# How to design a 2-level fractional factorial experiment given some prior knowledge

We're designing a trial to test four factors (call them A, B, C and D) for an experiment. Each factor has two levels: + and -. The + of factor A is believed to lead to better results and the - of factor B is also believed to lead to better results. We know nothing about C and D, nor whether any interaction effects exist or not.

We want to get the following goals:

1. Find the combination of factors to get the best result.
2. Build a model containing A, B, C and D to predict the result of experiments. (This requires that A and B should still be in this design)

How can we get a fractional factorial design based on our prior knowledge of the effects of A and B?