Design resolutions describe how much the effects in a fractional factorial design are aliased with other effects. When you do a fractional factorial design, one or more of the effects are confounded, meaning they cannot be estimated separately from each other. Usually, you want to use a fractional factorial design with the highest possible resolution for the amount of fractionation required. For example, it is usually better to choose a design where main effects are confounded with 3-way interactions (Resolution IV) instead of a design where main effects are confounded with 2-way interactions (Resolution III).
Resolution III, IV, and V are most common:
- Resolution III
- No main effects are aliased with any other main effect, but main effects are aliased with 2-factor interactions.
- Resolution IV
- No main effects are aliased with any other main effect or 2-factor interactions, but some 2-factor interactions are aliased with other 2-factor interactions and main effects are aliased with 3-factor interactions.
- Resolution V
- No main effects or 2-factor interactions are aliased with any other main effect or 2-factor interactions, but 2-factor interactions are aliased with 3-factor interactions and main effects are aliased with 4-factor interactions.
The design resolution tells us how badly the design is confounded. For example, a resolution of IV indicates that main effects are confounded or mathematically indistinguishable from three-way interactions, and two-way interactions are confounded or mathematically indistinguishable from other two-way interactions.
References
Minitab Support. What is the design resolution in a factorial design? – Minitab
