JSM 2004 - Toronto

Abstract #301637

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Activity Number: 407
Type: Contributed
Date/Time: Thursday, August 12, 2004 : 8:30 AM to 10:20 AM
Sponsor: General Methodology
Abstract - #301637
Title: Optimal Incomplete Designs with Two Blocks
Author(s): Bo Jin*+ and John P. Morgan
Companies: Virginia Polytechnic Institute and State University and Virginia Polytechnic Institute and State University
Address: 1801 Grayland St., Blacksburg, VA, 24060,
Keywords: incomplete block designs ; A-optimality ; D-optimality ; E-optimality ; binary designs ; nonbinary designs
Abstract:

Suppose there are v treatments to compare using n experimental units. The units are partitioned into b blocks of k units each. A block design is an assignment of the v treatments to the bk units. Denote the class of all possible such assignments as D(v,b,k). We investigate the optimal incomplete block designs when there are two blocks using A-, D- and E- criteria. Binary designs of a certain pattern are shown to be A- and D-optimal in D(v,2,k). However, binary designs are not always E-optimal in D(v,2,k). In fact, E-optimality of binary designs depends on the magnitude of the ratio k/v. Among other results, it is found that in a restricted class, binary designs are E-optimal if 1/2< k/v< 5/6; certain nonbinary designs are E-optimal if 5/6< k/v< 1; both the binary designs and the nonbinary designs are E-optiaml if k/v=5/6.

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