#### Abstract

The coefficient of variation (CV), defined as the ratio of the standard deviation to the mean, is often used in experimental situations. The exact distribution of the sample CV from a normally distributed population is complicated and obtaining a confidence interval for the population CV in this situation would require using the non-central t distribution and sequential techniques (Koopmans, et al., 1964). This paper explores the use of approximate distributions in determining confidence limits for the CV. The gamma distribution is used to model data appropriate for the calculation of the CV. A Monte Carlo simulation is performed to evaluate the effectiveness of four different intervals developed in this paper. A data set from a forestry experiment is analyzed using one of these techniques.

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

#### Recommended Citation

Payton, Mark E.
(1996).
"CONFIDENCE INTERVALS FOR THE COEFFICIENT OF VARIATION,"
*Conference on Applied Statistics in Agriculture*.
http://newprairiepress.org/agstatconference/1996/proceedings/8

CONFIDENCE INTERVALS FOR THE COEFFICIENT OF VARIATION

The coefficient of variation (CV), defined as the ratio of the standard deviation to the mean, is often used in experimental situations. The exact distribution of the sample CV from a normally distributed population is complicated and obtaining a confidence interval for the population CV in this situation would require using the non-central t distribution and sequential techniques (Koopmans, et al., 1964). This paper explores the use of approximate distributions in determining confidence limits for the CV. The gamma distribution is used to model data appropriate for the calculation of the CV. A Monte Carlo simulation is performed to evaluate the effectiveness of four different intervals developed in this paper. A data set from a forestry experiment is analyzed using one of these techniques.