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Academy · Research Writing · Power and sample size
Statistical Power and Sample Size: The Logic of Sample-Size Calculation
A sample-size calculation reconciles four quantities: the effect considered worth detecting, the expected variability, and the levels of Type I and Type II error that the study is prepared to accept.
Statistical power is the probability that a study will detect a true effect of a specified size, if such an effect exists, and is conventionally set at 80% or 90%. A sample-size calculation derives the number of participants required from a target power, a target significance level, an expected effect size and an estimate of variability.
Learning objectives
- The four inputs of every sample-size calculation and the source of each.
- Why power is conventionally set at 80% or 90%, not 100%.
- Why an underpowered study's non-significant result cannot be read as evidence of no effect.
Common misconceptions
- “A larger sample is always preferable, so oversizing a study carries no real cost.” Jones and colleagues note that oversizing a study wastes resources and, in a trial of an unproven intervention, may expose more participants than necessary to an intervention of uncertain benefit or harm. Sample size should be calculated as the minimum required for adequate power rather than maximised.
- “A power of 80% means that the study is 80% likely to be correct.” Power is the probability of detecting a true effect of the specified size if it exists. It does not indicate the probability that the conclusion of the study is correct overall, which also depends on the accuracy of the assumed effect size and variability estimates.
The four inputs of a sample-size calculation
Jones, Carley and Harrison set out the standard four inputs: the significance level (alpha, typically 0.05), the desired power (typically 80% or 90%), the smallest effect size considered clinically worth detecting, and an estimate of the outcome's variability (such as its standard deviation, for a continuous outcome)1. The effect size is usually the most contested input in practice: it should be the smallest difference that would change clinical or research decisions, not simply the effect the researchers hope to observe, and it is often estimated from pilot data or previously published studies.
Rationale for setting power at 80% or 90%
Higher target power requires a larger sample, and the relationship is not linear: increasing power from 80% to 95%, for a fixed effect size and variability, substantially increases the required sample size1. The 80% convention represents a practical balance: accepting a 20% chance of missing a true effect (a Type II error) in exchange for a feasible sample size, while 90% is sometimes chosen for studies where missing a true effect is judged especially costly.
Interpretation of a non-significant result from an underpowered study
A study that falls short of its planned sample size, or was never adequately powered, produces a non-significant result that is genuinely ambiguous: it is consistent with a true null effect, but equally consistent with a real effect that the study lacked the power to detect1. If recruitment falls short, authors should report the achieved sample size, the reasons for the shortfall, effect estimates and confidence intervals. The resulting uncertainty should be discussed rather than interpreted through observed post hoc power, and a non-significant finding from an underpowered study should be described as inconclusive rather than as evidence that the intervention has no effect.
Key points
Key points
A sample-size calculation requires four stated inputs — alpha, target power, the smallest clinically meaningful effect size and an estimate of variability — and a non-significant result from an underpowered study should be interpreted as inconclusive rather than as evidence of no effect.
Practical application
Practical application
- All four inputs should be stated explicitly in the methods section. Authors should report alpha, target power, the assumed effect size with its justification and the variability estimate used, in addition to the resulting sample size.
- The effect size should be justified as clinically meaningful rather than convenient. It should be based on the difference that would change practice or decisions, preferably with a cited source, rather than on the smallest value that renders the required sample size feasible.
- If recruitment fell short of the target, the achieved sample size, effect estimates and confidence intervals should be reported. Authors should also state the reasons for the shortfall and discuss the resulting uncertainty, rather than using observed post hoc power to interpret the findings.
Frequently asked questions
80% is the conventional minimum in most fields, though the appropriate target depends on the cost of missing a true effect in that specific context; some high-stakes studies target 90% or higher.
Post-hoc power calculations based on the observed effect size are generally discouraged by statisticians as uninformative and potentially misleading; a confidence interval around the observed effect is the preferred means of communicating the precision achieved by the study retrospectively.
No. Sample-size calculations address precision and the ability to detect a specified effect, not whether the underlying research question or outcome measure is well chosen.
References
- Jones SR, Carley S, Harrison M. An introduction to power and sample size estimation. Emergency Medicine Journal. 2003;20(5):453-458. read 10 October 2026. View on PubMed Central
Every source above is a peer-reviewed article, a publisher’s record of one, or a standard issued by the body that owns it. Each carries the date it was last read. Where a standard moves, this article is revised rather than left up with a note.
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Pubrica Academy. (2026, October 10). Statistical Power and Sample Size: The Logic of Sample-Size Calculation. Pubrica. https://pubrica.com/academy/concepts-definitions/statistical-power-and-sample-size/
Pubrica Academy. “Statistical Power and Sample Size: The Logic of Sample-Size Calculation.” Pubrica, 10 Oct. 2026, pubrica.com/academy/concepts-definitions/statistical-power-and-sample-size/.
Pubrica Academy (2026) Statistical Power and Sample Size: The Logic of Sample-Size Calculation. Pubrica. Available at: https://pubrica.com/academy/concepts-definitions/statistical-power-and-sample-size/ (Accessed: 15 October 2026).
Pubrica Academy. “Statistical Power and Sample Size: The Logic of Sample-Size Calculation.” Pubrica. October 10, 2026. https://pubrica.com/academy/concepts-definitions/statistical-power-and-sample-size/
Pubrica Academy, ‘Statistical Power and Sample Size: The Logic of Sample-Size Calculation’ (Pubrica, 10 October 2026) <https://pubrica.com/academy/concepts-definitions/statistical-power-and-sample-size/> accessed 15 October 2026.
Pubrica Academy. Statistical Power and Sample Size: The Logic of Sample-Size Calculation. [Internet]. Pubrica; 2026 Oct 10 [cited 2026 Oct 15]. Available from: https://pubrica.com/academy/concepts-definitions/statistical-power-and-sample-size/
Pubrica Academy, “Statistical Power and Sample Size: The Logic of Sample-Size Calculation,” Pubrica, Oct. 10, 2026. [Online]. Available: https://pubrica.com/academy/concepts-definitions/statistical-power-and-sample-size/
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title = {Statistical Power and Sample Size: The Logic of Sample-Size Calculation},
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}This article is written to be learned from. Cite it if you are referring to what it says; if you are using the evidence behind it, cite the sources listed above instead.
Sample-size reporting check
For use when writing the sample-size justification in the methods section.
[ ] Alpha stated [ ] Target power stated (80% or 90%, or other, justified) [ ] Effect size stated and justified as clinically meaningful, with source [ ] Variability estimate stated, with source [ ] Achieved sample size, reasons for any shortfall, effect estimates and confidence intervals reported
Pubrica AcademyWritten and maintained by Pubrica’s subject matter experts. Articles are revised when the underlying standards change, and each article states the date on which it was last reviewed.
How Pubrica can help
Pubrica’s biostatisticians prepare and justify sample-size calculations with all four inputs stated and referenced, suitable for a methods section or an ethics submission.