Guest post by Bradley Jones
Almost a hundred years ago R. A. Fisher‘s boss published an article espousing OFAT (one factor at a time). Fisher responded with an article of his own laying out his justification for factorial design. I admire the courage it took to contradict his boss in print!
Fisher’s argument was mainly about efficiency – that you could learn as much about many factors as you learned about one in the same number of trials. Saving money and effort is a powerful and positive motivator.
The most common argument I read against OFAT these days has to do with inability to detect interactions and the possibility of finding suboptimal factor settings at the end of the investigation. I admit to using these arguments myself in print.
I don’t think these arguments are as effective as Fisher’s original argument.
To play the devil’s advocate for a moment consider this thought experiment. You have to climb a hill that runs on a line going from southwest to northeast but you are only allowed to make steps that are due north or south or due east or west. Though you will have to make many zig zags you will eventually make it to the top. If you noted your altitude at each step, you would have enough data to fit a response surface.
Obviously this approach is very inefficient but it is not impossible. Don’t mistake my intent here. I am definitely not an advocate of OFAT. Rather I would like to find more convincing arguments to persuade experimenters to move to multi-factor design.
Related: The Purpose of Factorial Designed Experiments – Using Design of Experiments – articles by R.A. Fisher – articles on using factorial design of experiments – Does good experimental design require changing only one factor at a time (OFAT)? – Statistics for Experimenters