Intuition to the Resolution of a fractional factorial design In design of experiments, is there an intuitive way to understand (and explain) the idea of the "resolution" of the design?
 A: The concept of resolution is applied to fractional factorial experiments. Following the excellent Statistics for Experimenters: Design, Innovation, and Discovery, 2nd Edition, for a half-design (that is, using one half of a full facorial deign), the resolution is the length (number of letters in) its generating relation. For quarter-design, with two words in its generating relation, it would be the length of the shortest word, and similarly for smaller fractions. 
For instance, a full factorial design on three (two-level) factors, denoted A, B, C, we could define a half-fraction by C=AB. Multiplying through with C this is equivalent with e (identity element, or vector of only ones)=ABC, which is the generating relation, of length three, so resolution III. The form C=AB shows that the main effect of C is aliased with the interaction AB, showing that this design is mostly useful if we can assume no interactions. 
So, intuitively, we can say


*

*Resolution III, some main effects aliased with two-factor interactions.

*Resolution IV, some main effects aliased with three-factor interactions, and some two-factor interactions aliased with other two-factor interactions.

*Resolution V, some main effects aliased with four-factor interactions, some two-factor interactions aliased with three-factor interactions, but never with other two-factor interactions, ... 
