STATISTICAL METHOD
Mediation Analysis
Statistical Consulting for Indirect Effects
We apply mediation analysis within your study design, estimating the indirect effect directly with a bootstrap confidence interval, examining time order and confounding, and stating plainly what the design can and cannot say about mechanism.
No Commitment Required
Strictly Confidential
In-House PhD-Level Statisticians
Fixed Project Fee
Same-Day Response
METHOD OVERVIEW
What Is Mediation Analysis?
Mediation analysis asks whether the effect of an exposure on an outcome operates through an intermediate variable, the mediator. In linear models the indirect effect is the product of the exposure-to-mediator path and the mediator-to-outcome path, and the direct effect is what remains. Because that product is not normally distributed, its uncertainty is estimated with a bootstrap or Monte Carlo confidence interval, not with separate significance tests. Reading the indirect effect as a causal pathway requires assumptions about confounding and time order that the data alone cannot verify. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, provides mediation analysis within your study design, with the relevant checks, effect estimates, uncertainty measures, interpretation and publication-ready reporting.
WHEN TO ENGAGE
When Is Mediation Analysis Appropriate?
Mediation fits a question about how or why an exposure changes an outcome, and these are the research situations in which researchers most often ask us to plan or confirm the model.
Mechanism Behind an Intervention A trial or program reports an effect, and the team has a measured mediator, such as self-efficacy or adherence, that is hypothesized to carry part of it.
Mediator Measured Before Outcome Exposure, mediator and outcome were measured at successive times, so the order is built into the design and the indirect effect can be estimated and interpreted with care.
Cross-Sectional Mediation Question All variables were collected at one time, and the model can show consistency with a pathway but not its order, which the interpretation has to say plainly.
Reviewing a Reported Mediation The mediation rested on separate significant paths, or a reviewer asked for the indirect effect itself. Independent Statistical Review examines the estimate and its assumptions.
ANALYTICAL APPROACH
How We Apply Mediation Analysis
Within the family of Regression & Predictive Modeling, a mediation model is specified from the causal story first, and the estimation follows from the design.
Causal Structure and Time Order We draw the assumed structure of exposure, mediator, outcome and confounders, and check that the measurement order supports it. A cross-sectional model cannot show which variable came first.
Confounding of the Mediator Randomizing the exposure protects its links to the mediator and the outcome, but not the mediator-outcome link. We list its confounders, adjust for those measured and probe unmeasured ones.
Estimating the Indirect Effect We estimate the product of the two paths directly and build its interval by percentile bootstrap or Monte Carlo sampling, not by the Sobel test or the outdated causal steps of Baron and Kenny.
Scale, Outcome Type and Size With binary or count outcomes the product of coefficients mixes scales, so we use potential-outcomes definitions. Indirect effects also need larger samples than single paths to be estimated precisely.
DELIVERABLES
What You Receive
As part of our Quantitative Data Analysis service, the mediation model is delivered with the estimates, checks and files needed to report and defend it.
Data & Variable Review Variable timing, the measurement of the mediator, missing data and covariates that could confound the mediator-outcome link are reviewed before the model is specified.
Method-Specific Checks Each path model's residuals, influential cases, exposure-mediator interaction and the sensitivity of the indirect effect to unmeasured confounding are examined, with the bootstrap settings recorded.
Statistical Results The a, b, direct and total effects with 95% confidence intervals, the indirect effect with its bootstrap or Monte Carlo interval, and the sensitivity analysis results.
Publication-Ready Tables & Figures A path diagram with estimates, an effects table and a plot of the indirect effect with its interval, formatted to APA 7, AGReMA reporting or the journal's requirements, ready to insert.
Interpretation The indirect effect is described as the part of the association that runs through the mediator under stated assumptions, with causal wording only where the design supports it.
Reproducible Analysis Files SPSS syntax calling Hayes's PROCESS macro, R scripts, Stata do-files or Mplus inputs reproduce every model, so results can be rerun if the data or the covariate set change.
ALTERNATIVE METHODS
When Another Method May Be More Appropriate
We choose the model by the structure of the question. These methods fit better when several pathways run at once, constructs are latent, repeated measures fix the order or an indirect effect varies.
01
Path Analysis
When several mediators, outcomes or chains of mediators belong in one model, a path model estimates them together, with fit statistics and a full set of indirect effects.
02
Structural Equation Modeling (SEM)
When the mediator or outcome is a latent construct measured by several items, a structural model corrects the measurement error that attenuates regression-based paths.
03
Cross-Lagged Panel Models
When exposure and mediator are measured repeatedly, lagged paths give the time order that a single-wave mediation model assumes but cannot show from its own data.
04
Moderated Mediation
When the indirect effect is expected to be stronger for some people than for others, a conditional model formally tests whether it depends on a moderator.
CASE EXAMPLE
How We Work in Practice
An illustration of how a mechanism question moves from a planned model to an indirect effect that can be reported with its limits.
ILLUSTRATIVE EXAMPLE · PARKS AND RECREATION PROGRAM RESEARCH · UNITED STATES
A city parks and recreation department randomized residents to tailored or standard walking reminders and wanted to know whether engagement carried part of the effect on activity.
The draft plan followed the causal-steps sequence, requiring a significant total effect first. Before outcomes were seen, we replaced it with direct estimation of the indirect effect and a percentile bootstrap interval, with no precondition on the total effect. Reminders were randomized but engagement was not, so baseline activity, age and device type were adjusted for, and engagement was measured in weeks 1 to 4 and activity at week 12, fixing the order. A sensitivity analysis asked how strong unmeasured confounding of engagement and activity would have to be to remove the indirect effect.
Outcome: The team received the indirect, direct and total effects with 95% confidence intervals, the bootstrap setup, the confounding sensitivity analysis, a path figure and the analysis syntax.
This example does not describe a real client or project. We never share details of actual client work, in line with the confidentiality we promise every researcher. This illustrative example is included to show the type, scope, and standard of work involved in this kind of analysis.
SOFTWARE
Statistical Software for Mediation Models
Mediation models run in SPSS, R, Stata and Mplus, including Hayes's third-party PROCESS macro in SPSS, with syntax or scripts provided where applicable.
RESEARCH DISCIPLINES
Mediation Questions Across Research Fields
Mediation appears wherever a mechanism is proposed, each field with its own measurement timing, confounders and reporting conventions.
A Defined Process for Your Analysis
We review your dataset, research question and design before any work begins, so the scope, deliverables, timeline and fixed project fee are clear from the outset.
01
Share Your Research Materials
Send your dataset, research question, study design and any existing analysis plan or output. We will let you know if anything else is needed to assess the project.
02
Receive Your Assessment
Your statistically trained Research Coordinator reviews the project and confirms the required analysis, deliverables, timeline and fixed project price before work begins.
03
Analysis & Delivery
Once you confirm the scope, an in-house statistician completes the agreed analysis and delivers the outputs, interpretation and reporting files.
RESEARCHER VOICE
What Researchers Say
Feedback from a researcher who needed to estimate and report the indirect effect, not rely on separate significance tests.
“I had already started the Mediation Analysis, but I was not confident about how to estimate and report the indirect effect rather than relying on separate significance tests. The team checked the setup against our study design, explained the decisions in plain language, and returned results we could actually use. The final output was concise, clearly interpreted, and ready to use in our research reporting.”
RESEARCH RESPONSIBILITY
Statistical Support Without Taking Over Your Research
We provide the statistical work for your mediation model, and the study, its meaning and its authorship stay entirely with you.
Agreed Statistical Support We provide the agreed methodological, analytical and statistical reporting support for your mediation model, within the scope confirmed before work begins.
No Intellectual Contribution OnlineSPSS claims no intellectual contribution to your research. Our work is statistical support, and authorship remains yours.
Your Research Decisions The hypothesized mechanism, the mediator chosen and the causal reading of the indirect effect remain with you, and our interpretation stays within what the design supports.
Confidential Handling Research data and project details are handled confidentially and are not published. An NDA is available where required, and can be arranged before sensitive materials are shared.
FREQUENTLY ASKED QUESTIONS
Questions About Mediation Analysis
Short answers to what researchers ask before testing a mechanism, from total effects and causal claims to confidentiality and the assessment process.
Do I still need a significant total effect first?
No. The causal-steps approach of Baron and Kenny required one, but an indirect effect can exist when the total effect is not significant, for example when direct and indirect effects have opposite signs. We estimate the indirect effect itself, with a bootstrap or Monte Carlo interval, and report the total effect beside it.
Can I claim mediation from cross-sectional data?
Not as a causal pathway. A model on data collected at one time can show whether the pattern is consistent with the hypothesized indirect effect, but it cannot show which variable came first, and a model with mediator and outcome reversed often fits equally well. Stronger evidence comes from a randomized exposure, a mediator measured before the outcome or repeated measurement, and the wording follows the design.
Should I use PROCESS, SEM or causal mediation methods?
PROCESS is a third-party macro by Hayes for SPSS, SAS and R that fits regression-based models with bootstrap intervals, and it suits observed variables and a continuous outcome. Latent constructs call for SEM, several linked outcomes for path analysis, and binary outcomes or exposure-mediator interaction for potential-outcomes causal mediation. We choose by design and state why.
Can you review an analysis that has already been completed?
Yes, we can review a completed mediation analysis before submission or a response to reviewers. We check the time order, the confounders of the mediator-outcome link, the interval for the indirect effect, the scale of the effects and the causal wording, and confirm what stands or needs to change.
How do you protect my dataset and research confidentiality?
Your dataset, output files and any protocol or analysis plan are handled confidentially, and project information is not published. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
Still have a question? Find more answers in our full FAQ.
NEXT STEP
Need Support With a
Mediation Model?
Share your research question, study design and data. We assess whether a mediation model fits your question and confirm the approach before any work begins.
No Commitment Required
Strictly Confidential
Fixed Project Fee
In-House PhD-Level Statisticians
Same-Day Response
Serving Researchers Since 2014