Performing comparisons after a cluster analysis

#1
I have a data set of N subjects, and P variables, with some vars measuring performance on a task, and some measuring subjects' intrinsic characteristic. Each of the performance variables consists of the proportion of correct responses (range 0 to 1.0) to some set of questions. The characteristic variables (such as verbal IQ) are ordinal, and may or may not follow a normal distribution.

The subjects have been bifurcated into two groups by cluster analysis (using the performance vars).

I'd like to compare the two clusters on each performance and characteristic measure to test if they are significantly different from each other on that measure. However, the clustering process entails a violation of assumptions (i.e. random assignment to a group) of standard statistical tests. What sort of tests should I use to test if the two clusters differ on the measures? Thank you.
 
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