Optimal nested row-column designs for blocks of size 2×2 under dependence

Abstract.

This paper examines nested 2 ×2 row-column designs when within-block observations are assumed to be dependent. The model considered has fixed block effects, which may also include row and/or column effects. Optimal binary and non-binary designs, constructed from semi-balanced arrays, are given under both generalised and ordinary least squares estimation. It is shown that binary designs are optimal when dependence is low. In general, however, the optimal designs are highly specific to the correlation values.