Coefficient of Variation Confidence Interval Sample Size Calculator

Methodology

The coefficient of variation is the population standard deviation divided by the population mean, assuming a ratio-scale outcome. The planning CV is used as the anticipated value of this parameter. The design goal is precision of estimation rather than hypothesis-test power.

Approximate sample-size calculation

Let α = 1 − confidence level, CV be the planning coefficient of variation, and w be the desired total confidence-interval width. With z = Φ⁻¹(1 − α/2), an initial approximation is

The procedure then evaluates the approximate CV confidence interval at the current integer sample size and rescales the sample size according to the ratio of the calculated interval width to the requested width. This update is performed twice, giving the final value n₃.

The implementation follows the algorithm documented for size.ci.cv(alpha, CV, w) in Douglas G. Bonett's statpsych package: an initial normal-quantile approximation followed by two confidence-interval-width refinements. The published example size.ci.cv(.05, .25, .10) returns a sample size of 60.

Assumptions and interpretation

1. The CV is meaningful for ratio-scale measurements, where zero has a meaningful interpretation.
2. The planning CV should represent a plausible value for the population CV; using the largest plausible value gives a more conservative precision requirement.
3. The calculation targets the width of a two-sided confidence interval. It does not introduce a power term because this is a precision-based estimation problem.
4. The method is an approximation and is intended for planning; actual confidence-interval width depends on the realized sample statistics.

References

Bonett, D. G. (2021). Statistical Methods for Psychologists, Volume 1. The statpsych package documents size.ci.cv(alpha, CV, w) as an approximate sample-size method for estimating a population coefficient of variation with desired confidence-interval precision.

Bonett, D. G. (2025). statpsych R package documentation, function size.ci.cv. The documented example size.ci.cv(.05, .25, .10) returns 60.

Vangel, M. G. (1996). “Confidence Intervals for a Normal Coefficient of Variation.” The American Statistician, 50(1), 21–26. doi:10.1080/00031305.1996.10473537.

PASS documentation is provided by NCSS as the documentation source for its variance and standard-deviation sample-size procedures; PASS describes confidence-interval procedures as solving for sample size from a stated confidence level and precision requirement.