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A set of methods that addresses the difficulty, reliability, validity, and fairness of test items. It is an improvement on classical test theory, which has the same goals but uses less advanced statistical techniques. The basic tool of item response theory (IRT) is logistic regression, which is a kind of regression designed to study dichotomous outcome variables, such as right or wrong. Logistic regression is used to calculate the odds that test takers will answer a question correctly. The odds for a particular item add up to its item characteristic curve (ICC). Easy and hard items have different curves.

IRT is most commonly applied to educational testing. A good test will be composed of items that differentiate (discriminate) among students. Items that all students get right, ...

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