FRIDAY, September 22, 2006
Time: 1:30 PM
Constant Hall 1043

Title: Robustness of Block Designs

John P. Morgan
Department of Statistics
Virginia Tech

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 problems arise leading to loss of units or of entire blocks during the conduct of the experiment. If such loss occurs, will the resulting residual design still be in some sense optimal? Can the original selection of the design be made so as to protect against the negative consequences of loss of material? These questions are the focus of this talk. We develop general concepts including minimum efficiency aberration for evaluating robustness of block designs to such loss, then examine these concepts as applied 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.