TWO-FACTOR EXPERIMENTS WITH SPLIT UNITS CONSTRUCTED BY CYCLIC DESIGNS AND SQUARE LATTICE DESIGNS

* We consider nested row-column designs with split units for a two-factor experiment. The most optimal design in this case is that of using for the whole plots a Latin square while for the subplot treatments with a completely randomized design for each whole plot. Such a design, in fact optimal, utilizes many experimental units and quite a large space. Hence to construct new designs of reduced size of the experiment we use a cyclic design for the whole plot treatments and a square lattice design for the subplot treatments. The proposed designs are generally balanced and they allow for giving the stratum efficiency factors, especially useful to design of experiments. Key-Words: * cyclic design; general balance; square lattice design; stratum efficiency factor. AMS Subject Classification: * 62K15, 62K10, 05B05.