Moderation Analysis: How to Run It Online and Report It in APA7
Moderation asks whether the strength or direction of the relationship between X and Y depends on a third variable, the moderator (W). It is tested with an interaction term X × W.
What is Moderation Analysis?
Moderation asks whether the strength or direction of the relationship between X and Y depends on a third variable, the moderator (W). It is tested with an interaction term X × W.
When to use it
Use it when you expect an effect to be stronger for some people or conditions than others, for example stress harming wellbeing less when social support is high.
Example question: Does social support weaken the effect of stress on wellbeing?
Preparing your data
One row per participant with the predictor X, the moderator W and the outcome Y as numeric columns. The interaction term is created for you or by multiplying the centred X and W.
Example dataset (simulated; first rows of 150): id, stress (X), social_support (W), wellbeing (Y); stress_c and support_c are mean-centred copies.
| id | stress | social_support | wellbeing | stress_c | support_c |
|---|---|---|---|---|---|
| 1.0 | 2.72 | 5.05 | 4.1 | -0.34019999999999984 | 0.9631333333333334 |
| 2.0 | 3.79 | 4.15 | 4.25 | 0.7298 | 0.06313333333333393 |
| 3.0 | 3.46 | 4.8 | 4.96 | 0.39979999999999993 | 0.7131333333333334 |
| 4.0 | 3.06 | 3.57 | 4.84 | -0.00019999999999997797 | -0.5168666666666666 |
| 5.0 | 3.62 | 3.14 | 2.06 | 0.5598000000000001 | -0.9468666666666663 |
| 6.0 | 3.47 | 5.31 | 4.75 | 0.40980000000000016 | 1.2231333333333332 |
Download the full example CSV to practise. If the tool asks for a different layout, follow the instructions on its page.
How to run it on StatFas
- Open the Moderation Analysis tool. You do not need an account to run an analysis.
- Enter your data or upload your file, laid out as described in Preparing your data.
- Select your variables. Select X, W and Y. Mean-centre continuous X and W before forming the interaction if the tool does not do it.
- Choose any options the tool offers (for example the confidence level, a post hoc test or the error bar type) and run the analysis.
- Read the results on the page. Check the assumptions first, then the test statistic, the p-value and the effect size.
- To save your results, log in or create a free account. Every analysis stays free; the account is only needed to download.
Assumptions and checks
- The regression assumptions hold (linearity, independent errors, similar residual spread, roughly normal residuals).
- Mean-centre continuous predictors so the main effects are interpretable and multicollinearity is reduced.
- A significant interaction must be probed: examine the effect of X at low, average and high levels of W (simple slopes).
- Interactions need larger samples than main effects because they are usually small.
Key numbers to look at
- Interaction coefficient (b3) for X × W with its p-value and CI.
- Change in R2 (ΔR2) due to the interaction.
- Simple slopes: the effect of X at W = −1 SD, the mean and +1 SD.
- Interaction plot: non-parallel lines indicate moderation.
Effect size
Report ΔR2 for the interaction. Interaction effects are usually small, so values of about .01 to .03 are common in published studies. Report the simple slopes with confidence intervals.
Benchmarks such as small, medium and large are conventions (Cohen, 1988), not rules. Interpret size in the context of your field.
Reporting Moderation Analysis in APA7 style
Template
Worked example (simulated data)
The numbers below were computed from the example CSV above, so you can reproduce them. They illustrate the format and are not real findings.
APA7 reminders: italicise statistical symbols (M, SD, t, F, p, r), report exact p-values to two or three decimals (use p < .001 for very small values), omit the leading zero for values that cannot exceed 1 (.45, not 0.45), and put degrees of freedom in parentheses. See the APA7 cheat sheet.
Common mistakes
- Interpreting the main effects as unconditional once an interaction is in the model.
- Splitting a continuous moderator at the median; this loses information.
- Not plotting or probing a significant interaction.
Related analyses and alternatives
- Mediation: If the third variable explains the effect rather than changing it.
- Two-way ANOVA: If both predictors are categorical.
- Linear Regression: For models without an interaction.
Not sure which analysis you need? Use the test chooser.
Frequently asked questions
What does it mean to mean-centre?
Subtract the sample mean from each score so the variable has a mean of zero. A zero then means an average score, which makes the main effects interpretable.
Is moderation the same as interaction?
Yes. Moderation is the research question and the interaction term is how it is tested statistically.
References
American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). https://doi.org/10.1037/0000165-000
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
Hayes, A. F. (2022). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach (3rd ed.). Guilford Press.
This guide is for learning and for preparing results for your own reports. You remain responsible for choosing an appropriate analysis, checking its assumptions and interpreting the results. Follow the formatting rules of your journal or institution where they differ from APA7.