MANE 6313¶
Week 14, Module F¶
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¶
Apply Sequential Analysis for CCD
Sequential Analysis in rsm()¶
- Package rsm() provides capabilities of adding center points and/or star points to factorial analysis
- Consider example for Dean, Voss and Draguljic[^1]
Initial Design¶
- The initial design is a single replicate of a \(2^4\) factorial with no center points
Initial Design with Response¶
First Model¶
- Only coefficient information is shown
- Model can not be further refined
Star Points¶
- One centerpoint and the axial points are added
- Since \(\alpha=\sqrt(2)\), the value must inputted manually
Augmented Design with Response¶
Model 2¶
Model 3¶
- \(\alpha=0.05\) used to determine if a terms should be kept in the model
Partial F-test¶
Model 3 Discussion¶
- Partial F-test indicates all terms removed for model 2 when model 3 was created all are statistically not significant
- Bad design because lack of fit test is not available (see below)
- Adding two or more centerpoints would allow Lack of Fit test to be performed (at least 2 replicated values required)
-
Remaining analysis should be performed:
- Residual analysis
- Graphical analysis
- Stationary point analysis
[^1]: Dean, Voss and Draguljic (2017). Design and Analysis of Experiments, 2nd Edition. Springer Press.