On an Approximate Test for Homogeneity of Coefficients of Variation

Summary

The coefficient of variation (c. v.) ζ = σ/ξ, or ratio of standard deviation to mean (ξ > 0), is a useful parameter and measure of variability in certain situations since it is expressed in absolute units. Thus in comparing results on repeated clinical data when k (≥ 2) different measurement techniques are utilized in analyzing the same or paired specimens, it is of interest to compare the corresponding sample c. v.’s z ₁, ... , z _k respectively for the k techniques. For this situation the following note presents a test which is based on McKay’s approximation [4] to the distribution of the sample c. v. for the normal distribution, and utilizes Pitman’s method [5] for the hypothesis of equality of scale parameters of Gamma variates.