Abstract
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 T 2 using the same experimental units. If the effects of the treatments T 1 are thought to still be present, either in a direct fashion as part of an on-going experiment, or as residual effects of a prior experiment, then they effectively 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 T 2 to the units? Among the results proven here are (i) a BIBD for T 2 that achieves bottom-stratum orthogonality with respect to T 1 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.
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