--- [EMAIL PROTECTED] wrote: > To answer my own question, I think the attached perl script nicely > shows > the difference between std-dev and gini by this output:
The Gini Coefficient is invariant under scaling, but not under translation. Standard deviation is invariant under translation, but not under scaling. If you want a better comparison between the two, you might try comparing Gini to stdev/mean. Also, Gini, like standard deviation, can be calculated for a population or a sample. The Perl code is inconsistently using the formulas for the Gini of a population, but the standard deviation of a sample. The Wikipedia article is confusing to the point of being erroneous. To calculate the Gini coefficient for a population, use the Brown formula with: X_k = k / n Y_k = S_k / S_n where: S_k = sum of w_i for i = 1 to k (w_i) i = 1 to n, is the sequence of values (e.g. income) for each member of the population, sorted in increasing order. With this setup, the Brown formula can be restated as: T = sum of w_i * (n+1-i) for i = 1 to n G = 1 - 2*(T/S_n - 0.5) / n This is algebraically equivalent to the formula given earlier on this list. __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com ---- election-methods mailing list - see http://electorama.com/em for list info
