This paper shows that microarray experiments are split-plot, or split-unit, designs. The larger size experimental unit (the whole plot) is the array, and the treatment applied to this unit is the treatment given to the cells which produce the cDNA that is hybridized to the array. The smaller size experimental unit (the subplot) is the spot on the array, and the treatment applied to this unit is the gene giving rise to the DNA or oligonucleotide attached at that spot. Various treatment and design structures can be applied to the whole plot and the subplot; we consider the model equations appropriate to different designs. Preliminary normalization of the data can be avoided by including appropriate blocking terms in the model equation. We show how conventional analysis of variance can be used to test for significant differences in expression, and consider multiplicity corrections and graphical methods for identifying important expression differences.