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 experilJlent that use different blocking schemes. This research was motivated by the problem of designing experiments for two-color microarrays, which are an impo,rtant tool in modern molecular biology. Microarrays are used to quantify levels of gene transcription, which can loosely be considered the 'level of activity' of a gene. Microarrays can make these measurements for thousands of genes at a time. Two-color microarrays are small slides containing thousands of spots. Each spot contains single-stranded DNA molecules corresponding to a particular gene in the I genome of an organism under study.
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