Systematic Row-And-Column Designs Balanced for Low Order Polynomial Interactions between Rows and Columns
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1993 · Volume 55 · Issue 3
DOI: 10.1111/j.2517-6161.1993.tb01935.x
Abstract
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× 2Mand 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.
Keywords
polynomial trend effects, quadratic response surfaces, row-and-column designs, systematic designs
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