Hi Utsav,

1. Short answer: Yes, you’re correct. Longer answer: Theil’s U is based on the conditional entropy between the variables, so U(x,y) is based on S(x|y) (where S is the entropy), and so — you’re checking the values of x given y.
2. I think you misinterpret what Cramer’s V is. Unlike Theil’s U, it doesn’t answer the question “what is x if I know y” or the other way around. Cramer’s V is actually just like Pearson’s R for continuous numbers — it tells you the relations between x and y, meaning it answers “do they behave the same way?”. It’s a completely different thing than Thiel’s U.