This summer I have the opportunity to read more closely R. A. Bailey, Design of comparative experiments. Cambridge University Press, 2008. One thing I really like about her approach is its incorporation of linear algebra and probability theory, which is essentially estimation theory. This provides an unambiguous picture of what is going on in an experiment, the assumptions that are in play, and the relevance and meaning of particular statistical tests. Below, I explicate some of the fundamental subspaces of an experiment.