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

TL;DR

This paper introduces a new non-parametric transformation method based on Mallows distance to compare the location and variance differences between two groups, applicable to any distribution type.

Contribution

It presents a novel transformation approach with convexity properties for distribution comparison, extending to other distances like Kolmogorov-Smirnov.

Findings

Method effectively compares distributions regardless of their form.

Convexity of the transformation ensures robustness and computational feasibility.

Application to real data demonstrates practical utility.

Abstract

Despite of many measures applied for determine the difference between two groups of observations, such as mean value, median value, sample stan- dard deviation and so on, we propose a novel non parametric transformation method based on Mallows distance to investigate the location and variance differences between the two groups. The convexity theory of this method is constructed and thus 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, such as Kolmogorov-Smirnov distance. The application of our method in real data is performed as well.