What Is Actually Equated in “Test Equating”? A Didactic Note

The current literature on test equating generally defines it as the process necessary to obtain score comparability between different test forms. The definition is in contrast with Lord’s foundational paper which viewed equating as the process required to obtain comparability of measurement scale between forms. The distinction between the notions of scale and score is not trivial. The difference is explained by connecting these notions with standard statistical concepts as probability experiment, sample space, and random variable. The probability experiment underlying equating test forms with random scores immediately gives us the equating transformation as a function mapping the scale of one form into the other and thus supports the point of view taken by Lord. However, both Lord’s view and the current literature appear to rely on the idea of an experiment with random examinees which implies a different notion of test scores. It is shown how an explicit choice between the two experiments is not just important for our theoretical understanding of key notions in test equating but also has important practical consequences.