Interaction

Two factors do not act independently — the effect of A depends on the level of B.

Also known as: interaction effect, two-factor interaction, 2fi

An interaction exists when the effect of one factor depends on the level of another. In regression form it appears as a product term $β_{A B} \cdot x_{A} \cdot x_{B}$ .

Int (A \times B) = \frac{1}{2} [(\overset{y}{ˉ}_{A + B +} - \overset{y}{ˉ}_{A - B +}) - (\overset{y}{ˉ}_{A + B -} - \overset{y}{ˉ}_{A - B -})]

Graphical diagnostic: interaction plot — crossing lines suggest an interaction, parallel lines suggest main effects only
Two-factor interactions (2fi) are usually the most interpretable in practice
Higher orders (3fi, 4fi) are typically small and, in many designs, aliased with main effects for efficiency (aliasing)

Used in

DoE Planner
DoE Advisor
Regression Analysis
Regression (Attributive)
Contour Plot

In the Algorithm Lab

doe/doe-planner
regression/regression-coefficients

Sources

Montgomery, D. C. — Design and Analysis of Experiments, 10th Edition, Chapter 6
Box, Hunter & Hunter — Statistics for Experimenters, 2nd Edition

Interaction

See also

Used in

In the Algorithm Lab

Sources