Introduction to Applications Academic Article uri icon

abstract

  • The main properties of the Gini mean difference (GMD) and the extended Gini (EG) were presented in the first part of the book. We have concentrated on those properties that enable the user to replicate almost everything that can be done when relying on the variance. In some sense we can claim that (almost) every analysis that is performed when using the variance can be done with the GMD, and sometimes with the EG as well. This means more than doubling the number of possible models that can be used because every variance-based model can be replicated by a Gini-based model. This fact raises the question whether it is worth to pursue this direction of research or not and what are the pros and cons of using the Gini methodology. We note that generally speaking when the underlying distribution is multivariate normal then there is nothing to be gained from using the GMD method. The reason is simple: when the underlying distribution is multivariate normal then the estimates of the means, the variances, and the correlations (by Pearson) are sufficient statistics for describing the data, and therefore nothing is gained by using an alternative system for describing the data on one hand, while a loss of efficiency follows because the parameters of the normal distribution are estimated in a circumvent way. However, as pointed out by Huber (1981) and Gorard (2005) even a small deviation from the ideal world of the normal distribution can lead to an advantage of using other measures of variability.

publication date

  • January 1, 2013