Analysis of Total Differences with Application to Productivity Improvement

Abstract

One way analysis of Gini’s mean difference (ANOMD) about mean and median is derived where the total sum of differences is partition into exact between sum of differences and exact within sum of differences. ANOMD has advantages: ensures stability in statistical inferences; has flexibility to test for any location measure and total sum difference does not depend on any fixed location. However, the variance-gamma distribution is used to fit the sampling distributions of between sum differences and within sum differences. Consequently, two tests of equal population medians and means are introduced under the assumption of the normal distribution. Moreover, two measures of effect sizes are re-defined and studied in terms of ANOMD. The ANOMD model is applied to productivity improvement data and it is found that the percentage of explained variation given by ANOMD is more than the percentage given by ANOVA.