Best Nonparametric test for nominal and continuos variables

[Forinstance]

Hello everybody.

I'm looking for the best test to find an association between two variables:

- a test score (continuous, ranging from 0 to 100);
- a yes or no binary variable (like, for instance, being clever or not)

Variables are not normally distributed and their relation is not linear (nor a common curve). So I'll go with nonparametric statistics.

Could you suggest me the best statistics to analyze this case?

I was planning to use all of these:

- Goodman lambda (since one variable is nominal, otherwise would have used Goodman gamma);
- Chi square (for test scores I also have the ordinal version - low, medium, high);
- rank biserial correlation;
- U mann Whitney.

What do you think?
Can I use U mann Whitney? If not because one variable is nominal, what can replace it?

Thanks a lot for all your help!

 

[Karabiner]

There is already a thread about your study and your questions concerning it, why do you duplicate it.

 

[Forinstance]

I just thought this had to be presented as a new question, since the other was only about correlation. Now it's about the best test and the use of U of Mann-Whitney in my case.

I'm not very used to this forum yet. If it is the right thing to do, I'll keep posting in the old thread.