On Symmetrizing Transformation of the Sample Coefficient of Variation from a Normal Population

Abstract

Variance-stabilizing transformation (VST) for the sample coefficient of variation is often used as a normalizing transformation and may be used for inference on the population coefficient of variation. However, for small samples, the VST may not be symmetric and hence there is a scope of improvement in its performance by seeking a symmetrizing transformation. This article investigates such a transformation that has been obtained by solving a differential equation. The solutionmay be complex; hence, a numerical strategy is employed in order to make the approximation practically useful. This transformation has been compared with explicitly available VST. The approach has been illustrated on real data from an agricultural experiment concentrating on inference on single samples; however, the method may be generally applicable to multiple samples when testing the homogeneity of coefficients of variation for many populations by following usual normal-theory-based methods applied on transformed statistics.