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Title: Kronecker-type products useful in constructions of non-orthogonal split-plot x split-block designs Authors:  Iwona Mejza - Poznan University of Life Sciences (Poland) [presenting]
Katarzyna Ambrozy-Deregowska - Poznan University of Life Sciences (Poland)
Abstract: The split-plot x split-block design is a known design in field experimentation that is often used to carry out three-factor experiments. It is called a mixed SPSB design, and in the complete (orthogonal) version it is a combination of split-plot and split-block orthogonal designs. Often, however, due among other things to limitations of the experimental material, experiments are planned in incomplete (non-orthogonal) designs. To obtain an incomplete SPSB design with optimal efficiency for selected contrast groups, different construction methods and other experimental designs, so-called generating designs with known statistical properties, belonging to the class of block designs, are used. The incompleteness of a generated design planned in advance may relate to one factor, two factors or all three. To compare methods, an ordinary Kronecker product and a semi-Kronecker (Khatri-Rao) product were used in construction procedures. With both methods, some generated SPSB designs were obtained where the levels of each factor were allocated to a balanced square lattice design. A comparison of the methods of constructing designs, with respect to stratum efficiency factors for some contrasts of treatment parameters and with respect to the size of an experiment, is given.