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

What is the difference between a mediator and a moderator?

This difference comes from the 1986 paper of Baron and Kenny in the Journal of Personality and Social Psychology (volume 51, pages 1173–1182). In those days researchers were using both words for the same thing. But the two are different.

The mediator is the variable through which the effect travels. Job stress increases burnout, and burnout increases the wish to leave the job. So burnout is the route by which stress reaches turnover intention. A moderator is not on this route at all, it only changes how strong the effect comes. A nurse with a supportive ward in-charge may burn out less under the same stress. Then supervisor support is moderating the stress → burnout path.

One simple check works well. Read your hypothesis once with the word “through” and once with “depends on”. “Stress affects turnover intention through burnout” is a mediation statement. “The effect of stress on burnout depends on support” is a moderation statement. If both readings sound okay for your variable, your theory has to pick one role, and the framework chapter has to explain about why it picked that one. For drawing each type of arrow, see our guide to the theoretical and conceptual framework.

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

These days examiners are asking for a direct test of the indirect effect with a bootstrap interval.

The old causal steps approach checks four things. First, does X predict Y? Then does X predict M, and does M predict Y when X is held constant? Last, does the X → Y path become smaller? The indirect effect itself is never tested. Later the first step, a significant total effect, was found to be not needed. Zhao, Lynch and Chen (Journal of Consumer Research, 2010) argued that many projects got dropped because they failed this step, even when an indirect effect was present.

Then there is the Sobel test (Sobel, 1982). It takes the indirect effect as normally distributed, but when you multiply two coefficients the result is usually skewed. On his mediation web page David Kenny writes that the test “should no longer be used”. Bootstrapping resamples your data some thousands of times and makes the interval from all those resampled estimates, so no normality assumption is needed. For one mediator or more, the method was laid out by Preacher and Hayes in Behavior Research Methods (2008).

In PROCESS

Andrew Hayes wrote PROCESS as a macro for SPSS, SAS and R, and the R version was released in 2020. His book Introduction to Mediation, Moderation, and Conditional Process Analysis (third edition, 2022) explains how it works.

1. 1

   Check the scales first

   Do reliability and validity checks before any of the paths.

2. 2

   Choose model 4

   Put in X, Y and M and select model 4. Controls like age or experience go in the covariates box.

3. 3

   Keep the bootstrap default

   By default PROCESS takes 5,000 bootstrap samples and gives percentile intervals. Mention this number in the methods section.

4. 4

   Read the indirect effect

   When the 95% bootstrap interval of the indirect effect does not include zero, you have evidence for mediation. Report a, b, c, c-prime and the indirect effect also.

In AMOS and SmartPLS

If your constructs are latent variables, mostly you will test the mediation inside the SEM itself. In AMOS, go to Analysis Properties, tick “Indirect, direct and total effects” and turn on bootstrapping. What AMOS gives is the total indirect effect only. When the model has more than one mediator, each specific indirect effect needs a user-defined estimand that you write. The bootstrapping output of SmartPLS shows both total and specific indirect effects. We have put AMOS and SmartPLS side by side in our AMOS vs SmartPLS guide.

Should you call it full or partial mediation?

Guides keep asking for these two labels in thesis even now, whereas most methodologists want them gone. After adding M, if c′ is no more significant scholars write “full”, and if it stays significant they write “partial”. The problem is that significance moves with sample size. Rucker, Preacher, Tormala and Petty (Social and Personality Psychology Compass, 2011) showed this. The same indirect effect tends to get the full label in a small sample and the partial label in a large one. Effect sizes were what they wanted reported, in place of the two words.

Zhao and his co-authors gave another set of types, and many management theses use them now. When the indirect and direct effects are both significant and have the same sign, it is complementary mediation. Both significant but with opposite signs is competitive mediation. If the direct effect is not significant, it is indirect-only. They also describe two kinds of non-mediation.

My suggestion is to report the indirect and direct effects along with their intervals, and leave the reading to the numbers. If some RAC member still asks “full or partial?”, Zhao’s terms with citation will do.

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

Your regression should already have X and W. To it you add the product X × W. When this product term comes significant, it means the effect of X depends on W. PROCESS model 1 makes the product term for you. If regression output itself is new for you, first go through how to interpret regression output.

In mean-centring you subtract the mean from each variable and only then multiply. The output becomes easier to read. Now the coefficient of X shows its effect at the average W. Without centring it shows the effect at W = 0, and a 1–5 scale has no zero value. The interaction coefficient, its p-value and R² do not change with centring. Echambadi and Hess proved this in Marketing Science (2007), and the paper’s title says it directly, “Mean-centering does not alleviate collinearity problems in moderated multiple regression models”. Centre your variables for easier reading, and don’t expect centring to solve multicollinearity.

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

• Simple slopes: this gives the effect of X at some chosen values of W. By default PROCESS takes the 16th, 50th and 84th percentiles, and with the moments option you get the mean and ±1 SD. Draw these lines in a graph also, since DC members mostly look at the figure first.
• Johnson–Neyman: this finds the value of W where the effect of X becomes significant or stops being significant. Use the jn option to get it. It helps most when W is a continuous scale.

When a moderator works on one part of a mediation chain, it is called moderated mediation. In PROCESS, model 7 places W on the X → M path and model 14 places it on the M → Y path. The test for it is the index of moderated mediation (Hayes, Multivariate Behavioral Research, 2015). When the bootstrap interval of the index does not include zero, the indirect effect depends on W.

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

Let us take an invented study. One scholar collects survey data from staff nurses working in private hospitals in Kerala. Her variables are job stress (X), burnout (M), turnover intention (Y) and supervisor support (W). She writes the hypotheses in 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.

For H1 she runs model 4. H2 and H3 are tested together in model 7. Her sample has to be big enough, and our sample size guide covers that. The scales should also clear a CFA before any of this (see EFA vs CFA). We made up all numbers below only to show the format.

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.

Put the path diagram along with this paragraph. The raw software output can go to appendix. General reporting rules are in our page on choosing a statistical test.

Common mistakes in thesis mediation and moderation analysis

External examiners write their longest comments on the first mistake in this list.

• Claiming burnout causes turnover intention, when all three variables were collected in one questionnaire on the same day.
• The hypothesis says mediator but the analysis tests an interaction term, or it is the other way round. Keep the diagram open beside your output a day before DC meeting and tick each arrow.
• Giving up a mediation hypothesis only because the total effect came non-significant, and never testing the indirect effect.
• Bringing in gender or age as a moderator at analysis time, just because that column was there in the questionnaire.
• Not reporting the confidence intervals, or forgetting to say how many bootstrap samples were used.

What a cross-sectional survey can show

When you say mediation, you are telling a causal story. But one survey collects X, M and Y at the same time. It can show that your data fit the chain you proposed. It cannot rule out the reverse, that turnover intention is feeding burnout. Or a bad posting may be pushing up both. Kenny warns on his page that cross-sectional estimates are many times invalid unless some strong assumptions hold, and he suggests measuring X before M and Y.

So in your write-up use “consistent with” and avoid “proves”. Mention this limitation clearly in the final chapter. If you are still at the synopsis stage, think about a two-wave survey. The options are explained in our guide to research design types.