Three-Way Interaction Calculator
Test whether the moderating effect of W itself depends on a second moderator Z, with the three-way interaction test and conditional effects of X at combinations of W and Z.
Updated · By Bibin XavierData 250 × 9
| Employeetext · 250 levels | Leadershipnumeric | Trustnumeric | Engagementnumeric | Autonomynumeric | Tenure_Yearsnumeric | Performancenumeric | Agenumeric | Femalenumeric · coded |
|---|---|---|---|---|---|---|---|---|
| E001 | 4.56 | 3.94 | 4.12 | 3.21 | 4.9 | 5.36 | 28 | 1 |
| E002 | 4.42 | 3.02 | 4.35 | 3.12 | 10 | 4.26 | 43 | 1 |
| E003 | 4.82 | 4.94 | 4.78 | 4.23 | 19.4 | 4.06 | 21 | 0 |
| E004 | 4.65 | 4.08 | 3.53 | 3.37 | 5.4 | 4.22 | 21 | 0 |
| E005 | 6.43 | 4.58 | 5.35 | 3.31 | 10.9 | 6.12 | 44 | 0 |
| E006 | 4.86 | 5.49 | 5.41 | 4.61 | 15.5 | 4.72 | 38 | 0 |
| E007 | 2.9 | 3.79 | 5.55 | 2.84 | 12.2 | 4.86 | 35 | 0 |
| E008 | 4.6 | 4.11 | 3.5 | 4.37 | 2.3 | 5.09 | 39 | 0 |
Variables and options
Results
250 rows · example dataConceptual diagram: Model 3
Outcome: Performance
| Predictor | coeff | se | t | p | LLCI | ULCI |
|---|---|---|---|---|---|---|
| constant | 3.4031 | 2.2518 | 1.511 | .132 | -1.0325 | 7.8387 |
| Leadership | 0.2298 | 0.4849 | 0.474 | .636 | -0.7254 | 1.1850 |
| Autonomy | 0.2414 | 0.5767 | 0.419 | .676 | -0.8945 | 1.3774 |
| Tenure_Years | 0.1965 | 0.2319 | 0.847 | .398 | -0.2604 | 0.6533 |
| Leadership × Autonomy | -0.0381 | 0.1254 | -0.304 | .762 | -0.2850 | 0.2089 |
| Leadership × Tenure_Years | -0.0341 | 0.0524 | -0.651 | .516 | -0.1374 | 0.0691 |
| Autonomy × Tenure_Years | -0.0870 | 0.0577 | -1.507 | .133 | -0.2007 | 0.0267 |
| Leadership × Autonomy × Tenure_Years | 0.0179 | 0.0132 | 1.351 | .178 | -0.0082 | 0.0439 |
Note. R = .4030, R² = .1624, MSE = 0.6911, F(7, 242) = 6.705, p < .001. Highest-order interaction test: Leadership × Autonomy × Tenure_Years: ΔR² = .0063, F(1, 242) = 1.825, p = .178.
Conditional effects of Leadership at values of the moderators
| Autonomy | Tenure_Years | Effect | se | t | p | LLCI | ULCI |
|---|---|---|---|---|---|---|---|
| 2.989 | 2.684 | 0.1676 | 0.1145 | 1.463 | .145 | -0.0580 | 0.3932 |
| 2.989 | 7.100 | 0.2524 | 0.0804 | 3.139 | .002 | 0.0940 | 0.4108 |
| 2.989 | 12.216 | 0.3507 | 0.1180 | 2.973 | .003 | 0.1184 | 0.5831 |
| 4.035 | 2.684 | 0.1779 | 0.0932 | 1.910 | .057 | -0.0056 | 0.3614 |
| 4.035 | 7.100 | 0.3452 | 0.0635 | 5.441 | < .001 | 0.2202 | 0.4702 |
| 4.035 | 12.216 | 0.5391 | 0.0900 | 5.988 | < .001 | 0.3617 | 0.7164 |
| 5.092 | 2.684 | 0.1883 | 0.1576 | 1.195 | .233 | -0.1221 | 0.4988 |
| 5.092 | 7.100 | 0.4389 | 0.1043 | 4.209 | < .001 | 0.2335 | 0.6444 |
| 5.092 | 12.216 | 0.7293 | 0.1317 | 5.539 | < .001 | 0.4699 | 0.9886 |
Note. Moderator values are the 16th, 50th and 84th percentiles.
Interaction plot (Tenure_Years at its middle value)
Interpretation
The Leadership × Autonomy × Tenure_Years interaction is not statistically significant and adds 0.63% to the explained variance in Performance. There is no reliable evidence that the effect of Leadership depends on the moderators.
How to cite this tool
Using these results in a thesis, journal article, report or class assignment? Please cite this free tool so others can find it. It keeps the site free.
APA 7
Xavier, B. (2026). Three-Way Interaction Calculator [Web application]. FreeStatisticalTools.com. https://freestatisticaltools.com/three-way-interaction-calculator/
BibTeX
@software{xavier_moderatedmoderation_2026,
author = {Xavier, Bibin},
title = {Three-Way Interaction Calculator},
publisher = {FreeStatisticalTools.com},
year = {2026},
url = {https://freestatisticaltools.com/three-way-interaction-calculator/},
note = {Web application}
}Suggested sentence for your methods section: “The analysis was carried out with the free Three-Way Interaction Calculator tool on FreeStatisticalTools.com (Xavier, 2026).”
What is a three-way interaction (moderated moderation)?
A three-way interaction, or moderated moderation, tests whether the way W moderates the effect of X on Y itself depends on a second moderator Z. This tool estimates PROCESS Model 3 and probes the effect of X at every combination of W and Z.
When to use a three-way interaction (moderated moderation)
Use a three-way interaction when a moderation effect is expected to differ across levels of a second moderator.
Assumptions
- Linear relationships and correctly specified causal ordering (X before M before Y), justified by theory or design.
- Independent observations and, for OLS standard errors, constant residual variance (choose HC3 if this is doubtful).
- No unmeasured confounding of the paths between mediators and the outcome.
How to set up your data
One row per case and one numeric column per variable. Code dichotomous variables 0/1. Moderators with two values are probed at those two values; continuous moderators at the 16th, 50th and 84th percentiles, or the mean ± 1 SD.
How to use this tool
- Enter your data. Paste columns from Excel, Google Sheets or SPSS with variable names in the first row, or upload a CSV or Excel file. The example data shows the expected layout.
- Choose the variables. Select the x (predictor), y (outcome), moderator w and moderator z.
- Set the options. Fill in process model, confidence level, moderator values and standard errors.
- Read the results. Results update automatically. Read the plain-English interpretation, then use Copy table to paste APA-style tables into Word and Copy for the results sentence.
How to report a three-way interaction (moderated moderation) in APA style
Report the three-way interaction coefficient, its test and ΔR², then the conditional effects of X at combinations of W and Z.
Frequently asked questions
How do I interpret a three-way interaction?
If X × W × Z is significant, the two-way X × W interaction differs across levels of Z. Look at the conditional effects of X at combinations of W and Z.
Which lower-order terms are included?
All of them: X, W, Z, X × W, X × Z and W × Z, as PROCESS does.
How large a sample do I need?
Three-way interactions usually need several hundred cases to detect, because interaction effects are often small.
Related tools
PROCESS is a macro for SPSS, SAS and R written by Andrew F. Hayes. This tool is an independent implementation of the published regression methods and model numbering (Hayes, 2022) and is not affiliated with, endorsed by or derived from the PROCESS software.
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