The Design Options section for a definitive screening design enables you to specify the blocking structure, the number of blocks, and the number of extra runs. Block effects are orthogonal to the main effects. Block sizes need not be equal.
The section contains the following options:
No Blocks Required
Indicates that the design will not contain a blocking factor. This is the default selection.
Add Blocks with Center Runs to Estimate Quadratic Effects
Adds the number of blocks specified in the Number of Blocks text box. Constructs a design where block effects are orthogonal to main effects and where the model consisting of all main and quadratic effects is estimable. See Add Blocks with Center Runs to Estimate Quadratic Effects
Add Blocks without Extra Center Runs
Adds the number of blocks specified in the Number of Blocks text box. Adds only as many center runs as required by the design structure. Constructs a design where block effects are orthogonal to main effects, but the model consisting of all main effects and quadratic effects might not be estimable. See Add Blocks without Extra Center Runs.
Note: Use the Add Blocks without Extra Center Runs option only if you can assume that not all quadratic effects are important.
Number of Blocks
Indicates the number of blocks to add. The number of blocks that you can add ranges from two to the number of factors.
Number of Extra Runs
Adds non-center runs that enable you to conduct effective model selection. See Extra Runs and Effective Model Selection for DSDs.
Tip: Adding runs to your design with the Extra Runs option enhances your ability to detect effects in the presence of many active effects. The recommended number of Extra Runs is four, which dramatically improves the power of the design to identify active second-order effects.
Make Design
Generates the design, presents it in the Design section, and provides evaluation information in the Design Evaluation section. The Output Options panel also appears, enabling you to create the design table.
This section describes the two blocking options:
• Add Blocks with Center Runs to Estimate Quadratic Effects
• Add Blocks without Extra Center Runs
Note: For more information about the construction and properties of blocked designs that estimate quadratic effects, see Jones and Nachtsheim (2016). The paper also contains information about treating the blocks as random effects.
The Add Blocks with Center Runs to Estimate Quadratic Effects option constructs a design with these properties:
• Block effects are orthogonal to main effects.
• The model consisting of all main and quadratic effects is estimable.
If a design contains only continuous factors, a blocked design for k factors having these properties can be constructed:
• Remove the center run from the DSD design for k factors.
• Assign conference matrix foldover pairs to the same block.
• Add one center run to each block.
When some factors are categorical, the Add Blocks with Center Runs to Estimate Quadratic Effects option adds pairs of center runs within certain blocks. This structure ensures orthogonality and the ability to estimate all main and quadratic effects.
Because the only requirement on block size is that a block contains a foldover pair, the number of blocks can range from 2 to k, if k is even and from 2 to k+1, if k is odd. See Conference Matrices and the Number of Runs. JMP attempts to construct blocks of equal size.
The Add Blocks without Extra Center Runs option constructs a design that has a single center run when all factors are continuous and two center runs when some factors are categorical. The resulting design has these properties:
• Block effects are orthogonal to main effects.
• Block effects might be confounded with a linear combination of quadratic effects. This implies that the model consisting of all main and quadratic effects might not be estimable.
For this reason, use this option only if you can assume that some quadratic effects are negligible.
Construct a blocked design for k factors without extra center runs:
• Assign conference matrix foldover pairs to the same block.
• If all factors are continuous, assign the single center run to a single block.
• If there are categorical factors, the unblocked definitive screening design requires the addition of two center runs to the foldover pairs defined by the conference matrix. See Conference Matrices and the Number of Runs. To construct the blocked design without extra center runs, these two center runs are added to a single block.
Because the only requirement on block size is that a block contains a foldover pair, the number of blocks can range from 2 to k, if k is even and from 2 to k+1, if k is odd. See Conference Matrices and the Number of Runs. JMP attempts to construct blocks of equal size.