
GINI MEAN DIFFERENCE LOG RATIOName:
where \( n \) is the sample size. The Gini mean difference was proposed by Gini (1912) and is the average absolute differences in all pairs of observations. Note that this is a measure of dispersion that does not depend on a measure of location. This command computes the log of the ratio of the Gini mean differences of two variables. If the Gini mean differences are equal, the ratio of the Gini mean differences is equal to 1 and the log of the ratio is equal to 0. This can be the basis of a robust alternative approach to testing for equal dispersion. Tena (2009) discusses this in more detail.
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; <par> is a parameter where the computed Gini mean difference log ratio is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET A = GINI MEAN DIFFERENCE LOG RATIO Y1 Y2 SUBSET Y2 > 0
Gini (1921), "Measurement of Inequality in Incomes," The Economic Journal, 31, pp. 124126.
SKIP 25 READ AUTO83B.DAT Y1 Y2 RETAIN Y2 SUBSET Y2 > 0 . BOOTSTRAP SAMPLES 10000 TITLE CASE ASIS LABEL CASE ASIS CASE ASIS . TITLE Bootstrap Plot for Gini Mean Difference Log Ratio X1LABEL Bootstrap Sample X2LABEL Dataset: AUTO83B.DAT Y1LABEL Gini Mean Difference Log Ratio . BOOTSTRAP GINI MEAN DIFFERENCE LOG RATIO PLOT Y1 Y2 . LET LCL = ROUND(B025,3) LET UCL = ROUND(B975,3) JUSTIFICATION CENTER MOVE 50 5 TEXT Lower 95% Confidence Limit: ^LCL, Upper 95% Confidence Limit: ^UCL LINE DOTTED LINE COLOR RED DRAWSDSD 15 ^LCL 85 ^LCL DRAWSDSD 15 ^UCL 85 ^UCLThe following output is generated Bootstrap Analysis for the GINI MEAN DIFFERENCE LOG RATIO Response Variable One: Y1 Response Variable Two: Y2 Number of Bootstrap Samples: 10000 Number of Observations: 249 Mean of Bootstrap Samples: 0.03965 Standard Deviation of Bootstrap Samples: 0.09176 Median of Bootstrap Samples: 0.03783 MAD of Bootstrap Samples: 0.06284 Minimum of Bootstrap Samples: 0.27461 Maximum of Bootstrap Samples: 0.39343 Percent Points of the Bootstrap Samples  Percent Point Value  0.1 = 0.23102 0.5 = 0.18724 1.0 = 0.16822 2.5 = 0.13632 5.0 = 0.10981 10.0 = 0.07637 20.0 = 0.03855 50.0 = 0.03783 80.0 = 0.11801 90.0 = 0.15871 95.0 = 0.19106 97.5 = 0.22295 99.0 = 0.26068 99.5 = 0.28081 99.9 = 0.32864 Percentile Confidence Interval for Statistic  Confidence Lower Upper Coefficient Limit Limit  50.00 0.02371 0.10227 75.00 0.06510 0.14687 90.00 0.10981 0.19106 95.00 0.13632 0.22295 99.00 0.18724 0.28081 99.90 0.23955 0.35192 
 
Date created: 07/14/2023 Last updated: 07/14/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 