A Comparative Analysis of the Gini Index

Around the world, the Gini index is used to represent income inequality and is compared between regions. Proposed by Corrado Gini in 1912, the index summarizes the income disparity of an area into a single value that falls between zero and one [1]. There are numerous methods for evaluating the Gini index [2]. Considering its global use, it is essential for these different approaches to provide consistent results for a region. This paper compares the Gini indices obtained using three of the earliest developed methods. These methods include Gini’s original method, the relative mean difference method, and the geometric method. The geometric method, specifically, can be applied either algebraically or geometrically. In this report these three approaches were applied to the 2017 Canadian income distribution from Statistics Canada. To ensure a fair analysis, the methods were also applied to the Canadian income distributions from 1999 and 2010, with their calculations being summarized in Appendices A and B respectively.From the investigation, it was discovered that Gini’s original method and the relative mean difference method, (collectively referred to as the algebraic methods), provided identical results for all three data sets. However, the geometric methods, referring to the Trapezoid Rule and Logger Pro technology, provided values that differed from one another and the algebraic methods. This highlights the importance of acknowledging the method used to derive the Gini Index to ensure consistency and to allow a valid interpretation. The results of this paper also suggest that the algebraic methods should be preferred over the geometric methods when dealing with discrete data to ensure consistent results.