Properties of superimposed BIBDs

✍ Scribed by J.P. Morgan

• Book ID: 104340653
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 121 KB
• Volume: 73
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(98)00056-1

✦ Synopsis

Superimposed designs in the sense to be considered in this paper arise in the following manner. First, a balanced incomplete block design is implemented to compare a set of treatments T 1. At some later time, it is desired to compare a second set of treatments T2 using the same experimental units. If the e ects of the treatments T1 are thought to still be present, either in a direct fashion as part of an on-going experiment, or as residual e ects of a prior experiment, then they e ectively become another blocking factor to be accounted for in the estimation of contrasts for T 2. What then is the optimal assignment for the set T2 to the units? Among the results proven here are (i) a BIBD for T2 that achieves bottom-stratum orthogonality with respect to T1 is optimal for the usual analysis, and (ii) most of the known BIBDs that achieve this orthogonality are also optimal for the analysis with recovery of interblock information, even if not achieving block-stratum orthogonality, provided the number of replicates is not too large.