The cube's 8 corners are the 8 combinations of three two-level factors A, B, C (each set to −1 or +1). A hidden "true" response surface is defined as y = A·bA + B·bB + C·bC + (A·B)·bAB + noise. Every glowing corner is one experimental run; its colour and size encode the measured response at that combination.
In Full factorial mode all 8 corners are run, so the interaction contrast Est. A×B = mean(y | A·B=+1) − mean(y | A·B=−1) can be computed directly — it recovers the true A×B strength even though A, B and C were all varied at once.
In OFAT (one-factor-at-a-time) mode only 4 runs are used: a baseline, then one run that flips A alone, one that flips B alone, one that flips C alone. Main effects are estimated as a simple difference from baseline — but no run ever changes two factors together, so the interaction is never observed. OFAT silently assumes A×B = 0, and the "A×B error" stat shows exactly how wrong that assumption is whenever the true interaction is non-zero.
Full factorial: 8 runs → all main effects + all interactions estimable
OFAT: 4 runs → main effects only, interactions invisible
- Main effect A/B/C — how strongly each factor alone pushes the response up or down.
- A×B interaction — how much the effect of A depends on the current level of B (a real synergy or antagonism between the two factors).
- Measurement noise — random error added to every run, so estimates wobble like they would with a real instrument.
Real-world relevance: this is why designed experiments (factorial, fractional factorial, Box–Behnken, central composite) beat changing one variable at a time — the same or fewer runs recover interactions that OFAT can never see, which is often where the real gains (or real failures) in a process are hiding.