Is there a way to test correlation between Data X and Binary output Y?

Question

I'm trying to find a Python method/library for testing correlation between the independent variables X and the binary output Y..

So for example, lets say I have the following data and output:

X           Y
0.65       1
0.11       0
0.13       0
0.35       1
0.21       0
...

Lets say the output Y is 1 if (X > 0.3) and 0 otherwise. If I don't know this correlation (the threshold value 0.3), is there a statistical method/test to find out the degree of correlation between X and Y?

So for example, some method that returns

x = [0.65, 0.11, 0.13, 0.31, 0.21]
y = [1, 0, 0, 1, 0]
print some_test(x, y)

==> returns "degree of correlation = 1.0"

Thanks

Answer 1

You are looking for a point biserial correlation, which is used when one of your variables is dichotomous.

from scipy import stats
stats.pointbiserialr(x,y)

If you simply want to know whether X is different depending on the value of Y, you should instead use a t-test.