What it shows
The total effect of fertilizer on plant height, c = 0.8 cm per g, and the same relation split through a mediator, soil nitrogen.
Path a (fertilizer to nitrogen) is 4 mg/kg per g, path b (nitrogen to height) is 0.15 cm per mg/kg, and the direct path c′ is 0.2 cm per g.
How to read it
Follow the orange arrows for the indirect path: X to M, then M to Y. The black arrow runs from X straight to Y: the total effect c on top, the direct effect c′ below.
Multiply along the orange path for the indirect effect, ab = 4 × 0.15 = 0.6 cm per g.
Add the direct path to get the total: c = c′ + ab = 0.2 + 0.6 = 0.8 cm per g.
The paths (illustrative values)
- a = 4 mg/kg per g: each gram of fertilizer raises soil nitrogen by 4 mg/kg.
- b = 0.15 cm per mg/kg: each mg/kg of nitrogen adds 0.15 cm, with fertilizer held constant.
- c′ = 0.2 cm per g: the direct effect, with soil nitrogen held constant.
- ab = 0.6 cm per g, the indirect effect; c = 0.8 cm per g, the total effect.
Ways to use it in teaching
Students compute ab and c from the three path values, then check that c = c′ + ab.
Set it beside the moderation diagram: a mediator explains how X affects Y, a moderator when or how strongly.
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
- Hayes, A. F., & Preacher, K. J. (2010). Quantifying and testing indirect effects in simple mediation models when the constituent paths are nonlinear. Multivariate Behavioral Research, 45(4), 627–660. https://doi.org/10.1080/00273171.2010.498290
- Mediation (statistics). (n.d.). In Wikipedia. Retrieved October 19, 2026, from https://en.wikipedia.org/wiki/Mediation_(statistics)
