Resolution III fractional factorial designs

The sparsity of effects principle (see Box and Meyer, 1986) makes resolution III and IV fractional factorial designs particularly effective for factor screening. This principle states that, when many factors are studied in a factorial experiment, the system tends to be dominated by the main effects of some of the factors and a relatively small number of two-factor interactions. Thus resolution IV designs with main effects clear of two-factor interactions are very effective as screening... 

Plackett-Burman designs Do not consider a Plackett-Burman design as a first choice. These designs are Resolution III designs, but the confounding pattern in such designs is more difficult to analyze than that of fractional factorial designs. 

The full factorial design may not be practical. Perhaps it is not possible for one operator to run two assays on one day. Then a fractional factorial design can be used. The design shown in Table 5 is resolution III design with four experimental trials. As machine is aliased with the interaction between operator and day, the main effect due to machine can be estimated only if we assume there is negligible interaction between operator and day. Often, interactions can be assumed to be negligible based on prior knowledge or the science that is known about the situation. 

Fractional factorial designs allow main effects and some interaction effects to be estimated at minimal cost, but the result is not without ambiguity - main effects may be confounded with first-order interactions (designs of resolution III) or first-order interaction effects confounded with one another (resolution IV). 

The notion of resolution has been extended lo experimental designs other than fractional factorial designs. For example, the Hadamard designs are said to be of resolution III. even when JV is not equal to a power of 2. 

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