Sample size and power planning
The smallest effect worth detecting is set from prior evidence or practical relevance, and the sample is sized to detect it with stated power, or to estimate it with stated precision, before recruitment begins.
GCRI · Labs
Statistics for research design
Probability and statistics decide what a study can conclude: how large a sample must be, where signal ends and noise begins, how big and how precise an effect is. They are also a common source of failure, through underpowered designs, misread significance tests and analytic flexibility, which is why this lab treats statistical planning as part of the protocol.
01Register
Statistics for research design on the record.
Method recordSTEM method
- MethodProbability and statistics
- Applied inLabs
- Data4 inputs
- Checks4 validation steps
- Canonical pageSTEM Commons
02Application
What probability and statistics does here.
Probability and statistics provide the mathematical framework for describing uncertainty and learning from data. They underpin estimation, testing and prediction in every risk discipline. In research and evidence, methods and modelling and innovation, statistical methods quantify the likelihood and uncertainty of losses across interconnected systems. They make the evidence behind risk decisions explicit and reproducible. The canonical description is on the STEM Commons.
Meta-analysis with bias assessment
Effects from many studies are pooled with random-effects models, heterogeneity is examined, and funnel plots and selection models test whether small-study effects or publication bias distort the pooled estimate.
Multiverse and specification analysis
Every defensible combination of exclusions, covariates and outcome definitions is run and reported together, so readers see how far a conclusion depends on analytic choices.
03Methods and evidence
How statistics for research design is modelled, measured and tested.
The model, its assumptions, its data and its uncertainty, in the form a scientist or engineer would check. Structures follow published methods. The values drawn are illustrative, not findings.
Model, equations and assumptions
The model structure used for statistics for research design, the assumptions it makes and how each is tested.
Risk of element i
Ri = f(Hi, Ei, Vi, Ci)hazard, exposure, vulnerability and coping capacityExpected annual loss
EAL = ∑k pk · Lkover events k with annual probability pkCoupled systems
xt+1 = A xt + B ut + εtA carries the couplings, u the shock, ε the error| Assumption | Why it is made | How it is tested |
|---|---|---|
| Hazard and exposure are independent within an event | Keeps the loss integral tractable | Compare with a copula fit on joint records |
| Couplings are linear near the operating point | Lets shocks propagate through A | Perturb beyond the linear range and compare |
| Vulnerability curves transfer between places | Local curves are rarely available | Validate against observed losses where they exist |
- Inputs
- versioned datasets with provenance
- Outputs
- distributions, never single numbers
- Code
- released with the model card and tests
- Reproduction
- same data, code, environment and seed
FAIR guiding principles · GO FAIR and FORCE11W3C PROV · World Wide Web ConsortiumGuidance on consistent treatment of uncertainties · IPCCCEOS Analysis Ready Data · Committee on Earth Observation Satellites
04Data
What the method consumes.
Datasets and records used by probability and statistics on this platform, with the role each plays and the label its values carry. Sources are listed in the source register.
| Data | Role | Label |
|---|---|---|
| Registered analysis plans | Fixing hypotheses and tests in advance | DECLARED |
| Raw experiment and trial data | Re-analysis and diagnostic checks | OBSERVED |
| Published effect sizes | Meta-analytic pooling | REPORTED |
| Simulation studies | Power and error-rate planning | MODELLED |
05Process
How the process runs.
Process
Statistics for research design: Catastrophe model pipeline
Catastrophe models usually have hazard, vulnerability, exposure and financial modules, and produce loss tables, average annual loss, exceedance curves, PML and TVaR.
01 Hazard
- 01Event catalogueDataset · Model developerThe hazard module holds a large catalogue of simulated events that represents a wide range of plausible scenarios.
- 03Hazard moduleModel · Model developerFor each event the hazard module gives the local hazard intensity that the vulnerability module reads.
02 Exposure and damage
- 02ExposureDataset · Ethics committeeThe exposure module houses the portfolio data, such as location-specific information.
- 04Vulnerability moduleModel · Model developerThe vulnerability module quantifies the expected damage to the exposures from an event.
03 Financial
- 05Financial moduleModel · Ethics committeeThe financial module calculates losses from all event scenarios. Ground-up, gross and net losses differ as shown below.
- 06Event loss tableDataset · Ethics committeeAn event loss table lists each event with its annual occurrence probability and its loss for the portfolio.
- 07Year loss tableDataset · Ethics committeeSome models also sample simulated years from event losses. This outline does not describe their format.
04 Metrics
- 08Exceedance probability curvesModel · Ethics committeeThe occurrence curve gives the chance that the largest loss in a year exceeds an amount. The aggregate curve does so for the sum of losses.
- 09AAL, PML and TVaRModel · Ethics committeeAverage annual loss sums event probability times loss. PML is one point on the occurrence curve.
05 Use of results
- 10Use of resultsDecision · Ethics committeeThe tail metrics are used when considering a portfolio’s exposure and the level of catastrophe reinsurance an insurer requires.
Outline of an external standard or method, from its public sources. It describes what the framework says, not a record of any run. It does not show that Nexus or any partner performs, certifies or approves a step. A gate is a step of the method, never a Nexus approval.
06Validation
How results are checked.
Results are checked through diagnostics, cross-validation and sensitivity to assumptions. Independent replication confirms findings.
| Check | How it is done |
|---|---|
| Planned versus reported tests | Every reported test is matched to the plan; unplanned tests are labelled exploratory |
| Assumption diagnostics | Residuals, independence and distributional assumptions are checked and reported |
| Multiplicity control | Corrections or hierarchical testing are applied where many outcomes or subgroups are tested |
| Independent re-analysis | A second analyst reproduces key estimates from the raw data |
Inference depends on assumptions about independence, distribution and sampling that may not hold. Small or biased samples limit reliability.
08Stewardship
Who maintains the method.
Systems Science and Modelling stewards probability and statistics for the Consortium and reviews how it is applied across platforms.
09Connected
Where this page leads across the Consortium.
10Questions
Questions and answers.
What are the limits of probability and statistics in this field?
Inference depends on assumptions about independence, distribution and sampling that may not hold. Small or biased samples limit reliability.
How are results checked?
Results are checked through diagnostics, cross-validation and sensitivity to assumptions. Independent replication confirms findings.
Are the values on this page real?
The data names, roles and checks are real descriptions of practice. The canvas shows a design of the method’s use, not a run; no result is reported here.
Where else is this method applied?
The canonical method page lists every platform that applies it.
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