Design of an Experiment with Three-Level Factors - Generator & Aliases Tab

Designing 3(k-p) Experiments

Select the Generator & aliases tab of the Design of an Experiment with Three-Level Factors dialog to access information about correlations between main effect vectors and 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). If the current design is blocked, then the blocking is also accomplished by "sacrificing" higher-order interactions. (Note that for 3(k-p) designs, the generators for the fractional design and blocking are listed in the Summary box at the top of the dialog.) This option allows you to view the correlation matrix for the design matrix, and thus to determine the confounding of main effects, interactions, and blocking variables.  The issue of confounding in 2(k-p) and 3(k-p) designs is explained in the Introductory Overview. After clicking this button, two spreadsheets are displayed.

Correlations of effects

The first spreadsheet contains the correlations for the effects, the interactions, and the blocking variables (if the current design is blocked).

Main effects

Because each main effect has three levels (and thus two degrees of freedom), there are two columns and rows for each main effect in this matrix. 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. When computing the correlation matrix, for each two-way interaction, four 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.

Block effects

To compute the correlations for the block effects, when computing the correlation matrix, STATISTICA will create noblocks-1 new variables. The values for a blocking variable i for each run are computed as:

Bi = -1	if block = 1
=1	if block = i+1
=0	otherwise

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 Unconf. Effects (excl. blocks), shows the effects and interactions that are unconfounded (uncorrelated) with other main effects and interactions. The second column, labeled Unconfounded if blocks included contains the main effects and interactions that are (1) unconfounded (uncorrelated) with other main effects and interactions, and (2) that are unconfounded with the blocking variables (coded as described above). If there is no blocking in the current design, then only the first column will be displayed in this spreadsheet.