Forest Products Laboratory

A Confidence Interval on a Coefficient of Variation Shared by k Normally Distributed Populations

This page is a form for calculating a confidence interval on a coefficient of variation shared by k normally distributed populations. Here is FORTRAN source code for a standalone program that calculates the confidence interval.

We also have programs that do the following:

• Obtain a two-sided confidence interval on a coefficient of variation of a normal distribution
• Obtain a one-sided lower confidence bound on a coefficient of variation of a normal distribution
• Obtain a one-sided upper confidence bound on the coefficient of variation of a normal distribution
• Obtain confidence bounds on the coefficient of variation of a lognormal distribution
• Obtain confidence bounds on the ratio of the coefficients of variation of two normally distributed populations
• Perform a likelihood ratio test of the hypothesis that k normally distributed populations share the same coefficient of variation

The theory behind these programs is described in three publications:

• Confidence Bounds for Normal and Lognormal Distribution Coefficients of Variation, 2003, Research Paper 609, USDA Forest Products Laboratory, Madison, Wisconsin.
• Confidence Bounds and Hypothesis Tests for Normal Distribution Coefficients of Variation, 2007, Research Paper 638, USDA Forest Products Laboratory, Madison, Wisconsin.
• Verrill, S. and Johnson, R.A. (2007). "Confidence Bounds and Hypothesis Tests for Normal Distribution Coefficients of Variation." Communications in Statistics -- Theory and Methods, Volume 36, Number 12, pages 2187-2206.