On Attempting to Do What Lord Said Was Impossible: Commentary on van der Linden's “Some Conceptual Issues in Observed‐Score Equating”

Abstract

van der Linden (this issue) uses words differently than Holland and Dorans. This difference in language usage is a source of some confusion in van der Linden's critique of what he calls equipercentile equating. I address these differences in language. van der Linden maintains that there are only two requirements for score equating. I maintain that the requirements he discards have practical utility and are testable. The score equity requirement proposed by Lord suggests that observed score equating was either unnecessary or impossible. Strong equity serves as the fulcrum for van der Linden's thesis. His proposed solution to the equity problem takes inequitable measures and aligns conditional error score distributions, resulting in a family of linking functions, one for each level of θ. In reality, θ is never known. Use of an anchor test as a proxy poses many practical problems, including defensibility.