On the asymmetry of biological frequency distributions

Abstract

The long-standing problem of determining whether the skewness in a sample frequency distribution is the manifestation of the intermixing of disparate groups characterizable by a normal mixture distribution or the manifestation of non-mixture, skew-producing determinants is discussed. Biometrical tools for modeling and quantifying the significance of the skewness in a trait of interest that invite interpretations other than those formed in mixtures or “subgroups” are elaborated. Statistical methods for testing whether a normal mixture distribution better characterizes a set of data than the proposed (or any other) skewed, single-population-oriented models are offered. The power of these tests is examined through Monte Carlo experimentation. A brief application in hypertension research demonstrates some of the problems and methods discussed in the paper.