power-and-sample-sizelisted

# Skill: power-and-sample-size > **Invoked by:** `applied-statistician` (primary). Prerequisite for [`../experiment-analysis/SKILL.md`](../experiment-analysis/SKILL.md) — no experiment ships without it. > > **When to invoke:** "how big a sample do I need?"; "is this test big enough to trust a null result?"; planning any A/B test or comparison. > > **Output:** required n per group (or achievable power/MDE), the four inputs that produced it, and a runnable snippet. ## The four interlocking quantities Fix any three; the fourth is determined: | Quantity | Meaning | Conventional default | |---|---|---| | **α** (significance) | tolerated false-positive rate | **0.05** | | **power** (1 − β) | probability of detecting a true effect of the target size | **0.80** (Cohen 1988) | | **effect size / MDE** | the smallest effect worth detecting | business-meaningful; else Cohen d = 0.2/0.5/0.8 | | **n** | sample size (per group) | the output you usually solve for | ## Procedure 1. **Pin the MDE first** — the smallest effect that would change the decision. Prefer a business-meaningful number (e.g., "a 1.5-point conversion lift pays for the change"); fall back to Cohen's conventions only when no pilot/benchmark exists. 2. **Pick α and power** (defaults 0.05 / 0.80 unless the cost of a false positive/negative argues otherwise). 3. **Match the calculation to the planned test** (two-proportion for conversion rates, two-sample t for a continuous mean, etc.). 4. **Solve for n** and report it