Statistical Analysis

Workflow inheritance

For complex tasks, first apply the global codex-workflow-protocol skill. This skill only adds domain-specific knowledge, gates, and validation requirements. It must not weaken the global completion, escalation, or verification rules.

Workflow

1. Translate the user question into estimand, outcome, predictors/groups, unit of analysis, and dependency structure.
2. Inspect data quality, missingness, measurement scale, outliers, and study design before choosing tests.
3. Choose the simplest defensible analysis: descriptive summary, hypothesis test, regression, survival model, Bayesian model, or simulation.
4. Check assumptions and identify robust or nonparametric alternatives.
5. Report effect sizes, uncertainty intervals, p-values only when appropriate, multiplicity caveats, and practical significance.
6. Validate by rerunning calculations, checking sensitivity choices, and making the code reproducible.

Completion boundary

Do not claim completion from a smoke simulation, tiny dryrun, notebook import, or one successful toy run alone. Simulation, inference, or theorem-heavy research coding is complete only when the estimand, model assumptions, data-generating or likelihood assumptions, and requested validation evidence are checked at the intended scale or a precise residual risk is reported.

Bayesian/domain-specific acceptance should include prior justification, convergence diagnostics where applicable, posterior predictive or sensitivity checks where applicable, and a clear distinction between exploratory and confirmatory claims.

References

• Read references/statistical-decision-notes.md for test/model selection and reporting conventions.
• Read references/legacy-full-skill.md for older examples and extended background.
• Use statsmodels for Python model implementation, pymc for PyMC models, bayesian-ppl-diagnostics for convergence and PPL diagnostics, and simpy for process-based simulation.

Validation

• The analysis states assumptions, missing-data handling, and unit of analysis.
• Results distinguish exploratory, confirmatory, and sensitivity analyses.
• Budget warnings for full Bayesian/statistics domain installs are advisory only.