Experimental Design for Two-Color Microarrays Applied in a Pre-Existing Split-Plot Experiment

Microarray applications for the study of gene expression are becoming accessible for researchers in more and more systems. Applications from field or laboratory experiments are often complicated by the need to superimpose sample pairing for two-color arrays on experimental designs that may already be complex. For example, split-plot designs are commonly used in biological systems where experiments involve two types of treatments that are not readily applied at the same scale. We demonstrate how effects that are confounded with arrays can still be estimated when there is sufficient replication. To illustrate, we evaluate three methods of sample pairing superimposed on a split-plot design with two treatments, deriving the variance associated with parameter estimates for each. Design A has levels of the whole plot treatment paired on the same microarray within a level of the subplot treatment. Design B has crossed levels paired on the same microarray. Design C has levels of the treatment applied to subplots paired on the same microarray within a whole plot. Designs A and B have lower variance than design C for comparing the levels of the whole plot treatment. Designs B and C have lower variance for comparing the levels of the subplot treatment and design C has lower variance for comparing the levels of the subplot treatment within each level of the whole plot treatment. We provide SAS code for the analyses of variance discussed.