1. 1.Basic Principles & Definitions 2.The Advantage 3.Two-Factorial Design 4.Number of Replicates 5.General Factorial Design 6.Response Surfaces & Contour Plots Factorial Designs

2. 1.Basic Principles & Definitions 2.The Advantage 3.Two-Factorial Design 4.Number of Replicates 5.General Factorial Design 6.Response Surfaces & Contour Plots Factorial Design – all possible combinations Main Effect – Difference of average response Interaction –Effect of one factor depends on the level of the other factor –Regression model –Introduce curvature into response surfaces & contour plot –Interactions can mask main effects B-B- B-B- B+B+ B+B+ Effect of A: 21 Effect of B: 11 30 4020 52 ←Factor A→ ←Factor B→ ←Factor A→ Response B-B- B-B- B+B+ B+B+ Effect of A: 1 Effect of B: -9 40 5020 12 ←Factor A→ ←Factor B→ ←Factor A→ Response

3. 1.Basic Principles & Definitions 2.The Advantage 3.Two-Factorial Design 4.Number of Replicates 5.General Factorial Design 6.Response Surfaces & Contour Plots More Efficient – compared to 1- factor testing More Informative – includes interactions

4. 1.Basic Principles & Definitions 2.The Advantage 3.Two-Factorial Design 4.Number of Replicates 5.General Factorial Design 6.Response Surfaces & Contour Plots In general, a levels of factor A, b levels of factor B and n replicates requires abn tests. Effects model () has terms for: –Effect of A –Effect of B –Effect of A-B Interaction –Error 2 Factor ANOVA to establish significance of each term. –SS T =SS A +SS B +SS AB +SS E –Each SS divided by it’s degree of freedom is a mean square (MS) Expected value of each of the first 4 MS values is the sum of σ 2 and the relevant effect The last value, MSE, is all σ 2. If the relevant effect is significant, then the ratio of MS:MSE > 1 –Ratios of MS distributed as ‘F’ if everything is noise. If the ratio is improbable then all is not noise. So the ANOVA output contains a ‘P-Value’ for ‘F o ’ that should be less than 0.05 if we wish to consider the effect significant.

5. 1.Basic Principles & Definitions 2.The Advantage 3.Two-Factorial Design 4.Number of Replicates 5.General Factorial Design 6.Response Surfaces & Contour Plots If the model should have terms for A, B, and AB, then n >= 2. n also improves resolution (the difference in means can still be determined even if they are close together)

6. 1.Basic Principles & Definitions 2.The Advantage 3.Two-Factorial Design 4.Number of Replicates 5.General Factorial Design 6.Response Surfaces & Contour Plots Three way (& more) interactions are possible, but unusual Response surface can be more complex if more complex interactions are present.

7. 1.Basic Principles & Definitions 2.The Advantage 3.Two-Factorial Design 4.Number of Replicates 5.General Factorial Design 6.Response Surfaces & Contour Plots Graphical Representations of the Model Response Surface Contour Plot