Systematic Row-And-Column Designs Balanced for Low Order Polynomial Interactions between Rows and Columns

SUMMARY Systematic row-and-column designs intended to accommodate low order polynomial rows × columns interaction effects are discussed. Latin square, Graeco-Latin square and quasi-Latin square designs of size 2N × 2M and size 9 × 9 are examined by using plot pseudofactor methods. Latin square and Graeco-Latin square designs of size 5 × 5 and 7 × 7 are examined by using a published technique for the design of quantitative factorial experiments with a prime number of factor levels. A 6 × 6 Latin square design is constructed by trial and error. Finally, the control of positional effects by fitted quadratic response surfaces is discussed.