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Despite of many measures applied for determine the difference between twogroups of observations, such as mean value, median value, sample stan- darddeviation and so on, we propose a novel non parametric transformation methodbased on Mallows distance to investigate the location and variance differencesbetween the two groups. The convexity theory of this method is constructed andthus it is a viable alternative for data of any distribu- tions. In addition,we are able to establish the similar method under other distance measures, suchas Kolmogorov-Smirnov distance. The application of our method in real data isperformed as well.

A Novel Non-Parametric Approach to Compare Paired General Statistical Distributions between Two Interventions