Item response theory (IRT)

Item response theory (IRT) is a family of models describing how a person's level on a latent trait relates to how they answer each item. Unlike classical test theory, which focuses on the total test score, IRT estimates properties of every item — such as its difficulty (where on the trait scale it's most informative) and its discrimination (how sharply it separates people) — and places items and people on the same underlying scale.

Because it models each item separately, IRT enables things classical methods can't do easily: computer-adaptive testing (choosing the next item based on prior answers), equating scores across different item sets, and measurement precision that varies along the trait continuum rather than assuming one reliability for everyone. It underpins many large-scale educational and clinical assessments.