Listy Biometryczne-Biometrical Letters Vol.36(2), 1999, pp.85-126

A design is said to have nested blocks if the set of experimental units (plots) is partitioned into blocks and each block is further partitioned into subblocks. A review is given of estimators and their variances when information is combined from the plots stratum and the subblocks stratum. The relative size of these two stratum variances is usually unknown but a plausible range may be suggested by previous experiments. A method of comparing designs is proposed and is illustrated for several examples. It is shown that a design may be optimal for the intrablock analysis when subblocks are ignored, and also optimal for the intra-subblock analysis when blocks are ignored, without being optimal for the combination of information. Nevertheless, some theorems are proved showing that certain designs are optimal over certain classes of design when information is combined and the subblocks stratum variance is at least as big as the plots stratum variance. Heuristic strategies are proposed for finding good designs in other situations.

Combining information, nested balanced block design, nested blocks, nested regular graph design, optimal design
^*Dedicated to Professor Tadeusz Caliński on his 70-th birthday