Optimality of block designs used in one way elimination of heterogeneity

Abstract

Block designs are usually used in experiments where it is important to eliminate heterogeneity at least in one direction. From the class of designs it is desired to choose a design which will estimate the elementary treatment contrasts with maximum precision.

The optimality criteria are based on the dispersion matrix of all possible elementary contrasts. The A-optimality criterion based on the information matrix was derived.

Usually for comparing test treatments with a control RBD is used with the control treatment replicated in all blocks. The same objective could be achieved by using Balanced Treatment Incomplete Block Designs (BTIBD). BTIBD was found to be more efficient than RBD with the control treatment replicated in all blocks. Optimalities of BTIBD were also examined.

When a BTIBD was augumented with certain number of blocks, such that the augmented blocks contains only the test treatments the resulting design was found to be E-optimal.