Design of a Central Composite (Response Surface) Experiment - Design Characteristics Tab
Select the Design characteristics tab of the Design of a Central Composite (Response Surface) Experiment dialog box to access options to determine which axial distance will be used in the design, and whether or not (and how many) center points will be added (for additional details, see also Box and Draper, 1987). The concepts of design orthogonality and rotatability are explained in the Introductory Overview. Note that regardless of which option is selected here, the Alpha values and number of points shown in the Summary box (displayed at the top of the Design of a Central Composite (Response Surface) Experiment dialog box) always pertain to the standard design; however, the selection affects the final design that is displayed via the Summary: Display design option on the Quick and Display design tabs and the Correlation matrix of main effects and interactions option on the Generators & aliases tab.
- Compute/use alpha for rotatability
- When the Compute/use alpha for rotatability option button is selected, the axial distance Alpha will be computed as:
a = (nc)1/4
where nc refers to the number of points in the cube portion of the design. Thus, the axial distance in this case does not depend on the number of center points in the design.
- Compute/use alpha for orthogonality
- When the Compute/use alpha for orthogonality option button is selected, and the design is not blocked, then Statistica computes the axial distance Alpha as:
a = [{(nc + ns + n0)1/2 - nc1/2 }2 * nc/4]1/4
where nc, ns, and n0 refer to the number of cube points, star points, and center points, respectively. When the design is blocked (k blocks), then Statistica computes Alpha for orthogonal blocking as:
a = {k*(1+ns0/ns)/(1+nc0/nc)}1/2
where ns0 and nc0 refer to the number of center points in the star and cube portions of the design, respectively.
Thus, when you select the Compute/use alpha for orthogonality option, then the axial distance Alpha depends on the number of center points in the design.
- Face centered star points (e.g., ±1).
- , ±1). Select the Face centered star points option button to set the star-point values as equal to the respective factor minima and maxima.
- Add center points (for orthogonality & rotatability)
- Select the Add center points (for orthogonality & rotatability) option button to add center points to the design to achieve (approximate) orthogonality and rotatability. Specifically, Statistica adds to the design center points so that the total number of center points is equal to:
n0 4*nc1/2 + 4 - 2k
(See Khuri and Cornell, 1987.) Note that in this case the value in the center points field (in the Add to the design group box on the Add to design tab) will be ignored. Note that the Add center points (for orthogonality & rotatability) option button is only available if the current design is not blocked.