Comparison of skewness coefficient, coefficient of variation, and Gini coefficient as inequality measures within populations

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Abstract
The moment skewness coefficient, coefficient of variation and Gini coefficient are contrasted as statistical measures of inequality among members of plant populations. Constructed examples, real data examples, and distributional considerations are used to illustrate pertinent properties of these statistics to assess inequality. All three statistics possess some undesirable properties but these properties are shown to be often unimportant with real data. If the underlying distribution of the variable follows the often assumed two-parameter lognormal model, it is shown that all three statistics are likely to be highly and positively correlated. In contrast, for distributions which are not two-parameter lognormally distributed, and when the distribution is not concentrated near zero, the coefficient of variation and Gini coefficient, which are sensitive to small shifts in the mean, are often of little practical use in ordering the equality of populations. The coefficent of variation is more sensitive to individuals in the right-hand tail of a distribution than is the Gini coefficient. Therefore, the coefficient of variation may often be recommended over the Gini coefficient if a measure of relative precision is selected to assess inequality. The skewness coeficient is suggested when the distribution is either three-parameter lognormally distributed (or close to such), or when a measure of relative precision is not indicated.