# Statistical Power > Calculate study sample size, power, minimum detectable effects, and sensitivity curves for a planned analysis. Use experimental-design to choose or lay out the study; use an analysis workflow for collected data. - Skill: `c1trusovo831/statistical-power` (Agent Skill, multi-file: 9 files) - Install (CLI): `npx skillmds@latest add c1trusovo831/statistical-power` - Raw SKILL.md: https://api.skillmd.com/api/skills/c1trusovo831/statistical-power/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: Productivity - License: MIT license - Author: C1TRuSovo831 (https://skillmd.com/u/c1trusovo831) - Updated: 2026-09-22 - Page: https://skillmd.com/skills/c1trusovo831/statistical-power --- # Statistical Power & Sample Size Calculate required sample size, power, or MDE for the planned analysis. For a fixed test and its assumptions, sample size, effect size, significance level (α), and power (1 − β) determine one another. State assumptions and report sensitivity to plausible effects rather than presenting an unsupported single sample size. Choose the study structure with **experimental-design** before calculating power; return to it when laying out the final allocation. Analysis of collected data is a separate workflow; use the relevant analysis skill if available. ## The one decision that drives everything: the effect size Power calculations are only as trustworthy as the effect size you feed them. **Do not invent a number.** Use, in rough order of preference: 1. A **minimally important effect** — the smallest effect that would actually change a decision or matter scientifically/clinically (the "smallest effect size of interest", SESOI). This is the most defensible basis: you power to detect what matters, not what you hope to see. 2. A **pilot or prior-study estimate**, but shrink it — published and pilot effects are inflated by publication bias and the winner's curse. Powering on a raw pilot estimate routinely underpowers the real study. 3. A **convention** (Cohen's small/medium/large) only as a last resort, and say so explicitly. Whatever you pick, run a **sensitivity analysis**: report how required n changes across a plausible range of effect sizes, not a single point. A power analysis presented as one number hides its biggest source of uncertainty. See `references/effect_sizes.md` for benchmarks and conversions between d, f, r, η², odds ratios, and Cohen's h/w. > **Avoid post-hoc ("observed") power.** Computing power from the effect size you just estimated is circular: it is a deterministic function of the p-value and tells you nothing new. If a study is already done and you want to know what it could have detected, report a **sensitivity analysis** (MDE at the achieved n) or, better, the confidence interval around the observed effect. This is a common reviewer complaint — do not produce observed power even if asked without flagging the issue. --- ## Select the calculation | Task | Read | | --- | --- | | Choose or convert an effect size | [Effect sizes](references/effect_sizes.md) | | Standard t-tests, ANOVA, proportions, correlations, chi-square, or linear regression | [Closed-form argument tables and recipes](references/closed_form_recipes.md) | | GLMs, mixed/repeated-measures models, cluster trials, survival, mediation, interactions, or other nonstandard analyses | [Simulation-based power](references/simulation_based_power.md) | | Install dependencies or call bundled `power.py` / `simulate_power.py` | [Calculation setup and examples](references/calculation_workflow.md) | | Write or audit a sample-size justification | [Reporting template, pitfalls, and sources](references/reporting.md) | For simulation, generate realistic data and analyze each replicate with the exact planned test/model. Report assumptions, simulation count, and the Monte Carlo confidence interval; small power differences may be simulation noise. ## Adjustments people forget These routinely make the difference between an adequately powered study and an underpowered one. Apply them explicitly and state that you did. - **Multiple comparisons.** If the analysis tests *m* hypotheses with a Bonferroni-style correction, power each test at the corrected α (e.g. α/m), which raises n. Better: power on the family-wise or FDR-controlled procedure directly via simulation. Ignoring this silently underpowers every secondary endpoint. - **Attrition / dropout / unusable samples.** Power gives the n you need *analyzed*. Inflate the *enrolled* n: `n_enroll = ceil(n_analyzed / (1 − dropout_rate))`. A 20% dropout rate means enrolling 25% more than the formula returns. - **Clustering (design effect).** When observations are nested (patients within clinics, cells within animals, repeated measures within subject), the effective sample size is smaller than the raw count. Inflate by the design effect `DEFF = 1 + (m − 1)·ICC`, where *m* is cluster size and ICC the intraclass correlation. Treating clustered data as independent is **pseudoreplication** and badly overstates power — for cluster-randomized designs, simulate instead. - **One- vs. two-sided.** Two-sided is the default and almost always the right choice; a one-sided test buys power only by refusing to detect an effect in the unexpected direction. Justify any one-sided test. - **Unequal allocation.** Equal groups are most efficient for a fixed total n. If allocation is fixed by design (e.g. 2:1 treatment:control), pass `ratio=` so the calculation reflects it. --- ## Workflow 1. **State the design and the planned analysis.** The test you will run determines the power method. If the analysis is a mixed model or GLM, go straight to simulation. 2. **Choose the effect size** on a defensible basis (SESOI > shrunk pilot > convention) and write down the justification. 3. **Set α and target power.** Conventional defaults are α = 0.05 (two-sided) and power = 0.80; 0.90 is common for confirmatory/clinical work. State them. 4. **Compute** with `scripts/power.py` (closed-form) or `scripts/simulate_power.py` (simulation). 5. **Sensitivity analysis.** Recompute across a range of plausible effect sizes and produce a power curve. This is the deliverable, not a single number. 6. **Apply adjustments** for dropout, clustering, and multiplicity. 7. **Report** with the inputs and reproducibility details in [the reporting template](references/reporting.md). --- ## Scripts and completion - `scripts/power.py`: `sample_size`, `power`, `mde`, and `power_curve` for standard tests. - `scripts/simulate_power.py`: `simulate_power` and `find_sample_size`, with worked two-group, logistic, cluster-randomized, and linear mixed-model examples. The deliverable includes the planned analysis, justified effect-size range, α and sidedness, target power, allocation, required analyzed/enrolled sample sizes, dropout/clustering/multiplicity adjustments, and sensitivity results. Include the data-generating assumptions and Monte Carlo interval for simulations. When this skill materially contributes to a manuscript, report, presentation, or code release, follow [the current-version citation procedure](references/reporting.md#citing-scientific-agent-skills).