MANE 6313
Week 11, Module E
Student Learning Outcome
- Select an appropriate experimental design with one or more factors,
- Select an appropriate model with one or more factors,
- Evaluate statistical analyses of experimental designs,
- Assess the model adequacy of any experimental design, and
- Interpret model results.
Module Learning Outcome
Describe sequential analysis and fold over on a factor.
Fold-over on a Factor
- To separate an interesting effect, e.g. C, go to the approppriate column in the design matrix and change the sign for all rows in that column
- Folding over on a factor will result in a combined design that:
- Main effect of factor will not be aliased with other two-factor interactions,
- In general, all two-factor interactions involving the factor used for the fold-over will not be aliased with other two-factor interactions
Example Problem
- Taken from Devore, Change and Sutherland
- \(2^{7-4}\) resolution III design
- Generators are 4=12, 5=13, 6=23 and 7=123 (DCS uses numbers instead of letters)
Example Problem - Design Matrix
Design using R
R Design Details
R: Response Variable
Half-normal Plot
Fold-over on A
- Change the sign for all rows of design column matrix for variable A; run another fraction
Fold-Over on A in R
Aliasing Information from Design
Half-Normal Plot for Fold-over
Interpretation of Half Normal Plot
- All main effects are not aliased with other main effects or two factor interactions (A, C, D)
- From aliasing scheme for AG, BF and/or CD and/or EH (with or without AG being large)
- From aliasing scheme for AD, -BE and/or -CF and/or -FH (with or withont AD being large)
- From aliasing scheme for AB, CH and/or -DE and/or FG (with or without AB being large)
- From aliasing scheme for AE, -BD and/or CG and/or FH (with or without AE being large)
Initial Model
Aliasing in Folded Model
