What it shows
A moderation model: fertilizer (X) affects plant height (Y), and sunlight (W) points at that arrow, not at Y, because it changes the relation.
The effect of fertilizer is 0.35 cm per g at 4 hours of sun, 0.8 at 7 hours and 1.25 at 10 hours.
How to read it
An arrow that lands on another arrow is an interaction: the moderator changes the size of the X to Y effect.
On the slopes plot, lines that are not parallel show the interaction in this model; with real data, it is the test of the interaction term (b3) that shows whether moderation is there.
The model (illustrative values)
- height = 14 + 0.8 F + 0.5 (S − 7) + 0.15 F (S − 7), with F in g and S in hours of sun per day.
- Slope of fertilizer: 0.35 cm per g at 4 hours, 0.8 at 7 hours, 1.25 at 10 hours.
- Predicted heights at 4 hours: 12.5, 14.25, 16 and 17.75 cm; at 10 hours: 15.5, 21.75, 28 and 34.25 cm.
Ways to use it in teaching
Students compute the slope at 4 and 10 hours from the model, then find them on the plot.
Ask why sunlight was a controlled variable in the first experiment and a moderator here.
Contrast with the mediation diagram, which uses the same X and Y.
For how studies name and control their variables, see our guide to research variables.
Sources
- Baron, R. M., & Kenny, D. A. (1986). The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51(6), 1173–1182. https://doi.org/10.1037/0022-3514.51.6.1173
- Moderation (statistics). (n.d.). In Wikipedia. Retrieved October 19, 2026, from https://en.wikipedia.org/wiki/Moderation_(statistics)
