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

Aliases of Interactions: Design Generators

Select the Generators & aliases tab of the Design of an Experiment with Two-Level Factors dialog to access the options described here.

Aliasing of effects

Click the Aliasing of effects button to display spreadsheets containing the aliases of main effects and interactions, that is, to display the confounding of main effects with interactions and of two-way interactions with higher-order interactions. In fractional factorial designs, higher-order interactions are "sacrificed" in order to accommodate additional factors (main effects).  The issue of confounding in 2(k-p) designs and the concept of resolution are explained in the Introductory Overview.

Note: the column headers in the spreadsheets contain the fundamental identity for the design. The fundamental identity of the design completely defines all confounding of factors. For a discussion of the interpretation of the fundamental identity, refer to the Introductory Overview.

For more information on reading this spreadsheet, see How to Read the Aliases of Main Effects and Interactions Spreadsheet.

Alias matrix

Click the Alias matrix button to study the confounding of main effects and two-way interactions via a correlation matrix of the columns of the design. In this matrix, main effects that were created as aliases of two-way interactions will show a correlation of 1.0 with those interactions.

Generators of fractional design

Click the Generators of fractional design button to display a spreadsheet containing the fractional design generators. As discussed in the general introduction of 2(k-p) designs (see the Introductory Overview), in fractional factorial designs, some factors are created as aliases of higher-order interactions. These higher-order interactions are commonly referred to as design generators. For more information on reading this spreadsheet, see How to Read the Aliases of Main Effects and Interactions Spreadsheet.

Generators of blocking variable

Click the Generators of blocking variable button to display a spreadsheet containing the generators (aliases) of the blocking factors. As discussed in the general introduction of 2(k-p) designs (see the Introductory Overview, it is sometimes necessary to run the experiment in "chunks" or blocks. Also, blocking may be desired in order to reduce the error variance for the ANOVA (if the blocking factor accounts for a significant amount of variability). To ensure that the blocking does not confound the estimation of main effects and interactions, blocking is introduced into the design as an additional orthogonal factor. This requires assigning higher-order interactions to this factor (or two factors, if 4 blocks are requested, or three factors, if 8 blocks are requested, etc.). Thus, the blocking factors in those designs are the aliases of higher-order interactions.