A comparison of two observed-score equating methods that assume equally reliable, congeneric tests

Abstract

For the external-anchor test equating model, two observed-score methods are derived using the slope and intercept assumptions of univariate selection theory and the assumptions that the tests to be equated are congeneric and equally reliable. The first derivation, Method 1, is then shown to give the same set of equations as Levine’s equations for random groups and unequally reliable tests and the "Z predicting X and Y" method. The second derivation, Method 2, is shown to give the same equations as Potthoff’s (1966) Method B and the "X and Y predicting Z" method. Methods 1 and 2 are compared empirically with Tucker’s and Levine’s equations for equally reliable tests; the conditions for which they may be appropriately applied are discussed. Index terms: Angoff’s Design V equations, congeneric tests, equally reliable tests, Levine’s equations (equally reliable), linear equating, observed-score equating, test equating, Tucker’s equations.