Dear Caddy,

I am considering using a fractional factorial design for the first time. It’s so great that the design enables me to reduce the number of experimental conditions I need to implement by half! But, I have two questions.

(1) The statistician in our team says we will need the same sample size for a fractional versus complete design, even though we have half the experimental conditions. Why is this?

(2) Am I correct that I need to rely on statistical software to tell me which specific conditions to implement? What software do you recommend?

Signed,

Fractionally Happy

Dear Fractionally Happy,

(1) The statistician in your team is correct. Any fractional factorial design has exactly the same sample size requirements as the corresponding complete factorial design.

Caddy knows this is counterintuitive, but fractional factorial designs do not confer any advantages in terms of sample size requirements. In a factorial design, whether complete or fractional, statistical power is nearly unrelated to the number of participants per experimental condition. Instead, statistical power depends on the number of participants per factor level, across conditions, along with the usual other considerations (e.g., choice of alpha, anticipated effect size).

Instead, the economy of fractional factorial designs comes from reduction in the logistical burden of implementing a factorial experiment, since it can be easier to implement half the experimental conditions. Of course, ALL factorial designs, when properly implemented, are tremendously efficient in terms of sample size requirements as compared to alternatives such as conducting a separate experiment to examine each component.

(2) You’re correct too!  The experimental conditions in a fractional factorial design are selected on purely statistical grounds, although critical input from the investigator about the scientific objectives of the experiment is used in the process. We tend to recommend SAS (the FACTEX procedure) and R (the FRF2 package), but there are various software options (another is Minitab).

For more about this and other topics related to fractional factorial designs, see Chapters 3, 4, and 5 in Collins (2018). You are welcome to set up a consulting session with us to discuss fractional factorial designs. We are also working on a new short course on fractional factorials. Sign up for our newsletter to stay on top of this and other CADIO news!