Design of an Experiment with Two- and Three-Level Factors - Generators and Aliases Tab

Aliases of Interactions: Design Generators

Designs for Factors at 2 and 3 Levels

Select the Generators & aliases tab of the Design of an Experiment with Two- and Three-Level Factors dialog to access information about correlations between main effect vectors and 2-way interaction vectors.

Correlation matrix (main effects and interactions)

In fractional factorial designs, higher-order interactions are "sacrificed" in order to accommodate additional factors (main effects). Click the Correlation matrix (main effects and interactions) button to view the correlation matrix for the design matrix, and thus to determine the confounding of main effects and interactions; two spreadsheet will be displayed. The issue of confounding in 2(k-p), 3(k-p), and fractional factorial designs with factors at 2 and 3 levels is explained in the Introductory Overview.

Correlations of effects

The first spreadsheet contains the correlations for the effects and the interactions.

Main effects

Because the main effects for 3-level factors have two degrees of freedom, there are two columns and rows for each main effect for those factors. When there are three levels for a factor, you can test for the linear main effect and the quadratic (non-linear) main effect (see Introductory Overview). Specifically, for computing this matrix, the main effects are coded:

Codes
Factor Setting	Linear Effect	Quadratic Effect
Low	-1	-1
Center	0	2
High	1	-1

Interaction effects

To compute the correlations for the interaction effects, Statistica will create new (added to the design) variables as the product of the main effects. By default, only the linear by (times) linear interactions will be computed.

Include interactions by quadratic components

If the Include interactions by quadratic components check box is selected, Statistica will also compute the interactions by the quadratic components (for the 3-level factors). When computing the correlation matrix, for each two-way interaction involving a 3-level factor, the appropriate number of new (added to the design) variables are created: (1) the product of the linear by (times) linear main effects, (2) the product of the linear by quadratic main effect, (3) the product of the quadratic by linear main effect, and (4) the product of the quadratic by quadratic main effect.

Unconfounded effects

The second spreadsheet displays the list of unconfounded effects. This spreadsheet is constructed by searching through the correlation matrix of effects described above: For each main effect and interaction in the correlation matrix of effects, Statistica will search through all columns representing the other main effects and interactions. The first column of this spreadsheet, labeled Unconfounded /w Main Effects, shows the effects and interactions that are unconfounded (uncorrelated) with the main effects. The second column, labeled Unconfounded /w Interactions, contains the labels Yes or No to indicate whether the respective effect is unconfounded with the two-way interactions.