Statistical interpretation
Statistical power and sample size: what a study was designed to detect
Power is the probability that a planned analysis will detect a specified effect when that effect and the design assumptions are true. A sample-size calculation is therefore a transparent model of expectations, not a universal minimum or guarantee of a meaningful result.
Educational content only. Not medical advice.
Power belongs to a specified design and effect
Power depends on the endpoint, planned statistical test, assumed treatment effect, variability or event rate, allocation ratio, significance threshold, and sample size. Changing any component changes the calculation. A statement that a study had adequate power is incomplete unless readers can see what effect it was powered to detect and how the assumptions were chosen.
Larger samples improve precision but do not repair bias
Increasing sample size generally narrows uncertainty and improves the chance of detecting smaller effects. It cannot correct invalid measurement, selective enrollment, broken randomization, outcome switching, or systematic missingness. A very large biased study can estimate the wrong quantity precisely, while a small rigorous study may provide a useful but imprecise estimate.
Attrition and multiplicity affect planning
Plans often inflate enrollment to account for expected loss of evaluable data, but attrition is not solved simply by adding participants. Reasons for missingness still matter. Multiple primary endpoints, interim analyses, clustering, repeated measures, or unequal allocation can also change effective power and should be incorporated prospectively rather than adjusted after results appear.
A negative result is not proof of no effect
When a confidence interval remains wide, the data may be compatible with benefit, no important difference, or harm. Calling the trial underpowered after seeing a non-significant result can be misleading if no prespecified calculation or effect target is shown. Read the estimate and interval, compare them with the smallest effect of interest, and examine whether the original assumptions matched observed variability and event rates.
Evidence limits
- Power calculations depend on assumptions that may differ from observed trial data.
- A target power level does not guarantee successful recruitment, measurement, or analysis.
- Post hoc power adds little beyond the observed estimate and confidence interval.
Sources and further reading
These sources ground the definitions and evidence boundaries on this page. A citation is a route for verification, not an endorsement of a product or personal use.
U.S. Food and Drug Administration
Multiple Endpoints in Clinical Trials
Official guidance on endpoint families, multiplicity, prespecification, and Type I error control.
Open sourceU.S. Food and Drug Administration / ICH
E9(R1) Statistical Principles for Clinical Trials: Estimands and Sensitivity Analysis
Official framework connecting trial objectives, estimands, intercurrent events, analysis, and interpretation.
Open sourcePubMed Central
CONSORT 2010 Statement: Updated Guidelines for Reporting Parallel Group Randomised Trials
Peer-reviewed reporting guideline for randomization, allocation, masking, participant flow, outcomes, and analysis populations.
Open sourceCommon questions
What does 80 percent power mean?
Under the stated assumptions, the planned analysis has an 80 percent chance of meeting its criterion if the specified effect is truly present.
Is a larger study always better?
It is usually more precise, but size cannot fix systematic bias or an irrelevant endpoint.
Does non-significant mean underpowered?
Not necessarily. Inspect the effect estimate, confidence interval, prespecified assumptions, and smallest meaningful effect.
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