Specialty › Precision & CI width

Single mean

Precision-based sizing finds the n that gives a confidence interval on a mean a target half-width — the alternative to sizing from a hypothesis test.

What is Single mean?

Precision-based sample sizing flips the framing of power analysis: instead of 'how many subjects do I need to reject H₀ with 80% probability?', it asks 'how many subjects do I need to estimate the mean to within ±E?'. This is the right framing for descriptive studies (cohort prevalence, biomarker mean) where you're not testing a hypothesis.

The required n grows quadratically with the desired half-width — halving the CI width quadruples the required n.

When should I use Single mean?

  • Single-arm descriptive study with a mean as the primary estimand.
  • Calibration / reference-interval studies.

What data does it need?

σ + target half-width E + confidence level.

What does it report?

Required n (or achieved E if n given).

Formula

n = (z_{1−α/2} · σ / E)²

How do I interpret the result?

Frame the desired half-width E in terms of clinical significance: 'within ±2 mmol/L of the true mean' is more meaningful than 'within 5% relative error' for most clinicians.

See also

References

  • Bland (2015). An Introduction to Medical Statistics, 4th ed.