How do you Show a Difference between Two Groups (Clustering) I am approaching a data problem. My data set consists of observations of (X,Y) coordinates indicating a position on some grid. There are two groups based on a variable Z. Group A is all the points where Z>10 and Group B is all the points where Z&lt;10.

Would it be a good idea to separately cluster the 2 groups of (X,Y) coordinates, then compare the location of clusters to reach some conclusion about how Z affects the location of the points? 

I want to say something statistically about how differently, if at all, the group A and group B points are clustered. So I can say that the difference is because of Z.
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?