Full Factorial Designs, Explained

Part of our complete guide to DOE for biologists.

A full factorial design tests every possible combination of every factor's levels. Two factors at two levels each gives you 4 runs. Three factors gives you 8. Five gives you 32. Nothing is left untested, which means nothing is ambiguous in the result either — this is the one design where you never have to ask "was that effect real, or was it actually something else I couldn't separate it from?"

Why that matters: no aliasing

With every combination tested, every main effect and every interaction between factors can be estimated completely independently of every other one. Compare that to a fractional factorial, which deliberately runs only a subset of combinations and, as a result, ends up unable to fully separate certain effects from each other (see Fractional Factorial Designs and Aliasing for what that actually means). A full factorial has none of that trade-off. It's the cleanest possible design — when you can afford it.

The catch: it doubles with every factor

The run count is 2 raised to the number of factors. That's fine at two or three factors — 4 or 8 runs is nothing. By six factors it's 64 runs; by ten, over a thousand. Long before you get there, the cost of testing every combination stops making sense next to a fractional design that answers almost the same question in a fraction of the runs.

Where it still makes sense

At a small number of factors — roughly three or fewer — there's no real reason to use anything else. The run count is already low, so fractionating it wouldn't save you much, and you get to keep every effect estimated cleanly for free. BioDOE uses a full factorial automatically at this factor count for both screening and characterization goals — you don't have to ask for one specifically, it's just the design that makes sense when you have this few factors.

Beyond that range, see Which DOE Design Should I Use? for how BioDOE picks a fractional factorial, a Definitive Screening Design, or a response-surface design instead, depending on what you're trying to find out.

Start free — full factorial designs are available on the free Starter plan.