In the Design List, if you select a fractional factorial design with all continuous or two-level categorical factors, and possibly a blocking factor, the Display and Modify Design outline opens after you click Continue. Modify your design using the reports in this outline. See Modify Generating Rules in a Fractional Factorial Design for an example of changing the generating rules to construct a design.
Specify the defining relation for the design. The defining relation determines which fraction of the full fractional factorial design that JMP provides. See Change Generating Rules.
The defining relation for a design is determined by the words in the generating rules. A word is represented by a product of factors, but it is interpreted as the elementwise product of the entries in the design matrix for those columns. A defining relation consists of words whose product is a column of ones, called the identity.
Generating Rules for the Standard 25-3 Design shows the default-generating rules for a 25-3 design (five factors and eight runs).
In each column of the Change Generating Rules panel, the factor listed at the top and the factors in the column whose boxes are selected form a word in the defining relation. For example, the first column indicates that Temperature = Feed Rate*Catalyst*Stir Rate is a word in the defining relation.
The principal fraction of a full factorial design is the fractional factorial design obtained by setting all the defining relations equal to the identity. By default, the factorial design that JMP provides is the principal fraction. Notice that the +/- box is selected by default for all generating rules, so that each word in the defining relation equals the identity.
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Define I to represent a column consisting of the values +1. Because all factor levels are -1 or +1, the word in the first column is equivalent to Temperature*Feed Rate*Catalyst*Stir Rate = I. The word in the second column is equivalent to Concentration*Catalyst*Stir Rate = I. Together, these give the defining relations for the 25-3 design:
The aliasing structure in the Aliasing of Effects outline is determined by the defining relations and the fact that factor levels are +1 and -1. Recall that the first generating rule is Temperature = Feed Rate*Catalyst*Stir Rate and the second is Concentration = Catalyst*Stir Rate.
The second equality follows from replacing Catalyst*Stir Rate by Concentration using the second generating rule.
Now, post-multiply the first and third expressions by Concentration to obtain the following expression:
Because the column for Concentration in the design matrix contains values of -1 and +1, the term Concentration*Concentration represents a column of +1 values. The expression becomes the first alias relation shown in the Aliasing of Effects outline: