Test Equating by Common Items and Common Subjects: Concepts and Applications

Since the invention of z-scores (standardized scores), comparison among different tests has been widely conducted by test developers, instructors, educational researchers, and psychometricians. Equating, calibration, and moderation are terms used to describe broad levels of possible comparison among educational assessments (Dorans, 2004; Feuer, Holland, Green, Bertenthal, & Hemphill, 1999; Linn, 1993; Mislevy, 1992). Equating is at one end of the linking continuum, involving the most stringent requirements of equivalence among the assessments and examinee populations to be linked, and compares tests that measure the same construct and have been designed to be equivalent. Less equivalent conditions involve calibration, which compares tests that measure the same construct but vary in design or difficulty, and moderation, which compares tests that measure different constructs. Psychometric approaches to linking assessments include linear equating, equipercentile equating, and item response theory (IRT). This article is a practical guide to conducting IRT test equating in two different scenarios: