Computer-based tests (CBTs) often use random ordering of items in order to minimize item exposure and reduce the potential for answer copying. Little research has been done, however, to examine item position effects for these tests. In this study, different versions of a Rasch model and different response time models were examined and applied to data from a CBT administration of a medical licensure examination. The models specifically were used to investigate whether item position affected item difficulty and item intensity estimates. Results indicated that the position effect was negligible.