Designs for two-colour microarray experiments can be viewed as block designs with two treatments per block. Explicit formulae for the A- and D-criteria are given for the case that the number of blocks is equal to the number of treatments. These show that the A- and D-optimality criteria conflict...

Multitiered experiments are characterized by involving multiple randomizations, in a sense that we make explicit. We compare and contrast six types of multiple randomizations, using a wide range of examples, and discuss their use in designing experiments. We outline a system of describing the...