statistics-probability-guide skill

Overview

This skill is a compact, expert-oriented guide to statistics and probability covering probability theory, common distributions, hypothesis testing, regression, and Bayesian methods. It consolidates practical rules, formulas, and workflows for applied analysis while flagging areas that need updated references. Use it as a structured checklist and teaching aid for statistical tasks and model validation.

How this skill works

The skill inspects key topics and provides concise explanations, decision rules, and example workflows for frequent statistical problems. It highlights validation checkpoints, known gaps, and a research checklist to ensure concepts and recommendations remain current. Modules can be loaded topic-by-topic after verification to tailor guidance to a specific analysis or teaching need.

When to use it

• Designing hypothesis tests and interpreting p-values or confidence intervals.
• Choosing and applying probability distributions for modeling data.
• Selecting and validating regression models (linear, logistic, regularized).
• Implementing Bayesian workflows and prior-posterior checks.
• Teaching core statistical concepts or preparing reproducible analysis notes.

Best practices

• Always verify assumptions (independence, normality, homoscedasticity) before applying parametric methods.
• Document data provenance and preprocessing steps to support reproducibility.
• Prefer effect sizes and uncertainty intervals alongside p-values.
• Use cross-validation and holdout sets to assess model generalization.
• Record new sources and update the research checklist when integrating recent findings.

Example use cases

• Running a clinical pilot analysis: choose appropriate tests, compute power, and report intervals and assumptions.
• Building a predictive model: compare linear, regularized, and tree-based models with cross-validation.
• Teaching a short course: present concise modules on distributions, inference, and Bayesian updating.
• Auditing an analysis: follow the checklist to confirm assumptions, transformations, and result robustness.
• Converting a legacy statistical guide into an up-to-date reference by logging new literature and evidence.

FAQ