Coefficients of variation: an approximate F-test

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 χ2 approximation given 1932 by A. T. McKay. It is proved that McKay’s approximation is noncentral beta distributed.