I want to begin learning about factorial experiments and, specially, fractional factorial design.
What would be a simple, plain English explanation, to get the big picture of this topic? Besides, an illustrative example to show the power of the technique and the underlying computations would be awesome.
This answer is work in progress. I am currently try to learn fractional factorial designs, and I'll update this answer as I learn more about it.
A full factorial experiment is when you are testing the effects of all possible configurations $A_0 \times \cdots \times A_k$ of an experiment, where the size of each set $A_i$ is finite. This is means that if you are testing 5 variables, where two have 5 possible states and the remaining three have 3 possible, then you would have to test for $5^23^3 = 675$ configurations.
Although a full factorial experiment is a desirable design wherein one could gather information on all the main effects, in some contexts one must be economical with the resources required to run the total experiment. This where fractional factorial designs come in. The aim of these designs is to maximize the information gathered by running a fraction of the configurations, which they choose based on the validity of the following three principles:
Lower order effects are more likely to be important than higher order effects. Therefore, when resources are scarce one should prioritize lower order effects.
The number of effects that have a large impact is small - Pareto principle.
In order for an interaction to be significant, at least one of its parent factors should be significant.
I don't yet understand specific methods used to choose subsets. I will update this answer with an example as soon as I understand how that is done.
