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.