### Forkman, Johannes

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

Report2005

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: 003ISBN: 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