Mediation and moderation analysis: the difference and how to test each

What is the difference between a mediator and a moderator?

The distinction goes back to Baron and Kenny’s 1986 paper in the Journal of Personality and Social Psychology (volume 51, pages 1173–1182). Researchers were using the two words interchangeably. They aren’t.

A mediator carries the effect. Job stress raises burnout, burnout raises the wish to quit, so burnout is the route by which stress reaches turnover intention. A moderator sits outside that route and turns the effect up or down. Nurses with a supportive ward in-charge may burn out less under the same stress, so supervisor support moderates the stress → burnout path.

A quick test: read your hypothesis with “through” and then with “depends on”. “Stress affects turnover intention through burnout” is mediation. “The effect of stress on burnout depends on support” is moderation. If both sound plausible for the same variable, your theory has to choose, and the framework chapter has to say why. Our guide to the theoretical and conceptual framework shows how to draw each kind of arrow.

How do you test mediation: Baron and Kenny, Sobel or bootstrapping?

Test the indirect effect directly, with a bootstrap confidence interval. Examiners now expect it.

The causal steps approach asks whether X predicts Y, whether X predicts M, whether M predicts Y with X controlled, and whether the X → Y path shrinks. It never tests the indirect effect itself. Its first step, a significant total effect, also turned out to be unnecessary. Zhao, Lynch and Chen (Journal of Consumer Research, 2010) argued that projects had been abandoned for failing that step even when an indirect effect was present.

The Sobel test (Sobel, 1982) assumes the indirect effect is normally distributed, when a product of two coefficients is usually skewed. David Kenny’s mediation web page says it “should no longer be used”. Bootstrapping resamples your data thousands of times and builds the interval from the resampled estimates, with no normality assumption; Preacher and Hayes set out the method for single and multiple mediators in Behavior Research Methods (2008).

In PROCESS

PROCESS is Andrew Hayes’s macro for SPSS, SAS and R (the R version came out in 2020), explained in his book Introduction to Mediation, Moderation, and Conditional Process Analysis (third edition, 2022).

1. 1

   Check the scales first

   Reliability and validity come before paths.

2. 2

   Choose model 4

   Enter X, Y and M, select model 4, and add any control variables from your framework as covariates.

3. 3

   Keep the bootstrap default

   PROCESS draws 5,000 bootstrap samples and reports percentile intervals by default. State the number in your methods section.

4. 4

   Read the indirect effect

   If the 95% bootstrap interval for the indirect effect excludes zero, you have evidence of mediation. Report a, b, c, c-prime and the indirect effect.

In AMOS and SmartPLS

With latent variables you will usually test mediation inside the SEM. In AMOS, tick “Indirect, direct and total effects” under Analysis Properties and switch on bootstrapping. AMOS reports the total indirect effect; for each specific indirect effect in a model with several mediators, you define a user-defined estimand. SmartPLS reports total and specific indirect effects in its bootstrapping output. Which program suits your study is covered in our AMOS vs SmartPLS guide.

Should you call it full or partial mediation?

Many supervisors still ask for these labels; many methodologists advise against them. “Full” means the direct effect c′ became non-significant once M was added; “partial” means it stayed significant. But significance depends on sample size. Rucker, Preacher, Tormala and Petty (Social and Personality Psychology Compass, 2011) showed that the same indirect effect tends to be labelled full in a small sample and partial in a large one, and recommended dropping the terms in favour of reporting effect sizes.

Zhao and colleagues offered a typology that many management theses now use: complementary mediation (indirect and direct effects both significant, same sign), competitive (both significant, opposite signs), indirect-only (direct effect not significant), and two kinds of non-mediation.

I’d report the indirect and direct effects with their intervals and let the numbers speak. If your RAC insists on a label, use Zhao’s terms and cite them.

How do you test moderation, and what does mean-centring do?

Add the product X × W to a regression that already contains X and W. A significant product term means the effect of X depends on W. PROCESS model 1 builds the term for you. If regression output itself is unfamiliar, read how to interpret regression output first.

Mean-centring (subtracting the mean before multiplying) helps interpretation: the coefficient of X becomes its effect at the average level of W, rather than at W = 0, a value a 1–5 scale doesn’t have. It does not change the interaction coefficient, its p-value or R². Echambadi and Hess proved this in Marketing Science (2007), in a paper titled “Mean-centering does not alleviate collinearity problems in moderated multiple regression models”. Centre for readability, not as a multicollinearity cure.

Then probe the interaction, because a significant term tells you the slope changes but not where.

• Simple slopes: the effect of X at chosen values of W. PROCESS uses the 16th, 50th and 84th percentiles by default; the moments option gives the mean and ±1 SD. Plot the lines; a DC reads a figure faster than a table.
• Johnson–Neyman: the value of W at which the effect of X crosses into or out of significance, requested with the jn option. Useful when W is a continuous scale.

When a moderator acts on part of a mediation chain, you have moderated mediation. PROCESS model 7 puts W on the X → M path and model 14 on the M → Y path. Test it with the index of moderated mediation (Hayes, Multivariate Behavioral Research, 2015): if its bootstrap interval excludes zero, the indirect effect depends on W.

How do you report mediation and moderation in a thesis? A worked example

Take a hypothetical study. A scholar surveys staff nurses in private hospitals in Kerala about job stress (X), burnout (M), turnover intention (Y) and supervisor support (W). Written the way our hypothesis guide suggests:

• H1: Burnout mediates the positive relationship between job stress and turnover intention.
• H2: Supervisor support weakens the relationship between job stress and burnout.
• H3: The indirect effect of job stress on turnover intention through burnout is weaker when supervisor support is high.

H1 is model 4; H2 and H3 together are model 7. She needs enough respondents (see our sample size guide), and her scales should have passed a CFA first (see EFA vs CFA). The numbers below are invented for illustration.

Hypotheses were tested with PROCESS v4 (Hayes, 2022), models 4 and 7, with 5,000 bootstrap samples and percentile confidence intervals. Job stress was positively related to burnout (a = 0.52, 95% CI [0.42, 0.62]), and burnout to turnover intention controlling for job stress (b = 0.41, 95% CI [0.29, 0.53]). The indirect effect through burnout was 0.21 (95% bootstrap CI [0.14, 0.29]), supporting H1. The direct effect remained significant (c′ = 0.18, 95% CI [0.06, 0.30]), indicating complementary mediation (Zhao et al., 2010). The stress × support interaction on burnout was negative (B = −0.15, 95% CI [−0.25, −0.05]), supporting H2. The indirect effect was 0.26 at low support (16th percentile), 0.21 at the median and 0.16 at high support (84th percentile); the index of moderated mediation was −0.06 (95% bootstrap CI [−0.10, −0.03]), supporting H3.

Add the path diagram, and move the raw output to an appendix. For general reporting conventions, see choosing a statistical test.

Common mistakes in thesis mediation and moderation analysis

The first one is the one external examiners write the longest comments about.

• Writing that burnout causes turnover intention when all three variables came from one questionnaire filled in on one day.
• Hypothesising a mediator and then testing it as an interaction term, or the reverse. Check the diagram against the analysis before your DC meeting.
• Dropping a mediation hypothesis because the total effect was not significant, without ever testing the indirect effect.
• Adding gender or age as a moderator at the analysis stage because the variable happened to be in the questionnaire.
• Leaving out the confidence intervals or the number of bootstrap samples.

What a cross-sectional survey can show

Mediation is a causal story. A single survey measures X, M and Y at the same moment, so it can show that the data fit your chain; it can’t rule out that turnover intention feeds burnout, or that a bad posting drives both. Kenny’s page warns that cross-sectional estimates are often invalid unless strong assumptions hold, and suggests measuring X before M and Y.

Write “consistent with”, not “proves”, and name the limitation in your final chapter. If you are still at the synopsis stage, a two-wave survey is worth a look; our guide to research design types explains the options.