Fractional Factorial Designs and Aliasing, Explained
Part of our complete guide to DOE for biologists.
A full factorial tests every combination of every factor and leaves nothing ambiguous — but it doubles in size with every added factor, which makes it impractical past a handful. A fractional factorial runs a carefully chosen fraction of those combinations instead — a half, a quarter, an eighth — and gets back main-effect estimates that are almost as good, at a real cost: some effects become impossible to tell apart from each other. That cost is called aliasing, and it's not a flaw in the method, it's the actual trade you're making on purpose.
What aliasing actually means
Imagine two witnesses always show up to the same events together, never separately. You can measure the combined effect of their presence, but you can never know how much of it came from one versus the other — every observation you have confounds them. Aliasing is the same idea applied to statistical effects: in a fractional factorial, certain effects are calculated from exactly the same combination of runs, so the design literally cannot separate them. If Factor A's main effect is aliased with the Factor B–Factor C interaction, a "significant A" result might really be that interaction wearing A's name.
Resolution tells you which effects get tangled
Not all aliasing is equally bad, and Resolution is the label for how bad it is in a given design:
- Resolution III: main effects are aliased with two-factor interactions. The riskiest common case — a real interaction can masquerade as a main effect.
- Resolution IV: main effects are clear of two-factor interactions, but two-factor interactions can be aliased with each other. This is the target BioDOE builds toward for screening designs — main effects, the thing a screen exists to find, come out clean.
- Resolution V: main effects and two-factor interactions are all clear of each other. Higher-order interactions (three-way and up) can still be aliased with something, but those are rare enough in practice that this level is usually treated as fully clean.
Higher resolution costs more runs for the same number of factors — there's no way around that trade.
How BioDOE handles this for you
You don't pick a resolution by name in BioDOE. Choosing "Find what matters" (screening) targets Resolution IV automatically; "Map the shape" (characterization) targets Resolution V. If the exact resolution you'd want isn't constructible for your specific factor count, BioDOE steps down one resolution level rather than silently accepting a worse aliasing pattern without telling you — and if even that isn't available, it falls back to a Plackett-Burman screen instead. See Plackett-Burman Designs, Explained for why that's a real fallback, not the first choice.
For a lot of factor counts in the screening range, BioDOE now also has a better option than a fractional factorial at all — see Definitive Screening Designs, Explained for a design that adds curvature detection without the aliasing trade-off between main effects and center-point information.
Start free — fractional factorial screening and characterization designs are available on the free Starter plan.