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# Sample size: Confidence Interval for a Coefficient of variation from duplicate measurements

## Description

Calculates the required minimum sample size for the estimation of a confidence interval with a required width for the Coefficient of variation from duplicate measurements. The calculations are performed according to the general methodology given by Machin et al., 2009. It is assumed that the calculation of the Coefficient of variation uses the Logarithmic method.

Note that the calculation does not include a null hypothesis value or a factor for power (1−β). Therefore the estimated sample size does not give a certainty that a particular value will fall inside or outside the confidence interval. The number of cases is only the number required to attain a specified confidence interval width.

## Required input

• Confidence level (%): select the confidence level: 90, 95 or 99%. A 95% confidence level (the value for a 95% confidence interval) is the most common selection. You can enter a different confidence level if required.
• Coefficient of variation (%): the expected coefficient of variation, expressed as a percentage.
• Confidence interval width (2-sided): this is the required total width of the confidence interval. For example when a CV is 8% with 95% Confidence Interval 6 to 10, then the confidence interval width is 4.

## Example

A preliminary study in 20 sample pairs resulted in a coefficient of variation of 8% with 95% CI of 2.3 to 13.7%. The calculations used the logarithmic method.

The desired 95% confidence interval is 6 to 10%. How many sample pairs are needed for this narrower confidence interval?

For confidence level you enter 95, for coefficient of variation 8 and for confidence interval width you enter 4 (=10−6).

Click Calculate

The program gives a minimum required sample size of 37. This means that if the study is repeated with 37 sample pairs, and this new study again results in a coefficient of variation of 8%, the 95% confidence interval will be 6 to 10%.

## Literature

• Machin D, Campbell MJ, Tan SB, Tan SH (2009) Sample size tables for clinical studies. 3rd ed. Chichester: Wiley-Blackwell.