👥 Sample Size Calculator

Sample Size Planning Framework

Compact checklist to choose or justify sample size with statistical validity, resource efficiency, and ethical balance.

1. Core Formulas (Most Frequent)

2. Minimal Workflow

1. Clarify objective (estimate / detect difference / correlation).
2. Select α (commonly 0.05) and desired power (≥0.80).
3. Specify target effect (δ, p difference, r) using prior data or conservative assumption.
4. Choose appropriate formula or power method (software) for design.
5. Adjust for design: clustering, stratification, unequal allocation, finite N.
6. Inflate for expected attrition/non‑response.
7. Round up; document every assumption source.

3. Parameter Selection Heuristics

• Unknown p ⇒ use 0.5 (max variance).
• Lacking effect size ⇒ pilot or literature meta‑analysis; else pick minimal clinically important difference.
• Attrition inflation: n_final = n_calc / (1 − drop%)
• Unequal allocation k = n₂/n₁ ⇒ inflate by (1+k)²/(4k).

4. Design Adjustments

• Cluster trials: multiply by DEFF = 1 + (m−1)ICC.
• Strata with disproportionate sampling: compute per stratum then sum.
• Sequential / adaptive: add interim looks penalty (alpha spending).
• Multiple endpoints/tests: control FWER (Bonferroni) or FDR → raises n if strict.

5. Quick Z & Power Reference

6. Quality / Sanity Checks

• Result smaller than pilot sample? Re‑examine variance/effect assumptions.
• Computed n impractically large ⇒ consider redefining effect or alternative design.
• Effect size inflation risk: compare assumed δ to historical distribution.

7. Common Pitfalls

• Post‑hoc “retrospective power” misuse (report CI instead).
• Ignoring correlation in repeated measures (overestimates n).
• Using t‑test formula when outcome is proportion / count.
• Not adjusting for high anticipated non‑response.
• Overly optimistic δ leading to underpowered study.

8. FAQ

• Why p=0.5 default? Maximizes p(1−p) giving largest required n (safe upper bound).
• Power vs significance? Power controls false negatives; α controls false positives—they balance study risk.
• When use FPC? When sample > ~5–10% of finite population.
• Cluster vs individual n? First compute individual n then multiply by design effect.

9. Action Tip

Create a reproducible “assumptions table” (α, power, effect, variance, design effects, attrition) and store with protocol—prevents silent later changes and supports transparency.