESPONSE THEORY (20 m)

Item response theory (IRT) is a body of theory describing the application of mathematical models to data obtained from questionnaires and tests as a basis for measuring abilities, attitudes, or other variables. It is used for statistical analysis and development of assessments, often for high stake tests such as the Graduate Record Examination. At its most basic level, it is based on the idea that the probability of getting an item correct is a function of a latent trait or ability. For example, a person with higher intelligence would be more likely to correctly respond to a given item on an intelligence test.

Formally, IRT models apply mathematical functions that specify the probability of a discrete outcome, such as a correct response to an item, in terms of person and item parameters. Person parameters may, for example, represent the ability of a student or the strength of a person's attitude. Item parameters include difficulty (location), discrimination (slope or correlation), and pseudoguessing (lower asymptote). Items may be questions that have incorrect and correct responses, statements on questionnaires that allow respondents to indicate level of agreement, or patient symptoms scored present/absent.

Among other things IRT theory provides a basis for evaluating how well assessments work, and how well individual questions on assessments work. In education, Psychometricians apply IRT in order to achieve tasks such as developing and refining exams, maintaining banks of items for exams, and equating for the difficulties of successive versions of exams (for example, to allow comparisons between results over time).

IRT is often referred to as latent trait theory, strong true score theory, or modern mental test theory