Sample‑size calculations - purpose and principles
Sample‑size calculation is a fundamental design step for any quantitative study. It defines how many participants are needed to test the primary hypothesis with acceptable risks of false positives and false negatives. A correctly determined sample size:
- Protects against Type II error (false negative) by ensuring adequate statistical power.
- Avoids unnecessary cost, time and participant exposure from over‑recruitment.
- Makes study conclusions interpretable: a null result from a well‑powered study is informative; a null from an underpowered study is not.
Regulators and guideline bodies require that sample‑size methods, assumptions and any planned interim analyses are prospectively specified in protocols and registries (MHRA; NICE). Failing to pre‑specify sample size or continuing recruitment until a desired result is found introduces bias (data‑driven stopping, p‑hacking) and invalidates conventional frequentist error rates.
Core components required for any calculation
Every sample‑size calculation must be tied to the trial’s primary outcome and hypothesis. Minimum inputs are:
- Primary outcome type (binary, continuous, time‑to‑event, rate).
- Null and alternative hypotheses; whether the test is one‑ or two‑sided.
- Clinically meaningful effect size to detect (minimal clinically important difference) and its justification.
- Expected control‑group event rate or outcome standard deviation (from prior studies, registries or pilot data).
- Chosen Type I error (α) and target power (1 - β). Typical defaults: α = 0.05 (two‑sided), power 80-90%.