STATISTICAL METHOD
Monte Carlo Simulation Analysis
Statistical Consulting for Simulation Studies
We design and run Monte Carlo simulation analysis around your research question, building realistic data-generating scenarios, choosing enough replications, and reporting bias, coverage, power or error rates with Monte Carlo error, in publication-ready form.
No Commitment Required
Strictly Confidential
In-House PhD-Level Statisticians
Fixed Project Fee
Same-Day Response
METHOD OVERVIEW
What Is Monte Carlo Simulation?
A Monte Carlo simulation study generates many artificial datasets from a specified data-generating mechanism, applies analysis methods to each, and summarizes performance across the replications, such as bias, interval coverage, Type I error or power. It plans sample size where no analytic formula exists and compares estimators under stated conditions, and its conclusions hold only for the scenarios simulated. Markov chain Monte Carlo, the sampler used to fit most Bayesian models, is a related computational engine, not a simulation study. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, provides Monte Carlo simulation analysis within your study design, with the relevant checks, effect estimates, uncertainty measures, interpretation and publication-ready reporting.
WHEN TO ENGAGE
When Is a Simulation Study Appropriate?
A simulation study fits questions about how a design or method behaves when no formula answers them, and these are the research situations in which researchers most often ask us to build one.
Power for a Complex Design A study has clustering, dropout or several outcomes, no closed-form power formula applies, and Monte Carlo power analysis estimates power and the sample size needed.
Comparing Estimators or Methods Two analysis strategies, or a new estimator, need comparing on bias, coverage and error rates under conditions you can specify and control.
Checking Type I Error Control A planned model, adaptive rule or multiplicity strategy may inflate false positives, and simulation under the null checks it before the study begins.
Simulation Questioned by Reviewers A reviewer doubted the generating assumptions or the number of replications. Independent Statistical Review checks the scenarios and the Monte Carlo error.
ANALYTICAL APPROACH
How We Run a Simulation Study
Within the family of Bayesian & Computational Methods, a simulation is built only after the question it must answer has been defined.
Aims and Data Generation We follow the ADEMP structure, setting out aims, data-generating mechanisms, estimands, methods and performance measures before any code runs, so the study answers one stated question.
Realistic Assumptions Conclusions are only as credible as the generating assumptions, so we take values from pilot data or the literature and vary them over plausible and adverse scenarios, not a single case.
Replications and Error Every performance estimate has a Monte Carlo standard error. We choose enough replications to make it small against the differences that matter, and report it beside each estimate.
Seeds and Scenarios We fix the seed, store the random-number state for each scenario and record software versions, so the whole study reruns identically and any single scenario can be rerun alone.
DELIVERABLES
What You Receive
As part of our Research Planning & Study Design service, the simulation is delivered with the scenarios, checks and files needed to report and defend it.
Data & Variable Review Pilot data, published estimates and the planned design are reviewed to set defensible parameter values, covariate structure, clustering and missingness for the simulated data.
Method-Specific Checks The generator is validated by recovering known parameters, non-converging fits are counted and reported, and Monte Carlo error is checked at the chosen number of replications.
Statistical Results Bias, empirical standard error, coverage, Type I error or power for each scenario and method, each with its Monte Carlo standard error, and the sample size that meets your target.
Publication-Ready Tables & Figures Scenario tables and figures, such as power curves or coverage plots with Monte Carlo error shown, formatted for the journal, an APA 7 report or the protocol.
Interpretation Results are written for the scenarios simulated, with their dependence on the assumptions made explicit, and with no claim beyond the conditions that were actually tested.
Reproducible Analysis Files R scripts, Python code, Stata do-files or SAS programs are provided with the seeds and scenario definitions, so every table can be regenerated or rerun under new assumptions.
ALTERNATIVE METHODS
When Another Method May Be More Appropriate
A simulation answers how a method behaves across generated data, so it is not always the right tool. These methods fit when a formula, your own sample or a fitted model answers the question.
01
Independent Samples t-Test
Power for a standard two-group mean comparison has an exact analytic solution, so simulating it adds effort without adding any accuracy to the answer.
02
Bootstrapping
When you hold a real sample and need the uncertainty of a statistic, resampling that sample serves, whereas a simulation draws data from an assumed model.
03
Linear Mixed Models (Multilevel Modeling)
Once clustered or repeated data are collected, a mixed model analyzes them directly, and simulation is used only to plan or stress-test such a model beforehand.
04
Bayesian Analysis
When the aim is a posterior distribution for parameters from your own data, a Bayesian model fitted with MCMC applies, not a study of how methods perform.
CASE EXAMPLE
How We Work in Practice
An illustration of how a simulation study moves from a defined question to a reportable, defensible recommendation.
ILLUSTRATIVE EXAMPLE · PRODUCT RELIABILITY ENGINEERING · UNITED STATES
An electronics manufacturer's reliability lab planned a life test of a new component and needed the sample size for a trustworthy interval on its tenth percentile of life.
Failures would be rare and most units would survive the planned test, so large-sample planning formulas and the standard interval’s coverage were both in doubt. Before any test data existed, we specified the simulation: Weibull lifetimes with parameters from the predecessor component and wider adverse scenarios, censoring at the planned test length, and Wald and likelihood-ratio intervals compared on coverage and width. We used enough replications to keep the Monte Carlo standard error of coverage small, fixed the seed and counted failed fits. We stated that findings held only for the assumed Weibull form.
Outcome: The lab received the scenario definitions, the coverage and width of both intervals with Monte Carlo standard errors, the sample size meeting the precision target, and the code with its seed.
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 Simulation Studies
Simulation studies are programmed in R, Python, Stata or SAS, with the seed, scenarios and software versions recorded in the code provided.
RESEARCH DISCIPLINES
Simulation Studies Across Research Fields
Simulation studies appear across research fields, each with its own designs, plausible parameter ranges 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 the simulation assumptions and number of replications checked, and a reproducible file for later revisions.
“Our dataset looked straightforward until we got into Monte Carlo Simulation and realized whether the simulation assumptions and number of replications were adequate. The team sorted out the analytical setup and gave us a clear explanation of what could and could not be concluded. We also received a reproducible analysis file, which made later revisions much easier.”
RESEARCH RESPONSIBILITY
Statistical Support Without Taking Over Your Research
We provide the statistical work for your simulation study, 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 simulation study, 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 research question, the scenarios you judge realistic, interpretation and conclusions remain with you, and our interpretation stays within what the simulated conditions support.
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 Monte Carlo Simulation
Short answers to what researchers ask before a statistical simulation study, from replications and MCMC to confidentiality and the assessment process.
Do I need a simulation, or is a power formula enough?
Often a formula is enough. For standard designs, such as a two-group mean comparison or a simple regression, analytic power calculations are exact or accurate and easier to defend. Simulation earns its cost when the design has clustering, dropout, several outcomes, an adaptive rule or an estimator with unknown behavior, and we say plainly which case applies.
How many replications does a simulation study need?
There is no universal number. The Monte Carlo standard error of each estimate falls as replications increase, so we choose the number that makes it small relative to the differences that matter and report it. Estimating a 95% coverage rate to within about a percentage point takes on the order of a thousand replications or more.
Is MCMC the same as a Monte Carlo simulation study?
No. MCMC draws dependent samples from a posterior distribution to fit a Bayesian model to your data, whereas a simulation study generates many artificial datasets to evaluate how a method performs. Both use random numbers, but they answer different questions, and a simulation study can fit Bayesian models inside it.
Can you review an analysis that has already been completed?
Yes, we can review a completed simulation study before submission or a response to reviewers. We check the aims and scenarios, how realistic the generating assumptions are, the number of replications and Monte Carlo error, how non-converging fits were handled and the reporting, and confirm what stands or needs to change.
How do you protect my dataset and research confidentiality?
Your pilot data, simulation code 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
Monte Carlo Simulation?
Share your research question, study design and data. We assess whether a simulation study 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