Optimal row–column design for three treatments

Parvu, Valentin

doi:10.1016/j.jspi.2006.02.006

Cited by 5 publications

(2 citation statements)

References 17 publications

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“…As pointed out by Morgan and Parvu (2007), finding A-and E-optimal row-column designs with a large number of nonreplicated treatments is mathematically intractable at the current stage. These designs use the minimum number of experimental units A-and E-optimal (M, S)-optimal A-and E-optimal (M, S)-optimal 1 2 3 4 1 2 3 5 1 2 3 4 5 1 2 3 4 6 4 5 6 8 4 5 6 9 5 6 7 8 10 5 6 7 8 11 7 8 9 3 7 8 9 1 9 10 11 12 3 9 10 11 12 1 5 9 1 10 5 9 1 10 6 11 4 1 13 6 11 12 to compare the maximum number of treatments in a rowcolumn layout.…”

Section: Discussionmentioning

confidence: 99%

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Optimal Row–Column Designs in High-Throughput Screening Experiments

2010

Technometrics

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Saturated row-column designs are studied to eliminate row and column effects in primary high-throughput screening experiments. All paired comparisons of treatments in the designs recommended are estimable within each microplate in spite of the existence of row and column effects. The (M, S)-criterion is used to select optimal and eliminate inefficient designs. It turns out that all (M, S)-optimal designs are binary, that is, no treatments appear twice in any row or column. Optimal designs are not unique with respect to design isomorphism. A series of (M, S)-optimal designs is constructed and all paired comparisons of treatments in the constructed designs are estimable regardless of the two-way heterogeneity. An (M, S)-optimal design for 8 × 12 microplates is provided and optimal designs of other dimensions can be constructed systematically.

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Section: Discussionmentioning

confidence: 99%

“…31-32). Morgan and Parvu (2007) solved the A-optimality problem for three treatments. A design whose smallest canonical efficiency factor is at least as large as that of any other design is E-optimal.…”

Section: Introductionmentioning

confidence: 99%