Faced with cost, time, or other pressures to keep an experiment
small, blocking can be an effective tool for increasing precision of
treatment comparisons. The simplest implementation of blocking is a
division of experimental units into two equi-sized subsets,
allocating one degree of freedom to explain unit heterogeneity.
Small experiments will have block size $k$ smaller than the number
of treatments $v$ being compared. This talk attacks the problem of
optimal allocation of treatments to two small, equi-sized blocks.
Solutions depend on the optimality criterion employed as well as the
ratio $\frac{k}{v}$.
This work evolved in response to a design request from an engineer
working with vehicle traction on sandy surfaces. The talk begins
with a discussion of that experiment and the evolution of its
design. We will touch on practical issues such as unrealistic
expectations, the destructive effects of sloppy experimental
procedure, and the gap between textbook design and the engineer's
needs.
Meet the speaker in Room 212 Cockins Hall at 4:30
p.m. Refreshments will be served.
