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<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.