Sobel Test Z Mediation Calculator
Classic Sobel first-orderdeltaZab/sqrt(b²sa²+a²sb²), zero-pathcovarianceassumption; not Aroian/Goodman variant, bootstrap or causal identification. Actual independently qualified instrument/cohort/matching units; no diagnosis, causal outcome, validated personal prediction or universal clinical cutoff.
Description
The Sobel statistic uses a first-order variance approximation for a product of paths.
The Sobel statistic uses a first-order variance approximation for a product of paths.1
The classic form assumes zero covariance between the estimated path coefficients. The calculation and input requirements are explained below.
When to use Sobel Test Z Mediation Calculator
Enter finite path coefficients and nonnegative path standard errors.
How to use Sobel Test Z Mediation Calculator and how it works
- Prepare the measurements or independently established model inputs described below, with matching units and observation scope.
- Enter the required fields and run Sobel Test Z Mediation Calculator.
- Read the result fields using the formula, output units, signs and ordering explained below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualPathA | Actual Path A. Use the units and matching context stated in the calculation below. | number | Required; finite; other constraints below |
| actualPathB | Actual Path B. Use the units and matching context stated in the calculation below. | number | Required; finite; other constraints below |
| actualPathASe | Actual Path A Se. Use the units and matching context stated in the calculation below. | number | Required; nonnegative; finite; other constraints below |
| actualPathBSe | Actual Path B Se. Use the units and matching context stated in the calculation below. | number | Required; nonnegative; finite; other constraints below |
Enter finite path coefficients and nonnegative path standard errors. Require b squared times SE(a) squared plus a squared times SE(b) squared to be positive. Divide ab by its square root. No p-value, path covariance, Aroian correction or causal inference is supplied.
sobelZ=a*b/sqrt(b^2*SEa^2+a^2*SEb^2) Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.value | Numeric result under the formula and output units explained above. | number |
{
"input": {
"actualPathA": 2,
"actualPathB": 3,
"actualPathASe": 1,
"actualPathBSe": 1
},
"output": {
"result": {
"value": 1.6641005886756874
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Simple Slope at +/-1 SD Calculator for a complementary operation: A linear interaction model has a predictor slope that depends on moderator value.
Use Mediation Indirect Effect a*b Calculator for a complementary operation: A linear mediation product multiplies two compatible path coefficients.
References
-
Sobel Test Z Mediation Calculator — tool.io
Similar or alternative tools
- Simple Slope at +/-1 SD Calculator
A linear interaction model has a predictor slope that depends on moderator value.
- Mediation Indirect Effect a*b Calculator
A linear mediation product multiplies two compatible path coefficients.