A test-theoretic approach to observed-score equating

Observed-score equating using the marginal distributions of two tests is not necessarily the universally best approach it has been claimed to be. On the other hand, equating using the conditional distributions given the ability level of the examinee is theoretically ideal. Possible ways of dealing with the requirement of known ability are discussed, including such methods as conditional observed-score equating at point estimates or posterior expected conditional equating. The methods are generalized to the problem of observed-score equating with a multivariate ability structure underlying the scores. This article is based on the author's Presidential Address given on July 7, 2000 at the 65th Annual Meeting of the Psychometric Society held at the University of British Columbia, Vancouver, Canada. The author is most indebted to Wim M.M. Tielen for his computational assistance and Cees A.W. Glas for his comments on a draft of this paper.