Efficient 2 k Factorial Designs for Blocks of Size 2 with Microarray Applications

When a two-level design must be run in blocks of size two, there is a unique blocking scheme that enables estimation of all the main effects. Unfortunately, this design does not enable estimation of any two-factor interactions. When the experimental goal is to estimate all main effects and two-factor interactions, it is necessary to combine replicates of the experiment that use different blocking schemes. In this paper, we identify such designs for k ≤ 8 factors that enable estimation of all main effects and two-factor interactions with the fewest number of replications. In addition, we give a construction for general k that gives more economical designs than previously published. Last, we consider issues particular to the design of two-color microarray experiments. For example, we propose a methodology to ensure dye balance in these experiments without increasing the number of replications.