| name | statistical-problem-formulation |
| description | Formulate statistical research problems with formal notation, target parameters, assumptions, hypotheses, evaluation criteria, and theory targets.
|
| metadata | {"category":"domain","trigger-keywords":"problem formulation,statistical formulation,estimand,assumptions,data model,hypothesis,theory target","applicable-stages":"1,2,3,4,5","priority":"1"} |
Statistical Problem Formulation
Overview
Use this skill before any method design, theory, experiment, or report writing.
The goal is to transform a broad topic into a precise statistical problem.
Required Formulation Elements
| Element | Questions |
|---|
| Observed data | What is observed? What is the sample size? Are samples iid, dependent, clustered, censored, or selected? |
| Data model | What family of distributions or data-generating processes is considered? |
| Target | What parameter, decision, prediction, or risk is the object of study? |
| Assumptions | What must hold for the target to be identifiable or the method to work? |
| Hypotheses | What claims should be supported, refuted, or made inconclusive? |
| Criteria | What metrics define success or failure? |
| Theory target | What property should be derived: bias, variance, consistency, rate, coverage, error bound, robustness, or impossibility? |
Handoff Schema
The problem formulation should be precise enough to support this structured
handoff:
