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 up to eight 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. Lastly, 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.
Bioinformatics | Computational Biology | Design of Experiments and Sample Surveys | Microarrays
Kerr, Kathleen F., "2^k Factorials in Blocks of Size 2, with Application to Two-Color Microarray Experiments" (March 2006). UW Biostatistics Working Paper Series. Working Paper 227.