“How many participants do we need?” cannot be answered until the study declares what an adequate sample is supposed to accomplish. A study designed to detect a treatment difference uses a different logic from one designed to estimate a prevalence, mean, or performance measure within an acceptable margin of error.
Power and precision are related because both usually improve with more information. They are not interchangeable objectives.
01Power begins with a testing objective
In a conventional two-group superiority trial, a power-based calculation specifies a primary outcome, target difference, variability or control event rate, significance level, desired power, allocation ratio, and anticipated loss or nonadherence. The target difference is the effect the study is designed to detect with a stated probability under those assumptions.
The DELTA² guidance emphasizes that the target difference should be both important and realistic, informed by relevant evidence and stakeholders. Choosing a large effect merely to make the required sample small produces a study that may miss smaller but still important effects. Choosing a very small effect without operational justification may demand a sample the institution cannot recruit.
Power is also conditional. “The study has 80% power” is incomplete without the target effect, analysis, variance, event rate, and other assumptions. If those inputs are wrong, the achieved operating characteristics differ from the plan.
02Precision begins with an estimation objective
An estimation study asks how narrowly a parameter should be estimated. A prevalence study may seek a 95% confidence interval with a specified half-width. A pilot study may need an adequately precise recruitment or retention estimate. A diagnostic or prediction study may target precision for sensitivity, calibration, or another performance measure.
The inputs depend on the estimand and interval method. For a proportion, expected prevalence affects the required sample. For clustered data, the effective information depends on cluster size and intracluster correlation. For time-to-event outcomes, the number of events may matter more than the total enrolled.
A precision calculation should state the planned confidence level, estimand, expected parameter values, desired width, and adjustment for design features or missingness. Saying “a sample of 100 is sufficient for estimation” is not a reproducible justification.
03Examine both views when decisions need both
A trial may be powered to detect a target difference yet still produce an interval too wide for a practical decision if the actual event count is low or assumptions change. DELTA² recommends considering expected confidence-interval width as an aid when choosing the target difference and sample size.
Conversely, an estimation study can produce a precise estimate that does not answer a comparative hypothesis. The calculation should match the primary objective, not a familiar formula or software menu.
04Avoid common shortcuts
A universal rule such as “ten participants per variable” is rarely a complete sample-size rationale. Neither is copying a sample from a previous study without checking differences in outcome, design, population, analysis, and loss to follow-up. A pilot estimate may help with variance or event-rate inputs, but a small pilot can be highly uncertain and is usually not a reliable source for an expected treatment effect.
Post hoc power calculated from the observed effect adds little to the estimate and confidence interval. Once the study is complete, interpret the effect and uncertainty directly rather than using observed power to relabel the result.
05Make the calculation auditable
The protocol should report every input, its source, the formula or simulation method, software and version where relevant, sensitivity calculations, inflation for missing data or design effects, and the final recruitment target. SPIRIT 2025 expects the sample-size rationale and key assumptions to be documented, and CONSORT 2025 supports transparent reporting in the final trial report.
Review the calculation with a one-sentence test: “This study needs N analyzable participants to [detect a specified difference with stated power]” or “to [estimate a specified parameter with stated interval width].” If the sentence cannot be completed, the sample size is not yet linked to the scientific objective.
The most defensible calculation is not the one with the most decimals. It is the one whose purpose, assumptions, and consequences can be understood and challenged before recruitment begins.
When several objectives compete, name the one that governs the sample and show whether the resulting number is adequate for the others. Secondary analyses should not inherit an unsupported claim of adequacy merely because they use the same participants.
References
- DELTA² Guidance on Target Differences and Sample Size ↗ — power, target differences, expected interval width, feasibility, and reporting. Accessed 27 July 2026.
- SPIRIT 2025 Statement ↗ — protocol requirements for objectives, outcomes, analyses, and sample-size rationale. Accessed 27 July 2026.
- SPIRIT-Outcomes 2022 Extension ↗ — complete outcome definition and target-difference justification. Accessed 27 July 2026.
- CONSORT 2025 Statement ↗ — transparent reporting of trial design, analyses, and results. Accessed 27 July 2026.
This article is educational and intended for research purposes. It does not provide individual medical advice, diagnosis, or treatment. No patient data were used.