Home / DOE / Additional Information / Screening vs. Modeling
Screening vs. Modeling¶
The Create Design menu is divided by headings, and two of them are Modeling and Screening. This page says what the designs in each group can and cannot estimate, so the grouping in the menu reads as more than a label.
The menu¶
| Heading | Designs under it |
|---|---|
| Modeling | Create 2-Level Factorial Design, Create 3-Level Factorial Design, Create N-Level Factorial Design, Create CCD Design, Create Box-Behnken Design |
| Screening | Create Plackett-Burman Design, Create Taguchi Design |
| Special | Setup Historical Analysis, Create Custom Design, Create D-Optimal Design |
| Import | Import From DOE PRO XL |
What the screening designs estimate¶
A Plackett-Burman design holds up to one fewer factors than it has runs. Filled to that capacity it has nothing left for interactions: a 12-run design with 11 factors has 12 rows and 12 coefficients to estimate including the constant, so no degrees of freedom remain.
How much a design like that gives up is not reported. Quantum XL computes aliasing information for two-level factorial designs and for the two-level Taguchi arrays (L4, L8, L12, L16 and L32) only. A Plackett-Burman design gets no alias table, no defining relation and no resolution line at all, and neither do Box-Behnken, CCD, N-level factorial, custom and D-Optimal designs, or the three-level Taguchi arrays.
A Taguchi array does not behave in one fixed way either. Each array has a capacity, L4 up to 3 factors, L8 up to 7, L12 up to 11, L16 up to 15, L32 up to 31, and the builder accepts anything from two factors upward. Three factors in an L8 is a full factorial in 8 runs with every interaction estimable; seven factors in the same array is saturated. How much aliasing you get depends on how many of the array's columns you use.
Overspending the degrees of freedom is a question, not a refusal. The interaction editor shows Degrees of freedom remaining: n as you work, and if you leave the page with more used than the design has it asks Degrees of freedom are less than zero. Would you like to go back and remove some interactions? Answering Yes returns you to the page; answering No lets the model through as it stands.
What the modeling designs estimate¶
| Design | Interactions | Quadratic terms |
|---|---|---|
| 2-level factorial, full | all of them | none in the model the design builds, since two settings per factor cannot describe a curve. Add center points and a quadratic becomes available, because the factor then has three distinct settings |
| 2-level factorial, fractional | those the resolution allows, and the dialog reports the resolution before you commit | the same: none by default, available once center points give a third setting |
| 3-level and N-level factorial | all of them | yes, for every quantitative factor with three or more levels |
| CCD | those the base design's resolution allows | yes, from the axial points |
| Box-Behnken | those the design supports | yes, from the three levels |
The resolution reported on the two-level and CCD selection pages is the precise statement of what is aliased with what. The dialog writes it as Resolution: numeral. description, and the descriptions are these:
| Resolution | The dialog's own description |
|---|---|
| Full | There is no aliasing. |
| III | Main effects are aliased with two-ways. |
| IV | Main effects are aliased with three-ways, and two-ways are aliased with two-ways. |
| V | Main effects are aliased with four-ways, and two-ways are aliased with three-ways. |
| VI | Main effects are aliased with five-ways, and two-ways are aliased with four-ways. |
| VII | Main effects are aliased with six-ways, and two-ways are aliased with five-ways. |
| VIII | Main effects are aliased with seven-ways, and two-ways are aliased with six-ways. |
A full factorial reports Full where the numeral would go, because nothing is aliased. The two-level grid produces Full and III to VIII and nothing else: a resolution II string exists in the software but no cell in the grid can reach it.
From resolution IV upward the description has a second clause, about the two-way interactions. At IV they are aliased with each other; at V and above they are not.
Where to see the aliasing in your own design¶
It is all on the design sheet. Below the run data, under the heading Aliasing information, are the resolution, the blocked resolution if the design is blocked, the defining relation under Identity, and the Alias Table. On a blocked design the block lines are the first lines of that same alias table, not a separate table. See Blocking.
The design sheet also carries the design's description, including the fraction, the factor count and the run count.
The regression sheet has no alias table. With the DOE Advisor on it can carry a line pointing back at the design sheet's table, in one of two forms:
- This design is resolution n; click here to go to the aliasing table. when the design's own resolution is II, III or IV.
- This design has blocked resolution n; click here to go to the aliasing table. when the blocked resolution is in that range instead. This one comes from the blocking confound rather than from the design's own resolution.
Neither line appears on a Taguchi or Plackett-Burman design, even on a saturated L8, which is resolution III and does have a real alias table on its design sheet. The advisor treats both as screening designs and skips its aliasing check for them entirely. Neither line appears on an uncoded regression either. Aliasing otherwise shows up on the regression sheet only inside a term's coded name, as A=BC. The design class also decides which other checks the advisor runs: see The DOE Advisor.