SYSTEMATIC ROW-AND-COLUMN DESIGNS BALANCED FOR LOW-ORDER POLYNOMIAL INTERACTIONS BETWEEN ROWS AND COLUMNS

Systematic row-and-column designs intended to accommodate low order po lynomial rows x columns interaction effects are discussed. Latin squar e, Graeco-Latin square and quasi-Latin square designs of size 2N x 2M and size 9 x 9 are examined by using plot pseudofactor methods. Latin square and Graeco-Latin square designs of size 5 x 5 and 7 x 7 are exa mined by using a published technique for the design of quantitative fa ctorial experiments with a prime number of factor levels. A 6 x 6 Lati n square design is constructed by trial and error. Finally, the contro l of positional effects by fitted quadratic response surfaces is discu ssed.