  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.
