Measures of spread, inequality, and dissimilarity Hist 5011

1. Spread and inquality Measures of spread and inequality –Range –Standard deviation and variance –Interquartile range (and other percentile differences) –Lorenz curve and Gini index –Other inequality measures

2. Measures of dissimilarity Duncan’s Index of dissimilarity: –What percentage of the population would have to be moved between categories to make two distributions the same?

Index of Dissimilarity 1. For each category, take absolute differences between the proportion in each group 2. Sum the absolute differences 3. Divide by 2 4. D is the proportion (or percentage) in each group which has to be reallocated to give the same distribution as in the other group

Example: St. Gillis vs Elsene Origin Group Sint- Gillis Elsene Belgium46,160,1 Europe35,623,0 Africa2,04,5 Morocco11,45,1 Turkey1,20,6 Other3,76,7 Difference Absolute Difference Sum = D = 19.5

Standard deviation and interquartile range To the data

The U.K. Income Distribution 2001/02

Lorenz curve

Comparison of 1961 and 2001/2

Corrado Gini ( )

Gini coefficient

Gini index Bounded between zero (complete equality) and one (complete inequality). Treats deviations from equality the same regardless of where the occur within income distribution. Typically between 0.25 and 0.35 for developed countries.

Calculation G: Gini coefficient X k : cumulated proportion of the population variable Y k : cumulated proportion of the income variable

Sample spreadsheet: lindert-gini.xls