Moving the cut score on Rasch scored tests

Empirically based item selection guidelines are presented for moving the cut score on equated tests consisting of n dichotomous items calibrated assuming the Rasch model. The cut score on a test form B, c(B), may be made higher than test form A's cut score, c(A), in the following ways: (1) select items for test form B such that the variance of test form B's item difficulties, sigma(2)(B), will be equal to test form A's sigma(2)(A), but test form B's mean item difficulty, mu(B), will be less that of test form A, mu(A); (2) given c(A) > n/2, select items for test form B such that mu(B) s(2)(A). To make c(B) lower than c(A), the direction of the changes listed above for the two tests item difficulties sigma(2) and mu should be reversed. Derivations of lemmas that underlie the guidelines are provided as well as a simulated example.