1 / 7

Factorial Designs

Factorial Designs. 40. 12. Effect of A: 1 Effect of B: -9. B -. ←Factor B→. Response. B +. B +. B -. 20. 50. ←Factor A→. ←Factor A→. 30. 52. Effect of A: 21 Effect of B: 11. ←Factor B→. B +. Response. B +. B -. Factorial Design – all possible combinations

Download Presentation

Factorial Designs

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Factorial Designs

  2. 40 12 Effect of A: 1 Effect of B: -9 B- ←Factor B→ Response B+ B+ B- 20 50 ←Factor A→ ←Factor A→ 30 52 Effect of A: 21 Effect of B: 11 ←Factor B→ B+ Response B+ B- • 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- 20 40 ←Factor A→ ←Factor A→

  3. More Efficient – compared to 1-factor testing • More Informative – includes interactions

  4. 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. • SST=SSA+SSB+SSAB+SSE • 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 σ2 and the relevant effect • The last value, MSE, is all σ2. • 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 ‘Fo’ that should be less than 0.05 if we wish to consider the effect significant.

  5. 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. Three way (& more) interactions are possible, but unusual • Response surface can be more complex if more complex interactions are present.

  7. Graphical Representations of the Model Response Surface Contour Plot

More Related