Experiment!: Planning, Implementing and Interpreting

9.7 Design Resolution

The number of factors occurring in the defining relationship is called the resolution and describes the degree of confounding in a fractional factorial design. The higher the resolution, the more information is obtained from the experiment. The resolution is written using roman numerals. For example, if the defining relation is I = ABCD the resolution is IV (four). It is easy to visualize the types of confounding that occur with a resolution of IV by holding up four fingers on one hand. Figure 9.7 shows that you can group them two and two (index and middle finger in one group, ring and little finger in the other). This represents confounding between a pair of two-way interactions. You can also group them as one plus three (for instance index finger in one group and the rest in the other). This represents confounding between main effects and three-way interactions.

Figure 9.7 A simple technique for translating resolution into confounding patterns, here shown for resolution IV. Grouping four fingers two and two represents confounding between a pair of two-way interactions. Grouping them one and three corresponds to confounding between a main effect and a three-way interaction. © Öivind Andersson.

With a resolution V design you could either group the five fingers as one plus four or as two plus three. This represents confounding between main effects and four-way ...