Mediation Analysis
Mediation Analysis (Baron-Kenny / Bootstrap) · Also known as: indirect effects analysis, path-based mediation, PROCESS macro mediation, Aracılık Analizi (Mediation / PROCESS)
Mediation analysis is a statistical procedure that tests whether the effect of an independent variable X on an outcome Y operates wholly or partly through a third variable M, called the mediator. Formalised by Baron and Kenny in 1986, it decomposes the total effect of X on Y into a direct path (c′) and an indirect path (a × b), quantifying how much of the relationship is carried by the mediating mechanism.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
+4 more
When to use it
Use mediation analysis when you have a theoretically motivated causal chain X → M → Y and wish to test whether the mediator explains the relationship. All three variables should be measured; the causal direction must be justified by theory, not inferred statistically. The analysis handles continuous, binary, or ordinal variables with appropriate model extensions. A minimum sample of approximately 50 is needed, though 200 or more is recommended for stable bootstrap estimates. Key assumptions to verify are: linearity of the a path (X → M) and b path (M → Y), absence of severe multicollinearity (VIF < 10), and residual normality checks for each sub-model. Confounders that could explain M-Y or X-M associations must be controlled.
Strengths & limitations
- Decomposes a total effect into interpretable direct and indirect components, enabling mechanistic inference.
- Bootstrap confidence intervals make no distributional assumptions about the indirect effect, outperforming the older Sobel test for small-to-moderate samples.
- Applicable across multiple software environments, including Hayes's PROCESS macro for SPSS and R, the pingouin library for Python, and the mediation package for R.
- Can be extended to multiple mediators, moderated mediation, and latent variable models within structural equation modelling frameworks.
- Establishes statistical mediation but not causal mediation unless the study design (e.g. experimental manipulation of M) rules out confounding of the M → Y path.
- The product a × b assumes no interaction between X and M in predicting Y; violations require moderated mediation models.
- Requires a minimum sample size (around 50, preferably 200+) for reliable bootstrap estimates; small samples produce wide, uninformative confidence intervals.
- Temporal ordering — X precedes M precedes Y — must be established conceptually or by study design, not by the analysis itself.
Frequently asked
What is the difference between full and partial mediation?
Full mediation occurs when the direct effect c′ becomes statistically non-significant after the mediator is included in the model, suggesting that all of X's effect on Y travels through M. Partial mediation occurs when c′ remains significant but is smaller in magnitude than the total effect c, indicating that M carries only part of the relationship. Modern guidance recommends reporting the size of the indirect effect and its confidence interval rather than labelling results as full or partial, as the distinction depends heavily on sample size.
Why is bootstrap preferred over the Sobel test?
The Sobel test approximates the sampling distribution of a × b as normal, which is inaccurate because the product of two regression coefficients is typically skewed, especially in moderate samples. Bootstrap resampling constructs an empirical distribution directly from the data without distributional assumptions, yielding more accurate confidence intervals and greater statistical power. With samples of 200 or more and 5 000 bootstrap draws, the percentile or bias-corrected accelerated (BCa) bootstrap interval is the recommended approach.
How large a sample do I need?
Baron and Kenny's original steps can be applied from around 50 observations, but the bootstrap confidence interval for the indirect effect becomes adequately narrow and the test meaningfully powered only with roughly 200 or more cases. When the anticipated indirect effect is small or the paths are weak, power analyses using Monte Carlo simulation (available in specialised software) can determine the required N more precisely.
Can I use mediation analysis with non-continuous outcomes or mediators?
Yes, with appropriate extensions. When Y or M is binary, the model sub-components use logistic or probit regression. Hayes's PROCESS macro implements several such variants. For latent variables, structural equation modelling software such as lavaan (R) or Mplus handles mediation with full-information estimators. The core logic of decomposing total effects into direct and indirect components remains the same across these extensions.
Sources
- Baron, R. M. & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research. Journal of Personality and Social Psychology, 51(6), 1173–1182. link ↗
- Hayes, A. F. (2022). Introduction to Mediation, Moderation, and Conditional Process Analysis: A Regression-Based Approach (3rd ed.). The Guilford Press. ISBN: 978-1462549030
- Preacher, K. J. & Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40(3), 879–891. DOI: 10.3758/BRM.40.3.879 ↗
How to cite this page
ScholarGate. (2026, June 1). Mediation Analysis (Baron-Kenny / Bootstrap). ScholarGate. https://scholargate.app/en/statistics/mediation-analysis
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Confirmatory factor analysisPsychometrics↔ compare
- Moderated MediationStatistics↔ compare
- Moderation AnalysisCausal inference↔ compare
- Path AnalysisStatistics↔ compare
- Structural Equation ModelingResearch Statistics↔ compare