### Forkman, Johannes

- Department of Energy and Technology, Swedish University of Agricultural Sciences

Report, 2005
# Coefficients of Variation ? an Approximate F-Test

Forkman, Johannes

Forkman, Johannes (ed.)

Basic inferential methods for analysing coefficients of variation in normally distributed data are studied. The assumptions of normally distributed observations and a constant coefficient of variation are discussed and motivated especially for immunoassay data. An approximate F-test for comparing two coefficients of variation is introduced. All moments of the proposed test statistic are shown to be approximately equal to the moments of an F distribution. It is proved that the distribution of the logarithm of the test statistic equals the distribution of the logarithm of an F distribution plus some error variables that are in probability of small orders. The approximate F-test is compared with eight other tests in a simulation study. The new test turns out to perform well, also in case of small sample sizes. A generalized version of the approximate F-test is defined for the case that there are several estimates of each coefficient of variation, calculated with different averages. The test is based on a chi2 approximation given 1932 by A. T. McKay. It is proved that McKay?s approximation is noncentral beta distributed

coefficient of variation; normal distribution; confidence interval; hypothesis test; McKay?s approximation

Licentiate thesis (Swedish University of Agricultural Sciences, Department of Biometry and Engineering)

2005, number: 003

ISBN: 91-576-6886-8

Publisher: SLU

### Forkman, Johannes

- Department of Energy and Technology, Swedish University of Agricultural Sciences

- Department of Energy and Technology, Swedish University of Agricultural Sciences

https://res.slu.se/id/publ/7671