Choosing a Fraction
main topic 

When you create a fractional factorial design, Minitab uses the principal fraction by default. The principal fraction is the fraction where all signs are positive. However, there may be situations when a design contains points that are impractical to run and choosing an appropriate fraction can avoid these points.

A full factorial design with 5 factors requires 32 runs. If you want just 8 runs, you need to use a one-fourth fraction. You can use any of the four possible fractions of the design. Minitab numbers the runs in "standard" (Yates) order using the design generators as follows:

1  D = -AB   E = -AC
2  D =  AB   E = -AC
3  D = -AB   E =  AC
4  D =  AB   E =  AC

In the blocking example, we asked for the third fraction. This is the one with design generators D = -AB and E = AC.

Choosing an appropriate fraction can avoid points that are impractical or impossible to run. For example, suppose you could not run the design in the previous example with all five factors set at their high level. The principal fraction contains this point, but the third fraction does not.