Optimal Allocation for Comparing k Test Treatments to Positive and Negative Control with Unequal Weighting Under A-optimality and MV-optimality

Experiments in real life often involve comparisons of test treatments to more than one control. However, the controls may not always be of equal importance. In this paper we introduce weighted MV optimality criterion and present a detailed study using both weighted A and MV optimality criteria, of the problem of optimally comparing a set of test treatments to two controls (positive and a negative) that are of unequal importance to the experimenter.