A powerful alternative to Williams' test with application to toxicologicaldose-response relationships of normally distributed data

The comparison of increasing doses of a treatment to a negative control is frequently part of toxicological studies. For normally distributed data Wil liams (1971, 1972) introduced a maximum likelihood test under total order r estriction. But until now there seems to have been no solution for the arbi trary unbalanced case. According to the idea proposed by Robertson et al. ( 1988) we will apply in this article the basic concept of Williams on the cl ass of multiple contrast tests for the general unbalanced parametric set-up . Simulation results for size and power and two examples for estimating the minimal toxic dose (MTD) are given.