Question

What will the generic confounding pattern be for a 2^5-2 (resolution III) experiment design?

Answer 1

For example, the five factor 2^{5 − 2} can be generated by using a full three factor factorial experiment involving three factors (say A, B, and C) and then choosing to confound the two remaining factors D and Ewith interactions generated by D = A*B and E = A*C. These two expressions are called the generators of the design. So for example, when the experiment is run and the experimenter estimates the effects for factor D, what is really being estimated is a combination of the main effect of D and the two-factor interaction involving A and B.

An important characteristic of a fractional design is the defining relation, which gives the set of interaction columns equal in the design matrix to a column of plus signs, denoted by I. For the above example, since D = AB and E = AC, then ABD and ACE are both columns of plus signs, and consequently so is BDCE. In this case the defining relation of the fractional design is I = ABD = ACE = BCDE. The defining relation allows the alias pattern of the design to be determined.