statistical-power

# Statistical Power & Sample Size ## Overview Power analysis answers one of the most consequential questions in study planning: **how large a sample do you need to reliably detect an effect of a given size, and what could you detect with the sample you can afford?** An underpowered study wastes resources and produces inconclusive or irreproducible results; an overpowered one wastes participants, money, and (in clinical work) exposes more people to risk than necessary. Getting this right *before* data collection is the single highest-leverage statistical decision in a project. Four quantities are locked together for any given test: **sample size (n)**, **effect size**, **significance level (α)**, and **power (1 − β)**. Fix any three and the fourth is determined. Every calculation in this skill is some rearrangement of that relationship. This skill covers the two ways to do power analysis: - **Closed-form** formulas (fast, exact for standard tests) — see `references/closed_form_recipes.md`. - **Simulation / Monte Carlo** (works for *any* design or model you can simulate and analyze) — see `references/simulation_based_power.md`. For choosing and converting effect sizes — usually the hardest part — see `references/effect_sizes.md`. ## When to Use This Skill - Determining required sample size before collecting data (a priori power analysis) - Finding the minimum detectable effect (MDE) for a fixed, already-determined sample size - Producing power curves (power vs. n, or pow...