An important property of a fractional design is its resolution or ability to separate main effects and low-order interactions from one another. Formally, the resolution of the design is the minimum word length in the defining relation excluding (1). The most important fractional designs are those of resolution III, IV, and V: Resolutions below III are not useful and resolutions above V are wasteful in that they can estimate very high-order interactions which rarely occur in practice. The 25 − 2 design above is resolution III since its defining relation is I = ABD = ACE = BCDE.
| Resolution | Ability | Example |
|---|---|---|
| II | Not useful: main effects are confounded with other main effects | 22 − 1 with defining relation I = AB |
| III | Estimate main effects, but these may be confounded with two-factor interactions | 23 − 1 with defining relation I = ABC |
| IV |
Estimate main effects unconfounded by two-factor interactions |
24 − 1 with defining relation I = ABCD |
| V |
Estimate main effects unconfounded by three-factor (or less) interactions |
25 − 1 with defining relation I = ABCDE |
| VI |
Estimate main effects unconfounded by four-factor (or less) interactions |
26 − 1 with defining relation I = ABCDEF |
The resolution described is only used for regular designs. Regular designs have run size that equal a power of two, and only full aliasing is present. Nonregular designs are designs where run size is a multiple of 4; these designs introduce partial aliasing, and generalized resolution is used as design criteria instead of the resolution described previously.
Read more about this topic: Fractional Factorial Design
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