Q:

geometric methods in the design of experiments

In the preface to Coxeter's well-known Introduction to Geometry, he writes

"Geometry is useful not only in algebra, analysis, and cosmology, but
  also in kinematics and crystallography (where it is associated with
  the theory of groups), in statistics (where finite geometries help in
  the design of experiments), and even in botany." (Emphasis mine.)

This is dated 1961. I took an experimental design course using the Box, Hunter, Hunter text, but cannot imagine the connection Coxeter has in mind. My Google searches don't reveal much. I was hoping for any clarification or references.

A:

The following book:  Combinatorics of Experimental Design by Anne Penfold Street & Deborah J. Street is a book-length answer to your question. 
In short, some block designs can be interpreted as finite geometries. I am not sure how helpful this is in practice, since that particular point of view is limited and cannot give very many block designs.  (coming back and extending with some examples).

