What is the best way of finding the correlation with dependent observations?

Question

We have two measures X and Y that we apply on each class 30 times as follow:

Class    X            Y
A        0.25         0.6
A        0.3          0.4
B        0.6          0.2
B        0.8          1

For simplicity, I just showed two runs (out of 30) for each class. The number of classes that we are testing is 331. This results in the 9930 points in the following plot:

Note that observations from class A might have a similar behaviour when compared to observations from the class B.

We want to know whether there is a correlation exists between measure X and Y for all the classes. Is the spearman correlation helpful in this scenario?