Explain the concept of interaction effects in factorial experiments.
Instruction: Describe what interaction effects are and how they can impact the interpretation of factorial experiment results.
Updated
Official answer
An interaction occurs when the effect of one factor depends on the level of another, on the outcome scale being analyzed.
Consider a randomized 2×2 experiment with factors A and B coded 0 or 1. Suppose the four mean outcomes are 10 for neither factor, 12 for A only, 13 for B only, and 19 for both. The effect of A is 12 - 10 = 2 when B is off and 19 - 13 = 6 when B is on. The interaction contrast is 6 - 2 = 4 outcome units.
An additive model would predict 10 + 2 + 3 = 15 for both factors; the observed mean of 19 differs by 4. With 0/1 coding, that contrast is the coefficient of A×B in a model containing both main effects. Other coding conventions change coefficient scaling.
Show all four cell means with uncertainty. Pre-specify plausible interactions and account for multiple exploration. An interaction on an additive scale need not have the same interpretation on a logarithmic or probability scale.