Power of a Trial
Why power matters
Power is the probability a study will detect a prespecified true effect (the minimum important difference, MID) if it exists - formally 1 - β, where β is the Type II error rate. Common targets for prospectively designed trials are 80% (β = 0.20) or 90% (β = 0.10) (NICE Appendix F).
Low power increases the risk of false negatives: a non‑significant result may reflect insufficient sample size rather than absence of a clinically important effect. Conversely, adequate power improves the chance of detecting real effects but does not guarantee clinical relevance.
How power relates to sample size and effect size
Power is determined by several interdependent factors. For a given alpha (Type I error), higher power can be achieved by:
- larger sample size, which reduces the standard error.
- larger true effect (a larger MID is easier to detect).
- lower outcome variability (smaller SD for continuous outcomes or higher event rates for binary outcomes where that increases information).
- appropriate trial design choices (for example, one‑ vs two‑sided tests, and explicitly accounting for clustering).
Practical inputs for sample‑size / power calculations A valid calculation explicitly states:
- alpha (commonly 0.05, two‑sided) and the desired power (commonly 80% or 90%).
- the effect size/MID to detect (absolute or relative; for binary outcomes, absolute risk reduction (ARR) or...