Improved tests for the equality of normal coefficients of variation

The problem of testing the equality of coefficients of variation of independent normal populations is considered. For comparing two coefficients, we consider the signed-likelihood ratio test (SLRT) and propose a modified version of the SLRT, and a generalized test. Monte Carlo studies on the type I error rates of the tests indicate that the modified SLRT and the generalized test work satisfactorily even for very small samples, and they are comparable in terms of power. Generalized confidence intervals for the ratio of (or difference between) two coefficients of variation are also developed. A modified LRT for testing the equality of several coefficients of variation is also proposed and compared with an asymptotic test and a simulation-based small sample test. The proposed modified LRTs seem to be very satisfactory even for samples of size three. The methods are illustrated using two examples.