How to use
- Choose "From coefficients" and enter a (X → M) with its SE and b (M → Y, controlling X) with its SE.
- Or choose "From raw data" and paste three columns, X, M and Y, one row per case.
- The indirect effect a × b is significant when the Sobel p is below 0.05 or the bootstrap CI excludes 0.
- Copy the APA line.
Options explained
- a, b, c, c′
- a is X → M, b is M → Y controlling for X, c is the total effect X → Y and c′ the direct effect controlling for M. The indirect effect is a × b = c − c′.
- Sobel, Aroian, Goodman
- Three formulas for the SE of the indirect effect; Aroian adds a term and Goodman subtracts it. They agree closely in large samples; Sobel is the one usually reported.
- Bootstrap
- The data are resampled with replacement 5000 times, a × b is computed each time, and the 2.5th and 97.5th percentiles form the 95% CI. It doesn't assume a normal indirect effect and is now preferred.
Worked example
From coefficients: the default is a = 0.5 (SE 0.1) and b = 0.4 (SE 0.12).
| Test | SE | z | p |
|---|---|---|---|
| Sobel | 0.0721 | 2.774 | 0.0055 |
| Aroian | 0.0731 | 2.736 | 0.0062 |
| Goodman | 0.0711 | 2.813 | 0.0049 |
The indirect effect of 0.2 is significant. APA style: Sobel z = 2.77, p = .006.
From raw data: the sample has 12 rows of X, M and Y.
| Path | B | SE | p |
|---|---|---|---|
| a: X → M | 0.904 | 0.073 | < 0.001 |
| b: M → Y (controlling X) | 0.954 | 0.220 | 0.002 |
| c: X → Y (total) | 1.138 | 0.084 | < 0.001 |
| c′: X → Y (direct) | 0.275 | 0.206 | 0.214 |
The indirect effect a × b = 0.863, with a 95% bootstrap CI (5000 resamples) of 0.344 to 1.603. It excludes 0, so the mediation is significant and accounts for about 76% of the total effect.
Frequently asked questions
Standardized or unstandardized coefficients?
a, b and their SEs must come from the same output. Usually the unstandardized B and SE from your regression.
If c′ isn't significant, is it "full mediation"?
That was the old language. Most methodologists now recommend reporting the indirect effect with its CI and the direct effect, without the full/partial labels.
Does it match the PROCESS macro?
The paths and the Sobel test match. Bootstrap intervals differ slightly from run to run in PROCESS because of random resampling, usually in the third decimal. This tool uses a fixed seed, so the same data always give the same interval.
Can it handle covariates or several mediators?
No, only simple mediation with one X, one M and one Y.
Privacy
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