How do you Show a Difference between Two Groups (Clustering)
Use MANOVA:

https://en.wikipedia.org/wiki/Multivariate_analysis_of_variance


  In statistics, multivariate analysis of variance (MANOVA) is a
  procedure for comparing multivariate sample means. As a multivariate
  procedure, it is used when there are two or more dependent
  variables, and is typically followed by significance tests
  involving individual dependent variables separately. It helps to
  answer:
  
  
  Do changes in the independent variable(s) have significant effects on the dependent variables?
  What are the relationships among the dependent variables?
  What are the relationships among the independent variables?