Factorial DOE: Main Effects, Interactions and What the Lab Actually Computes
A transparent 2² experiment from cell means to interaction effects.
What the showcase models
The lab is a compact two-factor, two-level factorial experiment. Four treatment combinations represent A−B−, A+B−, A−B+ and A+B+. Sliders alter the underlying factor contributions so the response surface and calculated effects move together.
Equations
The main effect of A is the mean response at A+ minus the mean response at A−; B is calculated analogously. The AB interaction is the difference between the effect of A at B+ and the effect of A at B−, equivalently a contrast across the four cell means.
An interaction means the effect of one factor depends on the level of the other. It is not merely two large main effects occurring together.
Controls and interpretation
Changing a main-effect control should translate the corresponding pair of treatment means in a structured way. Changing interaction should change the nonparallelism of the response pattern. The visual and numerical contrasts are intended to tell the same story.
Assumptions and limits
This is an educational deterministic 2² example, not an inferential DOE package. Real experiments require replication or an error model, randomization, consideration of blocking, residual diagnostics and attention to practical as well as statistical significance.
Validation checks
A pure A effect should produce an A contrast while B and AB remain near zero. A pure interaction should create opposing simple effects even when a main effect is small. Reversing an effect sign should reverse the corresponding contrast.