The accuracy of a new diagnostic test is often determined by comparison with a reference test which also has unknown error rates. Maximum likelihood estimation of the error rates of both tests is possible if they are simultaneously applied to two populations with different disease prevalences. The estimation procedure assumes that the two tests are independent, conditional on a subject's true diagnostic status. If the tests are conditionally dependent, error rates for both tests can be substantially underestimated. Estimators for the prevalence rates in the two populations can be positively or negatively biased, depending on the relative magnitude of the two conditional covariances and the value of the prevalence parameter.