J.P. Morgan
Department Statistics
Virginia Tech
Robustness Considerations for Block Designs
In designing an experiment where treatments are to be compared and
experimental units are to be blocked, one usually picks from among a large
catalog of optimal block designs (see,
e.g., www.designtheory.org).
Standard optimality theory does not, however, address the consequences
should experimental problems arise leading to loss of units or of entire
blocks. If such loss occurs, will the resulting "residual" design still be
in some sense optimal? Stated another way, can the original selection of
the design be made so as to protect against the negative consequences of
loss of material? These and related questions are the focus of this talk.
We develop general concepts, including minimum efficiency aberration, for
evaluating robustness of block designs to loss of experimental material.
These concepts are examined through application to the balanced incomplete
block designs (BIBDs).
Intense combinatorial study of BIBDs since the time of Fisher and Yates
has led to a great many designs with the same numbers of treatments, blocks,
and block size. While the basic analysis does not differentiate among
different BIBDs with the same parameters, they do differ in their capacity
to withstand loss of experimental material. Competing BIBDs are compared
for their robustness in terms of average loss and worst loss. A table of
most robust BIBDs is compiled. Minimum efficiency aberration for BIBDs
sometimes translates as minimum intersection aberration.
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