What it shows
A 2 × 2 factorial experiment: two motors, A and B, each run at 2000 and 3000 RPM, with mean power used in watts as the response. The cell means are illustrative, not data from an experiment.
The left panel is the design itself, four cells with their marginal means. The right panel is the interaction plot, one line per motor. The panel underneath works out both main effects and the interaction.
How to read it
Each main effect compares the two marginal means for one factor: 725 W against 425 W for speed, and 650 W against 500 W for motor.
The interaction asks whether one factor’s effect depends on the other. Raising the speed adds 200 W for motor A but 400 W for motor B.
On the plot, that difference shows as lines that are not parallel. Parallel lines would mean no interaction.
The numbers
- Motor A: 400 W at 2000 RPM, 600 W at 3000 RPM; mean 500 W.
- Motor B: 450 W at 2000 RPM, 850 W at 3000 RPM; mean 650 W.
- Speed means: 425 W at 2000 RPM, 725 W at 3000 RPM.
- Main effect of speed: 725 W − 425 W = 300 W. Main effect of motor: 650 W − 500 W = 150 W.
- Interaction (difference between the speed effects): (850 W − 450 W) − (600 W − 400 W) = 200 W. On the same scale as the main effects, the interaction effect is half of that, 100 W.
Ways to use it in teaching
Change one cell so that the lines become parallel and ask students what happens to the interaction.
Ask what a one-factor-at-a-time experiment, changing speed only on motor A, would have concluded about speed.
Use the two interaction figures (200 W and 100 W) to have students check which convention a textbook or software package uses.
For where an experimental design fits among the other choices in a methodology chapter, see our guide to research design.
Sources
- Factorial experiment. (n.d.). In Wikipedia. Retrieved October 19, 2026, from https://en.wikipedia.org/wiki/Factorial_experiment
