Comparison of IRT True-Score and

Two methods of ’equating ’ tests are compared, one using true scores, the other using equipercentile equat-ing of observed scores. The theory of equating is dis-cussed. For the data studied, the two methods yield almost indistinguishable results. Most item response theory (IRT) equating is currently attempted by the true-score equating procedure described in Lord (1980, chap. 13). Lord also described an IRT equipercentile observed-score procedure, which until now seems to have been little used in operational work, perhaps because it is more complicated and more expensive than the true-score procedure. This paper discusses theoretical considerations and reports an empirical research study comparing the results of applying these two procedures to real test data. Note that IRT plays only a subsidiary role in observed-score equipercentile equating; similar results could be expected for conventional equipercentile equating, assuming that the IRT model holds. Kolen (1981) found the equipercentile observed-score IRT procedure to be one of the better of nine procedures compared in his empirical research study. However, his criterion was stability in cross-validation. Although stability is certainly desirable, stability is not a proper criterion for choosing the best equating method: Incorrect equating procedures may yield more stable results than correct procedures. Sections 1 and 2 outline the true-score procedure and the observed-score equipercentile procedure, respectively. Section 3 discusses the theoretical advantages and disadvantages of each procedure. Section 4 describes the real test data used to provide a comparison of the two methods. Section 5 describes the procedures used for estimating item and ability parameters. Section 6 reports and summarizes the empirical results. IRT models the probability of a correct response by an examinee to a test item as a monotonically increasing function of ability. The model used here is the three-parameter logistic model given by where Pi(O,) is the probability of examinee a answering item correctly, bi is the difficulty of item i, 9 ai is the discrimination index for item