A full factorial design has runs for all combinations of the levels of the factors. The sample size is the product of the levels of the factors. For twolevel designs, this is 2k where k is the number of factors.
Full factorial designs are orthogonal for all effects. It follows that estimates of the effects are uncorrelated. Also, if you remove an effect from the analysis, the values of the other estimates do not change. Their pvalues change slightly, because the estimate of the error variance and the degrees of freedom are different.
A regular fractional factorial design also has a sample size that is a power of two. For twolevel designs, if k is the number of factors, the number of runs in a regular fractional factorial design is 2k – p where p < k. A 2k – p fractional factorial design is a 2p fraction of the kfactor full factorial design. Like full factorial designs, regular fractional factorial designs are orthogonal.
A full factorial design for k factors provides estimates of all interaction effects up to degree k. But because experimental runs are typically expensive, smaller designs are preferred. In a smaller design, some of the higherorder effects are confounded with other effects, meaning that the effects cannot be distinguished from each other. Although a linear combination of the confounded effects is estimable, it is not possible to attribute the variation to a specific effect or effects.
For most designs that involve categorical or discrete numeric factors at three or more levels, standard designs do not exist. In such cases, the screening platform generates main effects screening designs. These designs are orthogonal or near orthogonal for main effects.
For cases where standard mixedlevel designs exist, the possible designs are given in the Design List. The Design List provides fractional factorial designs for pure threelevel factorials with up to 13 factors. For mixed twolevel and threelevel designs, the Design list includes the complete factorials and the orthogonalarray designs listed in Table of MixedLevel Designs.
Note: By default, Cotter designs are not included in the Design List. To include Cotter designs, deselect Suppress Cotter Designs in the Screening Design red triangle menu. To always show Cotter designs, select File > Preferences > Platforms > DOE and deselect Suppress Cotter Designs.
For k factors, a Cotter design has 2k + 2 runs. The design structure is similar to the “vary one factor at a time” approach.
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For each of the next k runs, one factor in turn is set at its low level and the others high.

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For each of the next k runs, one factor in turn is set at its high level and the others low.

When you construct a Cotter design, the design data table includes a set of columns to use as regressors. The column names are of the form <factor name> Odd and <factor name> Even. They are constructed by summing the oddorder and evenorder interaction terms, respectively, that contain the given factor.
For example, suppose that there are three factors, A, B, and C. Cotter Design Table shows how the values in the regressor columns are calculated.