Calculator Inputs
Example Data Table
| Path | Meaning | Estimate | Standard Error |
|---|---|---|---|
| a | Exposure to mediator | 0.42 | 0.11 |
| b | Mediator to dichotomous outcome | 0.70 | 0.18 |
| c | Total exposure effect | 0.54 | Not required |
| c prime | Direct exposure effect after mediator | 0.25 | 0.17 |
Formula Used
Indirect effect: a × b
Sobel standard error: square root of b²SEa² + a²SEb²
z statistic: indirect effect divided by its standard error
Confidence interval: indirect effect ± critical z × standard error
Indirect odds ratio: exp(a × b)
Approximate proportion mediated: indirect effect divided by total effect c, multiplied by 100
For dichotomous outcomes, b, c, and c prime usually come from logistic regression. These values are interpreted on the log odds scale before odds ratios are calculated.
How To Use This Calculator
- Fit the mediator model and copy the exposure coefficient as the a path.
- Fit the logistic outcome model and copy the mediator coefficient as the b path.
- Enter the total exposure effect from the outcome model without the mediator.
- Enter the direct exposure effect from the outcome model with the mediator.
- Add standard errors for a and b.
- Choose alpha, then press calculate.
- Download CSV or PDF results for reporting.
Understanding Dichotomous Mediation
Mediation explains how an exposure may influence an outcome through another variable. When the outcome is dichotomous, the final model often uses logistic regression. This calculator works with path estimates from fitted models. It keeps the workflow simple, but it still reports the main values researchers usually review.
Why Binary Outcomes Need Care
A binary outcome has two states, such as yes or no. Logistic models estimate log odds, not raw probability changes. Because odds ratios are not collapsible, the indirect, direct, and total paths should be interpreted on the chosen model scale. The calculator therefore shows both logit scale effects and odds ratio summaries.
Core Calculation Idea
The exposure to mediator path is called a. The mediator to outcome path is called b. Their product gives the approximate indirect effect. The total exposure effect is c. The remaining direct exposure effect is c prime. Comparing these values helps describe whether the mediator carries part of the association.
What The Results Mean
The indirect effect shows the estimated pathway through the mediator. Its odds ratio is found by exponentiating the product. A value above one suggests higher odds through that pathway. A value below one suggests lower odds. The Sobel statistic and confidence interval provide a quick uncertainty check.
Best Use Cases
Use this tool after fitting the required regression models elsewhere. Enter coefficients and standard errors from those models. The method is useful for teaching, quick checks, manuscript tables, and sensitivity screening. It should not replace a complete causal mediation analysis when assumptions are complex.
Good Reporting Practice
Report the model type, covariates, sample size, coefficient scale, and confidence level. Explain whether the mediator is continuous or binary. State that the outcome model is logistic. When possible, compare this approximate result with bootstrap or simulation based estimates. Clear reporting makes mediation findings easier to audit.
Limits To Remember
This calculator assumes compatible models and valid path estimates. It does not test confounding, exposure mediator interaction, or temporal order. It also cannot judge whether the selected mediator is causal. Treat the output as a structured summary. Use subject knowledge and study design before drawing strong conclusions. Always review assumptions again when publishing regulated or clinical research findings.
FAQs
What is dichotomous outcome mediation?
It is mediation analysis where the final outcome has two categories. Examples include pass or fail, recovered or not recovered, and churned or retained.
What does the a path mean?
The a path measures how the exposure relates to the mediator. It usually comes from a regression model where the mediator is the dependent variable.
What does the b path mean?
The b path measures how the mediator relates to the binary outcome, usually after adjusting for the exposure and selected covariates.
Why does this calculator use logit coefficients?
Binary outcomes are often modeled with logistic regression. Logistic regression produces log odds coefficients, which can be converted into odds ratios.
What is the indirect odds ratio?
It is exp(a × b). It summarizes the mediated pathway on an odds ratio scale, based on the entered logit path estimates.
Is the Sobel test enough for publication?
It may be useful for screening and teaching. Many studies also report bootstrap, simulation, or causal mediation estimates when assumptions are important.
Can I use binary mediators?
You can enter coefficients from compatible fitted models. Interpret results carefully, because model scale and link functions affect mediation estimates.
What should I report with the result?
Report the models, covariates, coefficients, standard errors, confidence level, sample size, and whether values are on the logit or odds ratio scale.