Factorial designs involve testing several (n) factors at two levels, high and low. A Fractional Factorial experiment uses only a half (2^{n1}), a quarter (2^{n2}), or some other division by a power of two of the number of treatments that would be required for a Full Factorial Experiment.
A Full Factorial design with 3 factors (2^{3} design) would require 8 treatments. The example shows a 2^{31} design, it requires only 4 treatments:
Treatment

A

B

C

1

1

1

+1

2

+1

1

1

3

1

+1

1

4

+1

+1

+1

The Fractional Factorial design is created by aliasing Factor C with the Interaction AB. This is a Resolution III design.
